JSST2021
The 40th JSST Annual International Conferenceon Simulation Technology

Conference Proceedings

Doshisya University
Kyoto, JAPAN
September 1–3, 2021

Supporting Companies

iiSession ScheduleDay 1 (Wednesday, 1st September, 2021)
Time

Hall A

Hall B

Hall CHall D

09:30 – 09:45

Opening Ceremony (Hall A)

09:45 – 10:45

Plenary Talk 1 (Symposium 1, Hall A)

10:45 – 11:00

Group Photo (Hall A)

11:00 – 12:15

Symposium 1 1
Invited Talk 1
Tutorial Talk 1
Session 1 (2)Hall E

OS8 1

OS3 + OS9 1

OS2 1

OS7 1

Session 5 (4)Session 8 (3)Session 12 (3)Session 16 (3)Lunch Time

12:15 – 13:30

Corporate Seminar 1 (Hall A)
13:30 – 14:15

Differential equations and machine learning/neural networks
Koji Maruyama (Wolfram Research)

14:30 – 15:30

15:45 – 16:45

17:00 – 18:00

Symposium 1 2

OS8 2

OS3 + OS9 2

OS2 2

OS7 2

Session 2 (3)Session 6 (3)Session 9 (3)Session 13 (3)Session 17 (3)Symposium 1 3

OS8 3

OS3 + OS9 3

OS6 1

OS11 1

Session 3 (3)Session 7 (3)Session 10 (3)Session 14 (3)Session 18 (3)Symposium 1 4

Symposium 2 1

OS6 2

OS11 2

Session 4 (3)Session 11 (3)Session 15 (2)Session 19 (2)iiiDay 2 (Thursday, 2nd September, 2021)
Time

Hall A

11:30 – 12:30

12:30 – 13:30

Hall CHall DHall E

Plenary Talk 2 (Symposium 2, Hall A)

09:00 – 10:00

10:15 – 11:15

Hall B

Symposium 1 5
Session 20 (3)Symposium 2 2
Invited Talk 2
Invited Talk 3
Session 22 (2)Symposium 3 1

OS11 3

OS1 1

Session 24 (3)Session 26 (3)Session 28 (3)Symposium 1 6

Symposium 2 3

Symposium 3 2

OS10 1

OS1 2

Session 21 (3)Session 23 (2)Session 25 (3)Session 27 (3)Session 29 (3)Lunch Time
Corporate Seminar 2 (Hall A)

13:30 – 14:15

The Trends of Latest Personal Supercomputer: Performance and App Support Status
Keiou Nishimura and Rika Yamashita (Visual Technology)

14:30 – 15:00

Plenary Talk 3 (Symposium 3, Hall A)

15:00 – 15:05

Announcement about JSST2022 (Hall A)

15:15 – 16:15

Shotgun Presentations of Student Session (Hall A)

16:30 – 18:00

Student Session (Poster Session, Remo)iv

Day 3 (Friday, 3rd September, 2021)
Time

Hall A

11:30 – 12:45

Symposium 3 3

OS4 1

RS 1

Session 30 (3)Session 33 (3)

OS4 2

RS 2

Session 31 (2)Session 34 (2)Hall DHall E

OS10 2

OS5 1

Session 39 (3)Session 42 (3)Symposium 3 4

OS10 3OS5 2

Session 37 (3)Session 40 (3)Session 43 (3)Tutorial Talk 2
Session 36 (2)Lunch Time

12:45 – 13:30

13:30 – 14:15

Hall CPlenary Talk 4 + Invited Talk 4 (Symposium 3, Hall A)

09:00 – 10:00

10:15 – 11:15

Hall BOS4 3

Symposium 2 4

Symposium 3 5

OS10 4OS5 3

Session 32 (2)Session 35 (2)Session 38 (2)Session 41 (2)Session 44 (2)14:15 – 14:30

Break

14:30 – 15:00

Closing Ceremony (Hall A)v

Symposium
Plenary Talk
Presenter:

Prof. Hiroaki Natsukawa
Academic Center for Computing and Media Studies,
Kyoto Universit

Title:
Understanding System Dynamics by Combining Data-Driven Analysis andInformation Visualizatio

Abstract:
Natural systems are often complex and dynamic. Reductionism is notuniversally applicable for natural complex systems found in biology andelsewhere where behavior is driven by complex interactions between many
components acting together in time nonlinear dynamic systems. In this talk, I
will introduce a minimalist paradigm, empirical dynamic modeling (EDM), forstudying non-linear systems. It is a data-driven approach that uses timeseries information to study a system by reconstructing its attractor (ageometric object) that embodies the rules of a full set of equations for thesystem. Particularly, I will introduce a few recent works of visual analytics tosupport the identi cation and mechanistic interpretation of system statesusing integration EDM with visualization techniques, leads to ourunderstanding of complex dynamics

Biography:
Hiroaki Natsukawa is a junior associate professor / senior lecturer in
Academic Center for Computing and Media Studies, Kyoto University. He
received a Ph.D. in engineering from Kyoto University in 2013. Althoughformally trained as a researcher in the eld of biomedical engineering at
Kyoto University, He has successfully crossed elds into other areas such as
information visualization, neuroscience, and more recently into nonlinear
dynamics. Currently, he has worked in the eld of information visualizationand his work focuses on developing visual analytics systems enabling datavi

driven analytical reasoning by empirical dynamic modeling in collaboration
with UC San Diego. He is currently an associate editor of Journal of
Visualization, was a The 36th Annual Meeting of Japan Biomagnetism andBioelectromagneics Society Local Committee, IEEE Paci cVis 2019 Poster
Co-chairs, IEEE Paci cVis 2018 Publication Chair, The 47th Symposium of
Visualization Society of Japan Organizer, NICOGRAPH International 2017
Local Committee Chair, JSST2016 Publication Chair, JHBM18 Local
Committee.

Invited Talk
Presenter:

Prof. Tomohiro Sogabe
Department of Applied Physics, Nagoya Universit

Title:
Computation of Singular Values for Generalized Tensor Su(Joint work with Asuka Ohashi (National Institute of Technology, Kagawa

Abstract:
We consider computing singular values of the generalized tensor sum of thefor

T := In ⊗ Im ⊗ A + In ⊗ B ⊗ Iℓ + C ⊗ Im ⊗ Iℓ,(1

where is the × identity matrix and A ∈ R ℓ×ℓ, B ∈ R m×m, A ∈ R n×n . The
mathematical symbol ⊗ denotes tensor product (or Kronecker’s product). A
simple example of the tensor product is given below.

a11b11a11B a12 B
a21b11A ⊗ B :==
[a21B a22 B]
a11b21
a21b21vii

a12b11
a22b11
a12b21
a22b21

a11b12
a21b12
a11b22
a21b22

a12b12
a22b12
a12b22
a22b22

where A := a
. Similarly, A ⊗ B ⊗ C is calculated recursively by[ 21 a22]

a11 a12(A ⊗ B) ⊗ C or (A ⊗ B) ⊗ C . The size of the generalized tensor sum in (1)is of n 3 × n 3, which can be extremely large even if matrices , , are small.
Indeed, for , , being 1,000 × 1,000 matrices, the generalized tensor su
can be a 1,000,000,000 × 1,000,000,000 matrix
Though the generalized tensor sum can be very large, it is easy to compute
some fundamental quantities of linear algebra, such as determinant andeigenvalues. In fact, the eigenvalues ofcan be written as the sum of
eigenvalues of relatively much smaller matrices , , andthan . On theother hand, unlike eigenvalues, it is dif cult to compute the singular values osince there is no such a simple relation between the singular values oand the singular values of , , andIn this talk, we present recent progress on ef cient computational algorithms[1,2,3] for some speci c singular values of the generalized tensor sum ,which are based on the use of the notion of numerical multilinear algebra
Reference[1] A. Ohashi, T. Sogabe, On computing maximum/minimum singular valuesof a generalized tensor sum, Electronic Transaction on Numerical Analysis,
43 (2015), pp. 244-254[2] A. Ohashi, T. Sogabe, On computing the minimum singular value of atensor sum, Special Matrices, 7 (2019), pp. 95-106[3] A. Ohashi, T. Sogabe, On computing an arbitrary singular value of a tensor
sum, in preparation

Biography:
Tomohiro Sogabe was graduated from the department of Applied Physics, theUniversity of Tokyo in 2001 and received Ph.D. from the same university in2006. He worked at Nagoya university as an assistant professor, and Aichi
prefectural university as an associate professor. He is currently an associate
professor at the department of Applied Physics, Nagoya University, Japan. He
served as editors of JSIAM Letters, the Transactions of JSIAM, and currently
he serves as an editor of JJIAM journal, Springer. He will be a member of theboard of directors of JSIAM from June 2021. His research interests include
numerical linear algebra, numerical multilinear algebra, and scienti ccomputing. He published more than 70 international journal papers and 15
domestic journal papers include applied mathematics journals, computational
physics journals and quantum computing journal, such as AMC, AML, ETNA,
JCAM, JJIAM, NLAA for applied mathematics; IEEE TMTT, JCP, PRB, PRE
for computational physics; QIC for quantum computing journalviii

Tutorial Talk
Presenter:

Prof. Kuniyoshi Abe
Faculty of Economics and Information, Gifu Shotoku
Gakuen Universit

Title:A Numerical Study of Parallel Variants of GPBiCG
Method with Stabilization Strategy for Solving Linear Equation(Joint work with Soichiro Ikuno and Gerard L.G. Sleijpen

Abstract:
The hybrid Bi-conjugate gradient (Bi-CG) methods such as Bi-CG stabilized(Bi-CGSTAB), Generalized Product-type based on Bi-CG (GPBiCG) are wellknown for ef ciently solving linear equations, but we have seen theconvergence behavior with a long stagnation phase. In such cases, it isimportant to have Bi-CG coef cients that are as accurate as possible. We
introduce the stabilization strategy for improving the accuracy of the Bi-CG
coef cients.
On present petascale high-performance computing hardware, the main
bottleneck for ef cient parallelization is the inner products which require a
global reduction. The parallel variants of Bi-CGSTAB reducing the number ofglobal communication phases and hiding the communication latency havebeen proposed. In this paper, therefore, following the analogy of Cools et al.,we design parallel variants of GPBiCG, and examine the convergence speedof the parallel variants with the stabilization strategy

Biography:
Kuniyoshi Abe obtained Ph. D at Nagoya University in 1999. He began his
career as Assistant professor at Anna National College of Technology in
1998. He moved to Advanced Computing Center, RIKEN as a Contract
researcher in 1999. He was associate professor at Faculty of Economics andInformation, Gifu Shotoku University in 2003, and is professor from 2012. His
research eld is numerical linear algebra, especially, he is interested in fastand iterative solvers for linear equationsix

Symposium2
Plenary Talk
Presenter:

Prof. Hajime Ishihara
Department of Materials Engineering Science, Osaka Universit

Title:
Interaction of Optical Vortex and Matter Systems: from Microscopic to
Macroscopic Regimes and Linkage between The

Abstract:
A remarkable effect in the interaction between the optical vortex and mattersystems is the transfer of the orbital angular momentum. A lot of theoreticaland experimental demonstrations have been conducted for macroscopic
rotational manipulation of matters from microscale to nanoscale objects. On
the other hand, in the microscopic regime, the optical vortex changes theselection rule of electronic transitions, which induces unconventional spin
dynamics in solids. Interestingly, the macroscopic and microscopic degrees of
freedom are sometimes linked to each other in a unique way via linear andnonlinear optical responses. In this talk, I will present some examples of theabove topics and puzzling aspects about them

Biography:
Hajime Ishihara is a Professor in Graduate School of Engineering Science at
Osaka University. Since 2016, he has been the project representative of
JSPS Grand-in Aid for Scienti c Research on Innovative Area “Nano-Material
Manipulation and Structural Order Control with Optical Forces”. His researchinterests are the microscopic interaction between light and nanostructures
and the optical functionalities arising from their interaction. He is the fellow of
the Japan Society of Applied PhysicsxInvited Talk
Presenter:

Prof. Yoshiki Kohmura
RIKEN SPring-8 Cente

Title:
Generation of X-ray Vortices by Bragg Re ection from Crystals andMicroscopy to Diagnose Topological Charge Distributio

Abstract:
We developed a method to transfer the structure of dislocation in a crystal to
the Bragg X-ray wave front and performed a phase measurement that could
diagnose the dislocation. This method helps to enhance the functionality ofmaterials affected by dislocations. The two-beam X-ray interferometry was
performed to measure the Bragg re ected X-ray wave front from a spiraldislocation area in a SiC crystal. As a result, a pair of fork patterns wasobserved. The number of fringes changed by +1 and -1 at the phaseanomalies due to generation of an X-ray vortex with the topological charge of+1. Kinematic diffraction simulation showed that X-ray vortices are generated
on Bragg re ected X-rays from spiral dislocation areas. This result is realized
by using suf ciently large spatial coherence of the irradiated X-rays

Biography:
Yoshiki Kohmura is currently a Team Leader of Synchrotron Radiation
Imaging Instrumentation Team at SPring-8 facility, Japan. He received his
PhD in the Department of Physics, Graduate School of Science, theUniversity of Tokyo in 1994. He has been working for RIKEN SPring-8 Center
since 1996. He is involved in developing various x-ray optical elements andmethodologies for synchrotron radiation experiments. In the past ten years,
he studied the novel waveguiding phenomenon of x-rays occurring insideslightly deformed crystals and its application to fast switching of x-raysxi

Invited Talk
Presenter:

Dr. Toru Tsujimura
National Institute for Fusion Science, National
Institutes of Natural Science

Title:
Propagation Properties of Optical Vortex in Magnetized Plasm

Abstract:
We investigated theoretically propagation properties of an optical vortex witha helical wavefront in cold uniform magnetized plasmas in an electron
cyclotron (EC) range of frequencies. We describe the effects of the helical
wavefront of the vortex EC wave on the wave elds in magnetized plasmas
as anisotropic media. These effects become signi cant as the topologicalcharge of the vortex EC wave increases or the distance from the phasesingularity becomes small. The different propagation properties are also
con rmed in the propagation of Laguerre–Gaussian beams on threedimensional simulations with the nite element method. We found aremarkable phenomenon on mode conversion in the vortex EC wave
propagation, which suggests an optical vortex can be a new tool to heat highdensity plasmas

Biography:
Toru Ii Tsujimura received the B.Eng., M.Eng., and D.Eng. Degrees from the
University of Tokyo in 2009, 2011, and 2014, respectively. Since 2014, he has
been working as an assistant professor at National Institute for Fusion
Science, National Institutes of Natural Sciences (NINS). His current research
focuses on wave heating in fusion plasma at the Large Helical Device. He
was a representative of NINS programs for cross-disciplinary study in 2018and 2019, leading the program on helical wavefront measurements of opticalvortices emitted by high-energy electronsxiiSymposium3
Plenary Talk
Presenter:

Prof. Kenichi Yoshikawa
Self-organization Science Research Center, Doshisha
University / Institute for Advances Study, Kyoto Universit

Title:
Cooperation of Real-World Modeling with Simulation toward the Problem“What is Life?

Abstract:
Living matter is manipulating large number of different molecules to create
spatio-temporal self-organization. Currently, many numerical studies havebeen carried out to shed light on the underlying mechanisms of life.
Sometimes, these studies remain as a possible explanatory interpretation
because of the complexity of actual living systems. In the present talk, I would
like to show some examples of real-world modeling, which help us to obtaindeeper understanding in biological systems. 1) Emergence of cell-likestructure and function under crowding condition with macromolecules. 2) Selforganization of cellular assembly. 3) Self-generation of macroscopic regularmotion for the assembly of nano-scaled self-propelling objects

Biography:
Name
Kenichi Yoshikawa
URL: http://dmpl.doshisha.ac.jp/
Academic Degree
PhD, Physical Chemistry, Graduate School of Engineering, Kyoto University(1976)

xiii

Professional Appointments
1998 – 2012
Professor, Department of Physics, Graduate School of Science, Kyoto
University
2011 – 2014
Chair, Commission of Biological Physics C6, IUPAP
2012 –
Professor, Faculty of Life and Medical Sciences, Doshisha University
2019Specially Appointed Prof., Institute for Advances Study, Kyoto Universit

Plenary Talk
Presenter:

Prof. Helmut Schiessel
Cluster of Excellence Physics of Life, Technical
University Dresde

Title:The mechanical genom

Abstract:
In addition to the classical layer of genetic information, DNA molecules also
carry other layers of information. Two possible layers are discussed. One is amechanical layer, namely that the base pair sequence in uences themechanical and geometrical properties of the DNA molecules which in turnmight guide their packing inside the cell. A second possible layer is the speedof translation in the protein-producing ribosomes where the speed in uences
the quality of the protein product. We demonstrate that the degeneracxivBiography:
Helmut Schiessel studied physics in Freiburg where he did his Ph.D. intheoretical polymer physics in 1997. He then worked as a postdoc at two
Universities of California, in Santa Barbara and in Los Angeles. In 2000 hejoined the MPI for Polymer Research in Mainz where he was in charge of abiophysics research project. From 2005 to 2020 Schiessel headed the chairof Theoretical Physics of Life Processes at the Lorentz Institute, Leiden
University. Since January he heads the group Theoretical Physics of Living
Matter at the Cluster of Excellence Physics of Life.

Invited Talk
Presenter:

Prof. Yoshiteru Yonetani
National Institute for Quantum and Radiological
Science and Technolog

Title:
Water on the DNA Surface: Microscopic Insight from Molecular Dynamics
Simulation

Abstract:
Water on the DNA surface exhibits characteristic behavior such as ice-likewater network along the narrow groove of DNA. By using molecular dynamics
simulations, we obtained detailed picture for such water; our characterization
fully describes the water network patterns and their sequence variation[Biophys. J. 97, 1138 (2009)]. Analysis on such water network further
revealed microscopic origin of the slow water-exchange kinetics [Biophys.
Chem. 160, 54 (2012)]. As another relevant topic, I will also mention a relation
with DNA damage production. Our recent study [Chem. Phys. Lett. 749,
137441 (2020)] found that site-dependent water accessibility for DNA
backbone is well correlated with the probabilities of DNA damage production
by OH radical attacking. This suggests that the site-dependent hydration
property is a key factor for DNA damage production

xv

Biography:
Yoshiteru Yonetani received B.E. and Dr. degrees from Keio University in1998 and 2002, respectively. He worked as a postdoctoral researcher at Nara
Women’s University (2002-2003) and Japan Atomic Energy Agency(2004-2008). He is currently a senior researcher in National Institutes of
Quantum and Radiological Science and Technology. His current interests
include molecular dynamics and quantum dynamics in biological andchemical physics

Tutorial Talk
Presenter:

Dr. Miyuki Sasaki
Collaborative Laboratories for Advanced
Decommissioning Science, Japan Atomic Energy
Agenc

Title:
Visualization of Dose Rate Distribution around Fukushima Daiichi Nuclear
Power Plant using Arti cial Neural Networks

Abstract:
This study proposes a method of visualizing the ambient dose rate
distribution using arti cial neural networks (ANN) from airborne radiation
monitoring results. The ANN method was applied to the results of the airborne
radiation monitoring which was conducted around the Fukushima Daiichi
Nuclear Power Plant by an unmanned aerial vehicle. The ANN wasconstructed by training data consisting of input variable dataset (radiation
count rate, altitude, topographic data, photographic RGB data) and objective
variable dataset (the air dose rate data at 1 m above the ground level). The
reliability of the ANN method was evaluated by comparison with the groundbased survey data. The dose rate map created by the ANN method
reproduced ground-based survey results better than traditional methods

xviBiography:
Miyuki Sasaki received Dr. Eng. degrees from the University of Nagoya,Japan, in 2021. She became a researcher at the Japan Atomic Energy
Agency in 2015. Her current research interests include radiation
measurementxviiCommittee
General Chair:
Hiroaki Nakamura (National Institute for Fusion Science
Conference Chair:
Takahiro Kenmotsu (Doshisha University
Conference Co-Chair:
Susumu Fujiwara (Kyoto Institute of Technology)
Katsuhiko Yamaguchi (Fukushima University
Program Chair:
Seiki Saito (Yamagata University)
Hiroshi Tamura (Chuo University
Program Co-Chair:
Nobuaki Ohno (University of Hyogo)
Yoshihide Shibata (National Institute of Technology, Gifu College )Yoshihisa Fujita (Ritsumeikan University
Post-Conference Chair:
Susumu Fujiwara (Kyoto Institute of Technology
Post-Conference Co-Chair:
Tomoko Mizuguchi (Kyoto Institute of Technology)
Hiroaki Ohtani (National Institute for Fusion Science)
Daisuke Ishihara (Kyushu Institute of Technology
Publication Chair:
Taku Itoh (Nihon University)
Publication Co-Chair:
Hiroto Tadano (University of Tsukuba)
Soichiro Ikuno (Tokyo University of Technology)
Finance Chair:
Hiroki Sakuta (Doshisha University
Publicity Chair:
Satoshi Takatori (Doshisha University
Exhibition Chair:
Yoji Matsumoto (Cybernet Systems Co., Ltd.
Conference Adviser:
Amane Takei (University of Miyazaki)
Takuo Yasunaga (Kyushu Institute of Technology)
Motoi Wada (Doshisha University)

xviii

Table of Contents
Day 1 (Wednesday, 1st September, 2021)
Plenary Talk 1 (Numerical Simulation and Visual Analytics of Nonlinear Problems)
9:45 – 10:45, Hall A(Plenary) Understanding system dynamics by combining data-driven analysis and information
visualization ................................................................................................... 1
Hiroaki Natsukawa

Symposium 1 on Numerical Simulation and Visual Analytics of Nonlinear Problems,Session 01, Invited and Tutorial Talks, 11:00 – 12:00, Hall A(Invited) Computation of singular values for generalized tensor sum ................................3
Tomohiro Sogabe(Tutorial) A Numerical Study of Parallel Variants of GPBiCG Method with Stabilization Strategy
for Solving Linear Equations ............................................................................... 6
Kuniyoshi Abe

OS8: Numerical Harmonic Analysis and Signal Processing, Session 05, 11:00 – 12:20,
Hall B
Feature Extraction of Distorted Sound Waveforms and Estimation of Distortion Effects and Their
Settings ......................................................................................................... 8
Taiga Ishida, Toshio Suzuki and Emiko Ishiwata
A digital image watermarking based on high-frequency components with additive low-frequencyof the dual-tree complex discrete wavelet transform ...................................................12
Masayuki Shimoshimbara and Teruya Minamoto
Detection of maliciously image blurred portions using dyadic wavelet transform ................ 16
Takaki Hiramatsu and Teruya Minamoto
Feature Extraction Method for Detecting Early Stage Colorectal Cancer from Endoscopic Images
Using Dual-Tree Complex Wavelet Packet Transform ................................................ 20
Daigo Takano and Teruya Minamotoxix

OS3+OS9: Complex and Ultimate Systems (OS3), Complex Networks andComplex Systems (OS9),Session 08, 11:00 – 12:00, Hall C
Computation of Compressive Flow in Pulsed Focusing Engine (Fugine) Set in Shock Tube ... 24
Daiki Okada, Hiroki Kijima, Tomotaka Kobayashi and Ken Naitoh
Computations on high efﬁciencies of pulsed focusing engine for rocket ........................... 28
Tomotaka Kobayashi, Hayato Suzuki, Hiroki Kijima and Ken Naitoh
A simple model of on–demand transporter ..............................................................32
Yuhei Okubo, Takashi Shimada and Toru Ohira

OS2: Simulation Technology in Origami, Session 12, 11:00 – 12:00, Hall D
Numerical evaluation on the out-of-plane properties of bio-inspired honeycomb cores with extra
hollows ........................................................................................................35
Mudong Li, Sachiko Ishida and Kazuya Saito
Sound Insulation Simulations focusing on Height of Origami Core .................................39
Aya Abe and Ichiro Hagiwara
Application to anti-vibration table of two-layered origami structures ...............................43
Yingxue Bai and Sachiko Ishida

OS7: Advanced Numerical Analysis and Software Technology, Session 16, 11:00 – 12:00,
Hall E
Application of Ordinary State-based Peridynamics in Bimaterial Modeling .......................46
Huy Anh Nguyen, Hanlin Wang and Satoyuki Tanaka
Accurate and Fast Electrostatic Field Analysis with Unstructured Numerical Human Body Model
Using Parallel Geometric Multi-Grid Method .......................................................... 50
Masamune Nomura and Amane Takei
High Performance Implementation of Skyline Solver for Many Core Environment ..............52
Hiroshi KawaixxSymposium 1 on Numerical Simulation and Visual Analytics of Nonlinear Problems,Session 02, 14:30 – 15:30, Hall A
High-Performance Solver for EFG-Type Saddle-Point Problem: Improved Variable-Reduction
Method ........................................................................................................53
Atsushi Kamitani, Teruou Takayama and Ayumu Saitoh
Parallel implementation of the approach for solving saddle point problems using block
structure .......................................................................................................55
Hiroto Tadano
A Paralellization Strategy for Incomplete Decomposition-based Preconditioning for Solving Linear Systems ...................................................................................................59
Taiga Yamashita, Taku Itoh and Hiroto Tadano

OS8: Numerical Harmonic Analysis and Signal Processing, Session 06, 14:30 – 15:30,
Hall BAn analysis of electrocardiograms through the wavelet transform with pseudo differential operator
like operators .................................................................................................63
Masudur Rahman, Minoru Yoshida, Toshinao Kagawa, Shuji Kawasaki, Shunya Nagai, Hidetoshi
Oya, Yumi Yahagi and Takayuki Okai
Application of Wavelet-Taylor-Galerkin method to the 1D Euler equations ....................... 67
Kyosuke Yamamoto and Taishi Matsuura
Wavelet Galerkin method for three-dimensional boundary value problems with MPC technique
71
Satoyuki Tanaka, Thin Thin Htut, Hanlin Wang and Hiroshi Okada

OS3+OS9: Complex and Ultimate Systems (OS3), Complex Networks and Complex
Systems (OS9), Session 09, 14:30 – 15:30, Hall C
Driving forces for structural transitions in atomic clusters in collective eigen-time-delay
coordinates ................................................................................................... 75
Yusuke Ogasawara and Tomohiro Yanao
Multiagent simulation of infectious propagation of COVID-19 ......................................78
Atsushi Tanaka and Jin Suzuki
A prediction algorithm of drosophila lifespan toward high-throughput screening in genetic
research ....................................................................................................... 82
Masaya Hata, Ki-Hyeong Seong and Siu Kangxxi

OS2: Simulation Technology in Origami, Session 13, 14:30 – 15:30, Hall D
New semi origami structure for collision energy absorption and its manufacturing method .... 86
Yang Yang and Ichiro Hagiwara
Development of a Pattern for Continuous Manufacturing of Complex 3D Shapes with Kirigami
HoneyCombs .................................................................................................90
Luis Diago, Junichi Shinoda and Ichiro Hagiwara
3D structural form creation of earwig fan using the algorithmic design tool .......................94
Kazuya Saito and Chisaki Kitajima

OS7: Advanced Numerical Analysis and Software Technology, Session 17, 14:30 – 15:30,
Hall E
Performance evaluation of wave-sound analysis code: ADVENTURE Sound ....................96
Akihiro Kudo and Amane Takei
Development of Huge-Scale Microwave analysis code: ADVENTURE Fullwave ............... 98
Amane Takei
Heat Transfer Analysis with Uncertainty Using Non-Statistical Uncertainty Quantiﬁcation
Method and Parallelized Heat Transfer Analysis Tool ............................................... 100
Sota Goto, Amane Takei, Shigeki Kaneko and Shinobu Yoshimura

Symposium 1 on Numerical Simulation and Visual Analytics of Nonlinear Problems,Session 03, 15:45 – 16:45, Hall A
Photonic Crystal Frequency Demultiplexer Design for Electromagnetic Wave using FDTD and
MEMD ...................................................................................................... 102
Ran Dong, Daisuke Shigeta, Yoshihisa Fujita and Soichiro Ikuno
Numerical Investigation on Superconducting Linear Acceleration System: Shape Optimization of
Current Distribution in Electromagnet ................................................................. 106
Teruou Takayama, Takazumi Yamaguchi, Ayumu Saitoh and Atsushi Kamitani
Three-Dimensional Analysis of Magnetic Shielding Current in High-Temperature Superconducting Tape ..................................................................................................... 108
Takazumi Yamaguchi, Hiroaki Ohtani, Shinsuke Satake and Nagato Yanagixxii

OS8: Numerical Harmonic Analysis and Signal Processing, Session 07, 15:45 – 16:45,
Hall B
Some suitable settings for Haar-like four-point orthogonal transform .............................110
Kensuke Fujinoki and Yuji Senda
Estimation method for scale-shift relationship between two speech signals based on FourierMellin transform ........................................................................................... 114
Akira Morimoto, Ryuichi Ashino and Takeshi Mandai
Some properties of fractional wavelet transform ......................................................118
Mawardi Bahri and Ryuichi Ashino

OS3+OS9:Complex and Ultimate Systems (OS3), Complex Networks and Complex
Systems (OS9), Session 10, 15:45 – 16:45, Hall C
A Study on Tracking Individual Pedestrian Trajectories in a Walking Crowd Using Openpose 122
Minagi Miyokawa and Hideo Miyachi
Transient Trajectories on Chaotic and Random Neural Network (CRNN) ....................... 126
Hitoaki Yoshida, Takeshi Murakami, Zhongda Liu and Satoshi Kawamura
Performance evaluation of collaboration networks by simulations of interacting discovery
processes .................................................................................................... 130
Tetsuo Imai

OS6: Multi Dimensional Communication Networks, Session 14, 15:45 – 16:45, Hall D
Analysis of information ﬂoating at an intersection considering trafﬁc lights ..................... 134
Kazuyuki Miyakita, Naoyuki Karasawa, Hiroshi Tamura and Keisuke Nakano
Effects of human body shadowing and entering and leaving of mobile nodes on information ﬂoating in a one-dimensional street .......................................................................... 138
Naoyuki Karasawa, Kazuyuki Miyakita, Hiroshi Tamura and Keisuke Nakano
On the edge Grundy number and the number of vertices in grid graphs .......................... 142
Hiroshi Tamura and Keisuke Nakanoxxiii

OS11: Simulation in Nuclear Fusion, Session 18, 15:45 – 16:45, Hall E
Simulation of GAMMA 10/PDX plasmas by a plasma ﬂuid model based on the anisotropic ionpressure (AIP model) ......................................................................................146
Satoshi Togo, Naomichi Ezumi, Mizuki Sakamoto, Md. Shahinul Islam, Tsukasa Sugiyama,
Kousuke Takanashi, Tomonori Takizuka and Kenzo Ibano
Detached helium plasma simulation with collisional-radiative model .............................150
Hirohiko Tanaka, Isaya Saeki, Noriyasu Ohno, Shin Kajita, Taichi Ido, Hiroki Natsume, Akiyoshi
Hatayama, Kazuo Hoshino, Keiji Sawada and Motoshi Goto
Development of the efﬁcient electrostatic plasma particle simulation code for the study of fusion
boundary layer plasmas ...................................................................................152
Hiroki Hasegawa and Seiji Ishiguro

Symposium 1 on Numerical Simulation and Visual Analytics of Nonlinear Problems,Session 04, 17:00 – 18:00, Hall A
Improved linear notch mechanics based on congruent condition of stress distribution for all notchedmaterials .....................................................................................................156
Wataru Fujisaki, Ryunosuke Sakamoto and Yuto Shikata
Fully explicit computational method for gas-solid two-phase ﬂow with large temperature
variation ..................................................................................................... 160
Daisuke Toriu and Satoru Ushijima
Radiation ﬁeld analysis using deep learning algorithms ............................................. 164
Katsuhiko Yamaguchi, Masaharu Matsumoto, Yuto Kondo, Kenji Suzuki and Jun Kinugawa

Symposium 2 on Analysis of Optical Vortex Field and Applications, Session 11,
17:00 – 18:00, Hall C
Laguerre-Gaussian beam formation by spatiotemporal coherent motion of electrons .......... 167
Shin Kubo, Yuki Goto, Toru Ii Tsujimura and Toru Kobayashi
Application of optical vortex to laser-induced ﬂuorescence velocimetry of ions in a plasma ..170
Shinji Yoshimura, Kenichiro Terasaka and Mitsutoshi Aramaki
FDTD analysis of propagation of millimeter wave vortex in magnetized cold-plasma ......... 173
Kazuki Chiba and Hideki Kawaguchixxiv

OS6: Multi Dimensional Communication Networks, Session 15, 17:00 – 17:40, Hall D
Various characteristic evaluation on magnetically-coupled intra-body communication using threedimensional ﬁnite element modeling of a human upper-body ...................................... 175
Kenichi Ito
Excitation of Metal Plate Using Folded Dipole Antenna ............................................ 179
Takumi Nishime, Hiroshi Hashiguchi, Naobumi Michishita and Hisashi Morishita

OS11: Simulation in Nuclear Fusion, Session 19, 17:00 – 17:40, Hall E
Development of hydrogen recycling model on carbon divertor by molecular dynamics
simulation ...................................................................................................183
Yuki Kojima, Hiroaki Nakamura, Keiji Sawada, Gakushi Kawamura, Masahiro Kobayashi, Masahiro
Hasuo, Masato Iida, Mayuko Miura and Seiki Saito
Investigation of hydrogen recycling process on tungsten divertor ..................................186
Seiki Saito, Mayuko Miura, Hiroaki Nakamura, Keiji Sawada, Gakushi Kawamura, Masahiro
Kobayashi and Masahiro Hasuo

xxv

Day 2 (Thursday, 2nd September, 2021)
Plenary Talk 2 (Analysis of Optical Vortex Field and Applications), 9:00 – 10:00, Hall A(Plenary) Interaction of optical vortex and matter systems: from microscopic to macroscopic
regimes and linkage between them ......................................................................188
Hajime Ishihara

Symposium 1 on Numerical Simulation and Visual Analytics of Nonlinear Problems,Session 20, 10:15 – 11:15, Hall A
Improvement of Visibility in Feature Emphasis Visualization of 3D Measured Point Cloud .. 191
Mizuki Katahira, Kyoko Hasegawa, Liang Li and Satoshi Tanaka
Improving Depth Perception of Transparent Objects in Stereoscopic Vision using Ambient
Occlusion ................................................................................................... 194
Kota Kataoka, Yuishi Sakano, Naohisa Sakamoto, Kyoko Hasegawa, Liang Li and Satoshi Tanaka
Adaptive Opacity Control using Implicit Function for Visualizing Large-Scale 3D Measurement
Point Clouds ................................................................................................ 197
Masaya Kishimoto, Motoaki Adachi, Kyoko Hasegawa, Liang Li and Satoshi Tanaka

Symposium 2 on Analysis of Optical Vortex Field and Applications, Session 22,
Invited Talks, 10:15 – 11:15, Hall B(Invited) Generation of X-ray vortices by Bragg reﬂection from crystals and microscopy to diagnose topological charge distribution .................................................................... 201
Yoshiki Kohmura(Invited) Propagation properties of optical vortex in magnetized plasma ........................ 204
Toru Tsujimuraxxvi

Symposium 3 on Advanced Concept and Methodology in Bioscience, Session 24,
10:15 – 11:15, Hall C
Possibility of Visualisation of electrostatic potential by electron microscopy ....................207
Takuo Yasunaga and Yasuhisa Honda
Linear response theory applied to molecular dynamics simulations ............................... 209
Kazumi Omata, Ryuta Kawanami, Hiroaki Nakamura and Susumu Fujiwara
Molecular simulations on dynamics of lipid bilayers and water molecules .......................213
Yuji Higuchi, Hiroaki Ito, Naofumi Shimokawa, Yuta Asano, Takuya Kuwahara and Mafumi
HishidaOS11: Simulation in Nuclear Fusion, Session 26, 10:15 – 11:15, Hall D
Molecular Dynamics Simulation on Hydrogen Isotope Molecules Emitted from Amorphous
Carbon .......................................................................................................216
Hiroaki Nakamura, Seiki Saito, Keiji Sawada, Masahiro Kobayashi and Masahiro Hasuo
Studies on ion heating through the merging of spherical tokamaks by means of particle
simulations ..................................................................................................219
Shunsuke Usami, Ritoku Horiuchi, Toseo Moritaka and Yasushi Ono
Visualization analysis of intersection points of energetic tritons and plasma facing wall in LHD
by virtual-reality system .................................................................................. 221
Hiroaki Ohtani, Suguru Masuzaki, Kunihiro Ogawa and Seiji Ishiguro

OS1: Veriﬁed Numerical Computations, Session 28, 10:15 – 11:15, Hall E
Constructive a priori error estimates for Poisson’s equation with discontinuous coefﬁcients .. 224
Kazuaki Tanaka and Mitsuhiro T. Nakao
Numerical veriﬁcation for positive solutions of the Hénon equation on bounded domains .... 226
Taisei Asai, Kazuaki Tanaka and Shin’ichi Oishi
Acceleration of Error-Free Transformation of Matrix Multiplication using GPU Tensor Cores 229
Katsuhisa Ozaki, Daichi Mukunoki and Takeshi Ogita

xxvii

Symposium 1 on Numerical Simulation and Visual Analytics of Nonlinear Problems,Session 21, 11:30 – 12:30, Hall A
Generation of Implicit Surface Based on Isoparametric Elements ................................. 232
Taku Itoh
A Study for Recognizing and Simulating Deliberate Emotional Expressions in Japanese
Utterance ....................................................................................................236
Chihiro Asada, Yuichi Tamura, Ryo Nagata and Katsunari Sato
Continuous collision avoidance model between pedestrians ........................................ 240
Kotori Tsutsumi, Yuichi Tamura and Katsunari Sato

Symposium 2 on Analysis of Optical Vortex Field and Applications, Session 23,
11:30 – 12:10, Hall B
Creation of hexagonal close-packed photonic-ring with optical vortex ........................... 244
Kanta Takahashi, Haruki Kawaguchi, Kei Umesato, Yoshihiko Arita, Keisaku Yamane, Ryuji
Morita, Ken-ichi Yuyama, Satayuki Kawano, Katsuhiko Miyamoto and Takashige Omatsu
Quantum interference of spontaneous optical vortex photon emission in a cylindricalwaveguide ...................................................................................................246
Satoshi Tanaka, Kazuki Kanki, Yuki Goto, Shin Kubo and Tomio Petrosky

Symposium 3 on Advanced Concept and Methodology in Bioscience, Session 25,
11:30 – 12:30, Hall C
Numerical Simulation and Experiments of Intermittent Camphor Boats ..........................248
Takatoshi Ichino
Particle layer effect of liquid marble on Belouzov–Zhabotinsky reaction ........................ 251
Yasunao Okamoto, Jun’ya Tanoue, Daigo Yamamoto and Akihisa Shioi
Numerical calculation for near-wall accumulation of swimming microorganism ............... 255
Takuya Ohmura, Yukinori Nishigami and Masatoshi Ichikawa

xxviiiOS10: Computational Electromagnetics and Its Applications, Session 27, 11:30 – 12:30,
Hall D
Analysis of Foreign Object Detection for Wireless power transfer Using Differential Coils .. 257
Yunyi Gong, Yoshitsugu Otomo and Hajime Igarashi
On Equivalent Circuit Representation of Transformer Considering Eddy Currents ............. 261
Qiao Liu, Yoshitsugu Otomo and Hajime Igarashi
Numerical Optical Modeling of Nanostructures using Fractal Dimension ........................265
Yoshihisa Fujita, Hiroaki Nakamura, Soichiro Ikuno and Susumu Nakata

OS1: Veriﬁed Numerical Computations, Session 29, 11:30 – 12:30, Hall E
Preconditioner for Ill-conditioned Tall and Skinny Matrices ........................................268
Atsushi Minamihata, Katsuhisa Ozaki, Takeshi Ogita and Shin’ichi Oishi
Veriﬁed Numerical Computations for a Standard Eigenvalue Problem Without Directed
Rounding ....................................................................................................270
Takeshi Terao, Katsuhisa Ozaki, Takeshi Ogita and Toshiyuki Imamura
Acceleration of Iterative Reﬁnement for Symmetric Eigenvalue Decomposition ................273
Yuki Uchino, Katsuhisa Ozaki and Takeshi Ogita

Plenary Talk 3 (Advanced Concept and Methodology in Bioscience), 14:30 – 15:00,
Hall A(Plenary) The mechanical genome ..................................................................... 275
Helmut Schiesselxxix

Day 3 (Friday, 3rd September, 2021)
Plenary Talk 4 and Invited Talk 4 (Advanced Concept and Methodology in Bioscience),
9:00 – 10:00, Hall A(Plenary) Cooperation of Real-World Modeling with Simulation toward the Problem“What is Life?” ............................................................................................ 277
Kenichi Yoshikawa(Invited) Water on the DNA surface: microscopic insight from molecular dynamics
simulations ..................................................................................................279
Yoshiteru Yonetani

OS4: Design and Simulations for System Integration, Session 30, 10:15 – 11:15, Hall A
Development of an optimal routing system for traveling among farm ﬁelds ..................... 282
Takuma Nemoto, Naoki Niitsuma and Norihiro Kamamichi
Elbow Joint Angle Estimation Method Using 1D-CNN with Quantized EMG Generated by SR
and multi-sensor ........................................................................................... 285
Daichi Kashimoto and Teruyoshi Sadahiro

RS1, Session 33, 10:15 – 11:15, Hall B
Simulation of Team Cooperation Considering Team Cognition – Effect of Mutual Beliefs on Team
Performance ................................................................................................ 293
Sumie Cho, Taro Kanno, Daichi Mitsuhashi and Kazuo Furuta
Agent-based simulation of consumer panic buying: feasible measures for mitigating
its effect ..................................................................................................... 297
Sotaro Kawanishi, Rithika Dulam, Kazuo Furuta and Taro Kanno
Comprehending and mitigating the implications of consumer panic buying ..................... 301
Rithika Dulam, Kazuo Furuta and Taro KannoxxxSymposium 3 on Advanced Concept and Methodology in Bioscience, Session 36,
Tutorial Talks, 10:15 – 11:05, Hall C(Tutorial) Visualization of dose rate distribution around Fukushima Daiichi Nuclear Power Plant
using artiﬁcial neural networks .......................................................................... 305
Miyuki Sasaki
Estimation of distribution of Uranium as shielding body using machine learning ...............308
Haruka Yamazaki, Yuto Kondo and Katsuhiko Yamaguchi

OS10: Computational Electromagnetics and Its Applications, Session 39, 10:15 – 11:15,
Hall D
Application of Multilayered Division Method to Scattering by Slanted Gratings ............... 311
Hideaki Wakabayashi, Masamitsu Asai and Jiro Yamakita
On the regular tetrahedral layout of helices for a quasi-isotropic chiral particle ................. 315
Masamitsu Asai, Hideaki Wakabayashi and Jiro Yamakita
An investigation of deﬂated ICCG method for ﬁnite element analysis of eddy current
problem ......................................................................................................318
Kota Watanabe and Wataru Kotani

OS5: Coupled-Simulation and Co-Simulation, Session 42, 10:15 – 11:15, Hall E
Eulerian coupling simulation method for dynamics of air and shock-absorbing structure ..... 320
Ryohei Katsumata, Koji Nishiguchi, Tokimasa Shimada, Hiroya Hoshiba and Junji Kato
Coupled analysis for active control and energy harvesting from ﬂow-induced vibration ....... 324
Shigeki Kaneko and Shinobu Yoshimura
Finite element approach to ﬂuid-structure interaction with contact ................................ 328
Tomohiro Sawada and Junichi Matsumoto

OS4: Design and Simulations for System Integration, Session 31, 11:30 – 12:10, Hall A
Locomotion Control of Snake-like Robot utilizing Friction Forces: Feasibility Veriﬁcation via
Two Wheeled Robot .......................................................................................330
Shunsuke Nansai and Hiroshi Itoh
Degradation diagnosis of Lithium-ion batteries considering operation temperature ............ 334
Yuuki Odagaki, Kosuke Toda, Norihiro Kamamichi, Masami Iwase and Yasuyuki Satohxxxi

RS2, Session 34, 11:30 – 12:10, Hall B
Analysis of electrostatically induced current in humans when in contact with a stepladder underpower transmission lines ..................................................................................338
Yuta Ishida and Shoji Hamada
Effects of the number of observations on 4D-Var data assimilation: preliminary experiments 342
Yasuyoshi Horibata

Symposium 3 on Advanced Concept and Methodology in Bioscience, Session 37,
11:30 – 12:30, Hall C
Rate of double strand breaks of genome-sized DNA in tritiated water: dependence on tritium
concentration, water temperature, and DNA concentration ......................................... 346
Yuji Hatano, Hiroto Shimoyachi, Tatsya Asano, Takahiro Kenmotsu, Takuro Wada, Yasuhisa Oya,
Hiroaki Nakamura and Susumu Fujiwara
Tritium-induced damage on polymers and biopolymers: Molecular dynamics simulations andtheoretical calculations ....................................................................................349
Susumu Fujiwara, Haolun Li, Ryuta Kawanami, Kazushi Terakawa, Tomoko Mizuguchi, Hiroaki Nakamura, Yoshiteru Yonetani, Kazumi Omata, Seiki Saito, Takuo Yasunaga, Ayako Nakata,
Tsuyoshi Miyazaki, Takao Otsuka, Takahiro Kenmotsu, Yuji Hatano and Shinji Saito
Effect of tritium beta decay in deoxy-D-ribose on duplex of telomeric DNA .................... 352
Kento Ishiguro, Hiroaki Nakamura, Takuo Yasunaga, Susumu Fujiwara, Tomoko Mizuguchi,
Ayako Nakata, Tsuyoshi Miyazaki, Takahiro Kenmotsu, Yuji Hatano, Shinji Saito and Yoshiteru
Yonetani

OS10: Computational Electromagnetics and Its Applications, Session 40, 11:30 – 12:30,
Hall D
Examination of Coil Resistance Measurement during Wireless Power Transfer and Comparison
with Finite Element Analysis ............................................................................ 356
Daigo Yonetsu, Yuji Nakano and Naoya Hamano
Study on Parallel Coupled Analysis of High-Frequency Electromagnetic Field and Heat Conduction Problems of Numerical Human Body Model .................................................... 360
Shin-ichiro Sugimoto, Amane Takei and Masao Ogino
Analysis of electrostatically induced short-circuit current in a human body on a 500 kV transmission tower ................................................................................................... 366
Shoji Hamada

xxxii

OS5: Coupled-Simulation and Co-Simulation, Session 43, 11:30 – 12:30, Hall E
Comparative Study of Strongly Coupled Fluid and Structure Systems With Computational
Control ...................................................................................................... 370
Vinay Shankar and Daisuke Ishihara
Passive motions and aerodynamic performance of insect’s ﬂapping wings simulated using the
pixel wing model and the strong coupling method ................................................... 374
Minato Onishi and Daisuke Ishihara
Comparative study on partitioned iterative algorithms for coupled multiple phenomena in piezoelectric energy harvesters .................................................................................378
Naoto Takayama, Daisuke Ishihara, Prakasha Ramegowda and Shunsuke Nozaki

OS4: Design and Simulations for System Integration, Session 32, 13:30 – 14:10, Hall A
Simulation of Cable-Laying Snake-like Robot Locomotion on Cable Rack ......................380
Hayato Nagae, Junta Takarabe, Kouji Uchiyama, Masami Iwase and Yasuyuki SatohPath tracking ﬂight of engine-driven multicopter for forest inventory .............................384
Yuto Terada, Kazuya Sato, Naoki Masuda, Masami Iwase and Yasuyuki Sato

Symposium 2 on Analysis of Optical Vortex Field and Applications, Session 35,
13:30 – 14:10, Hall B
Angular momentum of electromagnetic wave radiated from a relativistic electron moving on a
spiral orbit .................................................................................................. 388
Elham Salehi
Structure formation of chiral needle by modeled force ﬁelds with helical phase using molecular
dynamics simulation ...................................................................................... 390
Shu Habu and Hiroaki NakamuraxxxiiiSymposium 3 on Advanced Concept and Methodology in Bioscience, Session 38,
13:30 – 14:10, Hall C
The study on the stability of DNA structure by steered molecular dynamics simulations ......394
Tomoko Mizuguchi, Naoto Fukushima, Takashi Aoki, Masato Hashimoto and Susumu Fujiwara
Reactive molecular dynamics study on damaged polyethylene after hydrogen abstraction byradiation .....................................................................................................396
Haolun Li, Susumu Fujiwara, Hiroaki Nakamura, Tomoko Mizuguchi, Ayako Nakata, Tsuyoshi
Miyazaki, Shinji Saito and Wataru Sakai

OS10: Computational Electromagnetics and Its Applications, Session 41, 13:30 – 14:10,
Hall D
Comparison of beam-wall interaction models using boundary element method ................. 400
Kazuhiro Fujita
Design study of BiCG-Stab matrix solver circuit for FIT scheme based on dataﬂow
architecture ................................................................................................. 402
Chenxu Wang, Seiya Ota and Hideki Kawaguchi

OS5: Coupled-Simulation and Co-Simulation, Session 44, 13:30 – 14:10, Hall E
Importance of 3-D piezoelectric coupled analysis in evaluation of thin piezoelectric bimorph
deformation .................................................................................................404
Shoichi Aikawa, Daisuke Ishihara, Naoki Iwamaru and Prakasha Ramegowda
Comparative study on linear and quadratic solid direct-piezoelectric solvers with shell
inverse-piezoelectric solver to analyze a thin piezoelectric bimorph device ......................406
Prakasha Chigahalli Ramegowda and Daisuke Ishihara

xxxiv

JSST2021

Understanding system dynamics by combining datadriven analysis and information visualization
Hiroaki Natsukawa
Academic Center for Computing and Media Studies, Kyoto University
natsukawa.hiroaki.3u@kyoto-u.ac.jp

Abstract. Natural systems are often complex and dynamic. Reductionism is not universally
applicable for natural complex systems found in biology and elsewhere where behavior isdriven by complex interactions between many components acting together in time nonlinear
dynamic systems. In this talk, I will introduce a minimalist paradigm, empirical dynamic modeling (EDM), for studying non-linear systems. It is a data-driven approach that uses time-series
information to study a system by reconstructing its attractor (a geometric object) that embodies
the rules of a full set of equations for the system. Particularly, I will introduce a few recent
works of visual analytics to support the identification and mechanistic interpretation of system
states using integration EDM with visualization techniques, which leads to our understandingof complex dynamics.
Keywords: Visual analytics, Nonlinear dynamics

1. Introduction
Natural systems are often complex and dynamic; therefore, relationships between measured
time series variables are generally not static; instead, these relations dynamically change ineither a nonlinear or state-dependent manner. For example, in ecology, competition between
small desert mammals changes with the amount of rainfall [1]; or predation on insect herbivores
varies with vegetation structure [2]. To achieve sustainable use of natural resources and conservation of ecosystems, such as those listed in the sustainable development goals (SDGs) [3],it is necessary to monitor the abundance of species included in the ecosystem and understandthe interspecies relationship, which changes depending on the state of the system. Moreover,
we must understand what type of state the ecosystem has and how this state changes over time.
Because it is difficult to accurately quantify these time-varying interspecies relationships using a conventional linear approach, Deyle et al. proposed a state-of-the-art method that specifically measures relationships changing in a state dependent manner between time series variables; this method is one element of empirical dynamic modeling (EDM) [4]. EDM is a collection of methods to study systems using attractors reconstructed from time series data based on
nonlinear state space reconstruction. Specifically, this is an equation-free approach with minimal assumptions for inductive data-science explorations of natural complex systems.

1

JSST2021

2. visEDM

A core strength of data-driven nonlinear analysis, such as EDM, is that system dynamics are
not prescribed a priori, but inferred from empirical evidence. A fundamental weakness can be
the overwhelming task of interpreting results and identifying intersystem drivers. Therefore, inorder to overcome the weaknesses of EDM and to better understand dynamic systems, we propose visEDM that integrates methods that appropriately characterize these dynamics (i.e.,
EDM) with visualization techniques that can help analyze the behavior of the system [5].
As illustrated in Figure 1, we developed a visual analytics system that links the constructionof dynamic networks, state identi- fication, annotation, and the construction of a state transition
graph (STG) by summarizing 2D trajectories. The proposed system supports the identificationand interpretation of the system state using EDM-constructed dynamic graphs.
In this talk, I present the methodology of EDM and report a case study of ecosystem analysis
by visEDM. I also introduce the latest researches on data-driven analysis using EDM, and discuss future prospects.

Figure 1. Schematic of visual analytics to study nonlinear interactions with empirical dynamic modeling (EDM)

References[1] M. Lima, SKM. Ernest, JH. Brown, A. Belgrano, NC. Stenseth: Chihuahuan desert kangaroo rats: Nonlinear effects of population dynam- ics, competition, and rainfall, Ecology, 89:9 (2008), 2594-2603.
[2] C. Gratton, RF. Denno: Seasonal shift from bottom-up to top-down impact in phytophagous insect populations, Oecologia, 134:4 (2003),487-495.
[3] United Nations. Transforming our world: the 2030 agenda for sustain- able development.,
2015.
[4] ER. Deyle, RM. May, SB. Munch, G. Sugihara: Tracking and forecasting ecosystem interactions in real time, Proceedings of the Royal Society B: Biological Sciences,283:1822 (2016), 20152258.
[5] H. Natsukawa, ER. Deyle, GM. Pao, K. Koyamada, G. Sugihara: A visual analytics approach for ecosystem dynamics based on empirical dynamic modeling, IEEE Transactions on Visualization and Computer Graphicsc, 27:2 (2021), 506-516.

2

JSST 2021

Computation of singular values for generalized tensor
sum
Tomohiro Sogabe1,* and Asuka Ohashi2
1 Department of Applied Physics, Nagoya University, Japan
2 National Institute of Technology, Kagawa College, Japan∗ sogabe@na.nuap.nagoya-u.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.136

3

JSST 2021

A Numerical Study of Parallel Variants of GPBiCG
Method with Stabilization Strategy for Solving Linear
Equations
Kuniyoshi Abe1,* , Soichiro Ikuno2 , Gerard L.G. Sleijpen3
1 Faculty of Economics and Information, Gifu Shotoku University
2 School of Computer Science, Tokyo University of Technology
3 Department of Mathematics, Utrecht University∗ abe@gifu.shotoku.ac.jp

Abstract. The hybrid Bi-conjugate Gradient (Bi-CG) methods such as Bi-CGSTAB and
GPBiCG are well-known for eﬃciently solving linear equations, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG
coeﬃcients that are as accurate as possible. We introduce the strategy for stabilizing the
Bi-CG coeﬃcients. On present petascale high-performance computing hardware, the main
bottleneck for eﬃcient parallelization is the inner products which require a global reduction.
The parallel variants of Bi-CGSTAB reducing the number of global communication phases
and hiding the communication latency have been proposed. In this paper, therefore, following the analogy proposed by Cools et al., we design parallel variants of GPBiCG. Then we
examine the convergence speed of the parallel variants with the stabilization strategy.
Keywords: linear equations, Krylov subspace methods, Generalized Product-type Bi-CG,
parallel variants, stabilization strategy

1. Introduction
The hybrid Bi-conjugate Gradient (Bi-CG) methods such as Bi-CG STABilized (Bi-CGSTAB),
BiCGstab(), BiCG×MR2 and Generalized Product-type Bi-CG (GPBiCG) methods are
well-known for eﬃciently solving linear equations Ax = b, for x, where A is a givenn-by-n matrix, and b is a given n-vector. The convergence of GPBiCG/BiCG×MR2 and
BiCGstab() is faster and more robust than that of Bi-CGSTAB. We have sometimes seen
the convergence behavior with a long stagnation phase. In such cases, it is important to have
Bi-CG coeﬃcients that are as accurate as possible. The stabilization strategy [4] for the
Bi-CG coeﬃcients is as accurate as possible has been proposed.
On present petascale high-performance computing hardware, the main bottleneck foreﬃcient parallelization is the inner products which require a global reduction. The resulting
global synchronization phases cause communication overhead on parallel computers. The

6

reduction of the synchronization bottleneck, i.e., the idea of reducing the number of global
communication phases and hiding the communication latency in the Krylov subspace methods has been presented for the Conjugate Gradient (CG) and Generalized Minimal RESidual(GMRES) methods [1, 3, 5]. In addition to reducing the number of global synchronization
points, the idea of hiding global communication latency by overlapping communication
with computations has been proposed. Cools et al. have developed a parallel variant of BiCGSTAB which is referred to as the pipelined Bi-CGSTAB method [2]. In our talk of JSST2019 we have proposed the parallel variants of Bi-CGSTAB, which have faster convergence
speed than the pipelined Bi-CGSTAB method proposed by Cool et al.
In this paper, therefore, we design the pipelined variants of GPBiCG. We examine theconvergence behavior of the pipelined variants and the eﬀectiveness when applying the stabilization strategy by numerical experiments.

2. Parallel variants of GPBiCG method
The standard GPBiCG has three global reduction steps for the inner products required in thecomputations of αk , βk , and ζk and ηk . First, the inner product for the computation of αkis merged with that of βk to reduce the number of global communication phases. Then the
denominator of αk is computed by the inner products between an initial shadow vector and arecurrence for vector updates. The inner products for the computation of αk+1 can be moved
above that of βk , i.e., the communication avoiding variant is derived. In the communication
avoiding variant, the first computation of the matrix-vector multiplication (abbreviated asMV) is separated from the first reduction phase.
Next, the first computation of MV is moved below the first global reduction phase foroverlapping communication with computation. Thus the MVs are computed below the innerproducts. After the local computation of the inner products has been executed on eachworker, each global reduction can be overlapped with the computation of the corresponding
MV. This overlap hides the communication latency behind the computation of the explicit
MV, i.e., the pipelined variant is obtained.
This research was partly supported by JSPS KAKENHI Grant Number 19K12008.

References[1] Chronopoulos, A.T., Gear, C.W.: s-step iterative methods for symmetric linear systems. J. Comput. Math. 25, 153–168 (1989)[2] Cools, S., Vanroose, W.: The communication-hiding pipelined BiCGStab method for the parallel
solution of large unsymmetric linear systems. Parallel Comput. 65, 1–20 (2017)[3] Erhel, J.: A parallel GMRES version for general sparse matrices. ETNA 3, 160–176 (1995)[4] Sleijpen, G.L.G., van der Vorst, H.A.: Maintaining convergence properties of BiCGstab methods
in finite precision arithmetic. Numer. Algorithms 10, 203–223 (1995)[5] Sturler, E.D.: A parallel variant of GMRES(m). In: Proceedings of the 13th IMACS World
Congress on Computational and Applied Mathematics. vol. 9. IMACS, Criterion Press (1991)

7

JSST 2021

Feature Extraction of Distorted Sound Waveforms
and Estimation of Distortion Eﬀects and Their
Settings
Taiga Ishida1,* , Toshio Suzuki2 , Emiko Ishiwata2
1 Graduate School of Science, Tokyo University of Science
2 Faculty of Science Division I, Tokyo University of Science∗ 1420504@ed.tus.ac.jp

Abstract. In this study, we improve the formulas for previously reported features extracted
from distorted sound waveforms using a wavelet transform. By replacing integration witha diﬀerence scheme, the computation time is reduced. Experiments show that using the
proposed features makes it easier for a person with no guitar experience to estimate a target
guitar sound.
Keywords: Distorted sound, Wavelet transform, Sound approximation, Feature extraction

1.

Introduction

Distorted sound is used in various types of music. In general, distortion on a guitar iscreated by using distortion pedals. To produce the desired sound, guitarists must select theappropriate type of distortion eﬀect and tune its parameters, Drive, Tone and so on. This isdiﬃcult even for experienced guitarists.
A previous study [1] extracted features from a waveform of distorted sound using awavelet transform. In the present study, we improve the formula for calculating the valuesof these features and reduce the computation time. Moreover, we conduct experiments to determine whether a person with no guitar experience can produce a desired sound by selecting
a distortion eﬀect and estimating its settings using the values of the proposed features.

2.

Improvement of features

A previous study [1] on amplification and clipping defined two features that represent the
distortion level using the Haar wavelet. Now, we improve the formulas for these two features
regarding the distortion level to reduce computation time.
Let f (t) be the signal from an electric guitar. We assume that f (t) is normalized suchthat maxt | f (t)| = 1. Distorted sound is created in two steps. In the first step, the signal is amplified. It is transformed from f (t) to fˇ(t) = C f (t) for some constant C > 1.

8

In the second step, the signal is clipped using {a clipping
such as f˜(t) ={ transform,}}max −1, min 1, fˇ(t) , as shown in Figure 1.
Diﬀerent combinations of the constant C andthe type of clipping transform produce diﬀerent
sounds, making it diﬃcult to select a distortion
Figure 1: Waveforms of f (t), fˇ(t), and f˜(t)eﬀect and estimate its settings.
The feature that represents amplification is defined as follows [1]:
(
)
∫ ∞
t−b
1
f (t)ψHdt ,(1)
E1 (a) = maxb aa−∞where ψH (t) is the Haar wavelet. ψH (t) equals 1 for 0 ≤ t < 1/2, −1 for 1/2 ≤ t < 1 and 0
for the other points. The value of this feature increases with increasing() distortion level. Ifaa′|a| is suﬃciently small, E1 can be approximated as 4 maxb f b + 2 by using the secondorder central diﬀerence formula. E1 represents the maximum( ) variation of f . To obtain the∫∞4gradient of f , we consider Ẽ1 (a) = maxb a2 −∞ f (t)ψH t−ba dt instead of E 1 . In the same)(way, Ẽ1 can be approximated as maxb f ′ b + a2 . By using the first-order central diﬀerence
formula, we define the feature that represents amplification as follows:
DA = maxbf (b + a) − f (b)
.
a

(2)

With this improved formula, where DA denotes the maximum gradient of f , the computation time is reduced by a factor of 2000 ∼ 3500 by replacing integration with a diﬀerence
scheme.
The feature that represents clipping is defined as follows [1]:()∫ ∞ ∫ ∞
1t−b
4
E2 (a) =dt db.
(3)| f (t)| ψHa−∞ −∞When the Haar wavelet ψH completely overlaps the clipped part of the distorted sound f (t),the integral of (3) with respect to t becomes zero. Hence, the value of this feature decreases
with increasing distortion level. However, this feature has irregular behavior when the distortion level is small because E2 (a) indirectly measures the amount of( clipping.
We thus)2 ∫ ∞1
improve the formula for E2 , and consider e2 (a, b) = a4 −∞ | f (t)| 4 ψH t−b
dt
.
For
b∈R
a
(
)
1
and a > 0 is suﬃciently small, e2 can be approximated as g′ b + 2a if g(t) = | f (t)| 4 . More. We define DC = card(clip(D)) for clip(D) = {b ∈ R | D ≤ ε},over, let D = g(b+a)−g(b)awhere ε > 0 is a constant for detecting clipped parts and card(A) denotes the number of
elements if A is a finite set or the cardinality if it is an infinite set. DC directly measures theamount of clipping.
DA or DC is computed from the discretized signal with a sampling rate F s. Therefore,
we set a = 2/F s. To verify the benefit of DC , we prepared ten kinds of distorted soundswith diﬀerent distortion levels. The association between the distortion level and the value of9

Figure 3: Clipped parts of a waveform

Figure 2: Behavior of DC

DC is shown in Figure 2. The clipped parts can be clearly extracted, as shown in Figure 3.
We can reduce the computation time by a factor of 100 ∼ 200 by replacing integration witha diﬀerence scheme.
Moreover, in [1], not only the feature of distortion level, the feature that represents thebrightness of timbre is defined as follows:∫1 ∞2
ω fˆ(ω) dω,
E0 =
(4)
S −∞
∫∞
where fˆ(ω) is the Fourier transform of f (t) and S = −∞ | fˆ(ω)|2 dω, which is the average ofthe frequency components of the distorted sound f .

3.

Experiments on distortion eﬀects

We conducted an experiment with 11 participants to evaluate our formulas. We createda target sound and six comparison sounds, I-VI, which have diﬀerent values for features
DA , DC , and E0 . The features of the target sound are denoted as D∗A , DC∗ , and E0∗ . Table 1
shows the ratios of the feature values for the six comparison sounds. The participants first
listened to the target sound and sounds I-VI. They then scored sounds I-VI on a scale of 0 to
5 on how similar they are to the target sound.
The results show that 82% of the participants Table 1: Ratio of feature values for six
gave sound V, whose values for the three features comparison sounds
are closest to those for the target sound, the highDA /D∗A DC /DC∗ E0 /E0∗
est score (i.e., it was the most similar to the target
I
0.75
0.55
0.82
sound). None of the participants identified sounds
II
0.93
0.50
1.12
I and IV as most similar to the target sound. These
III
0.90
0.50
1.01
results show that sounds with similar DA , DC , and
IV
1.08
1.12
2.01
E0 values sound similar to the human ear.
V
1.01
1.07
1.09
We also conducted an experiment with three
VI
0.42
1.07
0.97
participants to verify the utility of using DA , DC ,and E0 . These participants had never played anelectric guitar. In this experiment, the target sound was recorded using an eﬀect called“Distortion”, a built-in distortion eﬀect of the BOSS Micro BR BR-80 digital recorder.
The parameters for this eﬀect were set to Drive=55 and Tone=30. The participants were
instructed on how to make a sound using an electric guitar and the BR-80 digital recorder.

10

Table 2: Estimated eﬀect and settings
based on feature values
Participant
A
B
C

Eﬀect
Distortion
Lead
Distortion

Drive
100
90
55

Tone
30
40
50

Figure 4: Waveforms of target and estimatedsoundsIn the first phase, participants were not given the D∗A , DC∗ , and E0∗ values. They selected
one of the twenty built-in distortion eﬀects and estimated the values of Drive and Tone bycomparing the target sound with the sound produced by the guitar. In the second phase, they
were given the D∗A , DC∗ , and E0∗ values. They selected the distortion eﬀect and estimated thevalues of Drive and Tone by comparing D∗A , DC∗ , and E0∗ values to the DA , DC , and E0 values
for the sound produced by the guitar.
Table 2 is the estimation results in the second phase by three participants. We recorded
the sounds obtained with the estimated values and analyzed their waveforms. None of theparticipants could identify the built-in eﬀect without the D∗A , DC∗ , and E0∗ values. The waveform obtained without using the feature values (orange line) is quite diﬀerent from that for
the target sound (blue line) in Figure 4. The sounds estimated without using feature values
are not similar to the target sound. In contrast, two participants identified the eﬀect “Distortion” based on the feature values, but they could not estimate the values of Drive or Tone.
This may be due to the diﬀerences in the force and angle of picking the strings. Participant
B selected a diﬀerent built-in eﬀect; nevertheless, the waveform for the estimated sound(green line) for this participant is similar to that for the target sound, as shown in Figure 4.

4.

Conclusion

In this study, we improved the formulas for two features for distorted sounds defined in aprevious study. The computation time is reduced by replacing integration with a diﬀerence
scheme. We showed that sounds with similar DA , DC , and E0 values sound similar to thehuman ear. A person with no guitar experience can create a sound close to the target soundby using these features. In the future, we will collect more experimental data and analyze
the correlation among feature values using multidimensional scaling.

References[1] Toshio Suzuki, Keiichi Zempo, Tamotu Kinoshita: Approximation of Distortion Sound
via Fourier and Wavelet Transform, 25th International Congress on Sound and Vibration(ICSV25), Hiroshima, Japan, 9, July, (2018).

11

JSST 2021

A digital image watermarking based onhigh-frequency components with additive
low-frequency of the dual-tree complex discrete
wavelet transform
MASAYUKI SHIMOSHIMBARA1,* and TERUYA MINAMOTO1
1 Graduate School of Science and Engineering, Saga University, Saga, Japan∗ simosimm@ma.is.saga-u.ac.jp

Abstract.
We propose a digital watermarking method based on the dual-tree complex discrete
wavelet transform (DT-CDWT), which enables us to obtain 16 frequency components. In
our previous work, we proposed the watermarking method based on the dyadic wavelet
transform (DYWT) which enables us to obtain only four frequency components and intervalarithmetic (IA). Our new method is the modiﬁed version of the previous one. We embeda watermark into the high-frequency components with additive low-frequency components
obtained by the DT-CDWT, whereas we do not use IA. The experimental results show thatthe proposed method has the better image quality of a watermarked image than the previous
one and is more robust against some attacks.
Keywords: Wavelet transform, Dual-tree complex discreate wavelet transform, Watermark

1.

Introduction

Many digital watermarking methods using wavelet transform have been developed [1],[2],[3],[4],[5]. In our previous study [4], we developed the blind digital image watermarking
method based on the dyadic wavelet transform(DYWT) and interval arithmetic(IA). We
also proved that the high-frequency components obtained by the DYWT and IA contain the
low-frequency component. Our previous results in [5] showed that the high-frequency components containing the low-frequency components played an important role to develop arobust watermarking against several attacks. On the other hand, we also developed the digital watermarking based on the dual-tree complex discrete wavelet transform (DT-CDWT)
and IA. However, we did not discuss the high-frequency component’s properties obtainedby the DT-CDWT and IA.
The aim of this study is to develop a digital watermarking method based on the highfrequency components containing the low-frequency components obtained by the DT-CDWT

12and investigate its robustness. Applying the DT-CDWT to an image, we obtain four lowfrequency components and 12 high-frequency components. We intentionally add the four
low-frequency components to 12 high-frequency components at each. Experimental results
demonstrate that the addition of the low-frequency and high-frequency components play animportant role to develop the robust digital watermarking.
This paper proceeds as follows. We ﬁrst present our watermarking embedding and extraction procedure. Next, the experimental results are presented in Section 3 and a summaryand discussion are given in Section 4.

2.

Watermarking algorithm

The algorithm for embedding and extraction of a watermark is in a similar manner as in[5]. The embedding procedure is as follows:
1. Apply the DT-CDWT to a host image. Then, 16 frequency components CRR , CRI , C IR ,C II ,DRR , DRI , DIR , DII , ERR , ERI , E IR , E II , FRR , FRI , F IR and F II are obtained, where I
and R stand for imaginary and real, respectively. Here, C, D, E and F represent the
low-frequency components and high-frequency components in the vertical, horizontal, and diagonal directions, respectively.
2. Select one component from the D, E, and F components to embed the watermark (forsimplicity, we assume that the D component is selected).
3. Add the low-frequency components CRR , CRI , C IR , C II multiplied by a factor β to thecomponents DRR , DRI , DIR , DII , respectively. We set S ← D + βC.
4. The sliding window is applied to the component S . The formula for the sliding window is shown below.
S (m, n) = sgn(S (m, n)) ·

K X
L
X
1
1
|S (m + k, n + l)|,2K + 1 2L + 1 k=−K l=−L

where K and L are natural numbers and constants. Also, sgn(x) is a sign function like
1(x > 0)sgn(x) = 0(x = 0) .
−1 (x < 0)
5. Embed the watermark into the 4 components obtained above. The embedding formula
is shown below.
W M(i, j) = S (i, j) × (1 + W(i, j) ∗ α)
where W M is the high-frequency component after embedding the watermark, and W
is the watermark to be embedded. The quantity α is a hiding factor that adjusts therobustness.

13

6. Choose W M instead of D, use other components, and then apply the inverse DTCDWT. The watermarked image K is thus obtained.
The extraction algorithm is as follows:
1. Decompose the watermarked image K into the 16 components using the DT-CDWTgand choose the watermarked components W
M.
2. Extract the binary-valued watermark by computing:e i = |Wg
W
Mi | − |S i |, i ∈ {RR, RI, IR, II}
ee =
W

4
X

ei,
W

i=1

e = sgn(We e ).
W

3.

Experimental results

In this experiment, we conﬁrmed that adding the low frequency component to the highfrequency component of the DT-CDWT improves the noise tolerance. Table 1 shows thepeak signal-to-noise ratios (PSNR) of the watermarked image and the extracted watermark
after adding a Gaussian noise to the watermarked image with the diﬀerent values of β. We
embedded a watermark into the four D components. The PSNR of the watermarked image
in the conventional method [5] is 33.7075 and the PSNR of the extracted watermark is
5.0202. Figure 1 shows that the watermarked images and extracted watermarked images by
the method [5] and the proposed method when β = 4.
β
PSNRs of the watermarked image
PSNRs of extracted watermark

433.7932
5.0371

4.4
33.44195.2017

4.6
33.27295.2316

4.8
33.09595.2636532.92175.3690

Table 1: The PSNRs of the watermarked images and watermarks extracted from the watermarked ones subjected to a Gaussian noise with the diﬀerent values of β.

Figure 1: The watermarked images subjected to a Gaussian noise and extracted watermarksby the method [5] (ﬁrst and third form the left) and the proposed method (second and fourthfrom the left) when β = 4.
Figure 1 shows that the watermark is extracted by the proposed method and the conventional method. Although both extracted watermarks are degraded, we can identify the14watermark at a single glance. It seems that the quality of these images are almost the sameat a single glance, however, the PSNR of the extracted watermark by the proposed method
is slightly larger than the one by the conventional method. In fact, the former is 5.0371 andthe latter is 5.0202 when the PSNRs obtained by the conventional and proposed method are
33.7075 and 33.7932, replectively In this experiment, the watermark was embedded into the
D components, whereas similar results as in Figure 1 and Table 1 can be obtained by embedding it into the E or F components. Adding low-frequency components to high-frequency
components makes the watermarking more robust against attacks, however, this leads to an
image quality degradation of the watermarked image.

4.

Conclusion

We proposed a watermarking method using the high-frequency components with additive low-frequency components obtained by the DT-CDWT. We have conﬁrmed that thismethod is more robust against attacks than the conventional method. In the future, we haveto further investigate the robustness against other attacks. We also need to ﬁgure out why
the high-frequency components with additive low-frequency components make the watermarking better resistant to attacks.

Acknowledgements
This work was partially supported by JSPS KAKENHI Grant Number 19K03623.

References[1] Jing Liu, Jingbing Li, Jieren Cheng, Jixin Ma, Naveed Sadiq,Baoru Han, Qiang Gengand Yang Ai: A Novel Robust Watermarking Algorithm for Encrypted Medical Image
Based on DTCWT-DCT and Chaotic Map, Computers,Materials & Continua, Vol.
61,(2019), 889–910.
[2] Nadhir Nouioua, Ali Seddiki, Abdelkrim Ghaz: Blind Digital Watermarking Framework Based on DTCWT and NSCT for Telemedicine Application, Traitement du Signal, Vol. 37,(2020), 955–964.
[3] Mohamed Lebcir, Suryanti Awang, Ali Benziane: Robust Blind Watermarking Technique Against Geometric Attacks for Fingerprint Image Using DTCWT-DCT, Iraqi
Journal of Science, Vol. 61,(2020), 2715–2739.
[4] Teruya Minamoto, Ryuji Ohura: A blind digital image watermarking method basedon the dyadic wavelet transform and interval arithmetic, Applied Mathematics andComputation, Vol. 226,(2014), 306–319.
[5] Teruya Minamoto,Ryuji Ohura: A digital image watermarking for authentication
based on the dual-tree complex discrete wavelet transform and interval arithmetic,
International Journal of Wavelets, Multiresolution and information Processing, Vol.
11,Issue 4, (2013), 1360005, 19pages.

15

JSST 2021

Detection of maliciously image blurred portions using
dyadic wavelet transform
TAKAKI HIRAMATSU1* and TERUYA MINAMOTO1
1 Graduate School of Science and Engineering , Saga University, Japan∗ hiramatt@ma.is.saga-u.ac.jp

Abstract. We propose a detection technique to ﬁnd maliciously blurred portions in images
using the dyadic wavelet transform (DYWT). In recent years, the widespread use of image
editing software has made it easy for anyone to alter images. Blurring is one of the mostcommon image tampering and is used to delete small details from an image. Since noiseproperties in tampered images may change, the development of a blur tampering method
will lead to the development of a fake image detection method. In our method, we apply the DYWT to an image and then obtain one low-frequency and three high-frequency
components. Using the diﬀerence between the low-frequency component and its original
image, we detect the blurred portions by thresholding. Our experimental results show thatthe proposed method can detect the portions suspected of maliciously blurred ones.
Keywords: Wavelet transform, Dyadic wavelet transform, Image forgery detection

1.

Introduction

In recent years, the rapid spread of electronic devices has made it easy for anyone to edit
digital image content and the number of image tamperings has been increasing on the web.
The image tamperings are sometimes used to spread fake news. To prevent malicious image
manipulations, many image tampering detection technologies have been actively developed.
Image tampering detection techniques can be divided mainly into two categories. One
is to detect tampering by embedding a digital watermark or signature in advance. The otheris to detect tampering only from the tampered image [1]. The former method requires acertain image processing in advance, while the latter does not. Up to now, image tampering
detection techniques have been studied mainly for copy and paste and splicing tampering[2][3]. However, retouching tampering detection techniques, such as image blurring, arerare [4].
The purpose of this study is to develop a new method to detect maliciously blurred portions in images based on the dyadic wavelet transform (DYWT) without any requirements ofprior image processing.The DYWT decomposes the original image into one low-frequency
component and three high-frequency components. Since the low-frequency components is

16

an approximation to its original image with the same size of the original one, the diﬀerence
between the original image and its low-frequency component is expected to extract a certain
information for the image containing some blurred portions. Our experimental results showthat the proposed method can detect the portions suspected of maliciously blurred ones.

2.

DYWT

The DYWT has multiscale and shift-invariant properties and decomposes an image into
its one low-frequency component and three high-frequency components. The size of all four
ones is the same as the original one [5]. Setting S as an original image and applying the
DYWT to S , we obtain the low-frequency component C, the vertical high-frequency component D, the horizontal high-frequency component E, and the diagonal high-frequency component F [6]. Figure 1 shows the frequency components obtained by applying the DYWT
to Lenna.

Figure 1: Lenna image S (top) , low-frequency component C, vertical high-frequency component D, horizontal high-frequency component E, and diagonal high-frequency component
F (from left to right).

3.

Blurred portions detection method
The procedure for blurred portions detection is as follows:
1. Apply the DYWT to the original image S . Then, the one low-frequency component
C, three high-frequency component D, E, and F are obtained.
2. Compute the component H by using the following expression.
H[i, j] = |S [i, j] − C[i, j]|17

3. Compute the median value Me from H.
4. Generate the component O using the following expression.

1 When H[i, j] < MeO[i, j] = 0 Others
Since the blurred portion in the components H has extremely small values from ourexperience, the region satisfying O[i, j] = 1 can be judged as the blurred one by the naked
eye.

4.

Experimental results

The experiment was conducted using partially blurred images and its original image.
Some of the experimental results are shown in Figure 2. It can be seen that the non-forgery
image has ﬂickering throughout the image, whereas the forgery image has non-ﬂickering
portion in the blurred area. The right cheek region is unnaturally ﬂat in comparison to theleft one.

Figure 2: Untampered Lenna image (top left), the component O obtained by the proposed
method (top right), partially blurred images where the blurred portion is marked (ﬁrst andthird from the left at the bottom) and the component O obtained by the proposed method(second and fourth from the left at the bottom).

5.

Conclusion

In this paper, we proposed a method for detecting maliciously blurred portions in images
using the DYWT. Using the diﬀerence between the original image and its low-frequency

18

component, we detect the maliciously blurred portion by the naked eye. This method does
not require any image processing in advance such as watermarking method and does notdepend on the ﬁle format. Up to now, our method is only able to detect partially blurred
region. Therefore, it is necessary to improve our method so as to detect other tampered
regions automatically.

Acknowledgements
This work was partially supported by JSPS KAKENHI Grant Number 19K03623.

References[1] Dittmann, J., Steinmetz, A., and Steinmetz, R. : Content-based digital signature formotion pictures authentication and content-fragile watermarking, International Conference on Multimedia Computing and Systems -Proceedings 2, pp. 209-213 (1999)[2] Anuja Dixit, R. K. Gupta: Copy-Move Image Forgery Detection a Review, International Journal of Image, Graphics and Signal Processing, 8(6), pp.29-40 (2016)[3] Jwaid, M.F., Baraskar, T.N. : Study and analysis of copy-move & splicing image
forgery detection techniques, Proceedings of the International Conference on IoT in
Social, Mobile, Analytics and Cloud, I-SMAC 2017, 8058268, pp. 697-702 (2017)[4] Hashem, F.S., Sulong, G. : Passive aproaches for detecting image tampering: A review,
Jurnal Teknologi, 73(2), pp. 31-36 (2015)[5] Mallat, S. : A Wavelet Tour of Signal Processing:The Sparse Way. Third Edition.
Academic Press (2008)[6] T. Minamoto, K. Tsuruta and S. Fujii : Edge-preserving image denoising methods
based on dyadic lifting schemes, IPSJ Transactions on Computer Vision and Applications, Vol.2, pp. 48-58 (2010)19

JSST 2021

Feature Extraction Method for Detecting Early Stage
Colorectal Cancer from Endoscopic Images Using
Dual-Tree Complex Wavelet Packet Transform
Daigo Takano1,* and Teruya Minamoto1
1 Graduate School of Science and Engineering, Saga University, Saga, Japan∗ takanod@ma.is.saga-u.ac.jp

Abstract. Colorectal cancer is one of the most common and deadly types of cancer in Japan,
and many methods to detect early colorectal cancer from endoscopic images have been developed. Most modern methods are based on machine learning methods, especially deeplearning (DL). These methods can detect the cancer with high accuracy, but a large numberof data is required and we don’t know how these methods detect cancers. We propose a feature extraction method for detecting early stage colorectal cancer from endoscopic images
using the Dual-Tree Complex Wavelet Packet Transform (DT-CWPT). Our method does
not require a large amount of data and can explain the reason for detecting early colorectal
cancers.
Keywords: Wavelet Transform,Dual-Tree Complex Wavelet Transform,Wavelet Packet

1.

Introduction

In recent years, deep learning techniques have been used in many cases and can detect
early cancer with high accuracy from endoscopic images. However, there are mainly two
defects. One is that these techniques require a large number of data, the other is a ”blackbox” problem in machine learning, that is, humans cannot understand the reason why thesetechniques have come to a speciﬁc decision.
We aim to propose a new feature extraction method for detecting early-stage colorectal cancer from endoscopic images. The features can be extracted from a small amount ofdata and can be interpreted by humans. To achieve our aim, we use the Dual-Tree Complex Wavelet Transform (DT-CWT) [1] and Wavelet Packet [2]. According to our interview
with doctors, they focus on the normal regions and determine the regions that are diﬀerent
from the normal ones as the abnormal regions when they try to detect early-stage colorectal
cancers. Since the DT-CWT has the directional selectivity, it is expected to detect the difference between abnormal and normal regions based on the DT-CWT. To obtain more detailfeatures from endoscopic images, we use the Dual-Tree Complex Wavelet Packet Transform (DT-CWPT) which decompose not only the low-frequency components but also the20high-frequency components, whereas the DT-CWT decompose the low-frequency component only[3] . We then apply PCA to the components obtained by the DT-CWPT and make agraph depending on the ﬁrst and second principal components of PCA. Experimental results
show that the graph depicts the diﬀerence between the abnormal and normal regions.

2.

Proposed method

The proposed method is described as follows:
1. Apply the DT-CWPT to colonoscopy images to obtain multiple frequency components.
Applying the DT-CWT to an image, we obtain four components depending on real (R)and imaginary (I) ﬁlters such as, DRR , DRI , DRI , DII for the component D, for example.
In this study, only use the DRI .Here, dRI,(n,m)
j,ny ,n x in (1) represents the frequency components
obtained by applying the real (R) ﬁlter in the vertical direction and the imaginary (I) ﬁlterin the horizontal direction to the input image at level j. The notations ny and n x indicate
the locations in the horizontal and vertical directions, respectively. We distinguished thefrequency components by labeling them with m and n.
DR,(n,m)j,n x ,ny =DI,(n,m)j,n x ,ny =II,(n,m)dRR,(n,m)j,ny ,n x + d j,ny ,n x2IR,(n,m)d j,ny ,nx + dRI,(n,m)
j,ny ,n x
2

(1)
(2)

2. Compute the variance from the obtained frequency components at each and perform PCA
on all variances.
Applying the Wavelet Packet transform at level j to an image, we obtain 4 j components.
Therefore, the total number of components obtained by the DT-CWPT at level j is 4 j+1 .
For example, we obtain 64 components at level2. but, We don’t use low frequency components. Figure 1 shows the components obtained by applying the DT-CWPT at level 2 forendoscopic image. The blue dots in the ﬁgure represent normal images, and the red dots
represent abnormal images. The x-axis is the value in (1), and the y-axis is the value in (2).
As can be seen from Figure 1, the points in the normal image are concentrated in the center,
while those in the abnormal image are relatively scattered. Therefore, We compute variances of 63 components, and use like 63-dimensional vector. Finally, we performed PCA
on these vectors.
3. Draw a scatterplot between the ﬁrst and second principal components.
We make scatterplot between the ﬁrst (x-axis) and second (y-axis) principal components.

21

Figure 1: Examples of the frequency components obtained by the DT-CWPT at level 2

3.

Experimental results

We deﬁne ”normal images” as images that do not contain any abnormal regions, and ”abnormal images” as images that contains abnormal regions. Figure 2 shows an actual endoscope
image. The marked region in the image is early stage colon cancer. 800 images were cre-Figure 2: An endoscopic image where the region of early-stage colon cancer was marked
by a doctor.
ated by cropping 400 normal and 400 abnormal images in 64 × 64 size. We converted all
images to CIE L*a*b* color space and apply our method to the a* and b* components of
the images.
The scatterplot obtained by proposed method are shown in Figure 3. Again, blue dots
indicate normal images, and red dots indicate abnormal images. Figure 3 shows that we canalmost distinguish between normal and abnormal regions.

22

Figure 3: The value of the ﬁrst and second principal components calculated from the variance of frequency components

4.

Conclusion

From the experimental results, we conﬁrmed that the DT-CWPT is useful for extracting thefeatures of early-stage colorectal cancer from endoscopic images. However, we have notbeen able to completely separate normal and abnormal regions. In future work, we want toreveal the property of images that cannot be correctly classiﬁed and develop a method toclassify normal and abnormal regions with high accuracy.

Acknowledgements
This work was partially supported by JSPS KAKENHI Grant Number 19K03623.

References[1] Kingsbury, Nick.: ”Complex Wavelets for Shift Invariant Analysis and Filtering of
Signals”, Applied and Computational Harmonic Analysis, 10, no.3 (2001), pp.234–53.
[2] R. R. Coifman,Y. Meyer, and M. V. Wickerhauser.: ”Wavelet analysis and signal
processing.” Wavelets and Their Applications, pp.153–178,1992.
[3] Bayram I., SelesnickW. I., On the Dual-tree Complex Wavelet Packet and M-band
Transform , ”IEEE Transactions on Signal Processing”, Vol.56, no.6 (2008), pp.22982310.

23

JSST2021

Computation of Compressive Flow in Pulsed Focusing Engine (Fugine) Set in Shock Tube
Daiki Okada1*, Hiroki Kijima1, Tomotaka Kobayashi1, Ken Naitoh1
Faculty of Science and Engineering, Waseda University, Japan1*

okapy_ilsag@suou.waseda.jp

Abstract. In order to realize high thermal efficiency, in our previous research, we proposed a
new engine concept based on pulsed supermulti-jets colliding at a single point around the chamber center through a focusing process [1]. The shock tube experiments were conducted forsupermulti-jets colliding in the reaction chamber of a prototype engine with 14 jet-nozzles andside-passages [2]. The present report shows the first computational result for the new engine
including all of the jet-nozzles and side-passages installed in the shock tube. Computed pressure on a sensor installed near the collision point of jets can be quantitatively compared withthe experiment.
Keywords: Pulsed supermulti-jets colliding, 14 jet-nozzles and side-passages, Shock tube,

Pressure on a sensor

1. Introduction
The engine which uses a new compressive combustion principle based on supermulti-jets
colliding was proposed [1]. This principle generates strong single point compression andleads to single-point auto ignition, due to supermulti-jets colliding with a pulse (Fig. 1). It has
the potential of high thermal efficiency of low exhaust gas because of its high point compression and low heat loss on the wall due to the effect of burned gas encased by supermulti-jets
colliding, with additional compression due to position or rotating cascades. The jets also encase the combustion noise, leading to less noise.
Based on the principle, the engine which has 14 jet-nozzles and side-passages having curved
pipes between nozzles and straight passages was created and has experimented to be set in theshock tube on the condition that the high pressure domain is 310[kPa] and the low pressuredomain is 40[kPa] [2] (Fig. 2). Computations focused around the collision point with no sidepassages including curved pipes were conducted [2] (Fig. 3).
In this paper, unsteady three-dimensional computation for the engine with 14 jet-nozzles andside-passages set in the shock tube was conducted, which corresponds to the shock tube experiment (Fig. 4). Computed pressure on a sensor installed near the collision point of jets wascompared with the experimental results.

24

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Fig. 1. A diagram of a new compressive
combustion principle

Fig. 2. A diagram of the experiment set inshock tube

Fig. 3. The analytical subject of the computation focused around the collision point

Fig. 4. The analytical subject of the engine with 14 jet-nozzles and side-passages set in theshock tube

2. Simulation method
The simulation method is to be solved the unsteady compressible Navier-Stokes equation inthree-dimensional space which is described in a non-conservative form by using the BISCALES method [3] including the CIP method [4] and the SOR method.
In the experiment set in the shock tube, the length of the compression device including thenozzles and side-passages for supermulti-jets colliding with pulse is 143[mm], the shock tube
length of the high pressure domain is 2500[mm], and the shock tube length of the low pressuredomain in front of the compression device is 3550[mm] (Fig. 2). (For the analytical subject ofcomputation (Fig. 4), the analytical domain is shortened to reduce CPU time and memory. The
length of the compression device is 100[mm], the length of the high pressure domain is 57[mm],and the length of the low pressure domain in front of the compression device is 75[mm].) Nozzle diameter d=6.5[mm], Chamber diameter D=18[mm], D/d ratio=2.7, and Sensor diameter=12[mm] are same for both computation and experiment. As the initial conditions, the temperature and the velocity are 298.2[K] and 0[m/s]. The high pressure domain is 310[kPa] andthe low pressure domain is 40[kPa] (Fig. 4). Grid sizes are 0.25[mm] in the compression device
and 0.50[mm] in the shock tube. Number of grid points is 131 million (400x492x492,
500x258x258 points)

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3. Computational result and experiment evaluation
Fig. 5 presents computational results of pressure and temperature time histories. The pressure
and temperature at the geometrical collision point of jets firstly rise to 626.8[kPa] and 656.4[K]at about 395[𝜇𝑠]. The pressure and temperature secondly rise more when supermulti-jets collide with the pressure sensor surface at about 400[𝜇𝑠]. The peak value of computed pressure
on the center of the sensor is 1003[kPa] (Fig. 6). The peak value of pressure measured in shocktube experiment was about 726.7[kPa] [2]. This difference between computational and experimental pressures is attributable to the fact that the pressure obtained from the sensor is averaged
on the sensor surface. Thus, the computed pressure should be averaged on the sensor surface
while changing the number of grid points for averaging (Fig. 6). The peak value (802.7[kPa])of computed pressure averaged with the sensor surface diameter 0.5[mm] is the closest to theexperiment. However, as the pressure sensor used in the experiment may detect the pressure
averaged by the sensor surface diameter 2.0~4.0[mm], the computed pressure is smaller thanthe experiment. In case of computation for the engine with 14 jet-nozzles and side-passages set
in the shock tube (Fig. 4), the pressure just before entering the chamber is 88.89[kPa], and thepressure at collision point is 626.8[kPa]. In case of computation in which there are no sidepassages (Fig. 3), the pressure just before entering the chamber was 102.6[kPa], and the pressure at collision point was 963.1[kPa] [2]. Comparing two computations in Figs. 3 and 4, difference of the pressure just before entering the chamber is 13.71[kPa] (102.6[kPa]–88.89[kPa]).
Combined pressure difference due to 14 jet-nozzles is 191.9[kPa] (13.71[kPa]x14). Additionally, combined momentum energy difference due to 14 jet-nozzles just before entering thechamber between Figs. 3 and 4 is 161.3[kPa]. The value 353.2[kPa] (191.9[kPa]+161.3[kPa])
is close to the difference of pressure at collision point, 336.3[kPa] (963.1[kPa]–626.8[kPa]).
Computational pressure loss by pipe friction in a jet-nozzle and side-passage (15.86[kPa])
which is larger than the theoretical value (6.562[kPa]) may bring the difference of pressure atcollision point between Figs. 3 and 4, also the difference of pressure on the sensor between
experiment and Fig. 4.

Fig. 5. Computational results of pressure and temperature time histories

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Fig. 6. Time histories of computed pressure on sensor averaged by sensor surface diameter

4. Conclusion
Computation with the added shape of 14 side-passages and shock tube was conducted, whichcorresponds to the shock tube experiment. Computational results of pressure on the sensor werelower than the experiment. To evaluate pressure loss in jet-nozzles and side-passages accurately,
multi-grid systems [5] may be useful.

References[1] K. Naitoh, K. Nakamura, T. Emoto: A New Cascade-Less Engine Operated from Subsonic to Hypersonic Conditions, Journal of Thermal Science, 19-6 (2010), pp.481-485.
[2] R. Konagaya: Principle Study on the Compression Combustion Engine Based on Supermulti-jets Colliding with Pulse, Doctoral Dissertation of Waseda University (2020).
[3] K. Naitoh, K. Kuwahara: Large eddy simulation and direct simulation of compressible
turbulence and combusting flows in engines based on the BI-SCALES method, Fluid Dynamics Research 10 (1992), 299-325.
[4] H. Takewaki, T. Yabe: The Cubic-Interpolated Pseudo Particle (CIP) Method: Application to Nonlinear and Multi-dimensional Hyperbolic Equations, JOURNAL OF COMPUTATIONAL PHYSICS 70 (1987), 355-365[5] H. Suzuki, H. Kijima, D. Igarashi, T. Kobayashi, R. Konagaya, and K. Naitoh: Multigrid
numerical analysis on principle of collision of pulsed supermulti jets, JSASS 64 (2020).
[6] Yakhot, V. and Orszag, S.A.: Renormalized group analysis of turbulence I. Basic theory,
J. Sci. Computing 1 (1986), pp. 3-51

Appendix
The three-dimensional unsteady compressible Navier-Stokes equation is basically employed
as the governing equation. The boundary conditions of velocity and thermodynamic quantities
at the downstream are given by the Thompson non-reflection condition (the method of characteristics) and those at the wall is given by the Neumann condition and non-Slip condition [3].
The computation set in shock tube (Fig. 2) is in the laminar flow because supermulti-jets collide
before turbulence transition. However, for straight pipe flows, there was very little differencein computational results between the turbulence model and the laminar flow model [2]. Then,
vortices and turbulence will appear in the combustion chamber [6]. Thus, as a subgrid turbulence model, the Yakhot-Orszag model simplified for a large eddy simulation (LES) was addedin this study.

27

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Computations on high efficiencies of pulsed focusing
engine for rocket
Tomotaka Kobayashi1*, Hayato Suzuki1, Hiroki Kijima1, Ken Naitoh1
Faculty of Science and Engineering, Waseda University, Japan1*

winningshot1996@asagi.waseda.jp

Abstract. We proposed a new engine concept based on pulsed supermulti-jets colliding at asingle point around the chamber center through a focusing process, in order to realize highthermal efficiency due to nearly-complete insulation effect and relatively-silent high compression (Naitoh, et al. 2010). This engine concept can be applied for various usages including
automobiles, power generation, aircrafts, and rockets. As the evidence for air-breathing conditions such as aircraft and automobiles, we principally performed some fundamental combustion
experiments for a prototype engine with 14 jet-nozzles, which indicate the potential of highthermal efficiency and insulation effect (Konagaya, et al. 2020). However, at very high altitudeof rockets, free redundant dense atmospheric air cannot be used as insulation gas layer aroundreaction chamber wall, i.e., hydrogen or oxygen must be used for insulation gas, which maylead to waste of unburned gases. The present report proposes a novel way for overcoming thisproblem.
Keywords: Pulsed supermulti-jets colliding, Combustion and Thermal efficiencies, Rocket

1. Introduction
A new compressive combustion principle based on supermulti-jets colliding with pulse wasproposed for combustion engines [1]. Strong compression is caused by the collision of thejets and auto ignition occurs around the combustion chamber center (Fig. 1).

Fig. 1. A diagram of a new compressive combustion principle

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It has the potential of high thermal efficiency because of chamber-center high compression
and low heat loss on the wall due to the encasing of burned gas by the supermulti-jets, incases with additional compression due to position or rotating cascades. The jets also encase
the combustion noise, leading to less noise.
This engine concept can be applied for various usages including automobiles, power generation, aircrafts, and rockets.
As the evidence for air-breathing conditions such as aircraft and automobiles, we principally
performed some fundamental combustion experiments for a prototype engine with semispherical 14 jet-nozzles, which indicate the potential of high thermal efficiency and insulation
effect [2].

2. Our previous computation at startup of pulsed focusing engine forrocketHowever, at very high altitude of rockets, free redundant dense atmospheric air cannot be
used as insulation gas layer around reaction chamber wall, i.e., hydrogen or oxygen must be
used for insulation gas, which may lead to waste of unburned gases.
Let us see Fig. 2 (left), which shows computational results of reacting flow during the firstengine cycle (at startup) for semi-spherical distributions of 14 jets, which shows lots of unburned hydrogen gas wasted from the nozzles close to the external area (close to lower part ofthe combustion chamber). [3] The present waste of unburned gas has no problem for atmospheric air breathing engines such as those installed in aircrafts and automobiles, because atmospheric air is redundant and free. However, this problem must be overcome for rockets.
Thus, we add more jets for enclosing the jets more as shown in Fig. 2 (right). We qualitatively
confirmed that the number of jets increasing brings higher thermal efficiency, higher combustion efficiency, and higher power (thrust). [3] [See the governing equation and computational
methods in appendix.]
However, we found that the efficiencies and power are still insufficient.

Fig. 2. Computation of reacting flow in primitive pulsed focusing engine for rocket [3]29JSST2021

3. Further analysis at startup of pulsed focusing engine for rocket
In the present section, we set two new improvements for obtaining higher efficiencies. Firstis increase in the number of jets, i.e., 24-jets corresponding to that in Fig. 2 (right), although
the number of jets was 14 in the primitive computation of Fig. 2 (left). Second is supply of
premixed gas of hydrogen and oxygen through each jet nozzle, although oxygen and hydrogen are separately supplied, which leads to less mixing and also the amount of combustible
gases.
Figure 3 demonstrates the computational result during the first engine cycle, while the combustion chamber is initially filled with atmospheric air (not pure oxygen and including no hydrogen). From the temperature distribution in Fig.3 (left), this figure is at the timing that allof the shock fronts at the head of 24-jets collide. We can see a high temperature and highpressure around the reaction chamber center. However, Figure 3 (right) indicates no mixtureof hydrogen and oxygen around the chamber center, because initial atmospheric air still remains around the chamber center. [See the governing equation and computational methods inappendix.]
We should find the reason of no hydrogen and oxygen around the chamber center, whereas
high temperature and high pressure appear at the chamber center. The reason is very simple.
As textbooks on compressible fluid dynamics [4] explain for students, shock front proceeds
ahead of gas injected from the nozzles, i.e., only pressure wave such as shock wave proceeds
inside the gas at upstream of the shock front. Thus, high temperature gas around chamber
center without hydrogen and oxygen cannot burn, which results in combustion at the region
with pressure lower than relatively high pressure region around combustion chamber center,i.e., the contact surface between hot gas of air and cool gas of H2+O2 entering from the nozzles shown in Fig. 3 (right). The present combustion occurrence at lower compression condition results in lower thermal efficiency and also no ignition of lower temperature O2+H2
mixture around chamber wall, leading to low combustion efficiency.

Fig. 3. Computational result of reacting flow at first engine cycle for premixed gas of oxygenand hydrogen (24-jets)
However, we find that this computational result has no problem for obtaining high thermaland combustion efficiencies for the second engine cycle. It is stressed that unburned mixture
gas of hydrogen and oxygen at the end of the first engine cycle moves to the chamber centerin the second engine cycle, because the new jet flow pushes the unburned mixture gas toward

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the chamber center.

4. Conclusion
Computation and theoretical consideration shown above bring that the sphere-like distribution of jets will lead to high thermal and high combustion efficiencies after the second engine
cycle, if further fine optimizations are done on details of jet nozzles distribution and also period of pulse.

References[1] K. Naitoh, K. Nakamura, T. Emoto: A New Cascade-Less Engine Operated from Subsonic to Hypersonic Conditions, Journal of Thermal Science, 19-6 (2010), pp.481-485.
[2] R. Konagaya, K. Naitoh, T. Kobayashi, Y. Isshiki, et al.: Two Prototype Engines with
Colliding and Compression of Pulsed Supermulti-Jets through a Focusing Process,Leading to Nearly Complete Air Insulation and Relatively Silent High Compression for
Automobiles, Motorcycles, Aircrafts, and Rockets, SAE Technical Paper 2020-01-0837(2020). doi:10.4271/2020-01-0837[3] S. Kawaguchi, R. Konagaya, K. Tsuru and K. Naitoh: Computations for Improving the
Performance of a New Hydrogen-Oxygen Rocket Engine Based on Supermulti-jets Colliding with Pulse, 2018 AIAA Aerospace Sciences Meeting, AIAA 2018-0668 (2018).
doi:10.2514/6.2018-0668 (Also in S. Kawaguchi, master thesis (directed by Ken Naitoh,
Waseda University), 2018)[4] T. Ikui and K. Matsuo, Compressible Fluid Mechanics, Rikougakusha, (2001).
[5] H. Takewaki, T. Yabe: The Cubic-Interpolated Pseudo Particle (CIP) Method: Application to Nonlinear and Multi-dimensional Hyperbolic Equations, JOURNAL OF COMPUTATIONAL PHYSICS 70 (1987), 355-365[6] K. Naitoh and K. Kuwahara, Large eddy simulation and direct simulation of compressible turbulence and combusting flows in engines based on the BI-SCALES method. J. of
Fluid Dynamics Research, Vol. 10, pp. 299-325. (1992).
[7] K. Naitoh, Y. Takagi, and K. Kuwahara, Cycle-resolved computations of compressible
vortical flows in automotive engines. Computers and Fluids, Vol. 22, pp. 623-648 (1993).
[8] Yakhot, V. and Orszag, S.A.: Renormalized group analysis of turbulence I. Basic theory,
J. Sci. Computing 1 (1986), pp. 3-51.

Appnendix: Governing equation and computational method
The unsteady compressible Navier-Stokes equation in the three-dimensional space which is
described in a non-conservative form with the BI-SCALES method [6,7,8] is solved by using
the CIP method [5] and SOR method. As a subgrid turbulence model, the Yakhot-Orszag model
simplified for a large eddy simulation (LES) was used [8]. The boundary conditions of velocity
and thermodynamic quantities at the downstream are given by the Thompson non-reflection
condition (the method of characteristics) and those at the wall is given by the Neumann condition and non-slip condition. [6]31JSST 2021

A simple model of on–demand transporter
Yuhei Okubo1,* , Takashi Shimada2 , Toru Ohira1
1 Nagoya University, Japan
2 The University of Tokyo, Japan∗ d20001h@math.nagoya-u.ac.jp

Abstract. We consider a theoretical model of a “transporter” in two dimensions. We define“town” by square 2-D grids. In the town, we place multiple “parcels” with randomly chosen
specified pick-up and delivery addresses. The transporter goes around these addresses todeliver parcels. We observe the transporter’s total traveling distance for the delivery of all
the parcels. We find that it can be approximately obtained by the number of parcels and thesize of the town.
Keywords: Transporter, Delivery, Traveling distance

1. Introduction
Delivery services let us increasingly enjoy the purchase of goods and foods without physically moving. It has also become an important service under the current situation with the
COVID-19. Increasing demand, on the other hand, has caused shortages of delivery personnel and vehicles, which is leading to increasing delivery costs. It is, therefore, crucial that
we allocate appropriate resources that match the volume of delivery as well as the size ofthe area without reducing the level of service for customers.
Against this background, we consider a theoretical model of delivery or transporting problem in two–dimensions. In this work, we studied the properties of delivery when the transporter has the following strategy: a transporter moves to the nearest point, which either has
a parcel to pick up or is one of the delivery locations among parcels that the transporter
currently holds. In particular, we analyze by measuring the total distance of delivery paths.

2. ModelWe construct a theoretical model of a transporter. On the “town” with square grid streets,“parcels” are placed randomly each of which has its delivery location. A “transporter” goesaround to pick up and deliver parcels. He/She can hold multiple parcels and move northsouth and east-west directions. Let a transporter move according to the following rule:
1. Determine the first destination to the closest point of pick-up addresses from the current transporter s position.

32

2. Let the transporter go to the destination, then pick up the parcel.
3. Determine the next destination to the closest point of delivery addresses or the otherpick–up ones.
4. Go back to step (2) until all parcels have been picked up and delivered.

3. Simulations and Analysis
We analyze the behavior of the model mainly by computer simulations. We set the sizeof the town as M × M grid points and the number of parcels as C. We have simulated
10,000 statistical samples for each parameter pair of (M, C) with M = 20, 30, 40, 50, andC = 3n(n = 1, 2, ...40).
We have computed the average total traveling distance ⟨L⟩ for the entire delivery for eachparameter set. (We estimate average error is of the order of 1 % ).

Figure 1: Total travelling distance

Figure 2: Scaled total travelling distance

The results are shown in Fig. 1. To investigate the functional relations, we scale ourresults. The result is shown in Fig. 2 and we have found√⟨L⟩ ≃ 2M C
(1)which is estimated from the slope of the lines in Fig. 2.
This relation can be described approximately with the following theoretical explanation. We
consider the case of large M and C so that we can argue that related variables are continuous.
Let n(t) be the number of parcels still to be delivered at time t. Considering the density ofparcels at t is n(t)/M 2 , we can roughly estimate the average traveling distance to pick up anddeliver the current parcel l(t) as
n(t)
1
≈
,
(2)
2
M
l(t)2
which leads toMl(n(t)) ≈ √
.
(3)
n(t)

33

The total average traveling distance ⟨L⟩ can be obtained by summing (integrating) l(t) for all
the parcels starting from n(t = 0) = C to the last one:
⟨L⟩ ≈

∫ 1

l(n)(−dn) =

∫ C

C

1

√
M
√ dn ≈ 2M C
n(4)This agrees approximately our estimation of the parameters above through simulations.

4. RELATED TOPICS AND OUTLOOKWe have investigated related topics such as models of computer packet congestions, 1dimensional foraging process, and group chase and escapes, where there are agents involvedthat have the purpose of picking up and/or delivering objects [1, 2, 3, 4]. Here, we have presented yet another model that belongs to the same category.
We have found numerically that we can approximate the average travel length of delivery
trips give the size of the town and the total number of parcels.
As future investigations, we can consider the eﬀect of multiple transporters. By changing
and/or mixing of strategies (movement rules of normal/express delivery apply to all transporters or allocate), we would like to investigate a way to deliver all parcels with a minimum
traveling distance with moderate load.

References[1] Ohira T, Sawatari R (1998), Phase transition in a computer network traﬃc model.
Physical Review E, 58:193-196[2] Shimada T, Ohira T (2019), Diﬀusion constant of a forager on a one-dimentional periodic system, in the 25th Proceedings of Traﬃc Symposium, Nagoya Japan[3] Kamimura A, Ohira T (2010), Group chase and escape. New Journal of Physics,
12:053013[4] Masuko M, Hiraoka T, Ito N, Shimada T (2017), The eﬀect of laziness in group chaseand escape. J. of Physical Society of Japan, 86:085002

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Numerical evaluation on the out-of-plane propertiesof bio-inspired honeycomb cores with extra hollows
Mudong Li1*, Sachiko Ishida1, Kazuya Saito2
1

Department of Mechanical Engineering, Meiji University
2
Faculty of Design, Kyushu University*

ce202076@meiji.ac.jp

Abstract. In this study, we designed new bio-inspired honeycomb cores with extra hollows
inspired by a microstructure which can be seen in beetle elytron plates. The new cores can be
fabricated as the conventional corrugated method. We numerically confirmed that the extra
hollows contribute to enhance the compressive strength of the honeycomb cores, comparedwith the equivalent-volumed conventional hexagonal honeycomb cores.
Keywords: Honeycomb cores, Structural material, Composite material, Finite element analysis,
Biomimetics

1. Introduction
Honeycomb cores are widely used as core material of sandwich panels in aerospace applications and transportation systems because of its light weight, high compressive strength and highenergy absorbing capacity [1]. Previous studies showed that cylindrical hollow trabeculae inbeetle elytron plates (BEPs), which are placed at the vertexes of primary hexagonal honeycombcores, are contributed to increase the compressive strength of BEPs [2]. This study implies thepossibility of designing stronger structural materials by adding the extra hollows in conventional hexagonal cores. However, this original geometry can only be 3D-printed, which is notsuitable for high-speed manufacturing. In this study, we revised the original geometry to apply
the corrugated method. Through theoretical estimations and finite element analyses, the newgeometry enhanced compressive properties in out-of-plane direction.

2. Design and theoretical estimation
Corrugated method is one of the conventional fabrication methods of honeycomb cores. Thinwalled materials are folded into corrugated shapes, stacked and glued together. We arranged
the new geometry of honeycomb cores by arraying square hollows between adhesive surfaces
shown in Fig. 1. The size of the square hollows x is derived by 𝑥 = 1 ∕ √3(2 + √2)𝑎 , wherea is the size of primary core. The thickness of adhesive surfaces is expressed as 2t, where t is
the thickness of the single surface. Axis z represents the out-of-plane direction of honeycomb

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cores. This revised model shown in Fig.1, which includes eight primary cores, and seven squarehollows, was used on the following analysis.

(a)Fig. 1 Honeycomb cores with extra hollows(b)Fig. 2 Design details

Following the theory by Timoshenko et al. [3], the elastic buckling load Pcr of a simple
supported rectangular plate is described in the following equation:𝑃𝑐𝑟 =𝑘𝜋 2 𝐸 𝑡 3
12(1 − 𝜈 2 ) 𝑙(1)

where E is Young’s modulus of the material, ν is Poisson’s ratio, t and l represent the thickness
and width of the rectangle (see Fig. 2), respectively. Factor k is determined by the shape of therectangle, but we approximate it as a constant value k = 4.0 here. As these material properties
are fixed, the buckling load of honeycomb cores is determined by the core thickness and thecore size, which does not depend on the core height. The square hollow consists of four
rectangular plates, each side of the plates is shorter than one side of hexagonal primary cores.
In a quick estimation, when the thickness t is doubled, the buckling load increses by eight times;
when the width l is halved, the buckling load is doubled. This is the reason why the extra squarehollows can increase the compressive strength.

3. Finite element analysis
We numerically performed compressive simulation by finite element analysis application, ANSYS. The material properties of aluminum which we set up for analysis are shown in Table. 1.
Out-of-plane displacements with the constant speed at 1.0 mm/s were given on the upper sidesof the analysis models, and the lower sides were simply supported. The dynamic analysis was
carried out, but the speed was sufficiently slow to ignore the effect of strain rate. To evaluate
the increase rate of ultimate compressive strength, we made comparison between the revised
model with hollows and the conventional hexagonal model which has equivalent volume.
Figure 3 describes that the revised model enhanced compressive strength by approximately
45%, but the amount of enhancement was lower than the expectation by Eq. 1. The gaps
between theoretical estimated buckling load and analyzed ultimate strength were possibly
caused by the effect of elastic buckling modes appeared in the analysis, which are notconsidered in the theory. Figure 4 shows the elastic buckling modes before plastic collapse.
The deformation by elastic buckling in the primary cores was larger than that in the extra
hollows, but the larger number of the buckling waves was observed in the extra hollows.
Different buckling modes in primary cores and extra hollows interfered each other across theadhesive surface. Thus, the model with extra hollows reached its elastic limit sooner than
expected due to the complex buckling phenomenon. Moreover, we prepared two other analysis

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models whose core size was the same with different core heights and thicknesses. All of theseresults showed the same tendency.

4. Conclusions
Table. 1 Material properties

Fig. 3 Force-displacement diagram of honeycomb cores with and without extra hollows

Fig. 4 Elastic buckling modes of primary cores (left) and the extra hollow (right)
before plastic collapse.

In this study, the revised geometry of honeycomb cores inspired by BEPs was proposed. It
consisted of primary cores and square hollows in adhesive surfaces. The buckling mode andthe compressive strength were investigated through theoretical estimation and finite element
analysis. The simulation result showed the out-of-plane compressive strength of the revised
model increased 45% compared to the conventional cores. The mechanical properties of therevised model will be investigated experimentally in our future work.

Acknowledgement
This study is financially supported by JSPS KAKENHI Grant No. 21K03755.

References[1] T. Sato (2002), Development and application of honeycomb core materials and sandwich
structures, CMC Publishing (in Japanese).
[2] J. Chen, X. Zhang, Y. Okabe, K. Saito, Z. Guo, L. Pan: The deformation mode and37

JSST2021
strengthening mechanism of compression in the beetle elytron plate, Material and Design, 131 (2017), 481-486.
[3] S. Timoshenko & J. Gere (1988), Theory of elastic stability (2nd ed.), McGraw-Hill Book
Company.

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Sound Insulation Simulations focusing on Height ofOrigami Core
Aya Abe1*, Ichiro Hagiwara1
1

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University*

aya_abe@meiji.ac.jp

Abstract. We have developed a new truss core panel by origami forming to get the higher
aspect ratio than that by multi-stage press molding. Our object is to apply the new origami truss
core to the train floor. Whether or not this goal can be achieved depends on whether this neworigami truss core with a high aspect ratio has excellent sound insulation characteristics. Therefore, as a development of the analysis technology by FEM which accurately estimates the soundinsulation characteristics, at first, the relation between the aspect ratio and the sound insulation
performance is discussed in the flat plate with one core.
Keywords: Origami forming, Finite element method, Helmholtz equation

1. Introduction
As a part of our origami engineering approach to sound insulation, our group has been performing research with the aim of industrializing octet truss-type cores (truss cores) that use
space filling structures composed of regular tetrahedrons and half regular octahedrons. Trusscores were expected to be used as flooring for trains, but both good sound insulation characteristics and bending stiffness are required for this application. It has been reported that a longer
core height produces better sound insulation characteristics. However, there is a limit to thecore height available in the multi-stage pressing approach[1]. Therefore, we developed the origami engineering method to solve the core height problem and then decided to reexamine thesound insulation properties of these cores.

2. Calculation Method for Sound Insulation Characteristic Evaluation
2.1 Examination of sound insulation calculations
The definition of the transmission loss (TL) used in sound insulation calculations is the ratioof the energy of the incident sound wave to the energy of the transmitted sound wave. The
equation (1) is used in this paper. 𝑝𝑖𝑛 is the incident sound pressure, and 𝑝𝑜𝑢𝑡 is thetransmitted sound pressure.

39

JSST2021|𝑝 |𝑇𝐿 = 20 log10 |𝑝 𝑖𝑛 |

(1)

𝑜𝑢𝑡

In the previous paper[2], the problem is solved when the specimen was a rigid body, and themagnitudes of the incident and reflected waves are equal. However, this method cannot beapplied when the specimen cannot be clearly regarded as a rigid body, e.g., when the effect of
attaching a sound absorbing material is to be analyzed. Therefore, a method to obtain thetransmission loss by separating the incident sound pressure from the reflected sound pressure
theoretically is studied here.
2.2 Incident sound pressure calculation method in sound insulation characteristic
simulation method
Helmholtz's equation (2) holds in the acoustic tube model[3].

𝜕2 𝑢
𝜕𝑥 2

1 𝜕2 𝑢(2)= 2

𝑐 𝜕𝑡 2

Here, 𝑢 is the particle velocity, 𝑥 is the one-dimensional position coordinate, and 𝑡 is thetime. The solution of Eq. (2) can be obtained by Eq. (3). Assuming a harmonic motion for theparticle velocity,(3)𝑢(𝑥, 𝑡) = 𝐴𝑒 𝑗(𝜔𝑡−𝑘𝑥) + 𝐵𝑒 𝑗(𝜔𝑡+𝑘𝑥)

From the boundary conditions calculated by FEM, the solution 𝑢 becomes Eq. (4). Here, ω isthe angular frequency, e is Napier's constant, k is the wave number, and j is the imaginary unit.
𝑢0 , D are the amplitude of the particle velocity of the excitation plate, and of the soundinsulation plate, respectively. This model is one-dimensional, and l is the length of the tube.

𝑢(𝑥, 𝑡) =𝑢0 𝑒 𝑗2𝑘𝑙 −𝐷𝑒 𝑗𝑘𝑙
𝑒 𝑗2𝑘𝑙 −1

𝐷𝑒 𝑗𝑘𝑙 −𝑢(4)𝑒 𝑗(𝜔𝑡−𝑘𝑥) + 𝑒 𝑗2𝑘𝑙 −10 𝑒 𝑗(𝜔𝑡+𝑘𝑥)

The incident sound pressure 𝑝𝑖𝑛 |𝑥=𝑙 is obtained by multiplying the first term of the particle
velocity 𝑢(𝑙, 𝑡) in Eq. (4) by the air density ρ and the sound velocity c, so it becomes Eq. (5).
𝑢 𝑒 𝑗𝑘𝑙 −𝐷

𝑢 𝑒 𝑗𝑘𝑙 −𝐷𝑒 𝑗2𝑘𝑙

𝑝𝑖𝑛 |𝑥=𝑙 = 𝜌𝑐 ∙ 𝑒0𝑗2𝑘𝑙 −1 𝑒 𝑗𝜔𝑡 , 𝑝𝑟𝑒𝑓𝑙𝑐𝑡 |𝑥=𝑙 = 𝜌𝑐 0 𝑒 𝑗2𝑘𝑙 −1

𝑒 𝑗𝜔𝑡

(5)

Here, D is obtained from Eq. (6).
2𝑢 𝑒 𝑗𝑘𝑙

1−𝑒 𝑗2𝑘𝑙(6)

𝐷 = 1+𝑒0 𝑗2𝑘𝑙 + 𝑝𝑥=𝑙 ∙ 𝜌𝑐(1+𝑒 𝑗2𝑘𝑙 )40

JSST2021

3. Comparison of The Two Methods for Flat Plate Transmission Loss
3.1 Analysis modelFig.1 shows the simulation model. A flat plate is used as the test piece. It is calculated by
COMSOL Multiphysics®[4]. The boundary condition between the acoustic tube and the test
piece is free. The total number of elements is 640 (comprising 624 solid elements and 16 shellelements) and the number of nodes is 1025. The sound insulation plate is a steel plate with athickness of 0.8 mm and the plate’s material properties are listed in Table 1. The sound pressure
observation point is located 1 mm in front of the sound insulation plate in the x-axis direction.

Fig.1 Simulation model and a microphone position in case of a test piece plate
Table 1 Specification of material of the panels
Material

Young’s modulus [N/m2]

Density [kg/m3]

Poisson ratio

Steel

2.05×1011

7.85×103

0.28

3.2 Comparison of the transmission loss
The transmission loss obtained by two(the previous and the proposed) methods are comparedin Fig.2. In the transmission loss obtained based on the theoretical value (green line), the local
value increases occur. With the exception of these points, transmission loss values from bothmethods are almost identical at each frequency. Therefore, in the flat plate model, the validityof the method proposed in this paper is verified.

Fig.2 Comparison of transmission loss between FEM and theoretical calculation

41

JSST2021

4. Differences in Sound Insulation Characteristics Depending on The
Aspect Ratio of Flat Plate With a Vertical Core
The following three different shapes of core are used as test pieces. The weight is set to be thesame as that of the flat plate with the thickness of 0.8 mm. It can be said that the thinner theplate thickness and the higher the core height (the higher the aspect ratio), the more likely it is
to have high peaks in the low frequency range.

Fig.3 Differences in transmission loss depending on the aspect ratio

5. CONCLUSION
We have developed a new method for sound insulation analysis by using the differential solution of Helmholtz equation which is expressed using the sum of the forward and the backward
waves explicitly with the boundary condition given by FEM.This new method give the same
result for a flat plate as the previous method. Furthermore, we have new findings such as thelonger aspect ratio gives more gathering sound effect by this new method using several flat
panels with single cores including long aspect ratio core generated by origami forming. In the
future work, we would apply this method to the flooring in trains which is necessary to havegood sound insulation characteristics.

References[1] S.Tokura and I.Hagiwara: Forming process simulation of truss core panel, Journal ofComputational Science and Technology, Vol.4, No.1 (2010), pp.25-35. DOI:
10.1299/jcst.4.25[2] A.Abe, H.Yashiro, and I.Hagiwara: Development of vertical incident sound insulation
simulation technology using finite element method and application to lightweight core，Transactions of the JSME (in Japanese), Vol.86, No.891 (2020), DOI:
10.1299/transjsme.20-00126.
[3] Y.Suzuki, M.Akagi, A.Ito, H.Sato, A.Yuki and K.Nakamura: The Acoustical Society ofJapan ed., Introduction to acoustics (2011), pp. 170-191, Corona Publishing (in Japanese).
[4] COMSOL Multiphysics® v. 5.5. www.comsol.com. COMSOL AB, Stockholm, Sweden.

42

JSST2021

Application to anti-vibration table of two-layered
origami structures
Yingxue Bai1, Sachiko Ishida1*
1

Department of Mechanical Engineering, Meiji University, Kanagawa, Japan*sishida@meiji.ac.jp

Abstract. In this study, we numerically investigated spring properties and isolation performancesof an anti-vibration table using four two-layered origami structures as feet. The two-layered structure was designed exactly as the cylindrical foldable structure with a torsional buckling pattern inorder to simplify construction of our one-layered isolator and to cancel a twisting motion while
folded and deployed. Transient response analysis revealed that the resonance frequency of the antivibration table was sufficiently low as long as the weight applied on the top of the table wasreasonably tuned and the table vibrated within the quasi-zero-stiffness region.
Keywords: Vibration control, Nonlinear vibration, Quasi-zero-stiffness spring, High-static-lowdynamic-stiffness spring, Structure design, Bistability, Origami

1. Introduction
In this study, an application of a cylindrical foldable structure with the torsional buckling pattern toan anti-vibration table is considered. The cylindrical foldable structure with the torsional buckling
pattern is known as a bistable structure, which has only two stable states; an initial spatial state anda flat folded state. By combining the bistable structure to a linear compressive spring in parallel,
the combined spring stiffness can be designed to be zero. Since a resonant frequency of a zerostiffness spring is zero theoretically, vibration can be isolated in a wide frequency range. According
to the theory, Ishida et al. [1] and Inamoto et al. [2] investigated the vibration isolator consisting of
the foldable structure with a quasi-zero stiffness, and numerically and experimentally evaluated theisolation performance. However, the foldable structure was remodeled as a truss structure and twisting motion during folding and deployment was not considered. In this study, the original foldable
structure is focused again for simplification and users’ convenience, and devised to cancel the twisting motion for application to an anti-vibration table. The spring properties and isolation performances of the devised structures are numerically analyzed.

2. Modeling
A two-layered foldable structure was modelled by combining two one-layered foldable structuresin the Z direction in a way such that the inclined fold lines were distributed symmetrically. The
height of the structure was simply doubled. Since the upper and lower layers required separate linear

43

JSST2021
𝐾𝐾

155.1mm𝐾𝐾 ′𝐾𝐾

Fig. 1 Side views of a two-layered foldable structure (left) and a vibration isolator (right)

500 mmInput

900 mm1200 mm

Output

800 mmFig. 2 Analytical model of an anti-vibration tablesprings at center (Fig. 1), the relationship between the stiffnesses of the two springs in series 𝐾𝐾 ′and of each spring 𝐾𝐾, was obtained by 𝐾𝐾 ′ = 𝐾𝐾/2 .

Next, a board was placed on the four two-layered isolators, which worked to make the four isolators
vibrate together to Z direction and also play a role as a display board of the anti-vibration table. The
positions and the directions of the inclined fold lines were symmetric as shown in Fig. 2. Finally,an anti-vibration table was obtained by combining the four two-layered vibration isolators and theboard (Fig. 2). The relationship among stiffnesses of eight springs 𝐾𝐾𝑠𝑠𝑠𝑠𝑠𝑠 , the two springs 𝐾𝐾 ′ andthe one spring 𝐾𝐾 was given by 𝐾𝐾𝑠𝑠𝑠𝑠𝑠𝑠 = 4𝐾𝐾′ = 2𝐾𝐾. The stiffness 𝐾𝐾𝑠𝑠𝑠𝑠𝑠𝑠 was adjusted to suppress thetotal stiffness of the four two-layered structures at given displacement range.

3. Results
3.1 Spring properties
The bottom surfaces of the four two-layered isolators were fixed and a compressive displacement
was quasi-statically applied on the board from 0 mm to 155 mm to Z direction. Then, the reaction
force generated was measured. In the folding process, the lower layer was twisted in clockwise;
while, the upper layer in counterclockwise. As this motion was symmetric between the lower and
top layers, the torsion was cancelled. Figure 3 shows the spring property of the anti-vibration table.
Quasi-zero stiffness appeared in a range from 110 mm and 130 mm in height, which corresponds
to a weight of 93 kg to 90 kg to be applied.
3.2 Transmissibilities
Transient response analysis was executed on the anti-vibration table to evaluate transmissibilitiesof the system. Sinusoidal signal was applied on the bottom surfaces of the four two-layered isolatorsand output signal was measured on the top board with regards to a single frequency as shown in
Fig. 2. Thus, the transmissibility was calculated as an amplification ratio; i.e., the amplitude of theoutput signal over that of the input signal.

44

JSST2021
1.4

0
-500

0

20

40

60

80

100 120 140 160

pk-pk 10 mm

-1500
-2000

93kg
93.00 kg
90.5
90.50 kg
90.25kg
90.25 kg
90.kg
90.00 kg

-2500
-3000

1.2
Transmissibility

Forces [N]

-1000

1
0.8
93kg

0.6

90.5kg0.4

90.25kg

0.2

-3500

90kg

0
Height [mm]012Frequency [Hz]3

Fig. 3 Spring property of the anti-vibration ta-

Fig. 4 Transmissibility of the anti-vibration

ble consisting of the four two-layered folda-

table with vibration amplitude of Ain = 5 mmble structures

Figure 4 shows the transmissibility of the anti-vibration table in case of input vibration amplitude
𝐴𝐴𝑖𝑖𝑖𝑖 = 5.0 mm with a weight of 90.00 kg, 90.25 kg, 90.50 kg, and 93.00 kg. Resonance was slightly
observed at 0.5 Hz with a weight of 90.00 kg, 90.25 kg, and 90.50 kg, because the stiffness wasconsiderably close to but not exactly zero. This small resonance can be negligible as the resonancefrequency was sufficiently low and the transmissibility decreased sharply at higher frequencies.
However, with a weight of 93.00 kg, the anti-vibration table clearly resonated at 1.0 Hz. It was
supposed to possess a quasi-zero stiffness as shown in Fig. 3, but the equillibrium position wasclose to the boundary of the quasi-zero stiffness so that dynamic oscillations possibly moved out of
the quasi-zero-stiffness range.

4. Conclusions
In this study, an anti-vibration table using the four two-layered foldable structures was numericallydesigned and the performance on vibration isolation was investigated by transient response analysis.
The torsional motion of the one-layered foldable structure was suppressed on the anti-vibrationtable. The resonance frequency of the anti-vibration table was sufficiently low as long as the weight
applied on the board was reasonably tuned.

Acknowledgement
This research was financially supported by a grant-in-aid for scientific research from Japan Society
for the Promotion of Science under no. 17K18166.

References[1] S. Ishida, K. Suzuki, and H. Shimosaka: Design and Experimental Analysis of Origami-inspired Vibration Isolator with Quasi-zero-stiffness Characteristic, ASME Journal of Vibration
and Acoustics, 139 (5), 051004.
[2] K. Inamoto, and S. Ishida: Improved Feasible Load Range and Its Effect on the Frequency
Response of Origami-Inspired Vibration Isolators With Quasi-Zero-Stiffness Characteristics,
ASME Journal of Vibration and Acoustics, 141 (2), 021004.

45

JSST 2021

Application of Ordinary State-based Peridynamics inBimaterial Modeling
Huy Anh Nguyen1 , Hanlin Wang1 , Satoyuki Tanaka1,*
1 Graduate School of Advanced Science and Engineering, Hiroshima University, Japan∗ satoyuki@hiroshima-u.ac.jp

Abstract. This study presents the application of ordinary state-based peridynamics (OSBPD) in the treatment of the bimaterial interface. OSB-PD offers an effective approach tomodel a structure with multiple interfaces because of its simplicity and ease of computer
implementation. In the current study, a multi-inclusion unit cell model is used to investigate
the accuracy of the OSB-PD as compared to the finite element method (FEM). The OSB-PD
shows a close agreement with FEM in terms of deformation response.
Keywords: Peridynamics, Bimaterial, Inclusion

1.

Introduction

Peridynamics (PD) is a reformulation of the classical continuum mechanics (CCM) introduced by Silling [1] to overcome the difficulties of CCM in modeling discontinuities suchas cracks. PD is a purely nonlocal theory which takes into account the nonlocal interactions between material points, and its governing equation is an integro-differential equation
which does not contain any spatial derivatives as oppsed to CCM. Therefore, the PD equation is valid everywhere in the domain regardless of whether the discontinuities exist or not.
There are three main types of PD formulations in the literature, i.e. bond-based PD (BBPD), ordinary state-based PD (OSB-PD), and non-ordinary state-based PD (NOSB-PD). In
this paper, we focus on investigating the capabilities of OSB-PD in modeling bimaterial
structures. The remainder of the paper is organized as follows. In Section 2, the OSB-PD
formulation and bimaterial modeling are presented. Finally, an analysis of a structure withmultiple inclusions is carried out to demonstrate the effectiveness of OSB-PD in Section 3.

2.

Ordinary state-based peridynamic formulation

In PD, a material point is considered to interact with other points within a finite distance δ.
As shown in Fig. 1, a material point, initially located at x, is associated with its own family
H x , and it interacts with other family members x0 through bonds. Similarly, material points
x0 also interacts with other material points in their own families H x0 . The relative position46

vector between x and x0 is defined as ξ = x0 − x. During the deformation, the material points
x and x0 undergo displacements u and u0 , respectively. Furthermore, the positions of x and
x0 in the deformed state can be specified as y = x + u and y0 = x0 + u0 .

Hx
δ

u

x
ξ

u’

y

t

t’
y’

x’
δ

Hx’

y
z

x Undeformed state

Deformed stateFig. 1 Nonlocal interactions between material points x and x0 , and the resulting force density
vectors
The PD equations of motion at a material point, x, at any instant of time t, can be
expressed as [1–3]Z
ρ(x)ü(x, t) =(t(u0 − u, x0 − x, t) − t 0 (u − u0 , x − x0 , t))dH + b(x, t),(1)
Hxwhere ρ is the mass density, ü is the acceleration, b is the body force density vector. H x
denotes the horizon of a material point at position x. The shape of a family is represented
by a circle with a radius of δ. The force density vector t can be formulated by Madenci andOterkus [3] as!
θ|y0 − y| − |ξ| y0 − y
00t(u − u, x − x, t) = 2adδ Λ + 2δb
,
(2)
|ξ|
|ξ|
|y0 − y|x −xwhere Λ = |yy0 −y−y| . |x0 −x| and θ is the dilatation at point x [3].
The PD parameters a, b, and d in Eq. (2) can be expressed in terms of bulk modulus κand shear modulus µ as derived by Madenci and Oterkus [3] for plane stress as
0

0

1
2
6µ
a = (κ − 2µ), b =
, d=
.
2
πhδ4
πhδ3

(3)

For a bond extending across the interface, the average material properties of the bond canbe achieved as
L
α= L
,
(4)
L2
1
α1 + α2where α is the material property, L1 denotes the length of the bond in material 1, L2 denotes
the length of the bond in material 2, and L = L1 + L2 is the total length of the bond.

47

3.

Application

0.3 m

A square unit cell containing four equal circular inclusions as shown in Fig. 2 is analyzed.
The model is fixed on the left side and is subjected to a uniform tensile loading on the rightside. The positions of the four inclusions are symmetrical to the axes, and each inclusion
has a radius of r = 0.1 m. As depicted in Figs. 3 and 4, there is a good agreement between
FEM and PD results. The displacement distributions smoothly vary at the interfaces in x
and y directions, and the deformation of the plate is symmetrical to the axes. However, thedeformation variation is irregular due to the presence of inclusions.
The contours of strain in PD are shown in Fig. 5. It can be seen from the figure that the
distributions are symmetrical to the axis. Furthermore, the concentrations of strain due to themismatch deformation between the inclusion and matrix occur at the interface as expected.

r

r
y

0.4 m

x

1 MPa
r

0.3 m

r

0.3 m

0.4 m

0.3 m

Fig. 2 Geometry and BCs for the plate with four inclusions problema)b)Fig. 3 Horizontal displacement a) PD b) FEM

4.

Conclusion

In this study, OSB-PD is used to investigate a structure with multiple material interfaces.
In general, there is a good agreement in predictions between FEM and OSB-PD. OSB-PD

48

a)

b)

Fig. 4 Vertical displacement a) PD, b) FEM

a)

b)

c)

Fig. 5 Contour of strain a) x-normal strain , b) y-normal strain, c) shear strainprovides the flexibility in modeling structures with multiple inclusions. Although not being
shown in this present study, the crack modeling is another feature of PD. As a result, PD
is extremely appropriate for problems involving the presence of different types of defects
including inclusions, voids, or cracks.

References[1] S. A. Silling: Reformulation of elasticity theory for discontinuities and long-range
forces, Journal of the Mechanics and Physics of Solids, 48:1 (2000), 175–209.
[2] S. A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari: Peridynamic states and constitutive modeling, Journal of Elasticity 88:2 (2007), 151–184.
[3] E. Madenci, E. Oterkus: Peridynamic theory and its applications, Springer New York,(2014).
[4] H. A. Nguyen, H. Wang, S. Tanaka, S. Oterkus, E. Oterkus: An in-depth investigationof bimaterial interface modeling using ordinary state-based peridynamics, Journal of
Peridynamics and Nonlocal Modeling, (2021).

49

JSST2021

Accurate and Fast Electrostatic Field Analysis with
Unstructured Numerical Human Body Model Using
Parallel Geometric Multi-Grid Method
Masamune Nomura1*, Amane Takei2
1

University of Miyazaki, Interdisciplinary Graduate School of Agriculture and Engineering
2
University of Miyazaki, Faculty of Engineering*
hl13034@student.miyazaki-u.ac.jp

Abstract. In electrostatic field analysis using a numerical human body model constructed withvoxels, the electric field strength is overestimated near the staircase boundary of different materials (called staircasing errors). To reduce this staircasing errors, mesh smoothing based on
the marching cubes method is developed and applied to a part of the numerical human bodymodel. In addition, to reduce the increase in computational time for electrostatic field analysis
due to this mesh smoothing using unstructured lattices, the geometric multi-grid method dealing with unstructured lattices is applied. As a result, this mesh smoothing method reduces thestair casing errors and this geometric multi-grid method takes up to 1/3 of the computation timeof a general linear algebra solver.
Keywords: Electrostatic analysis, Geometric multigrid method, Numerical human body model,
Mesh Smoothing

1. Introduction
To reduce the staircasing errors, mesh smoothing based on the marching cube method [1] isapplied to the numerical human body model constructed with voxels. The visualization resultof the mesh applied to a part of the human body model is shown in the figure below. From thevisualization results, it can be seen that the 90° angle of the voxel model is removed by meshsmoothing. The results of the electrostatic field analysis also show that the overestimation of
the electric field strength due to the staircase approximation at the boundaries of dissimilarmaterials is reduced by smoothing. Mesh smoothing is effective for this model, but elementsin this model using mesh smoothing is huge, and the computation time increases significantly.

b. Electrostatic analysis
a. MeshFigure 1. Voxel model(Left ankle)

50

a. Meshb. Electrostatic analysis
Figure 2. Smoothing model(Left ankle)

JSST2021
To address this problem, the unstructured multigrid method based on the refinement algorithmof UG4 is used in this study. As a result, this Geometric Multi-Grid method (GMG) takes up to
1/3 of the computation time of a general linear algebra solver.

2. Electrostatic field analysis with unstructured GMG
Electrostatic field analysis is performed on the voxel model and smoothing model in Fig. 1,
and the iteration count and computation time for the GMG and the preconditioned CG method(ILUCG) are compared. As boundary conditions for this numerical analysis, electrodes are attached to the heel and toe parts of the model, and a voltage difference of 1 V is set. Table 1
shows the iteration count and computation time (72 cores) of GMG and ILUCG for each model.
The voxel model and smoothing model are refined until the number of elements reaches several
hundred million elements. The maximum refinement levels of the voxel model and smoothingmodel are 4 and 3, respectively. Table 1 shows that the GMG on the smoothing model requires
fewer iterations than the voxel model. This is because smoothing reduces staircassing errors at
the boundary of dissimilar materials and improves the accuracy of the interpolation in the geometric multigrid method. It is also found that the voxel model takes up to 1/6 of the computation time of ILUCG and the smoothing model takes up to 1/3 of that. Figure 3 shows that theComputation time of ILUCG and GMG for each refinement level. From Fig. 3, it can be seenthat the increasing rate of computation time due to refinement of GMG is much smaller thanthat of ILUCG. This shows the effectiveness of the unstructured geometric multigrid method
for mesh-smoothed, high-accuracy, large-scale human body models.
Table 1 Iteration counts and computation time

Model

Voxel

Smooth

Ref.
1
2
3
4
1
2
3

GMG
Iter. TimeNaN NaN
63
34
36
163
32
1,060
25
86
27
240
28
1,518

ILUCG
Iter.
Time
506
3
970
43
1,858 490
3,671 6,532
621
93
1,237 409
2,342 4,957

computation time[sec](72cores) of GMG and ILUCG for each model

ILU_CG_voxel
ILUCG_smooth
GMG_voxel
GMG_smooth

7000
6000
5000
4000
3000
2000
1000
0
1

2

3

4

refiment level

Figure 3. Computation time for each refinment level

3. Conclusion
We infer that the difference in the convergence of the multigrid method between the voxel
model and the smoothing model is remarkable for the whole human body model. We will discuss the calculation results for the whole human body model in the JSST2021 conference.

References[1] A. Takei, et al, “High-Accuracy Electromagnetic Field Simulation Using Numerical Human Body Models” IEEE Trans. on Mag. , Vol. 52, No. 3, 2016.

51

JSST 2021

High Performance Implementation of Skyline Solver
for Many Core Environment
Hiroshi Kawai1*
1

Faculty of Information Systems and Arts, Toyo University*

kawai063@toyo.jp

Abstract. ADVENTURE AutoLinAS (pronounced as ‘O-to-li-na-shi’) is a linear algebraic
solver library, dedicated for simulation-based research and development. It is designed for thesimulation users to develop their own solvers. Currently, the library is used among many researchers and simulation users, mainly in universities and national research centers. Its functionalities and supported platforms are explained. AutoLinAS applications of various kinds ofsimulation methods are demonstrated also.
Keywords: Skyline Solver, Direct Solver, High Performance Computing, Supercomputing, Manycore, HPC

1. Introduction
To build your own simulation code, its linear algebraic solver, either direct or iterative, isvery important for the performance of the code. Therefore, HPC (High Performance Computing) is the key technology to accelerate the linear algebraic solver part. Modern HPC environment, however, is getting more and more complicated, and it might have already beenvery difficult for an ordinary researcher or a software developer to utilize them effectively.
ADVENTURE AutoLinAS is a simple and handy linear algebraic solver library.
AutoLinAS is dedicated for basic vector / matrix operations and linear algebraic solvers usedin the continuum mechanics field, is now under development. It covers both direct solvers
and iterative solvers. It also contains basic building blocks for making a linear algebraic
solver itself, such as dense and sparse matrix operations. Interface to other HPC-related libraries, such as BLAS / LAPACK / Intel MKL, Fujitsu SSL, are also provided. Implementations of the library for various kinds of high performance computing platforms, such as Intelx86 (Skylake-SP) and Fugaku/Fujitsu PRIMEHPC FX-1000, are available. Each of them ishighly tuned for the underlying hardware architecture. Based on AutoLinAS library, a highperformance implementation of skyline solver is developed. Its performance evaluation will
be done on various multi-core / many core CPU architectures.

References[1] ADVENTURE project HP: http://adventure.sys.t.u-tokyo.ac.jp/

52

JSST 2021

High-Performance Solver for EFG-Type Saddle-Point
Problem: Improved Variable-Reduction Method
Atsushi Kamitani1,* , Teruou Takayama1 , Ayumu Saitoh1
1 Graduate School of Science and Engineering, Yamagata University∗ kamitani@yz.yamagata-u.ac.jp

Abstract. Discretization of an elliptic boundary-value problem with the extended elementfree Galerkin method yields a saddle-point problem. For the purpose of fast solving the
problem, the improved Variable-Reduction Method (iVRM) is developed. All projectors are
determined without the QR decomposition in the iVRM and, hence, the computational costof the iVRM can be suppressed to O(N). Here, N is the number of nodes.
Keywords: Element-free Galerkin method, Krylov space method, Saddle-point problem

1.

Introduction

In order to remove the concept of elements from the ﬁnite element method, the Element-Free
Galerkin (EFG) method [1] and the eXtended Element-Free Galerkin (X-EFG) method [2]have been so far proposed. However, application of either method to an elliptic boundaryvalue problem yields a saddle-point problem that is extremely diﬃcult to solve numerically.
Throughout the present study, the problem is called an EFG-type saddle-point problem. Although the Variable-Reduction Method (VRM) [3] was developed for solving the problem,
it contains the costly QR decomposition.
The purpose of the present study is to reformulate the VRM without using the QR decomposition and to investigate applicability of the obtained method to an EFG-type saddlepoint problem.

2.

EFG-Type Saddle-Point Problem

If a two-dimensional (2D) Poisson problem is discretized by use of the X-EFG method with
N nodes and k boundary nodes, we get the following linear system:[][ ] [ ]
A C x
b
=
.
(1)
T
D
O λ
c
Here, A ∈ RN×N is positive semideﬁnite and C, D ∈ RN×k are full-column rank. Furthermore,
the coeﬃcient matrix in (1) is nonsingular. Besides, both x ∈ RN and λ ∈ Rk are unknown
vectors.

53

Figure 1: Residual histories of direct
GMRES, VRM and iVRM for the casewith N = 66049.

Figure 2: Dependence of the CPU time τon the number of nodes N.

In order to solve (1) numerically, Krylov space methods have been so far applied directlyto (1). In the present study, direct application of GMRES to (1) is called direct GMRES.

3.

Improved Variable-Reduction Method

For the purpose of solving (1) for the case where A is dense, the authors proposed theVRM. In the VRM, after C and D are ﬁrst QR factorized, λ is eliminated from (1). Next,
the resulting linear system is solved with GMRES. However, even for the case where A issparse, the computational cost of the VRM amounts to O(N 2 ) due to the QR decomposition.
To overcome this diﬃculty, we have developed the improved VRM (iVRM). In theiVRM, the linear system, A† x = b† , is solved for x with GMRES, where A† ≡ UAU + F,b† ≡ U(b − Ac∗ ) + c∗ and U ≡ I − F. Here, I and F denote an identity matrix and a projector
onto Im C along (Im D)⊥ , respectively, and c∗ ∈ RN is a vector calculated from c. Note thatthe iVRM does not require the QR decomposition. Hence, if A is sparse, its computational
cost can be reduced to O(N).
An EFG-type saddle-point problem originating from a 2D Poisson problem is solved
with direct GMRES/VRM/iVRM. The residual histories and the dependence of the CPU
time on the number of nodes are depicted in Figures 1 and 2, respectively.

References[1] T. Belytchko et al.: Int. J. Numer. Mech. Eng., Vol. 37 (1994) 229-256.
[2] A. Kamitani et al.: Plasma Fusion Res., Vol. 6 (2011) Art. No. 2401074.
[3] A. Kamitani et al.: Int. J. Appl. Electromagn. Mech., Vol. 59 (2019) 157-163.

54

JSST 2021

Parallel implementation of the approach for solving
saddle point problems using block structure
Hiroto Tadano1,*
1 Center for Computational Sciences, University of Tsukuba∗ tadano@cs.tsukuba.ac.jp

Abstract. Saddle point problems arise in many scientiﬁc applications. Recently, we haveproposed an eﬃcient approach for solving saddle point problems using block structure. The
main computation part of our approach is the solution of a linear system with multiple
right-hand sides. Since the multiple right-hand sides of the linear system are mutually independent, the linear system can be solved in parallel by distributing the right-hand sides
in a parallel computing environment. In this presentation, a parallel implementation of ourapproach is presented, and its parallel performance is evaluated.
Keywords: Saddle point problems, Block Krylov subspace methods, Parallelization

1.

Introduction

This paper focuses on saddle point problems of the form:[][ ] [
]
A B
x
f
=
,
CT O
y
g

(1)

where A ∈ Rn×n is a nonsingular matrix, B ∈ Rn×m and C ∈ Rn×m (n > m) are full rank
matrices, x, f ∈ Rn and y, g ∈ Rm . The saddle point problems (1) arise in many scientiﬁcapplications such as structural analysis, ﬂuid dynamics, and so on. Since the solution of (1)is the time-consuming part of the applications, it is desired to solve (1) as fast as possible.
Recently, we have proposed an approach for solving the saddle point problems using
block structure [1] to solve (1) eﬃciently. The main computation part of this approach isthe solution of a linear system with the matrix A and multiple right-hand sides. In [1], it isshown that Block Krylov subspace methods can solve this linear system more eﬃciently than
Krylov subspace methods. Since the multiple right-hand sides are mutually independent,
this linear system can be solved in parallel by distributing the right-hand sides in a parallel
computing environment.
In this presentation, a parallel implementation of our approach is presented. In addition, its performance in a parallel computing environment is evaluated through numericalexperiments.

55

2.

The approach for solving saddle point problems using block
structure

In this section, the approach for solving the saddle point problems (1) using block structure[1] is brieﬂy described. The saddle point problems (1) is expressed as follows:{
Ax + By = f ,(2)
C T x = g.
From Eq. (2), the solution vectors x and y of (1) can be computed as follows:x = A−1 f − A−1 By,
(
)−1 (
)
y = C T A−1 B
C T A−1 f − g .
Hence, the matrix U ≡ A−1 B ∈ Rn×m and the vector u ≡ A−1 f ∈ Rn are required to computethe solution vectors.
[]
By deﬁning the matrices X̂ ≡ [U u] ∈ Rn×(m+1) and B̂ ≡ B f ∈ Rn×(m+1) , the linear
system with multiple right-hand sides:AX̂ = B̂(3)

can be obtained. By solving the linear system (3), the solution vectors x = u − Uy and
(
)−1 (
)
y = CTU
C T u − g can be computed.

3.

Parallel implementation

In this section, a parallel implementation of our approach is presented. Throughout thispaper, P denotes the number of MPI processes. In addition, for simplicity, it is assumed thatn and m are divisible by P.

3.1.

Preconditioning for the linear system AX̂ = B̂Since the solution of the linear system with multiple right-hand sides (3) is the most timeconsuming part of our approach, it is essential to apply a preconditioner to (3) to reducethe computation time of iterative methods. Although it is known that the incomplete LU
factorization preconditioner is eﬃcient, the most computation part of this preconditioner issequential computation. Hence, it is diﬃcult to bring out the computation performance of
this preconditioner in a parallel computing environment.
To compute a preconditioning matrix eﬃciently in a parallel computing environment, thesparse approximate inverse (SAI) preconditioner [2] is employed. The SAI preconditioner
generates a preconditioning matrix M ∈ Rn×n such that M ≈ A−1 by solving the n leastsquare problems min ∥Am j − e j ∥2 ( j = 1, 2, . . . , n), where m j and e j are jth column vector ofmj

M and the identity matrix I, respectively. The nonzero structure of the matrix M is speciﬁedby the user. Since these least square problems are mutually independent, the preconditioning
matrix M can be computed in parallel by assigning n/P problems to each MPI process.

56

3.2.

Solution of the linear system AX̂ = B̂Let us consider solving the linear system (3) in parallel. Since the column vectors of matrix
B̂ are mutually independent, it is easy to parallelize the solution of (3). The matrices X̂ andB̂ are split as follows:[][]X̂ = X̂ (0) X̂ (1) . . . X̂ (P−1) , B̂ = B̂(0) B̂(1) . . . B̂(P−1) ,where X̂ (p) , B̂(p) ∈ Rn×(m/P) (p = 0, 1, . . . , P − 1). By splitting the matrices X̂ and B̂, thefollowing P linear systems with multiple right-hand sides can be obtained.
AX̂ (p) = B̂(p) , p = 0, 1, . . . , P − 1.

(4)

The linear system AX̂ (p) = B̂(p) with m/P right-hand sides is assigned to the pth MPI process. Hence, the number of right-hand sides when using OpenMP/MPI Hybrid parallelization is relatively larger than that when using Flat MPI parallelization. Although the Block
Krylov subspace methods are eﬃcient methods for linear systems with multiple right-handsides in terms of the number of iterations, the computation complexity of most computing
kernels is proportional to the square of the number of right-hand sides. Therefore, a longcomputation time may be required to solve (4) when the number of MPI processes is small
and OpenMP/MPI Hybrid parallelization is used.

3.3.

Computation of the solution vectors

To compute the solution vector y, the linear system with the coeﬃcient matrix C T U needs tobe solved. After that, the solution vector x can be computed by using y. At this time, in our
implementation, these computations are performed by a single MPI process. Parallelizationof this computation phase is our future work.

4.

Performance evaluation

The computation performance of our implementation is evaluated through numerical experiments. As the matrix A of (1), torso3 from the SuiteSparse Matrix Collection [3] is used.
The size n and the number of nonzero elements of A are 259,156 and 4,429,042, respectively.
The number m of columns of B and C is set as 3, 000. The elements of these matrices are
given by a random number generator. The nonzero structure of the preconditioning matrix M
computed by the SAI preconditioner is the same as that of A. The Block GWBiCGSTABrQ
method [4] is adopted to solve the linear systems with multiple right-hand sides (4).
Computations are carried out on the Cygnus Supercomputer operated at the Center for
Computational Sciences, University of Tsukuba. Each compute node is equipped with twosockets of Intel Xeon Gold 6126 2.6GHz (12 cores). The number of MPI processes percompute node is 24 when Flat MPI is used. When OpenMP/MPI Hybrid is used, each MPI
process is assigned to a socket, and the computations in each MPI process are parallelized
by OpenMP with 12 threads. The compiler and MPI library used in numerical experiments
are Intel Fortran ver. 19.1.3 and OpenMPI ver. 4.0.3, respectively. The used compile option
is -axCORE-AVX512 -align array64byte.

57

<latexit sha1_base64="/7e5fIoGUjfH7BzfpJxF4VmTTeQ=">AAANVnicnVdLb9xUFD5TCC1DQtOyQWJjSINYtBNPUmiLFKkSIBBi0TZJGylJIz/uBDce2/gxeYxmBRISf4AFK5CQQPwMNvwBJPoTEMsiwQIhvnOuPa/MeBx8Nfa993znfXx8x458L0lN82ntwnPPz71w8dKL9ZfmF16+vHjl6sMkzGJHbTmhH8bbtpUo3wvUVuqlvtqOYmW1bV89sg/fY/qjjooTLww205NI7bWtg8BreY6VYitcPKJd8iigiDJKqUsrtEUJKYpxX8GORS5+AYVYvY+7A1wb9AA0RnwC6ibW2+rL1t9Yf0wbGJtDs1Uy8Wti5wM6hh6W7Y3I+BA7FiifisZQdIe0RvtAreNpyliBNOZWsCjDrAy7P4ZtAKugvbe/uGQ2TLmMs5NmPlmi/LoXXpn7ARFyxzx3yIfFCcYOPDOhIaU9RM+CPSm8Y7qiHtXBm0k8I9AcOsT9AKudfDfAmmUmdB2/DmiDHZZ3DJ4QstjPHhm0bP5q/mg+M38xfzJ/N/8pkR/IM4Yszh7LsjGzseeX2NUV7ezXCZ621qmi/ctfvbrx10wu1pUii32uUv9TatFtsWxQfxwRR/N3Tr9+tvHug+Xum+Z35h/w+1vzqfkzPA86fzrf31cPvoH05fw33S4fs1Aqji1rz/B9HO2JNdM5UmSoBQ5dyeVIL89rGcruWxhLLBQdSQW08zy6wOwKPqAnkNiSyHuw+wQ0JesMqxRSGHmA2fh+vUT/cLVVQaWwWNfTMtBF/jt5//AkMuwV491SmRGeLdxZ7tlYjtJ8SLalZ8TwuwsaR8CX6k4RMSWxK9OmLbTFXm9GVTDikE4rYW6gA7l9S6tweFLxPlBuacfoSm/I+rJvCI+F53ns80XfwYwq5MxlwHlS38PIYTnDGYhgUyJ4nXOtpQpnW7Cu1E5UieMz0EPpFdw1LdHkn3mzpnEnqE9Lvg2aO8YIUTO8coTG9lST5UjHcCpGiGstlbqrKt+TvqLfJQU9RXTZ1kGvrWqnkjhbY+/2NB5XNIayM9DbEL0xOCbV0TRZLTlFnIdjOEuN3H6u++xMbyiX4Oa5bUifyir6vjazVx3nPamIxnm61aB76pov/Bnn0xZ28/6v68fAGcfIvwscm6LHTPtSuHkN6a+BnhuYvT7lXqDLZHb+l8yqWoucFN5zf3AxuH4Hb+sKMsren8j+OnB1SBodkyp4XSSOVvD1CbzFKLAcdR3/8U5n4PTXoLfxPMpPDYbEZWBrl5ZwRuzJqWaSrt7EXa0nlcobtn7UK/3FGEiqz8hdGxFL0EFjifcOzuV7sh9L3+OYN+Usuws/+Kt9DOo1eiwYfb7j99DIPbomPk3Pa6GJI7AqEeCzR13O4HfkMvTk1s18cqfZP4M/XG0032ms3b+5dPd2fhq/RK/RG/QWdN+iu/QR3cN/Fae2WTutfV77Yv63+X8X5hYuauiFWs7zCo1cC4v/AXycn5k=</latexit>

Flat MPI
OpenMP/MPI Hybrid

40

Flat MPI
OpenMP/MPI Hybrid
Ideal

30

102

Speedup

Computation time [sec]<latexit sha1_base64="YfhMqpn1m7zT8mXu26l7nK/7PB4=">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</latexit>

20
10

101
0

4

8

12

16

20

24

Number of compute nodes, N

28

0

32

(a) Computation time.

0

4

8

12

16

20

24

Number of compute nodes, N

2832(b) Speedup.

Figure 1: Computation time and speedup as a function of the number of compute nodes.
Figure 1 shows the computation time and speedup as a function of the number of compute nodes. Here, N denotes the number of used compute nodes. As shown in Fig. 1 (a),for N < 8, the computation time when using Flat MPI was shorter than that when using
OpenMP/MPI Hybrid. On the other hand, for N > 8, the computation time when using
OpenMP/MPI Hybrid was shorter than that when using Flat MPI. Figure 1 (b) shows the
speedup as a function of N. The speedup of OpenMP/MPI Hybrid was superior to thatof Flat MPI. Moreover, the speedup of OpenMP/MPI Hybrid exceeded the ideal speedup.
When N = 32, the speedup of OpenMP/MPI Hybrid and Flat MPI were 35.2 and 7.39,
respectively. The detailed results will be shown at the Conference.

Acknowledgement
This research was supported by JSPS KAKENHI Grant Number JP20K11840. This research used computational resources of the Cygnus Supercomputer provided by Multidisciplinary Cooperative Research Program in Center for Computational Sciences, University ofTsukuba.

References[1] H. Tadano, S. Ishikawa: An eﬃcient approach for solving saddle point problems using
block structure, J. Adv. Simulat. Sci. Eng., 8:1 (2021), 114–127.
[2] M. Benzi, M. Tůma: A sparse approximate inverse preconditioner for nonsymmetriclinear systems, SIAM J. Sci. Comput., 19:3 (1998), 968–994.
[3] T. A. Davis, Y. Hu: The university of Florida sparse matrix collection, ACM Trans.
Math. Software, 38 (2011). (https://sparse.tamu.edu)[4] H. Tadano, R. Kuramoto: Accuracy improvement of the Block BiCGSTAB method forlinear systems with multiple right-hand sides by group-wise updating technique, J. Adv.
Simulat. Sci. Eng., 6:1 (2019), 100–117.

58

JSST 2021

A Paralellization Strategy for Incomplete
Decomposition-based Preconditioning for Solving
Linear Systems
Taiga Yamashita1,* , Taku Itoh2 , Hiroto Tadano3
1 Graduate School of Industrial Technology, Nihon University, Japan
2 College of Industrial Technology, Nihon University, Japan
3 Center for Computational Sciences, University of Tsukuba, Japan∗ cita20015@g.nihon-u.ac.jp

Abstract. To eﬃciently solve linear systems by Krylov subspace methods, an incomplete
decomposition-based strategy with parallel processing has been proposed. Basically, theincomplete decomposition-based Krylov subspace methods are not very suitable for parallel processing, since sequential process is contained in their algorithms. In the proposed method, the algorithms are transformed so that they consist only of inner products
and matrix-vector products by excluding the sequential process. Hence, the incomplete
decomposition-based Krylov subspace methods may be more easily parallelized than thoseof the original ones.
Keywords: Krylov subspace methods, Incomplete decomposition, Parallel processing, Linear systems, Preconditioning

1.

Introduction

This paper focuses on linear systems:
Ax = b,(1)

where A ∈ RN×N is a given matrix, x ∈ RN is an unknown vector, and b ∈ RN is a given
vector. To solve the linear systems, many kinds of Krylov subspace methods have been
applied [1]. In addition, incomplete decomposition methods such as IC and ILU have employed for accelerating solving the linear systems by Krylov subspace methods. Note thatthe incomplete decomposition methods are basically sequential algorithms. For this reason, the incomplete decomposition-based Krylov subspace methods are not very suitablefor parallel processing.
The purpose of this study is to propose an incomplete decomposition-based strategy
for solving linear systems in parallel processing. To this end, the sequential process in
the incomplete decomposition is excluded from the iteration process of Krylov subspacemethods.

59

2.

Incomplete Decomposition Methods

In what follows, we especially focus on incomplete LDU decomposition (iLDU) based
Krylov subspace methods for solving asymmetric linear systems. We employ an algorithm
described in [2] as iLDU. In the algorithm, the preconditioning matrices L, D and U arecomposed so that A ≃ LDU is satisﬁed. Note that the non-zero structures of L and U are thesame as those of A in the algorithm. In addition, D is a diagonal matrix.
In the iteration process of iLDU based Krylov subspace methods, calculating such asu = (LDU)−1 rk is required for each iteration, where rk is the residual vector for the kth
iteration. The vector u can be obtained by solving the following two equations.
{
Ly = rk ,(2)
DUu = y.
Since they are sequential process, the performance of parallel processing for iLDU based
Krylov subspace methods deteriorates.

3.

Parallelization Strategy for Incomplete Decomposition-based
Preconditioning

In this section, we consider excluding the sequential process (2) in the iteration process. To
this end, we explicitly obtain M = (LDU)−1 by solving
LDU M = E,(3)

before the iteration step of iLDU based Krylov subspace methods is started, where E ∈RN×N is the identity matrix. By obtaining the matrix M, the algorithms of iLDU based
Krylov subspace methods are transformed so that they consist only of inner products andmatrix-vector products. Namely, iLDU based Krylov subspace methods may be more easily
parallelized than those of the original ones.
Note that the matrix M may become a dense one, if (3) is solved exactly. Since dense
matrices are sometimes diﬃcult to retain on the memory, we obtain a sparse matrix M̂ by
the following procedures so that M̂ ≃ M.
1. Solve Ly j = e j .
2. Solve DU m j = y j .
3. Compose m̂ j by extracting some non-zero components of the vector m j based on somecriteria. The non-zero components of m̂ j are retained based on the CCS (compressedcolumn storage) format [3].
4. Delete the memory allocated to m j .
Here, E = [e1 , e2 , . . . , eN ], M = [m1 , m2 , . . . , mN ] and M̂ = [ m̂1 , m̂2 , . . . , m̂N ]. In addition,e j , m j and m̂ j are the jth vectors of the matrices E, M and M̂, respectively ( j = 1, 2, . . . , N).
Note that m̂ j can be determined in parallel, although the procedures 1–4 are sequential.
As examples of the criteria for the procedure 3, the following may be considered.

60

1. If ai j , 0 then m̂i j = mi j , else m̂i j = 0 (i = 1, 2, . . . , N).
2. If |mi j | > c j then m̂i j = mi j , else m̂i j = 0 (i = 1, 2, . . . , N).
Here, ai j is the (i, j)-element of the matrix A, and mi j and m̂i j are ith components of m j andm̂ j , respectively. In addition, c j is a parameter that may be determined as
N
∑

cj =

|mi j |

i=0

N

.

(4)

Note that the above criteria are separately employed.

4.

Numerical Experiments

In this section, numerical experiments are conducted to investigate the performance of thestrategy. To this end, linear systems based on poisson3Db [4] as a coeﬃcient matrix together with poisson3Db b [4] as a right-hand side vector are solved by BiCGStab [5] withpreconditioning. The preconditioning matrices are generated by an incomplete LDU decomposition [2] or the strategy described in Section 3. Here, N = 85623. In what follows,
we refer to BiCGStab with the incomplete LDU decomposition as iLDU-BiCGStab, and
BiCGStab with the strategy as M-BiCGStab.
Computations were performed on Cygnus at the CCS (Center for Computational Sciences), University of Tsukuba. Cygnus for each node equips dual 12-core Intel Xeon Gold
6126 2.6 GHz processors, 192 GB RAM, CentOS, and Intel C++ Compiler ver. 19.0.5 withdouble-precision arithmetic. In addition, parallelization is performed by OpenMP on one
node, and optimize options for all codes are -O3 -axCORE-AVX512. Besides, we set an
environment variable, KMP AFFINITY=scatter.
First, the dependence of execution time and speed-up ration on the number T of threads
for generation of preconditioning matrices is shown in Fig. 1(a). In this ﬁgure, ‘iLDU + M’
denotes the proposed strategy. We see from Fig. 1(a) that the speed-up ratio of proposed
strategy is about 16.8 for T = 24 in comparison with T = 1. In addition, the speed-up
ratio of iLDU is almost the same for all numbers of threads. Hence, the algorithm of the
proposed strategy is suitable for parallelization in comparison with the original incomplete
LDU decomposition. Note that the execution time of the proposed strategy is larger thanthat of iLDU for all numbers of threads.
Next, for iteration process, the dependence of execution time and speed-up ration on thenumber T of threads is shown in Fig. 1(b). We see from this ﬁgure that the speed-up ratioof M-BiCGStab is about 4.86 for T = 24 in comparison with T = 1. Besides, the speed-up
ratio of iLDU-BiCGStab is about 1.51 for T = 24 compared with T = 1. Thus, M-BiCGStab
is more suitable for parallelization than iLDU-BiCGStab. However, the total execution timeof M-BiCGStab is greater than that of iLDU-BiCGStab. Note that the number of iterationsfor M-BiCGStab and that for iLDU-BiCGStab are 796 and 113 for T = 24, respectively.
Namely, the execution time for each iteration of M-BiCGStab and that of iLDU-BiCGStab

61

(a)

(b)

Figure 1: Dependence of Execution time and speed-up ratio on the number of threads for(a) generation of preconditioning matrices and (b) iteration process.

are about 0.00313 s and 0.0158 s. Hence, the the execution time for each iteration of MBiCGStab is about 5.06 times faster than that of iLDU-BiCGStab.
From the results, although the speed-up ratio of M-BiCGStab is higher than that of
iLDU-BiCGStab, the total execution time of M-BiCGStab is greater than that of iLDUBiCGStab, for this case. We consider that the performance of M-BiCGStab may be more
eﬃcient for larger cases. In addition, there is a possibility that the algorithm for generating
the preconditioning matrices may be improved, by utilizing the structures of matrices. Other
results and further details will be presented at the conference.

Acknowledgement
Numerical calculations were performed using Cygnus at the CCS, University of Tsukuba.

References[1] Y. Saad: Iterative Methods for Sparse Linear Systems (2nd Edition), SIAM, Philadelphia, PA (2003).
[2] K. Murata, M. Natori, Y. Karaki: Large-scale Numerical Simulations, Iwanami Shoten,
Tokyo (1990) (in Japanese).
[3] I. S. Duﬀ, R. G. Grimes, J. G. Lewis: Sparse matrix test problems, ACM Trans. Math.
Soft., 15:1 (1989), 1–14.
[4] SuiteSparse Matrix Collection, Formerly the University of Florida Sparse Matrix Collection, accessed on Aug. 2, 2021. [Online]. Available: https://sparse.tamu.edu/[5] H. A. van der Vorst: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG
for the Solution of Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput., 13:2
(1992), 631–644.

62

JSST 2021

An analysis of electrocardiograms through the wavelet
transform with pseudo diﬀerential operator like
operators
M. Rahman1,* , T. Kagawa2 , S. Kawasaki3 , S. Nagai2 , T. Okai4 , H. Oya4 ,Y. Yahagi5 , M.Yoshida1
1 Graduate School of Engineering, Kanagawa Univ.
2 Faculty of Engineering, Kanagawa Univ.
3 Faculty of Science and Engineering , Iwate Univ.
4 Faculty of Information Engineering, Tokyo City Univ.
5 Dept.of Mathematical informatics, Tokyo Univ. of Information Science∗ masudur 2006@yahoo.com

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.96

63

JSST2021

Application of Wavelet-Taylor-Galerkin method
to the 1D Euler equations
1
1

Faculty of Engineering, Information and Systems, University of Tsukuba
2

1

Yamamoto Kyosuke and 2Matsuura Taishi

Sumitomo Heavy Industries, Ltd (Research while in Univ. of Tsukuba)

yamamoto_k@kz.tsukuba.ac.jp, 2taishi.matsuura@shi-g.com

Abstract. In the present study, the Euler equation is numerically solved by the Wavelet-TaylorGalerkin (WTG) method and its effectiveness is confirmed; it is found that the WTG method
can obtain a numerical solution with high accuracy, while suppressing numerical oscillations
compared with popular finite difference methods, such as the Lax Wendroff method.
Keywords: Wavelet-Taylor-Galerkin method, Euler equations

1. Introduction
The finite element method (FEM) is the most popular method for numerically solving
partial differential equations (PDE), as well as the finite differential method (FDM). Since almost all mechanical and social systems can be described by PDE, we can apply FEM to them.
It enables us to solve various problems of modern society by computers. FEM has been generalized by the weighted residual method (WRM). The most common scheme of WRM is called
the Galerkin method. Suppose that a PDE is given by 𝑅𝑅(𝑢𝑢) = 0. If the given PDE is an advection equation, in which 𝑡𝑡, 𝑥𝑥, 𝑢𝑢(𝑡𝑡, 𝑥𝑥) and 𝑐𝑐 denote the time, position, physical quantity and advection velocity, respectively, we have
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
+ 𝑐𝑐
= 𝑅𝑅,
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕

where 𝑅𝑅 is also called residual. The approximate solution of the analytical solution for 𝑢𝑢(𝑡𝑡, 𝑥𝑥)
is expressed by the following equation:𝑢𝑢(𝑡𝑡, 𝑥𝑥) = 𝒖𝒖(𝑡𝑡) ⋅ 𝑵𝑵 (𝑥𝑥),where 𝑵𝑵 (𝑥𝑥) is the basis function vector and 𝒖𝒖(𝑡𝑡) is the numerical solution vector. This operation is called interpolation. Since we cannot always set the residual 𝑅𝑅 nor the average of theresiduals ∫ 𝑅𝑅d𝑥𝑥 to zero, we instead make the assumption that the average of the weighted residuals is always zero, for any weight 𝜔𝜔(𝑥𝑥):𝐿𝐿� 𝜔𝜔𝜔𝜔d𝑥𝑥 = 0,0where [0, 𝐿𝐿] is the defined area. Substituting the approximate solution 𝝎𝝎 ⋅ 𝑵𝑵 (𝑥𝑥) of the analytical solution 𝜔𝜔(𝑥𝑥) into this equation, we obtain the finite element equation. For example, the67

above advection equation can be transformed into the following equation
𝐿𝐿

𝐿𝐿

𝐿𝐿

JSST2021Ṫ + �� 𝑵𝑵 𝜕𝜕𝑵𝑵 d𝑥𝑥� {𝒖𝒖}� = 0.
𝝎𝝎T � 𝑵𝑵 (𝑥𝑥)𝑅𝑅(𝑢𝑢)d𝑥𝑥 = 𝝎𝝎T ��� 𝑵𝑵 𝑵𝑵 T d𝑥𝑥� {𝒖𝒖}
𝜕𝜕𝜕𝜕
0
0
0
𝐿𝐿

T

𝐿𝐿

Putting 𝐌𝐌 = �∫0 𝑵𝑵 𝑵𝑵 T d𝑥𝑥� and 𝐂𝐂 = �∫0 𝑵𝑵 𝜕𝜕𝑵𝑵d𝑥𝑥�, the finite element formula is as follows:𝜕𝜕𝜕𝜕𝐌𝐌𝒖𝒖̇ + 𝐂𝐂𝒖𝒖 = 𝟎𝟎.

This kind of operation is general and can be applied to any PDE. For the basis functions, Lagrange or Hermite interpolation functions are common. In the case of the Discontinuous Galerkin (DG) method, the Legendre interpolation function is used. On the other hand, a scaling
function, which is used in the wavelet transform[1], is also an orthonormal basis and can be usedas the basis function vector 𝑵𝑵 (𝑥𝑥). When a scaling function is used for the basis function 𝑵𝑵 (𝑥𝑥),the geometry matrix 𝐌𝐌 becomes an unitary matrix, which makes the calculation very efficient.
If the scaling function is applied to Taylor-Galerkin method[2], we call it Wavelet Taylor Galerkin (WTG) method[3]-[4].
When 𝜙𝜙(𝑥𝑥) denotes the scaling function, 𝜙𝜙𝑗𝑗,𝑘𝑘 (𝑥𝑥) is defined as the following:𝑗𝑗

𝜙𝜙𝑗𝑗,𝑘𝑘 (𝑥𝑥) = 2−2 𝜙𝜙(2−𝑗𝑗 𝑥𝑥 − 𝑘𝑘),
where both 𝑗𝑗 and 𝑘𝑘 are integers. 𝑗𝑗 indicates the approximate resolution and 𝑘𝑘 represents thecorresponding node number. In other words, the node position must be 𝑥𝑥𝑘𝑘 = 𝑘𝑘𝑘𝑘𝑘𝑘.

2. Basic Theory
Let 𝜌𝜌, 𝑢𝑢, 𝑝𝑝 and 𝑒𝑒 be the fluid’s density, flux, pressure, and total energy per unit volume, respectively. The Euler equation is given by
𝜕𝜕𝑸𝑸 𝜕𝜕𝑬𝑬
+
= 𝟎𝟎.
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕

where 𝑸𝑸 = [𝜌𝜌 𝜌𝜌𝜌𝜌 𝑒𝑒]T is the conserved quantity and 𝑬𝑬 = [𝜌𝜌𝜌𝜌 𝑝𝑝 + 𝜌𝜌𝑢𝑢2 (𝑒𝑒 + 𝑝𝑝)𝑢𝑢]T is the flux.
The second-order Taylor expansion of the conserved quantity 𝑸𝑸 is given by
𝑸𝑸𝑛𝑛+1 = 𝑸𝑸𝑛𝑛 + 𝛥𝛥𝛥𝛥𝜕𝜕𝑸𝑸 1 2 𝜕𝜕 2 𝑸𝑸
+ 𝛥𝛥𝑡𝑡.
𝜕𝜕𝑡𝑡2
𝜕𝜕𝜕𝜕 2where 𝑛𝑛 is the time step. The second-order term in this equation can be transformed, using the
𝜕𝜕𝑬𝑬
, as
Jacobi matrix 𝐀𝐀 ≡ 𝜕𝜕𝑸𝑸
𝜕𝜕 2 𝑸𝑸 𝜕𝜕 𝜕𝜕𝑸𝑸𝜕𝜕𝜕𝜕𝑬𝑬𝜕𝜕 𝜕𝜕𝑬𝑬
𝜕𝜕
𝜕𝜕𝑸𝑸
𝜕𝜕
𝜕𝜕𝑬𝑬
= � � = �−�=−
= − �𝐀𝐀
�=
�𝐀𝐀
�,
2
𝜕𝜕𝑡𝑡
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕

where
0
⎡ 1
(𝛾𝛾 − 3)𝜌𝜌𝑢𝑢2
2
𝐀𝐀 = ⎢⎢⎢𝑒𝑒−𝛾𝛾 𝑢𝑢 + (𝛾𝛾 − 1)𝑢𝑢3𝜌𝜌⎣1−(𝛾𝛾 − 3)𝑢𝑢𝑒𝑒 3𝛾𝛾 − (𝛾𝛾 − 1)𝑢𝑢2
𝜌𝜌 2

𝛾𝛾 is the heat capacity ratio. Thus, we obtain

68

0

⎤
𝛾𝛾 − 1⎥
⎥.
⎥
𝛾𝛾𝛾𝛾
⎦

JSST2021
𝑸𝑸𝑛𝑛+1 = 𝑸𝑸𝑛𝑛 − 𝛥𝛥𝛥𝛥𝜕𝜕𝑬𝑬 𝑛𝑛
𝜕𝜕𝑬𝑬 𝑛𝑛 1 2 𝜕𝜕
+ 𝛥𝛥𝑡𝑡
�𝐀𝐀𝑛𝑛
�,
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
2

Let 𝑸𝑸𝑛𝑛𝑖𝑖 be the conserved quantity at 𝑖𝑖-th node: 𝑸𝑸𝑛𝑛𝑖𝑖 = [𝜌𝜌𝑖𝑖 (𝑛𝑛𝑛𝑛𝑛𝑛) 𝜌𝜌𝑖𝑖 (𝑛𝑛𝑛𝑛𝑛𝑛)𝑢𝑢𝑖𝑖 (𝑛𝑛𝑛𝑛𝑛𝑛) 𝑒𝑒𝑖𝑖 (𝑛𝑛𝑛𝑛𝑛𝑛)]T .
When we now apply WRM with the scaling function as the basis, we further obtain
𝑸𝑸𝑛𝑛+1= 𝑸𝑸𝑛𝑛𝑖𝑖 −𝑖𝑖

𝐿𝐿−1
𝛥𝛥𝛥𝛥 𝐿𝐿−1
1 𝛥𝛥𝑡𝑡2 𝐿𝐿−1
(1)
(1,1)
(0,2)
𝑛𝑛
𝑛𝑛
� 𝑬𝑬𝑖𝑖+𝑘𝑘
𝑎𝑎𝑘𝑘 +
��
�𝐀𝐀𝑛𝑛 𝑬𝑬 𝑛𝑛 𝑏𝑏+ 𝐀𝐀𝑛𝑛𝑖𝑖+𝑘𝑘 𝑬𝑬𝑖𝑖+𝑙𝑙
𝑏𝑏𝑘𝑘𝑘𝑘 �,
𝛥𝛥𝛥𝛥 𝑘𝑘=−𝐿𝐿+1
2 𝛥𝛥𝑥𝑥2 𝑘𝑘=−𝐿𝐿+1 𝑙𝑙=−𝐿𝐿+1 𝑖𝑖+𝑘𝑘 𝑖𝑖+𝑙𝑙 𝑘𝑘𝑘𝑘

(𝑝𝑝)(𝑝𝑝.𝑞𝑞)where 𝑘𝑘 and 𝑙𝑙 are integers. Also, the coefficients 𝑎𝑎𝑘𝑘 and 𝑏𝑏𝑘𝑘
(𝑝𝑝)𝑎𝑎𝑘𝑘 = �+∞−∞(𝑝𝑝,𝑞𝑞)𝑏𝑏𝑘𝑘𝑘𝑘

=�

+∞

−∞

are

𝜙𝜙0,0 (𝑥𝑥)𝜕𝜕 𝑝𝑝 𝜙𝜙0,𝑘𝑘(𝑥𝑥)d𝑥𝑥 ,𝜕𝜕𝑥𝑥𝑝𝑝𝜙𝜙0,0 (𝑥𝑥)𝜕𝜕 𝑝𝑝 𝜙𝜙0,𝑘𝑘𝜕𝜕 𝑞𝑞 𝜙𝜙0,𝑙𝑙(𝑥𝑥)(𝑥𝑥)d𝑥𝑥,𝜕𝜕𝑥𝑥𝑝𝑝𝜕𝜕𝑥𝑥𝑞𝑞respectively. If 𝑸𝑸𝑛𝑛𝑖𝑖 is known, we can solve this equation to obtain 𝑸𝑸𝑛𝑛+1, though we need to𝑖𝑖
introduce the artificial viscosity.
In order to suppress the numerical oscillations, the obtained velocity 𝑢𝑢𝑛𝑛+1
should be re𝑖𝑖
placed by 𝑢𝑢̅𝑛𝑛+1
as following:𝑖𝑖

𝑢𝑢̅𝑛𝑛+1= 𝑢𝑢𝑛𝑛+1
+ 𝜀𝜀
𝑖𝑖
𝑖𝑖

𝑛𝑛+1
+ 𝑢𝑢𝑛𝑛+1|𝑢𝑢𝑛𝑛+1
𝑖𝑖+1 − 2𝑢𝑢𝑖𝑖
𝑖𝑖−1 |
𝑛𝑛+1(𝑢𝑢𝑛𝑛+1+ 𝑢𝑢𝑛𝑛+1
𝑖𝑖+1 − 2𝑢𝑢𝑖𝑖
𝑖𝑖−1 ).
𝑛𝑛+1
𝑛𝑛+1
�𝑢𝑢𝑖𝑖+1 + 2𝑢𝑢𝑖𝑖 + 𝑢𝑢𝑛𝑛+1�
𝑖𝑖−1

However, this formula is derived from the idea based on FDM. Thus, in this study, novel artificial viscosity of which based idea comes from WTG method is also introduced and comparedwith the former:(2)

𝑢𝑢̅𝑛𝑛+1= 𝑢𝑢𝑛𝑛+1
+ 𝜀𝜀
𝑖𝑖
𝑖𝑖

�∑𝐿𝐿−1
𝑢𝑢𝑛𝑛+1 𝑎𝑎𝑙𝑙 �
𝑙𝑙=−𝐿𝐿+1 𝑖𝑖

𝐿𝐿−1

(2)

� 𝑢𝑢𝑛𝑛+1
𝑎𝑎𝑙𝑙 .
𝑖𝑖(2)�∑𝐿𝐿−1
𝑢𝑢𝑛𝑛+1 �𝑎𝑎𝑙𝑙 �� 𝑙𝑙=−𝐿𝐿+1
𝑙𝑙=−𝐿𝐿+1 𝑖𝑖

3. Numerical Simulation
A one-dimensional shock tube problem is set up as shown in Fig.1, and applied
WTG and FDM methods for comparing the numerical solutions. As the WTG, we prepare two
types: one is the As the FDM in this study, Lax-Wendroff method[5] is applied.

Fig.1 The initial condition / boundary condition of Shock Tube Problem
The results obtained by the WTG method using Coiflet's scaling function and thefinite difference method (FDM, Lax-Wendroff method) are shown in Fig. 2. When calculating

69

JSST2021

the results of the WTG method, two cases are prepared: one where the artificial viscosity is
calculated in the same way as in FDM, and another where the artificial viscosity is done in thesame way as in WTG. The results show that the numerical solution obtained by the WTG
method with the WTG-type artificial viscosity is the closest to the analytical solution: the amplitude of the numerical oscillations is sufficiently suppressed by the WTG method comparedto FDM, and the positions of the shock wave surfaces are calculated at near positions as in
FDM. Although further improvement is still needed, it is confirmed that the WTG method isan effective numerical analysis method for the Euler equation.

Fig. 2 The results of WTG simulation
The WTG method with WTG type artificial viscosity is a better option for numerically solving the Euler equation. This scheme can suppress the amplitude of numerical oscillations well. However, a technical issue that we must set all nodes in regular distance still remains.

References[1] Liandrat, J. and Tchamitchian, Ph., “Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation,” ICASE Report (1990),
pp.90-83.
[2] Donea, J., “A Taylor-Galerkin method for convective transport problems,” International Journal for Numerical Methods in Engineering, 20 (1984),
pp.101-119.
[3] Kumar, B. R. and Mehra, M., “A Wavelet-Taylor Galerkin method for parabolic and hyperbolic partial differential equations,” International Journal ofComputational Methods, 2 (1) (2005), pp.75-97.
[4] Kumar, B. R. and Mehra, M., “Wavelet-Taylor Galerkin method for the Buegers Equation,” BIT Numerical Mathmatics, 45 (2005), pp.543-560.
[5] Peter D. Lax, Burton Wendroff, “Systems of Conservation Laws,” Communications on Pure and Applied Mathematics, 17 (1964), pp.381-398.

70

JSST 2021

Wavelet Galerkin method for three-dimensionalboundary value problems with MPC technique
Satoyuki Tanaka1,* , Thin Thin Htut1 , Hanlin Wang1 , Hiroshi Okada2
1 Graduate School of Advanced Science and Engineering, Hiroshima University
2 Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo

University of Science∗ satoyuki@hiroshima-u.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.78

71

JSST 2021

Driving forces for structural transitions in atomic
clusters in collective eigen-time-delay coordinates
Yusuke Ogasawara1 and Tomohiro Yanao1,*
1 Department of Applied Mechanics and Aerospace Engineering, Waseda University∗ yanao@waseda.jp

Abstract. This study explores driving forces for structural transitions in atomic clusters
using collective eigen-time-delay coordinates. Hyperspherical radius of an atomic cluster
serves as a collective coordinate characterizing structural transitions between two distinct
structures. We apply a time series of the hyperspherical radius to the Hankel alternative
view of Koopman analysis to construct a reduced-order linear system of eigen-time-delay
coordinates with an intermittent forcing. This intermittent forcing can signify precursors
to structural transitions in a probabilistic manner. We argue the similarity between thisintermittent forcing and the mechanical driving forces for structural transitions in clusters.
Keywords: Driving forces, Hankel alternative view of Koopman, Eigen-time-delay coordinates, Atomic clusters, Structural transitions, Hyperspherical radius

1. Introduction
Prediction of abrupt state transitions in chaotic dynamical systems attracts significant interest in nonlinear dynamics and data science. Examples are abundant in celestial mechanics,
turbulent dynamics, biological systems, and molecular dynamics. For an accurate prediction of state transitions, identification of precursors is important. Precursors are sometimes
associated with driving forces. This study thus explores driving forces for structural transitions in atomic clusters based on the methods of time series analysis [1, 2] and geometricmechanics [3].

2. Methods and results
Structural transitions of six-atom Lennard-Jones clusters in vacuum serve as a prototypical model of abrupt state transitions in chaotic dynamical systems throughout this study.
This cluster has two geometrically distinct local equilibrium structures, called OCT and
CTBP, corresponding to the minima of the total potential energy. When the total energy is
suﬃciently high, the cluster undergoes structural transitions between the two equilibrium
structures.

75

We apply the hyperspherical coordinates and take the largest hyperspherical radius among
the three, a1 (≥ a2 ≥ a3 ), as the collective variable that can characterize structural transitionsin the six-atom cluster. We then input the time series of the hyperspherical radius a1 (t),where t is time, into the procedure of the Hankel alternative view of Koopman (HAVOK)
analysis [1], and obtain a reduced-order linear model of diﬀerential equations,
)
)
(
(
d v1
v1
=A
+ Bv3 ,
(1)
v2
dt v2
where v1 and v2 are eigen-time-delay coordinates. v3 is an intermittent forcing derived fromthe data. The coeﬃcients A and B are 2 × 2 and 2 × 1 matrices respectively, which are
determined by a regression method called the sparse identification of nonlinear dynamicalsystems [2]. The intermittent forcing v3 showed some characteristic behaviors right before
structural transitions. For example, the signal of v3 tends to be strong in OCT right before
transitions into CTBP, and the signal of v3 tends to be weak in CTBP right before transitions into OCT. These characteristic behaviors could serve as precursors to the structuraltransitions in a probabilistic sense since they are faint requiring a statistical characterization.
We also argue the similarity and correspondence between v3 in Eq. (1) and mechanicalforces [3] in the classical (Euler-Lagrange) equations of motion for a1 ,
n−1
∑
d2 a1
∂VLJ
2
2
2
,
=
Γ(a
,
a
)ω
+
Γ(a
,
a
)ω
+
a
γ1k
−
1 2 121 3 13
1
2
∂a1
dt
k=4

(2)

where Γ(ai , a j ) is a function of hyperspherical radii, ωi j and γ1k are internal angular velocities, n = 6 is the number of atoms, and VLJ is the interatomic Lennard-Jones potential.
Physically, the first three terms on the right hand side of Eq. (2) are internal centrifugal
forces and the forth term is the potential force. We have evidenced that these mechanicalforces in Eq. (2) can drive structural transitions of clusters in a probabilistic sense. Moreover, behaviors of these forces were very similar to those of v3 in Eq. (1), indicating thatv3 could also be interpreted as a driving force mediating structural transitions. We finallypresent an analytical account for the similarity between v3 and the mechanical driving forces.
In summary, we have first reduced the dynamics of atomic clusters into a linear systemof eigen-time-delay coordinates with an intermittent forcing using HAVOK. We have thenevidenced the similarity between the intermittent forcing and the mechanical driving forces
for structural transitions in atomic clusters.

References[1] S. L. Brunton, B. W. Brunton, J. L. Proctor, E. Kaiser, J. N. Kutz: Chaos as an intermittently forced linear system, Nature Communications, 8:1 (2017), 1–9.
[2] S. L. Brunton, J. L. Proctor, J. N. Kutz, Discovering governing equations from databy sparse identification of nonlinear dynamical systems, Proceedings of the National
Academy of Sciences, 113 (2016), 3932–3937.

76

[3] T. Yanao, W. S. Koon, J. E. Marsden, Intramolecular energy transfer and the driving
mechanisms for large-amplitude collective motions of clusters, J. Chem. Phys., 130(2009) 144111.
[4] J. F. Gibson, J. Doyne Farmer, M. Casdagli, S. Eubank, An analytic approach to practical state space reconstruction, Physica D, 57 (1-2) (1992) 1–30.

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Multiagent simulation of infectious propagation of
COVID-19
Jin Suzuki1 and Atsushi Tanaka2,*
1,2 Graduate School of Science and Engineering, Yamagata University∗ tanaka@yamagata-u.ac.jp

Abstract. In this paper it is investigated how the COVID-19 infectious disease spread using
multiagent simulation. Simulation spaces are a building for a closed space and a park for an
open space. And three kinds of infectious forms, air, contact and droplet are compared. As
a result, it is confirmed that the more the density of people is higher, the more the infection
increases significantly. The consideration of effective vaccination of COVID-19 is expectedin the future.
Keywords: COVID-19, Infection, Multiagent simulation

1. Introduction
The fury of COVID-19 originated in Wuhan, China in November 2019 has been spread
rapidly all over the world and we can say it is the pandemic situation without no doubt. Recently some vaccines have been developed and vaccinations in many countries have started
though, they are not enough yet and the emergence of some strong variant strains stir up
our anxiety. It is well-known that infections of COVID-19 spread mainly by air, contact anddroplet, and some aspects of droplet have been visualized by supercomputer “FUGAKU”[1].
In addition, studies of COVID-19 have been very active and wide-ranging, they include not
only viruses themselves but also information propagation of them[2, 3]. Though Japanese
government is stepping up efforts to stem the tide of people for the prevention of infection,
the situation has not been made the desired progress and the state of emergency has been
invoked three times so far. Thus it is investigated how the infection spread by the flow ofpeople using multiagent simulation. From the simulation results, it is verified the higher
human density becomes, the higher the risk of infection arises.

2. Simulation procedure
2.1.

Simulation framework

Multiagent simulation is a framework which consider a lot of moving around particles as
autonomous agents. It can enumerate human activities and many behaviors of things in78

Figure 1: Overview of the park space. There locates a monument at the center. There arealso some chairs in the park.
broad perspective, so it is one of the powerful simulation methods. Its applications covera broad range of topics like traffic congestion, evacuation behaviors, offensive strategy etc.
The more precisely we describe it, the more complicated its coding tends to be. Therefore
we make use of time-tested multiagent simulation framework called as “Artisoc” in thisstudy[2]. Though it is free software, we can describe the situation very precisely and carryout simulation easily.

2.2.

Simulation settings

We consider three kinds of virus infection modes, air contact and droplet. Here we enumerate simulation settings roughly as follows.
• 20 % of infected person spread virus all over.
• For every agent its age and immunizing power are configured. Its power and whether
they notice symptom or not depend on their ages.
• In contact infection case, the infection rate arises when the agent contacts infectedone.
• In air and droplet infections, the infection rate arises when there exits virus at theposition of the agent.
We study two models for simulation spaces, a building and a park. The former is a threestory closed space without any obstacles. The later is an open space though, there locates amonument and some chairs everywhere(Fig.1). We carry out all simulations 10 times andaverage them.

79

0.4

0.4

Air
Contact
Droplet

0.35
0.3

0.3
Infection rate

Infection rate

Air
Contact
Droplet

0.35

0.25
0.2
0.15

0.25
0.2
0.15

0.1

0.1

0.05

0.05

0

0
0

2

4

6
8
Density

10

12

14

0

(a) Building model

2

4

6
8
Density

10

12

14

(b) Park model

Figure 2: Density correlation of infection rate. We can easily find the more density is high,the more the infection rate will arise.
0.4

0.4

Air
Contact
Droplet

0.35
0.3

0.3
Infection rate

Infection rate

Air
Contact
Droplet

0.35

0.25
0.2
0.15

0.25
0.2
0.15

0.1

0.1

0.05

0.05

0

0
0

50

100

150

200 250
Time

300

350

400

0

(a) Building model

50

100

150

200 250
Time

300

350

400

(b) Park model

Figure 3: Time evolution of infection rate. In the building, the infection by touch spreadwidely, while in the park, the infection through air spread significantly.

3. Numerical results
Since the risk of infection is said to become higher if many people pack at some place, weinvestigate the relation of packing density and infection rate in detail at first(Fig.2). In thisfigure, the horizontal and vertical axes show the number of persons in 100 cells and theinfection rate respectively. For both building and park models, we investigate infection rates
in three kinds of infection modes.
Then we show time evolutions of infection rates for each case in Fig.3. Here time meanscomputational steps in simulation, and corresponds to the speed of human walk.

4. Discussion
4.1.

Correlation between density and infection rate

In the contact mode, the infection rate is higher for high human density. In the air mode, isis relatively higher for high human density in the park model. That is because they always
spread virus to the space, then the area of high virus density become large. On the contraryin the droplet mode, it is relatively low comparing with other two modes, and its fluctuation80

is also small all over. That is because viruses in the space are localized, and so they are hardto spread.

4.2.

Time evolution of infection

In the contact mode, the increasing rate is high in the building model, while it is low in thepark model. That is because in the latter case, the human population increases and decreases,
and so most contacts relatively new ones and the infection probability is hard to increase.
In the air mode, the increasing rate of infected person is high in the park model. That is
because the infection probability of newly entered agents becomes higher because the areaof viruses in the space becomes larger. At last in the droplet mode, it increases slightly inthe building model, while it is almost constant in the park model. That is because uninfectedagents rarely pass through infected area because virus becomes more localized and some
infected agents go out naturally. On the contrary, in the building mode, the space is closed,
so it increases a little higher.

5. Summary
In this paper it is investigated how the COVID-19 infectious disease spread using multiagent
simulation. Simulation spaces are a building for a closed space and a park for an open space.
And three kinds of infectious forms, contact, air and droplet are compared. As a result, it
is confirmed that the more the density of people is higher, the more the infection increases
significantly. For the future work, we would like to investigate several other spacial models
and take the diversity of agents into account. Moreover since the vaccinations of COVID-19
have started in many countries, we will investigate which agent is the most effective to be
vaccinated for the control of virus diffusion.

References[1] Makoto Tsubokura: Droplet/Aerosol Dispersion Simulation on Supercomputer Fugaku for the Fight against COVID-19, IPSJ MAGAZINE, 62:2 (2021), 64–66.
[2] J. Zarocostas: WHO’s newly launched platform aims to combat misinformation
around COVID-19, www.thelancet.com, 395 (2020), 676.
[3] Atsushi Tanaka and Fujio Toriumi: Characteristics of Information Propagation in
COVID-19 Crisis, Proc. Int. Symp. on Nonlinear Theory and its Application, (2020),
54–57.
[4] https://mas.kke.co.jp/en/.

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A prediction algorithm of drosophila lifespan toward
high-throughput screening in genetic research
Masaya Hata1, Ki-Hyeong Seong2, Siu Kang1*
1

Department of Bio-Systems Engineering, Graduate School of Science and Engineering, Yama-gata University
RIKEN cluster for Pioneering Research, RIKEN Tsukuba Institute (Current affiliation: Insect
Design Technology Group Division of Insect Advanced Technology Institute of Agrobiological
Sciences, NARO)
2*siu@yamagata-u.ac.jp

Abstract. Drosophila has been often used in genetic research field. We tried to predict
lifespan of individual drosophila through the combination of image processing and deeplearning by convolutional neural network. As a result, 68% of flies predicted by the algorithm
showed 10% consistency compared with manual detection of actual lifetime measured by anexperimental expert. It is expected that the present result contributes to high-throughput
screening in gene- and drag-discovery related with the extend of lifespan.
Keywords: Biological image analysis, Machine learning, Deep neural network

1. Introduction
Drosophila is model animal in genetic research filed and the insect has been frequently
used in screening through several gene manipulation such as gene knock-in/out, etc. It has
been well known that drosophila preserve many parts of disease-related genomic sequencessame as the ones in human being. So, searching and examining the disease-related phenotype
in drosophila directly contributes to human health and promotion of quality of life in humansociety.
We previously developed the drosophila individual activity monitoring and detection system (DIAMonDs) toward high-throughput screening related with drosophila life-events [1].
The system provides automatic and high-accurate detection of drosophila life-events such as
pupariation, eclosion, and death with single animal resolution.
In the present study, we tried to develop an prediction algorithm of drosophila life-span justthrough the time-lapse images of drosophila population.

2. Method
2.1.

Time lapse images of drosophila population

We scanned the drosophila population images on the plate in an incubator. Sequential images were obtained with 1 minute intervals for about 40 hours. An image includes 288 wellswith adult drosophila (Fig 1a). All the image acquisition process was performed at RIKEN

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Tsukuba Institute.

2.2. Pre-processing for learning
Pre-process for the learning of life-span prediction is as follows:First, all the images are separated into patch images with 56 x 56 pixel including an adultdrosophila in a well (Fig 1b).
Second, all animal bodies were detected as binary labeling through the animal body detection algorithm we previously developed (Fig 1c, [1]).
Third, as training/test data for learning, the image subsets of 50 frames were prepared withsliding window without overlapping (Fig 2). The extraction in all the animals was performed
until just before the death timing of an individual showing a minimum lifespan.

Fig 1

Time lapse image of drosophila population and an example of binary label

Fig 2

Extraction of subset images as training data83

JSST 2021

2.3. Learning for prediction
The deep neural network was trained for the image subsets described in previous section.
The structure of the network was shown in Fig 3. Animal population was separated into train
and test data with 9:1. Each animal has 4,420 image sequences and each sequences includes
50 frames. Training was performed for 1,500 epochs with 128 batch size, Adadelta as optimizer, and Huber loss function. In inference phase after the training, the network predicted
the remaining lifetime of individual drosophila.

Fig 3

Network architecture for lifespan prediction

3. Results
Fig 4-6 show scatter plots for comparison between actual- and predicted-lifespans obtainedby binary-, segmented- and original-images, respectively. Segmented images were obtainedby convolution between binary- and original-images. A prediction accuracy was characterized
as root mean square error (RSME) between actual- and predicted-lifespans. An accuracy of
predictions from original image showed higher accuracy than the prediction from binary image.

Fig 4

Prediction from binary images

Fig 5

84

Prediction from segmented images

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Fig 6

Prediction from original images

4. Conclusions
In the present study, we tried to predict drosophila lifespan by performing image analysis
and deep learning onto the time lapse image of drosophila population. As a result, more thanhalf percent of individuals was predicted with high accuracy compared with actual lifespans.
It was also revealed that segmentation before learning leads to the decrease of accuracy oflifespan prediction. In order to improve the prediction accuracy, network architecture andpre-processing should be modified in future study.

Reference[1] K.H. Seong, T. Matsumura, Y. Shimada-Niwa, R. Niwa, S. Kang (2020) “The Drosophila
Individual Activity Monitoring and Detection System (DIAMonDS)”, eLife, DOI:
10.7554/eLife.58630

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JSST2021

New semi origami structure for collision energy
absorption and its manufacturing method
Yang Yang1*, Ichiro Hagiwara1
Institute for Advanced Study of Mathematical Sciences, Meiji university, Japan University

1*

piscesyy0227@gmail.com

Abstract. FCM(Full cut member) is shown to have splendid performance for the truck crash
box and the simulation method is developed for its devised manufacturing method. Applying
this simulation model to the crash model with 3mm thickness shows the thickness distribution
is very small. The performance for the collision energy absorption from the model gained bymanufacturing simulation is better than the one from the model with constant plate thickness
gained by CAD in terms of much lower initial peak load and almost same energy absorption.
Keywords: Full cut member, Half cut member, Crash box, Liquid press manufacturing method

1. Introduction they work effectively
Origami structures are splendid also for collision energy absorption and there are 3 types oforigami structures. One is 4 folding lines such as bellows fold which are studied by Zhonggroup. On the other hand, 6 folding lines such as RSO and RTO which are studied by Hagiwara
group. The 3rd one is semi origami structures such as HCM and FCM which are studied also
by Hagiwara group. Although origami structure such as RSO (Reversed Spiral Origami structure) has splendid performance also for crash energy absorption [1], it is difficult to develop
inexpensive and excellent manufacturing technology for the origami structure. We have developed the inexpensive and excellent manufacturing technology named “Partially heated torsion
manufacturing method” for RTO (Reversed Torsion Origami structure” [2] which has been developed to imitate RSO. It has also shown the excellent absorption performance with a half cut
type member (HCM) [3] which can be placed as a semi origami structure of which reason will
be described below. Here full cut type member (FCM) is developed by extending the HCM andis discussed how FCM works effectively to the truck crash box. And, it is discussed about the
manufacturing technique for the FCM.

2. Truck crash box
The vehicle crash boxes are set between the bumper and side members so that only bumper andcrash boxes are deformed for the light collision. In this case, the bumper and the crash boxes
are replaced which leads an advantage over automobile insurance. The performance expected
for the crash box is that over a certain limit energy absorption, below a certain level initial peak86

JSST2021
load and it is collapsed from the tip to the back in order. Beads which consist of cut and protrusion structures are properly placed on the crash boxes so that it can be elapsed in the axis
direction without bending. However even though this ideal collapsed mode is achieved, it iscollapsed only 70% of its length due to its bulkiness and the initial peak load is too high whichbrings sometimes the dangerous situation to the passengers. It is very effective the origami
structures to solve these problems where most of researchers use the 4 folding lines such as
bellows fold with 4 lines at every intersection on the other hand our group uses the 6 folding
ones such as RSO and RTO with 6 ones at every intersection. The advantages of origami structures especially with RSO and RTO are as follows;1) folding lines on the side of the column
which guides to the collapse in the axial direction,2) receiving vertical loads diagonally which
guides initial peak load below a level,3) setting the layers which prevents the lowered crosssection size too large,4) keeping the foldable condition at each intersection. The FCM shownin Fig.1 to consider here does not charge only No.4) as well as the HCM so that they are positioned to be semi origami structures. As shown in Fig.1, the cross section is symmetry and it isshown that centered angle of quarter section is divided n equally for n=6 in Fig.1. The radii(𝑟1 , 𝑟2 , 𝑟3 , 𝑟4 , 𝑟5 ) from the center to the key points are selected as shape parameters. The column
is divided N equally along the axis direction and for segment difference on even number crosssections the radii have different ∆ each from (𝑟1 , 𝑟2 , 𝑟3 , 𝑟4 , 𝑟5 ) as shown in Fig.2. The targets
are as follows; 1) weight to be below 5.04Kg for current weight 5.6Kg 10% or less),2) crush
mode: collapse from the tip,3) energy absorption: 70KJ or more for current 76KJ,4) peakload:335KN or less for current 10% or less.

3. Study on collision simulation
3・1 Simulation method
Rectangular shell elements are used for crash box, the number of nodes is 5836 and the numberof elements is 6178. The rigid wall is fixed completely and the frontend cross section has only
degree of freedom perpendicular to rigid wall. The initial velocity is 56km/h. Vehicle weight
3000kg is given on the rear end face. The contact surface with coefficient of friction 0.1 isdefined between crash box model and the rigid wall. The material of crash box is SPCE coldrolled steel sheet of which density is 7.85*10-6kg/mm3，Young modulus is 206Gpa，Poisson
ratio is 0.3 and yield stress is 215Mpa. LS-DYNA is used for the simulation.
3・2 Simulation results
3・2・1 Study on cross section shape
Fig. 1(a) shows FCM with 7 layers and ∆= 0. Fig.1(b) shows the Model (1) of cross section
shapeis controlled by changing (𝑟1 , 𝑟2 , 𝑟3 , 𝑟4 , 𝑟5 ). (𝑟1 = 50.92𝑚𝑚, 𝑟2 = 44.39𝑚𝑚, 𝑟3 =35.27𝑚𝑚, 𝑟4 = 32.56𝑚𝑚, 𝑟5 = 28.61𝑚𝑚 ) and volume reduction rate is 20%. With thismodel, it is collapsed from the tip.
3・2・2 Study on segment difference
Based on FCM, the nodes on the odd cross sections are constant and the segment differences∆= 10% of each radius length are given to the nodes on the even cross sections. As a result，
the shape along the axis direction is valley-mountain-valley as shown in Fig.2 where the segment difference on the 2nd and 4th cross sections. Weight, collision energy absorption andinitial peak load are summalized for each case in Table1. This concludes segment difference iseffective to collapse mode control and gives good influence for reaction load.

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(a)
Fig.1

Axial direction(b) Cross section

Different cross-section shapes by changing the lengths of 𝑟1 , 𝑟2 , 𝑟3 , 𝑟3 , 𝑟4 , 𝑟5 .

Fig.2
Model (2) of different section shapes by setting the division section along the axial direction. V
means valley and M means mountain.

Table 1
Structure

Comparison results of different cross-section shapes

Thickness

Mass

Peak

EnergyEnergy

Front

[mm]

[kg]

force[kN]absorption

absorption/M

collapse[KJ]

ass[KJ/kg]

Original (1)/CAD data

3.5

5.6

372

76

13.5

〇

Original (2)/ CAD data

3.0

4.8

320(〇)

64

11.9

〇

Model (1)/ CAD data

3.0

4.1(〇)

286(〇)

72(〇)

17.5

〇

Model (2)/ CAD data

3.0

4.2(〇)

294(〇)

75(〇)

17.9

〇

Model (3)/Simulation data

3.0

4.2(〇)

272(〇)

70(〇)

16.7

〇

4. Liquid press manufacturing method
FCM can be manufactured by liquid press manufacturing method in the flow of the following(1) to (4)as shown in Fig.3．
（1）Square pillar material is closed on both sides by round core bar and fixing metal fittings.
Liquid is filled in the square pillar material through the centered hole of the round core bar．
（2）Square pillar material filled with liquid is installed on the mold and it is molded bypress.
（3）The mold is opened. The molded material is pulled out and the liquid inside is takenout.
（4）At last, unnecessary parts of both ends of the forming product are cut and crush box is
generated．

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We have developed the simulation technique for the liquid press manufacturing method [14].
Using this technique to the model in Fig.2. As a result, the maximum and the minimum thickness are 3.5mm and 2.5mm so that plate thickness change is within 16.7%. The FCM of Model(3) based on the manufacturing results has the almost same performance as the one based on
CAD as shown in Table1.

Fig.3

The proposed manufacturing method.

5. Conclusion
Here FCM is shown to have splendid performance for the truck crash box and the simulation
method is developed for its devised manufacturing method. Applying this simulation model tothe crash model with 3mm thickness shows the thickness distribution is within 16.7%. The
performance for the collision energy absorption from the model gained by manufacturing simulation is better than the one from the model with constant plate thickness gained by CAD interms of much lower initial peak load and almost same energy absorption. In the near future
the manufacturing equipment will be developed based on this manufacturing method.

References[1] I. Hagiwara, S.Nadayosi, Folding Process of Cylindrical Structures Using Origami Model.,International Journal of Automotive Engineering, Vol.34, No.4 (2003), pp.145-149 (inJapanese).
[2] D. Liang, Y. Yang, C. Kong, Y. Jing, W. Zhao, X. Zhao, I. Hagiwara, Reversed Torsion Type
Crash Energy Absorption Structure and Its Inexpensive Partially Heated Torsion Manufacturing Method, Transactions of the JSME，Vol.87, No.895 (2021-3), p. 20-00425.
[3] X. Zhao, ,Y. Hu, I. Hagiwara, Study on Crash Characteristics of Energy Absorption Abilityof Half Cut Type Vehicle Side Member Structure by Using Origami Engineering, Transactionsof the JSME, Series A,Vol.76, No.769 (2010-9), pp.1131-1138.
[4] Hagiwara, I., M., Tsuda, M. and Kitagawa, Y., Method of Determining Positions of Beads,
Japanese Patent, Patent Number JP2727680B2 (1991).

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Development of a Pattern for Continuous Manufacturing
of Complex 3D Shapes with Kirigami Honeycombs
Luis Diago1,2,* , Junichi Shinoda2 , Ichiro Hagiwara1
1 MIMS, Meiji University
2 Interlocus Inc∗ luis_diago@meiji.ac.jp

Abstract. Recent developments show that honeycomb structures built by a continuous production process can be successful in industrial applications at different
scales (from nanosciences to aerospace applications) because of their material savingsand low weight; while maintaining the mechanical properties required in the application. However, these properties cannot be well exploited when the three-dimensional
shapes to be built have complex geometries because the theory supporting the production process is centered on an axial slice and two two-dimensional curves forthe representation of the three-dimensional shapes. This work extends the range
of applications of the technology by means of a new design methodology based on
the constructive geometry of solids that allows combining the hexagonal honeycomb
cell into complex three-dimensional structures by means of boolean operations while
maintaining an optimal utilization of the material within a continuous production
process.
Keywords: Kirigami honeycombs, manufacturing, constructive solid geometry

1.

Introduction

The term ”kirigami honeycomb” was introduced by Nojima and Saito in [1] where
they use the cross section of the 3D shape to describe the panel and include cuts inthe pattern to obtain its 3D structure. Then, they generalized the method ([2], and[3]) from the representation of 3d shapes by means of two curves in the cross sectionof the shape ([2]) and with a mapping to polar coordinates ([3]) to represent curved
shapes in the direction perpendicular to the cross section. Recently, Caslish andGershenfeld ([4]) designed a continuous folding machine to construct the Kirigami
patterns obtained by the previous method. However, the use of the two curves in
the cross section of the shape limits the representation of more complex shapes. In
our proposal, the design method is generalized for more complex shapes based on
3 fundamental contributions: 1) the need to represent the shape by 2 curves in the
cross section to represent any 3D shape is eliminated, 2) the ”honeycomb cores” are90

embedded in the 3D shape by means of boolean operations on the 3D shape and 3)
an optimal method of assigning folding lines, cutting and gluing areas was developed
for the manufacturing of the panel. In the following the main approach is detailed.

2.

Materials and Methods

In [3], Saito, Fujimoto, and Okabe tried to expand the number of shapes to representby transforming the coordinates from the pattern to the polar system. In this way
they could scale the width and height of the pattern in the direction perpendicular tothe cut cross section of the shape. However they can only represent scaled versionsof the 2 curves of the cross section. Saito, Peregrino and Nojima [2], said that it is
impossible to fold non-convex unit cells from a single paper because the total angles
surrounding a slit edge are over 360 degrees, so the slit with has a negative value andthe paper will overlap at the slits. Similar to Caslish and Gershenfeld ([4]), to ensurethat no sections of the folding pattern overlap, we first calculate the height values(max-min) a′i, j , b′i, j , c′i, j , di,′ j based on the five faces of the unit cell. Then we calculate
column-wise shifts wi and vi such that ai, j = a′i, j + wi , bi, j = b′i, j + wi ,ci, j = c′i, j + vi , anddi, j = di,′ j + vi determine a non-overlapping pattern. To guarantee no overlaps occur inthe pattern, Caslish and Gershenfeld ([4]) set v0 = w0 = 0 and calculate recursively:′
wi = max(di1,j − ai, j ) + wi1(1a)vi = max(bi, j − ci, j ) + wi

(1b)

Instead of using above equations, in our approach we use the following two-stepalgorithm to avoid overlap and minimize the amount of un-used materials in the
final pattern. The algorithm 1 can work with any solid model and the pattern is
Algorithm 1 Two-step Algorithm to minimize the amount of un-used materials
1: procedure createPattern(model, C, Dir) ▷ The 3D model, cell size and direction
2:
bbox ← model.BoundBox
3:nx ← bbox.XLength/C√4:ny ← 3 ∗ bbox.Y Length/(3 ∗ C)
5:
for i = 0 to nx do
6:for j = 0 to ny do▷ First pass
7:
Compute min-max of 5 faces in Cell j (a’,b’,c’,d’)8:Compute Cell j .BoundBox
9:
Update Columni .BoundBox with Cell j .BoundBox
10:
11:
12:
13:
14:

for j = 0 to ny do▷ Second pass
Fk ← Create 5 faces in Cell j
Pk ← model.common(Fk )▷ Boolean operation
Pattern ← Pk .rotate(Dir)▷ Update the pattern
Optimize Pattern with Pattern.BoundBox, Glue, Mountain & Valley lines

automatically computed by the boolean and rotation operations in steps 12 and 13.

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3.

Preliminary Results

The proposed Algorithm 1 have been programmed in Python version 3.8.6 within
FreeCAD Version 0.19.23578 and macOS High Sierra (10.13). Figure 1 shows andexample of a honeycomb created with the Stanford Bunny1 using 3 diferent directions(x, y, z). The dimensions of the model are 86.33mm x 66.71mm x 85.21mm and thesize of the file is 25.3MB. The cell size used for the experiment was 10mm. The
upper panels show the top view of the model and the lower part shows the isometricview of the created honeycomb model for each direction. Figure 2 shows the patterngenerated for Z direction.

x

y

z

Figure 1: Example of Bunny in 3 directions.

4.

Conclusions and Future works

Kirigami, a traditional Japanese paper-cutting art, has also proven its worth inorigami engineering by cutting a portion of the paper to increase the degree of freedom in molding. Honeycomb has been recognized as an excellent structure since thetimes of Greece and Rome, but the method of mass production of honeycomb wasdeveloped in England during WWII with a touch of Japanese Tanabata decoration,
sparking the birth of origami engineering. The degree of freedom of molding increased, and if a complex structure could be formed continuously, a strong structure
was possible, but there was a problem. This work showed that any structure can1

the solid model is avalilable at https://grabcad.com/library/stanford-bunny-solid-model/files

92

Figure 2: Example of pattern generated for Z direction.
be made in one piece, which can be called a meta-material thanks to the solution
proposed in this paper. Currently, a continuous cutting, gluing and folding machineis under development for manufacturing the designed patterns.

References[1] Nojima, T., and Saito, K. Development of Newly Designed Ultra-Light Core
Structures, JSME Int. A 2006, 49(1), pp. 38–42. doi:10.1299/jsmea.49.38[2] Saito, K., Pellegrino, S., and Nojima, T. Manufacture of Arbitrary Cross-Section
Composite Honeycomb Cores Based on Origami Techniques. ASME. J. Mech.
Des. May 2014; 136(5): 051011. doi:10.1115/1.4026824[3] Saito, K, Fujimoto, A, and Okabe, Y. Design of a 3D Wing Honeycomb Core
Based on Origami Techniques. Proc. of the ASME IDETC/IEC. Volume 5B:
40th Mechanisms and Robotics Conference. Charlotte, North Carolina, USA.
August 21–24, 2016. V05BT07A026. ASME. doi:10.1115/DETC2016-60419[4] Calisch, SE, and Gershenfeld, NA. Towards Continuous Production of Shaped
Honeycombs. Proceedings of the ASME 2018 13th International Manufacturing
Science and Engineering Conference. Volume 3: Manufacturing Equipment andSystems. College Station, Texas, USA. June 18–22, 2018. V003T02A007. ASME.
doi:10.1115/MSEC2018-6646.

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3D structural form creation of earwig fan using thealgorithmic design toolKazuya Saito1*, Chisaki Kitajima2
Faculty of Design, Kyushu University
Graduate School of Human-Environment Studies, Kyushu University*k-saito@design.kyushu-u.ac.jp
12

Abstract. Earwigs can fold their wings most compactly among insects, therefore have the large
potential for engineering applications. The previous study has clarified the method of designing
the crease pattern of this earwig fan. Here we show the method to create new three-dimensional
forms of the earwig fan by simulating their folding process with the algorithmic design tool.
The result enabled to create a compact deployment structure with a frame and hinges, and todesign dome shape structures based on earwig fan folding.
Keywords: Algorithmic design, Biomimetics, Folding Simulation, Origami

1. Introduction
Technology used to fold large structures into compact shapes are needed in a variety of products
from daily use articles like umbrellas and folding fans to solar battery panels on satellites. In nature,various organisms have been tackling the same problem as represented by insect wing folding.
These naturally developed structures are interesting research targets from the viewpoint of biomimetics. There is a wide variety of ways that insects store their wings, but the most compact andcomplex folding patterns can be founded in the hind wings of earwigs. The special folding process reduces surface area ten to 15 times or more depending on the species [1]. Authors revealed that the complex folding pattern of these earwig fans can be reconstructed by very simple
geometric rules [2]. The proposed design software enables to customize the fan shape into various
shapes [3]. However, to apply the earwig fan to the actual deployed structures, it is necessary tocorrectly design not only the crease pattern but also the shape and arrangement of the hinge andframe. In addition, the proposed design software could only output 2D crease patterns, and expansion to 3D structures such as domes or parabolic surfaces was a challenge.
Here we show the method to design earwig-fan based 3D deployable structures by using the algorithmic design tool. The proposed software can simulate the 3D shape in the folding process, enabling to design shapes and positions where the frame and hinges do not interfere, and to customize
the pattern to the dome shapes.

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2. Folding Simulation of Earwig Fan
We developed the design software using Rhino 7 (Robert
McNeel & Associates) and Grasshopper [3]. A customized code was used to simulate the folding process of the
input crease pattern. By placing the hinge parts on thesimulated fold lines, it is possible to prevent the hinges
from colliding during the folding process (Fig. 1).

3. Earwig Fan DomeBy cutting out a part of the crease pattern and introducing vertices smaller than 360 degrees, it is possible togive a positive curvature to the earwig fan and make it adome shape. Here, by cutting out so that the folding conditions are maintained, it is possible to construct the deployable dome structure. We improved the design soft- Fig. 1
Folding simulation of theware and made a code to design the shape of this earwig earwig fan.
fan dome (Fig. 2). By using this software, it is possible
to design a deployment dome with a specified diameterand height.

4. Conclusion
We created a new three-dimensional form of the earwig
fan by simulating the folding process of the earwig wing
fan with the algorithmic design tool. The result enabled
to create a compact deployment structure with a frame
and hinges, and to design a dome shape based on earwig
fan folding.

Fig. 2
dome.

Designing of Earwig fan

Acknowledgements
This work has been partially supported by JST FOREST (Grant Number JPMJFR203E4).

References[1] K. Saito, et al.: Earwig fan designing: Biomimetic and evolutionary biology applications,
Proceedings of the National Academy of Sciences, 117(2020), 17622-17626.
[2] K. Saito et al.: Earwig fan designing: biomimetic and evolutionary biology applications,
Open Science Framework. https://osf.io/j9ufg/. Accessed 25 June 2020.dd[3] R. McNeel, Grasshopper (2014). https://www.grasshopper3d.com/. Accessed 18 May
2020.

95

JSST 2021

Performance evaluation of wave-sound analysis code:
ADVENTURE_Sound
Akihiro Kudo, Amane Takei2
1

Department of Engineering for Innovation, Tomakomai Collage, Japan
2

Faculty of Engineering, University of Miyazaki, Japan*

kudo@tomakomai-ct.ac.jp

Abstract. In this presentation, a performance evaluation of a wave-sound analysis code basedon an iterative domain decomposition method is explained that is named ADVENTURE_Sound. A wave-equation for the wave-sound analyses is solved taking a speed
potential as an unknown function. In this code, an iterative domain decomposition
method is employed as a parallel technique. To solve subdomain problems by the direct
method, the direct method based on the LDLT decomposition method is introduced . In
this paper, some numerical results are discussed in the view point of a performancefor parallel computing environments.
Keywords: wave-sound analysis, Parallelized finite element method, Domain decomposition
method, ADVENTURE_Sound.

1. Introduction
A wave-sound analysis based on a numerical analysis method, such as the finite element method, has become widespread due to recent improvements in computer performance and numerical calculation technology. In the case of accurately reproducing
an analysis model of complicated shape, it is necessary to use many small the elements.
In the case of analyzing the state of wave-sound propagation in a wide range, a wide
analysis domain is examined. Furthermore, to perform a high-accuracy analysis, it isnecessary to model the analysis domain with a sufficiently small element for the wavelength, and, in this case, the number of elements also increases. Increasing the number of elements increases the scale of the problem. Therefore, a method that can calculate large-scale problems has come to be demanded. Moreover, large-scale problems
must be solved with high accuracy. In the presentation, a large-scale analysis code:
ADVENTURE_Sound is introduced, and some numerical result in the performance
evaluation for the parallel computing environment: Workstation Cluster is shown.

2. Governing equations and algorithm for parallel computing
In ADVENTURE_Sound, the wave-sound analysis is considered. To derive a weak form, the Galerkin method is applied to the Helmholtz equation [1]. The finite element approximation and discretized,
the following equation is obtained:∇𝛷 ∙ ∇𝛷 ∗ 𝑑𝛺 −𝑗𝜔𝜌𝑍𝛷 𝛷 ∗ 𝑑𝛤 − 𝑘2𝛷 𝛷 ∗ 𝑑𝛺 = 0.

(1)𝛺where 𝛷 is the speed potential that is the unknown function. 𝑘 and 𝜔 are the wave

96

JSST 2021

number and angular frequency, 𝜌 is the medium density, and 𝑍 is the specificacoustic impedance.
The equation contains complex numbers and becomes a complex symmetric matrix. In
the present study, the speed potential 𝛷 is obtained using the conjugate orthogonal
conjugate gradient (COCG) method. The finite element approximation (1) is rewritten as
𝐾𝑢 = 𝑓 by the coefficient matrix 𝐾, the unknown vector 𝑢, and the right-hand side vector 𝑓.
Next, Ω is divided into 𝑁 subdomains (Eq. (2)). Eq. (3) and (4) are obtained from Eq. (2) [2].
( )

0
0
⎡ 𝐾
0
⋱
0
⎢
( )
⎢
𝐾
⎢
0
0
⎢ ( ) ( )⋯ 𝑅( )𝐾 ( )
⎢𝑅 𝐾
⎣
() ()

𝐾 𝑢

𝑅

()

=𝑓
𝐾

()

()

() ()

−𝐾 𝑢

−𝐾

()

𝐾

()

𝐾

( ) ( )

𝑅
⋮

⎤ ( )
( )
⎥ ⎡𝑢 ⎤ ⎡𝑓 ⎤( ) ( )⎥⎢ ⋮ ⎥ ⎢ ⋮ ⎥𝐾 𝑅⎥ ⎢ ( ) ⎥ = ⎢𝑓 ( ) ⎥⎥⎥ ⎢𝑢 ⎥ ⎢() () () ⎣ 𝑢 ⎦⎣ 𝑓 ⎦𝑅 𝐾 𝑅 ⎥⎦

(2)(𝑖 = 1, … , 𝑁)
𝐾

()

𝑅

()

(3)

𝑢 =

𝑅

()

𝑓

()

−𝐾

()

𝐾

()

𝑓

()

()

(4)
()

where 𝑓 ( ) is the right-hand vector for 𝑢 , and 𝐾
is the inverse matrix of 𝐾 . Equation(4) is referred to as an interface problem and is an equation for satisfying the continuity between
domains in the domain decomposition method. For simplicity, rewrite equation (5) as follows:
𝑆𝑢 = 𝑔,𝑆=()

𝑅 𝑆( )𝑅(), 𝑆( ) = 𝐾

()

−𝐾

()

𝐾

()

()

𝐾 .

(5)

3. Numerical example
For examining ADVENTURE_Sound on a real-world problem, we model the environment of
acoustic experiments. The computations are performed on a 16-node (62-core) PC cluster (Intel(R) Xeon(R) CPU E5-2650L; 1.80 GHz; L2 20480 KB) with 32 GB RAM per node. The
simulation statistics and the numerical are shown in Table 1 and 2, respectively. More detailthins will be shown at the conference.
Table 1 Simulation Statistic
Frequency
No. of Elements
No. of DOF

No. of cores per node
No. of nodes

442[Hz]911,133
1,249,959
10-node workstation cluster with Intel(R) Xeon(R) CPU E52650L, 1.8 GHz
16
8Main memory per node

32 [GB/node]

Platform

Table 2 Numerical result
Elapsed time
Memory requirements

509.153 [s]0.26 [GB/node]

References[1] A. Takei, A. Kudo: Over 100 million degrees of freedom scale wave sound analysis
based on parallel finite element method, JSST, 12:2 (2020), 76-84.
[2] A. Takei, S. Sugimoto, M. Ogino, S. Yoshimura, H. Kanayama: Full wave analyses ofelectromagnetic fields with an iterative domain decomposition method, IEEE Trans. on
Magn., 46:8 (2010), 2860-2863.

97

JSST 2021

Development of Huge-Scale Microwave
analysis code: ADVENTURE_Fullwave
Amane Takei1
1

Faculty of Engineering, University of Miyazaki, Japan*takei@cc.miyazaki-u.ac.jp

Abstract. In this presentation, a huge-scale microwave analysis code based on an iterative domain decomposition method is explained that is named ADVENTURE_Fullwave. A stationary vector wave equation for the high-frequency electromagnetic field analyses issolved taking an electric field as an unknown function. Then, to solve subdomain problems by the direct method, the direct method based on the LDLT decomposition method
is introduced in subdomains. The simplified Berenger’s PML is introduced which theseeight corners are given the average value of all PML’s layers.
Keywords: Microwave analysis, 𝐸 method, Parallelized finite element method, Domain decomposition method, ADVENTURE_Fullwave.

1. Introduction
Electromagnetic field analysis based on a numerical analysis method, such as the finite element method, has become widespread [1] due to recent improvements in computer performance and numerical calculation technology. In the case of accurately reproducing an analysis model of complicated shape, it is necessary to use many small
the elements. In the case of analyzing the state of electromagnetic waves propagation
in a wide range, a wide analysis domain is examined. Furthermore, to perform a highaccuracy analysis, it is necessary to model the analysis domain with a sufficiently
small element for the wavelength, and, in this case, the number of elements also increases. Increasing the number of elements increases the scale of the problem. Therefore, a method that can calculate large-scale problems has come to be demanded. Moreover, large-scale problems must be solved with high accuracy. In the presentation, alarge-scale analysis code: ADVENTURE_Fullwave is introduced, and detail of the parallel algorism is shown.

2. Governing equations and algorithm for parallel computing
In ADVENTURE_Fullwave, the full-wave analysis based on an 𝐸 method [1] is considered. 𝐄! and 𝐉" are finite element approximations of electric field 𝐄 [V/m] and current density 𝐉 [A/m2], respectively. The permeability is given by 𝜇 = 𝜇# 𝜇$ [H/m], 𝜇#is the vacuum permeability [H/m], and 𝜇$ is the relative permeability. The complex
permittivity is given by 𝜀 = 𝜀# 𝜀$ − 𝜎⁄𝑗𝜔 [F/m], 𝜀# is the vacuum permittivity [F/m],
𝜀$ is the relative permittivity, and 𝜔 is the angular frequency [rad/s]. The following
equation is the finite element equation to be solved:" (1⁄𝜇)rot𝐄! ∙ 𝑟𝑜𝑡𝐄! ∗ 𝑑𝑣 − 𝜔$ " 𝜀𝐄! ∙ 𝐄! ∗ 𝑑𝑣 = 𝑗𝜔 " 𝐉% ∙ 𝐄% ∗ 𝑑𝑣 .
#

#

#

98

(1)

JSST 2018
The equation contains complex numbers and becomes a complex symmetric matrix. In
the present study, the electric field 𝐄, which is unknown, is obtained using the conjugate orthogonal conjugate gradient (COCG) method. The finite element approximation (1)is rewritten as 𝐾𝑢 = 𝑓 by the coefficient matrix 𝐾, the unknown vector 𝑢, and the right-handside vector 𝑓. Next, Ω is divided into 𝑁 subdomains (Eq. (2)). Eq. (3) and (4) are obtained
from Eq. (2).
(()(() (()+

0
0
⎡ 𝐾&&
0
⋱
0
⎢
(,)
⎢
𝐾&&
⎢
0
0
⎢ (() (()+
⋯ 𝑅(,) 𝐾 (,)+
⎢𝑅* 𝐾&**&*⎣(-) (-)(-)

𝐾&& 𝑢& = 𝑓&
*

(#)

(#)

(-) (-)− 𝐾&* 𝑢*⎤ (()(()⎥ ⎡ 𝑢& ⎤ ⎡ 𝑓& ⎤⎥⎢ ⋮ ⎥ ⎢ ⋮ ⎥⎥ ⎢ (,) ⎥ = ⎢𝑓 (,) ⎥.
⎥ ⎢𝑢& ⎥ ⎢ & ⎥(-) (-) (-)+ ⎣ 𝑢 ⎦⎣ 𝑓* ⎦F 𝑅* 𝐾** 𝑅* ⎥ *
⎦
-/(

(2)

(𝑖 = 1, … , 𝑁)(#) '((#)&

𝐾&* 𝑅*⋮(,) (,)+
𝐾&* 𝑅*

(3)
*

(#)

(#))

(#)

(#)

(#) '( (#)(#))&' 𝑅! )𝐾!! − 𝐾%! ,𝐾%% - 𝐾%! . 𝑅! / 𝑢! = ' 𝑅! )𝑓! − 𝐾%! ,𝐾%% - 𝑓% .
#+(

#+(

(')

*+

(4)
(')

where 𝑓% (') is the right-hand vector for 𝑢% , and /𝐾)) 1 is the inverse matrix of 𝐾)) . Equation(4) is referred to as an interface problem and is an equation for satisfying the continuity between
domains in the domain decomposition method. For simplicity, rewrite equation (5) as follows:
𝑆𝑢% = 𝑔,

-

𝑆=5

'.+

(')

('),

𝑅% 𝑆 (') 𝑅%

(')

('),

(')

*+

, 𝑆 (') = 𝐾%% − 𝐾)% /𝐾)) 1

(')

𝐾)% .

(5)

3. Numerical example
For examining ADVENTURE_Fullwave on a real-world problem, we model the environmentof a commuter train, including 48 human bodies placed inside it. In such a commuter train,dielectrics, such as reflecting barriers, walls, handrails, etc. and human bodies exist. The electromagnetic field distribution may change with the differences of geometric arrangement between these materials. Therefore, when developing the numerical environmental model use forcalculation, it is necessary to perform the modeling in such a way that the real environment
may be reproduced correctly. The train plan is referred for the modeling of the train. The computations are performed on a 20-node (160-core) PC cluster (Intel(R) Core(TM) i7-9700K, 3.60
GHz) with 36 GB RAM per node. The simulation statistics are shown in Table 1.
More detail thins will be shown at the conference.
Table 1 Simulation Statistic
Analysis Frequency
No. of Elements
No. of DOF
Platform
No. of cores
Main memory per node
Elapsed Time [s]1.0 GHz
15,712,684
15,599,463
20-node PC cluster withIntel Core i7-9700K 3.60 GHz
160
32 GB
1,998

References[1] A. Takei, S. Sugimoto, M. Ogino, S. Yoshimura, H. Kanayama: Full wave analyses ofelectromagnetic fields with an iterative domain decomposition method, IEEE Trans. on
Magn., 46:8 (2010), 2860-2863.

99

JSST2021

Heat Transfer Analysis with Uncertainty Using
Non-Statistical Uncertainty Quantification Method
and Parallelized Heat Transfer Analysis Tool
Sota Goto1*, Amane Takei2, Shigeki Kaneko1, Shinobu Yoshimura1
1

Department of Systems Innovation, School of Engineering, The University of Tokyo
2
Faculty of Engineering, University of Miyazaki*goto-sota0926@g.ecc.u-tokyo.ac.jp

Abstract. Uncertainty Quantification (UQ) is a research field that has been used for the reliability design of devices and systems, and has been attracting interest in recent years. In thisresearch, we utilized non-intrusive method, which is one of UQ methods that have very highcomputational efficiency and then integrated it with ADVENTURE_Thermal, a large-scaleheat transfer analysis software. Also, using the integrated analysis method, we analyze thesteady-state heat conduction equation in which heat conductivity is regarded as a random field,
and the validity of the proposed method is shown by comparing its analysis results with thoseof Monte Carlo simulation.
Keywords: Uncertainty Quantification, Probabilistic Collocation, Non-Intrusive method,
Karhunen-Loeve expansion, Polynomial Chaos expansion

1. Introduction
In numerical analysis, it is essential to analyze stochastically when the geometric structure,physical properties as represented by Young’s modulus, and boundary conditions of the analysis objects. The field of evaluating uncertainties of input parameters in simulation is called
Uncertainty Quantification (UQ). UQ is a field that has attracted more attention in recent years
because it is used for reliability evaluation, optimization, and safety evalua-tion in the designof systems and devices.
One of the most common and widely used methods for uncertainty quantification is theMonte Carlo method [1]. Monte Carlo method evaluates probability distributions of output
parameters by generating random numbers that follow a specific probability distribution of
input parameters with uncertainty, and then calculating the response value for each random
number. Monte Carlo method makes it possible to use a deterministic simulator as a black box,
it is computationally expensive because the accuracy depends on the sampling size. Therefore,
it may cause difficulties in large-scale analysis such as seismic wave analysis.
On the contrary, Spectral Stochastic Finite Element Method (SSFEM) [2], which is a100

JSST2021
method for evaluating uncertainty without sampling, was devised by Ghanem and Spanos. In
this method, the input and response probability fields are functionally expanded in probability
space using two spectral expansions, and the probability distribution of the response value canbe evaluated in a single matrix calculation. Although this method has high computational efficiency, it is not easy and takes much labor to construct a reliable simulator that can handle
large-scale problems because it requires modifying the existing deterministic simulator.
In this study, we apply the uncertainty quantification method which has the advantages ofboth Monte Carlo method and SSFEM, that is reusability of deterministic codes and high computational efficiency, to the numerical solution of the steady-state and nonsteady-state heat
conduction equation where the thermal conductivity is assumed as a stochastic field, and evaluate its effectiveness by comparing it with Monte Carlo method. We utilized ADVENTURE_Thermal code [3] as a large-scale heat transfer analysis software. Some numerical examples will be shown and discussed at the JSST2021 conference.

References[1] Christopher Z Mooney, “Monte carlo simulation”, No. 116. Sage, 1997.
[2] A.Lehikoinen, “Spectral Stochastic Finite Element Method for Electromagnetic Problems with Random Geometry”, Electrical, Control and Communication Engineering, Vol.
6, pp.5-12, 2014
[3] “ADVENTURE Project Homepage:” https://adventure.sys.t.u-tokyo.ac.jp/ (accessed
Jun. 24, 2021).

101

JSST 2021

Photonic Crystal Frequency Demultiplexer Design forElectromagnetic Wave using FDTD and MEMD
Ran Dong1,* , Daisuke Shigeta1 , Yoshihisa Fujita2 , Soichiro Ikuno1
1 School of Computer Science, Tokyo University of Technology
2 College of Information Science and Engineering, Ritsumeikan University∗ randong@stf.teu.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.65

102

JSST 2021

Numerical Investigation on Superconducting Linear
Acceleration System: Shape Optimization of Current
Distribution in Electromagnet
Teruou Takayama1,* , Takazumi Yamaguchi2 , Ayumu Saitoh1 , Atsushi Kamitani1
1 Graduate School of Science and Engineering, Yamagata University, Japan
2 School of Physical Sciences, The Graduate University for Advanced Studies,

SOKENDAI, Japan∗ takayama@yz.yamagata-u.ac.jp

Abstract. The enhancement of the acceleration performance of a superconducting linear
acceleration (SLA) system to inject the pellet container has been investigated numerically.
To this end, a numerical code used in the FEM has been developed for analyzing the shielding current density in high-temperature superconducting films. In addition, the normalized
Gaussian network (NGnet) method and the non-dominated sorting genetic algorithms-II has
been implemented in the code for the shape optimization of an acceleration electromagnet.
The results of the computations show that the speed of the pellet container for the current
profile of the optimized coil is significantly faster than that for the homogeneous current distribution in the electromagnet. Moreover, it is found that the NGnet method is an eﬀective
tool for improving the acceleration performance of the SLA system.
Keywords: Finite element analysis, Genetic algorithm, Linear accelerator, Nuclear fuel,Thin film

1.

Indroduction

Recently, a high-temperature superconducting (HTS) linear acceleration system has been
proposed for injecting pellets into the plasma core. Hereinafter, this system is referred toas the superconducting linear acceleration (SLA) system. This system can electromagnetically accelerate containers with frozen hydrogen pellets by using an HTS film, such as alinear motor car. In the system, two types of films are used for acceleration and levitation.
Although the estimated required speed of the SLA system to reach the plasma core is morethan 5 km/s, it is not clear how much pellet speed can be obtained experimentally since the
SLA system has not yet been applied to pellet injection.
In order to simulate an SLA system we have developed a numerical code for analyzinga shielding current density in an HTS film. In the present study, we try to implement thegenetic algorithm (GA) to improve the acceleration performance of the SLA system. The

106

Figure 1: Time dependence of the pellet velocity v.

Figure 2: Current distribution in the electromagnet for the NGnet method. Here, theorange area indicates the on-state of the filament. The inner and outer radii of the electromagnet are 5 cm and 7 cm, and the lengthof the electromagnet is given by 10 cm.

GA has been used for the design optimization of electromagnetic devices because of therecent improvements in computing performance.
The purpose of the present study is to enhance the acceleration performance for the
SLA system numerically. To this end, we implement the non-dominated sorting genetic
algorithm II (NSGA-II) of the multi-objective optimization in the FEM code for analyzing
the shielding current density in an HTS film. Moreover, we adopt the normalized Gaussian
network (NGnet) method [1] for the shape optimization of the acceleration electromagnet.

2.

Numerical Results

In this section, we optimize the current distribution of the acceleration electromagnet toincrease the pellet speed on the basis of the NGnet method for the shape optimization of theelectromagnet. In Fig. 1, we show the time dependence of the pellet velocity v. The figure
shows that the pellet velocity estimated by the NGnet method is much higher than the valueof v obtained by the homogeneous current distribution in the electromagnet.
In Fig. 2, we show the current distribution of the filaments for the NGnet method. We
see from this figure that the electromagnet becomes a concave shape. Consequently, theNGnet method is an eﬀective tool for improving the acceleration performance of the SLA
system. This reason that the maximum value of the optimized current distribution using theNGnet method is larger than that for the conventional electromagnet.
In future works, to further investigate the validity of the optimal solution in the above
results, we increase the number of the filaments and change the parameters of the NGnet
method and the NSGA-II.

References[1] J. Moody and C. J. Darken: Fast learning in networks of locally-tuned processing
units. Neural Comput., 1:2 (1989), 281–294.

107

JSST 2021

Three-Dimensional Analysis of Magnetic Shielding
Current in High-Temperature Superconducting Tape
Takazumi Yamaguchi1,* , Hiroaki Ohtani1,2 , Shinsuke Satake1,2 , Nagato Yanagi1,2
1 School of Physical Sciences, The Graduate University for Advanced Studies, Japan
2 National Institute for Fusion Science, Japan∗ yamaguchi.takazumi@nifs.ac.jp

Abstract. The shielding current in the high-temperature superconducting (HTS) tape has
been investigated by using the edge-based ﬁnite element method (FEM). The time evolutionof the shielding current distribution can be determined by solving the Maxwell equation withthe edge-based FEM. The numerical result shows that the shielding current concentratedly
ﬂows in the HTS layer.
Keywords: Edge-based ﬁnite element method, high-temperature superconductor, shielding
current density.

1.

Introduction

A high-temperature superconducting (HTS) tape [1] is used for developing a linear motorcar,
an MRI, and a fusion reactor. In the HTS tape, an HTS layer is piled with a stabilizing layer
on a material substrate. The material substrate is made of Hastelloy, and the stabilizing layer
is made of Cu and/or Ag. When an electric current is applied to the HTS tape, it ﬂows only in
the HTS layer. However, in the place where the superconducting characteristics of the HTS
tape are deteriorated locally, the electric current ﬂows from the HTS layer into the stabilizing
layer. Because the deterioration of the superconducting characteristics is caused by defects
such as small holes and cracks, it is necessary to clarify the inﬂuence of the defects on the
superconducting characteristics. The purpose of the present study is to three-dimensionallyanalyze the electromagnetic ﬁeld in the HTS tape with considering the spatial distributionof the electric conductivity.

2.

Numerical Simulation

In the present study, it is assumed that an HTS tape is composed of an HTS layer and a Cu
stabilizing layer (see Fig. 1). For simplicity, a material substrate is not taken into consideration. This is because the interface between the material substrate and the stabilizing layer isinsulated. In addition, an electromagnet in which an AC current j0 ﬂows is placed above the108Figure 1: A schematic view of the numericalmodel.

Figure 2: The typical distribution of theshielding current density (the tape size is
10 mm × 20 mm × 1 mm).

HTS tape. A shielding current density j is generated in the HTS tape by an applied magnetic
ﬂux density B0 generated by the electromagnet. The shielding current density j is governedby the following Maxwell equation:∂(B + B0 ), j = σE.
(1)∂tHere, B is a magnetic ﬂux density generated by j, and E is an electric ﬁeld in the HTS tape.
Furthermore, µ and σ are a magnetic permeability and an electric conductivity, respectively.
Note that, in the HTS layer, σ is a non-linear function of j. The value of σ is determined byusing the critical-state model [2]. By using the A-method [3], Eq. (1) becomes equivalent to
the following equation:∂∇ × (µ−1 ∇ × A) = −σ ( A + A0 ),(2)∂twhere A and A0 are a vector potential of B and that of B0 , respectively. Equation (2) with
the natural boundary condition is discretized by using the edge-based ﬁnite element method[3] to obtain the following equation:
{
}
da
da0
−1
= − C (K a) +
,
(3)
dt
dt
∇ · B = 0,

∇ × (µ−1 B) = j,

∇×E=−

where K and C are ﬁnite element matrixes corresponding to µ and σ, respectively. In addition, a and a0 are vectors corresponding to A and A0 , respectively. Both the spatial
distribution and the time evolution of j can be determined by solving Eq. (3).
The typical distribution of the shielding current density in the HTS tape is shown in
Fig. 2. The shielding current density concentratedly ﬂows in the HTS layer. In the future
work, an electromagnetic ﬁeld in HTS tapes with defects will be investigated.

References[1] Y. Shiohara et al.: J. Japan Inst. Met. Mater., 80:7 (2016), 406–419.
[2] H. Ueda et al.: J. Cryo. Super. Soc. Jpn., 48:9 (2013), 472–484.
[3] R. Albanese et al.: Advances in Imaging and Electron Physics, 102 (1997), 1–86.

109

JSST 2021

Some suitable settings for Haar-like four-point
orthogonal transform
Kensuke Fujinoki1,* and Yuji Senda1
1 Department of Mathematical Sciences, School of Science, Tokai University∗ fujinoki@tokai-u.jp

Abstract.
In this paper, some settings for the Haar-like four-point orthogonal transform are considered. We show that two custom settings are available to realize the transform, which
are a combination of taking the disjoint subsets and the design of an orthonormal matrix.
Exploring suitable conditions for these settings, some numerical results for nonlinear approximation of images are presented.
Keywords: Linear orthogonal transform, Haar transform, Image processing, Nonlinear approximation

1.

Introduction

In conventional wavelet analysis of a tensor product of Haar wavelets in two dimensions,a digital image is divided into 2 × 2 blocks and the four points of each block are decomposed into the average and the three diﬀerences [1]. As an alternative, we have presented amethod of dividing an image into disjoint subsets of four points that are not 2 × 2 blocks andperforming the same orthogonal transform as the Haar transform for each subset [2, 3].
Our previous study showed that there are several ways of taking disjoint subsets of animage, and that diﬀerent combinations of the subsets result in performance diﬀerences insome image processing tasks [3]. We also showed how to design coeﬃcients of an orthonormal matrix to be used in the transform. Assembling the orthonormal matrix involves
some parameters, so we also investigated an optimal pair of parameters for nonlinear image
approximation [2].
In this paper, we report our further study of the case where the two independent conditions for the Haar-like four-point orthogonal transform are combined, which are the selections of the disjoint subsets and the coeﬃcients. We explore some suitable conditions forthese settings through an application to nonlinear image approximation.

110

2.

Haar-like transform

We begin with a brief introduction of the Haar-like four-point orthogonal transform. Let
A ∈ Z2×2 and m = | det A|. A scaling function and wavelets associated with a lattice (Z2 , A)satisfy the dilation equation and the wavelet equation, respectively:∑
ϕ(x) = | det A|1/2
hk ϕ(Ax − k),k∈Z2ψℓ (x) = | det A|1/2∑

gℓ,k ϕ(Ax − k),ℓ = 1, . . . , m − 1,k∈Z2

where {hk }k∈Z2 and {gℓ,k }k∈Z2 ,1≤ℓ≤m−1 are sequences for ℓ2 (Z2 ).
()
2 0
We consider A =, and m = | det A| = 4. Let {xk }k∈Z2 be a signal. The Haar-like
0 2
four-point orthogonal transform of the signal corresponds to a linear orthogonal transformwith the sequences of the scaling function and wavelets, which is deﬁned by x2k+k0 y2k+k0 
y
 x


 2k+k1  = M  2k+k1  ,
y
 x


 2k+k2  2k+k2 x2k+k3y2k+k3where {kℓ ∈ Z2 }0≤ℓ≤m−1 is translation vectors and


h1
h2
h3 
 h0g1,0 g1,1 g1,2 g1,3  .
M = 
g2,0 g2,1 g2,2 g2,3 g3,0 g3,1 g3,2 g3,3

(1)

The inverse transform is realized using M ∗ , which is the complex conjugate transpose of M
because we assume that the matrix M ∈ R4×4 is an orthonormal matrix, i.e., MM ∗ = M ∗ M =I4 , where I4 is the fourth-order identity matrix.
From these formulas, this transform yields the correlation of four points for each disjoint subset of an image {x2k+kℓ }k∈Z2 ,0≤ℓ≤m−1 with an orthonormal matrix M. Thus, wehave two options to design the transform. One is the combination of the four subsets{x2k+kℓ }k∈Z2 ,0≤ℓ≤m−1 taken in the transform, and here we ﬁx k0 = (0, 0)T , k1 = (1, 0)T and
select each translation vector from{( ) ( )}{( ) ( ) ( ) ( )}
0
0
1 −1
1
−1
k2 ∈
,
, k3 ∈
,
,
,
.
(2)
1 −1
1
1
−1 −1
The second option is the design of the orthonormal matrix M. There are many parameters to design the matrix (1), but according to the results of Rosca [4, 5], these parametersof 4 × 4 entries reduce to only two parameters α1 and α2 as

1
1
1
1

 

h1
h2
h3  2222
 h0()
 
1
1
g
α1
α2
− 2 + α1 + α2 


g
g
g
2
1,0
1,1
1,2
1,3


 ,
(
)
 = 
M = 
1
1

−
+
α
+
α
α
g2,0 g2,1 g2,2 g2,3   ( α2
1
2
1
2

) 2
 1
g3,0 g3,1 g3,2 g3,3
α1
α2
− 2 + α1 + α2 12
(3)

111

where α1 ∈ [−5/6, 1/2] and α2 ∈ [−1/2, 5/6] . Furthermore, thanks to the orthonormal
conditions, we can derive α2 from α1 , so we only need to ﬁx one or the other to assemble anorthonormal matrix M for the transform [2].

3.

Numerical results

We carried out numerical experiments to ﬁnd suitable settings for the Haar-like four-point
orthogonal transform. In these experiments, we applied the transform to some images andthen reconstructed the transformed images from a few of the largest coeﬃcients. At thesame time, we changed the translation vectors and the coeﬃcients deﬁned by (2) and (3),respectively, in order to observe the behavior of the transform.
Figure 1 shows the results of the peak signal-to-noise ratio (PSNR) for Lenna. The percentages of the largest coeﬃcients used for the reconstruction are 1[%], 2[%], 3[%], 4[%],and 5[%]. We observe that there is a periodic behavior in the relationship between α1 and its
PSNR value for all the cases. While this periodicity was also observed in our previous study[2], we see in Figure 1 that it is reversed when we set k3 = (−1, ·)T . Furthermore, we can expect better performance with k3 = (1, ·)T rather than with k3 = (−1, ·)T . From these results,
k3 is the most important among the translation vectors, and {k2 = (0, ±1)T , k3 = (1, 1)T }and {k2 = (0, −1)T , k3 = (1, −1)T } are suitable combinations which provide relatively highperformance. Similar results were conﬁrmed for other types of images.

4.

Conclusion

In this paper, we investigated some properties of the Haar-like four-point orthogonal transform. We considered two settings of the transform, which are the combination of translation
vectors and the selection of coeﬃcients, through an application to nonlinear image approximation. Although these settings are minor, experimental results showed that changing thesesettings has a considerable eﬀect on the performance of reconstructing images.

References[1] S. Mallat: A Wavelet Tour of Signal Processing, 3rd ed., Academic Press, 2008.
[2] K. Fujinoki: Nonlinear approximation of images with Haar-like four-point orthogonal transforms, Proceedings of the 16th IEEE International Conference on Wavelet
Analysis and Pattern Recognition (ICWAPR 2019), Kobe, Japan, 110–115 (2019).
[3] K. Fujinoki: Properties of Haar-like four-point orthogonal transforms for image processing, in: S. Latiﬁ (eds) 17th International Conference on Information Technology–
New Generations (ITNG 2020), Advances in Intelligent Systems and Computing, 1134,
Springer, Cham, 233–239 (2020).

112

k 2=(0,1), k3=(1,1)

32

PSNR [dB]

34
1[%]
2[%]
3[%]
4[%]
5[%]

k 2=(0,-1), k 3=(1,1)
1[%]
2[%]
3[%]
4[%]
5[%]

32

PSNR [dB]

34

30
28
26

30
28
26

24

24
-0.5

0

0.5

1

-0.5

0

1

k 2=(0,1), k3=(-1,1)

32

PSNR [dB]

34
1[%]
2[%]
3[%]
4[%]
5[%]

30
28
26

1[%]
2[%]
3[%]
4[%]
5[%]

30
28
26

24

24
-0.5

0

0.5

1

-0.5

0

1

k 2=(0,1), k3=(-1,-1)

PSNR [dB]

34
1[%]
2[%]
3[%]
4[%]
5[%]

32

28
26

1[%]
2[%]
3[%]
4[%]
5[%]

30
28
26

24

24
-0.5

0

0.5

1

-0.5

0

1

0.5

1

1

k 2=(0,1), k3=(1,-1)

34
1[%]
2[%]
3[%]
4[%]
5[%]

k 2=(0,-1), k 3=(1,-1)
1[%]
2[%]
3[%]
4[%]
5[%]

32

PSNR [dB]32

PSNR [dB]1

k 2=(0,-1), k 3=(-1,-1)

32

30

34

0.5
1

PSNR [dB]341k 2=(0,-1), k 3=(-1,1)

32

PSNR [dB]

34

0.5
1

30
28
26

30
28
26

24

24
-0.5

0

0.5

1

-0.5

1

0

0.5

1

1

Figure 1: PSNR for Lenna with diﬀerent choices of translation vectors k2 and k3 , and parameter α1 . Left column: k2 = (0, 1)T . Right column: k2 = (0, −1)T .
[4] D. Rosca: Haar wavelets on spherical triangulations, in: N. A. Dogson, M. S. Floater,
M. A. Sabin (Eds.), Advances in Multiresolution for Geometric Modelling, Springer,
Berlin, 407–419 (2005).
[5] D. Rosca: Optimal Haar wavelets on spherical triangulations, Pure Math. Appl., 15:4
(2006), 429–438.

113

JSST 2021

Estimation method for scale-shift relationshipbetween two speech signals based on Fourier-Mellintransform
Akira Morimoto1,* , Ryuichi Ashino1 , Takeshi Mandai2
1 Mathematics and Informatics, Osaka Kyoiku University
2 Center for Physics and Mathematics, Osaka Electro-Communication University∗ morimoto@cc.osaka-kyoiku.ac.jp

Abstract. An algorithm, which estimates scale, gain, shift parameters among two speech
signals with a scale-shift relationship, is proposed. Several experiments show the usefulnessof the algorithm.
Keywords: Fourier-Mellin transform, scale-shift relationship, scale parameter, shift parameter

1.

Introduction

The Mellin transform [1, 2] is well known as a scale invariant transform. The Fourier-Mellintransform has a scale-shift invariant property. It is widely applied in various fields, forexample, mammalian hearing [3], rhythm description [4], gray-Level image description [5],etc. We [6] proposed an algorithm to decide whether two speech signals have a scaleshift relationship. In this talk, we present an algorithm which evaluates scale, gain, shiftparameters for two speech signals with a scale-shift relationship.

2.

The Fourier-Mellin transform

The Fourier transform of f (t) ∈ L1 (R) isbf (ξ) = F [ f ](ξ) =∫Rf (t) e−iξt dt.

The Fourier-Mellin transform of f (t) ∈ L1 (R) is∫pbf (ξ) |ξ|ω dξ,F M[ f ](p, ω) =R

where p ≥ 1 and ω > 0.

114

For scale parameter α > 0, gain parameter β > 0, and shift parameter γ ∈ R, we define
fα,β,γ (t) = β f (αt − γ).
The Fourier transform of fα,β,γ is

β −i γ ξ b( ξ )dfα,β,γ (ξ) = e α f.
ααThe Fourier-Mellin transform of fα,β,γ isF M[ fα,β,γ ](p, ω) = α(ω+1−p) β p F M[ f ](p, ω).
Taking the logarithm of (1), we have()
log F M[ fα,β,γ ](p, ω) − log (F M[ f ](p, ω)) = (ω + 1 − p) log α + p log β.

3.

(1)

(2)

Estimation algorithm for α, β, γFor two speech signals f (t) and g(t), we would like to know whether two signals have ascale-shift relationship g(t) = β f (αt − γ). The following algorithm 1 checks the scaleshift relationship. If the relationship exists, the algorithm evaluates scale, gain and shiftparameters.
Algorithm 1. For two speech signals, we do the following steps.
1. Set p = 4. Calculate the Fourier-Mellin transforms of f and g.
2. SetR(p, ω) = log (F M[g](p, ω)) − log (F M[ f ](p, ω)) .
3. Plot a graph of R(p, ω) against ω.
4. If the graph is a linear function of ω, then calculate α and β which satisfy the equationR(p, ω) = (ω + 1 − p) log α + p log βin the sense of the least squares, else two speech signals do not have a scale-shift relationship.
5. Make h(t) = β f (αt).
6. Calculate a correlation between h(t) and g(t − s):∫h(t) g(t − s) dt,
C(s) = R∥h∥ ∥g∥where ∥g∥ is the L2 (R) norm of g.
7. Set Q = max s |C(s)|. If Q is large enough, then two speech signals have the relationshipg(t) = β f (αt − γ), where C(s) attains its maximum at s = γ, else two speech signals do nothave a scale-shift relationship.
We give numerical experiments as Figure 1. These experiments show the usefulness of
the algorithm.

115

Blue: f(t), Red: g(t)

1
0.5

0.5

0

0

-0.5

-0.5

-1

0

5

10

Blue: f(t), Red: g(t)

1

-1

15

0

5

2

2

1

1

0

0

-1

-1
-2

-2
0

1

2 w

3

0

4

Red: g(t), Blue: h(t)

1

10

15

R(p, w), p = 4

R(p, w), p = 4

0.5

0

0

-0.5

-0.5

-1

-1

-1.5

3

4

Red: g(t), Blue: h(t)

1

0.5

2 w

1

-1.5
0

0.3

5

10

15

0

Correlation between g(t) and h(t)1015Correlation between g(t) and h(t)
0.3

0.2

0.2

0.1

0.1

0

0

-0.1

-0.1

-0.2

-0.2

-0.3
-5

5

0

5

-0.3
-5

0

5

Figure 1: Numerical experiments. Left: two speech signals with scale-shift relationship.
Right: two speech signals without scale-shift relationship. First row: f (t) and g(t). Second
row: R(p, ω), p = 4. Third row: g(t) and h(t), Fourth row: Correlation between g(t) and
h(t).

116

Acknowledgement
This work was partially supported by JSPS KAKENHI Grant Numbers 20K03653 and21K03351. We use speech signals provided by NII-SRC: PASL-DSR [7] and AIJ-SMLE [8].

References[1] R. Godement: Analysis III, “Analytic and Diﬀerential Functions, Manifolds and Riemann Surfaces”, Springer, 2015.
[2] L. Cohen: The scale representation. IEEE Transactions on Signal Processing,41(1993), 3275–3292, doi: 10.1109/78.258073.
[3] R. A. Altes: The Fourier-Mellin transform and mammalian hearing, J Acoust Soc Am.,
63(1978), 174–183, doi: 10.1121/1.381708.
[4] U. Marchand and G. Peeters: Scale and shift invariant time/frequency representation
using auditory statistics: Application to rhythm description, 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), (2016), 1–6,
doi: 10.1109/MLSP.2016.7738904.
[5] S. Derrode and F. Ghorbel: Robust and Eﬃcient Fourier-Mellin Transform Approximations for Gray-Level Image Reconstruction and Complete Invariant Description, Computer Vision and Image Understanding, 83(2001), 57–78, doi:
10.1006/cviu.2001.0922.
[6] A. Morimoto: An Estimation of a Scale Parameter Based on the Fourler‐ Mellin
Transform, Proceedings of the Tenth International Conference on Information, (2021),
11–15.
[7] Speech Resources Consortium, National Institute of Informatics:(dataset). https://doi.org/10.32130/src.PASL-DSR

PASL-DSR[8] Architectural Institute of Japan: Sound Material in Living Environment (Gihodoshuppan, Chiyodaku, Tokyo, Japan, 2004).

117

JSST 2021

Some properties of fractional wavelet transform
Mawardi Bahri1 and Ryuichi Ashino2,*
1 Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia
2 Mathematics and Informatics, Osaka Kyoiku University, Osaka 582-8582, Japan∗ ashino@cc.osaka-kyoiku.ac.jp

Abstract. The fractional wavelet transform can be interpreted as a generalization of the classical wavelet transform in the the fractional frequency domain. The direct relation between
the fractional Fourier transform and classical wavelet transform is presented. Some generalproperties of the fractional wavelet transform are presented.
Keywords: fractional wavelet transform, fractional Fourier transform, reproducing kernel

1.

Introduction

It is known that the classical wavelet transform (WT) is a useful mathematical tool, which
has been broadly implemented in quantum physics, signal processing and many other fields
of science and engineering [1, 2, 3]. In recent years, a number of eﬀorts have been increasing
interest in generalizing the classical wavelet transform using the fractional Fourier transform(FRFT). As for recent applications of the fractional Fourier transform to speech enhancement, see [4]. In [5, 6, 7], the authors have studied an extension of the WT in the FRFT
domain, the so-called the fractional wavelet transform (FRWT). The generalized transform
is constructed by including the Fourier kernel with the FRFT kernel in the definition of
the WT. They also have derived its essential properties like linearity, orthogonality relation,
reconstruction formula and the inequalities.
In [8, 9], the author has derived some properties of the fractional Fourier transform utilizing the direct interaction between the classical Fourier transform and the fractional Fouriertransform. Based on this idea, we can obtain some properties of the fractional wavelet
transform using the basic relation between the fractional wavelet transform and the classicalwavelet transform. This work is intended as a mathematical overview of general propertiesof the fractional wavelet transform such as the orthogonality relation and inversion formulaand the other properties.

2.

Continuous fractional wavelet transform (CFRWT)

We start by introducing the wavelet transform. Let the shifting parameter be b ∈ R andscaling parameter be a ∈ R+ . We denote the shifting and scaling of the function f by118

τb f (t) = f (t − b) and fa (t) = a−1/2 f (t/a), respectively. The family of wavelets are functionsof the form:
)
(
1
t−b
Ψa,b (t) = τb Ψa (t) = √ Ψ
,
(1)
a
a
that are generated from the mother (basic) wavelets Ψ ∈ L2 (R). This leads to the definitionof the continuous wavelet transform of f ∈ L2 (R) with respect to the mother wavelet Ψ as∫T Ψ f (a, b) =f (t)Ψa,b (t) dt
R

1
= √
a

)
t−b
f (t)Ψ
dt.
a
R
(

∫

(2)

Let us consider the family of fractional mother wavelets described by()
1t − b − i (t2 −b2 ) cot θ
Ψa,b,θ (t) = √ Ψe 2aa= Ψa,b (t)e− 2 (t −b ) cot θ .
i

2

2

(3)

The most important property of family of fractional mother wavelets (3) is the admissibility
condition as follows.
Definition 2..1. We call a mother wavelet Ψ ∈ L2 (R) associated with the FRFT is admissible
if and only if the following admissibility condition is satisfied:
∫
2 da
i
2
CΨ,θ =< ∞.
(4)
F θ {e− 2 (·) cot θ Ψ}(aξ)
aR+
In this case, CΨ,θ is a real positive constant independent of ξ satisfying |ξ| = 1.
Lemma 1. Suppose that

∫
CΨ =

R+

|F {Ψ}(aξ)|2

da
< ∞.
a

(5)

is the admissibility condition for the conventional wavelet transform. The relationship between (4) and (5) is described byCΨ = sin θ CΨ,θ .
Note that the Fourier transform of (1) takes the form√Ψ̂a,b (ξ) = a e−ibξ F {Ψ}(aξ).

(6)

(7)

The following Lemma 2 gives a relationship between (3) and its FRFT.
Lemma 2. Let Ψ be a mother wavelet. Then, the family of the fractional mother wavelets(3) can be expressed in terms of the FRFT as
F θ {Ψa,b,θ }(ξ) = Ψ̂θa,b,θ (ξ)√ i 2 2i 2 2i
2
= a e 2 (b +ξ ) cot θ−ibξ csc θ− 2 a ξ cot θ F θ {e− 2 (·) cot θ Ψ}(aξ).

119

(8)

Let us define the continuous fractional wavelet transform (CFRWT).
Definition 2..2 (CFRWT). The CFRWT of f ∈ L2 (R) with respect to mother wavelet ψ ∈L2 (R) associated with the FRFT is defined by
)
(
∫
∫
1
t − b i (t2 −b2 ) cot θθT Ψ f (a, b) =f (t)ψa,b,θ (t) dt = √f (t)Ψ
e2
dt.
(9)
a
a R
R
The following lemma explains an interesting connection between the CFRWT and the
CWT.
Lemma 3. Let Ψ, f ∈ L2 (R). Then,i 2
T Ψθ f (a, b) = e− 2 b cot θ T Ψ f˜(a, b),

(10)

i 2
f˜(t) = f (t)e 2 t cot θ .

(11)

where

Lemma 4. Let Ψ ∈ L2 (R). Then, the CFRWT (9) has a fractional Fourier representation
form
∫
√
i 2 2
i 2
2
i
2
θ
T Ψ f (a, b) = ae− 2 (b +ξ ) cot θ+ibξ csc θ+ 2 a ξ cot θ F θ {e− 2 (·) cot θ Ψ}(aξ) fˆθ (ξ) dξ. (12)R

The inverse FRFT of fˆθ ∈ L1 (R) is defined by the integral∫
θ −1 ˆθ(F ) { f }(t) =fˆθ (ξ)K θ (t, ξ) dξ,R(13)

where K θ (t, ξ) is the complex conjugate of K θ (t, ξ). Then, we have√a i a2 ω2 cot θ θ − i (·)2 cot θθ θΨ}(aω) fˆθ (ω).
(14)
Fb {T Ψ f (a, b)}(ω) =e2F {e 2θC
The next results provide the fundamental properties of the CFRWT such as the inversion
theorem and orthogonality relation. They are generalizations of corresponding properties ofthe WT.
Theorem 1. Let Ψ ∈ L2 (R) satisfy the admissibility condition defined by (4). Then, forf ∈ L2 (R), the following inversion formula holds:∫ ∫1daf (t) =
(15)
Ψa,b,θ (t) T Ψθ f (a, b) db 2 .
2π sin θ CΨ,θ R+ R
a
Theorem 2. Assume that the basic wavelet φ ∈ L2 (R) related to the FRFT satisfies theadmissibility condition (4). For f , g ∈ L2 (R) ∩ L1 (R) we have∫ ∫daT Ψθ f (a, b) T Ψθ g(a, b) db 2 = 2π sin θ CΨ,θ ( f, g)L2 (R) ,
(16)
a
R+ R
and

∫

∫
R+

R

da
2
T ΨA f (a, b) db 2 =a∫R+∥T Ψθ f (a, b)∥2L2 (R)120da= 2π sin θ CΨ,θ ∥ f ∥2L2 (R) .
a2

(17)

The next result is reproducing kernel related to the FRWT, which is an extension of the
reproducing kernel of the classical wavelet transform (see Mallat [2]).
Theorem 3 (Reproducing kernel). Let Ψ be an admissible wavelet. If
KΨ (a, b, θ; a′ , b′ , θ′ ) =()
1
Ψa,b,θ , ψa′ ,b′ ,θ′ L2 (R) ,2π sin θ CΨ,θthen KΨ (a, b, θ; a′ , b′ , θ′ ) is a reproducing kernel, i.e.,∫ ∞∫ ∞daθ′′ ′T ψθ f (a, b)KΨ (a, b, θ; a′ , b′ , θ′ ) db 2 .
T ψ f (a , b ) =
a
0
−∞

(18)

(19)

References[1] K. Gröchenig, Foundation of Time-Frequency Analysis, Birkhäuser, Boston, MA,
2001.
[2] S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA,
2001.
[3] R. Ashino, S. Kataoka, T. Mandai and A. Morimoto, Blind image source separations
by wavelet analysis, Appli. Anal., 91(4), 617–644, 2012.
[4] P. Kunche, N. Manikanthababu, Fractional Fourier Transform Techniques for Speech
Enhancement, Springer, 2020.
[5] J. Shi, N. Zhang, X. Liu, A novel fractional wavelet transform and its applications, Sci.
China Inf. Sci, 55(6), 1270–1279, 2012.
[6] A. Prasad, S. Manna, A. Mahato, and V. K. Singh, Generalized continuous wavelet
transform associated with the fractional Fourier transform, J. Comput. Appli. Math.,
259, 660–671, 2014.
[7] A. Prasad and P. Kumar, The continuous fractional wavelet transform on generalized
weighted Sobolev spaces, Asian-European Journal of Mathematics, 8(3), 11 pages,
2015.
[8] Z. I. Zayed, On the relationship between the Fourier and fractional Fourier transforms,
IEEE Signal Processing Letters, 3(12), 310–311, 1996.
[9] Z. I. Zayed, A convolution and product theorem for the fractional Fourier transform,
IEEE Signal Processing Letters, 5(4), 101–103, 1998.

121

JSST2021

A Study on Tracking Individual Pedestrian
Trajectories in a Walking Crowd Using Openpose
Minagi Miyokawa1, Hideo Miyachi2
1

Graduate School of Environmental And Information Studies, Tokyo City University
2

Department of Informtion Systems, Tokyo City University
1

g2183130@tcu.ac.jp

Abstract. In urban design, it is important to study the behavior of pedestrians. In the past,measurement of the amount of walking in the field was the mainstream for such research, but
in recent years, analysis using image processing has been progressing. However, it is difficult
to analyze video images directly due to restrictions on personal information protection. Therefore, we propose a two-step human behavior analysis method that extracts posture informationof a person from a video image and then tracks the person. In this paper, we conducted a rudimentary experiment to verify the validity of the method.We acquired a video of three people
walking crossways from the side, and obtained a reasonable plane trajectory. .
Keywords: Pedestrian Trajectory, Multi objects detection, Openpose, Pose Estimation

1. Introduction
Studying pedestrian behavior not only contributes to safe traffic, but also makes a significant
contribution to urban design [1]. For example, when people walk through a shopping district,
it is difficult to cross the flow of passing traffic to enter a store. To solve this problem, the area
can be designed to slow down the flow of people in front of the store [2]. Usually, the design
starts with knowing the current flow of people. To do so, a field survey is indispensable. For
that field survey, image analysis of surveillance cameras installed in the city is effective, but
due to privacy protection issues, we are not allowed to analyze the videos while visually checking them. However, it is allowed to analyze the video after primary image processing to makeit non-personally identifiable. In this research, we are investigating the use of machine learning
to track the trajectory of individual people by applying primary image processing, thereby overcoming the privacy protection issue. In this paper, as a first step, we tried to acquire skeletal
information with a machine learning software called Openpose as a primary processing, andtrack the walking trajectory of an individual person from it.

2. Related works and the purpose of this study
Since the success of deep learning, there have been significant advances in object detection
techniques and a lot of research has been done to track people. However, learning images ofdifferent people to identify them requires a huge amount of training data, and dynamic tracking

122JSST2021
requires high-performance GPUs [3]. Benchmark tests have also been designed to compete for
efficiency improvements in multiple person detection [4]. Research has also been conducted to
improve detection accuracy and speed at limited shooting angles [5]. In this study, we propose
a two-stage approach, where instead of directly tracking people using machine learning, we
first detect people from videos with Openpose [6], which extracts skeletal information of people, and then use the skeletal information to track people. We believe that t8is approach solves
the problem of personal information protection and separates the learning algorithm for extracting skeletal information from the tracking algorithm, thus enabling efficient analysis ofhuman flows. Our goal is not to track a specific person (e.g., a criminal) completely, but toknow the behavior of each person in order to understand the complex flow of people.

3. Experimental method
Three people crossing each other were video-recorded from the side. The experiment took place
in a space of about 8m square in front of the elevator hall on the 7th floor of the Tokyo City
University Building No. 3. Two pedestrians walked from the right side of the camera facing
left and one from the left side facing right, crossing each other in the center. The walking paths
were not set explicitly, but the starting positions were set to the front, middle, and back so thatthe walkers could reach the other side without any movement to avoid. A smartphone was used
to capture 30 frames per second. Figure 1 shows an image taken at the beginning of the walk.
The skeleton information detected by Openpose is superimposed on the image.

Fig.1 Snapshot of the experimentFig.2 18 keypoints detected by Openpose

Openpose uses a non-parametric method called Part Affinity Fields (PAF) on 2D images
to learn associations between individuals and body parts. This allows for fast and accurate estimation of human posture regardless of the number of people in the image. However, it can
only estimate the posture of an individual person from a 2D image, and cannot estimate theposition or track the person in 3D. Openpose detects 18 nodes such as head, neck, and left andright shoulders, elbows, wrists, knees, and ankles, as shown in Fig. 2, and outputs them as afile in JSON format.
In this case, we are examining the flow of human tracking, which does not require accuracy. Therefore, we used approximate numbers to calculate the conversion from 2D images to
3D coordinates. The camera was set at a height of about 1m, the number of pixels per frame
was 2000x1000, and the angle of view was 60 degrees. Since a person moves up and down
while walking, it is not possible to convert all the key points into 3D coordinates, but considering the walking style, the height of the ankle when the foot touches the ground can be set as
Z coordinate = 0. In this study, the ground contact point was identified visually using the123JSST2021
knowledge of the gait pattern from the two-dimensional trajectory of the ankle. From one person's walking data, we calculated the 3D coordinates of three or four ground contact points,
and approximated them with a cubic function, which we used as the walking trajectory.
In this experiment, occlusion occurs when people starting from the left and right intersect.
However, the trajectories of the three people do not intersect in a complicated way. Therefore,
we used the approximate linear prediction from the trajectory before the occlusion occurred(10 points) to predict the person belonging to the point where the occlusion was resolved andbecame detectable.

4. Experimental results
Figure 3 shows the time-series variation of the XY coordinate values in the 2D image of the
keypoint “neck”. The horizontal axis shows the X coordinate values and the vertical axis shows
the Y coordinate values. Both are shown as the number of pixels with the lower left as theorigin. From this, it can be seen that the top line has no occlusion it indicates front person, thenext line is the center person, and the bottom line is the back person.

Fig.3 Movement of the detected neck position

Fig.5

Fig.4 Extraction of depth information

Walking trajectories of three people seen from above.

As an example of coordinate transformation, we show the coordinate transformation procedure for the farthest pedestrian. Figure 4 shows the XY coordinate values of the right heel.
Five large waves are measured, which is considered to be one step. In general, the movementof the heel during walking is a rapid rise when stepping out, followed by a gradual fall, andfinally a sliding contact with the ground. The heel then remains grounded while the opposite
foot is stepped forward. Therefore, it can be seen that the person is walking from right to left,
and the group of plots that are solid in Figure 4 shows the grounded state of the heel. Five of
these ground points are extracted and approximated by a cubic function to show the change in
depth direction. The change in the XY coordinate, which is obtained by subtracting this depth124

JSST2021
variation from the Y coordinate value, indicates the walking style of the person.The results ofcalculating the walking trajectories of three people using the procedure described in the previous section are shown in Fig.5, with the XY axis in meters. In this case, it was a simple problem,
so a simple linear prediction was enough to avoid mistaking the person before and after theocclusion. The trajectory shows that the person who walked at the far end changed his walking
direction toward the front because he hit a wall due to the limitation of the space, and it was
visually verified by video and confirmed to be a reasonable walking trajectory.

5. Conclusion
We proposed a two-step person tracking method that extracts skeletal information from walking
videos using Openpose (machine learning), and then tracks people based on this information.
As a result of a verification experiment of the proposed method, we were able to calculate areasonable movement trajectory for each of the three persons. In the future, we plan to verify
the effectiveness of the proposed method for complex walking situations, such as tracking offour or more people in a crowded situation.

References[1] Takaaki Furukawa and Hideaki Takayanagi: A Pedestrian Flow Survey Using Proportional
Distribution Origin-Destination Method, Journal of Civil Engineering and Architecture ,14(2020),537-546[2] Takeuchi, M., Yoshida, T., and Kaneda, T.: A Transition Analysis of Shopping Street Complex from the Viewpoint of Shop-Around Behavior, J. Archit. Plan. AIJ,
76:660(2011),361-368[3] Personal Information Protection Commission Secretariat: Report by the Personal Information Protection Commission Secretariat: Anonymously Processed Information, Towards Balanced Promotion of Personal Data Utilization and Consumer Trust, (2017)[4] S.-H. Bae and K.-J. Yoon: Confidence-based data association and discriminative deep appearance learning for robust online multiobject tracking, IEEE transactions on patternanalysis and machine intelligence, 40:3(2018), 595–610[5] K. Fang, Y. Xiang, and S. Savarese: Recurrent autoregressive networks for online multiobject tracking, arXiv preprint arXiv:1711.02741, (2017)[6] Milan, A., Leal-Taixé, L., Reid, I., Roth, S., & Schindler, K.: MOT16: A Benchmark forMulti-Object Tracking, ArXiv, abs/1603.00831, (2016)[7] R. Chandra, U. Bhattacharya, A. Bera and D. Manocha: DensePeds: Pedestrian Tracking
in Dense Crowds Using Front-RVO and Sparse Features, 2019 IEEE/RSJ International
Conference on Intelligent Robots and Systems, (2019),468-475[8] Z. Cao, G. Hidalgo, T. Simon, S. -E. Wei and Y. Sheikh: OpenPose: Realtime Multi-Person
2D Pose Estimation Using Part Affinity Fields, in IEEE Transactions on Pattern Analysis
and Machine Intelligence, 43:1(2021),172-186

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JSST2021

Transient Trajectories on
Chaotic and Random Neural Network (CRNN)
Hitoaki YOSHIDA1*, Takeshi MURAKAMI2, Zhongda LIU3, Satoshi KAWAMURA4
1

Faculty of Education, Iwate University, Japan
2Technical Division, Iwate University, Japan

3

Faculty of Science and Engineering, Ishinomaki Senshu University, Japan

4Super-Computing and Information Sciences Center, Iwate University, Japan*hitoaki@iwate-u.ac.jp

Abstract. The information security of IoT devices and embedded systems have rapidly increased in importance. We have studied the pseudo-random-number series (PRNS) that are
extracted from outputs of the chaotic and random neural network (CRNN). In particular, it
had been applied to the Controller Area Network (CAN) bus in modern vehicles. The behavior of transient trajectories has been studied in detail by using a junction diagram and the security has been confirmed by a secure interval in this work.
Keywords: Random number, Neural network, Information security, Controller area network

1. Introduction
The information security of IoT devices and embedded systems have rapidly increased in importance year by year. We have studied the computer-generated pseudo-random-number series(PRNS) extracted from outputs of the chaotic and random neural network (CRNN) with fixed-point
arithmetic (Q5.26) and the asymmetric piecewise-linear-function (APLF) as an activation function[1-4]. In particular, it had been applied to the Controller Area Network (CAN) bus in modern
vehicles [5]. The aim of this study is how to prevent the prediction of the time series from CRNN
outputs, and keep the security of systems. For this purpose, the behavior of transient trajectories
has been studied in detail and the security of PRNS has been confirmed in this work.

2. Transient Trajectory
Result in precedent works [3,4] suggests that the time series generated from CRNN is random and non-deterministic, and the lower bits show better randomness for security applications.
The closed trajectory from CRNN is periodic but isn’t a limit cycle, therefore the closed trajectory is called a non-attractive periodic trajectory (NPT). Most trajectories started from an
initial point move through a transient trajectory (TT) and eventually reach one of NPTs (Figure1), where an arrow shows a direction of the time course. Mainstream is the longest TT within

126

JSST2021
an experimental result. Transient time is the time from an initial point to a fusion point (FP)that is the fused point of NPT and TT. Branch Time is the time from an initial point of abranch to a junction on a mainstream (JM). TTs appear as if they joined at JM, but TTs are
independent trajectories, therefore JM is just a hypothetical point. NPT generally contains
more than one FP that is always accompanied by transient trajectories (Figure 1).
The experimental condition is fixed as an external input I = 0.000001 and a perturbation ID= 0.119725 in this work. The preliminary results are summarized as follows [3,4]: The
points in NPT are not appropriate for security applications because NPT has a period that isabout 9.5×108 on average. The number of points in the domain is 264 ≈ 1.8×1019, and the total
number of points in NPTs is just ≈1.8×1010, therefore the possibility of the point in NPT is only
10-7 %. On the other side, 42.7% of initial points join into the mainstream and finally join
into the NPT through the FP, and 23.8% of initial points join into the NPT through other FPs.
Initial Point
TT (Branches)

Fusion Point (FP)
Junction on
Mainstream (JM)
Initial Point

NPT

TT (Mainstream)

Figure 1: Non-Attractive Periodic Trajectory (NPT) and Transient Trajectory (TT).

3. Junction Diagram and Secure Interval
A junction diagram is useful to observe how to join branches of transient trajectories into themainstream and to find JMs, graphically (Figure 2, 3). In the junction diagram, a length of atransient trajectory (t) and a length of a branch (b) is plotted as a point s (t, b), which represents
an initial point. The abscissa of the graph is the transient time axis, and the ordinate represents
the branch time. Here, (t – b) gives the coordinate of JM, and time started from an initialpoint of the mainstream to JM is called junction time. The points sharing the same JM forma line that typically draws a same-angle-line towards the abscissa (θ = π/3 in Figure 2, and if
the scale of abscissa and ordinate is the same then θ = π/4). The line is called a portion because it is a part of TTs and sounds like pouring rain. The trajectories of all branches are toocomplicated to observe junctions, yet the diagram makes it simple owing to vanishing junctions
between branches shown in Figure 1 except for JM. The distribution of portions and maximal
length of portions are random, which will be discussed in detail in further study. The portion
isn't a trajectory itself, it is just a point-set of initial points. As for the relatively larger portion,
it seems to consist of many initial points.
Let us think about ith portion ( 𝑆𝑖 ={𝑠1 , 𝑠2 , ⋯ , 𝑠𝑚𝑎𝑥 }), and let the maximum length of a branch be bmax, and let the number of initialpoints be ni, the correlation analysis shows the positive correlation between bmax and ni (R2 =127

JSST2021
0.829). Analysis of the diagram also shows the minimal interval of portions is 20978 (theaverage interval is 2.94×107), therefore any neighboring portions are independent of each other.

Branch Time

Figure2.E+09
1: Distribution of Initial Points

1.E+090.E+00

0

2E+09

4E+09

6E+09

8E+09

1E+10

Transient Time
Figure 2: Junction Diagram (Consists of 4266 Initial Points).

Portion (Si)smax (tmax, bmax)
sj (tj, bj)
bmax

JM

bj
θ

FP

Mainstream

Initial Point ofMainstream

tj
tmax
bmax
Junction Time of Si

Figure 3: Schema of Junction Diagram.
Frequencies of JMs (equal to the number of initial points, s) are listed in Table 1 to estimate
the secure interval that hardly has JM (Table 1). The result suggests that the minimum cardinality of NPTs (pmin) can be adopted as the secure interval; pmin ≈ 5.155852×106 (empirical
5
value) [4]. The securer interval (psec) has been obtained as 5.74×10 , in which interval there
is no JM. If an initial value is reset at every pmin, fusion point formation is probably interrupted and consequently, TT may extend to (264×pmin) 2 ≈ 1051-1052. If an initial value is resetat every securer interval (5.74×105) it will be securer and TT may extend to (264×psec) 2 ≈ 1050.
Moreover, if another parameter (e.g. an external input or a perturbation) is slightly changed at
the interval, NPTs will completely change and as a result, TT may extend furthermore.

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JSST2021a)Table 1: Frequency of Junction on Mainstream (JM) .
Interval of Branch
Time
5Interval of Junction Time
0.00 –
5.16×106

5.16×106 –4.14×107

4.14×107 –
5.47×108

5.47×108 –1.00×1010

0

0

0

0

5.74×105 – 5.16×106

00

2 (0.0469%)

34 (0.797%)

5.16×106 – 1.00×1010

00

30 (0.703%)

4199 (98.5%)

0.00 – 5.74×10a) The cardinality of the mainstream is 9.999433773×10 9 ≈ 1.00×1010 in this work.

4. Conclusion and Future Study
To prevent prediction of the time series the transient trajectory should be restarted with a
new initial value within the secure interval that hardly has a junction on a mainstream (JM).
The secure interval has been estimated the same as the minimum frequency of NPTs (pmin) and5
the securer interval (psec) has been estimated as 5.74×10 . In the proposed method the lengthof the transient trajectory is expected to reach 1050–1052. The detailed result on the security of
the PRNS will be discussed in the further publication.

Acknowledgments
Part of the experimental results in this research was obtained using supercomputing resources at Cyberscience Center, Tohoku University. This work was supported by KAKENHI
Grant Numbers JP16K00180. Special thanks to the staff members of Iwate University SuperComputing and Information Sciences Center.

References[1] H. Yoshida, Y. Akatsuka and T. Murakami: Implementation of High-Performance PseudoRandom Number Generator by Chaos Neural Networks using Fix-Point Arithmetic with
Perturbation, Proceedings of Papers, NOLTA 2018, 2018, pp46-49.
[2] H. Yoshida, H. Fukuchi and T. Murakami: Implementation of High-Speed Pseudo-Random-Number Generator with Chaotic and Random Neural Networks, Proceedings of Papers, HICSS53 2020, 2020, pp.6418-6425.
[3] H. Yoshida and T. Murakami: Non-Attractive Periodic Trajectory Formation Mechanism
on Random and Chaotic Time Series, Knowledge Innovation Through Intelligent Software
Methodologies, Tools and Techniques, H. Fujita et al. (Eds.), IOS Press, 327 (2020),
pp.197-208.
[4] H. Yoshida and T. Murakami: Non-Attractive Periodic Trajectory Formation Mechanism
on Random and Chaotic Time Series PART II, Proceedings of Papers, NOLTA 2020, 2020,
pp.25-28.
[5] Zhongda Liu, Takeshi Murakami, Satoshi Kawamura, and Hitoaki Yoshida: Fast Stream
Cipher based Chaos Neural Network for Data Security in CAN Bus, Advances in Science,
Technology and Engineering Systems Journal, 5:5(2020), pp.63-68.

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JSST 2021

Performance evaluation of collaboration networks bysimulations of interacting discovery processes
Tetsuo Imai1
1 Graduate School of Information Sciences, Hiroshima City University∗ imai@hiroshima-cu.ac.jp

Abstract. In resent research and problem solving, there are many collaboration activities
among expert researchers in multiple fields. Their individual collaborative activities forma network which shows the nature of collaboration among researchers, there have not been
many eﬀorts to measure the performance of collaboration networks, however. There is amathematical model which represents knowledge discovery as an iterative process of extracting balls from urns and the model also represents information exchange with neighbors.
The social network structure seems to strongly aﬀects to the performance of the collaboration on it, actual amount of its aﬀection is not clarified yet. In this article, I attempt toevaluate the performance of collaboration networks by simulating the model of discovery
process with interaction. Specifically, I executed simulations on a nursing research coauthor
network, which is a sample of the collaboration networks, to investigate how the eﬃciencyof knowledge discovery is aﬀected by the structure of the collaboration network.
Keywords: Discovery processes, Urn model with triggering, Coauthor network, Nursing
research, Computer simulation

1.

Introduction

Since academia has been divided into many special fields, in resent research and problem
solving, there are many collaboration activities among expert researchers in multiple fields.
By accumulating a large number of such collaborations among researchers, a network is
constructed with researchers as nodes and collaboration relationships as edges, which isa structure that shows the nature of collaboration among researchers. A typical example
of collaboration networks is the coauthor network. This is a network that considers thecoauthor relationship in academic articles as a collaboration relationship, with the author
as the node and the coauthor relationship as the edge. The characteristics of the structureof coauthor networks have been a research subject since early times in the field of network
science and various analyses have been done so far, there have not been many eﬀorts tomeasure the goodness or badness of coauthorship networks, however.
One of the methods to measure the goodness of collaboration networks is how well thecollaboration in that network produces outcomes. Iacopini et al. mathematically modeled

130

new

old

reinforcementsocial interaction

reinforcement
adjacent possible

Figure 1: Behavior of socially interacting UMT in the case of a network with two nodes.
Each node is equipped with an urn obeying the UMT with the parameters ρ = 2, ν = 1. At
the time t, node i, j extracts a ball (i:Green, j : Red) respectively, then ρ additional balls of
the same colors are added to the its urns (reinforcement). In addition since for node j thecolor of drawn ball (Green) is a new one for it, ν + 1 balls of brand new colors are also added(discovery from the concept space of adjacent possible). At t + 1, node i has access to allof its balls plus two extra ones which are discovered by its neighbor j (social interaction)
without an addition to i’s urn. I represents a sequence of innovations.

the knowledge discovery process in human intellectual activity [1]. In their work, they used amodel of UMT(Urn Model with Triggering), which models intellectual search as an iterative
process of extracting balls from urns. Furthermore they added to this model an element ofinteraction with neighbors in a human social network to represent the knowledge exchange
activities that take place in the network. Moreover, they focused on the pace of individual
discoveries (they called it as novelty) made by each individual(node) in the network, andclarified that it obeys the law called Heaps’ law, and they investigated the actual value of thepower-index of the law and the ralationships among it and several network centralities bymathematical analysis and computer simulations. On the other hand, in their work they did
not specifically mention the amount of discoveries for the world (they called it as innovation)that whole individuals in the network generates.
In this arcidle, I investigated the amount of intellectual discoveries generated by theentire network by computer simulations based on their model, and how it diﬀers dependingon the network structure(topology). Specifically I investigated the pace of innovation of thecoauthor network on nursing research which I and coauthors had previously constructed.

131

2.

Model

In this section, I describe a model of the intelligent discovery process by Iacopini et al. [1](Fig. 1) I call their model as socially interacting UMT.
Let us consider an unweighted directed graph. Each node of the graph represents an
individual/agent, while a link (i, j) denotes the existence of a directed social relation fromindividual i to j (such that i can benefit from j). Each node i is equipped with an UMT
that describes the discovery process of the individual i. A state of the urn i at time t is
described as an ordered multiset Si (t) which denotes the sequence of balls generated up to
time t. At time t each individuals extract a ball from there own urns, then ρ balls of thesame color are added to the urn (reinforcement). In addition if a color of the extracted ballis the first time for node i, νi + 1 balls of brand new colors are added to the urn of node i(adjacent possible). Moreover, at each time t, the individual i draws a ball from an sociallyenriched urn, which is composed by its own urn plus the additional balls present at time t in
the urns of its neighbors, without an addition(social interaction). By these procedures, newcolors for everybody, which is called as innovations, increase at each time. In this article I
investigate the pace of innovations and how it is aﬀected by a structure of network.

3.

Coauthor network of nursing research

I used a coauthor network on nursing research as a sample of collaboration networks. The
coauthor network is constructed by assigning edges between nodes when there is a coauthor
relationship between two authors. If there are multiple coauthored articles between the two
authors, the number of assigned edges is as same number as articles, and if there are morethan three authors in an article, edges are assigned between all related authors. The target
articles are about nursing research, specifically, all original articles published from 1982
to 2018 in journals (including predecessor journals) published by the 44 member societiesof the Japan Association of Nursing Academies (JANA) are included. The bibliography
was obtained from the Ichushi database provided by the Japan Medical Abstracts Society(JAMAS). The total number of extracted articles is 9 700. There are 8 835 nodes and 96 556
directed edges in the constructed network.

4.

Evaluation

To evaluate the performance of the nursing research network as a collaboration network, I
simulate the socially interacting UMT on the network and measure the pace of innovations.
To evaluate the performance of the nursing research coauthor network, the same simulations
are executed on networks randomly generated by the configuration model and the pace ofinnovations are measured. Here the configuration model [3] is one of the network generation models, it can generate randomly reconnected networks while maintaining its degree
dictribution of the specific network(the nursing research coauthor network in this article).
Figure 2 shows the basic result of the simulations. It is shown that the pace of innovations of the nursing research coauthor network is slightly faster than those of each132

configurations model networks.
1e6
2.0
1.5

nursingResearch
configModel1
configModel2
configModel3
configModel4

1.0
0.5
0.0

Nursing research
2147634.4

0100

Config model 1
2050659.6

200

300

Config model 2
2042647.2

400

500

Config model 3
2046173.2

Config model 42048776.6

Figure 2: The basic results of the discovery process simulations by socially interacting
UMT. A plot shows the pace of innovations in each network and a table shows the numberof innovations at t = 500. All values are average of 5 trials. In the plot horizontal axis
indicates time step and vertical axis indicates the number of innovations. Each line for
configuration model networks are almost overlapping, because paces of those were almost
equal. Simulations were continued up to t = 500 and parameters of the socially interacting
UMT were ρ = 6, ν = 3, respectively.

References[1] Iacopini, Iacopo and Di Bona, Gabriele and Ubaldi, Enrico and Loreto, Vittorio andLatora, Vito, “Interacting Discovery Processes on Complex Networks”, Physical Review Letters, Vol. 125, No. 24, 248301, 2020.
[2] Francesca Tria, Vittorio Loreto, Vito D. P. Servedio, Steven H. Strogatz, “The dynamics of correlated novelties,” Scientific Reports, Vol. 4, 5890, 2014.
[3] Mark E. J. Newman, Steven. H. Strogatz, and Duncan J. Watts, “Random graphs with
arbitrary degree distributions and their applications,” Physical Review E, Vol. 64, No.
2, 026118, 2001.
[4] Tetsuo Imai and Takayasu Kawaguchi, “Clustering of nursing research journals basedon co-occurrences in co-author relationships,” Proceedings of the 38th JSST Annual
International Conference on Simulation Technology (JSST2019), pp. 133–136, 2019.
[5] Tetsuo Imai and Takayasu Kawaguchi, “Analysis of a co-author network of nursing research,” Abstract collection of the 2018 International Symposium on Nonlinear Theory
and its Applications (NOLTA2018), A1L-B5, 2018.

133

JSST 2021

Analysis of information ﬂoating at an intersection
considering traﬃc lights
Kazuyuki Miyakita1,* , Naoyuki Karasawa2 , Hiroshi Tamura3 , Keisuke Nakano4
1 Niigata University of International and Information Studies
2 Kaishi Professional University
3 Chuo University
4 Niigata University∗ miyakita@nuis.ac.jp

Abstract. In information ﬂoating (IF), mobile nodes transmit information to other nodes bydirect wireless communication only in transmittable areas to prevent unnecessary information diﬀusion. In this paper, we theoretically analyze the mean IF lifetime considering theeﬀect of traﬃc lights, which had not been considered in past IF researches to simplify the
analysis. From the numerical and simulation results, we discuss how the traﬃc lights aﬀect
the IF performance.
Keywords: information ﬂoating, traﬃc lights, theoretical analysis

1.

Introduction

Information ﬂoating (IF) is a type of epidemic communication in which direct transmissions
to other mobile nodes is permitted only in a limited area (transmissible area: TA). It is a technology for keeping information in a speciﬁc area while preventing unnecessary information
diﬀusion, and has been studied in recent years[1, 2, 3, 4].
In past IF researches, the performance of IF for various road models such as straightroads, crossroads, and lattice roads has been analyzed[1, 2, 3, 4]. In these analyses, theeﬀects of traﬃc lights have not been considered for simplicity. In this paper, we analyze IF
performance considering the eﬀects of traﬃc lights. Speciﬁcally, we theoretically analyze
the mean IF lifetime at an intersection with traﬃc lights. From the numerical and simulation
results, we discuss how the traﬃc lights aﬀect the IF performance.

2.

Deﬁnitions and assumptions

We consider a crossroad network model as shown in Fig. 1. Nodes ﬂow in from each of theW, E, N, and S directions according to a Poisson process with intensity λ. At the intersection,
there are traﬃc lights for vehicles. Suppose that the green light and the red light are switched134

Figure 2: Time slots and arrival time at the intersection of each node.
Figure 1: The model of an intersection.
alternately at time interval tr in the horizontal and vertical directions. Nodes move at velocity
v. If a node encounters a red light at the intersection, then the node stops at the intersection
and starts moving after the traﬃc light turns green.
TA is set only at the intersection for simplifying the analysis. Communication range ofa node is r. If a node having information is in the TA, the node transmits the information
to other nodes within the communication range of the node. Note that the node receiving
information does not have to be in the TA. We ignore the width of the road, the length of
a vehicle, and the distance between stopped vehicles at the intersection because these areconsidered to be much smaller than r.
In the initial time, the ﬁrst node having information arrives at the intersection fromdirection W, and the traﬃc light for the horizontal direction just turns green. IF continues
while the nodes arriving at the intersection can deliver information to other nodes. If a node
having information leaves the intersection without delivering the information to other node,
the IF ends. Denote the time duration from the initial time to the end of IF by T f . To evaluate
the IF performance, we use E(T f ), where E(·) means the mean of ·.
In the above model, the direction of a node after passing the intersection does not aﬀect
the IF performance obviously. Therefore, we do not consider the direction of a node after
passing the intersection in this paper.

3.

Analysis

In this section, we theoretically analyze E(T f ). Because precisely analyzing E(T f ) is diﬃcult, we use an approximation. In the analysis, we consider time slots whose length is tr as
shown in Fig. 2 and consider in which time slot the IF ends. In Fig. 2, black points represent
the times when nodes arrive at the intersection.
Here, we deﬁne the following symbols.
• sloti : ith time slot. Namely, sloti corresponds to time interval [(i − 1)tr , itr ).
• ti, j : Time when the jth node arrives at the intersection after time t = (i − 1)tr .

135

• Ni : Set of nodes that arrive at the intersection at ti,1 , ti,2 , · · · , ti,k , where k is an integerthat satisﬁes ti,1 ≤ rv , ti,2 ≤ ti,1 + rv , ti,3 ≤ ti,2 + rv , · · · , ti,k ≤ ti,k−1 + rv , ti,k+1 > ti,k + rv .
• Ai : Event where there is at least one node that stops at the intersection due to a red
light in Ni .
• M: Random variable representing the number of Ai s that continuously occur. Namely,
if A1 , A2 , · · · , Ai , and Ai+1 occur, then M = i, where Ai+1 means the complementary
event of Ai+1 .
If A1 occurs, then the IF continues until the start of the next time slot slot2 because atleast one node having information stops at the intersection. Here, even if A1 does not occur,
the IF may continue until the start of the next time slot. Such a case occurs if the last node of
Ni arrives at the intersection after time t = tr . However, such a case rarely occurs especiallyfor a large tr . Therefore, we approximately assume that the IF continues until the start ofslot2 if and only if A1 occurs. In the same manner, we approximately assume that the IFcontinues until the start of sloti+1 if and only if A1 , A2 , · · · , Ai occur. Under this assumption,
if A1 , A2 , · · · , Ai , Ai+1 occur, we have itr ≤ T f < (i + 1)tr because the IF will end in the
middle of sloti+1 . Therefore, we have E(M)tr ≤ E(T f ) < {E(M) + 1}tr . Here, as a lower
bound approximation, we approximately compute E(T f ) by E(M)tr .
E(M) can be represented as
E(M) =

∞i=0 Pr(A1 ) Pr(A2 ) · · · Pr(Ai ) Pr(Ai+1 )i,

(1)

where
Pr(Ai ) =

∞

n=0 Pr(|Ni | = n) Pr(Ai ||Ni | = n),Pr(|Ni | = n) = (1 − e−4λr )n e−4λr , nPr(Ai ||Ni | = n) = 1 − 12 .

(2)
(3)
(4)

From these equations, we ﬁnally haveE(T f ) = e 2−1 tr .
4λr

(5)

Note that this formula does not include the factor of v, which is contrary to intuition. Thisis because E(T f ) depends only on how many times Ai occurs, and the probability that Ai
occurs depends only on λ and r.

4.

Results and discussions

Figure 3 shows the numerical and simulation results of E(T f ). Parameters are as follows:r = 100 m, v = 10 m/s = 36 km/h, λ = 0.01 m−1 in (a), and λ = 0.005 m−1 in (b).
The horizontal axis means tr . From this ﬁgure, the numerical results agree well with thesimulation results, which means that the analysis in the preceding section is valid. We canalso see that E(T f ) linearly increases with tr .

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Theory
Simulation
No traffic lights

3000
2500

Mean floating time [s]Mean floating time [s]

3500

2000
1500
1000
500
0

0

20

40

60
tr [s]

80

100 120

400
350
300
250
200
150
100
50
0

TheorySimulation
No traffic lights

0(a) λ = 0.01 m−1

20

40

60
tr [s]

80

100 120(b) λ = 0.005 m−1
Figure 3: Results of E(T f ).

Figure 3 also includes the numerical results of E(T f ) in the case where there are notraﬃc lights for comparison. E(T f ) without traﬃc lights can be precisely computed by
4λr
E(T f ) = e 4λv−1 − rv . This formula can be easily derived from the formula for a random
clump[5].
Comparing the E(T f ) values for these cases, we can conﬁrm that E(T f ) with traﬃc lights
is signiﬁcantly larger than that without traﬃc lights. For example, if tr = 120 s, E(T f ) with
traﬃc lights is about 15 to 25 times that without traﬃc lights. However, when λ = 0.005
m−1 , E(T f ) with traﬃc lights is only about 400 s even when tr = 120 s. In order to further
increase the E(T f ), it is necessary to extend the TA outside the intersection.
Future works include the analyses of IF for extended TA and for more complicated roadmodels, movement models, and communication models. This work is partially supported
by JSPS KAKENHI Grant Number 19K04371.

References[1] A. V. Castro, G. Di Marzo Serugendo, et al., “Hovering Information - Self-organising
Information that Finds its Own Storage,” Technical Report, School of Computer Science and Information Systems, Birkbeck College, London, UK, BBKCS-07-07 (2007).
[2] K. Nakano, “Epidemic Communication, Information Floating and Safety/Security,”
IEICE Fundamentals Review, vol. 10, no. 4, pp. 282–292, April 2017.
[3] K. Nakano, K. Miyakita, “Information Floating on a Road with Diﬀerent Traﬃc Volumes Between Opposite Lanes,” Journal of Advanced Simulation in Science and Engineering, vol. 3, no. 1, pp. 97–113, Aug. 2016.
[4] K. Miyakita, N. Karasawa, Y. Inagawa, K. Nakano, “A Consideration on Traﬃc Guidance by Information Floating,” IEICE Transactions on Communications (Japanese
Edition), vol. J101-B, no.8, pp. 603–618, Aug. 2018.
[5] P. Hall, Introduction to the theory of coverage processes, John Wiley & Sons, 1988.

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Eﬀects of human body shadowing and entering andleaving of mobile nodes on information ﬂoating in a
one-dimensional street
Naoyuki Karasawa1 , Kazuyuki Miyakita2 , Hiroshi Tamura3 , Keisuke Nakano4
1 Kaishi Professional University
2 Niigata University of International and Information Studies
3 Chuo University
4 Niigata University∗ karasawa.naoyuki@kaishi-pu.ac.jp,

miyakita@nuis.ac.jp,
tamura@elect.chuo-u.ac.jp, nakano@ie.niigata-u.ac.jp

Abstract. In epidemic communication, mobile nodes such as vehicles and pedestrians spatially distribute and deliver information by direct wireless communication between themselves and their movement with information. Epidemic communication has a problem that
information is disorderly spread. To overcome this problem, information ﬂoating, which
permits mobile nodes to transmit information only in transmittable areas, has been proposedand discussed. In this paper, we evaluate performance of information ﬂoating by pedestrians
walking toward opposite directions along a one-dimensional street considering eﬀects of human body shadowing on communication range. In this performance evaluation, we supposethat pedestrians enter and leave the street while doing information ﬂoating, and show eﬀects
of such behavior of mobile nodes on performance of information ﬂoating.
Keywords: information ﬂoating, epidemic communication, human body shadowing, alley

1.

Introduction

In epidemic communication, mobile nodes such as vehicles and pedestrians spatially distribute and deliver information by direct wireless communication between themselves andtheir movement with information. Epidemic communication has a problem that information
is disorderly spread. To overcome this problem, information ﬂoating (IF), which permits
mobile nodes to transmit information only in transmittable areas (TAs), has been proposedand discussed[1, 2, 3, 4, 5, 6, 7, 8]. We consider IF by pedestrians walking toward opposite
directions along a one-dimensional street. We also consider the diﬀerence of densities ofpedestrians between both directions. In such IF, information exchanges between two mobile
nodes moving in same direction are required for continuing IF. In such situation, shadowing caused by the pedestrians’ body occurs because pedestrians often hold or carry user138

alleyx
streetTransmittable Area (TA)

Figure 1: Network Model.

equipment in close proximity to the own body[9, 10]. Then, we need to assume that thecommunication range is diﬀerent according to directions of two mobile nodes that information exchanges.
In [8], we evaluate eﬀects of human body shadowing on IF in a street assuming thatmobile nodes move along the street. In this paper, we consider the same problem in amore complicated mobility model because performance of IF is aﬀected by the mobility
characteristics of the mobile nodes. Here, we assume that pedestrians enter and leave thestreet while doing IF. We evaluate performance of IF under these assumptions to explore
the both of the eﬀect of human body shadowing and the eﬀects of such behavior of mobile
nodes.

2.

Assumptions and Models

In this paper, we consider a network model in Fig. 1. The nodes entering from left side of
TA and the nodes entering from right side of TA are distributed based on a Poisson processwith intensities λw and λb , respectively. Each node moves on a street at constant velocity
v. We consider the following two models. In Model 1, nodes do not enter and leave thestreet at any point in TA. In Model 2, nodes can enter and leave the street at some point
in TA. Here, the points at which nodes enter and leave the street are randomly distributed
for simplicity. Let X be the distance from the point that a node enters TA from alley to thepoint that the node enters another alley in Model 2. Assume that X obeys an exponential
distribution of mean xm . In order to compare Models 1 and 2 under the same node density,
we assume the following for node arrival in Model 2. In Model 2, nodes enter the serviceb )v. Each node that enters the service area moves to thearea randomly with intensity (λwx+λm
λwb.
right with probability λw +λb and moves to the left with probability λwλ+λb
In both of Model 1 and Model 2, the communication range of a node is r. A node having
information in TA can transmit information to other node if the distance between these nodes
is not longer than r. In this paper, we consider human body shadowing. We assume that thevalue of r is diﬀerent according to the directions of sender and receiver. If the sender andreceiver face each other, r = ra . If the sender and receiver move toward the same direction,r = rb . Due to the eﬀect of human body shadowing, we assume that ra ≥ rb .

139

3.

Simulation results and discussions

In this paper, we evaluate mean lifetime of IF, denoted by E(T f ), by computer simulations.
In the computer simulations, λw = 0.03m−1 , the length of TA is 500m, v = 1m/sec, xm =2000, 1000, 500, 250m. ra = 100m, and rb = 100m, 50m, 25m. Note that the parameter
rb = 100m means the case without human body shadowing, and the parameters rb = 50m
and rb = 25m mean the case with human body shadowing.
The simulation results of Model 1 and Model 2 are shown in Fig.2. The horizontal axis
represents λb , and the vertical axis represents E(T f ). From these results, if there is no humanbody shadowing (i.e., rb = 100m), E(T f ) in Model 2 is larger than that in Model 1. On theother hand, if the eﬀect of human body shadowing is large (i.e., rb = 25m), E(T f ) in Model
2 is smaller than that in Model 1. We consider the reason of these results as follows. The
eﬀect of nodes entering and leaving the street has both advantage and disadvantage in termsof continuation of IF. The advantage is that the topology of nodes can be rapidly changed,
which may contribute to delivering information to nodes that do not have information. The
disadvantage is that nodes having information may suddenly disappeared, which causes asmaller E(T f ). We consider that the advantage outweighs the disadvantage in the case ofno human body shadowing, and that the disadvantage outweighs the advantage in the casewhere the eﬀect of human body shadowing is large.
This work was partially supported by JSPS KAKENHI Grant Number 19K04371.

References[1] K. Nakano, “Epidemic Communication, Information Floating and Safety/Security,”
IEICE Fundamentals Review, vol. 10, no. 4, pp.282–292, April 2017. (in Japanese)[2] A. V. Castro, et al., “Hovering Information - Self-Organising Information that Finds
its Own Storage,” BBKCS-07-07, Technical Report, School of Computer Science andInformation Systems, Birkbeck College, London, UK, Nov. 2007.
[3] B. Liu, et al., “Analysis of the information storage capability of VANET for highway
and city traﬃc,” Transportation Research Part C: Emerging Technologies, vol.23,
pp.68–84, 2012.
[4] J. Virtamo, et al., “Criticality condition for information ﬂoating with random walk ofnodes,” Performance Evaluation, Volume 70, Issue 2, pp.114–123, Feb. 2013.
[5] K. Nakano, K. Miyakita, “Information ﬂoating on a road with diﬀerent traﬃc volumes
between opposite lanes,” Journal of Advanced Simulation in Science and Engineering,vol.3, no.1, pp.97–113, Aug. 2016.
[6] K. Nakano, K. Miyakita, “Analysis of information ﬂoating with a ﬁxed source of information considering behavior changes of mobile nodes,” IEICE Trans. Fundamentals,
vol.E99-A, no.8, pp.1529–1538, Aug. 2016.

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30000(b) rb = 50m
㻱㼠㼒㼋㼚㼛
Model 1Model 2 (x =2000m)
㻱㼠㼒㼋㼤㻞㻜㻜㻜

25000

m

m

20000

㻱㼠㼒㼋㼤㻡㻜㻜
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m

Model 2 (x =250m)
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E(T ) [sec]㻱㼠㼒㼋㼤㻝㻜㻜㻜
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10000
5000
0

0

0.001 0.002 0.003 0.004 0.005

Ob [1/m](c) rb = 25m
Figure 2: Simulation results of E(T f ), where ra = 100m and λw = 0.03m−1 .

[7] K. Miyakita, N. Karasawa, Y. Inagawa, K. Nakano, “A consideration on traﬃc guidance by information ﬂoating,” IEICE Trans. Comm. (Japanese Edition), vol.J101-B,
no.8, pp.603–618, April 2018. (in Japanese)[8] N. Karasawa, K. Miyakita, H. Tamura, K. Nakano, “Theoretical Analysis of Information Floating Considering Eﬀects of Human Body Shadowing of Mobile Nodes,” JSST
Technical Report, JSST-MDMC2021-1-02, pp.13–20, April 2021. (in Japanese)[9] D. Kotz, et al., “Experimental evaluation of wireless simulation assumptions,” Proc. ofthe 7th ACM Int. Symp. on Modeling, analysis and simulation of wireless and mobile
systems (MSWiM), pp.78-82, Oct. 2004.
[10] C. Bettstetter, C. Hartmann, “Connectivity of Wireless Multihop Networks in a
Shadow Fading Environment,” Wireless Networks 11, pp.571–579, Sept. 2005.

141

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On the edge Grundy number and the number of vertices in grid graphs
Hiroshi Tamura1*, Keisuke Nakano2
1

2Faculty of Science and Engineering, Chuo University, Japan
Graduate School of Science and Technology, Niigata University, Japan*tamura@elect.chuo-u.ac.jp

Abstract. Relationship between graph coloring and channel assignment in wireless communication is well known. However, almost studies are about the minimum number of colors
despite the difficulty of optimum coloring. In the previous study, we paid attention to graphcoloring assigned maximum number of colors called Grundy coloring. In this paper, we pickup the grid graphs that are applicable to topologies of sensor networks. For edge colorings,
we consider the grid graph that achieves the maximum number of colors.
Keywords: Wireless communication, Channel Assignment, Graph coloring, Edge Grundy coloring

1. Introduction
Relationship between graph coloring and channel assignment in wireless communication iswell known. However, almost studies are about the minimum number of colors. This number
is called the chromatic number of the graph and the problem of finding the chromatic number
is NP hard. In the previous study[1], we paid attention to graph coloring assigned maximum
number of colors called Grundy coloring. Because, it is important to find the required numberof channels. In [1], we showed some graphs expected to be assigned many colors theoretically. In this paper, we pick up the grid graphs that are applicable to topologies of sensor
networks. For edge colorings, we consider the grid graph that achieves the maximum number ofcolors.

2. Assumptions and definitionsFirst of all, we define greedy coloring[2]. A greedy coloring is a coloring of the elements(vertices or edges) of a graph formed by a greedy algorithm that considers the elements of thegraph in sequence and assigns each element its first available color. The number of colors
produced by the greedy coloring for the worst ordering of a given graph G is called its
Grundy number[3] and its coloring is called Grundy coloring. The vertex Grundy coloring is142

JSST2021
popular. The conventional edge coloring version called edge Grundy number and edge
Grundy coloring is discussed in [4].
We explain edge Grundy coloring. We consider a path graph(Fig.1(a)). In Fig.1(a), thenumber with parenthesis represents edge ordering. The edge greedy coloring of Fig.1(a) is
Fig.1(b).

(a)(b)
Fig.1 An edge ordering and coloring.

(a)(b)
Fig.2 An edge ordering and coloring.
Another case is in Fig.2. The number of colors is 2 in Fig.1(b) and 3 in Fig.2(b). Since
the edge Grundy number is the maximum number of colors, the edge Grundy number of thepath graph is 3.
In [1], we showed the graphs assigned many colors theoretically and vertex/edge orderingof coloring.
[Theorem 1][1]Let G be a graph. For a greedy coloring, the number of colors is not greater thanmax {deg(u) +1 | u is a vertex of G}, in case of vertex coloring,max{deg(u)+deg(v) -1| (u,v) is an edge of G}, in case of edge colorings,
where deg(u) is the degree of vertex u.
Theorem 1 shows the upper bounds of colors for Grundy number/ edge Grundy number.

3. Results
In this section, we consider grid graphs (Fig.3)

Fig.3 A grid graph G.
In the grid graph, the maximum number of colors in edge Grundy coloring
deg(u)+deg(v) - 1=4+4-1=7

143

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from Theorem1. In this paper, a grid graph means graph G of Fig.3 or a subgraph of G,

Fig.4(a) A colored grid graph G.

Fig.4(b) A tree T whose edge Grundy number is 7.

Graph G of Fig.4(a) is a colored grid graph and the edge Grundy number is 7. From thediscussion of [1], in case of deg(u)=deg(v)=4, the number of vertices of T in Fig.4(b) is
minimum of all trees whose edge Grundy number are 7. We obtain graph G by embedding T
to a grid graph.
In the assumption above, a color is assigned to an edge once, the color remains on the edge.
Hereafter, we adopt an operation to delete a color once assigned. Because, in communication
networks, when communication is terminated, the corresponding edge should be decolored.
Therefore, in a graph coloring, we assume the deleting operation of color on an edge. For
example, the edge Grundy number of G in Fig.5 is 2. However, in the following ordering, thenumber of colors is 3.
e2, e3, e2(x), e1, e2

Fig.5 A graph G.
Here, e2(x) represents deletion of the color of e2. This coloring is called Edge Grundy
coloring with decoloring. Since Grundy coloring with decoloring is a generalized Grundy
coloring, the number of colors may increase. However, it is easy to show that Theorem 1
holds.

144

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Fig.6(a) A grid graph G.

Fig.6(b) A tree T whose edge Grundy number is 7.

In G of Fig.6(a), the edge ordering for coloring is the follows.

e5,e6,e7,e4,e5(x),e9,e5,e6(x),e8,e10,e6,e7(x),e3,e2,e1,e7Finally, color 7 is assigned to e7. In edge Grundy coloring with decoloring, the number ofvertices of G of Fig.6(a) is minimum of all graphs whose edge Grundy number are 7. Becausefrom the discussion of [1], in case of deg(u)=deg(v)=4, the number of vertices of T in
Fig.6(b) is minimum of all trees whose edge Grundy number are 7. Therefore we obtaingraph G by embedding T to a grid graph.

Conclusions
In this paper, we show the graph, where the edge Grundy number is maximum and the number of vertices is minimum. Although the size of the graph is small, it is unclear whether the
maximum number of colors will actually be used in some cases. So, verification with computer simulation is necessary.

References[1] H. Tamura, S. Matsumoto, K. Nanano, M. Sengoku, On Graph Coloring with Relation
to Channel Assignment in Wireless Networks,
IEICE Trans. Fundamentals,
Vol.J102-A,No.7,pp.214-223,Jul. 2019.
[2] Tommy R. Jensen, Bjarne Toft: Graph Coloring Problem, John Wiley & Sons,1994.
[3] P. M. Grundy:"Mathematics and games", Eureka, 2: 6–8, 1939.
[4] Leizhen Cai and Xuding Zhu: "Game Chromatic Index of k-Degenerate Graphs, J.
Graph Theory, Vol.36, 3, pp.144-155, 2001.

145

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Simulation of GAMMA 10/PDX plasmas by a plasma
ﬂuid model based on the anisotropic ion pressure (AIP
model)
Satoshi Togo1,* , Naomichi Ezumi1 , Mizuki Sakamoto1 , Md. Shahinul Islam1 ,Tsukasa Sugiyama1 , Kosuke Takanashi1 , Tomonori Takizuka2 , Kenzo Ibano2
1 Plasma Research Center, University of Tsukuba
2 Graduate School of Engineering, Osaka University∗ togo@prc.tsukuba.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.185

146

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Detached helium plasma simulation
with collisional-radiative model
Hirohiko Tanaka1*, Isaya Saeki1, Noriyasu Ohno1, Shin Kajita2, Taichi Ido1,
Hiroki Natsume1, Akiyoshi Hatayama3, Kazuo Hoshino3, Keiji Sawada4, Motoshi Goto5
Graduate School of Engineering, Nagoya University
Institute of Materials and Systems for Sustainability, Nagoya University
3
Faculty of Science and Technology, Keio University
4
Institute of Engineering, Shinshu University
4
National Institute for Fusion Science, National Institutes of Natural Sciences12*h-tanaka@ees.nagoya-u.ac.jp

Abstract. To improve the accuracy of the detached helium plasma simulation, effective rate
coefficients obtained from the collisional-radiative (CR) model were introduced in the plasma
fluid code LINDA. The CR-based and the empirical source terms for the simulation have finite
differences, and computed detached plasmas using these source terms show qualitatively thesame but quantitatively different parameter profiles. This study also suggests the importanceof the choice of source terms particularly in future fusion devices.
Keywords: Detached plasma, Fluid simulation, Collisional-radiative model

1. Introduction
To realize the neuclear fusion reactor, sufficient reduction of the heat load toward the plasmafacing material (“divertor plate”) is an essential issue. For this purpose, the formation of thedetached plasma utilizing the plasma-neutral gas interactions is expected as a promising
method. However, the reliability of the detached plasma simulation is still insufficient possibly
due to simplified models related to atomic and molecular processes. To deal the detaild atomic
processes, this study focused on the collisional-radiative (CR) model in helium plasmas [1,2].
The effective rate coefficients were evaluated with the CR model and then applied to the onedimensional (1D) detached helium plasma simulation using the LINDA code [3,4,5].

2. Results and discussion
In the plasma fluid simulation, the rate coefficients are used to calculate the plasma particle,
momentum, and energy source terms. At first, we compared the rate coefficients and related
source terms obtained from the CR model and the empirical databases. As a result, differences

150

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between several CR-based and empirical source terms were found to be more significant inhigher plasma density case. Detached plasma simulations with CR-based and empirical source
terms showed qualitatively similar but quantitatively different parameter profiles, e.g., the density-peak amplitudes at the highly volume-recombining region (“recombination front”). To validate the simulation, parametric study under various calculation conditions and comparison
with experimental results are needed. Furthermore, because the impact attributed to the different source terms becomes stronger in higher density condition, the choice of source terms ismore important for simulations of future fusion devices with higher density plasmas in front of
the divertor plate.

References[1] T. Fujimoto: A collisional-radiative model for helium and its application to a discharge
plasma, Journal of Quantitative Spectroscopy and Radiative Transfer, 21 (1979) 439455.
[2] M. Goto: Collisional-radiative model for neutral helium in plasma revisited, Journal of
Quantitative Spectroscopy and Radiative Transfer, 76 (2003) 331-344.
[3] T. Furuta, H. Takeda, M. Toma, W. Sato, Y. Homma, Y. Sawada, Y. Nakashima, A.
Hatayama: Modeling of Plasma Transport in the Magnetic Mirror Configuration(GAMMA 10), Fusion Science and Technology, 63 (2013) 411-413.
[4] M.S. Islam, Y Nakashima, A Hatayama: Investigation of plasma behavior during noble
gas injection in the end-cell of GAMMA 10/PDX by using the multi-fluid code ‘LINDA’,
Plasma Physics and Controlled Fusion, 59 (2017) 125010.
[5] H. Tanaka, I. Saeki, N. Ohno, S. Kajita, T. Ido, H. Natsume, A. Hatayama, K. Hoshino,
K. Sawada, M. Goto: Detached helium plasma simulation by a one-dimensional fluid
code with detailed collisional-radiative model, Physics of Plasmas, 27 (2020), 102505.

151

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Development of the eﬃcient electrostatic plasma
particle simulation code for the study of fusion
boundary layer plasmas
Hiroki Hasegawa1,2* and Seiji Ishiguro1,2
1 National Institute for Fusion Science, National Institutes of Natural Sciences
2 Department of Fusion Science, The Graduate University for Advanced Studies,

SOKENDAI∗ hasegawa.hiroki@nifs.ac.jp

Abstract. The three-dimensional (3D) electrostatic particle-in-cell (PIC) simulation code
has been developed with the domain decomposition, in which the field and particle data are
distributed to domains on processes, in the basis of our original 3D-PIC code in which only
the particle data are distributed to processes. In an electrostatic plasma particle code, thePoisson’s equation should be solved in order to obtain the electric potential. In our originalcode, the fast Fourier transform (FFT) is used for this purpose. However, FFT needs all-toall communication. Thus, in the code developed in this study, the subroutine which provides
the simple interface to the FFT libraries adaptable to the domain decomposition is applied.
The code verification has been performed on FUJITSU FX100. We have obtained better
scalability and performance with the developed code than the original code.
Keywords: particle-in-cell, domain decomposition, fast Fourier transform, fusion boundary
layer plasma

1. Introduction
The simulations on supercomputers are one of powerful tools to investigate plasma phenomena in the fusion magnetic confinement devices. Although there are many numericalmethod to study the fusion plasmas, a particle-in-cell (PIC) simulation [1] is used to reveal
the kinetic, i.e., microscopic, dynamics in various plasma phenomena. We have also developed the three-dimensional (3D) electrostatic PIC simulation code called “p3bd” code [2] inorder to investigate the kinetic dynamics in the fusion boundary layer plasma and we haveshown the significant discoveries regarding the non-diﬀusive radial plasma transport in thefusion boundary layer plasma, e.g., Ref. [3]. Our future works regarding those topics needlarger scale simulations than that in our previous studies.
However, the p3bd code cannot calculate huge systems because only the particle data are
distributed to processes and all field data are copied to each process in the p3bd code. That152

is, in the simulations of huge systems, the field data cannot be stored in shared memories oneach processor with the distribution method used in the p3bd code. Thus, in this study, we
have developed the upgraded 3D-PIC code called “up3bd” code in which both the field andthe particle data are distributed to domains on processes.

2. Outline of the up3bd CodeIn this section, we briefly explain the calculation flow of the up3bd code, the domain decomposition, the Poisson solver with the fast Fourier transform (FFT), and the particle data
sort applied in the up3bd code.

2.1. Calculation FlowFirst, the initial positions and velocities of all simulation particles are set (in other words,
particle loading) by the subroutine “init”.
Next, the charge density on the grids is calculated from the particle positions, i.e., thecharges of particles are assigned to the grids by the subroutine “charge”.
Using the charge density on the grid, the electric potential is calculated by the Poisson’sequation. In the subroutine “field”, applying the finite diﬀerence equation of the Poisson’sequation, the electric potential is solved with the FFT [4]. The electric field is obtained fromthe diﬀerence of electric potential.
The acceleration of a particle is computed by the equation of motion in the subroutine“accel” and the position of a particle is developed in the subroutine “move” by means of
the leap frog method [1]. Although the force aﬀecting the charged particle is the Coulomb
force which needs N 2 computation, the plasma particle simulation needs only N computation because the Coulomb force between individual particles is neglected due to the Debye
shielding [5]. After the new positions of particles are calculated, the charge density is computed again.

2.2. Domain Decomposition
In the p3bd and up3bd codes, particles are absorbed at some boundaries [2] and the timedevelopments of absorbed particles are not calculated. Thus, the subroutine “pact” storesthe numbers of particles which are out of the system, i.e., have been absorbed. Also the subroutine “pact” keeps the numbers of particles moved to the next domains in other arrays. In
the up3bd code, the domains are aligned in the z direction, that is, the system is decomposed
one-dimensionally.
In the subroutine “adjust”, the data of non-active particles which are out of the systemand the domain are deleted and the empty arrays caused by the deletion of non-active particle
data is stuﬀed with the active particle data. Furthermore the data of particles moved to thenext domains is transferred to the next domains by the message passing interface (MPI)
communications. Before the data transfer, the data buﬀer array is prepared temporally andthe data of particles moved to the next domains is stored in this array. After that, the data inthis array are transferred to the processes in which the next domains exist.

1532.3. Poisson Solver with FFT
In our original code p3bd, the FFT subroutine for the single-process computation has beenused to solve the Poisson equation. Thus, the whole field data are copied to all processes in
the p3bd code. However, because the field data are distributed to processes with the domain
decomposition in the up3bd code, we should apply a FFT code adaptable to the domain
decomposition. Thus, in this study, we have developed the subroutine called “PoissonFFT2”
which provides the simple interface to the FFT libraries P3DFFT [6] and 2Decomp&FFT [7]in which FFTW [8] is used.

2.4. Sorting the Particle Data
In PIC simulations, the charge assignment needs large computer resource. If the numbersof the particles in the same cell are aligned continuously, the computation time is saved
because the frequency of loading the charge density array on cache memory becomes small.
Thus, in the subroutine “bsort”, the particle data are sorted by the in-place bucket sorting
method. The subroutine “bsort” is called once every several tens of time steps.

3. Code Verification

Elapse Time (s)The verification of the up3bd code has been performed on FUJITSU FX100 of National
Institute for Fusion Science (NIFS). As a result, the calculation shows that the performanceof the up3bd code is about twice as high as that of the p3bd code. Figure 1 presents the
weak scaling of the up3bd code. From these results, we obtain the eﬀective parallelism ratioas 99.959 %. Although the simulations shown in above do not include the sorting, Table 1
shows the comparison between the codes without or with the sorting and indicates that theperformance of the code with sorting is about 1.4 times as high as that of the code without
the sorting. As described above, we have obtained better scalability and performance withthe developed code than the original code.
1000

100

10

100

1000

Nodes
Figure 1: Relation between the number of nodes and the elapse time. Here, the system size
per 8 nodes is 64 × 64 × 256. The average number of particles per 1 cell is 144.

154

Table 1: Comparison between the codes w/o or with the sorting. Each simulation uses 8
nodes.
Elapse time [s] Ratio to peak performance [%]w/o bsortwith bsort (once every 40 times)

110
77.1

2.14
2.84

Acknowledgments
The simulations were carried out on the “Plasma Simulator (PS)” (FUJITSU FX100) of
NIFS. This work is performed with the support and under the auspices of the NIFS Collaboration Research programs (NIFS15KNSS058, NIFS17KNSS086, NIFS19KNSS119, andNIFS21KNSS155) and supported by JSPS KAKENHI Grant Numbers JP23740411 and
JP19K03787. Development of some numerical codes used in this work was supported inpart by the “Code development support program” of Numerical Simulation Reactor research
Project (NSRP), NIFS.

References[1] C.K. Birdsall, A.B. Langdon: Plasma Physics via Computer Simulation, McGrawHill, New York (1985).
[2] Hiroki Hasegawa, Seiji Ishiguro:
Development and Verification of the Threedimensional Electrostatic Particle Simulation Code for the Study of Blob and Hole
Propagation Dynamics, Plasma and Fusion Research, volume:12 (2017), 1401044–
1–1401044–9.
[3] Hiroki Hasegawa, Seiji Ishiguro: Three-dimensional eﬀect of particle motion on
plasma filament dynamics, Physics of Plasmas volume:26 (2019), 062104–1–062104–
5.
[4] W.H. Press et al.: Numerical recipes in Fortran 77 : The art of scientific computing(2nd ed.), Cambridge University Press, New York (1996).
[5] Francis F. Chen: Introduction to Plasma Physics and Controlled Fusion (3rd ed.),Springer International Publishing, Switzerland (2016).
[6] D. Pekurovsky: P3DFFT: a framework for parallel computations of Fourier transforms
in three dimensions, SIAM Journal on Scientific Computing, volume:34(4) (2012),
C192–C209.
[7] N. Li, S. Laizet: 2DECOMP&FFT - A highly scalable 2D decomposition library andFFT interface, Cray User Group 2010 conference (2010).
[8] Matteo Frigo, Steven G. Johnson: The Design and Implementation of FFTW3, Proceedings of the IEEE, volume:93(2) (2005), 216–231.

155

Improved linear notch mechanics based on congruent
condition of stress distribution for all notched materials
Wataru Fujisaki1*, Ryunosuke Sakamoto2, Yuto Shikata2
1

Department of Mechanical Engineering, Kyushu Sangyo University
2
Undergraduate school of Kyusyu Sangyo University*fujisaki@ip.kyusan-u.ac.jp

Abstract. This is a study on a new method to evaluate the brittle fracture strength of the all notchedmaterials correctly. The physical meaning of this fracture mechanics for notch problems is same as theone for crack problems. We discuss the application limit of conventional linear notch mechanics, andclarify the effectiveness of the improved method through calculations and tensile tests.
Keywords: Linear notch mechanics, Estimation method, Brittle fracture strength, FEM

1.

Application limit of conventional linear notch mechanics

One of the authors has proposed a generalized fracture criterion to predict the brittle fracture strengthof the notched materials with from a small hole to a big hole [1],[2]. Here, we call it the improved linear notch mechanics. It is useful to reduce the weight of products which contributes on effective utilization of earth resources and energy conservation. For plane materials, the fracture criteria is based on
one parameter, like as a maximum shear stress or a maximum von Mises stress. On the other hand, fornotched materials, Nisitani had proposed the linear notch mechanics (conventional LNM) using σmaxand ρ [3]. For example, the relationship between the notch radius ρ and the maximum stress σmax at
fracture of a glass fiber reinforced polycarbonate composite material [4] is shown in Fig.1.

Fig.1

Clear master curve in LNM

Fig.2

Unclear master curve in LNM

Here, σmax is the maximum stress on the notch root, ρ is the curvature radius of the notch, and the parameter 1/ρ is almost proportional to the stress gradient χ at the notch root for various size of notchesfrom a small notch to a medium notch. In this case, the conventional LNM holds under the condition
L/ρ>2.0. Here, L is the length of the ligament of the plate. On the other hand, Noguchi et.al. reported
the case in which the conventional LNM does not hold [5] as shown in Fig.2. You can see the valuesof L/ρ＝0.5 apart from other points, and we cannot make a clear master curve of the conventional
LNM．

156

Fig3

Two types of test pieces

Fig.4

Mesh pattern of the notch root

The question is, to how much value of L/ρ, does the conventional LNM hold? The past studies do notreveal it. In recent years, we have systematically calculate the relative stress gradients of center notches and side notches[2] using the test pieces as shown in Fig.3. To calculate the accurate stress gradient,the finite element method (SolidWorks simulation) with 0.3～1.4 million D.O.F and also the methodof fundamental solutions[6] are used. For FEM. The mesh pattern of the notch root is shown in Fig.4.
The length of the one element near the notch root is 0.01 mm which is nearly equal to the grain size ofcommon metal. The reason we choose these two types of test pieces is, when ρ becomes bigger, thedifference of the stress gradients becomes bigger. Therefore, it is ease to evaluate the application limitof conventional LNM using 1/ρ which is the shortcut parameter of the real stress gradient χ.

Fig.5

Stress gradients of center notches

Fig.6

Stress gradient of big notch

We summarized the relative stress gradients of the center notches from L/ρ=0～0.667 in Fig.5. Here,⊿x is the distance from the notch root, and ⊿x/ρ means the relative distance. Therefore, if the relative
stress gradients is same, the stress distribution is controlled by 1/ρ. As a result, for the center notch, thelimitation of application limit of 1/ρ can be distinguished as shown in Fig.5. We can see the conventional LNM can be hold in case of L/ρ>1.5. As ρ becomes bigger in L/ρ<1.5, the stress gradientchanges rapidly and the conventional LNM cannot be applied. This is the same in the case of the side
notches [2].

2.

Usefulness of improved LNM

Therefore, for a big notch problem, we cannot use ρ as the shortcut parameter anymore. For example,157

the comparison of the stress gradients of a big center notch and a big side notch ( L/ρ=0.5) is shown in
Fig.6 using the test pieces as shown in Fig.3 . In this case, you can see the large difference of the relative stress gradient appears, and this means that congruent condition of the stress distribution cannot
be assured by 1/ρ. Therefore, we have to apply the improved LNM which uses a stress gradient χ
directly.

Fig.7

Conventional LNM

Fig. 8

Improved LNM

We have conducted some tensile tests of Cu sheet specimens (W=40mm) systematically. Firstly, we
made the master curve of our experimental results based on the conventional LNM in Fig.7. Eachcondition of the tensile tests is repeated 6 times and the bar represents a 99% confidence interval. The
data of small circular notch size are on the master curve, while the data of the bigger circular notches(L/ρ=0.667; A, B and L/ρ=0.5; C and D) are apart from the master curve. Therefore, we cannot accurately estimate the fracture strength of A～D by the conventional LNM. On the other hand, the newmaster curve based on the improved LNM is shown in Fig.8. Here, the stress gradient χ is ⊿σy /⊿x.
It is clear that the data of A ～D are on the master curve. Therefore, we can correctly evaluate thefracture strength of notched materials with most size by using the improved LNM.

Fig.9 Physical background of improved LNM

Fig.10 Comparison of application limit

The physical background of the improved LNM is shown in Fig.9. Upper part is the linear crackmechanics using the stress intensity factor K. These two criteria are based on a congruent condition of
the stress distribution. If we would like to estimate the brittle fracture strength of the real product from158

the test piece, what we should do is to make the two stress distributions same. For crack problems, one
parameter K guarantees the same stress distribution. On the other hand, for notch problems, the twoparameters σmax, χ guarantee the same stress distribution. The application ranges of the two LNMs areillustrated in Fig.10. The conventional LNM can only be used above L/ρ>1.5. On the other hand, up tonow, it turned out that we can apply the improved LNM to the very big notch with L/ρ=0.5.

3.

Conclusion

We clarified that the conventional LNM can be applied to the medium size of notch (> L/ρ=1.5) andthe improved LNM which can be applied to the bigger size of notch. Up to now, we have conductedsystematic tensile tests and found this improved LNM can be applied to the very big notch problem
with L/ρ=0.5. This improved LNM is based on the stress congruent condition like as the stress intensity factor K. For the notch problems, the two parameters, namely the maximum stress σmax andthe stress gradient χ at the notch root, assure the same stress distribution under small scale yielding
condition. This improved LNM is effective to design the lightweight products including a big notch.

References[1] W.Fujisaki, Y.Takamiya,: Generalized Linear Notch Mechanics for Strength Evaluation, Proc.
Inter. Conf. Japan Society of Simulation and Technology,JSST2017,pp.1-4,2017.
[2] W.Fujisaki, H.Iwatsubo, Y.Takamiya : Effectivness of Generalized Linear Notch Mechanics in
View of Stress Gradient, Proc. Inter. Conf. Japan Society of Simulation and Technology,JSST2018,pp.1-4,2018.
[3] H.Nisitani: Linear Notch Mechanics as an Extention of Linear Fracture Mechanics, Proc. Inter.
Conf. Role of Fracture Mechanics in Modern Technology, (Eds; Sih,G.C. and Nisitani,H.),
pp.23-37,Elsevier,1987.
[4] Y.H. Kim, H.Nisitani: Fracture Criterion in Tension Test of Center Notched Plates of GFRP,Journal of Japan Society of Mechanical Engineering,Vol.56, pp.582-588,1990.
[5] H.Noguchi, Y.Aono: Application Limit of Linear Notch Mechanics, Journal of Japan Society of
Mechanical Engineering, Vol.61, No,589, pp.2044-2051, 1995.
[6] W.Fujisaki: Recent Studies in Meshless & Other Novel Computational Methods, pp.57-69, Tech
Science Press, 2010.
[7] W.Fujisaki, R.Yamasaki : Estimation of fracture strength using improved linear notch mechanics
for notched materials, Proc. 3rd. Inter. Conf. on Comp. Engineering and Science for Safe and Environmental Problems, COMPSAFE 2020,pp.1-4,2020.

159

JSST 2021

Fully explicit computational method for gas-solid
two-phase ﬂow with large temperature variation
Daisuke Toriu1,* and Satoru Ushijima1
1 Academic Center for Computing and Media studies, Kyoto University∗ toriu.daisuke.8v@kyoto-u.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.170

160

JSST2021

Radiation field analysis
using deep learning algorithms
Katsuhiko Yamaguchi*, Masaharu Matsumoto, Yuto Kondo, Kenji Suzuki, Jun Kinugawa
Faculty of Symbiotic Systems Science, Fukushima University*yama@sss.fukushima-u.ac.jp

Abstract. The spatial intensity distribution of γ-rays emitted from radionuclides was analyzed
using the deep Galerkin method, which is one of the deep learning algorithms, and comparedwith the conventional results by the particle transport Monte Carlo method. The results of bothmethods showed good agreement when the effect of the shield was small. This method can be
expected to speed up the calculation by using a deep learning machine equipped with GPUs.
Keywords: deep Galerkin method, γ-rays, radiation field analysis

1. Introduction
Calculating the spatial intensity distribution of γ-rays emitted from radionuclides is a necessary
technology in various fields such as medical treatment and nuclear power plants. Therefore,
many simulations using the particle transport Monte Carlo method have been performed until
now. However, Monte Carlo simulation requires placing meshes in each region of space, andalso a long calculation time. Recently, the deep Galerkin method (DGM), which can be calculated mesh-free, has attracted attention as one of the differential equation solving methods using
a deep learning algorithm [1]. In this study, we propose a new radiation field simulation using
DGM, which has the potential to overcome the difficulties of the Monte Carlo method.

2. Calculation Method
Poisson's equation was assumed as the basic equation of the radiation field in the two-dimensional region shown in Fig. 1. The radiation source was set in a circle with a radius of 0.1
centered on the positions of x = 0.5 and y = 0.5, and the other areas were set as vacuum regions.
First, two points, one coordinate point (x1, y1) inside the calculation area and one coordinate
point (x2, y2) on the boundary, are randomly selected. Next, using these two points as the inputof the DNN, the outputs f (x1, y1) and f (x2, y2) are obtained, and the parameters of the DNN
are optimized so that the following loss function L becomes zero.
222
ïì ¶ f ( x1 , y1 ) ¶ f ( x1 , y1 )ïüL=í++ r ( x1 , y1 ) ý + { f ( x2 , y2 ) - j ( x2 , y2 )}
2
¶x
¶y 2
ïî
ïþ
2

164

(1).

JSST2021
In addition, the radiation intensity distribution was calculated when there is a shield using
the radiation transfer equation [2] as below,
𝑐𝑜𝑠 𝜃

𝜕𝐼!
𝜕𝐼!
+ 𝑠𝑖𝑛 𝜃− 𝑆(𝑥, 𝑦, 𝜃) + 𝜇" (𝑥, 𝑦, 𝜃)𝐼! (𝑥, 𝑦, 𝜃) = 0
𝜕𝑥
𝜕𝑦

(2).

Here, In means the radiation intensity at each position. In addition, S indicates the production
term and μa indicates the absorption coefficient. Calculation results by DGM were compared
the ones by a Monte Carlo simulation code (PHITS) [3].

3. Results and Discussion
Figure 2 shows the results of the radiation intensity distribution calculated by DGM basedon (1). The two-dimensional map (left) draws that the radiation intensity is symmetrical fromthe center. The radiation intensity distribution on y = 0.5 (right) shows a graph that is inversely
proportional to the distance from the center. This result is in good agreement with the result
calculated by the Monte Carlo method for the radiation intensity distribution emitted from thepoint source placed in vacuum. Furthermore, it should be noted that this calculation result is
expressed as a continuous value that does not depend on the mesh.

Fig.1 Computational area set in 2D.

Fig.2 Calcuration results of the radiation intensity distribution by DGM.

165

JSST2021
Figure 3 shows the radiation intensity calculation result when the shield is placed near theradiation source. Figure 3(a) shows the calculation result by the Monte Carlo simulation, andaluminum is arranged as a shield at the position indicated by the white frame. Figure 3(b) is
the result by DGM, and it can be seen that it corresponds well with Figure 3 (a). As describedabove, since the results can be obtained without arranging the mesh in the calculation by DGM,
it is highly expected as a new simulation method.

Al(a) MC(b) DGM

Fig.3 Calcuration results of the radiation intensity distribution when there is a shield.

References[1] Sirignano and Konstantinos Spiliopoulos, “DGM: A deep learning algorithm of solving
partial differential equations”, Journal of Computational Physics, Vol.375, pp.1339-1364,
2018.
[2] D. Mihalas and B. Weibel-Mihalas: Foundations of Radiation Hydrodynamics, Dover, 1999.
[3] Yosuke Iwamoto, Tatsuhiko Sato, Shintaro Hashimoto, Tatsuhiko Ogawa, Takuya Furuta,
Shin-ichiro Abe, Takeshi Kai, Norihiro Matsuda, Ryuji Hosoyamada and Koji Niita
Benchmark study of the recent version of the PHITS code, J. Nucl. Sci. Technol. 54,
617-635 (2017)166

JSST 2021

Laguerre-Gaussian beam formation by
spatiotemporal coherent motion of electrons
Shin Kubo1,* , Yuki Goto2 , Toru I. Tsujimura2 , Toru Kobayashi3
1 College of Engineering, Chubu University
2 National Institute for Fusion Science
3 Department of Applied Energy, Nagoya University∗ kuboshin@isc.chubu.ac.jp

Abstract. The radiation from single electron in circular motion is shown to have a helicalphase structure. Such radiation from multi-electron system is expected to form a LaguerreGaussian (LG) beam which is identiﬁed as an optical vortex and proved to have an orbital
angular momentum (OAM). Spatiotemporal coherence of the electrons in circular motion
would be the key to form a LG beam with high purity and high eﬃciency. This paper
describes the method to clarify the eﬀect of spatiotemporal coherence to form LG beamwith OAM.
Keywords: Laguerre-Gaussian beam, orbital angular momentum, vortex, coherence

1.

Introduction

Optical vortex is recognized by Allen et al.[1] as one of the characteristic feature of LaguerreGaussian (LG) beam. They demonstrated LG beam carries orbital angular momentum(OAM).
Since then, optical vortex has been intensively investigated in both characterization and application of OAM. There the Laguerre-Gaussian beam are generated from normal Gaussian
beam utilizing optical converters, such as grating or phase plate. M. Katoh et al. demonstrated an electron in circular motion emits a radiation with twisted phase front[2, 3]. They
also indicated that electrons in cyclotron motion exist anywhere in the universe and optical vortex should be associated with the ubiquitous electron cyclotron emission (ECE). A
question arises why such ubiquitous optical vortex was not observed so far? One of thereasons is that the theoretical and experimental investigations had been focused mainly on
the intensity characteristics of the ECE and dedicated investigation had not been performedin view of OAM. The other important reason would be ECE from thermal electrons haverandom gyro-phases and the vortex feature will be cancelled out. This point had been partly
clariﬁed by Goto [4] by calculating far ﬁeld phase structure of the summation of several
electrons distributed homogeneously conﬁned in a ﬁnite area but with partly coherent gyrophase. An experiment to control the gyro-phase by accelerating electron cyclotron motion167

by an externally applied resonant electromagnetic wave is underway. It is worth investigating the condition of the spatiotemporal coherence to form LG beam. Far ﬁeld calculation
can be performed just like Fresnel-Kirchoﬀ integral of the radiation from each electron withgiven spatiotemporal coherence. The amount or the purity of the LG beam can be estimatedby utilizing the orthogonality of the Laguerre function. This paper describes how spatiotemporal coherence and structures of source density and phase of the radiating electrons aﬀects
the LG beam eﬃciency. Clarifying this condition leads to an active control of vortex ECE
or interpretation of forced vortex ECE by a resonant electromagnetic ﬁeld.

2.

Acceleration of electrons in a static magnetic ﬁeld by externally applied RF and radiation from them

If an electron moves in a propagating electro-magnetic wave with the electric ﬁeld Eext =Eext exp[−i(ωext t − kext · r)], Bext = (kext /ωext ) × Eext = nc × Eext , in a static magnetic ﬁeld
B0 = B0 ẑ, the motion of electrons can be described by a relativistic equation of motion[5],

e 
Ωe0
←
→
β̇ =
I −β⋄β+β × n×· Ẽext + (β × ẑ)(1)| {z }| {z }
me0 cγγ|{z}electric f ield contribution magnetic f ield contribution|{z} Lorentz f orceacceleration by oscillating external f ield

Here, e is electron charge with negative sign, Ωe0 is an electron cyclotron angular frequencyof electron rest mass me0 (≡ eB0 /me0 ).
The electric ﬁeld radiated from accelerated electron at distance R can be described by
R = |r − r′ | is a distance between the charged particle (position r′ ) and observer (position r),q̂ = (r−r′ )/|r−r′ | is a unit vector in the direction from particle to the observer, t′ = t−R(t′ )/cdeﬁnes a retarded time, β = uc is a normalized velocity of particle by light velocity c, andg = (1− q̂·β) deﬁnes a longitudinal relativistic Doppler factor. After some manipulations, theelectric ﬁeld at far-ﬁeld region r radiated from an accelerated electron at r′ can be describedas q̂ × ( q̂ − β) × β̇ e  (1 − β2
)(
q̂ −
β)
Erad (r, t) =+(2)
4πε0  g3 R2
g3 cR
t′
|
{z
} |
{z
}
near− f ield

f ar− f ield

The idea here comes that applying resonant external ﬁeld at electron cyclotron frequency, intensify the perpendicular energy of electrons and increases phase and space coherence of gyro-motion. Actually, in the non-relativistic regime, β̇ is proportional to the external
electric ﬁeld and gyration phase should become highly coherent intime and space with external wave ﬁeld[4, 5]. Furthermore the trial
to detect the optical vortex feature is underway. Here, the electrons
in a magnetic ﬁeld are accelerated by externally applied high powerright hand circularly polarized resonant wave and phase and intensity structure at far ﬁeld of second harmonic radiation from these168

electrons. Due to the non-linear dependence of β̇ on Eext and Erad on β̇ as shown in Eqns.
(1) and (2). Therfore, it is important to know how the spatiotemporal coherence of electron
motion aﬀects the total radiation as a LG beam. This investigation may indicate the way tocontrol or optimize the quality of the generated LG beam.

3.

Spatiotemporal coherence and LG beam formation

Given calculated far-ﬁeld Erad (r) pattern using formula (2) on some target plane assuming
spatiotemporal coherence , one can estimate the LGℓ,p beam purity ηℓ,p using the formulaR
E (r) · E∗LGℓ,p (r, ω)dS
S rad
(3)
ηℓ,p ≡ qR
qR
∗
∗
E
(r)
·
E
(r)dS
E
(r,
ω)
·
E
(r,
ω)dS
LGℓ,p
rad
S rad
S LGℓ,pHere,Erad (r, ω) =

n Z ∞
X
i=1

e  q̂i × ( q̂i − βi ) × β̇i  −iωte dt
g3i cRt′−∞ 4πε0(4)

is a summation of radiation ﬁeld from n electrons. Here, LG beam is deﬁned bys√ r2 
2p!  2r |ℓ| w0 p  2r2 
exp
−
L|ℓ|
ELGℓ,p (r, ω) = ep
π(p + |ℓ|)! w(z) w(z)w(z)2w( z)2r2 × exp[iℓϕ] · exp −ik0
exp −i(|ℓ| + 2p + 1)η e−iωt dt
(5)
2R(z)
2 


λ(z−z0 )2
2, R(z) = (z −here, ep is a unit vector expressing a polarization, w(z) = w0 1 + πw2
0


2 


n is Laguerre function deﬁned by0)0)z0,σ ) 1 + λ(z−zand η(z) = tan−1 λ(z−z
Lm
πw2
πw2
0

0

n
=
Lm

exp[r]r−n dm 

exp[−r]rn+m
m



(6)
m!
dr
The spatiotemporal coherence here can be interpreted as the distribution of electrons inreal and velocity space relative to externally applied RF ﬁeld, for example.

References[1] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and thetransformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45 (1992) 8185-8189.
[2] M. Katoh, M. Fujimoto, H. Kawaguchi et al. Angular Momentum of Twisted Radiation from an Electron in Spiral
Motion, Physical Review Letters 118 (2017) 094801–.
[3] M. Katoh, M. Fujimoto, N. S. Mirian, T. Konomi et al., Helical Phase Structure of Radiation from an Electron in
Circular Motion, Scientiﬁc Reports 7 (2017) 6130–.
[4] Yuki Goto, Shin Kubo and Toru Ii Tsujimura, Coherent Cyclotron Emission with a Helical Wavefront from Multielectron System Accelerated by the Circularly Polarized Wave, New Journal of Physics, in press (2021).
[5] Yuki Goto, Shin Kubo and Toru Ii Tsujimura, Cyclotron Emission with a Helical Wavefront from an Electron Accelerated by the Circularly Polarized Wave Journal of Advanced Simulation Science and Engineering 7 (2020) 34-50.

169

JSST 2021

Application of optical vortex to laser-induced
ﬂuorescence velocimetry of ions in a plasma
Shinji Yoshimura1,* , Kenichiro Terasaka2 , Mitsutoshi Aramaki3
1 National Institute for Fusion Science
2 Kyushu University
3 Nihon University∗ yoshimura.shinji@nifs.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.150

170

JSST2021

FDTD analysis of propagation of millimeter wave
vortex in magnetized cold-plasma
Kazuki Chiba1* and Hideki Kawaguchi**
Division of Information and Electronic Engineering, Muroran Institute of Technology.
*20043037@mmm.muroran-it.ac.jp**Kawa@mmm.muroran-it.ac.jp

Abstract. Since it was pointed out that an optical vortex carries orbital angular momentum in
1992, various kinds of research works on the optical vortex have been performed actively. In
addition, it was found that the vortex phenomena can exist in other frequency ranges such as
X-ray, ultraviolet, millimeter and so on. Recently it was theoretically shown that the millimeterwave vortex can propagate in magnetized cold plasma where plane wave is blocked by cut-off
condition. In this study, we present the FDTD simulation of the propagations of the milli-meter
vortex wave in the magnetized cold plasma.
Keywords: FDTD method, nuclear fusion plasma, optical vortex, milli-meter wave, magnetizedcold plasma

1. Introduction
An optical vortex has its proper characteristics of a spiral structure wavefront and transportation of orbital angular momentum[1]. Various applications such as large capacity optical communication and optical tweezers have been considered to employ these special characteristics.
Recently the vortex phenomenon in milli-wave frequency range was applied to a plasma heating in a nuclear fusion device and it was found from theoretical discussions that the vortex
milliwave may propagate in magnetized cold plasma in which a plane wave with the same
frequency can not propagate[2]. In this work, the propagation properties of the milli-wave vortex
in the magnetized cold plasma are investigated by using numerical simulation of the FDTD
method.

2. FDTD simulation of millimeter in magnetized cold plasma
In the FDTD simulation of the magnetized cold plasma, the plasma is considered as a dispersive medium described by the following Lorentz-Drude model,
𝑑𝑱
𝑱
𝑑𝑷+ 𝜈𝑱 + 𝜔0𝟐 𝐏 = 𝜀0 𝜔𝑝2 (𝑬 +× 𝑩𝟎 ) , 𝑱 =
𝑑𝑡
𝑒𝑛𝑒
𝑑𝑡
Then the electric field 𝑬 in (1) is calculated by the following Maxwell’s equations,

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𝛻 × 𝑯 = 𝑱 + 𝜀0

𝜕𝑬𝜕𝑯
, 𝛻 × 𝑬 = −𝜇0
𝜕𝑡
𝜕𝑡

(2)

On the other hand, the current density 𝑱 in (2) is provided from the calculation of (1). That is,
the time-domain calculation of (1) and (2) are carried out simultaneously.

3. Numerical example
Numerical model of the FDTD simulation of the milli-wave vortex in the magnetized cold
plasma is depicted in Fig.1. Circularly polarized HE11 mode with 84GHz frequency generated
in the corrugated wavegate is passed through the spiral dielectric plate at the downstream endof waveguide and transformed to the milli-wave vortex field on the another side of the spiraldielectric plate[3]. And the milliwave vortex is injected into the cold plasma region in which theexternal magnetic field 𝑩𝟎 is applied. In Fig.2, distributions of intensity of electric field of 𝑥𝑧 vertical cross-section are depicted for two kinds incident waves of the HE11 plane milli-wave(a) and milli-wave vortex (b). It is found that the milli-wave vortex can propagate the magnetized cold plasma which has cut-off condition for plane wave.
Spiral dielectric plate
HE11 mode with
84[GHz] frequency

Plasma region

𝑩𝟎
Circular corrugated waveguide

Millimeterwave vortex

Externally appliedmagnetized field

Fig.1 Numerical model of FDTD simulation of vortex wave in magnetized cold plasma.

Fig.2.

(a) Propagation of plane wave.

(b) Propagation of vortex wave.

References[1] L.Allen, M.W. Beijersbergen, R.J.C. Spreeuw and J.P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A.,
Vol.45, No.2 (1992), pp.8185-8189.
[2] T.Tsujimura and S,Kubo, Propagation properties of electron cyclotron waves with helical
wavefronts in magnetized plasma, Phys.Plasmas Vol.28,012502(2021).
[3] H.Kawaguchi, H.Nakamura, Evaluation of Mechanical Torque Acting on Scatterer in Mi
crowave Vortex Fields, IEEE Microwave and Wireless Components Letters, Vol.29, Issue7, pp.504-506, July (2019).

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Various characteristic evaluation
on magnetically-coupled intra-body communication
using three-dimensional finite element modelingof a human upper-body
Kenichi Ito1*
1

Niigata Institute of Technology*itoh@iee.niit.ac.jp

Abstract. This study examined the signal transmission loss characteristic, biosafety criteria,
and transmitting and receiving power efficiency on magnetically-coupled intra-body communication through computer simulation using three-dimensional finite element modeling (FEM)
of a human upper body. The transmitter and receiver were placed on the chest and upper arm,
respectively, and their coils were arranged at right angles to establish their positional relationship. Three types of coupling were chosen as the magnetic coupling methods: non-resonant
inductive, low-Q resonant, and high-Q resonant. The signal transmission loss for each coupling
method was 12~13 dB worse than the previous results on condition that their transmitter andreceiver coils were linearly arranged in parallel on both arms. When the coil was placed on thechest, the biosafety was as high as it was in the previous results. In addition, we have shown
the possibility that the power efficiencies of the two resonant couplings were higher than thatof the non-resonant inductive coupling.
Keywords: intra-body communication, signal transmission loss, biosafety, power efficiency

1. Introduction
Intra-body communication (IBC) is a new transmission method that uses a human body as thetransmission medium. Generally, although capacitive and galvanic coupling methods havebeen utilized [1], magnetic-coupling was recently proposed as the third method [2], which uses
coils as the antennas of the transmitters and receivers. The transmitter generates a magnetic
field signal by adding an alternating current to the transmitting coil, and the receiver detects
this signal as the current signal using the receiving coil. The signal transmission loss characteristic of this magnetically-coupled method relies heavily on adopted coupling methods. So
far, we have analyzed the characteristics of several magnetic-coupling methods in an attempt
to minimize signal loss [3]. In this study, we examined a general inductive (non-resonant) coupling method, and two types of resonant (low-Q and high-Q) coupling methods. Low-Q resonant coupling is a method in which the transmitting and receiving coils are resonated by adding
capacitances to them, whereas high-Q resonant coupling is a method in which the added coils
are resonated by placing the coils and capacitances in the vicinity of transmitting and receiving
coils.

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Although previous studies analyzed inter-coil distances of up to 100 cm (the communication range for IBC), their transmitting and receiving coils were linearly arranged in parallelon both arms. This study analyzed a more practical situation, in which the transmitting coil wasplaced on the chest in such a way that the direction of both transmitting and receiving coils
would be at right angles. The items that had to be analyzed were the signal transmission loss
characteristic, biosafety criteria (internal electric field intensity and localized specific absorption rate (SAR)) based on the international commission on non-ionizing radiation protection,and transmitting and receiving power efficiency.

2. Three-dimensional finite element modeling of a human upper body
Figure 1 illustrates the circuit-coupled FEM models, which are designed using COMSOL 5.5
software. The models mainly consist of air, an upper body, and transmitter and receiver circuits.
The model in Fig. 1(a) is used for non-resonant and low-Q resonant couplings, whereas themodel in Fig. 1(b) is used for high-Q resonant coupling. Coil 1 and coil 4 denote the transmitting and receiving coils, respectively, whereas, coil 2 and coil 3 represent the resonance coils
for high-Q resonant coupling. The turn number of coil 1 and coil 4 was set to 1, whereas it
was set to 2.5 for coil 2 and coil 3. The transmitter and receiver circuits (except for the coils)
were incorporated as the electric circuit elements.
Human upper body

Human upper body

Coil1

Coil1
Coil2

Coil4

Coil3
Coil4

(a)

(b)

Figure 1. Three-dimensional FEM of a human upper body.

3. Computer simulation
3.1. Simulation conditions
The signal loss quantity for each coupling method was evaluated at several inter-coil distances.
For both non-resonant and low-Q resonant couplings, the distance between coil 1 and coil 4
was set to 40, 50, and 60 cm (Fig. 1(a)). For high-Q resonant coupling, the distance between
coil 2 and coil 3 was set to the same previous values, and coil 1 and coil 4 were arranged incloser proximity to coil 2 and coil 3, respectively (Fig. 1(b)). The variable range of the measurement frequency was approximately 300 kHz– 10 MHz and the resonant frequency was set
to 2 MHz. The internal electric field intensity, localized SAR, and transmitting and receiving
power were computed at an inter-coil distance of 60 cm, and the internal electric field intensity
and localized SAR were compared to the basic restrictions for public exposure.

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3.2. Signal transmission loss frequency characteristic
The signal loss frequency characteristics at each inter-coil distance is depicted in Fig. 2. Frequency characteristics showed the same tendency as they did in the previous results [3]. In
short, for non-resonant coupling, the signal loss quantity at each inter-coil distance was minimum at 2 − 3 MHz; whereas, for low-Q and high-Q resonant couplings it was respectively
improved by 10 and 20 dB at the resonant frequency. Compared to the previous results [3]on condition that the transmitter and receiver coils were linearly arranged in parallel on botharms, the signal loss quantity at the same inter coil distance was approximately 12– 13 dB
worse for each coupling method.

3.3. Internal electric field intensity and localized SAR characteristics
The maximum values of the internal electric field intensity and localized SAR for each coupling method at an inter-coil distance of 60 cm is depicted in Fig. 3. The maximum values ofboth criteria were the largest for high-Q resonant coupling compared to those of other couplings
at a resonant frequency of 2 MHz. The maximum values of both criteria were 1 V/m and0.001 W/kg, respectively, and as before [3], they were two or four orders of magnitude smaller
than the basic restrictions for general public exposure: 1.35 × 10^4 𝑓 V/m and 2 W/kg, respectively. This indicated that biosafety was sufficiently high even though the coil was placedon the chest.

3.4. Transmitting and receiving power characteristics
The transmitting and receiving power characteristics at an inter-coil distance of 60 cm aredepicted in Fig. 4. As shown in Fig. 4(a), the transmitting power for non-resonant couplingdecreased as the frequency increased. On the other hand, the transmitting powers for low-Q
and high-Q resonant couplings were minimum at the resonant frequency, and these values wererelatively smaller than those for non-resonant coupling (2.5 % and 4 %). As shown in Fig.
4(b), the receiving powers for low-Q and high-Q resonant couplings showed nearly opposite
characteristics, and these values were relatively larger than those for non-resonant coupling(12 times and 200 times). This indicated that low-Q and high-Q resonant couplings had
higher power efficiencies than non-resonant coupling.

References[1] M. Seyedi, B. Kibret, D. T. H. Lai and M. Faulkner: A survey on intrabody communications for body area network applications, IEEE Trans. Biomed. Eng., 60:8 (2013), 20672079.
[2] J. park, P. Mercier: Magnetic human body communication, EMBC2015, (2015), 18411843.
[3] K. Ito: Signal transmission characteristic and biosafety evaluation on magnetically coupled intra-body communication, JSST2019 Oral, (2019), 178-181.
[4] Y. M. Gao, H. f. Zhang, et al.: Electrical exposure analysis of galvanic‑coupled intra‑body communication based on the empirical arm models, BioMed Eng OnLine, 17:71(2018).

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Attenuation [dB]

40cm

-40

50cm
-60

60cm

-80
-100

40cm

-40

50cm

-60

60cm

-80
-100
-120

-120
0.1

1
Frequency [MHz]

0.1

10

(a) Non-resonant coupling1
Frequency [MHz]10(b) Low-Q resonant coupling

Attenuation [dB]

-20
40cm

-40

50cm
-60

60cm

-80
-100
-120
0.1

1
Frequency [MHz]10(c) High-Q resonant coupling
Figure 2. Signal loss frequency characteristics.
1.E-03
Induct. 60cm

1.E-04
SAR [W/kg]

Electric Field [V/m]1

Induct. 60cm

0.1

LowQ 60cm

LowQ 60cm
1.E-05HighQ 60cm

1.E-06HighQ 60cm

0.01

1.E-070.1

1Frequency [MHz]

10

0.1

(a) Internal electric field intensity

1Frequency [MHz]10(b) Localized SAR

Figure 3. Internal electric field intensity and localized SAR characteristics.
1.20E-09

Receiving power [W]

1.20E-02
Transmitting power [W]Attenuation [dB]-20

1.00E-02
8.00E-03
6.00E-03

no reso.

4.00E-03

lowQ

2.00E-03

highQ

1.00E-09

no reso.

8.00E-10

lowQ

6.00E-10highQ

4.00E-10
2.00E-10
0.00E+00

0.00E+00
0.1

1Frequency [MHz]

0.1

10

(a) Transmitting power

1
Frequency [MHz](b) Receiving power

Figure 4. Transmitting and receiving power characteristics.

178

10

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Excitation of Metal Plate Using Folded Dipole
Antenna
Takumi Nishime* , Hiroshi Hashiguchi , Naobumi Michishita , Hisashi Morishita
Graduate School of Science and Engineering, National Defense Academy∗ ed21001@nda.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.128

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Development of hydrogen recycling modelon carbon divertor by molecular dynamics simulation
Yuki Kojima 1, Hiroaki Nakamura 2,3, Keiji Sawada 4, Gakushi Kawamura2,5, Masahiro
Kobayashi 2,5, Masahiro Hasuo 6, Masato Iida 1, Mayuko Miura 1, Seiki Saito 1*
1

Department of Information and Electronics, Faculty of Engineering, Yamagata University
2

Department of Helical Plasma Research, National Institude for Fusion Science
Department of Electrical Engineering, Graduate School of Engineering, Nagoya University
4
Department of Material System Engineering, Faculty of Engineering, Shinsyu University
5
Department of Fusion Science, Physical Sciences Research Section, The Graduate University for
Adcanced Studies
6
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto
University
3*saitos@yz.yzmagata-u.ac.jp

Abstract.
We develop a hydrogen recycling model on carbon divertor by molecular dynamics simulation.
In this model, neumerical simulation of one hydrogen atom injection into a carbon material is
performed. NVE ensemble is adapted for calculation of motion of atoms in the center of the
carbon material. As a result, the hydrogen molecules in relatively high state is observed.
Keywords: Molecular dynamics simulation, Recycling, Neuclear fusion.

1. Introduction
Plasma facing materials are bombarded by hydrogen plasma in magnetic confinement plasma
devices such as Large Helical Device (LHD) in National Institute for Fusion Science, Japan.
In the case of LHD, the divertor which directly contacts to plasma is made of carbon materials.
When the divertor plates are irradiated by hydrogen ions, some hydrogen atoms reflect andback to the plasma while the other hydrogen atoms retain in the divertor. The investigation ofthis recycling of hydrogen ions at the divertor is an important issue because this recycled hydrogen atoms or molecules affects the plasma parameter by the charge exchange recombinationand dissociative recombination. Therefore, in order to obtaine information of recycled hydrogen atoms and molecules on the divertor, we developed a hydrogen recycling model [1-4] bymolecular dynamics (MD) simulation of a hydrogen atom injection into a carbon material is183

JSST2021
performed to investigate the distribution of the rovibrational states, translational energy andemission angle of emitted hydrogen molecules in addition to atoms.

2. Simulation Model [1, 2]
A carbon amorphous structure consisting of 3872 carbon atoms and 2080 hydrogen atoms
shown in Fig. 1 is prepared for the target material. The size of the target material is40Å ×40Å ×30Å. The unit structure is determined by two steps as follows: an amorphous carbon structure which containing excess hydrogen atoms is prepared; excess hydrogen atoms are
removed by annealing the structure in Langevin thermostat using Molecular Dynamics (MD)simulations to creat stable structure. The density of carbon atoms are fixed at density which isdetermined by another MD simulation by depositing carbon atoms on a diamond substrate. The
initial material temparture is set to 300K. Brenner’s potential is employed for the interatomic
potential between carbon and hydrogen atoms. One hydrogen atom is injected into the target
material with incident energy 100 eV. The incident angle is set to parallel to z-axis. The x andy-coordinates of the starting position of the incident hydrogen atom are set randomly in therange of -5Å<x<5Å, -5Å<y<5Å as shown in Fig. 2. The simulation time is set to 50 ps. Angularand energy distridutions of recycled and reflected hydrogen atoms are calculated. The atomic
motions are solved under the NVE ensemble where the number of particles (N), volume (V),and total energy (E) are conserved. To obtain statistical data, 1500 simulations are performed
for the same condition with changing the x and y-coordinates of the incident positions by random numbers. The thermostat is attached the edge hatched region in Fig. 2.

Fig. 1: Simulation system.

Fig. 2: Surface of the target material.

3. Simulation Result [1]Figure 3 shows the distriburion of rotational state J of emitted hydrogen molecules. It is foundthat the hydrogen molecules in relatively high state exist. We would like to discuss the resultsin detail at the presentation. Please refer the reference [1] for the results of vibrational states of
emitted hydrogen molecules.

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Fig. 3: Distribution of rotational state J.

Reference[1] Seiki Saito, Hiroaki Nakamura, Keiji Sawada, Gakushi Kawamura, Masahiro Kobayashi,
Masahiro Hasuo: Molecular dynamics simulation model of hydrogen recycling on carbon
divertor for neutral transport analysis in large helical device, Contribution to Plasma
Physics, e201900152 (2020).
[2] S. Saito, H. Nakamura, K. Sawada, G. Kawamura, M. Kobayashi, and M. Hasuo: Development of a Molecular Dynamics Method with Heat Transfer into Bulk for Ion Injection into
Materials, Plasma Fusion Res, 15:2403073 (2020).
[3] K. Sawada, H. Nakamura, S. Saito, G. Kawamura, M. Kobayashi, K. Haga, T. Sawada, and
M. Hasuo: Neutral transport code for rovibrational population calculation of molecular hydrogen in large helical device plasmas, Contrib. Plasma Phys, 60:e201900153 (2020).
[4] Seiki Saito, Hiroaki Nakamura, Keiji Sawada, Masahiro Kobayashi, Gakushi Kawamura,
Masahiro Hasuo: Molecular dynamics simulation for hydrogen recycling on tungsten
divertor for neutral transport analysis, Japanese Journal of Applied Physics, SAAB08(2021), SAA08-1 – SAA08-11.

185

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Investigation of hydrogen recycling process
on tungsten divertor
Seiki Saito 1, Mayuko Miura 1, Hiroaki Nakamura 2,3, Keiji Sawada 4, Gakushi Kawamura2,5, Masahiro Kobayashi 2,5, Masahiro Hasuo 6
1

Department of Information and Electronics, Faculty of Engineering, Yamagata University
2

Department of Helical Plasma Research, National Institude for Fusion Science
Department of Electrical Engineering, Graduate School of Engineering, Nagoya University
4
Department of Material System Engineering, Faculty of Engineering, Shinsyu University
5
Department of Fusion Science, Physical Sciences Research Section, The Graduate University for
Adcanced Studies
6
Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto
University*saitos@yz.yzmagata-u.ac.jp
3

Abstract.
We develop a hydrogen recycling model on carbon divertor by molecular dynamics simulation.
In this model, neumerical simulation of one hydrogen atom injection into a carbon material is
performed. NVE ensemble is adapted for calculation of motion of atoms in the center of the
carbon material. As a result, the hydrogen molecules in relatively high state is observed.
Keywords: Molecular dynamics simulation, Recycling, Neuclear fusion.

1. Introduction
Tungsten divertor is exposed by hydrogen plasma in nuclear fusion device such as ITER. Somehydrogen ions are recycled at the divertor. The recycled hydrogen atoms and molecules affectthe plasma parameter of core plasma by the variety of reactions such as excitation, ionization,
recombination, and dissociation caused during their transportation in the edge plasma.
The transport of hydrogen atoms and molecules emitted from the wall can be calculated by theneutral transport code [1]. For the boundary condition of the calculation, the emission angle
and energy distribution are necessary. Moreover, the reaction rate of molecular assisted recombination (MAR) depends on the rotational and vibrational energies of hydrogen molecules.
Therefore, the distributions of rotational and vibrational energies are also necessary for the
calculation.
In this study, therefore, molecular dynamics (MD) simulation model [2-4] of hydrogen recycling at tungsten divertor is developed to analize the recycling process in atomic scale.

2. Simulation Model and Results
Figure 1 (a) shows the system of our MD simulation. Hydrogen-containing bcc tungsten

186

JSST2021
structure is prepared as a target material. One hydrogen atom is injected into the target
material with the incident energy of 100 eV. For the interaction between hydrogen andtungsten atoms, an EAM potential is employed.
The simulation results show the number of emitted hydrogen molecules increases as theratio of the number of hydrogen and tungsten atoms (H/W) in the material increases, although the H/W dependence of the number of emitted hydrogen atoms is not significant in
the range of our simulation 0.49 < H/W < 1.37. The analysis reveals that the hydrogen atom
travels on the surface of the tungsten material and remains there for a while because it istrapped on the surface of the tungsten material as shown in Fig. 1 (b).
(a)

(b)

Fig. 1 (a) MD model of hydrogen recycling on tungsten wall. Black and blue balls denotehydrogen and tungsten atoms respectively. (b) An example of formation process ofhydrogen molecules at the tungsten wall. [4] (Copyright: The Japan Society of Applied Physics)

Reference[1] K. Sawada, H. Nakamura, S. Saito, G. Kawamura, M. Kobayashi, K. Haga, T. Sawada, M.
Hasuo: Neutral transport code for rovibrational population calculation of molecular hydrogen in large helical device plasmas, Contrib. Plasma Phys, 60:e201900153 (2020).
[2] S. Saito, H. Nakamura, K. Sawada, G. Kawamura, M. Kobayashi, M. Hasuo: Molecular dynamics simulation model of hydrogen recycling on carbon divertor for neutral transport analysis in large helical device, Contrib. Plasma Phys, 60:e201900152 (2020).
[3] S. Saito, H. Nakamura, K. Sawada, G. Kawamura, M. Kobayashi, M. Hasuo: Developmentof a Molecular Dynamics Method with Heat Transfer into Bulk for Ion Injection into Materials, Plasma Fusion Res, 15:2403073 (2020).
[4] S. Saito, H. Nakamura, K. Sawada, G. Kawamura, M. Kobayashi, T. Sawada, M. Hasuo:
Molecular dynamics simulation for hydrogen recycling on tungsten divertor for neutraltransport analysis, Jpn. J. Appl. Phys. 60 SAAB08 (2020).

187

JSST 2021

Interaction of optical vortex and matter systems:
from microscopic to macroscopic regimes and linkage
between them
Hajime Ishihara1,*
1 Department of Materials Engineering Science, Osaka University∗ ishi@mp.es.osaka-u.ac.jp

Abstract. Characteristic features of optical vortices are its unique spatial structures and orbital angular momentum (OAM). Typical applications of the former are those to achieve
spatial resolution beyond normal diﬀraction limits. The latter aspect manifests as OAM
transfer from light to matter systems. In the OAM transfer, the microscopic light-matterinteraction causes macroscopic motions of matter systems. Thus, the macroscopic and microscopic degrees of freedom are sometimes linked to each other in a unique manner via
linear and nonlinear optical responses. In this talk, characteristic eﬀects of the optical vortex are discussed showing some theoretical studies of light-matter interaction.
Keywords: Optical vortex, Optical manipulation, Chiral interaction, Chiral helimagnet

1.

Introduction

The emergence of optical vortices has greatly widened the light-matter interaction schemeand promoted our understanding of chirality-related interactions. One of the characteristicfeatures of the optical vortex is its unique spatial structure. The ﬁeld intensity is low near
the singularity in the center of the beam, and the span length of this area is shorter than thelight wavelength. This feature is used in various applications to achieve spatial resolution
beyond normal diﬀraction limits. More importantly, the optical vortex has orbital angularmomentum (OAM), which is the origin of a variety of light-matter interactions. OAM of the
optical vortex is transferred to the matter system through their microscopic interaction. In
this talk, we introduce the theoretical proposal of super-resolution trapping of nanoparticles
as an example of a study using the former feature of the optical vortex. As the latter issue,
some transfer schemes of OAM are presented with discussing their macroscopic and microscopic aspects. Presented examples show some kinds of linkage between microscopic andmacroscopic degrees of freedom through the OAM transfer by the optical vortex.

2.

Super-resolution trapping of nanoparticles

188

Flexible optical manipulation of nanoparticles isnow still challenging. A strategy to realize it is touse a light frequency that is resonant with a transition energy between the electronic levels quantizedin nanostructures. Such resonance processes oftencause a nonlinear optical eﬀect. We have revealed
that the attractive force near the metallic nanogaps
becomes inverted when the optical nonlinearity isstrong. This phenomenon can be used to realize
super-resolution trapping of nanoparticles [1][2]. If
we irradiate nanoparticles trapped at nanogap array with the usual Gaussian beam and optical vortex beam simultaneously, particles at the overlapped
area of two beams are repulsed due to the force inversion, and only those around the beam center are
kept trapped (Fig. 1). Thus, the trapping area of theparticles becomes very narrow beyond the diﬀraction limit, which has a good analogy with STED
microscope [4] based on the unique spatial structureof the optical vortex.

Laguerre
Gaussian Beam

Incident
polarization

Figure 1: Schematic image of thesuper-resolution trapping. Nanoparticles at the overlapped area of the
optical vortex and Gaussian beam
are repulsed due to the force inversion, and only those around the beam
center are kept trapped.

OAM transfer to matter system: macroscopic and microscopic
aspects
%!$   !"#"$%&!"#"$%'!"#"$%(

%"" %##%"" %##




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 

( 

&! #$ 





$#$'

'! #$   $#$'

A typical phenomenon caused by OAM
transfer is the rotational manipulation ofabsorptive micro-particles [3]. This effect is understood as macroscopic OAM
transfer through the microscopic photon
absorption processes.
If nanoparticles are rotated by theelectronic resonance, more elaborate rolesof microscopic electronic transition are
clearly seen. Figure 2 shows the resultsof theoretical demonstrations of nanoparticle rotation. We assumed the aggregated three-level molecules as nanoparticles. The irradiation of the optical vortex with a frequency resonant with 1 → 2transition induces the rotation of nanoparticles. Interestingly, if the particles are irradiated with another beam for pumping to
make occupation probability of the level 2'! #$ 

3.

Gaussian Beam (   

&! #$ 





Figure 2: The three-level molecular aggregate(see inset) is rotated by an optical vortex. If
the aggregated particle is pumped and the occupation probability of the level 2 becomesover 0.5, the rotation direction becomes inverted.

189

above 0.5, a stimulated emission occurs, and the rotational direction becomes inverted (Fig.
2)[5]. This indicates that nonlinear optical processes based on the quantum mechanicalproperties aﬀect macroscopic OAM transfer. Thus, microscopic and macroscopic degrees
of freedom of motion are linked to each other in a unique manner through OAM transfer.
The other example of OAM transfer is also associated with microscopic electronic transitions. Photons with OAM can change the optical selection rule of electronic transitions
from the standard one. This eﬀect causes novel types of spin-spin interactions and induces
peculiar spin textures in solid states. In particular, we have demonstrated that this eﬀect
leads to modulation of the chiral magnetic order to the unconventional phase structure[6].
This is an interesting example of microscopic OAM transfer that produces unconventional
macroscopic spin structures.

References[1] M. Hoshina, N. Yokoshi, H. Okamoto and H. Ishihara, ”Super-Resolution Trapping:
A Nanoparticle Manipulation Using Nonlinear Optical Response”, ACS Photonics 5,
318–323 (2018)[2] H. Ishihara, ”Optical manipulation of nanoscale materials by linear and nonlinear resonant optical responses”, Adv. in Phys.: X, 6, 1885991 (2021)[3] H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, ”Direct observation of transfer of angular momentum to absorptive particles from a laser beam witha phase singularity”, Phys. Rev. Lett. 75, 826–829 (1995).
[4] S. W. Hell and J. Wichmann, ”Breaking the diﬀraction resolution limit by stimulated emission: stimulated-emission-depletion ﬂuorescence microscopy”, Opt. Lett.
19, 780–782 (1994)[5] M. Hoshina, N. Yokoshi and H. Ishihara, ”Nanoscale rotational optical manipulation”,
Opt. Exp. 28, 14980–14994 (2020)[6] Y. Goto, H. Ishihara and N. Yokoshi, ”Twisted light-induced spin–spin interaction in achiral helimagnet”, New J. Phys. 23, 053004 (2021)

190

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Improvement of Visibility in Feature Emphasis
Visualization of 3D Measured Point Cloud
Mizuki Katahira1*, Kyoko Hasegawa2*, Liang Li2*, Satoshi Tanaka2*
1

Graduate School of Information Science & Engineering, Ritsumeikan University
2
College of Information Science & Engineering, Ritsumeikan University*is0349ve@ed.ritsumei.ac.jp

Abstract. In recent years, the development of laser measurement technology has made it possible
to measure a variety of objects without any physical contact. The laser measured data are large 3D
point clouds, and many of them contain complex structures in detail. In order to accurately visualize
objects with complex structures, it is necessary to visualize the internal and external structures
simultaneously. Therefore, in this paper, we propose a method that combines " transparent
visualization," which can visualize both internal and external structures simultaneously, and"feature enhancement visualization," which improves visibility. In our method, feature-enhanced
visualization compensates for the decrease in visibility caused by the increase in the amount of
information, which is a drawback of transparent visualization, and 3D visualization results can bedisplayed more clearly. In addition, the effectiveness of the proposed method is verified byvisualizing using actual 3D measurement point clouds.
Keywords: Transparent visualization, Laser-scanned large-scale point cloud, Feature extraction

1. Introduction
The development of laser measurement technology has made it possible to measure various
objects, such as historically important buildings and historical documents, without directly
touching the objects. This has led to more active digital archiving of cultural assets. The dataobtained by laser measurement is a large 3D measurement point cloud, which often has acomplex internal and external structure. When both internal and external structures arepresented, the complexity of the 3D structure becomes more pronounced. In the past, stochastic
point-based rendering (SPBR) [1, 2], a rendering method using a stochastic algorithm, wasused for visualization, but the problem was the blurring of the shape due to the decrease inopacity. To solve this problem, we used feature-enhanced visualization, which emphasizes theedges of the object. Using feature-enhanced visualization, we can improve the visibility of thetarget object, which has been a problem in visualization using SPBR. However, in conventional

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feature-enhanced visualization, the visibility of the original point cloud is sometimes degradedby overemphasizing the 3D edges. In this paper, we propose a method to improve the overall
visibility of the object by transparently visualize the original point cloud and emphysising the
3D edge region at the same time.

2. Highlighting of feature region based on curvature
In this research, we use principal component analysis (PCA) to extract feature regions. Thisalgorithm of extracting feature regions is as follows:1.

Perform PCA on the coordinate values of the 3D point cloud in the sphere of optional
radius 𝑟 centered on the point 𝑃(𝑖) . 𝑟 is a parameter determined by the user.

2.

Calculate eigenvalues(𝜆1 ≥ 𝜆2 ≥ 𝜆3) from the covariance matrix obtained by PCA.

3.

Caluculate feature value 𝐹 (𝑖) by combining the eigenvalues.

4.

Emphasize points with 𝐹 (𝑖) greater than a threshold 𝑡. 𝑡 is a parameter determinedby the user.

Feature value 𝐹 (𝑖) is calculated as follows [3]:𝐹(𝑖) =𝜆3
𝜆1 + 𝜆2 + 𝜆3

(1)

In our method, feature extraction and enhancement are the same as the conventional method,
but the visualization method is different. In the conventional method, the entire point cloud isused as the visualization target, and the points of the feature extracted by the above method arehighlighted by changing the color of the points. However, the emphasis is too conspicuous andspoils the visibility of the original point cloud. On the other hand, the proposed method
visualizes both the entire point cloud and the point cloud from which the feature parts are
extracted. This means that the color of the point cloud to be emphasized is a fusion of theconventional emphasized color and the color of the original point cloud. In the feature regions,two points are visualized simultaneously, one from the original point data and one from thefeature point data. Therefore, we can emphasize the point cloud with a color close to the colorof the original point cloud and solve the visibility problem.

3. Experimental results
In this section, we demonstrate the effectiveness of our proposed method by reporting theresults of case studies performed on the data of Kyoto Women's University. Fig. 1(a) shows
the visualization results with highlighting feature regions by the conventional method, inwhich red points are feature regions. On the other side, in Fig. 1(b), the visibility of theoriginal point clouds has been improved by merging the emphasis color with the color of theoriginal point clouds. In both results, feature emphasis visualization improves the visibility
which was the problem of transparent visualization. In the case of Fig. 1(a), only one point

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cloud is drawn in the feature regions, and the emphasis color is too conspicuous, so thevisibility of the original point cloud is reduced by transparent visualization. In the case of Fig.
1(b), the visibility of the original point cloud is improved because both the original and thefeature point clouds are drawn simultaneously in the feature region.

(a) Visualization result of the conventional method[3] (b) Visualization result of the proposal method
Figure 1: Visualization results with highlighting feature regions on the point cloud data of
Kyoto Women's University.

4. Conclusion
In this paper, we proposed a method for feature enhancement visualization in transparent
visualization using stochastic point-based rendering. Using the proposed method, wewere able to improve the visibility of both the original point cloud and the 3D edge
region.

References[1] S. Tanaka, K. Hasegawa, N. Okamoto, R. Umegaki, S. Wang, M. Uemura, A. Okamoto,and K. Koyamada: See-Through Imaging of Laser-scanned 3D Cultural Heritage Objects
based on Stochastic Rendering of Large-Scale Point Clouds, ISPRS Ann. Photogramm.
Remote Sens. Spatial Inf. Sci., III-5, pp. 73-80, 2016.
[2] Tomomasa Uchida, Kyoko Hasegawa, Liang Li, Motoaki Adachi, Hiroshi Yamaguchi,
Fadjar I. Thufail, Sugeng Riyanto, Atsushi Okamoto, Satoshi Tanaka: Noise-robusttransparent visualization of large-scale point clouds acquired by laser scanning, ISPRS
Journal of Photogrammetry and Remote Sensing, vol. 161, pp.124-134, March 2020.
[3] Martin Weinmann, Boris Jutzi, Cle ́ment Mallet: Semantic 3D scene interpretation: A
framework combining optimal neighborhood size selection with relevant features,
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., II-5/W2 (2013), 313–318.

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Improving Depth Perception of Transparent Objects
in Stereoscopic Vision using Ambient Occlusion
Kota KATAOKA1*, Yuichi SAKANO2, Naohisa SAKAMOTO3
Kyoko HASEGAWA4, Liang LI4, Satoshi TANAKA4

Graduate School of Information Science and Engineering, Ritsumeikan University
2
National Institute of Information and Communications Technology: NICT
3
College of Engineering, Kobe University
4College of Information Science and Engineering, Ritsumeikan University1*

is0349er@ed.ritsumei.ac.jp

Abstract. We utilize transparent visualization that allows better visibility of the internal structure of 3D data in stereoscopic vision. Transparent visualization is expected to make it possible
to perceive the object structure more intuitively, even for complex solids. However, when 3D
data are rendered transparently, the depth cues change and the positional relationship becomesambiguous. This paper investigates the effect on depth perception of combining transparent
stereoscopic vision and ambient occlusion, which has high depth representation capability, toimprove transparent stereoscopic depth perception. Ten participants were asked to evaluate thedistance of an object from a reference point. The experimental results confirmed that depth
perception was improved by combining two types of depth cues, binocular disparity and ambient occlusion.
Keywords: Ambient occlusion, Autostereoscopic, Transparent visualization

1. Introduction
In the field of cultural assets and medical care, 3D data visualization has been actively performed. To understand the internal structure of complex 3D data, transparent visualization isused, which can visualize the appearance and internal structure simultaneosly. However, it isdifficult to perceive 3D information correctly when using transparent visualization, and it is
known that depth is often under estimated. Humans use various imformation to perceive depth,
and it is necessary to provide more depth cues to achieve accurate depth perception. One ofthese depth cues is the perception of shape-from-shading. When estimating depth from shading,the human visual system is considered to have two assumptions: “light-from-above,” whichassumes a sole light source and recognizes depth from shading, and “dark-is-deep,” which recognizes dark areas as deep. In addition, it is known that we perceive depth by switching between these two assumptions depending on the situation[1]. In this study, we examine how to194

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make the perceived depth closer to the actual depth by providing information on the perceptionof depth shape by shading using ambient occlusion (AO) for transparent stereopsis.

2. Ambient Occlusion
In this study, we use screen-space AO to provide shading. The algorithm to calculate the shading rate of the ambient occlusion is as follows [2]:1.

Generate 𝑁𝑠 sampling points randomly in a sphere of arbitrary radius r centered atpoint P according to the following equation (1). In equation (1), 𝑥, 𝑦 and 𝑧 are thecoordinates of the sampling point, u, v, and w are uniform random numbers with rangesof [0, 1], [−1, 1], and [0, 1], 𝑅 is a sampling radius.
𝑥 = 𝑟√1 − 𝑣 2 cos(2𝜋𝑢){𝑦 = 𝑟√1 − 𝑣 2 cos(2𝜋𝑢)(1)𝑧 = 𝑣𝑟𝑟 = 𝑤𝑅

2.

Compare the depth values at the sampling points in the screen space with the depth
values at the points in the data, and count the number of sampling points 𝑁𝑝 that aresmaller than the depth value.

3.

The ambient light coefficient occlusion is calculated as shown in equation (2) below.
𝑜𝑐𝑐𝑙𝑢𝑠𝑖𝑜𝑛 =

𝑁𝑝 ×2
𝑁𝑠

(2)

3. Experimental results
In this section, the effectiveness of AO is shown in an experiment to verify the depth obtained
from images with and without AO displayed on a naked-eye 3D display. Surface data withdepressed square weights were used for the experiment. Figures 1(a) and 1(b) are images
without AO applied, showing depressions with small depth and large depth, respectively. The
light source located slightly to the upper left casts a shadow on the image to the extent that theshape of the depression of the square can be recognized. Figures 1(c) and 1(d) show images
with AO applied, showing small and large depth depressions, respectively. Here, in addition to
the shadows described above, shadows are cast on the center and the tip of the depression by
AO. A light shadow is cast when the depression is small, and a dark shadow is cast when the
depression is large. As a result of the dark-is-deep property, Figs. 1(c) and 1(d) show greater
depth than Figures. 1(a) and 1(b) where AO is not applied.

4. Conclusion
In this paper, we proposed a depth enhancement method using AO to make the perceived depth
in transparent stereopsis closer to the actual depth. This proposed method enables more accurate depth perception in transparent stereopsis.

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JSST2021(a) without ambient occlusion, depth = 1.0(b) without ambient occlusion, depth = 2.5(c) with ambient occlusion, depth = 1.0(d) with ambient occlusion, depth = 2.5

Figure 1: Visualization results of transparent objects using ambient occlusion, 𝛼 = 0.9.

References[1] Sakano,Y.: Quantitative evaluation of perceived depth of transparently-visualized medical 3D data presented with a multi-view 3D display, International Journal of Modeling,
Simulation, and Scientific Computing Vol. 09, No. 03, 1840009 (2018).
[2] Fujita,Y.,Sakamoto,N.: Ambient occlusion for semitransparent streamlines with stochastic rendering technique, The 2nd Visualization Workshop, (2019).

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Adaptive Opacity Control using Implicit Function for
Visualizing Large-Scale 3D Measurement Point
Clouds
Masaya Kishimoto1*, Motoaki Adachi2, Kyoko Hasegawa3, Liang Li3,
Satoshi Tanaka3
1

Graduate School of Information Science & Engineering, Ritsumeikan University
2
Shrewd Sekkei Inc.
3
College of Information Science & Engineering, Ritsumeikan University*is0352rr@ed.ritsumei.ac.jp

Abstract. Stochastic point-based rendering (SPBR) is one of the methods for transparent visualization of 3D measurement point clouds, and it allows us to grasp the structure of the visualization target easily. However, the visibility of the structure is degraded when the internal
structure is intricate because the spatial relationship becomes unclear. In this paper, we propose a method for easily grasping the internal structure and appearance of large-scale measurement point cloud data obtained by 3D measurement by adaptively controlling the opacity
using a hyperquadric function. Using this method, we were able to visualize the internal
structure and external shape with high resolution.
Keywords: Implicit function, Adaptive opacity control, Large-scale 3D measurement point clouddata

1. Introduction
Recent improvements in computer processing speed and the development of laser measurement technology have made it possible to store cultural properties as large-scale 3D measurement point cloud data. Stochastic point-based rendering (SPBR) has been shown to be usefulas a visualization method for large-scale 3D point cloud data [1,2]. This visualization method
is a method to realize transparent visualization of measured point cloud data according to thepoint density, and it is also a method to visualize the structure of buildings with high precision
and accuracy [3]. Since the recorded points in a point cloud are often unevenly distributed, it ispossible to achieve high-definition visualization by using Poisson disk sampling (PDS) [4] tomake the point distribution of the point cloud uniform and then visualize it with SPBR. However, when the structure is complex, problems such as visibility reduction may occur due to the
obscuration of the front-back relationship. This research aims to propose a method to adaptively

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change the point density between the exterior and interior of a building in order to understandits structure. For this purpose, we use implicit functions to achieve non-uniform point densities
that take into account the shape of the building. The proposed method makes it possible toimprove the visibility of the interior structure and the exterior by controlling the opacity.

2. Non-uniform opacity control using hyperquadric functions
In SPBR, the density of the point cloud determines the uniform opacity. The number of points
𝑛 required to achieve opacity 𝛼 is:ln(1 − 𝛼)(1)𝑛=𝑠 𝐿R .
ln(1 − 𝑆)
Here, 𝑠 is the cross-sectional area of the point, 𝑆 is the area of the great circle of the measurement sphere, and 𝐿R is the parameter that adjusts the image quality. However, because
generating new points in a measurement point cloud is complex in practice, its opacity is increased or decreased by copying the points to achieve the opacity. The rate of increase or decrease in the number of points 𝑟 is calculated from the ratio of the total number of measurement points 𝑛0 as follows:
𝑛
(2)
𝑟= .
𝑛0
Therefore, in this study, we define a new non-uniform point increase/decrease rate by multiplying the point increase/decrease rate 𝑟 by hyperquadric functions 𝑓 in the implicit function
according to the shape of the measured point cloud. If the 𝑥, 𝑦, and 𝑧 coordinates of the center
point of the hyperquadric function in the point cloud are 𝑥8 , 𝑦8 , and 𝑧8 , respectively, and theradii of the 𝑥, 𝑦, and 𝑧 axes of the hyperquadric function to be set are 𝑎, 𝑏, and 𝑐, respectively, then the hyperquadric function to be used is:>>>𝑥 − 𝑥8 ?
𝑦 − 𝑦8 ?
𝑧 − 𝑧8 ?
(3 )𝑓(𝑥, 𝑦, 𝑧) = <
= +<
= +<
= − 1.
𝑎𝑏𝑐
In addition, in order to visualize the structure in an easy-to-understand manner, two types ofvisualization, one focusing on the internal structure and the other focusing on the external appearance, are used: the rate of increase/decrease 𝑟BC for focusing on the internal structure andthe rate of increase/decrease 𝑟DEF for focusing on the external appearance:𝑛(4)
𝑟BC = 𝑓 G ,𝑛0
𝑟DEF = (1 − 𝑓)G

𝑛
.
𝑛0

(5)

Here, 𝑑 is a parameter that controls the changing rate of the increase or decrease. By changing
the point density based on the position as described above, it is possible to achieve an opacitythat depends on the shape of the function.

3. Experimental results
In this chapter, we show the results of using the proposed method on the measured point clouddata of a red brick warehouse in Maizuru City, Kyoto prefecture, and a factory. First, Figure 1

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JSST2021(a) The conventional method(b) The proposed method
Figure 1: Comparison of transparent visualization results in external appearance on the point
cloud data of red brick warehouse. The values used are 𝑳R = 𝟓𝟎, 𝜶 = 𝟎. 𝟖, 𝒅 (on theroof area) = 𝟑𝟎, and 𝒅 (on the first and second floors) = 𝟓.
shows the comparison between the conventional method and the proposed method for visualizing the external appearance of the red brick warehouse. Figure 1(a) shows the data visualizedwith the conventional uniform opacity and the total number of points is 755,531,703, while
Figure 1(b) shows the data visualized with the newly set non-uniform opacity and the total
number of points is 430,956,554. Comparing the results of Figure 1(a) and Figure 1(b), it canbe seen that the appearance of the appearance-oriented visualization does not change muchbecause the external appearance is emphasized even if both opacities are used, but the total
number of points in Figure 1(b) using the proposed method is greatly reduced by outputting
points only in the external appearance using non-uniform opacity.
Figure 2 shows the comparison between the conventional method and the proposed method
for visualizing the internal structure of the point cloud data of the factory. In addition, when
visualizing the internal structure of the building, we processed it so that the visibility of theinternal structure of the building surrounded by the red circle in Figure 2(a) would be high.
Figure 2(a) shows the visualization using the conventional method with uniform opacity, whichshows that it is not easy to grasp the internal structure because it is blocked by the external
appearance. On the other hand, Figure 2(b) was visualized using non-uniform opacity using
equation (4), and the internal structure can be grasped because only the internal structure has ahigh point density. These results indicate that the method is useful for improving the visibilityof the internal structure and the external appearance of the complex structure of the199

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visualization target in transparent visualization of 3D measurement point clouds.

References[1] S. Tanaka, K. Hasegawa, N. Okamoto, R. Umegaki, S. Wang, M. Umemura, A. Okamoto,and K. Koyamada: See- Through Imaging of Laser-scanned 3D Cultural Heritage Objects based on Stochastic Rendering of Large-Scale Point Clouds, ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-5, (2016) pp. 73-80.
[2] S. Tanaka, K. Hasegawa, Y. Shimokubo, T. Kaneko, T. Kawamura, S. Nakata, S. Ojima,
N. Sakamoto, H. Tanaka, and K. Koyamada: Particle-Based Transparent Rendering of
Implicit Surfaces and its Application to Fused Visualization, EuroVis 2012, (2012) pp.
25- 29.
[3] T. Uchida, K. Hasegawa, L. Li, M. Adachi, H. Yamaguchi, Fadjar I. Thufail, S. Riyanto,
A. Okamoto, S. Tanaka: Noise- robust transparent visualization of large-scale point
clouds acquired by laser scanning,ISPRS Journal of Photogrammetry and Remote Sensing, vol. 161, (2020) pp.124-134.
[4] T. Wang, U. Kiichi: Stippling by Poisson Disk Sampling with Grayscale Ordering of
Pixels, The IEICE transactions on information and systems (Japasene edition), vol. 96(1),pp.262-265.

(a) The conventional method(b) The proposed method

Figure 2: Comparison of transparent visualization results in internal structure on the point
cloud data of the factory. The values used are 𝑳R = 𝟓𝟎, 𝜶 = 𝟎. 𝟖, and 𝒅 = 𝟓.

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Generation of X-ray vortices by Bragg reflection
from crystals and microscopy to diagnose topologicalcharge distribution

Yoshiki Kohmura1*, Kei Sawada, Kenji Ohwada2, Masaichiro Mizumaki3, Tetsu Watanuki2, Tetsuya Ishikawa1
RIKEN SPring-8 Center

12

National Institutes for Quantum and Radiological Science and Technology
3

Japan Synchrotron Radiation Research Institute*yoshiki.kohmura@riken.jp

Abstract. Two experiments were performed to generate X-ray vortices by the Bragg reflection
from crystalline materials. We tried two kinds of crystals having completely different latticeplanes. One is a perfect crystal with a depth distribution at surface which generated an X-ray
vortex with a fixed topological charge regardless of X-ray energy as predicted by the past theory. The other has a staircase lattice plane with a truncated spiral dislocation which generated
wave fields. We also demonstrated our novel method to diagnose the topological charge distribution of X-ray vortices by utilizing a Radial Hilbert Transform X-ray microscope.
Keywords: X-ray vortex formation, Bragg reflection by crystals, X-ray photonics

1. Introduction
As for the wave control at X-ray wavelength scale, we have verified the Berry phase theory
that predicted the X-ray wave guiding effect by anomalous X-ray translation inside a deformed
crystal [1-3]. These results imply that crystals with deformed atomic configurations will bepotential basis for the near future X-ray photonics. In this talk, we will summarize our resultson X-ray wave control using two different kinds of crystals, one with a modified surface depth
distribution on a perfect crystal and the other with a defect on a lattice plane. Some progess on
simulation studies, which takes into account of diffraction of x-rays, will be presented for theunderstanding of the X-ray properties in reflection.

2. Experimental Results for Generating X-ray Vortices using Bragg
Reflection on crystals.

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For generating X-ray vortices in the Bragg reflected wave, we have tried two crystals having
completely different lattice planes. Experimental setup and result for each crystal are shown
below.
As for the first crystal, lattice planes are perfectly periodic but the surface is deformed fromthe flat shape with a depth distribution. We will show that the X-ray wave fields having arbitrary and energy independent phase distribution can be generated by the Bragg reflection on
the crystal, verifying the theory predicting that this phase is proportional to depth on crystal
surface and lattice spacing. A two-beam interferometer with a plane reference wave clearlyvisualized X-ray vortices generated in the reflected wave downstream of a spiral phase plate
on a silicon crystal. A fixed topological charge was observed from a fixed lattice plane regardless of X-ray energy. This result is a further development from the previous work that achieved
the X-ray focusing using Bragg Fresnel zone plates [4]. Such energy tunable X-ray phase plates
would be ideal for the future phase-shifting elements in white-light interferometers or Zernike
phase-contrast microscopes. First note is that phase-shifting in visible white-light interferometers uses the translation of optical elements which is impossible in X-ray wavelength. Second
note is that the phase shift by the transmissive optical element is inversely proportional to the
X-ray energy and cannot be used for such an energy independent phase plate.
As for the second crystal, lattice planes having staircase structures known as the truncatedspiral dislocations (TSDs) are used. TSDs are found ubiquitously in various industrial functional devices such as in silicon carbide (SiC) crystal. Dot like structures from TSDs wereobserved at the surfaces of the SiC crystal using the X-ray topography [5]. We here tried todiagnose the phase distribution after Bragg reflection from a SiC crystal. We performed a kinematical diffraction simulation indicating that X-ray vortices are generated on Bragg reflected
X-rays from TSDs when the spatial coherence length of the irradiating X-rays is sufficiently
large. A two-beam X-ray interferometry, with a plane reference wave and an object wave passing through the TSD area, was carried out which manifested a pair of fork patterns indicatingthat wave fields resembling X-ray vortices were generated with the topological charge of +1 or-1. We regard that this is a novel and promising technique for discriminating TSDs and their
topological charges in functional devices. Our future research will increase the precision ofsuch discrimination by measuring a very thin crystal containing TSDs with the thickness of 1
micrometer or so, comparable to or thinner than the extinction depth, to avoid the effect ofmultiple diffraction effects.

3. Experimental Results for Diagnosing Topological Charge Distribution of X-ray Vortices.
Next topic is on a diagnosis of the topological charge distribution of the X-ray vortices using
Radial Hilbert Transform (RHT) X-ray Microscope. Our microscope used the Spiral Fresnel
zone plate (SFZP) as the objective lens to modify the wave front downstream of objects and to
add vorticity with the topological charge of l = –1 & +1 [6]. We also prepared a silicon demonstration specimen containing multiple spiral phase plates that transfers vorticity to the wave
fields with the topological charge of m = –1 and +1. We successfully proved our theoreticalfinding that the vorticity cancellation occurs to form a bright spot in the microscope image
when l + m = 0. RHT microscope enables us to sensitively derive the two-dimensional map of202

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X-ray vortices transferred from the spiral structures.
We plan to apply RHT microscope to observe X-ray vortices formed by Bragg refection fromcrystalline specimens. This research will help us to accelerate the evaluation of defects and thus
improve the quality of the next-generation functional materials, such as semiconductor powerdevices, light-emitting devices and high-rigidity metals.

References[1] K. Sawada, S. Murakami and N. Nagaosa: Physical Review Letters, 96 (2006), 1548021-4.
[2] Y. Kohmura, K. Sawada and T. Ishikawa: Physical Review Letters, 104 (2010), 2448011-4.
[3] Y. Kohmura, K. Sawada, S. Fukatsu and T. Ishikawa: Physical Review Letters, 110(2013), 057402-1-4.
[4] V. V. Aristov, Yu. A. Basov, G. N. Kulipanov, V. F. Pindyurin, A. A.Snigirev and A. S.
Sokolov: Nucl. Instr. And Meth. A 274 (1989), 390-393.
[5] Y. Yamaguchi and H. Matsuhata: J. Electron. Mater. 39 (2010), 715-.
[6] Y. Kohmura, K. Sawada, K. Ohwada, M. Mizumaki, T. Watanuki, T. Ishikawa: Optics
Express, 28, 16 (2020), 24115-24122.

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Propagation properties of optical vortex inmagnetized plasma
Toru I. Tsujimura1,* and Shin Kubo 2
1 National Institute for Fusion Science, National Institutes of Natural Sciences
2 College of Engineering, Chubu University∗ tsujimura.tohru@nifs.ac.jp

Abstract. The propagation properties of optical vortices with helical wavefronts in cold
uniform magnetized plasmas in the electron cyclotron (EC) frequency range are investigatedtheoretically. The eﬀects of helical wavefronts of vortex EC waves on the waveﬁeld in
magnetized plasma as an anisotropic medium are described. These eﬀects become more
prominent when the topological charge of the vortex EC wave becomes larger or the distancefrom the phase singularity becomes smaller. Diﬀerent propagation properties were also
observed in the propagation of a Laguerre-Gaussian beam in a three-dimensional simulation
using the ﬁnite element method. These results suggest that optical vortices can be a new toolfor heating high-density plasmas.
Keywords: Electron cyclotron wave, Optical vortex, Magnetized plasma, Laguerre-Gaussian
beamRadiofrequency (RF) waves are widely used for heating, current drive, and diagnostics inmagnetically conﬁned fusion plasmas. Knowing the propagation properties of RF waves
in magnetized plasmas is fundamental for designing RF systems such as launch antennas.
The propagation properties of RF waves conventionally originate from a plane wave, where
the phase of the waveﬁelds is assumed to be k · r − ωt. Here, k, r, ω, and t denote thewave vector, the position vector, the angular frequency, and time. Recently, it has been theoretically and experimentally shown that a single free electron in circular or spiral motion
radiates twisted photons with orbital angular momentum (OAM) along the electron circulation axis in addition to spin angular momentum [1, 2]. It is found that the emitted waveﬁeld
has a phase term expressed as lφ + kz z − ωt, where l is the topological charge and φ is theazimuthal angle around the optical axis z. A wave with a helical wavefront is commonly
called an optical vortex. Figure 1 is a schematic diagram showing the propagation of an
optical vortex. Optical vortices were initially discussed in terms of a particular mode ofelectromagnetic waves called the Laguerre-Gaussian (LG) mode, which was conventionally
thought to be artiﬁcially generated using optical elements. However, twisted photons are204

Wave vector

Wavefront

PhotonFigure 1: Schematic representation of the propagation of an optical vortex with a helical
wavefront together with a photon with OAM.
emitted naturally by the cyclotron motion of electrons and are more ubiquitous in laboratories and nature. Naturally, the question arises as to how the optical vortex propagates inan anisotropic medium, the magnetized plasma, and whether the unique property of the helical wavefront is beneﬁcial for heating, current drive, and diagnostics in magnetic fusion
plasmas.
In this work [3], the propagation properties of optical vortices with helical wavefronts
in a cold uniform magnetized plasma were theoretically investigated in the frequency rangeof an electron cyclotron (EC) wave. The eﬀect of the helical wavefront of the optical vortex on the waveﬁeld in the magnetized plasma is explained. A detailed description of thetheory will be given at the conference. It was found that these eﬀects become larger when
the topological charge of the optical vortex becomes larger or the distance from the phasesingularity becomes smaller. Diﬀerent propagation properties were also observed in the
propagation of a Laguerre-Gaussian beam in a three-dimensional simulation using the ﬁnite
element method with the commercial software COMSOL Multiphysics. It was found that apart of the ordinary-mode LG beam with topological charge l excited in the region of lower
electron density is converted into a high wavenumber extraordinary-mode LG beam withl − 1 at the upper hybrid resonance layer. Then, it propagates to the region with a higher
electron density.
In order to demonstrate the new propagation properties of vortex EC waves in heating
and current-drive experiments, it is necessary to generate optical vortices with the desired l in
the millimeter-wave transmission system and launch them into the magnetic fusion plasma.
A spiral phase mirror has been developed to generate optical vortices with the designed l in
the millimeter-wave frequency range [4]. Therefore, the optical vortex can be generated byinstrumenting the spiral phase mirror between the gyrotron and the launch antenna mirror
in the existing transmission line for EC heating and current drive. This modiﬁed system
will allow us to verify whether optical vortices can be a new tool for eﬃcient heating of205high-density plasmas.
This work was supported by the NINS program for cross-disciplinary study (Grant
Nos. 01311802 and 01311903), JSPS Grants-in-Aid for Scientiﬁc Research (Grant No.
JP19K14687), and NIFS Grant Nos. ULRR703 and ULRR036.

References[1] M. Katoh et al., Phys. Rev. Lett. 118, 094801 (2017).
[2] M. Katoh et al., Sci. Rep. 7, 6130 (2017).
[3] T. I. Tsujimura and S. Kubo, Phys. Plasmas 28, 012502 (2021).
[4] Y. Goto, T. I. Tsujimura, and S. Kubo, J. Infrared Milli. Terahz. Waves 40, 943 (2019).

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Possibility of Visualisation of electrostatic potential
by electron microscopy
Takuo Yasunaga1*, Yasuhisa Honda1
1

Department of Simulation, School of Technology, Kyushu Institute of Technology*yasunaga@phys.kyutech.ac.jp

Abstract.
Keywords: Electron microscopy, Electrostatic potential,

1. Introduction
In electron microscopy, the contrast of images is generated by the phase shift of electron waves
when electrons interact electrostatically with a sample. In other words, the image contrast
reflects the electrostatic potential where the electron cloud shields the positive charge of theatomic nucleus. Electron microscopy thus has the potential to capture the ionic nature and polarization of the electron cloud. Previous researches have proposed that it is possible to visualize partially charged atoms. The recent Mirco-ED (electron diffraction) method can provide us
structural information with a resolution of over 1 Å and capture the polarization of this electron
cloud. Here, by quantum chemical calculations, we compared the calculated electrostatic potentials of molecules with experimental results by micro ED. Thus we show the possibility ofdetection of the polarization of the electron cloud.

2. Results and Discussion
We detected diffraction patterns of acetaminophen by micro-ED and could solve the threedimensional structure except for hydrogen atoms at the atomic levels. However, the R-factor
was not good in case of using conventional methods. We considered that this should be due tothe electron density maps for reconstruction.
Thus, we automatically set the atomic coordinates of hydrogen atoms and calculated theelectrostatic potential of acetaminophen quantum chemically by GAMESS and Gaussian [1].
Fig 1 shows the density map and electrostatic potentials calculated by Gaussian. Indeed, an
oxygen atom of hydroxyl residue (left in Fig 1) was negatively charged, and a hydrogen atom
was positively charged and slightly polarized. Then we compared the structural factors of diffraction patterns with the simulated one from the electrostatic potentials, and the R-factor improved to show good fitness. This fitness offers the possibilities to elucidate the polarization.
Furthermore, we could move the hydrogen atom of the hydroxyl residue so as to show better
fitness to decrease the R-factor. This situation offers the possibility of refinement of atomic
coordinates using quantum chemical calculations. At present, the calculation time of quantum
chemical calculation is too long to refine the coordinates precisely. Still, we think the analysis
is helpful to consider the validity of the hydrogen coordinates etc.

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Fig. 1. Calculated electrostatic potential of acetoaminophen. The surface shows the iso-density surface and the colours indicate the electrostatic potential (red: negative potential, green:0, and blue: positive).

References[1] 巨大システムとしてのクライオ電子顕微鏡法の自動化から自働化への展開
安永 卓生, 田中 康太郎, 岩嵜 彩夏, 塚本 崇文, 本多 康久, 顕微鏡、2021 年 56 巻 1号 p. 43-47 https://doi.org/10.11410/kenbikyo.56.1_43

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Linear response theory applied to molecular dynamics simulations
Kazumi Omata1,2*, Ryuta Kawanami3, Hiroaki Nakamura4,5, Susumu Fujiwara6
1Clinical Research Center, National Center for Global Health and Medicine
Departments of Hematology, Rheumatology, and Infectious Diseases, Kumamoto University
3
Graduate School of Science and Technology, Kyoto Institute of Technology
4
Department of Helical Plasma Research, National Institute for Fusion Science5
Department of Energy Engineering and Science, Nagoya University
6
Faculty of Materials Science and Engineering, Kyoto Institute of Technology

2*komata@hosp.ncgm.go.jp

Abstract. We show that the linear response theory is applicable to molecular dynamics simulations in which sudden change in an external force plays a role for relaxation of a system. As
one of such systems, we focus on the structural change of tritium-substituted polyethylene induced by beta decays of substituted tritium, and derive the time derivative of the dynamicalquantity, which is conjugate to the force applied as perturbation in the framework of the linear
response theory, required to calculate the response function.
Keywords: Linear response theory, Molecular dynamics simulation, Structural change, Polymer,
Substituted tritium, Decay effect

1. Introduction
The linear response theory [1,2,3] describes the input-output relationship of a system in which
the intensity of input is so small that the output can be described approximately with a linear
function. The origin of this theory lies in studies of Brownian motion or Johnson–Nyquist
noise: the former is the random motion of a suspended particle which is driven by a random
force and the frictional force for a forced motion due to molecular collisions; the latter is theelectronic noise generated by the thermal agitation of electrons inside an electrical conductor
at equilibrium. A general proof of these phenomena is known as the fluctuation–dissipation
theorem. After 1950s, formal descriptions were given to the linear response theory throughanalyses of irreversible processes or nonequilibrium systems, and especially, Kubo developed
the method of a response function for this theory [1,2,3].
The present study shows that the linear response theory is applicable to molecular dynamics
simulations in which sudden change in an external force plays a role for relaxation of a system.
We review the linear response theory [1,2,3] in Sec.2, and in Sec.3, delineate the calculations

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practical for application of the linear response theory to the molecular dynamics simulations
for the structural change of tritium-substituted polyethylene induced by beta decays of substituted tritium [4,5,6,7].

2. Linear response theory
For the density function 𝑓𝑓 representing a statistical ensemble, the equation of motion is givenby𝜕𝜕𝜕𝜕
𝜕𝜕ℋ 𝜕𝜕 𝜕𝜕ℋ 𝜕𝜕= 𝑖𝑖ℒ𝑓𝑓 = [ℋ, 𝑓𝑓],
𝑖𝑖ℒ = �ℋ, � =
−
(2.1)
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕where ℋ denotes the Hamiltonian, and 𝑖𝑖ℒ is the Liouville operator. When the system is under an external force 𝐹𝐹(𝑡𝑡), the Hamiltonian is written as the sum of non-perturbed part 𝐻𝐻 and
perturbed part 𝐻𝐻 ′ :ℋ = 𝐻𝐻 + 𝐻𝐻 ′ ,𝐻𝐻 ′ = −𝐴𝐴�𝑞𝑞(𝑡𝑡), 𝑝𝑝(𝑡𝑡)� ∙ 𝐹𝐹(𝑡𝑡),(2.2)
and the corresponding density function
𝑓𝑓 = 𝑓𝑓0 + ∆𝑓𝑓,
(2.3)
changes according to eq.(2.1):
𝜕𝜕𝑓𝑓0= [𝐻𝐻, 𝑓𝑓0 ] = 0,
𝜕𝜕𝜕𝜕

𝜕𝜕∆𝑓𝑓
= [𝐻𝐻, ∆𝑓𝑓] − 𝐹𝐹(𝑡𝑡)�𝐴𝐴, 𝑓𝑓0 � = 𝑖𝑖ℒ∆𝑓𝑓 − 𝐹𝐹(𝑡𝑡)�𝐴𝐴, 𝑓𝑓0 �.
𝜕𝜕𝜕𝜕The solution of Eq.(2.4) for ∆𝑓𝑓 is𝑡𝑡′∆𝑓𝑓 = − � 𝑑𝑑𝑡𝑡 ′ 𝑒𝑒 𝑖𝑖�𝑡𝑡−𝑡𝑡 �ℒ �𝐴𝐴, 𝑓𝑓0 �𝐹𝐹(𝑡𝑡 ′ ).
−∞

(2.4)

(2.5)

Because 𝑓𝑓0 ~𝑒𝑒 −𝛽𝛽𝛽𝛽 , we obtain[𝑓𝑓0 , 𝐴𝐴] = −𝛽𝛽𝑓𝑓0 [𝐻𝐻, 𝐴𝐴] = 𝛽𝛽𝑓𝑓0 𝐴𝐴̇,(2.6)
where 𝛽𝛽 = 1/𝑘𝑘𝐵𝐵 𝑇𝑇, 𝑘𝑘𝐵𝐵 is the Boltzmann constant, and 𝑇𝑇 is the absolute temperature. The ensemble average ⟨Δ𝐵𝐵⟩ of the deviation in a physical quantity 𝐵𝐵 is given by𝑡𝑡⟨∆𝐵𝐵⟩ = � 𝐵𝐵∆𝑓𝑓𝑓𝑓𝛤𝛤 = � 𝑑𝑑𝑡𝑡 ′ 𝛷𝛷𝐵𝐵𝐵𝐵 (𝑡𝑡 − 𝑡𝑡 ′ )𝐹𝐹(𝑡𝑡 ′ ),(2.7)

𝛷𝛷𝐵𝐵𝐵𝐵 (𝑡𝑡) = ��𝑓𝑓0 , 𝐴𝐴 �𝐵𝐵(𝑡𝑡)𝑑𝑑𝛤𝛤 = 𝛽𝛽�𝐴𝐴̇(0)𝐵𝐵(𝑡𝑡)�.

(2.8)

−∞

where 𝛷𝛷𝐵𝐵𝐵𝐵 (𝑡𝑡) is the response function which is defined as

3. Application to molecular dynamics simulations
To apply the linear response theory to the molecular dynamics simulations of the structuralchange of tritium-substituted polyethylene induced by beta decays of substituted tritium[4,5,6,7], we derive the time derivative 𝐴𝐴̇ of the dynamical quantity 𝐴𝐴, which is conjugate

to the force applied, required to calculate the response function [7]. The dynamical quantity
in this study is the total potential energy difference of hydrogen-removed polyethylene before
and after beta decays of substituted tritium.

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This time derivative has three terms,(3.1)

𝐴𝐴̇𝐵𝐵 = 𝐸𝐸̇Bbefore − 𝐸𝐸̇Bafter ,𝐴𝐴𝐴𝐴̇ = 𝐸𝐸̇Abefore − 𝐸𝐸̇Aafter ,𝐴𝐴̇ 𝑇𝑇 = 𝐸𝐸̇Tbefore − 𝐸𝐸̇Tafter ,where, 𝐸𝐸Bbefore , 𝐸𝐸Bafter, 𝐸𝐸Abefore, 𝐸𝐸Aafter, 𝐸𝐸Tbefore, and 𝐸𝐸Tafter

(3.2)
(3.3)
represent the bond-stretching,bond-bending and torsional potentials before and after beta decays of substituted tritium, respectively. We arrive at the following expressions for 𝐴𝐴𝐵𝐵̇ , 𝐴𝐴𝐴𝐴̇ , and 𝐴𝐴𝑇𝑇̇ after simple but
cumbersome calculation.

𝑁𝑁−1

(3.4)

0
0
� 𝑖𝑖,𝑖𝑖+1 ∙ 𝒅𝒅̇𝑖𝑖,𝑖𝑖+1 ,𝐴𝐴̇𝐵𝐵 = 𝐾𝐾𝐵𝐵 ��𝑑𝑑𝑖𝑖,𝑖𝑖+1′ − 𝑑𝑑𝑖𝑖,𝑖𝑖+1
� 𝒅𝒅
𝑖𝑖=1

where 𝒅𝒅𝑖𝑖,𝑖𝑖+1 = 𝒓𝒓𝑖𝑖+1 − 𝒓𝒓𝑖𝑖 is the bond vector between the i-th united atom and the (i+1)-th
� 𝑖𝑖,𝑖𝑖+1 is the unit vector ofunited atom, 𝒓𝒓𝑖𝑖 is the position vector of the i-th united atom, 𝒅𝒅
00, 𝑑𝑑𝑖𝑖,𝑖𝑖+1′ are the equilibrium bond lengths before and after beta decays of𝒅𝒅𝑖𝑖,𝑖𝑖+1 , and 𝑑𝑑𝑖𝑖,𝑖𝑖+1
substituted tritium, respectively. As for 𝐴𝐴𝐴𝐴̇ , we have
𝑁𝑁−1

(3.5)

𝐴𝐴𝐴𝐴̇ = 𝐾𝐾𝐴𝐴 ��𝜃𝜃𝑖𝑖0 ′ − 𝜃𝜃𝑖𝑖0 � 𝜃𝜃̇𝑖𝑖 ,𝑖𝑖=2𝜃𝜃̇𝑖𝑖 =

̇
̇
̇
𝒅𝒅̇
�
� 𝑖𝑖−1,𝑖𝑖 ∙ 𝒅𝒅𝑖𝑖,𝑖𝑖+1 � − 𝒅𝒅
� 𝑖𝑖−1,𝑖𝑖 ∙ 𝒅𝒅
� 𝑖𝑖,𝑖𝑖+1 �𝒅𝒅
� 𝑖𝑖−1,𝑖𝑖 𝒅𝒅𝑖𝑖−1,𝑖𝑖 + 𝒅𝒅
� 𝑖𝑖,𝑖𝑖+1 ∙ 𝒅𝒅𝑖𝑖,𝑖𝑖+1 �� 𝑖𝑖−1,𝑖𝑖 ∙ 𝒅𝒅
+ 𝒅𝒅
𝑑𝑑𝑖𝑖−1,𝑖𝑖 𝑖𝑖,𝑖𝑖+1
𝑑𝑑𝑖𝑖,𝑖𝑖+1
𝑑𝑑𝑖𝑖−1,𝑖𝑖
𝑑𝑑𝑖𝑖,𝑖𝑖+1
� 𝑖𝑖−1,𝑖𝑖 ∙ 𝒅𝒅
� 2𝑖𝑖,𝑖𝑖+1
�1 − 𝒅𝒅,(3.6)

where 𝜃𝜃𝑖𝑖0 and 𝜃𝜃𝑖𝑖0 ′ represent the equilibrium bond angles before and after beta decays of
substituted tritium, respectively. 𝐴𝐴̇𝑇𝑇 is expressed as the following equations:𝐴𝐴̇ 𝑇𝑇 =

𝐶𝐶 =

𝑁𝑁−2

1
0
�{𝑛𝑛𝑖𝑖,𝑖𝑖+1 𝑉𝑉𝑖𝑖,𝑖𝑖+1 sin�𝑛𝑛𝑖𝑖,𝑖𝑖+1 �𝜙𝜙𝑖𝑖,𝑖𝑖+1 − 𝜙𝜙𝑖𝑖,𝑖𝑖+1
��
2
𝑖𝑖=2

0
′
− 𝑛𝑛𝑖𝑖,𝑖𝑖+1
𝑉𝑉𝑖𝑖,𝑖𝑖+1 ′ sin�𝑛𝑛𝑖𝑖,𝑖𝑖+1 ′�𝜙𝜙𝑖𝑖,𝑖𝑖+1 − 𝜙𝜙𝑖𝑖,𝑖𝑖+1′��}𝜙𝜙̇𝑖𝑖,𝑖𝑖+1 ,1

𝜙𝜙̇𝑖𝑖,𝑖𝑖+1 =𝐶𝐶 − 𝐷𝐷,sin 𝜙𝜙𝑖𝑖,𝑖𝑖+1

(3.7)
(3.8)

�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 ��𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �× ��𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 � ∙ �𝒅𝒅̇𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 + 𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅̇𝑖𝑖,𝑖𝑖+1 �+ �𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �∙ �𝒅𝒅̇𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 + 𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅̇𝑖𝑖+1,𝑖𝑖+2 ��,

211

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𝐷𝐷 =�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 � ∙ �𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �22�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 � �𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �×��𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 ��𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 ��𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 �∙ �𝒅𝒅̇𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 + 𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅̇𝑖𝑖,𝑖𝑖+1 �+�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 ��𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 ��𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �∙ �𝒅𝒅̇𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 + 𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅̇𝑖𝑖+1,𝑖𝑖+2 ��,�sin 𝜙𝜙𝑖𝑖,𝑖𝑖+1 � = �1 − �(3.10)
2

�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 � ∙ �𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �� ,�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 ��𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 �(3.11)

00′
where 𝜙𝜙𝑖𝑖,𝑖𝑖+1and 𝜙𝜙𝑖𝑖,𝑖𝑖+1′, 𝑛𝑛𝑖𝑖,𝑖𝑖+1 and 𝑛𝑛𝑖𝑖,𝑖𝑖+1, 𝑉𝑉𝑖𝑖,𝑖𝑖+1 and 𝑉𝑉𝑖𝑖,𝑖𝑖+1 ′ denote the equilibrium di-hedral angles, the periodicities and the energy barriers to rotation before and after beta decaysof substituted tritium, respectively. The sign of sin 𝜙𝜙𝑖𝑖,𝑖𝑖+1 is decided by that of

�𝒅𝒅𝑖𝑖−1,𝑖𝑖 × 𝒅𝒅𝑖𝑖,𝑖𝑖+1 � × �𝒅𝒅𝑖𝑖,𝑖𝑖+1 × 𝒅𝒅𝑖𝑖+1,𝑖𝑖+2 � ∙ 𝒅𝒅𝑖𝑖,𝑖𝑖+1 .

References[1] R. Kubo: Statistical-Mechanical Theory of Irreversible Processes. I. General Theory andSimple Applications to Magnetic and Conduction Problems, J. Phys. Soc. Jpn., 12:6
(1957), 570-586.
[2] R. Kubo: The fluctuation-dissipation theorem, Rep. Prog. Phys., 29 (1966) 255-284.
[3] R. Kubo, M. Toda, N. Hashitsume: Statistical Physics II, Springer-Verlag Berlin Heidelberg (1985).
[4] S. Fujiwara, H. Nakamura, H. Li, H. Miyanishi, T. Mizuguchi, T. Yasunaga, T. Otsuka,
Y. Hatano, S. Saito: Computational strategy for studying structural change of tritiumsubstituted macromolecules by a beta decay to helium-3, J. Adv. Simulat. Sci. Eng., 6:1(2019) 94-99.
[5] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, T. Yasunaga, T. Otsuka, T. Kenmotsu,
Y. Hatano, S. Saito: Structural change of tritium-substituted polymeric materials by abeta decay: A molecular dynamics study, Plasma Fusion Res., 14 (2019) 3401106.
[6] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, A. Nakata, T. Miyazaki, S. Saito: Structural change of damaged polyethylene by beta-decay of substituted tritium using reactive
force field, Jpn. J. Appl. Phys., 60 (2021) SAAB06.
[7] S. Fujiwara, R. Kawanami, H. Li, H. Nakamura, K. Omata, A theoretical approach tostructural change of a polymer induced by beta decays of substituted tritium based on
the linear response theory, in submission.

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Molecular simulations on dynamics of lipid bilayers
and water molecules
Yuji Higuchi1,* , Hiroaki Ito2 , Naofumi Shimokawa3 , Yuta Asano1 , Takuya
Kuwahara4 , Mafumi Hishida5
1 Institute for Solid State Physics, The University of Tokyo
2 Department of Physics, Chiba University
3 School of Materials Science, Japan Advanced Institute of Science and Technology
4 Fraunhofer IWM, MicroTribology Center µTC
5 Department of Chemistry, Faculty of Pure and Applied Sciences, University of Tsukuba∗ yuji.higuchi@issp.u-tokyo.ac.jp

Abstract. We studied the structure and dynamics of a phospholipid bilayer and water bymolecular dynamics simulations. We revealed the dependency of water dynamics on thechemical structure of lipid heads by all-atomic molecular dynamics simulations. When water molecules are strongly attracted to the positively charged group, hydrogen bond networks
in water molecules are broken. In contrast, weak hydration does not break the hydrogen networks. Next, we studied the morphological change of vesicles composed of neutral andcharged lipids by coarse-grained molecular dynamics simulations. We revealed the large
deformation process from the vesicle to the disk shape. The ﬂip of the lipids initiates thepore formation in the charged-lipid-rich domain.
Keywords: Molecular simulation, Phospholipid, Biomembrane

1.

Introduction

The phospholipid bilayer is the main component of the cell membrane, and therefore its
structures and properties are actively studied. Charged lipids are contained in biomembraneand play important roles such as protein adsorption and phase separation of lipids. However,
the eﬀect of charges on the structure and dynamics of lipids is still controversial. Thus, we
focus on charges of lipids and have studied the eﬀect of charges on the bilayer structures.
The interactions between charged lipid and water are also crucial for the self-assemble structures of phospholipid. The dynamics of water molecules around the hydrophilic head groups
in phospholipids are investigated by all-atomic molecular dynamics (MD) simulations [1].
Then, we perform coarse-grained (CG) MD simulations to reveal the eﬀect of the charge on
the phase separation and structure in phospholipid vesicle [2, 3, 4].

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DOPE

+

+
N

NH

DOPC

PO!-

PO!-

O

O

O

O

O

O

O

O

Figure 1: Snapshots of molecular dynamics simulations and molecular structures of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dioleoyl-sn-glycero-3phosphoethanolamine (DOPE).

2.

Results

We perform all-atomic MD simulations using LAMMPS [5] and DFTB+ [6] to reveal thewater dynamics around the phosphatidylcholine (PC) and phosphatidylethanolamine (PE)head group. Figure 1 shows typical snapshots of MD simulation. Molecular structures of
DOPC and DOPE are also shown, where the only diﬀerence is the ammonium group in
the head groups. The rotation relaxations of water are faster in PE than that in PC. This isconsistent with a previous experimental study using terahertz spectroscopy [7], conﬁrming
the validity of the simulation results. Radial distribution functions (RDF) show that the PE
lipid with NH3+ is strongly hydrated by water molecules, whereas PC lipid with N(CH3)3+ isweakly hydrated. Interestingly, strong hydration enhances the rotation of water molecules.
To reveal the mechanism, we compare the numbers of hydrogen bonds (HBs) between watermolecules around the head group. The HBs in PE are less than that in PC. Thus, we suggestthat the strong hydration in PE breaks the HB network and enhances the rotation of watermolecules.
Next, we study the morphological change in charged lipid bilayer vesicles by CG MD
simulation. We adopt the model by Cooke et al. for the CG model of the lipid membrane anduse the Debye-Hückel potential to include the electrostatic interaction. Two kinds of lipids
are composed of the vesicle, and the attractive interaction among them is set to separate
each other. When both lipids are neutral, phase separation is observed. When the vesicle
consists of negatively charged and neutral lipids, phase separation is delayed due to therepulsive interaction between charged lipids. Figure 2 shows a morphological change ofthe vesicle. After the phase separation, the pore is formed in the charged-lipid-rich domain.
Then, the vesicle changes to the disk shape. Remarkably, some lipid molecules ﬂip, andthen a pore is formed. The morphologies are summarized with the salt concentration, which214

Neutral lipid

Charged lipid

Pore

Figure 2: Morphological change of lipid bilayers from vesicle to disk by coarse-grained
molecular dynamics simulation.
is consistent with the experiment. This conﬁrms the validity of our CG MD simulations.
Thus, we successfully revealed the structure and dynamics of lipid bilayers in multi-scale.

References[1] Y. Higuchi, Y. Asano, T. Kuwahara, M. Hishida: Rotational Dynamics of Water at the
Phospholipid Bilayer Depending on the Head Groups Studied by Molecular Dynamics
Simulations, Langmuir, 37 (2021), 5329–5338.
[2] H. Himeno, H. Ito, Y. Higuchi, T. Hamada, N. Shimokawa, M. Takagi: Coupling
between pore formation and phase separation in charged lipid membranes, Phys. Rev.
E, 92 (2015), 062713.
[3] H. Ito, Y. Higuchi, N. Shimokawa: Coarse-grained molecular dynamics simulation of
charged lipid membranes: Phase separation and morphological dynamics, Phys. Rev.
E, 94 (2016), 042611.
[4] N. Shimokawa, H. Ito, Y. Higuchi: Coarse-grained molecular dynamics simulation for
uptake of nanoparticles into a charged lipid vesicle dominated by electrostatic interactions, Phys. Rev. E, 100 (2019), 012407.
[5] S. Plimpton: Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys., 117 (1995), 1–19.
[6] B. Hourahine, et al.: DFTB+, a software package for eﬃcient approximate density
functional theory based atomistic simulations, J. Chem. Phys., 152 (2020), 124101.
[7] M. Hishida, K. Tanaka, Y. Yamamura, K. Saito: Cooperativity between Water and
Lipids in Lamellar to Inverted-Hexagonal Phase Transition, J. Phys. Soc. Jpn., 83(2014), 044801.
[8] I. R. Cooke, K. Kremer, M. Deserno: Tunable generic model for ﬂuid bilayer membranes, Phys. Rev. E, 72 (2005), 011506.

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Molecular Dynamics Simulation on Hydrogen Isotope
Molecules Emitted from Amorphous Carbon
Hiroaki Nakamura1,2,* , Seiki Saito3 , Keiji Sawada4 , Masahiro Kobayashi1,5 ,Masahiro Hasuo6
1 National Institute for Fusion Science
2 Nagoya University
3 Yamagata University
4 Shinshu University
5 The Graduate University for Advanced Studies, SOKENDAI
6 Kyoto University∗ hnakamura@nifs.ac.jp

Abstract. We have been developing the hybrid code between molecular dynamics and heat
conduction solver (MD-HC), which drive the hydrogen emission rate from amorphous carbon. From our previous work, the emission rate strongly depends on the structure of theamorphous carbon. In the present paper, we show the target-structure dependence of thehydrogen emission rate by the MD-HC code.
Keywords: Molecular dynamics simulation, heat conduction equation, amorphous carbon,hydrogen emission, rotational state, vibrational state

1.

Introduction

Detached plasma is one of candidates to decrease the heat load to the divertor to realize nuclear fusion generation. Some portion of the detached plasma is generated by the Molecular
Assisted Recombination (MAR) process, where the population of the neutral particles has
a strong inﬂuence the reaction rate[1, 2]. Therefore, the information of the neutral particles emitted from the wall is essential for accurate estimation of the MAR[3]. In order toachieve this goal, we’ve been developing the hybrid code between molecular dynamics andheat conduction solver (MD-HC), which drive the hydrogen emission rate from amorphous
carbon[4].
In our previous work[4], we concentrate on the isotopic hydrogen molecules which are
emitted from the divertor plate, which is made of amorphous carbon. There, it was foundthat the emission rate strongly depends on the structure of the amorphous carbon. In thepresent paper, we show the target-structure dependence of the hydrogen emission rate by
the MD-HC code.

216

2.

Simulation model and method

We performed the MD simulation which are the same method as our previous work[2, 4].
The initial target of the amorphous carbon is made by the same way as the previous works.
However the conﬁguration is diﬀerent from the previous works, because the random numbers to distribute the velocity to all atoms is diﬀerent from that of the previous works. Usinga few random numbers, we prepare the various initial conﬁgurations of the amorphous carbon.

Figure 1: Simulation model of MD simulation. A hydrogen atom is injected to the amorphous carbon.

3.

Results and Discussions

The rovibrational energy of hydrogen molecules is determined from kinetic energy, potential
energy, and angular momentum of the two atoms in the center-of-mass system. We obtain
the information of the emitted hydrogen atom and molecules from the carbon. In Fig.2, we
also obtain the hydrogen distributions in the target and the initial depth distribution of theemitted hydrogen.

Acknowledgments
The research was supported by Grants-in-Aid for Scientiﬁc Research (C), Nos.18K11416,
19K03802 and 19K03800 from the Japan Society for the Promotion of Science, and by the
NIFS Collaborative Research Programs NIFS20KNTS066, NIFS20KKGS028 and
NIFS20KNSS150. The computations were performed using the JFRS-1 supercomputer system at Computational Simulation Centre of International Fusion Energy Research Centre

217

Figure 2: Hydrogen distributions in the target and the initial depth distribution of the emittedhydrogen.
(IFERC-CSC) in Rokkasho Fusion Institute of QST, Japan, Research Center for Computational Science, Okazaki, Japan and Plasma Simulator of NIFS, Japan.

References[1] K. Sawada, H. Nakamura, S. Saito, G. Kawamura, M. Kobayashi, K.
Haga, T. Sawada, M. Hasuo, Contrib. Plasma Phys., 60(2020) e201900153,
doi:10.1002/ctpp.201900153.
[2] S. Saito, H. Nakamura, K. Sawada, G. Kawamura, M. Kobayashi and H. Hasuo, Contrib. Plasma Phys., 60(2020) e201900152, doi:10.1002/ctpp.201900152.
[3] S. Saito, H. Nakamura, K. Sawada, M. Kobayashi, G. Kawamura and H. Hasuo,
Plasma Fus. Res., 15(2020) 240307, doi:10.1585/pfr.15.2403073.
[4] H. Nakamura,S. Saito, T. Sawada, K. Sawada, G. Kawamura, M. Kobayashi and H.
Hasuo, Jpn. J. Appl. Phys. submitted.

218

JSST2021

Studies on ion heating through the merging of spherical tokamaks by means of particle simulations
Shunsuke Usami1,2*, Ritoku Horiuchi1, Toseo Moritaka1, Yasushi Ono2
1

National Institute for Fusion Science, National Institute of Natural Sciences
2
The University of Tokyo*usami.shunsuke@nifs.ac.jp

Abstract. The ion heating through the merging of spherical tokamaks is investigated bymeans of particle simulations. Simulations show that part-of-circle structures of velocity distributions are formed, and thus effective heating by the Pick-Up-Like process occurs. Also,
part-of-circle structures are seen during merging and for long periods of time after merging.
Keywords: Particle simulation, Spherical tokamak, Heating, Magnetic reconnection

1. Introduction
Spherical tokamaks (STs) can confine higher-β plasmas than standard tokamaks or helicaldevices. In merging of STs, in which two STs are merged through magnetic reconnection, acase for β~40% was reported. The heating mechanism, however, remains to be unsolved. The
elucidation of heating mechanism can lead to the higher performance of future ST reactors.
We investigate ion heating processes by means of particle simulation.

2. Simulation results
Figure 1 shows the spatial profiles of the ion temperature at various times. At the initial time
(Fig. 1(a)), the temperature is low and uniform. At ωcet=1445 (Fig. 1(b)), the two STs are being merged at the central position and magnetic reconnection takes place. The temperature
becomes high in parts of the downstream. At ωcet=1807 (Fig. 1(c)), the merging process iscompleted, and high-temperature regions are expanded. Also, a new high-temperature regionis generated around the central position. At ωcet =2045 (Fig. 4(d)), 2581 (Fig. 4(e)), and 3097
(Fig. 4(f)), high-temperature ions are further expanded to wider regions.
In Fig. 2 we show ion velocity distributions at A1, B1, B2, C1, C2, D1, E1, and F1 designatedin Fig. 1. Figure 2(a) displays that initially a Maxwellian distribution holds. Figure 2(b)shows that the distribution is clearly spread compared with Fig. 2(a), nearly keeping a Maxwellian distribution, which means that genuine compression acts on ions. Figure 2(c) showsthat the distribution consists of three parts and the distribution shape is a part of a circle. This

219

JSST2021
feature indicates that ions are effectively heated by the Pick-Up-Like process [1,2], which issimilar to the Pickup [3,4]. Furthermore, ion velocity distributions at ωcet =1807, 2045, 2581,
and 3097 are depicted in Figs. 2 (d), (f), (g), and (h), which show that part-of-circle structures
are maintained during long periods of time after merging. In contrast, at C2, viscous heating
also occurs. Figure 2 (e) displays that a different type of effective heating acts on ions at C2.

Figure 1: Spatial profiles of the ion temperature at various times.

Figure 2: Ion velocity distributions at A1, B1, B2, C1, C2, D1, E1, and F1 in Fig. 1

References[1] S. Usami R. Horiuchi, H. Ohtani: Effective heating of nonadiabatic protons in magnetic
reconnection with a guide field, Phys. Plasmas, 24 (2017) 092101.
[2] S. Usami et al.: Dependence of the pickup-like ion effective heating on the poloidal andtoroidal magnetic fields during magnetic reconnection, Phys. Plasmas, 26 (2019) 102103.
[3] E. Möbius, et al.: Direct observation of He+ pick-up ions of interstellar origin in the solar
wind, Nature, 318 (1985) 426-429.
[4] J. F. Drake, et al.: A magnetic reconnection mechanism for ion acceleration and abundance enhancements in impulsive flares, Astrophys. J., 700 (2009) L16-L20.

220

JSST2021

Visualization analysis of intersection points ofenergetic tritons and plasma facing wall in LHD
by virtual-reality system
Hiroaki Ohtani1,2*, Suguru Masuzaki1,2, Kunihiro Ogawa1,2, Seiji Ishiguro1,2
National Institute for Fusion Science
The Graduate University for Advanced Studies, SOKENDAI*
ohtani.hiroaki @nifs.ac.jp
12

Abstract. We evaluated the trajectories of the energetic tritons from the triton generation distribution in Large Helical Device (LHD) by means of the collisionless Lorentz orbit code, andwe calculated the intersection points of the tritons and the plasma facing wall. The intersection
points were visualized in the virtual-reality world as spheres with the rendered internal vacuum
wall and the divertor plates. It became possible to directly observe the points distributed on thewall. This visualization played an important role in determination of the appropriate positionsof the material probes on the wall in the real LHD to observe the accumulated tritium on thewall experimentally.
Keywords: Virtual-reality visualization, Intersection points, Tritons, plasma facing wall

1. Introduction
Tritium recycle in the fuel system is one of the important issues in realization of a fusion power
generation system. Tritium inventory is the amount of accumulated tritiums which stay in the
shadow area and do not circulate in the tritium circulation system [1]. One of the shadow areasis the plasma facing wall where the tritium approaches directly. Therefore, there is concern
over the increase of the inventory at the wall [2,3,4]. To investigate the energetic triton accumulation experimentally on the vacuum wall, we planned to put material probes on the vacuum
vessel of the Large Helical Device (LHD). Since the size of the probe is much small comparedwith that of the wall, it is necessary to place the probe on the appropriate position on the wall.
For deciding specifically the position of the material probe, the intersection point of energetic
triton and the plasma facing wall is visualized in the vacuum vessel of the LHD with the divertor plates in the virtual-reality (VR) system [5]. The researcher can directly check the distribution of the intersection points on the plasma facing wall to decide where the probes shouldbe placed at the positions on the wall, watching many tritons collide on the wall and so many
tritons did not strike with the wall. In this paper, we report the calculation method of the triton
trajectory and the collision point, the VR visualization method of the triton intersection points,

221

JSST2021

and the visualization results.

2. Trajectory and intersection point of triton[6]The initial position of the triton by DD fusion reaction is determined from the neutron generation distribution calculated by FIT3D-DD code [7], and the trajectory of the triton with 1MeV
energy from the initial position is evaluated by the LORBIT code in which the Newtonian
equation of motion is solved without any collision effect [8]. The magnetic field in a vacuum
calculated from the coil current of LHD is used and no electric field is assumed in this paper.
The divertor plate and the vacuum vessel are represented by the triangle and polygons, respectively, based on the design data which was used in the installation and construction of the real
LHD. We calculate whether the triton trajectory exists inside or outside the triangles and thepolygons, and we detect the intersection point of the triton and the plasma facing wall. The
coordinate point of the intersection point is stored in the Cartesian coordinate system.

3. VR visualization method
We use CAVE-type VR system [9] called CompleXcope. A modified virtual-LHD [10,11]
based on C++, OpenGL and CAVELib library visualizes the intersection points of the tritons
and the wall as spheres by the point-sprite method with the interface routine of reading thecoordinate points of the intersection points, while the plasma interface wall, such as internal
vacuum wall and divertor plates, is rendered by Unity [12]. The commercial software, FusionSDK [13,14,15], superimposes and displays the spheres and the internal components of
LHD in the one VR world.

4. Visualization results
A viewer watches the intersection points(red spheres) of the tritons and the plasma
facing wall in the vacuum of LHD in CompleXcope as shown in Fig. 1. The viewer issurrounded by stereoscopic images with ahigh immersion feeling, and he can look at
the objects he is interested in with enlarging
the images and from any viewpoints It isfound that many tritons collide with the divertor plates, while some tritons strike thevacuum vessel wall.

Figure 1: A viewer watches the intersection points of the tritons and the wall in
the LHD by VR system.

5. Conclusion
We calculated the trajectories of energetic tritons which were generated in the deuterium operations in LHD, and we found the intersection points of the tritons and the plasma facing wallby using VR system “CompleXcope”. It was possible to analyze the collision point distribution
on the vacuum wall and the divertor plates. This visualization helped the experiment researcher
who planned to put the material probes on the plasma facing wall in the real LHD to determine

222the appropriate positions of the material probes.

JSST2021

Acknowledgements
This work is performed with the support and under the auspices of the NIFS Collaboration
Research program (NIFS19KNTS057, NIFS20KKGS026, NIFS20KOAH037), and by the
LHD project budget (NIFS20ULHH003, NIFS20ULHH034).

References[1] For example, https://www.iter.org/mach/FuelCycle.
[2] S. Masuzaki et al: Physica Scripta T170 (2020) 014068.
[3] M. Yajima et al.: Nuclear Materials Energy, 27 (2021) 100906.
[4] S. Masuzaki et al., Nuclear Materials and Energy, 26 (2021) 100884.
[5] H.Ohtani et al., submitted to J. Visualization (2021).
[6] K. Ogawa, et al.: Plasma Science and Technology, 21 (2019) 025102 (5pp).
[7] R.Seki, et al.: Plasma Fusion Res., 14, (2019), 3402126.
[8] M. Isobe, et al.: J. Plasma Fusion Res. SERIES, 8, (2009), 330.
[9] C. Cruz-Neira, et al.: SIGGRAPH’93: Proc. 20th Ann. Conf. Comp. Graphics Interactive
Tech. pp.135-142, (1993).
[10] A. Kageyama et al. Proc. ICNSP, 138 (1998).
[11] H. Ohtani, et al: Contrib. Plasma Phys. Vol.56, No.6-8, (2016) 692-697.
[12] https://unity.com/[13] https://www.fiatlux.co.jp/product/virtual/easyvr/[14] H. Miyachi et al: IEEE Comp. Soc. (2005) 530.
[15] H. Miyachi et al: IEEE Comp. Soc. (2007) 536.

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JSST 2021

Constructive a priori error estimates for Poisson’sequation with discontinuous coefficients
Kazuaki Tanaka1,* and Mitsuhiro T. Nakao2
1 Institute for Mathematical Science, Waseda University
2 Waseda Research Institute for Science and Engineering, Waseda University∗ tanaka@ims.sci.waseda.ac.jp

Abstract. Our objective is the Dirichlet boundary value problem of Poisson’s equation withdiscontinuous coefficients. We provide explicit a priori error estimates for solutions of the
problem and apply these to finite element approximations.
Keywords: A priori error estimates, Computer-assisted proofs, Numerical Verification, Poisson’s equation with discontinuous coefficients, Rigorous computations

1.

Introduction

We consider the boundary value problem of Poisson’s equation(−∇ · λ∇u = f in Ω,
u=0
on ∂Ω

(1)

with Ω = (0, 1)3 ⊂ R3 and f ∈ L2 (Ω). The coefficient λ discontinuous over Ω is defined asfollows. We divide Ω into the three parts Ω1 = (0, a)×I 2 , Ω2 = (a, b)×I 2 , and Ω3 = (b, 1)×I 2
with the inner boundaries Γa = {a} × I 2 , Γb = {b} × I 2 as displayed in Fig. 1. The coefficientλ ∈ L∞ (Ω) is piecewise constant that satisfies λ = λk > 0 in Ωk for k = 1, 2, 3.
1

Ω1

Ω2

Γ𝑎

Ω3

Γ𝑏

o

𝑦
𝑧

𝑥

0

0

𝑎

𝑏

1

Figure 1: Domain Ω for a fixed z.

224

The weak form of (1) is written as the following formZ(u, v)λ =f (x)v(x)dx ∀v ∈ H01 (Ω),
Ω

(2)

where
(u, v)λ := (λ∇u, ∇v)L2 (Ω) =X

λk (∇u, ∇v)L2 (Ωk ) , u, v ∈ H01 (Ω).

(3)

k=1,2,3We look for a solution u ∈ H01 (Ω) of (2). The bilinear form (·, ·)λ is continuous and coercive.
Therefore, the Lax-Milgram theorem ensures that the problem (2) has a unique solutionu ∈ H01 (Ω) for each f ∈ H −1 (the dual space of H01 (Ω)). Generally, solutions of (2) do notbelong to H 2 (Ω) but have H 2 -regularity in each subdomain Ωk . Therefore, u ∈ H01 (Ω) ∩T( k=1,2,3 H 2 (Ωk )).
Let Vh be a finite dimensional subspace of H01 (Ω) that depends on a parameter h, and letTΠ be some interpolation that maps H01 (Ω) ∩ ( k=1,2,3 H 2 (Ωk )) into Vh . Suppose that there
exists positive constants C(h) that satisfies
k∇(v − Πv)kL2 (Ωk ) ≤ C(h)|v|H 2 (Ωk )(4)Tfor all v ∈ H01 (Ω) ∩ ( k=1,2,3 H 2 (Ωk )). This interpolation constant C(h) exists such as when
we use the tri-linear interpolation Π = Pz Py P x . We define the orthogonal projection Rλh :H01 (Ω) → Vh by(v − Rλh v, vh )λ = 0 for all v ∈ H01 (Ω) and vh ∈ Vh .

(5)

Then, Rλh coincides with the solution uh of(uh , vh )λ = ( f, vh )L2 (Ω) ∀vh ∈ Vh .

(6)

We report the following estimation result:
Theorem 1. Let u ∈ H01 (Ω) be the solution of (2) and Rλh u (= uh ) ∈ Vh a solution of (6). For
Tsome interpolation Π that maps H01 (Ω) ∩ ( k=1,2,3 H 2 (Ωk )) into Vh , suppose that there exists
a positive constant C(h) satisfying (4). Then, we have the following a priori estimates:ku − Rλh ukλ ≤ C(h)||| f |||λ ≤ MλC(h)k f kL2 (Ω)(7)

ku − Rλh ukL2 (Ω) ≤ MλC(h)2 ||| f |||λ ≤ Mλ2C(h)2 k f kL2 (Ω) ,

(8)

and
where Mλ := max λ−1/2.
k
k=1,2,3

By applying Theorem 1 to the tri-linear interpolation with a uniform mesh size h, wehave the following a priori estimates.
Example 1. When min λk = 10−3 and h = 2−7 , we havekku − Rλh ukλ /||| f |||λ ≤ 2.49 × 10−3 ,ku − Rλh ukλ /k f kL2 (Ω) ≤ 7.87 × 10−2 ,ku − Rλh ukL2 (Ω) /||| f |||λ ≤ 1.96 × 10−4 ,ku − Rλh ukL2 (Ω) /k f kL2 (Ω) ≤ 6.19 × 10−3 .

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JSST 2021

Numerical veriﬁcation for positive solutions of theHénon equation on bounded domains
Taisei Asai1,* , Kazuaki Tanaka2 , Shin’ichi Oishi3
1 Graduate School of Fundamental Science and Engineering, Waseda University, Japan
2 Institute for Mathematical Science, Waseda University, Japan
3 Faculty of Science and Engineering, Waseda University, Japan∗ captino@fuji.waseda.jp

Abstract. For the Hénon equation, it is known that if the potential index is zero, then there is
no asymmetric positive solution, and if the potential index is suﬃciently large, then there aresome asymmetric positive solutions. However, the symmetry-breaking bifurcation point andthe total number of multiple solutions branching from its bifurcation point are not known
completely. In this talk, we introduce the numerical veriﬁcation method for the Hénon equation’s multiple solutions and present several numerical results on some bounded domains.
Keywords: Hénon equation, Numerical veriﬁcation method, Symmetry-breaking

1.

Introduction

We consider the Hénon equation which is the boundary value problem−∆u = |x − x0 |l |u| p−1 u in Ω,u = 0on ∂Ω,(1)

where Ω ⊂ RN (N ≥ 1) is a bounded domain, and x0 is set at the center of the domain
if Ω be a symmetric convex domain. The parameter l ≥ 0 is the potential index, and theparameter 2 ≤ p < p∗ (p∗ = ∞ if N = 1, 2 and p∗ = (N + 2)/(N − 2) if N ≥ 3) is thepolytropic index. It is known that if l = 0, then there is no asymmetric positive solution,and if l > 0 is suﬃciently large, then there are some asymmetric positive solutions even
if there is some symmetry in the domain. Its symmetry-breaking phenomena is forcused,
and the importance of the Hénon equation has led to active mathematical study on it overlast decade. For example, Tanaka [1] considered one-dimensianal problem, and he provedthat if l(p − 1) ≥ 4, the Morse index of the positive least energy solution equals 1 and theMorse index of the positive symmetric solution equals 2, and hence the positive least energy
solution is asymmetric and symmetry-breaking phenomena occur. It is also shown that ifl and p are suﬃciently small, then there is no positive asymmetric solution and the Morse
index of the symmetric positive solution equals 1. In another study, Shioji [2, 3] found the226minimum number of asymmetric positive solutions where Ω = {x ∈ RN : |x| < 1} (N = 2, 3).
However, the exact symmetry-breaking bifurcation point and the total number of multiple
solutions branching from its point are still not known completely.
The purpose of this study is to prove the existence of each multiple solutions of (1)using a numerical veriﬁcation method. Then, we also present a discussion of the correlation
between the symmetry of the solution and the domain by verifying on several boundeddomains.

2.

Numerical veriﬁcation

We ﬁrst deﬁne the operator f as

7→ | · −x0 |l |u(·)| p−1 u(·),
u(·)
f :

H 1 (Ω) → H −1 ,0where 2 ≤ p < p∗ (p∗ = ∞ if N = 1, 2 and p∗ = (N + 2)/(N − 2) if N ≥ 3). Furthermore, wedeﬁne the nonlinear operator F : H01 (Ω) → H −1 by F(u) := −∆u − f (u), which is given by
hF(u), vi = (∇u, ∇v)L2 − h f (u), vi for all v ∈ H01 (Ω),∫
where h f (u), vi = Ω (|x − x0 |l |u(x)| p−1 u(x))v(x)dx. The Fréchet derivatives of f and F at
φ ∈ H01 (Ω) are denoted by fφ0 and Fφ0 , respectively, and given by⟨⟩ ∫0
fφ u, v =(p|x − x0 |l |φ(x)| p−1 )u(x)v(x)dx for all u, v ∈ H01 (Ω),
(2)
Ω
⟨
⟩
⟨
⟩
Fφ0 u, v = (∇u, ∇v)L2 − fφ0 u, v
for all u, v ∈ H01 (Ω).
(3)
Then, we consider the following problem:
Find u ∈ H01 (Ω) s.t.

F(u) = 0,(4)

which is the weak form of the problem (1). Then, we apply the Newton–Kantorovich theorem [4], which enables us to prove the existence of a true solution u near a numericallycomputed approximate solution û.
In this talk, we will present the results of verifying the existence of true solutions u nearapproximate solutions û such as shown in Tables 1 to 3.
Table 1: Approximate solutions on Ω = (−1, 1) with p = 3, l = 1, 1.75.
l

1

1.75

4

5

6

6

4

5

5

4

4

3

3

2

2

3

3

û

2

2
1

0
-1

1

-0.5

0

0.5

1

0
-1

1

-0.5

0

0.5

1

227

0
-1

1

-0.5

0

0.5

1

0
-1

-0.5

0

0.5

1

Table 2: Approximate solutions on Ω = (−1, 1)2 with p = 3, l = 0, 2.
l

0

2

û

Table 3: Approximate solutions on Ω = {x ∈ R2 : |x| < 1} with p = 3, l = 0, 6.
l

0

6

û

References[1] S. Tanaka: Morse index and symmetry–breaking for positive solutions of one–dimensional Hénon type equations, Journal of Diﬀerential Equations, 255:7 (2013),
1709–1733.
[2] N. Shioji, K. Watanabe: Radial symmetry of n-mode positive solutions for semilinear
elliptic equations in a disc and its application to the Hénon equation, Topological
Methods in Nonlinear Analysis, 43:1 (2014), 269–285.
[3] N. Shioji: Existence of Many Nonradial Positive Solutions of the Hénon Equation in
R3 , Journal of Convex Analysis, 22:1 (2015), 61–80.
[4] P. Deuﬂhard, G. Heindl: Aﬃne invariant convergence theorems for Newton’s method
and extensions to related methods. SIAM Journal on Numerical Analysis, 16:1 (1979),
1–10.

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Acceleration of Error-Free Transformation of Matrix
Multiplication using GPU Tensor Cores
Katsuhisa Ozaki1,* , Daichi Mukunoki2 , Takeshi Ogita3
1 Department of Mathematical Sciences, Shibaura Institute of Technology
2 Riken Center of Computational Science
3 Division of Mathematical Sciences, Tokyo Woman’s Christian University∗ ozaki@sic.shibaura-it.ac.jp

Abstract. This study aims to provide an accurate numerical result of matrix multiplication using ﬂoating-point arithmetic. An error-free transformation of matrix multiplication
is proposed, which is very useful for proposing accurate numerical algorithms for matrix
multiplication. We improve the original error-free transformation by reducing the numberof matrix multiplications in the transformation. Numerical results on a recently provided
GPU by NVIDIA illustrate the eﬃciency of the proposed method.
Keywords: Matrix Multiplication, Graphics Processing Unit, Tensor Core, Accurate Numerical Algorithms

1.

Introduction

Floating-point arithmetic [1] is widely used in scientiﬁc computing due to its impressive performance. Matrix multiplication plays a crucial role in numerical linear algebra. However,
if a problem is ill-conditioned, heavy cancellation occurs in the dot product; a computed
result may be inaccurate due to the accumulation of rounding errors. In the worst case, arelative error is greater than one; the computed result has no correct digit. There have been
many discussions for improving the accuracy of numerical results, e.g., multiple-precision
arithmetic [2, 3, 4], double word arithmetic [5], and accurate numerical computations [6].
An error-free transformation for matrix multiplication has been proposed [7]. The
method is used for proposing accurate algorithms for matrix multiplication. Its performanceis exceptional due to the dependency of GEMM on basic linear algebra subprograms. Single precision arithmetic is much faster than double-precision arithmetic on some GPUs, e.g.,the RTX series by NVIDIA. Using such GPUs, Mukunoki et al. [8] proposed an error-freetransformation. Especially, the Tensor Core is eﬃciently used in computations. In this study,
we reduce the number of matrix multiplications and accelerate the error-free transformation.
Numerical results shown in the presentation illustrate the eﬃciency of the proposed method.

229

2.

Error-free Transformation using Tensor CoreLet Fw be a set of w-bit ﬂoating-point numbers, e.g., F64 is a set of ﬂoating-point numbers
represented by binary64. Denote flw (·) as a computed result using w-bit ﬂoating-point
n×p
arithmetic. For A ∈ Fm×n
and B ∈ Fw , we aim to obtain an accurate approximation of AB.
w
We brieﬂy introduce the error-free transformation proposed in [7]. Matrices A and B are
split such thatto satisfy

A = A1 + A2 + · · · + Ak ,Ai ∈ Fm×n
w , 1 ≤ i ≤ k,

B = B1 + B2 + · · · + Bℓ ,B j ∈ Fw , 1 ≤ j ≤ ℓ

n×p

(
)
flw Ai B j = Ai B j

for all (i, j) pairs. Then, AB can be transformed into an unevaluated sum of kℓ ﬂoating-point
matrices such that
k ∑
ℓ
∑
AB =
Ai B j .
i=1 j=1

In the original paper, numerical examples with w = 64 were presented.
Mukunoki et al. exploited fast low-precision arithmetic on GPUs [8]. The matrices
n×p
A ∈ Fm×n
64 and B ∈ F64 are split such that
−1
−1
P−1
1 P1 A1 + P2 P2 A2 + · · · + Pk′ Pk′ Ak′ ,′Pi Ai ∈ Fm×n
32 , 1 ≤ i ≤ k ,−1−1
B = B1 Q1 Q−1
1 + B2 Q2 Q2 + · · · + Bℓ′ Qℓ′ Qℓ′ ,B j Q j ∈ F32 , 1 ≤ j ≤ ℓ′A=

to satisfy

n×p

(1)

(
)
fl32 (Pi Ai )(B j Q j ) = Pi Ai B j Q j ,where Pi and Q j are diagonal matrices. Here, k′ and ℓ′ are larger than k and ℓ, respectively.
Then, we have
k′ ∑
ℓ′
∑
−1
AB =
P−1
i (Pi Ai )(B j Q j )Q j .
i=1 j=1

Besides,Pi Ai ∈ Fm×n
16 ,

n×p

B j Q j ∈ F16

holds true for n ≥ 2, and we can exploit the Tensor Core for (Pi Ai )(B j Q j ).
First, we apply the technique [9] to the original error-free transformation. Next, we
focus on the sparsity of Ai and B j . In the original error-free transformation, ⌈log2 n⌉ bitcarrying is assumed in a dot product in matrix multiplication. We consider the number of
non-zero elements for the splitting. Combing these strategies, we can eﬀectively reduce k′
and ℓ′ in (1). The detailed algorithm and numerical results will be shown in the presentationin JSST 2021.

230

References[1] IEEE standard for ﬂoating-point arithmetic. ANSI/IEEE Std 754-2008, 1–70.
[2] The GNU Multiple Precision Arithmetic Library, https://gmplib.org/.
[3] The GNU MPFR Library, https://www.mpfr.org/.
[4] exﬂib - extend precision ﬂoating-point arithmetic library, http://www-an.acs.i.
kyoto-u.ac.jp/˜fujiwara/exflib/.
[5] High-Precisiondhbsoftware/.

SoftwareDirectory,

https://www.davidhbailey.com/[6] T. Ogita, S.M. Rump, and S. Oishi: Accurate sum and dot product, SIAM Journal on
Scientiﬁc Computing (SISC), 26:6 (2005), 1955–1988.
[7] K. Ozaki, T. Ogita, S. Oishi, and S.M. Rump: Error-free transformations of matrix
multiplication by using fast routines of matrix multiplication and its applications, Numerical Algorithms, 59: 1 (2012), 95–118.
[8] D. Mukunoki, K. Ozaki, T. Ogita, and T. Imamura: DGEMM Using Tensor Cores,
and Its Accurate and Reproducible Versions, In: Sadayappan P., Chamberlain B.,
Juckeland G., Ltaief H. (eds) High Performance Computing. ISC High Performance
2020. Lecture Notes in Computer Science, 12151 (2020), 230–248.
[9] A. Minamihata, K. Ozaki, T. Ogita, and S. Oishi: Improved extraction scheme for accurate ﬂoating-point summation, In: The 35th JSST Annual Conference International
Conference on Simulation Technology, 2016.

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Generation of Implicit Surface Based on
Isoparametric Elements
Taku Itoh1,*
1 College of Industrial Technology, Nihon University, Japan∗ itoh.taku@nihon-u.ac.jp

Abstract. To decrease the memory cost of volume data-based method for generating animplicit surface g(x) = 0, a method based on isoparametric elements has been proposed,
where g(x) is a scalar ﬁeld generated from surface points obtained from three-dimensionalscanning devices. In this method, g(x) can be generated from volume data directly. Namely,
since the piecewise polynomials are not employed, their coeﬃcients do not need to retain in
the proposed method. Numerical experiments show that the result of the proposed method isvisually almost the same with that of the conventional one. In addition, the memory cost of
the proposed method can be decreased to 1/27 in comparison with that of the conventionalone.
Keywords: Implicit surface, Isoparametric elements, Volume data

1.

Introduction

This paper focuses on generation of a scalar ﬁeld g(x) for implicit surface. The scalar ﬁeld
has been employed for surface reconstruction from a set of surface points X = {x1 , x2 , . . . , xn }obtained from three-dimensional scanning devices. In addition, many methods have been
proposed for generating the scalar ﬁeld g(x) [1, 2, 3, 4]. An implicit surface is represented
as g(x) = 0. Note that the rendering cost for extracting g(x) = 0 tends to be high usually.
A method described in [3] has enabled to render g(x) = 0 in real-time on graphics
processing unit (GPU). In this method, a set of ﬁeld values fi, j,k (volume data) on N 3 uniform
grid points xi, j,k are required for generating g(x). In addition, piecewise polynomials basedon the B-spline are constructed from the ﬁeld values [3]. The ﬁeld values fi, j,k are obtainedby evaluating another scalar ﬁeld f (x) generated from X by such as multi-level partitionof unity implicits (MPU) method [2]. Namely, f (x) is indispensable as an intermediate forgenerating g(x).
A method for determining fi, j,k without the intermediate has been proposed [4]. In themethod, fi, j,k can be determined from X directly. Note that some coeﬃcients for constructing
piecewise polynomials have to be retained as well as [3], although the intermediate is not
required in [4]. Hence, the memory cost becomes large for the case where a complex-shaped
object is represented.

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On the other hands, isoparametric elements have been employed in the ﬁnite element
analysis [5]. The isoparametric elements are employed for interpolating values between
nodes in the analysis. If the isoparametric elements are embedded to the method in [4], thememory cost of [4] may be decreased.
The purpose of this study is to propose a method for generating an implicit surface basedon the isoparametric elements. To this end, the method described in [4] is modiﬁed so thatg(x) can be generated from fi, j,k directly. Namely, since the piecewise polynomials are not
employed, their coeﬃcients do not need to retain in the proposed method.

2.

Implicit Surface Based on Isoparametric Elements

By the method described in [4], the ﬁeld values fi, j,k can directly be determined from thegiven point data X = {x1 , x2 , . . . , xn } together with normals N = {n1 , n2 , . . . , nn }, where
n is the number of given points. We employ the ﬁeld values fi, j,k in the proposed method.
Figure 1 shows an example of a set of ﬁeld values fi, j,k on xi, j,k (1 ≤ i, j, k ≤ N) in a cubic
domain Ω. In this ﬁgure, the red and blue nodes are large and small ﬁeld values, respectively.
The detail procedures for obtaining the ﬁeld values fi, j,k are shown in [4].
Here, 8-nodes three-dimensional (3D) isoparametric elements are written as follows:
1N2 (t) = (1 + ξ)(1 − η)(1 − ζ),
81N4 (t) = (1 − ξ)(1 + η)(1 − ζ),
81
N6 (t) = (1 + ξ)(1 − η)(1 + ζ),
81
N8 (t) = (1 − ξ)(1 + η)(1 + ζ),
8

1
N1 (t) = (1 − ξ)(1 − η)(1 − ζ),
81N3 (t) = (1 + ξ)(1 + η)(1 − ζ),
81N5 (t) = (1 − ξ)(1 − η)(1 + ζ),
81
N7 (t) = (1 + ξ)(1 + η)(1 + ζ),
8where t = [ξ, η, ζ]T , ξ ∈ [−1, 1], η ∈ [−1, 1] and ζ ∈ [−1, 1]. Here, a scalar value function
g(x) is represented asg(x) =

N−1
∑ N−1
∑ N−1
∑

gi jk (t(x)),(1)

i=1 j=1 k=1

where gi jk (t(x)) is a local scalar value function in (i, j, k)-th cubic subdomain Ωi, j,k constructed by {xi, j,k , xi+1, j,k , xi+1, j+1,k , xi, j+1,k , xi, j,k+1 , xi+1, j,k+1 , xi+1, j+1,k+1 , xi, j+1,k+1 }, as shownin Fig. 2. Here, gi jk (t(x)) (1 ≤ i, j, k ≤ N − 1) is represented asgi jk (t(x)) = N1 (t) fi, j,k + N2 (t) fi+1, j,k + N3 (t) fi+1, j+1,k + N4 (t) fi, j+1,k+ N5 (t) fi, j,k+1 + N6 (t) fi+1, j,k+1 + N7 (t) fi+1, j+1,k+1 + N8 (t) fi, j+1,k+1 ,where fi, j,k is a ﬁeld value on xi, j,k (1 ≤ i, j, k ≤ N). Note that gi jk (t(x)) = 0 < Ωi, j,k .
To evaluate g(x), a subdomain Ωi, j,k that contains x is ﬁrst searched, and gi jk (t(x)) isevaluated. Here, t(x) = [ξ(x), η(y), ζ(z)]T is determined byt(x) =

2(x − xi, j,k ) − [1, 1, 1]T ∈ Ωi, j,k ,
∆d

233

(2)

Figure 2: Enlarged view of (i, j, k)th cubic subdomain Ωi, j,k constructedby {xi, j,k , xi+1, j,k , xi+1, j+1,k , xi, j+1,k , xi, j,k+1 ,xi+1, j,k+1 , xi+1, j+1,k+1 , xi, j+1,k+1 }.

Figure 1: An example of a set of ﬁeld values fi, j,k on xi, j,k (1 ≤ i, j, k ≤ N) in a cubic
domain Ω. The red and blue nodes are large
and small ﬁeld values, respectively.

where x = [x, y, z]T , xi, j,k = [xi , y j , zk ]T , and ∆d = |xi+1 − xi | = |y j+1 − y j | = |zk+1 − zk | asshown in Fig. 1. An implicit surface g(x) = 0 can be extracted by ray-marching method [3],marching-cubes method [6], or Bloomenthal’s polygonizer [7].

3.

Numerical Experiments

In this section, numerical experiments are conducted to evaluate the proposed method byemploying Bunny model (n = 34834) [8]. This model is ﬁrst rescaled so that the given
points are lie in a unit cube [0, 1) × [0, 1) × [0, 1).
As results of implicit surfaces of Bunny model obtained by conventional method [4]and proposed one are shown in Figs. 3(a) and 3(b), respectively (N = 400). We see fromthese ﬁgures that Bunny models are reconstructed by both methods. Although these results
are visually almost the same, the accuracy of the conventional method may be better thanthat of the proposed one. This is because the conventional method employs the quadratic
polynomials for interpolating the ﬁeld values fi, j,k . Note that, by employing the 8-points
3D isoparametric elements, the ﬁeld values fi, j,k are interpolated as linear function in the
proposed method. However, to represent the piecewise polynomial, 27 coeﬃcients have tobe retained for each subdomain, in the conventional method. In the proposed method, toevaluate g(x), fi, j,k on xi, j,k (1 ≤ i, j, k ≤ N) are required. Note that retaining xi, j,k (1 ≤i, j, k ≤ N) is not required, since xi, j,k can be calculated as xi, j,k = [(i − 1)∆d, ( j − 1)∆d, (k −1)∆d]T . Hence, in the proposed method, retaining the ﬁeld values fi, j,k (1 ≤ i, j, k ≤ N)
is only required. Since the number of piecewise polynomials in the conventional method
and that of ﬁeld values in the proposed one are the same, N 3 , the memory cost of proposed
method can be decreased to 1/27 in comparison with that of conventional one.
Other results and further details will be presented at the conference.

234

(a)

(b)

Figure 3: Results of implicit surfaces of Bunny model obtained by (a) conventional methodand (b) proposed method, respectively.

References[1] G. Turk, J. F. O’Brien: Modelling with Implicit Surfaces that Interpolate, ACM Transactions on Graphics, 21:4 (2002), 855–873.
[2] Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, H.-P. Seidel: Multi-level partition of unity
implicits, ACM Transactions on Graphics, 22:3 (2003), 463–470.
[3] S. Nakata, S. Aoyama, R. Makino, K. Hasegawa, S. Tanaka: Real-time isosurface
rendering of smooth ﬁelds, Journal of Visualization, 15:2 (2012), 179–187.
[4] T. Itoh, S. Nakata: Fast generation of smooth implicit surface based on piecewise
polynomial, Computer Modeling in Engineering & Sciences, 107:3 (2015), 187–199.
[5] D. V. Hutton: Fundamentals of Finite Element Analysis, McGraw-Hill, Boston (2004).
[6] W. E. Lorensen, H. E. Cline: Marching cubes: A high resolution 3D surface construction algorithm, Computer Graphics , 21:4 (1987), pp. 163–169.
[7] J. Bloomenthal, C. Bajaj, J. Blinn, M.-P. Cani-Gascuel, A. Rockwood, B. Wyvill, G.
Wyvill: Introduction to Implicit Surfaces, Morgan Kaufmann Publishers, Inc., San
Francisco (1997).
[8] The Stanford 3D Scanning Repository, accessed on Jun. 24, 2021. [Online]. Available:
http://www.graphics.stanford.edu/data/3Dscanrep/

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A Study for Recognizing and Simulating Deliberate
Emotional Expressions in Japanese Speech
Chihiro Asada1*, Yuichi Tamura2, Ryo Nagata2, Katsunari Sato1
Major in Human Centered Engineering, Nara Women’s University
2
Department of Intelligence and Informatics, Konan University*
chihiro.asada.mmg@gmail.com

1

Abstract. In this study, a classification method for Japanese utterances with deliberate emotional expressions was investigated. We generated annotation data for deliberate emotional expressions using existing speech data. From the classification results, using a support vector
machine, we found that our method could classify deliberate emotional expressions containedin utterances with a micro-averaged F1 score of 0.47.
Keywords: Affective computing, Speech emotion recognition, Support vector machine

1. Introduction
Although emotions are an essential part of human communication, it is difficult for a listenerto accurately recognize a speaker’s intended emotions. This problem can be reduced if aspeaker realizes that the intentions contained in their emotional expressions are not conveyedbased on the objective emotion recognition results of systems that help human– human interaction. Users of such computer systems can learn deliberate emotional expressions that arecomprehensible by others, and they can acquire a common understanding for communication.
In this study, we investigated a method for classifying deliberate emotional expressions thatare commonly recognized by a certain number of people in a conversation to develop such
systems. We aimed to achieve the following objectives.
1. Creation of annotation data for deliberate emotional expression using existing speech data.
2. Construction of a system to classify deliberate emotional expressions from non-verbal information using a support vector machine (SVM).
3. Analysis of the classification results to reveal the features of speech including deliberateemotional expressions.
Because Japanese people tend to recognize emotions using sounds rather than their content[2], we developed an emotion classification method using utterances. Furthermore, for the classification of emotions, we focus on a part of “emotion regulation” [3], which can change thebehavior of others. IHASZ et al. [4] used an emotion model that resembled emotion regulation
for classification; however, systems that objectively classify emotions to help users communicate with each other have not yet been researched. Therefore, this study examined the expansion of emotion recognition and simulation technologies.

2. Creation of training data
First, we created the annotated “Utsunomiya University Spoken Dialogue Database (UUDB)”[5] with deliberate emotional expressions. A total of 27 Japanese female undergraduate and236

JSST2021
graduate students participated in the annotation exercise. They listened continuously to the
speech of one person in a dialogue between two people and marked the parts where they perceived deliberate emotional expressions. The participants used two types of marks that we defined as “positive” and “negative,” which conveyed the intention to encourage and inhibit aperson’s conduct, respectively. We did not define the length of the mark because the length towhich people perceive deliberate emotional expressions is unclear. We used 1,433 utterancesby two Japanese females and 1,134 utterances by two Japanese males, for a total of 2,567 Japanese utterances from the UUDB. Due to missing annotation data, the actual number of participants who annotated varied for each speech, with a maximum of 26, a minimum of 24, and an
average of 25.
In the second step, we allocated labels to the utterance segments based on the marked resultsof the participants. The label was determined using the following process.

Fig.1. Matching the utterance segments in UUDB with the segments where the participants
perceived the specified deliberate emotional expression
1. We matched the marked results with the utterance segments in UUDB (Fig.1). Subsequently,
we counted the following numbers based on the matching results — 𝑃num : number of positive
marks, 𝐼num : number of negative marks, 𝑆num: number of participants in the annotation, and𝑁num : number of neutral (no deliberate emotional expression) for each utterance were calculated.
2. To determine the label, we calculated “the degree of intention,” which indicates the tendency of the intentions (positive, negative, or neutral) in utterances. Positive and negative degrees of intention in an utterance were respectively defined as
𝑃degree = 𝑃w 𝑃num 𝑎𝑛𝑑 𝐼degree = −𝐼w 𝐼num .
𝑃w and 𝐼w are parameters that can change the weight of the intentions. Because negative utterances receive more attention than positive ones [6], we experimentally set the parameters 𝑃w to
1.0, and 𝐼w to 2.0 to reduce the pattern of the trained model that misclassified the negative intentions. Furthermore, we calculated 𝐿degree, which represents the degree (encouraging or inhibiting trend) of the intention in an utterance. We also calculated 𝑁ratio, which is the percentage of participants who did not perceive deliberate emotional expressions for an utterance. The
calculations for 𝐿degree , and 𝑁ratio are as follows:𝐿degree =(𝑃degree +𝐼degree )𝑆num𝑁, 𝑁ratio = 𝑆 num .
num

3. We assigned labels to the utterances based on 𝐿degree, and 𝑁ratio . “Positive” and “negative”
were assigned for the cases where 𝐿degree ≥ 𝑇 and 𝐿degree ≤ −𝑇, respectively. For other utterances, “neutral” was assigned for the case where 𝑁ratio ≥ 𝑇. The threshold 𝑇 was set to 0.6.
When none of the above conditions were satisfied, “unknown” was assigned so that the system
could recognize “some intention” that was not “neutral,” although the participants’ judgments
differed.
In the third step, we created 386-dimensional feature vectors consisting of 384 dimensions of
acoustic features, which were extracted using the feature set IS09 of open SMILE [7], and two
dimensions of timeline data of the start and end times of utterances from UUDB. The latter two

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were included assuming a relationship between the timeline of the utterance and the strengthof the deliberate emotional expression.

3. Classification method
Considering that people approximately guess deliberate emotions, a linear soft-margin SVM
method was adopted as the classification method. In addition, the binary classification SVM
was extended to multiclass classification using a one versus other method. The ratio of training
data to test data was 7:3. The regularization parameter C was set to 0.00039 using the Bayesian
optimization with 10-fold cross-validation. The trained model was evaluated based on a microaveraged F1 score, confusion matrix, and recall score for each deliberate emotional expression.

4. Results and discussion

Fig.2 Confusion matrix of the test data
Table.1: (i) Number of each label and average of each label’s 𝐿degree. (ii) Average and standard deviation of marks for each label. (iii) Recall score for each deliberate emotional expression.
(iv) Average of 𝐿degree, and decision function score (unknown). (v) Average of 𝐿degree, anddecision function score (neutral).

Table. 1-(i) shows that more utterances were labeled as unknown or neutral than positive or
negative. Table. 1-(ii) shows that approximately 50% of the participants commonly perceived
negative, although there was more variability than the other labeled data. The micro-averaged
F1 score was 0.47, and approximately half of the test data was classified correctly. Table. 1(iii) shows that the recall score of the negative group was 34.48%. Fig. 2 shows the confusion
matrix of the test data. The darker the color of the color bar, the more data there is. This result

238

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suggests that there was no error in misclassifying negative as positive in the confusion matrix.
Based on these results, our system can facilitate communication by estimating the deliberateemotional expressions from utterances.
For the analysis of unknown and neutral labeled data, we used the average of 𝐿degree anddecision function scores of the unknown and neutral data that were misclassified as positive or
negative. The decision function score is a metric of the distance between the predicted data andhyperplane, where the highest score is the predicted value. Table.1-(iv) and (v) show the resultsof the analysis. The data that were misclassified as positive had the following characteristics:
the average of 𝐿degree tended to be positive for the smallest negative decision function score.
The data that were misclassified as negative had the following characteristics: the average
𝐿𝑑𝑒𝑔𝑟𝑒𝑒 was approximately zero for the smallest positive decision function score. These results
imply that some of the data misclassified as positive or negative were judged as positive or
negative, respectively. Therefore, better classification results can be obtained by changing thecriteria for labeling the training data.

5. Conclusion
In this study, a classification method for Japanese utterances with deliberate emotional expressions was investigated. Our method could classify intentions contained in utterances witha micro-averaged F1 score of 0.47. In addition, utterances labeled as negative were commonly
perceived as containing negative intentions by approximately 50% of the participants.

6. Acknowledgements
This work was supported by JSPS KAKENHI Grant Number JP18K11416.

References[1] B. Carlos, et al.: “Analysis of emotion recognition using facial expressions, speech andmultimodal information,” Proceedings of the 6th international conference on Multimodal interfaces, (2004), pp. 205-211.
[2] K. Shinobu, et al.: “Word and voice: Spontaneous attention to emotional utterances in
two languages,” Cognition & Emotion, volume:16.1, (2002), pp. 29-59.
[3] G. James J.: “Emotion regulation,” Handbook of emotions, (2008), pp. 497-513.
[4] P. L. IHASZ, et al.: “Emotion Recognition through Intentional Context-Towards Advancing In-game Affect Awareness,” International Journal of Affective Engineering,volume:18.1, (2019), pp. 17-25.
[5] M. Hiroki, et al.: “Constructing a spoken dialogue corpus for studying paralinguistic
information inexpressive conversation and analyzing its statistical/acoustic characteristics,” Speech Communication, volume:53, (2011), pp. 36-50.
[6] R. F. Baumeister, et al.: “Bad is Stronger than Good,” Review of General Psychology,
volume:5, (2001), pp. 323-370.
[7] F. Eyben, et al.: “openSMILE - The Munich Versatile and Fast Open-Source Audio Feature Extractor,” Proc. ACM Multimedia (MM), Florence: Italy, (2010), pp. 1459-1462.

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Continuous collision avoidance model
between pedestrians
Kotori Tsutsumi1*, Yuichi Tamura2, Katsunari Sato1
Nara Women’s University
2
Konan University*
uak_tsutsumi@cc.nara-wu.ac.jp
1

Abstract. The phenomenon whereby pedestrians who are facing each other continuously avoid
one another in the same direction and cannot move forward is known as “continuous collision
avoidance.” We propose a model for continuous collision avoidance based on the pedestrian
walking velocity. The simulation results demonstrated that the proposed model was effective
and could reproduce the phenomenon of continuous collision avoidance.
Keywords: Simulation of human flow, avoidance model

1. Introduction
While walking, it is likely that a pedestrian will collide with another oncoming pedestrian.
Both parties attempt to avoid the other, but if avoidance occurs in the same direction the firsttime, this will be repeated the next time and thereafter. This phenomenon is known as continuous collision avoidance (Fig. 1).
This study’s purpose is to simulate continuous collision avoidance. By simulating this phenomenon, it can be used in advance for designs such as walkways, corridors, and station gates.
Furthermore, by implementing it in a virtual reality (VR) environment as well as by acquiring
human behavioral data in the VR environment and providing feedback to the simulation parameters, it is possible to represent a more natural gait for the avatar. The social force model(SFM) proposed by Helbeing et al. [1] is a method for reproducing the flow of people. In our
proposed model in this study, a new equation is added and implemented so that continuous
collision avoidance would occur based on the SFM.

2. Algorithm of Continuous-avoidance Simulation
We propose an algorithm for continuous collision avoidance. The current position of thepedestrian (at a certain time 𝑡 − ∆𝑡) and the predicted position of the pedestrian ∆𝑡 later (t)were indicated by the black circle and dotted virtual circle (hereinafter referred to as “ghost”)
in Fig. 2. The SFM was used to determine the predicted position. As Fig. 2 illustrates, the position of the ghost was derived from 𝒗𝑖 (𝑡), which was the sum of the velocity vector (𝒗𝑖 （𝑡 −𝒇𝑖(𝑡)∆𝑡)) of the pedestrian at a certain time (𝑡 − ∆𝑡) and the velocity ( 2𝑚 ∆𝑡), which was calculated

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from the average acceleration vector originating from external forces, which was derived from𝒗𝑖 (𝑡).

Fig. 1: Continuous collision avoidanceFig. 2: Decision of predicted position

The external force was determined by the total force of the repulsive force received fromother pedestrians and the attractive force received from the destination, which was expressedby Eqs. (1) and (2) [2– 4]. In our proposed simulation model, when two pedestrians were about
to collide with one another, the external force was determined by Eq. (3).
𝑑𝒗𝑖
= 𝒇𝑖 (𝑡) + 𝛏𝑖
(1)
𝑑𝑡
𝑠𝑜𝑐
(𝑡) + ∑𝑗≠𝑖 𝒇𝑤𝑎𝑙𝑙
𝒇𝑖 (𝑡) = 𝒇0𝑖 (𝑡) + ∑𝑗≠𝑖 𝒇𝑖𝑗
𝑖𝑊 (𝑡)(2)(Dis > thr ∶ Dis is the distance between ghosts and thr is the decision threshold)𝑠𝑖𝑔𝒇𝑖 (𝑡) = 𝒇𝑖𝑗 (𝑡)(Dis ≤ thr)
(3)
where 𝛏𝑖 was the fluctuation term, 𝒇0𝑖 (𝑡) was the attractive force that pedestrian i experi𝑠𝑜𝑐(𝑡) was theenced from the destination, i.e., the propulsive force to the destination, and 𝒇𝑖𝑗
social repulsive force that caused pedestrian i to maintain a distance from another pedestrian j.
Moreover, 𝒇𝑤𝑎𝑙𝑙
𝑖𝑊 (𝑡) was the repulsive force of pedestrian i attempting to maintain a distance𝑠𝑖𝑔
from the wall, and 𝒇𝑖𝑗 (𝑡) was the force experienced by pedestrian i when a collision with
𝑠𝑜𝑐(𝑡), and 𝒇𝑤𝑎𝑙𝑙
another pedestrian j was about to occur. In this case, 𝒇0𝑖 (𝑡), 𝒇𝑖𝑗𝑖𝑊 (𝑡) were repre𝑠𝑖𝑔
sented by Eqs. (4), (5), and (6), respectively, whereas the added 𝒇𝑖𝑗 (𝑡) was represented by
Eq. (7).
𝒇0𝑖 (𝑡) =𝑣𝑖0 𝒆𝑖 −𝒗𝑖𝑠𝑜𝑐(𝑡) = 𝐴𝑖 exp (𝒇𝑖𝑗

𝜏𝑖𝑟𝑖𝑗 −𝑑𝑖𝑗

) 𝒏𝑖𝑗
𝐵𝑖
𝑑𝑖𝑊
𝑤𝑎𝑙𝑙
𝒇𝑖𝑊 (𝑡) = 𝐶𝑖 exp (−
) 𝒏𝑖𝑊
𝐷𝑖
𝑠𝑖𝑔
𝒇𝑖𝑗 (𝑡) = 𝐸𝑖 𝒎𝑖𝑗

In the above, 𝒗0𝑖

(4)
(5)
(6)
(7)

was the desired walking speed of pedestrian i; 𝒆𝑖 was the unit direction
vector to the destination observed from pedestrian i, 𝒗𝑖 was the current speed of pedestrian i,
𝜏𝑖 was the relaxation time for pedestrian i to recover the original walking path; 𝑟𝑖𝑗 was thesum of the body radii of pedestrians i and j; 𝑑𝑖𝑗 was the distance between the centers of pedestrians i and j; 𝒏𝑖𝑗 was the unit direction vector from pedestrians j to pedestrian i; 𝑑𝑖𝑊 was
the distance between pedestrian i and the wall; 𝒏𝑖𝑊 was the unit vector in the normal direction
from the wall that was received by pedestrian i, 𝒎𝑖𝑗 was the normal vector of 𝒏𝑖𝑗 ; and𝐴𝑖 , 𝐵𝑖 , 𝐶𝑖 , 𝐷𝑖 , and 𝐸𝑖 were model parameters : 𝐴𝑖 = 18.66, 𝐵𝑖 = 0.69, 𝐶𝑖 = 500, 𝐷𝑖 =0.08, 𝐸𝑖 = 0.2. We determined these values from a previous study [3]. The relaxation time 𝜏𝑖= 0.5, and the human body radius was set to 30 cm.
The distance between the ghosts was used for evaluation prior to a collision. When the position of the ghost of pedestrian i and the ghost of the oncoming pedestrian j were closer than
20 cm, the collision process was performed as per Eq. (3). If pedestrians i and j collided for the
first time, they avoided one another in either direction according to the vector perpendicular to241

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the vector connecting their centers. As Fig. 3 illustrates, the direction in which they avoided
one another was set randomly and distinguished by the 𝒎𝑖𝑗 symbol. For the second and subsequent collisions, the avoidance occurred in the direction of the vector opposite to the avoidance of the previous collision or stopped at this point. We referred to this algorithm as the “basic
avoidance algorithm”.
However, in the real world, a pedestrian might avoid a collision by maintaining a distanceand avoiding the other pedestrian before the other party notices. We believe that this would be
the case for people whose ghosts were located farther away; i.e., people who walk faster would
notice the other party at an earlier stage and avoid a collision. Therefore, in this study, we
improved the simulation by adding the condition whereby the collision was avoided at the pedestrian speed to the basic avoidance algorithm. As Fig. 4 illustrates, if the opponent was morethan twice the distance between ghost position and current position, avoidance was performed.
In this case, faster pedestrian movement resulted in earlier noticing of the other party and theability to perform avoidance behavior processing. We referred to this algorithm as the “improved avoidance algorithm”.

Fig. 3: Collision processing

Fig. 4: Algorithm based on walking speed

3. Experiments and results
We evaluated the number of collisions and the continuous collision avoidance that were obtained by simulation using the basic and improved avoidance algorithms. The width of the path
was assumed to be 2 m for the school corridor and 3.5 m for the sidewalk, which was necessary
for traffic. In both cases, the length of the path was set to 15 m. Furthermore, the number ofpeople walking on the path was set to be within the range of 5 to 15 for every two people.
Moreover, males or females were randomly selected. The initial velocity was randomly set
between 0.91 and 1.6 [m/s] for males and between 0.85 and 1.31 [m/s] for females, and thesimulation was repeated 10 times for each condition in Python. Fig. 5 shows an example of thesimulation run. Pedestrians who avoided collisions are indicated in red. Fig. 6 presents theresults of the data acquisition with the improved avoidance algorithm.

Fig. 5: Example of walking state Fig. 6: Results of collision judgement using proposed model
The number of consecutive collision avoidance processes increased as population density

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increased. Moreover, in some cases, the number of collision processes of the improved avoidance algorithm increased by more than 30% compared to the basic avoidance algorithm, but
the number of continuous collision avoidance processes was the same or lower.

4. Discussion
We found that the number of collisions and continuous collision avoidances tended to increase according to the number of people and the width of the road, i.e., the population density.
This result was as we expected, and we believed that the simulation worked correctly.
The improved avoidance algorithm resulted in a higher number of collisions. We consider
this to be because the improved avoidance model avoided collisions based on the position of
the pedestrian ghost and the position of the other party, rather than waiting until the two ghosts
were close to one another. If the position of the ghost was far from that of the pedestrian itself,i.e., if the ghost moved rapidly, the number of collisions would increase because the avoidance
process started in advance. Moreover, if only one of them took avoidance action, the other had
not yet taken avoidance action, so continuous collision avoidance did not develop and the collision could be avoided successfully. For this reason, the number of collisions was higher thanthat of the basic avoidance algorithm, but the number of continuous collision avoidance waslower. We consider that the improved avoidance algorithm could reproduce the walking of areal human compared with the basic avoidance algorithm.

5. Conclusion
We proposed a simulation model for continuous collision avoidance. We included an algorithm in which a person walked more rapidly; as a result, it could notice the oncoming party
earlier and exhibit avoidance behavior. As a result, it was confirmed that the higher the densityof people, the higher the number of collisions and continuous collision avoidance actions between people. Furthermore, the number of collisions of the improved avoidance algorithm increased compared to that of the basic avoidance algorithm, but the number of continuous collision avoidances tended to decrease. We expect that the improved avoidance algorithm reproduces a more appropriate and realistic situation of continuous collision avoidance in terms of
the incidence of one.

References[1] D.Helbing and P.Molnar,“Social Force model for pedestrian dynamics, ” Physical Review
E, vol. 51, no.5, pp.4282-4286, 1995
[2] H. Fujii, "Simulation of Human Flow," incorporated association Japan academic conference of simulation, Vol. 38 No3, pp. 42-46, 2019-09.
[3] Hitomi Iori, Satoru Fujita, and Toshio Hirotsu, "Two-phase simulation of crowds incorporating gait prediction," in Proc. of Multimedia, Distributed Coordination and Mobile Symposium 2017, 263-269, 2017-06-21[4] PDF document "Simulation of Congestion in Souvenir Shops Based on Social Forces
Model."
http://www.msi.co.jp/s4/solution/userscase_pdf/tmu_fukuoka.pdf (Ref: 2021.7.31)

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Creation of hexagonal close-packed photonic-ringwith optical vortex
Kanta Takahashi1, Haruki Kawaguchi1, Kei Umesato1, Yoshihiko Arita2,6,
Keisaku Yamane3, Ryuji Morita3, Ken-ichi Yuyama4, Satoyuki Kawano5,
Katsuhiko Miyamoto1,6, Takashige Omatsu1,6*
Graduate School of Engineering, Chiba University, Japan
School of Physics and Astronomy, University of St Andrews,United Kingdom
3Department of Applied Physics, Hokkaido University, Japan.
4
Department of Chemistry, Osaka City University, Japan.
5
Graduate School of Engineering Science, Osaka University, Japan.
6
Molecular Chirality Research Center, Chiba University, Japan*omatsu@faculty.chiba-u.jp
12

Abstract. We demonstrate, for the first time, the direct print of photonic-microrings formed ofdielectric nanoparticles on a receiver substrate by optical vortex laser induced forward transfer.
Such exotic phenomenon is discussed by numerical analysis of optical force acting on the dielectric nanoparticles under optical vortex.
Keywords: Optical vortex, Laser induced forward transfer, Optical force, Nanopartciles, Printed
nanophotonics

1. Introduction
Photonic-nanostructures enable us to manipulate light fields at the sub-wavelength scale, beyond the diffraction limit, to exploit new fundamental sciences and advanced technologies
through exotic light-matter interactions unattainable in nature [1].
An optical vortex possesses a ring-shaped spatial profile and an orbital angular momentum(OAM) owing to its helical wavefront, and it has currently been leading to new fundamental
physics and applications, such as optical manipulation, optical free-space telecommunications,quantum optics, and super-resolution microscopes. The optical vortex also opens the door towards advanced laser materials processing, including helical nanostructures fabrication [2,3].
In this paper, we here report on the first demonstration, to the best of our knowledge, of thedirect print of a monolayered photonic-microring with a hexagonal close-packed structure,
made of dielectric nanoparticles, on a receiver substrate simply by deposition of a single opticalvortex pulse. Such exotic phenomenon will offer advanced nanofabrication technologies andprovide new physical insights for light-matter interaction.

2. Result
A colloidal suspension of the monodisperse polystyrene nanoparticles (diameter: ca. 250 nm,
density: 1.57 wt%) was used as a donor material, and it was dropped on a glass substrate to244

JSST2021
form a 40 µm thick liquid film. A nanosecond laser (a wavelength of 532 nm, a pulse durationof 10 ns, and pulse energy of ca. 160 µJ) was employed as a laser source. Its output was converted to an optical vortex with ℓ=1 and loosely focused to be an annular spot with a diameterof ca. 50 µm on the film from the backside. A pL-scale single microdroplet was ejected froman irradiated film, and it was printed on a glass receiver substrate located 1 mm away from thedonor film.
Figure 1 (a) shows the images of the printed dot. Intriguingly, a hexagonal close-packed, monolayered (ca. 250 nm thick) and ring-shaped microstructure (diameter: 58-60 µm, width: 2.74.0 µm) (referred to here as a photonic-ring) made of dielectric nanoparticles was formed in
the printed dot, which reflected the ring-shaped spatial form of the irradiated optical vortex.
These results manifest that the nanoparticles are trapped at high density within the irradiatedoptical vortex field and they are then packed to form a photonic-ring in the microdroplet owing
to OAM transfer effects.The trapping potential depth for the nanoparticles under optical vortex
illumination can be also numerically estimated to be (~ -2260 kBT) by the surface integrationof Maxwell’s stress tensor on the nanoparticle, and it supports well the experiments.

Fig. 1 (a)Optical and scanning electron microscope images of a fabricated photonic-microring.
(b) Numerically simulated optical trapping potentials.

3. Conclution
We have demonstrated the direct print of a hexagonal close-packed and monolayered photonicmicroring, formed of nanoparticles, on a receiver substrate without any additional processes
simply by employing the optical vortex induced forward transfer. This exotic nanostructuringin microdroplet can be well supported by the numerical simulation based on the surface integration of Maxwell’s stress tensor on the nanoparticle.

References[1] V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V.
Kildishev: Negative index of refraction in optical metamaterials," Opt. Lett. 30 (2005),
3356-3358[2] K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, and T. Omatsu:
Transfer of Light Helicity to Nanostructures. Phys. Rev. Lett. 110 (14) (2013), 143603[3] R. Nakamura, H. Kawaguchi, M. Iwata, A. Kaneko, R. Nagura, S. Kawano, K. Toyoda,
K. Miyamoto, and T. Omatsu: Optical vortex-induced forward mass transfer: manifestation of helical trajectory of optical vortex. Opt. Express 27 (2019), 38019-38027

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Quantum interference of spontaneous optical vortex
photon emission in a cylindrical waveguide
Satoshi Tanaka1,* , Kazuki Kanki1 , Yuki Goto2 , Shin Kubo2,3 , Tomio Petrosky4,5
1 Department of Physical Science, Osaka Prefecture University, Japan
2 National Institute for Fusion Science, National Institutes of Natural Sciences, Japan
3 College of Engineering, Chubu University, Japan
4 Center for Complex Quantum System, University of Texas at Austin, USA
5 Institute of Industrial Science, The University of Tokyo, Japan∗ stanaka@p.s.osakafu-u.ac.jp

Abstract. We have studied a spontaneous photon emission from a molecular exciton in acylindrical waveguide in terms of the complex spectral analysis. The mode density of theBessel beam in a cylindrical waveguide exhibits the Van Hove singularity at the bottom ofeach continuum. The interaction of the dipole and the radiation ﬁeld is enhanced by the
Van Hove singularity when the exciton energy is close to the band edges, where the ordinary perturbation analysis breaks down. We have obtained the complex eigenstates of thetotal Hamlitonian in the form of the entangled states of the matter and single photon stateswith diﬀerent angular momenta. We have found that a quantum interference causes Fanogap structure in the emission spectrum. This Fano gap can be understood as the ingterfernce between the Markovian and the non-Markovian decays in the single photon emission
processes.
Keywords: Spontaneous photon emission, Van Hove singularity, Angular momentum

Recent advances in photonics technology make it possible to control optical processes
in the light and matter interactions with a single quantum level precision. The mode densityof the radiation ﬁeld in photonic crystals is designed so that the optical absorption, emission,and scattering processes are arbitrarily controlled in spatially conﬁned systems, such a cavity
QED and waveguide QED. In addition, spatial conﬁnement of radiation ﬁelds causes strong
coupling of light and matter to yield an entangled state exhibiting the quantum features, suchas the formation of polariton, vacuum Rabi oscillation and squeezed states[1].
In the present work, we study a spontaneous photon emission of a molecular exciton
dipole in a cylindrical waveguide. The radiation ﬁeld in the waveguide is two-dimensionallyconﬁned in the plane perpendicular to the axis, while it can propagate freely in the axis
direction. As a result, the eigenmodes of the radiation ﬁeld are classiﬁed by the longitudinal

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Figure 1: Spontaneous photon emission of a molecular exciton in a cylindrical waveguide.
(a) The molecular dipole is in the perpendicular plane, and (b) it has an axial component.
The transitions to the TE±1,1 and TM0,1 bands are drawn by the solid and dotted lines, respectively, and the resonant state energies are plotted by the dots. The surviving probabilities(black line) are also shown in the inset, where the Markovian components are depicted by
the red lines.

total angular momentum and the linear momentum along the cylinder axis[2]. The modedensity diverges at the photon band edges due to the one-dimensional Van Hove singularity
resulting in the strong coupling between the exciton and the radiation ﬁeld.
In this work, we consider a spontaneous photon emission of a molecular exciton positioned in a cylindrical waveguide. The eigenmodes of a cylindrical waveguide has been
known as the Bessel modes[2], which are classiﬁed by the total angular momentum, translational momentum along the axis, and the helicity. The eigenmodes exhibits the Van Hove
singularity at each band edges. We have solved the complex eigenvalue problem of the total
Hamiltonian and obtained the dressed exciton and the dressed photon modes which are represented as the quantum entanglement states of the exciton and the multiple single photon
states.
In Fig.1, we show the calculated spontaneous emission spectrum for diﬀerent molecularorientations: In (a) the dipole is oriented in the orthogonal plane to the axis, and in (b) it
is tilted toward the axis. The photon emissions are attributed to the transitions to TE±1,1
mode in (a), while the transition to TM0,1 is mixed in (b). In the latter, we ﬁnd the distinct
dip structure in the spectrum which is due to the quantum interference of the single photon
emission to both modes. We found that the large non-Markovian decay process due to the
Van Hove singularity contributes to the quantum interference as shown in the insets[3, 4].

References[1] R. Loudon, The Quantum Theory of Light (OUP Oxford, Oxford, 2000).
[2] J. D. Jackson, Classical electrodynamics, 3rd ed. ed. (Wiley, New York, {NY}, 1999).
[3] S. Tanaka, S. Garmon, and T. Petrosky, Phys. Rev. B 73, 115340 (2006).
[4] T. Fukuta, S. Garmon, K. Kanki, K.-i. Noba, and S. Tanaka, Phys. Rev. A 96, 52511 (2017).

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Numerical Simulation and Experiments ofIntermittent Camphor Boats
Takatoshi Ichino1*
Department of Computational Systems Biology, Faculty of Biology-Oriented Science and Tech-1

nology, Kindai University*

ichino@waka.kindai.ac.jp

Abstract. The camphor boats moved spontaneously on the water surface. When a camphor disk was connected to the inside of a larger plastic plate, intermittent motion(alternating between rest and rapid motion) was observed. In this presentation, weshow the mathematical model and numerical results of intermittent motion of camphor boat, and experimental results of collective motion of intermittent camphor boats.
Keywords: camphor boat, collective motion, numerical simulation

1. Introduction
The collection of self-propelled particles has rich variety behavior, such as nonequilibrium phase transition, and are observed in a wide range of biological system, such as
human crowed, fish schools, bird flocks, associated motor proteins. The experimental
investigation of collective motion has already reported, e.g., granular system driven
by vibrating plate, multiple robot system. In the theoretical studies, Vicsek et al. hasproposed simple model. The camphor boats moved spontaneously on the water surface
and interact with one another through the concentration of the camphor molecules on
the water. When a camphor disk was connected to the edge of a larger plastic plate,continuous motion was observed. The camphor molecules dissolved from camphor disk diffuse to the edge of the boat and are supplied constantly; thus, the driving force is kept constant.
On the other hands, when a camphor disk was connected to the inside of a larger plastic plate, intermittent motion (alternating between rest and rapid motion) was observed. In the resting state, the molecules dissolved from the camphor disk and diffuse to theedge of the boat. After the molecules reach the edge, the camphor molecules are developed onwater, and as a result, the boat accelerated. The molecules accumulated under the plate are
spread out on water and disappear. Then, the boat rapidly stops due to the viscous resistance.

248

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2. Numerical Section
Heisler et al. reported and reproduced in the numerical simulation based on reaction-diffusion
equations, and we adopted the modified it’s mathematical model. The dimentionless model is
as follows:𝜕 2 𝑥𝑖
𝜕𝑥𝑖
1
1
= −𝜇
+ 𝛤[
−
]
2
𝜕𝑡 2
𝜕𝑡
𝑐(𝑥𝑖 − 𝑙𝑏 )2 + 1
𝑐(𝑥𝑖 + 𝑙𝑓 ) + 1

(1)

𝑁

𝜕𝑐
𝜕2𝑐
=
− 𝑘𝑐 + 𝑎 ∑ 𝐹(𝑥 − 𝑥𝑖 )𝜕𝑡𝜕𝑥 2𝐹(𝑥) = {

(2)

𝑖=1

1

𝑓𝑜𝑟|𝑥| < 𝑟00

𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Here, xi is the dimensionless position of the camphor disk,  is the dimensionless viscosity
constant of the water, c is the dimensionless concetration of camphor, k is a constant combining
the effect of evaporation and dissolution, and aF represents the addition of camphor by camphor
disk, which is centered at the point xi and has half-length r0. lf and lb are the right- and left-side
length of boat from the camphor disk, respectively.

3. Experimental Section
A camphor disk (diameter: 3mm, thickness: 1mm, mass: 5mg) was prepared using apellet die set for Fourier transform infrared spectroscopy (FTIP). A plastic boat wasmade by cutting a polyester film (thickness: 1mm) into a discoid shape (diameter:20mm).

4. Results

Velocity

Figure 1 (a) and (b) showed the time series of the velocity of intermittent motion using numerical simulation and experiments, respectively.

Time

Fig. 1. Time series of the velocity in intermittent motion.(a) numerical simulation. (b) experiment.

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When several camphor boats floated in water circular container (diameter:
160mm), as a result, two types of states were observed with varying the number of theboats. One is an individual motion, the other is stationary state. The results of thecollective motion as follows: the number of boats, N, was changed from 5 to 45. The
collective motion of camphor boats exhibited two different motions depending on N,
which were (i) an individual motion and (ii) stationary state. When N was less than25, the boats moved individually, when N was greater than 25, all boats stopped andbecame stationary.

References[1] E. Heisler, et. al.: Swarming of self-propelled camphor boats, Phys. Rev. E, 85 (2012),
055201(R).
[2] N. J. Suematsu, et al.: Mode –Switching of the Self-Motion of a Camphor Boat Depneding on the Diffusion Distance of Camphor Molecules, J. Phys. Chem. C, 114 (2010),
9876-9882.
[3] S. Soh, et al.: Dynamic Self-Assembly in Ensembles of Camphor Boats, J. Phys. Chem.
B, 112 (2008), 10848-10853.
[4] N. J. Suematsu, et al.: Collective Behavior of Inanimate Boats, Phys. Rev. E, 81 (2010),
056210.
[5] E. Heisler et al.: Collective Motion and Phase Transitions of Symmetric CamphorBoats,
J. Phys. Soc. Jpn., 81 (2012), 074605.

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Particle layer effect of liquid marble
on Belouzov–Zhabotinsky reaction
Yasunao Okamoto1*1, Jun'ya Tanoue1, Daigo Yamamoto1, Akihisa Shioi1*2
Department of Chemical Engineering and Materials Science, Doshisha University, Japan1*1yaokamot@mail.doshisha.ac.jp*2ashioi@mail.doshisha.ac.jp

Abstract. In the Belouzov–Zhabotinsky (BZ) reaction with malonic acid, carbon dioxide gas
is generated, which sometimes causes difficulties during observation of the BZ reaction,
particularly in a small space. Our previous study showed that the bubble accumulation of thegenerated carbon dioxide was suppressed within a liquid marble. Therefore, in this report, therole of the particle layer surrounding a droplet is discussed. We assume that the particle layer
provides the nuclei for gas generation and as well as the paths for the carbon dioxide andoxygen gases, which are the product and inhibitor of the BZ reaction, respectively. Based on
this assumption, a mathematical model of the BZ reaction in a liquid marble using the reaction–diffusion equation is proposed. The result suggests that the period of chemical oscillation
depends on the local density of particles in the particle layer surrounding the liquid marble.
Keywords: Belouzov–Zhabotinsky reaction, Liquid marble, Chemical oscillation, Gas permeation

1. Introduction
The Belouzov–Zhabotinsky (BZ) reaction is a typical chemical oscillation that has
garnered significant research attention; the BZ reaction in a small reactor is one such example.
Liquid marble (LM) can be utilized for the design of small reactors. LM is a liquid droplet
stabilized by a particle layer and has been used in various applications owing to its uniquecharacteristics. One application involves the BZ reaction in LM (BZLM), for which thecommunication of the BZ reaction between multiple LMs [1], the size-dependency of theperiod [2], and the control of a robot [3] have been reported. The results of our previous study
indicated that the oscillation period changed with LM size and that the accumulation of carbon
dioxide (CO2) gas in the droplet was not observed in BZLM [2]. These can be caused by the
diffusion of oxygen (O2) from air and by the presence of a particle layer on the BZLM surface,respectively. However, the effect of the gas permeability through the particle layer on the
BZLM was not discussed. In this study, the role of the particle layer on BZLM was examinedusing a mathematical model with regard to the gas transfer rate. Assuming that the particle
surface in the layer provides the nuclei for the gas generation, i.e., no bubble formation, thenCO2 gas is continuously discharged from the liquid droplet through the layer. A mathematical251

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model based on this assumption was proposed, and the calculated results were compared withthe experimental results.

2. Method
2.1 Experiment
The BZ solution includes 0.20 M NaBrO3, 0.072 M NaBr, 0.40 M malonic acid, 1.00 M
H2SO4, and 2.00 mM ferroin. All chemicals were purchased from Fujifilm Wako Pure Chemical
Corporation. Thirty microliters of the solution were dropped onto hydrophobic silica powder(Aerosil, RY-300) to form BZLM. Three types of BZLMs were produced: one was named fullcoated BZLM, where all droplet surfaces were covered with the powder; the second was
prepared with approximately half the surfaces coated with the powder; and the third was thinly
coated with the powder. The latter was achieved by partially removing the powder using a
blower after the powder was fully coated. Each BZLM was placed in an O2 atmosphere, andthe period of chemical oscillation was measured. The O2 atmosphere was established in a closed
Petri dish via the decomposition of H2O2 catalyzed by FeCl3.
2.2 Model of reaction kinetics
For the calculation, an Oregonator that incorporated O2 as an inhibitor was used [4]. Eqs.
(1)–(5) are the reaction–diffusion equations for the following components: bromous acid (U),ferriin (V), bromide ion (W), CO2, and O2, respectively. Here, the one-dimensional coordinatethat corresponds to the diameter line of the BZLM is applied.
∂[U]/∂t = DU∂2[U]/∂x2 + k1[A]0[W] - k 2[U][W] + k 3[A]0[U] - 2 k 4[U]2…(1)
2
2∂[V]/∂t = DV∂ [V]/∂x + 2 k 3[A]0[U] - k 5[B]0[V]…(2)∂[W]/∂t = DW∂2[W]/∂x2 + k 1[A][W] - k 2[U][W] + k 6[R]2 + 2 k 8[Q]2
…(3)
2
2
2
∂[CO2]/∂t = DCO2∂ [CO2]/∂x + k 6[R]…(4)∂[O2]/∂t = DO2∂2[O2]/dx2 - k 7[R][O2] + k 8[Q]2…(5)
2[R] = (√(k7 [O2 ]) -8k5 k6 [B]0 [V]-k7 [O2 ]) /(4k6 )…(6)[Q] = √k7 [R][O2 ]/(2k8 )…(7)[j] expresses the concentration of chemical component, j. [A]0 and [B]0 represent the initialconcentrations of sodium bromate and malonic acid, respectively. R and Q denote themalonyl/bromomalonyl radical and corresponding peroxyl radicals, respectively. For theseradicals, the diffusion terms are ignored, and the reaction rates are much higher than those of
the other chemical components; then, steady-state approximations are applied. The generation
rate of CO2 was calculated using the reaction term k6[R]2.
As the BZ reaction is inhibited by oxygen, the previous experimental results suggestingthat BZLM can prevent oxygen inlet [2] seem to indicate that oxygen transport into the BZLM
is disturbed by the particle layer. It is reasonable to consider that the layer physically blocks
oxygen transport owing to its thick and condensed packing of the powder. However, because
CO2 generated by the BZ reaction seems to be discharged easily, the particle layer does notblock CO2 transport. This indicates that the role of the particle layer in oxygen transport is nota simple physical wall effect as CO2 transport would also be blocked. CO2 is continuously
generated by the BZ reaction, and thus accumulates inside the particle layer, which increases
the pressure. The generated CO2 did not form bubbles in the droplet, suggesting that CO2 gas
was probably formed at the droplet surface with the help of the particle layer. The accumulation
rate of CO2 on the particles was determined using the mass balance between the generation anddischarge rates. When the latter is lower than the former, a high-pressure zone forms locally252

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due to the accumulated CO2, producing gas flow from the BZLM to the outside. This gas flowintercepts the oxygen inlet from the outside and prevents oxygen from entering the BZLM. As
shown in Fig. 1, these processes may be modeled using the fluxes of CO2 and O2 at the liquidsurface, as shown in Eqs. (8) and (9).
NCO2, xmax = KCO2(pCO2 – pCO2, liq) – v[CO2]xmax…(8)NO2, xmax = KO2(pO2 － pO2, liq) – v[O2]xmax…(9)1/Ki = 1/ ki, gas + 1/ kparticle + 1/ ki, liq…(10)v = αRT [CO2] xmax / (πd2)…(11)
Here, xmax indicates the surface of the bulk liquid (Fig. 1); Ni, xmax and Ki represent the flux at
xmax and the overall mass transfer coefficient, respectively; the first term on the right-hand sidein both Eqs. (8) and (9) indicates the diffusion flux between the liquid and gas phases throughthe particle layer; ki, gas, kparticle, and ki, liq represent the mass transfer coefficients in the gas
boundary, particle layer, and liquid boundary, respectively; subscript i denotes the chemicalcomponents, O2 or CO2; pi expresses the partial pressure of the i-th component in the gas; pi, liq
is the partial pressure that is in equilibrium with the i-th component concentration in the liquid
at the same position (Fig. 1); the second term is the advection term by CO2 convection, as
discussed in the previous paragraph; v, R, and T denote the advection velocity, gas constant,and absolute temperature, respectively; πd2 is the surface area of a droplet in BZLM; and α isa proportionality constant. As mentioned above, we assume that CO2 flows through the particle
layer to the gas phase. This flow is driven by a pressure increase due to CO2 accumulation,
which should appear more remarkably when the particle layer is thicker. Therefore, the flowrate increases with increasing thickness of the particle layer. Following this assumption, it isexpected that a thicker particle layer corresponds to a larger value of α.
gasparticle layer
xmax

pi : partial pressurev (flow)higher pressure zone
pi, liq : pressure in equilibrium with [ i ][ i ] : concentration of iliquidFig. 1 Gas transfer model through the particle layer with advection.

3. Results and Discussions
In the experiment, the solution color fluctuates between red and blue. Fig. 2 shows theblue-colored component estimated using the brightness of each BZLM over time, which was
extracted using image analysis software, Image J. The larger the brightness value, the bluer thesolution. The frequency of color change decreased in the order of full-coated, half-coated, andthin-coated BZLM, finally disappeared in the thin-coated BZLM. Because O2 (inhibitor)
should theoretically elongate the period, the results demonstrate that the O2 transfer rate is thelowest for the full-coated BZLM. Interestingly, the O2 transfer rate of the half-coated (halfexposed) BZLM is considered to be lower than that of the thin-coated one.
Fig. 3 shows the oscillation period results obtained from the experiment and calculation.
The period of the experiment was the average of periods for 2,000 s. As shown in Fig. 3a, theexperimental period increased in the order of full-coated, half-coated, and finally disappearedin the thin-coated BZLM. Meanwhile, as shown in Fig. 3b, the calculated period increased witha decrease in α and finally diverged. Because the full-coated BZLM has a thicker particle layer
than the thin-coated one, the line symmetry-like pattern seen in Figs. 3a and b indicates that253

JSST2021
the present model can reproduce the experimental results qualitatively.
Almost half the area of the half-coated BZLM surface is exposed to air. Based on thepresent model, it is expected that the oscillation of the half-coated BZLM would not be active
compared to that of the thin-coated BZLM. However, the experimental results demonstrate thatthe oscillation of the half-coated BZLM is more active than that of the thin-coated BZLM. A
thick particle layer in the local area of the half-coated BZLM may contribute to the generationof a high pressure zone by CO2 accumulation. Then, the oscillation is locally activated on thesurface of the half-coated BZLM to produce a chemical wave. The wave propagation can beseen as a red–blue oscillation, as the droplet is very small. In the thin-coated BZLM, a highpressure zone is not produced at any location on its surface because the barrier effect is too
weak. This causes a smooth CO2 discharge and the disappearance of the high pressure zone,
resulting in easier penetration of O2 into the BZLM. Thus, the oscillation disappeared. Even
though the LM is a small reactor, the present results suggest that the heterogeny cannot beignored.

Fig. 2 Brightness changes over time in (a) full-coated, (b) half-coated, and (c) thin-coated
BZLMs.

Fig. 3 Oscillation period of BZLM obtained through (a) experiment and (b) model. The period
in the model was calculated from the concentration of V at the center corresponding to BZLM.

4. Conclusion
The present study suggests the interesting role of the particle layer of LM when it is applied
to the BZ reaction. The layer controls the gas transport through two unique characteristics: The
particle surface provides the nuclei of CO2, which enables its discharge without bubble
formation. The particles also provide a barrier for gas transport, causing a pressure difference
and resulting flow. This flow prevents oxygen from entering the droplet. Consequently, the BZ
reaction continued in LM for a long time without the inhibition of oxygen.

References[1]

C. Fullarton et al., J. Phys. Mater., 2, 015005 (2019)[2]

Y. Okamoto et al., J. Soc. Powder Technol. Jpn., 57, 2 (2019), 74-79[3]

M. A. Tsompanas et al., Sens. Actuators B, 295 (2019), 194-203[4]O. Steinbock et al., J. Phys. Chem. A, 104, 27 (2000), 6411-6415

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Numerical calculation for near-wall accumulation ofswimming microorganism
Takuya Ohmura1*, Yukinori Nishigami2, Masatoshi Ichikawa3
1

2

Biozentrum, University of Basel
Research Institute for Electronic Science, Hokkaido University
3
Department of Physics, Kyoto University*takuya.ohmura@mpi-marburg.mpg.de

Abstract. Swimming microorganisms play a crucial role in aquatic ecosystems. Identificationof mechanisms under their behaviors is necessary to understand those ecosystems
quantitatively. One class of swimming microorganisms, ciliates, lives in water environments
and tends to accumulate close to solid-liquid interfaces to obtain sedimented nutrients.
Considering this accumulation as a physical phenomenon like self-assembly of
microswimmers, the dynamics can be approached with a theoretical model. We performed
numerical calculations with a hydrodynamic model for swimming microorganisms, andcompared the numerical results with experiments. As a result, interestingly, the dynamics ofthe accumulation was described only by two physical factors. Our simulations revealed thesimple mechanism governs the microorganism’s complicated behavior to survive efficiently.
Keywords: Fluid dynamics, Swimming microorganism, Numerical calculation, Boundary element
method

1. Introduction
Microorganisms maintain ecosystems where they live. To understand detailed ecosystems, weshould know why and how the microorganisms behave in environments. Ciliates is a class of
single-celled microorganisms and lives in aquatic environments [1,2]. Although ciliates propel
freely in bulk water by beating cilia around their body, they tend to accumulate close to a liquidsolid interface, such as the bottom of a lake or a pond, the surface of waterweed or stones, etc.
[3,4,5]. Nutrient sediments at the interfaces, where ciliates can grow efficiently. While theethological reason for the accumulation has been clear, the physical dynamics was not unclear.
To clarify the dynamics for the accumulation of ciliates, we performed a numerical calculation
with a hydrodynamic model for swimming microorganisms [6,7].

2. Methods
To calculate swimming motion of ciliates close to a wall, the boundary element method (BEM)
was used in 3D. The BEM is appropriate for a moving object at low Reynolds number. An
initial model that we used to describe swimming ciliates was the squirmer model, which is oneof the simplest models for swimming microorganisms [8]. To develop the model more
realistically, we compared the numerical results with experiments of microscope observationof swimming ciliates and updated the model iteratively from the feedback of the difference.

3. Results
We calculated a numerical swimmer approaching a solid wall. To simplify the dynamics, two
simple parameters are changed in this calculation. One parameter is a cell shape, spherical andellipsoidal shape. While the spherical shape has been generally used for numerical research of255

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swimming microorganisms, the ellipsoidal shape approximately corresponds to actual ciliates.
Another parameter is an asymmetricity of swimming thrust force around the swimmer’s body.
When the ciliates swim in bulk water, the swimming thrust force is rotational symmetry.
However, our experiments indicated that the cilia attaching the wall didn’t beat and theswimming trust force became asymmetry.
A spherical swimmer and an ellipsoidal swimmer with the symmetry force repelled away fromthe wall due to hydrodynamic interaction, which means the swimmers cannot accumulate near
the wall. A spherical swimmer with the asymmetry force did not go away from the wall but
stopped on the wall, which means that the swimmer can accumulate but cannot move on thewall. An ellipsoidal swimmer with the asymmetry force slid along the wall, which corresponds
to the experiments. In addition, the sliding speed and the contacting angle of the ellipsoidal
swimmer with asymmetry force also correspond to the experimental results. The key factors
for the ciliates accumulation are the cell shape and the asymmetricity of thrust force.
In conclusion, we identified that the dynamics for the complicated behavior of the
microorganism can be described by the two simple physical parameters.

References[1] T. Weisse, R. Anderson, H. Arndt, A. Calbet, P.J. Hansen, D.J.S. Montagnes: Eur. J.
Protistol. 55 (2016), 50-74.
[2] T. Weisse: Eur. J. Protistol. 61 (2017), 331-358.
[3] H.S. Jennings: J. Comp. Neurol. Psychol. 14 (1904), 441-510.
[4] T. Fenchel: Ecology of Protozoa (1987), Springer, Berlin.
[5] T. Fenchel: Funct. Ecol. 6 (1992), 499-507.
[6] T. Ohmura, Y. Nishigami, A. Taniguchi, S. Nonaka, J. Manabe, T. Ishikawa, M.
Ichikawa: Proc. Natl. Acad. Sci. USA, 115 (2018), 3231-3236.
[7] Y. Nishigami, T. Ohmura, A. Taniguchi, S. Nonaka, J. Manabe, T. Ishikawa, M.
Ichikawa: Commun. Integr. Biol., 11 (2018), e1506666.
[8] T. Ishikawa, M.P. Simmonds, T.J. Pedley: J. Fluid Mech. 568 (2006), 119-160.
[9] M. J. Lighthill: Commun. Pure Appl. Math. 5 (1952) , 109-118.

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Analysis of Foreign Object Detection for Wirelesspower transfer Using Diﬀerential Coils
Yunyi Gong1,* , Yoshitsugu Otomo1 , Hajime Igarashi1
1 Graduate School of information Science and Technology, Hokkaido University∗ gongyunyi@em.ist.hokudai.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.20

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On Equivalent Circuit Representation ofTransformer Considering Eddy Currents
Qiao Liu1, Yoshitsugu Otomo1, Hajime Igarashi1
1Graduate School of Information Science and Technology, Hokkaido University*

liuqiao@em.ist.hokudai.ac.jp

Abstract: In the transformers working at a high frequency, the resistance and leakage inductance depend on frequency because of eddy currents. This paper presents an equivalent circuit
representation of the high frequency transformer considering eddy currents in the windings.
The Cauer equivalent circuit, which can easily be coupled with the external systems, is numerically obtained from the frequency characteristics of the input impedance of the transformer.
What’s more it is shown that the inrush current can be analyzed using the Cauer circuit.
Keywords: Eddy current, Transformer, Cauer circuit, Inrush current

1. Introduction
The operating frequency of power electronics circuits has been increased for reduction of device size. In the transformers working at high frequencies, the effect of eddy currents especially inthe windings become prominent [1]. Although the eddy current can be analyzed by using finite
element method (FEM), it would not be effectively coupled with power circuit and systems becauseof the large computing cost. For the design of power electronics systems, we need accurate and fastmodels of high frequency transformers [2].
In this work, we build the Cauer equivalent circuit from the impedance in frequency domainof a high-frequency transformer using the method based on the adjoint variable method [3]. The
equivalent circuit can easily be coupled with the power circuits in both frequency and time domain.
We analyze the inrush current of the transformer in time domain using the proposed method. It isshown that the results obtained from the proposed method are consistent with the results obtained
from the theoretical method [4] and FEM.

2. Model of transformera) Leakage Inductance
We consider the leakage flux in the transformer shown in Fig.1. Let us assume that the secondary side is short. In this situation, the main flux is canceled out so that the leakage flux is dominant. We also assume that the permeability of the core is infinite, and the magnetic field is negligible. Although the permeability of the steel sheet would be reduced as frequency increases, it is stillmuch larger than the air. Moreover, we assume that the winding is sufficiently long in 𝑦 and 𝑧 directions so that the magnetic and electric fields are represented by 𝑯 = 𝐻(𝑥)𝒛 and 𝑬 = 𝐸(𝑥)𝒚,respectively. By solving the one-dimensional magnetic diffusion equation derived from the Maxwell equations under the quasi-static approximation

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𝑑2𝐻− 𝛾 2𝐻 = 0
𝑑𝑥 2

(1)

Figre.1 Leakage inductance

Where 𝛾 = √𝑗𝜔𝜇0 𝜎, we obtain
𝐻(𝑥) = 𝐻1 𝑒 𝛾𝑥 + 𝐻2 𝑒 −𝛾𝑥(2)Applying the boundary condition into (2), we obtain [4]𝐻(𝑥) = 𝐻0

𝑛𝑠𝑖𝑛ℎ(𝛾𝑥) + (𝑛 − 1)𝑠𝑖𝑛ℎ (𝛾𝑡 − 𝛾𝑥)𝑠𝑖𝑛ℎ (𝛾𝑡)(3)Where 𝑛 and t are the layer number and is layer thickness, and x begins from the inner side ofeach layer. The magnetic field in the air gap and insulation layer, which are constant, can also be
obtained. From the stored magnetic energy in the winding and insulation layers, we find that theinductance is represented by
𝐿𝑙𝑘 =

=

2
∫ 𝜇𝐻𝐻 ∗ 𝑑𝑉
2𝐼 2
𝜇0 𝑙𝑤 𝑛𝑝 2𝑛𝑝 2 (𝑘1 + 2𝑘2 )(𝑝 + 1)
(𝑝 + 1)(𝑘1 − 4𝑘2 )1(++ (2𝑛𝑝 2 + 2𝑝𝑛𝑝 2 + + 1) 𝑡𝑖 )6ℎ𝑤 𝑎 (cosh(2𝑎𝑡) − cos(2𝑎𝑡)) 𝑝𝑎 (cosh(2𝑎𝑡) − cos(2𝑎𝑡))
𝑝

(4)

𝑤𝑢 𝜎

Where 𝑘1 = sinh(2𝑎𝑡) − sin(2𝑎𝑡) 𝑘2 = sin(𝑎𝑡) cosh(𝑎𝑡) − cos(𝑎𝑡) sinh(𝑎𝑡) 𝑎 = √ 20 𝑙𝑤 , ℎ𝑤 , 𝑛𝑝 ,𝑝, 𝑡𝑖 denote the length and height of the windings, the number of turns of the primary winding, theratio of the primary and secondary number of turns and thickness of the insulation layer.

b) AC Resistance
We also can evaluate the AC resistance of the transformer from𝑅𝑎𝑐 𝐼 2 = ∫ 𝜎𝐸𝐸 ∗ 𝑑𝑉

(5)

where we obtain 𝐸(𝑥) from (3). By performing integration in (5), we have𝑅𝑎𝑐 =(𝑝 + 1)(𝑘3 + 4𝑘4 )𝑙𝑤 𝑎𝑛𝑝(2𝑛𝑝 2 (𝑘3 − 2𝑘4 )(𝑝 + 1) +) (6)3𝜎ℎ𝑤 (cosh(2𝑎𝑡) − cos(2𝑎𝑡))𝑝

where 𝑘3 = sinh(2𝑎𝑡) + sin(2𝑎𝑡) , 𝑘4 = sin(𝑎𝑡) cosh(𝑎𝑡) + cos(𝑎𝑡) sinh(𝑎𝑡).

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We obtain the frequency-dependent impedance 𝑍(𝜔) = 𝑅𝑎𝑐 + 𝑗𝜔𝐿 from (4) and (6).

c) Equivalent circuit
We derive the Cauer equivalent circuit shown in Fig.2 which has the impedance consistent
with the above results. By finding the poles and residues of, we would be able to derive the Cauer
circuit. Here, we derive it using the numerical approach [3] in which we compute the resistance andinductance in the Cauer circuit so that its impedance coincides with the impedance computed fromthe above formulas in frequency domain.

Figure.2 Structure of the Cauer circuit

The impedance of the Cauer circuit is given by the continued fraction as𝑍(𝜔) = 𝑅𝑑𝑐 +

1
1
+
𝑗𝜔𝐿1

(7)

1
1
𝑅2 + 1+⋯𝑗𝜔𝐿2

3. Numerical Resulta) Construction of Cauer circuit
The parameters of the transformer are summarized in Table.1 where the permeability of thecore is assumed to be 2200. The circuit parameters of the Cauer circuit we derived from the results
given in the previous section are summarized in Table.2. We also compute 𝑍(𝜔) using FEM in
which the two-dimensional quasi-static Maxwell equations are solved. The resistance and reactanceare plotted against frequency in Fig.3 and 4. It’ concluded all the results are consistent.
Table.1 Transformer parameters

μr
2200

hw
26mm

lw
62.8mm

np/ns
6/6

t/ti
0.2/0.25mm

Table.2 Circuit parameters in Cauer circuit
R(Ω)
L(H)

𝑅𝐷𝐶 , 𝐿1
2.08E-03
1.98E-07

𝑅2 , 𝐿2
1.79E+00
3.43E-07

Figure.3 AC Resistance𝑅3 , 𝐿3
5.51E+01
1.70E-06

𝑅4 , 𝐿4
1.82E+02
4.93E-07

Figure.4 Reactance263

JSST2021b) Analysis of Inrush current
By using the Cauer circuit, we analyze the inrush currents at 0.1 and 1 MHz. For the timedomain analysis of the Cauer circuit, we use the circuit simulator, SPICE. In addition, we carry out
the time-domain analysis of the R-L circuit which has the frequency characteristics derived in section 2 using SPICE. For comparison, we compute the inrush currents by FEM for which we use
JMAG. The results are shown in Figs. 5 and 6, from which it is seen that the results are consistent.
The error in SPICE(Calculation) at 1MHz, computed from the formulas in Section 2, is due to thefact that only the fundamental mode is considered. The results computed by the Cauer circuit in
SPICE(Cauer) agree well with those computed by FEM.

Figure.5 Inrush current at 0.1MHz

Figure.6 Inrush current at 1MHz

4. Conclusions
We have derived the Cauer circuit from the frequency-dependent impedance of the high-frequency transformer considering the eddy currents in the winding. The transformer impedance represented in a closed form is obtained by solving the one-dimensional magnetic diffusion equation.
The circuit parameters in the Cauer circuit are determined so that its impedance is consistent withthat of the transformer model. The frequency characteristics of the impedance computed from the
Cauer circuit agree well with that of the transformer model. We have also analyzed the inrush current of the transformer considering the eddy currents using the Cauer circuit. Although the computed inrush currents by FEM are not consistent with those computed from the calculated impedance. In particular, the inrush currents computed from the Cauer circuit agree well with those computed by FEM.

References
[1]

[2]

[3]
[4]

S. Zhao, Q. Li, F. C. Lee, B. Li, High-Frequency Transformer Design for Modular Power Conversion from
Medium-Voltage AC to 400 VDC, IEEE Transactions on Power Electronics, vol.33, no. 9, pp.7545-7557,
2018.
D. Fu, F. C. Lee, S. Wang, Investigation on transformer design of high frequency high efficiency dc-dc
converters, 2010 Twenty-Fifth Annual IEEE Applied Power Electronics Conference and Exposition (APEC),
pp. 940-947, doi: 10.1109/APEC.2010.5433391, 2010.
Y. Otomo, H. Igarashi, Synthesis of Cauer Equivalent Circuit for Electric Devices from Computed andMeasured Data, IEEE Transactions on Power Electronics, vol.36, no. 4, 10.1109/TPEL.2020.3022167, 2021.
Z. Ouyang, J. Zhang, W. G. Hurley, Calculation of Leakage Inductance for High-Frequency Transformers,
IEEE Transactions on Power Electronics, vol. 30, no.10, pp.5769-5775, 2015.

264

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Numerical Optical Modeling of Nanostructures using
Fractal Dimension
Yoshihisa Fujita1,* , Hiroaki Nakamura2 , Soichiro Ikuno3 , Susumu Nakata1
1 College of Information Science and Engineering, Ritsumeikan University
2 National Institute for Fusion Science, National Institute of Natural Science
3 School of Computer Technology, Tokyo University of Technology∗ yfujita@fc.ritsumei.ac.jp

Abstract. Even a complicated structure can easily represent by the fractal dimension. Hence,
the fractal dimension can be expected to apply to the investigation of the optical propertiesof a nanostructure such as a photocatalyst. In this paper, optical modeling with the fractal
dimension is proposed and is improved using the evanescent ﬁeld.
Keywords: Fractal structure, FDTD method, Evanescent ﬁeld

1.

Introduction

It has been reported that the fuzzy nanostructure is generated by high-temperature helium
irradiation [1]. The geometric characteristics of fuzzy nanostructure suggest a high absorptance. At the moment, large-scale equipment is necessary in order to generate the fuzzy
nanostructure. In addition, it is diﬃcult to handle numerically the fuzzy nanostructure because the geometric scale is smaller than the wavelength. For that reason, the optical property of the fuzzy nanostructure has not become clear. The fractal dimension is a solution inorder to handle numerically the complex geometric structure. In fact, the fractal dimensionof the fuzzy nanostructure is estimated [2]. However, the relationship between the opticalproperties and the fractal dimension is not clear. The optical modeling using fractal dimension contributes largely since fractal patterns appear widely in nature.
An arbitrary fractal surface can be generated by the random fractal theory. The mid-point
algorithm is known as an implementation of the random fractal [3]. The optical properties
can be calculated using the ﬁnite-diﬀerence time-domain (FDTD) method. We already knowthat the fractal dimension is not enough as an element for the optical modeling from aprevious study [4]. This reason is due to the phenomenon that the electric ﬁeld is absorbed
by a part in contact with the metal. Therefore, it is necessary to consider that the evanescentﬁeld is incorporated into the optical modeling.
In this study, we numerically investigate the inﬂuence of the fractal dimension on the
optical properties. Moreover, we discuss the optical modeling using the evanescent ﬁeld.

265

(a) D = 2.1(b) D = 2.9(c) D = 2.1(d) D = 2.9

Figure 1: (a), (b) Normalized height map of fractal structure. (c), (d) Spatial distributionsof electric ﬁeld intensity when the electromagnetic wave is injected into (a) and (b), respectively. Here, D denotes the fractal dimension.

2.

Numerical Method and Results

In this study, we attempt to model the optical properties by following steps:
I. Generate the arbitrary fractal surface using the mid-point algorithm.
II. Evaluate the optical properties by injecting the electromagnetic wave to a fractal surface.
III. Lead to a relationship between fractal dimension and optical properties.
In order to clarify the relationship, the evanescent ﬁeld is estimated by calculating the accessible surface area [5].
The fractal structures generated using the mid-point algorithm are shown in Figs. 1(a)and (b). On the one hand, if the fractal dimensions are small, the surface is relatively smooth.
On the other hand, as the fractal dimension increases, the surface will be jagged. Then,the electromagnetic wave is injected into the above structure. The simulation result of theelectromagnetic wave propagation is shown in Figs. 1(c) and (d). We can see from this ﬁgurethat the electric ﬁeld is more concentrated than in the case of the low fractal dimension.
The detailed results will be shown in JSST2021.

266

References[1] S. Kajita, T. Yoshida, D. Kitaoka, R. Etoh, M. Yajima, N. Ohno, H. Yoshida,
N. Yoshida and Y. Terao: Helium plasma implantation on metals: Nanostructure formation and visible-light photocatalytic response, J. Appl. Phys., 113 (2013), 134301.
[2] S. Kajita, N. Yoshida, N. Ohno and Y. Tsuji: Growth of multifractal tungsten nanostructure by He bubble induced directional swelling, New J. Phys., 17 (2015), 043038.
[3] I. M. Rian and S. Asayama: Computational Design of a nature-inspired architectural
structure using the concepts of self-similar and random fractals, Automat. Constr., 66(2016), 43–58.
[4] Y. Fujita, H. Nakamura, S. Ikuno and S. Nakata: Numerical Analysis of Optical Properties in Metals with Fractal Structures, Proc. ISPlasma, (2021), 08P-29.
[5] L. J. Abbott, K. E. Hart and C. M. Colina: Polymatic: a generalized simulated polymerization algorithm for amorphous polymers, Theor. Chem. Acc., 132:1334 (2013).

267

JSST 2021

Preconditioner for Ill-conditioned Tall and SkinnyMatrices
Atsushi Minamihata1,* , Katsuhisa Ozaki2 , Takeshi Ogita3 , Shin’ichi Oishi4
1 Development of Social Studies, Kansai University of International Studies
2 College of Systems Engineering and Science, Shibaura Institute of Technology
3 Division of Mathematical Sciences, Tokyo Woman’s Christian University
4 Faculty of Science and Engineering, Waseda University∗ a-minamihata@kuins.ac.jp

Abstract. In this talk, we propose a triangular preconditioner for an ill-conditioned rectangular matrix, especially that is called an ill-conditioned tall and skinny matrix. To compute
QR factorization of a tall and skinny matrix quickly, some algorithms are proposed which
are rich in Blas-3 operations. The algorithms use preconditioner as Cholesky factor, sifted
Cholesky factor, or U-factor of LU factorization. A preconditioner based on an R-factor of
QR factorization of AT A is proposed. Numerical results are showing the effectiveness of our
proposed preconditioner for ill-conditioned tall and skinny matrices.
Keywords: preconditioner, ill-conditioned rectangular matrix, QR factorization

1.

Introduction

In this talk, we propose a triangular preconditioner for an ill-conditioned rectangular matrix,
especially that is called an ill-conditioned tall and skinny matrix. Tall and skinny matrix
A ∈ Rm×n satisfies m  n and AT A is a very small matrix compared with m × m matrix. A
triangular preconditioner is used for solving least squares problems and computing QR factorization. QR factorization plays an important role in solving least squares problems. QR
factorization is used for computing approximate solution x̃ of least squares problems andalso for computing rigorous error between x̃ and A+ b in [1, 2]. Householder QR, CGS, and
MGS algorithms are popular, but not effective algorithms for computing QR factorization ofa tall and skinny matrix. Fukaya et al. [3] proposed CholeskyQR2 algorithm on a large-scaleparallel system. CholeskyQR2 algorithm is rich in Blas-3 operations and parallelized easily.
However, CholeskyQR2 algorithm is often break down when a matrix is an ill-conditioned
matrix. To avoid breaks down, Fukaya et al. proposed shiftedCholeskyQR3 algorithm using
sifted Cholesky factorization. Terao et al. [4] proposed LU-Cholesky QR algorithms using
LU factorization on shared and distributed memory computers. CholeskyQR2, shiftedCholeskyQR3, and LU-Cholesky QR use a preconditioner for computing QR factorization as
Cholesky factor, sifted Cholesky factor, and U-factor of LU factorization, respectively. In

268this talk, we propose a preconditioner for A using an R-factor of QR factorization of AT A.
This preconditioner isn’t effective in some ill-conditioned cases. We modify the R-factor
and improve this preconditioner. Numerical results are showing the effectiveness of our
proposed preconditioner for ill-conditioned tall and skinny matrices.

References[1] S.M. Rump. ”Improved componentwise verified error bounds for least squares problems and underdetermined linear systems.” Numerical algorithms 66.2 (2014): 309322.
[2] S. Miyajima. ”Componentwise enclosure for solutions of least squares problems andunderdetermined systems.” Linear Algebra and its Applications 444 (2014): 28-41.
[3] T. Fukaya, Y. Nakatsukasa, Y. Yanagisawa, and Y. Yamamoto. ”CholeskyQR2: a simple and communication-avoiding algorithm for computing a tall-skinny QR factorization on a large-scale parallel system.” 2014 5th workshop on latest advances in scalable
algorithms for large-scale systems. IEEE, 2014.
[4] T. Terao, K. Ozaki, and T. Ogita. ”LU-Cholesky QR algorithms for thin QR decomposition.” Parallel Computing 92 (2020): 102571.
[5] T. Fukaya, R. Kannan, Y.Nakatsukasa, Y. Yamamoto and Y.Yanagisawa. ”Shifted
Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices.” SIAM
Journal on Scientific Computing 42.1 (2020): A477-A503.

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Verified Numerical Computations for a Standard
Eigenvalue Problem Without Directed Rounding
Takeshi Terao1,* , Katsuhisa Ozaki2 , Takeshi Ogita3 , Toshiyuki Imamura1
1 RIKEN Center for Computational Science
2 Shibaura Institute of Technology
3 Tokyo Woman’s Christian University∗ takeshi.terao@riken.jp

Abstract. In this paper, we consider verified numerical computations without directed rounding for an eigenvalue problem. Directed rounding for floating-point arithmetic depends on
computer environments and sometimes causes difficulty in implementing verification methods. If verification methods are designed without directed rounding, they can be implemented on various computers (e.g., CPU, GPU, and supercomputers). We propose a simple
and efficient verification method without directed rounding for a standard eigenvalue problem.
Keywords: Eigenvalue problem, Verified numerical computation, Portable algorithms

1.

Introduction

A standard eigenvalue problem for a symmetric matrix A ∈ Rn×n is Ax(i) = λi x(i) , where an
eigenvalue λi ∈ R and an eigenvector x(i) ∈ Rn . In this paper, we consider
AX = XΛ,
where a diagonal matrix Λ = diag(λ1 , . . . , λn ) ∈ Rn×n and an orthogonal matrix X =[x(1) , . . . , x(n) ] ∈ Rn×n . Numerical computations produce D̂ ≈ ∆ and X̂ ≈ X such thatAX̂ ≈ X̂ D̂,X̂ T X̂ ≈ I,

where I is the identity matrix.
The verified numerical computation for an eigenvalue problem gives an error boundfor λ̂i using only floating-point arithmetic. The verification methods are proposed in [1,2, 3, 4, 5, 6]. These employ interval matrix multiplication using directed rounding [7].
However, verification methods without directed rounding for a solution of a linear systemhave been investigated [8, 9]. Although rounding error analysis is lengthy and complicated,
this technique can be applied to verification methods for eigenvalue problems. This study
reduces the implementation cost and avoids complicated rounding error analysis and it isimproved from [10].

270

2.

The proposed method

Let A = AT ∈ Fn×n , where F is the set of floating-point numbers defined in the IEEE
standard 754, and assume that all approximate eigenpairs D̂ and X̂ ∈ Fn×n are obtained for
A. fl(·) is a computed result by floating-point arithmetic with rounding to nearest. Define
α1 ≥ kAX̂ − X̂ D̂k1 ,α2 ≥ kAX̂ − X̂ D̂k∞ ,β ≥ kX̂ T X̂ − Ik∞ ,where α1 , α2 , and β ∈ F. If β < 1, thenr
|λi − d̂i | ≤ fl

α1 · α2/(1 − 4u)
1−β

!
(1)

is satisfied for 1 ≤ i ≤ n [10], where u is the unit roundoff (e.g., u = 2−53 for binary64). For
the computation of the upper bounds α1 , α2 , and β, we use only floating-point arithmetic
with rounding to nearest based on the following theorem.
Theorem 1. Let non-negative vectors v, w ∈ Fn and a non-negative normalized floatingpoint number p ∈ F, andpρ(p,k) =, ku < 1.
1 − kuIf (n + 2)u < 1, then, all of the following

 



 

fl ρ(p,n+2) vT w , fl ρ(p,n+2) vT w , fl vT ρ(p,n+2) w
are upper bounds of pvT w.
dot(p, v, w) indicates a computed result of pvT w using floating-point arithmetic. ThenpvT w ≤ dot(ρ(p,n+2) , v, w) is satisfied from Theorem 1. Moreover, it is independent of acomputational order. Therefore, routines in Basic Linear Algebra Subprograms (BLAS)
for various computational environments can be applied to matrix-vector multiplication in
the verification methods. Using only Theorem 1 repeatedly, we can obtain α1 , α2 , and β.
Thus, the error bound from Eq. (1) can be computed. The numerical examples (shown in
the presentation) illustrate the efficiency of the proposed method.

Acknowledgments
This work has been supported by the COE research grant in computational science from
Hyogo Prefecture and Kobe City through Foundation for Computational Science.

References[1] Takeo Hoshi, Takeshi Ogita, Katsuhisa Ozaki, and Takeshi Terao. An a posterioriverification method for generalized real-symmetric eigenvalue problems in large-scale
electronic state calculations. Journal of Computational and Applied Mathematics, page112830, 2020.

271

[2] Shinya Miyajima. Numerical enclosure for each eigenvalue in generalized eigenvalue
problem. Journal of Computational and Applied Mathematics, 236(9):2545–2552,
2012.
[3] Shinya Miyajima. Fast enclosure for all eigenvalues and invariant subspaces in generalized eigenvalue problems. SIAM Journal on Matrix Analysis and Applications,35(3):1205–1225, 2014.
[4] Siegfried M Rump. Computational error bounds for multiple or nearly multiple eigenvalues. Linear Algebra and its Applications, 324(1-3):209–226, 2001.
[5] Shin’ichi Oishi. Fast enclosure of matrix eigenvalues and singular values via rounding
mode controlled computation. Linear algebra and its Applications, 324(1-3):133–146,
2001.
[6] Tetsuro Yamamoto. Error bounds for computed eigenvalues and eigenvectors. Numerische Mathematik, 34(2):189–199, 1980.
[7] Siegfried M Rump, Takeshi Ogita, Yusuke Morikura, and Shin’ichi Oishi. Intervalarithmetic with fixed rounding mode. Nonlinear Theory and Its Applications, IEICE,
7(3):362–373, 2016.
[8] Takeshi Ogita, Siegfried M Rump, and S Oishi. Verified solution of linear systems
without directed rounding. Advanced Research Institute for Science and Engineering,
Waseda University, 2005.
[9] Yusuke Morikura, Katsuhisa Ozaki, and Shin’ichi Oishi. Verification methods forlinear systems using ufp estimation with rounding-to-nearest. Nonlinear Theory and
Its Applications, IEICE, 4(1):12–22, 2013.
[10] Takeshi Terao, Katsuhisa Ozaki, Takeshi Ogita, and Toshiyuki Imamura. Verification
methods for a standard eigenvalue problem for a real symmetric matrix with roundingto-nearest. IPSJ SIG Technical Report (HPC), 2020(16):1–8, 2020 (in Japanese).

272

JSST 2021

Acceleration of Iterative Reﬁnement
for Symmetric Eigenvalue Decomposition
Yuki Uchino1,* , Katsuhisa Ozaki2 , Takeshi Ogita3
1 Graduate School of Engineering and Science, Shibaura Institute of Technology, Japan
2 Department of Mathematical Sciences, Shibaura Institute of Technology, Japan
3 Division of Mathematical Sciences, Tokyo Woman’s Christian University, Japan∗ mf20013@shibaura-it.ac.jp

Abstract. This study considers a reﬁnement algorithm for the eigenvalue decompositionof a real symmetric matrix. Various numerical algorithms have been developed for standard
eigenvalue problems. Recently, Ogita and Aishima proposed eﬃcient reﬁnement algorithms
for improving approximate eigenpairs obtained using a numerical algorithm. In this study,
we aim to reduce computational cost of those reﬁnement algorithms. Numerical experiments
illustrate the eﬃciency of the proposed algorithm.
Keywords: Iterative reﬁnement, Accurate numerical algorithms, Symmetric eigenvalue decomposition

1.

Introduction

Let A ∈ Rn×n be a real symmetric matrix, λi ∈ R the eigenvalues of A, and x(i) ∈ Rn thenormalized eigenvectors of A associated with λi . Assume that λ1 ≤ λ2 ≤ · · · ≤ λn . This
study investigates the eigenvalue decomposition of A:
A = XDX T ,where
D = diag(λ1 , λ2 , . . . , λn ) ∈ Rn×n ,(1)

X = (x(1) x(2) · · · x(n) ) ∈ R

(2)

n×n

.

Various numerical algorithms have been developed for calculating (1) and (2). The accuracyof approximate eigenvectors obtained using a numerical algorithm decreases with the gap
between the associated eigenvalue and its closest one. Therefore, using iterative reﬁnement
methods is useful for obtaining the eigenvalue decomposition with high accuracy.
Ogita and Aishima proposed reﬁnement algorithms for the eigenvalue decomposition of
A. Those algorithms converge quadratically, provided that an error matrix E ∈ Rn×n such273

that X = X̂(I + E), where I is the n × n identity matrix, for an initial guess X̂ of X satisﬁes
the following condition [1, Theorem 1, 2]:




 min |λi − λ j |



1≤i<
j≤n
1





,
∥E∥
<
min
(if all eigenvalues are simple),2 10n∥A∥2


100








|λi − λ j | λ ,λ min




1
1
i
j , 1≤i, j≤n






,
∥E∥ < min  (otherwise).



 2 3
10n∥A∥2100 
The reﬁnement algorithms are constructed via four high-accuracy matrix multiplications
X̂ T X̂, X̂ T AX̂, and X̂ Ẽ. Thus, they may yield high-accuracy results faster than those obtained using multiple-precision arithmetic (See the numerical results in [1, 2]). Ozaki et al.
proposed an algorithm for high-accuracy matrix multiplication using error-free transformation [3].
In this study, we design algorithms to obtain almost the same quality of results as reﬁnement algorithms proposed by Ogita and Aishima via three high-accuracy matrix multiplications AX̂, X̂ T (AX̂ − X̂diag(λ̃)), and X̂E, where λ̃i is an approximation of λi . We improveaccuracy of approximate eigenpairs provided by MATLAB [4] command eig with doubleprecision arithmetic using these reﬁnement algorithms with high-accuracy matrix multiplications proposed by Ozaki et al. We compare the performance of the proposed algorithms
with that of MATLAB command eig by Advanpix Multiprecision Computing Toolbox version 4.8.4.14478 [5]. For n = 5000, we obtained high-accuracy results 1.8 times faster thanthat obtained using the original algorithms proposed by Ogita and Aishima and 11 times
faster than those obtained using multi-precision arithmetic when the arithmetic precision
was set to 34 decimal digits in the ﬁrst iteration and 48 decimal digits in the second iteration.

References[1] T. Ogita, K. Aishima: Iterative reﬁnement for symmetric eigenvalue decomposition,
Jpn. J. Ind. Appl. Math., 35:3 (2018), 1007–1035.
[2] T. Ogita, K. Aishima: Iterative reﬁnement for symmetric eigenvalue decomposition II:
clustered eigenvalues, Jpn. J. Ind. Appl. Math., 36:2 (2019), 435–459.
[3] K. Ozaki, T. Ogita, S. Oishi, S.M. Rump: Error-free transformation of matrix multiplication by using fast routines of matrix multiplication and its applications, Numer.
Algorithms, 59:1 (2012), 95–118.
[4] MathWorks, https://jp.mathworks.com/.
[5] Advanpix: Multiprecision computing toolbox for MATLAB,
advanpix.com/.

274

https://www.

JSST2021

The mechanical genome
Helmut Schiessel

Cluster of Excellence Physics of Life, Technical University Dresden, Dresden, Germany
helmut.schiessel@tu-dresden.de

Abstract. In addition to the classical layer of genetic information, DNA molecules also carryother layers of information. Two possible layers are discussed. One is a mechanical layer,
namely that the base pair sequence influences the mechanical and geometrical properties of
the DNA molecules which in turn might guide their packing inside the cell. A second possible layer is the speed of translation in the protein-producing ribosomes where the speed influences the quality of the protein product. We demonstrate that the degeneracy of the genetic
code allows for multiplexing of all three layers of information.
Keywords: Monte Carlo simulation, DNA mechanics, genetic information, synonymous mutations, weighted graphs

1. Introduction
As early as 1989 it was suggested by Edward N. Trifonov that DNA could carry several
codes in addition to the classical code (the genes which encode for proteins) [1]. One of thesuggested layers, a chromatin code, was studied in detail later by Jonathan Widom who
claimed that base pair sequences carry a “nucleosome positioning code” [2]. Nucleosomes,
DNA-wrapped protein spools, are the first layer of the chromatin complex, the DNA-protein
complex that fills the nuclei of our cells. Other scientific communities have focused on otherpossible layer of information, often ignoring each other. This leads to the question whether
DNA molecules could carry several independent layers of information, multiplexed with eachother. To address this set of questions we build models of nucleosomes that account for thesequence-dependent DNA elasticity and study them using simulations (introducing the mutation Monte Carlo method) and analytical approaches (transfer matrix method and mapping ofbase pair sequences on weighted graphs).

2. Nucleosome sequence preferences
Nucleosomes show clear DNA sequence preferences [2]. We wanted to know the physicalorigin of these sequence preferences. We built a coarse-grained nucleosome model based on
the nucleosome crystal structure and found via Monte Carlo simulations that our model reproduces the experimentally known sequence preferences [3]. Since our model only accounts
for the sequence dependent elasticity and geometry of the DNA double helix, we conclude
that nucleosomes prefer certain positions on the DNA more than others because it requires
less DNA bending costs. Using an analytically exactly solvable model we can understandthese preferences in detail and can show that nucleosomes prefer DNA that it is intrinsicallycurved in the right direction [4].

275JSST2021

3. Multiplexing of genetic and mechanical signals
The question arises whether DNA sequences have evolved to put mechanical signals on DNA
to e.g. position stable nucleosomes at certain places and whether this is even possible on topof genes. We developed methods to demonstrate this by systematically exploring all sequences that encode for the same protein, making use of the degeneracy of the genetic code.
Using graph theory we were able to show that, at least within our nucleosome model, we canmodify sequences such to position nucleosomes anywhere on the genome of yeast with single
base pair precision, without modifying the encoded proteins [5].

4. Is there space for even more layers?
Since it was straightforward to modify the DNA shape or elasticity on top of genes, wechecked whether there is space for a third layer: the translation speed in ribosomes. It has
been claimed that the speed profile affects the co-translational folding of proteins [6]. We
demonstrate using graph theory that this is indeed possible, namely to independently put mechanical signals on genes and control the translational speed at the same time [7].

5. Mechanical cues on real genomes
We studied the genomes of various organisms and found mechanical signals, e.g. around thetranscription start sites [8, 9]. Remarkably, unicellular organisms show a signal opposite tothat of multicellular life forms and the way these signals are created varies from organism toorganism. Why there is such a rich zoo of “mechanical genomes” remains an open question.

References[1] E. N. Trifonov: Bulletin of Mathematical Biology, 51:4 (1989), 417-432.
[2] E. Segal, Y. Fondufe-Mittendorf, L. Chen, A. Thåström, Y. Field, I. K. Moore, J.-P. Z.
Wang, J. Widom: Nature, 442 (2006), 772-778.
[3] B. Eslami-Mossallam, R. D. Schram, M. Tompitak, J. van Noort, H. Schiessel: PloS
ONE, 11(6) (2016), e0156905.
[4] M. Zuiddam, R. Everaers, H. Schiessel: Phys. Rev. E, 96 (2017), 052412[5] M. Zuiddam, H. Schiessel: Phys. Rev. E, 99 (2019), 012422.
[6] K. C. Stein, J. Frydman: J. Biol. Chem., 294(2) (2019), 2076-2084.
[7] M. Zuiddam, B. Shakiba, H. Schiessel, in preparation[8] M. Tompitak, C. Vaillant, H. Schiessel: Biophys. J., 112 (2017), 505-511.
[9] J. Neipel, G. Brandani, H. Schiessel: Phys. Rev. E, 101 (2020), 022405.

276

Cooperation of Real-World Modeling with Simulation
toward the Problem “What is Life?”
Kenichi Yoshikawa1,2
Faulty of Life and Medical Science, Doshisha University
2
Institute for Advanced Study, Kyoto University

1*

keyoshik@mail.doshisha.ac.jp

Abstract. All living organisms have complicated but self-organized intracellular structures withvarious specific functions to maintain their lives. To gain insight into the underlying mechanismof the self-organization of cells, we have been performing cooperative studies of real-worldmodeling through the cooperation with numerical modeling. We may report; 1) Spontaneous
generation of cell-like structure and function under crowding condition with macromolecules. 2)
Self-organization of cellular assembly. 3) Occurrence of macroscopic regular motion for theassembly of nano-scaled self-propelling objects.
Keywords: Experimental modeling, Proto cell, Spatio-temporal self-organization

1. Introduction
Living cells on the earth maintain their active lives under highly crowding conditions; theconcentrations of macromolecules, such as RNA, proteins and DNA, are 0.3-0.5g/mL. It is wellknown in polymer physics that a mixed solution of different polymers tends to undergo phaseseparation because of the minimum contribution of mixing entropy, in contrast to the solution
containing
differentlowmolecular-weightchemicals.
Generally speaking, in crowding
polymersolutions,thecontribution of conformational
entropy coupled with selfavoiding volume effect, or
depletioneffect,becomessignificant instead of mixing
entropy.
Here,
we
will
demonstratethereal-world
experimental models, 4revealing
the significant role of suchcrowding effect on the selfemergence of cell-like structure
Fig.1
Specific localization of DNA and actin in
and also on the appearance ofwater/water droplets generated through simple mechanicalcharacteristic
biologicalmixing of binary polymer solution with polyethylene glycol(PEG) and dextran (DEX) containing γ-DNA (49kbp) andfunctions.
F-actin (polymerized actin). [1]2772. Real-world modeling of self-emerging cell-like structure
Fig.1 exemplifies the formation of cell-sized water droplets entrapping DNA and actin (skeletal
protein) under the aqueous environmental aqueous solution, where the solutions inside andoutside droplets are rich in dextran and polyethylene glycol (PEG), respectively. It is noted thatsuch droplets are generated spontaneously through simple mixing of DNA and actin in an aqueous
solution with dextran and PEG. Herein, it is noted that microdroplets caused by simple depletion
effects served a simple real-world model of a cellular system. These systems are generated undermarkedly different physicochemical interactions from that of coacervates, that is, aggregation
products through attractive interactions among macromolecules.

3. Numerical modeling on the confinement effect
The snapshots in Figs. 2(a) and 2(b) illustrate that the switching of the localization of a large sphere,
depending on its rigidity, hard and soft, respectively. The numerical results indicate that the soft large spheretends to situate in inner cavity but the rigid large sphere localizes on the periphery. By adapting such kindof numerical model, the following issues were found: the preferential location of the larger particle shifts
from the region near the cavity wall to the inner cavityby (1) decreasing the size of the smaller particles at ahigh enough particle density and (2) increasing thedensity of smaller particles of a given crowder size. It
may be interesting to note that, in living cells,organellar including nuclei and mitochondria exhibits
the positioning apart from the prefer of the
Fig.2
Switching on the spatial
surrounding membrane. Such kind of general trends
positioning of a large sphere dependingin cells is attributable to the depletion effect as
on its rigidity; hard and soft for left anddescribed in the present paper.
right pictures. [3]4. Important role of nonspecific effect in life
Besides the above-mentioned examples, we may show the importance of the depletion effect or crowding
effect on the structure and functions in living systems, including the self-organized assembly of multicellular system as the model of organoids and self-motility of organisms driven by the assembly offluctuating molecular motors.

References[1] N. Nakatani, H. Sakuta, M. Hayashi, S. Tanaka, K. Takiguchi, K. Tsumoto, K. Yoshikawa,
ChemBioChem, 19, 1370-1374 (2018). [2] H. Sakuta, F. Fujita, T. Hamada, M. Hayashi, K. Takiguchi, K.
Tsumoto, K. Yoshikawa, ChemBioChem, 21, 3323-3328 (2020). [3] C.-Y. Shew, S. Oda, K. Yoshikawa, J.
Chem. Phys., 147, 204901/1-12(2017).

278

JSST2021

Water on the DNA surface: microscopic insightfrom molecular dynamics simulations
Yoshiteru Yonetani1*,1

National Institutes for Quantum and Radiological Science and Technology (QST),*

yonetani.yoshiteru@qst.go.jp

Abstract. Water on the DNA surface exhibits characteristic behavior such as ice-like water
network along the narrow groove of DNA. By using molecular dynamics simulations, we obtained detailed picture for such water; our characterization fully describes the water network
patterns and their sequence variation [Biophys. J. 97, 1138 (2009)]. Analysis on such water
network further revealed microscopic origin of the slow water-exchange kinetics [Biophys.
Chem. 160, 54 (2012)]. As another relevant topic, I will also mention a relation with DNA
damage production. Our recent study [Chem. Phys. Lett. 749, 137441 (2020)] found thatsite-dependent water accessibility for DNA backbone is well correlated with the probabilities
of DNA damage production by OH radical attacking. This suggests that the site-dependent
hydration property is a key factor for DNA damage production.
Keywords: DNA, Hydration water, Hydroxyl radical, Radiation damage, Molecular dynamics

1. Structure and dynamics of DNA hydration water
Water plays an essential role in DNA structure formation and the related biological functions.
So far, molecular structures of DNA and the hydration water have been derived from experimental measurements using X-ray and neutron crystallography [1]. However, it is still difficult to obtain more details on the dynamical and sequence-dependent behaviors from the experimental approaches.
Computer simulation can provide such microscopic pictures. In 2007, we started our molecular dynamics (MD) studies on the DNA and hydration water. At first, we calculated spatial distribution of DNA hydration water. The MD result was compared with the experimental
data of X-ray crystallography and theoretical RISM calculations [2] to confirm the correspondences between the different methods. After that, we investigated sequence effect using
the two typical cases AATT and TTAA [3] and using 136 different sequences [4]. From thissystematic comparison, we found that an explicit correlation exists between the DNA structural fluctuation and the hydration patterns in the minor groove.
Water kinetics is also an interesting aspect of DNA hydration. It has been known that water molecules in the narrow minor groove of DNA exhibit long residence times over ~300 ps,
depending on the sequence. How does such slow kinetics appear? We found that access of an279

JSST2021
additional water molecule is a key step [5]. Such water access triggers the water departurefrom the DNA surface. Thus, if such an additional water does not access, the residing water
does not leave, leading to long residency. In this way, we could explain how water residence
times change with the surface environment. We expect that neutron scattering measurements
can provide experimental evidence for such dynamical behaviors; experimental studies on
DNA and hydration water are carried out with J-PARC facilities in Ibaraki, Japan [6, 7].

2. Water and DNA radiation damage
Water has a significant contribution to radiation-induced DNA damage. Water in a biologicalcell is highly excited by radiation of X-ray, γ-ray or heavy ion. Such water excitation produces several reactive species; hydroxyl (OH) radical is one of the major products. This attacking
to the DNA triggers abstraction of DNA hydrogen, leading to a critical damage of the DNA
molecular structure.
To gain the microscopic relationship between theradical attacking and the damage production, we
calculated OH radical distribution around DNA [8].
The MD result showed that the OH radical frequently visits the backbone of DNA (Fig. 1). Yet, current
statistics of radical distribution is not enough; Instead, water distribution was employed to assess
site-dependent accessibility. We found that the result
is well correlated with the experimental
site-dependent probabilities [9] as to DNA damage
production. This suggests that the site-dependent
solvent accessibility is key for the DNA damage
production.
Fig. 1: OH radical distribution.
Yellow denotes the region in which
OH radicals visit frequently.

References[1] Oxford Handbook of Nucleic Acid Structure, edited by S. Neidle (Oxford University
Press, New York, 1999).
[2] Y. Yonetani, Y. Maruyama, F. Hirata, H. Kono: Comparison of DNA hydration patterns
obtained using two distinct computational methods, molecular dynamics simulationand three-dimensional reference interaction site model theory, J. Chem. Phys., 128(2008), 185102.
[3] Y. Yonetani, H. Kono, S. Fujii, A. Sarai, N. Go: DNA deformability and hydration
studied by molecular dynamics simulation, Mol. Simul., 33 (2007), 103 - 107.
[4] Y. Yonetani, H. Kono: Sequence dependencies of DNA deformability and hydration in
the minor groove, Biophys. J., 97 (2009), 1138 - 1147.

280

JSST2021[5] Y. Yonetani, H. Kono: What determines water-bridge lifetimes at the surface of DNA?
Insight from systematic molecular dynamics analysis of water kinetics for various
DNA sequences, Biophys. Chem., 160 (2012), 54 -61.
[6] H. Nakagawa, Y. Yonetani, K. Nakajima, S. Ohira-Kawamura, T. Kikuchi, Y. Inamura,
M. Kataoka, H. Kono: Local dynamics coupled to hydration water determines
DNA-sequence-dependent deformability, Phys. Rev. E, 90 (2014), 022723.
[7] H. Nakagawa, Y. Yonetani, K. Nakajima, S. Ohira-Kawamura, T. Kikuchi, Y. Inamura,
M. Kataoka, H. Kono: Sequence-dependent hydration water dynamics of dodecamericDNA, JPS Conf. Proc., 33 (2021), 011101.
[8] Y. Yonetani, H. Nakagawa: Understanding water-mediated DNA damage production bymolecular dynamics calculation of solvent accessibility, Chem. Phys. Lett., 749 (2020),
137441.
[9] B. Balasubramanian, W. K. Pogozelski, T. D. Tullius, Proc. Natl. Acad. Sci USA 95(1998), 9738 - 9743.

281

JSST 2021

Development of an optimal routing system fortraveling among farm ﬁelds
Takuma Nemoto1,* , Naoki Niitsuma2 , Norihiro Kamamichi1,2
1 Department of Robotics and Mechatronics, School of Science and Technology for Future

Life, Tokyo Denki University
2 Robotics and Mechatronics, Graduate School of Science and Technology for Future Life,

Tokyo Denki University∗ nemoto@ctrl.fr.dendai.ac.jp

Abstract. This paper presents an optimal routing system for smart agriculture, which isdeveloped to enable inexperienced workers to travel among farm ﬁelds via the shortest route.
The system provides the shortest route, solving the traveling salesman problem (TSP) with
distance data between farm ﬁelds included in their road network, and shows the route on amap. The developed system can reduce the traveling distance by 6.89 % in a traveling routefor 72 farm ﬁelds and has been utilized on trial in an agricultural management entity.
Keywords: Smart agriculture, Optimal routing, Traveling salesman problem (TSP)

1.

Introduction

The agricultural population in Japan has been decreasing, and this fact demands to improve
the productivity to maintain the domestic agricultural supply. This demand encourages us
to save cost and labor through automation and standardization in agricultural work.
One of the causes decreasing the productivity is the time for traveling among farm ﬁelds.
The time tends to increase, caused by distributed ﬁelds in large-scale agricultural management entities. In such entities, inexperienced workers have diﬃculty to eﬃciently travel
among distributed ﬁelds because workers decide traveling routes empirically. The decidingof routes is repeatedly performed since visited ﬁelds are changed depending on tasks andsituations.
In this paper, we introduce an optimal routing system developed that enables inexperienced workers to travel among farm ﬁelds via the shortest route. This system shows theshortest route, solving the traveling salesman problem (TSP) with the road network among
farm ﬁelds [1], and has some output functionalities.

282

2.

Optimal routing system for traveling among farm ﬁelds

The structure of the optimal routing system developed is shown in Figure 1. The systemallows us to search the shortest route to travel among farm ﬁelds, loading two CSV ﬁles: theﬁelds data having the name, number, and coordinate of longitude and latitude of farm ﬁelds
and the path and distance data between the whole ﬁelds included in the ﬁelds data [1]. We
can get the shortest route, which is provided by solving the TSP with the exact algorithm[2], selecting the farm ﬁelds visited from the list constructed with the ﬁelds data and thenclicking the search button. The shortest route is shown on the map in the main window, andthe order of ﬁelds traveling on the route is indicated in the display under the map, where themap can be switched to an aerial photo. Moreover, the optimal routing system has the three
types of output functionalities: (a) printing the main window, (b) QR code providing a URL
to show the shortest route on Google Maps, and (c) ﬁle output which generates a HTML ﬁleincluding the shortest route map.

(a) Printing

CSV

Fields data

CSV(b) QR code

Path andHTML

distance data
Main window(c) File Output

Figure 1: Structure of the optimal routing system.
The eﬀectiveness of the optimal routing system has been demonstrated by comparing
the traveling route for 72 farm ﬁelds provided by the system to that decided empirically.
The experiment shows that the optimal routing system can reduce the traveling distance by
6.89 %.

3.

Conclusions

This paper has reported the development of an optimal routing system for traveling among
farm ﬁelds. The developed system can display on a map the shortest route to visit selectedfarm ﬁelds, solving the TSP with the exact algorithm. The system can also output theroute with the printing, QR code, and ﬁle generation. Although the system can reduce
the traveling distance and has been utilized on trial in an agricultural management entity, it
requires detailed road data, such as road width, for more eﬀective optimal routing, which is283

discussed in future work.

Acknowledgement
This work was supported by “On-farm demonstration trials of smart agriculture,” the Ministry of Agriculture, Forestry and Fisheries (Project number: 露 2C03, Enterprising body:
National Agriculture and Food Research Organization).

References[1] T. Nemoto, N. Niitsuma, N. Kamamichi: Optimal routing with road network information for traveling among farm ﬁelds, Proceedings of the 8th Multi-symposium on
Control Systems (MSCS 2021), (2021), 1I2-3. (in Japanese)[2] M. Namiki: Introduction of mathematical optimization with Python, Asakura Publishing Co., Ltd., (2018). (in Japanese)284

JSST 2021

Elbow Joint Angle Estimation Method
Using 1D-CNN with Quantized EMG
Generated by SR and Multi-sensor
D. Kashimoto1,* and T. Sadahiro1,*
1 Graduate School of Engineering, Oita University∗ v20e1017@oita-u.ac.jp,

sadahiro@oita-u.ac.jp

Abstract. Electromyogram (EMG) is used for a motion estimation as it contains informations of an intended motion. It is possible to estimate human motions in advance using
Electromechanical delay (EMD) of EMG. Moreover, a denoising method that uses Stochastic Resonance (SR) and multi-sensor is able to acquire longer EMD than LPF, except theacquired EMG is roughly quantized. In this study, a one-dimensional convolutional neuralnetwork (1D-CNN) is used as an estimation model using the roughly quantized EMG toestimate elbow angles. In order to show the advantage of 1D-CNN, the estimation results
between 1D-CNN and NDARX model using LPF-processed EMG or SR and multi-sensorprocessed EMG were compared.
Keywords: EMG, EMD, Multi-sensor, Stochastic Resonance, CNN

1.

Introduction

Electromyogram (EMG) is used for motion estimation as it contains information of humanintended motion. EMG has a time-lag between the onset of the EMG production to theactual motion, called Electromechanical delay (EMD). A prior human motion estimation
method exploiting EMD has been proposed [1]. In this study, Low Pass Filter (LPF) is used
as a preprocess of EMG, yet the acquired EMD is shorter thruough this process.
Recent developments which has been proposed by Sadahiro, et al. [2] revealed thata combination of Stochastic Resonance (SR) and multi-sensor has met with great successfor acquiring a longer EMD compared to LPF method. SR is a way to detect the weaksignal by adding on appropriate noise to the signal and passing through a hysteresis function.
Although SR is helpful to detect early changes in EMG, the EMG acquired after SR becomesthe ON-OFF signal. Multi-sensor are used to increase the number of quantization bits of
EMG after SR by summing up the all ON-OFF signals obtained from each muscle. EMG
made by SR and multi-sensor is a roughly quantized signal. Hence, elbow joint angles
estimation results by Multi Input Single Output ARX model with the roughly quantized
EMG as inputs were worse than those with LPF-processed EMG as input [3].
The purpose of this study is to estimate elbow joint angles in advance using a onedimensional convolutional neural network (1D-CNN) with roughly quantized EMG as inputs. 1D-CNN extracts features from the time direction by using convolution layers, and is285

preferable for handling time-series data. In order to show the advantage of 1D-CNN, estimation results of 1D-CNN are compared with estimation results of the Nonlinear Delayed
ARX (NDARX) model [1].

2.

Experimental Method

An experimental equipment that are consisted of BITalino EMG sensors, a goniometer (Biometrics Ltd.), and Arduino Due microcontroller [2]. EMG sensors were attached to biceps
brachii (ch1 to ch4) and triceps brachii (ch5 to ch8) as shown in Figure 1. The biceps
brachii and the triceps brachii correspond to the elbow ﬂexion and extension, respectively.
The goniometer is a device to measure elbow joint angles.
In order to estimate elbow joint angles using EMG, the experiment was conducted suchthat subject’s elbow extensions and ﬂexions were in accordance to the visual information
signals provided. The visual information signal was M-sequence signals passed throughLPF with a cutoﬀ frequency of 2 [Hz]. Bending angles of the elbow joint were between 0
to 90 [deg], and the straightened elbow was 0 [deg]. One trial on the experiment was set for10 [sec] and a total of 100 trials was conducted. Eighty trial data were used as training data,
and the rest as test data. To eliminate the eﬀects of muscle fatigue as much as possible, abreak of 1 [min] was taken after every ten trials.

Figure 1: EMG sensors arrangement

Figure 2: A comparison of uLPF and uS R ; Although the experiments were done
until 10 [sec], due to the page limitation, variations between 0 to 2 [sec] were shown.
The black line shows elbow joint angles measured by the goniometer. The red line
shows uS R . The blue line shows uLPF . The graph clearly shows that the wave forms ofuS R is a more roughly quantized EMG compared to uLPF . EMD is the time-lag between
actual motions and their EMGs. Wave peaks of uS R and uLPF are advanced compared toGonio. This indicates that uS R and uLPF both possess EMD except for uS R has a longer
EMD compared to uLPF .

3.

Elbow Joint Angle Estimation

3.1.

Preprocessing of EMG [2]To estimate human motions using EMG, some preprocesses are needed. In general, baseline
drift from raw EMG obtained from sensors are removed and the signals are rectiﬁed. Afterthese processes, smoothing process are done to reduce noise.
In this study, a second-order Butterworth ﬁlter with a cut-oﬀ frequency of 2 [Hz] is usedas the LPF, which has been widely adopted in the ﬁeld of EMG preprocessing. In order
to use LPF-processed EMG as an input for estimation models, only one channel signal per
muscle is needed. Hence, by using the EMGs from biceps brachii of ch1 and triceps brachiiof ch5 respectively, the input signal using LPF-processed EMG was deﬁned as286

uLPF = LPF(ch1) − LPF(ch5),(1)

where LPF() means the preprocessing by the LPF.
Using SR and multi-sensor is another method to remove noise. SR is a phenomenon
to enhance the sensitivity of a weak signal by adding white noise to EMG and passing it
through a rectangular hysteresis function. Multi-sensor sums up EMGs after SR for eachmuscle to increase the number of quantization bits. In this study, the standard deviationof the added white noise to the SR process was 0.05 times max, where max indicates the
maximum value of EMG at each channel. The upper and lower thresholds of the hysteresis
function were 0.35 times max and −0.1 times max, respectively. The inputs made by SR
and multi-sensor is deﬁned asuS R =

4∑

S R(chi) −

i=1

8
∑

S R(chi),

(2)

i=5

where S R() means the preprocessing by SR.
A comparison between uLPF and uS R is shown in Figure 2. It shows that uS R is a rougher
quantized signal and has advanced wave peaks compared to uLPF . Thus, the EMD obtained
through uS R is longer than uLPF .

3.2.

Estimation ModelIn this study, 1D-CNN was used as an estimation model from EMG to elbow joint angles,
as shown in Figure 3. This model extracts temporal features by performing convolution on
the input data and maxpooling on the resulted data. The number of ﬁlters in each layer was
16, and the ﬁlter size was 2. The activation function was ReLu, and the evaluation function
was RMSE. Inputs data were u[k], u[k − 1], ŷ[k + EMD − 1] and ŷ[k + EMD − 2]. u[k] isthe EMG signal at time k. y[k] is the elbow joint angles measured by the goniometer at timek. ŷ[k] is the estimated joint angle at time k. EMD means time steps of EMD. uLPF anduS R were used as u[k]. As mentioned in section 2, 80 trial data were used as training dataof 1D-CNN. Considering the time lag due to EMD, y[k + EMD] was set to the ground truth
for model training when u[k] was used as input. Therefore, it is possible to obtain ŷ[k] fromu[k], u[k − 1], ŷ[k + EMD − 1] and ŷ[k + EMD − 2]. In this study, the EMD of uLPF was set
to 120 and the EMD of uS R was set to 220.
As mentioned in the introduction, the NDARX model is used to compare the results of
1D-CNN. In this study, the number of previous inputs and outputs was two, and the numberof divided regions was 10.

3.3.

Estimation Results

The estimation results between 1D-CNN and NDARX were shown in Figure 4. Since theestimated signals are the future elbow joint angles, the estimated signals were delayed by thetime of EMD. Therefore the estimation signals using uLPF was delayed by 120 [msec], andthe estimation signals using uS R was delayed by 220 [msec]. From Figure 4, the 1D-CNN
estimation is similar to the actual signal of elbow joint angles compared to the NDARX
estimation. This results highlight that the estimation signal of 1D-CNN with uS R is comparable with uLPF . Therefore, 1D-CNN with uS R as inputs can be estimated further in advancecompared to the conventional methods.

287

Figure 4: The estimation results of 1D-CNN andNDARX; Although the experiments were done until 10 [sec], due tothe page limitation, variations between 0 to 5 [sec] were shown. The

Figure 3: A structure of 1D-CNN; black line shows elbow joint angles measured by goniometer. The
The blue line indicates convolution process. The orange line indicates maxpooling. u[k] is the EMG signal at time k.
ŷ[k] is the estimated joint angle at time k.
EMD means time steps of EMD.

4.

red line shows estimation result from 1D-CNN with uS R . The blueline shows estimation result from 1D-CNN with uLPF . The green line
shows estimation result from NDARX with uLPF . The purple line
shows estimation result from NDARX with uS R . In order to compare only their waveforms easily, the estimation results were shiftedusing the amount of EMD. The result shows that the 1D-CNN estimation is similar to the actual signal than the NDARX estimation. This
results highlight that the estimation signal of 1D-CNN with uS R is
comparable with uLPF . Therefore, 1D-CNN with uS R as inputs can be
estimated further in advance compared to the conventional methods.

Conclusion

As a result, 1D-CNN with the roughly quantized EMGs as input is an eﬀective method
to estimate elbow joint angles in advance. However, since EMD was determined basedon a priori knowledge after measuring the actual motion, it is not suitable for practicalapplications. Thus, as a future research, we will construct a method to determine actual
EMD before completing elbow joint angles acquisition. Additionally, in order to show thestatistical signiﬁcance of the proposed method, to increase the number of subjects is also
one of our future works.

Acknowledgement
The authors would like to thank Ms. Nur Hidayah Binti Samijan for carefully proofreading themanuscript. This work was supported by JSPS KAKENHI Grant Number JP18K04071.

References[1]

M. Hayashi, et al.: Development of zero-phase-tracking man-machine interface with electromechanical delay of electromyogram, Journal of the Robotics Society of Japan, 30:8 (2012),
767-778 (in Japanease).

[2]

T. Sadahiro, et al.: Experimental Veriﬁcation of Obtaining Longer EMD of EMG Using Multisensor and SR Phenomenon, The 38th JSST Annual International Conference on Simulation
Technology, (2019), 43–46.

[3]

D. Kashimoto, et al.: Comparison of elbow angle estimation from rough quantized emg signals
using stochastic resonance between diﬀerent hysteresis functions and number of sensors, The
39th SICE Kyushu Branch Annual Conference, (2020), 40–43, (in Japanease).

288

JSST 2021

Elbow Joint Angle Estimation from Smoothed EMG
Using Summing Network and Multi-sensor
Naoki Ikeda1,* and Teruyoshi Sadahiro1,*
1 Graduate School of Engineering, Oita University∗ v21e1001@oita-u.ac.jp,

sadahiro@oita-u.ac.jp

Abstract. Human motions are performed by muscle contractions, and electrical signals
called electromyogram (EMG) produced when a muscle contracts. EMG is used as an input
signal for man-machine interface (MMI). Electro Mechanical Delay (EMD) of EMG can
improve the responsivity of MMI. A noise reduction method using Stochastic Resonance(SR) and multi-sensor has been proposed to obtain longer EMD compared to the conventional method of low pass ﬁlter (LPF). Summing Network (SN) is another method to reducenoise using SR, and ﬁnely quantized EMG with longer EMD can be obtained by combining SN and multi-sensor. The purpose of this study is to estimate elbow joint angle fromdenoised EMG using SN and multi-sensor. Experimental results show that the proposed
method has better estimation results compared to the method using EMG made by SR andmulti-sensor as inputs.
Keywords: EMG, EMD, Stochastic Resonance, Summing Network

1.

Introduction

Human motion are performed by muscle contractions, and an electrical signals called electromyogram (EMG) produced when a muscle contracts. EMG contains various informations
about body movements, for example a timing and degree of muscle contraction. One of thefeatures of EMG is Electro Mechanical Delay (EMD). EMD is the time diﬀerence of about
30 to 100 msec between the production of EMG and the actual motion.
EMD of EMG can improve the responsitivity of man-machine interface[1]. In general, adenoising process using low pass ﬁlter (LPF) is necessary to estimate a motion from EMG.
However, LPF makes EMD shorter.
A denoising method that prevents the decrease of EMD has been studied. An example
of such method has been proposed by Sadahiro et al.[2], that uses Stochastic Resonance(SR) and multi-sensor. SR is a method to detect a weak signal by adding white noise to
the original signal and passing it through a hysteresis function[3]. A denoised EMG using
SR and multi-sensor becomes a roughly quantized signal. An estimation accuracy of elbow
joint angle using Multi Input Single Output (MISO) ARX model with this roughly quantized
EMG as inputs is unsatisfactory compared with denoised EMG using LPF as inputs[4].

289Number of quantization bits of the input signals can be made ﬁner by increasing the number
of EMG sensors, but it is restricted by surface area limitations of muscles.
The purpose of this study is to estimate elbow joint angle from denoised EMG using
Summing Network (SN) and multi-sensors. SN is a method proposed by Collins et al. thatcan obtain a ﬁner quantized signal compared to SR[5]. denoised EMG using SN is able toobtain ﬁnely quantized EMG with longer EMD without increasing the number of sensors[6].
In this paper, estimation results using MISO nonlinear ARX (NARX) with denoised EMG
using SN and multi-sensor and using SR and multi-sensor are compared by some experiments.

2.

Experiment

An experimental equipment that combined BITalino EMG sensors, goniometer (BiometricsLtd.) and Arduino Due micro controller were used to measure elbow joint angles and their
EMGs[2]. This experimental equipment is shown in Figure 1. EMG sensors for 4 channels
were attached to biceps brachii (ch 1 to 4) and triceps brachii (ch 5 to 8), respectively.
Figure 2 shows the arm with EMG sensors attached. The biceps brachii corresponds to theﬂexion of the elbow joint, and the triceps brachii corresponds to the extension of the elbow
joint. Goniometer is a device used for measuring elbow joint angles. In this study, thesampling frequency was set to 1 kHz.
Experiments were conducted that subjects bent and stretched their elbow joint following
visual instruction signals provided. The straightened elbow was set at 0 deg, and the bending
angle was set from 0 to 90 deg. One trial on the experiment was done for 10 s.
!"#$%&'()$*+',&-:&-;)('*2;#.,%%#&/*+'0

!" $

!" &

!" )

!" '

!" #

!" %

!" *

!" (

12*3#4'&/*5,&-

6'()'4#%#&.78,")(' !36*1#(9'&Figure 1: An experimental equipment．

3.

Denoising Method

3.1.

SR and multi-sensor

Figure 2: Attached positions of EMG sensors．

As mentioned in the introduction, a denoised EMG with a longer EMD can be obtainedby using SR and multi-sensor. Before conducting denoising process, drift removing andrectiﬁcation are done for raw EMG signals as preprocess. The SR process is done by adding
white noise to the preprocessed EMG and passing it through a hysteresis function. Denoised
EMG of each muscle is obtained by summing up all the SR-processed EMG on each muscle.
The standard deviation of the added white noise is 0.03 times MaxEMG, where MaxEMG
means the maximum value of a preprocessed EMG. The upper and lower threshold values of
the hysteresis function are 0.4 times MaxEMG and −0.05 times MaxEMG, respectively. The
hysteresis function binarizes EMG to 1 and 0, while the summed EMG from each muscle
are quantized as m-th power of 2, where m means the number of EMG sensors on eachmuscle.

290

3.2.

SN and multi-sensor

The SN process is done by using N-data of SR-processed EMGs that are processed with
diﬀerent white noises and by summing up their N-data[5]. Denoised EMG of each muscle
is obtained by summing up all the SN-processed EMG from each muscle.

3.3.

Denoising Results

A denoised EMG using SN and multi-sensor was compared with denoised EMG using LPF
and conbination of SR and multi-sensor. In this study, a second-order butterworth ﬁlter with
cutoﬀ frequency of 2 Hz was used as the LPF. Waveforms of biceps brachii’s EMGs using
each method are shown in Figure 3. Phase diﬀerences and cross-correlations between thedenoised EMG using LPF and the denoised EMG using the other methods are shown in Table 1. The phase diﬀerence indicates additional EMD compared with denoised EMG using
LPF. The cross correlation indicates similarity to denoised EMG using LPF. As mentioned
in the previous study[6], Figure 3 and Table 1 show that the denoised EMG using SN andmulti-sensor is closer to the denoised EMG using LPF compared to the method of using SR
and multi-sensor, although EMDs from each denoised EMG have almost same length.
Table 1: Simulation results of phase differences and cross-correlations; Because
the added white noises are diﬀerent for each process, the averages of 10 processes are shown asthese results.

Figure 3: Waveforms of biceps brachii’s EMGs using each method; The red solid line indicates denoised
EMG using SN (N=100) and multi-sensor. The green solidline indicates Denoised EMG using SR and multi-sensor. The
blue dashed line indicates denoised EMG using LPF.

4.

An elbow joint angle estimation

4.1.

MISO NARX Model

Processing method
Parallel number N
MuscleCross-correlation
Phase diﬀerence [ms]MuscleCross-correlation
Phase diﬀerence [ms]SR
1
0.649851.3
0.6928
53.2

SN
5
20
Biceps brachii
0.7878 0.8273
51.7
52.5
Triceps brachii
0.8042 0.8275
53.1
52.8

100
0.826451.9
0.823853.3

In this study, MISO NARX model was used to estimate an elbow joint angle from EMG.
NARX model is a nonlinear ARX model with coeﬃcients that are functions of outputs[7].
Equation of the MISO NARX model with m data inputs and one output is as follows
y[ j] + a1 (y[ j − 1])y[ j − 1] + · · · + an (y[ j − 1])y[ j − n] = b11 (y[ j − 1])u1 [ j − 1] + · · · +b1nu (y[ j − 1])u1 [ j − nu ] + · · · + bm1 (y[ j − 1])um [ j − 1] + · · · + bmnu (y[ j − 1])um [ j − nu ],(1)

where y[ j] and um [ j] are the output and the mth input at a time step j, respectively. an (y)and bmnu (y) are the coeﬃcient functions of the output and the m-th input, respectively.

4.2.

Estimation Results

Experimental results of elbow joint angle estimation by the MISO NARX model for each
input were compared. Waveforms of estimation results are shown in Figure 4. Root meansquared errors between estimated values and measurement values by the goniometer are291

shown in Table 3. It shows that the proposed method has better estimation results comparedto the method using EMG made by SR and multi-sensor as inputs.

Table 2: Root mean squared errors of estimated values using each method; Because the added white noises are diﬀerent foreach process, the averages of 10 processes areshown as below.

Figure 4: Estimation results; The red, green, and yellow
lines indicate estimation results with denoised EMG using SN
and multi-sensor, SR and multi-sensor, and LPF, respectively.
The blue dashed line indicates the measured value by the go-

Subject data LPF
A
01 0.2108
02 0.2049
B
01 0.2294
02 0.4163
C
01 0.2150
02 0.1905

SR SN(N=5) SN(N=20)
0.6217 0.4780
0.36870.8903 0.7011
0.50870.9688 0.8628
0.70380.9213 0.6509
0.58283.3631 1.8221
0.91911.1449 0.8783
0.6280niometer.

5.

Conclusion

In this study, elbow joint angles were estimated from denoised EMG using SN and multisensor. Experimental results show that the proposed method has better estimation resultscompared to the method using EMG made by SR and multi-sensor as inputs. In this study,
the estimation was performed without EMD. Thus, to estimate human motion using a modelthat is able to deal with EMD is one of our future works.

Acknowledgement
The authors would like to thank Ms. Nur Hidayah Binti Samijan for carefully proofreading
the manuscript. This work was supported by JSPS KAKENHI Grant Number JP18K04071.

References[1] M. Hayashi, et al.:Development of Zero-Phase-Tracking Man-Machine Interface with ElectroMechanical Delay of Electromyogram, International Journal of the Robotics Society of Japan, volume:30(2012), 767–778. (in Japanese)[2] T. Sadahiro, et al.: Experimental Veriﬁcation of Obtaining Longer EMD of EMG Using Multi-sensor and
SR Phenomenon， The 38th JSST, (2019), 43–46.
[3] K. Wiesenfeld, et al.: Stochastic resonance and the beneﬁts of noise: From ice ages to crayﬁsh and
SQUIDs, International Journal of Nature, volume:373, (1995), 33–36.
[4] D. Kashimoto, et al.: Joint Angle Estimation from Roughly Quantized EMG Signals in Simple Movements， The Japan Society of Mechanical Engineers Kyushu Student Association, (2020), 1–4. (inJapanese)[5] J.J. Collins, et al.: Stochastic resonance without tuning, International Journal of Nature, volume:376(1995), 236–600.
[6] N. Ikeda, et al.: An Elbow Joint Angle Estimation Method by a Low-pass less EMG using a Summing
Network and Multi-sensors, The Japan Society of Mechanical Engineers Kyushu Student Association,(2021), 1–4. (in Japanese)[7] A. Ohata, et al.: Identiﬁcation of Nonlinear ARX Model with Input and Output Dependent Coeﬃcients,
IEEE International Conference on Control Applications, (2006), 2577–2582.

292

JSST2021

Simulation of Team Cooperation Considering Team
Cognition – Effect of Mutual Beliefs on Team Performance
Sumie Cho1, Taro Kanno1, Daichi Mitsuhashi1, and Kazuo Furuta1
1

Department of Systems Innovation, School of Engineering, The University of Tokyo*zhang-chengyue@g.ecc.u-tokyo.ac.jp

Abstract. Computer simulation is an alternative method for investigating the cognitive aspects of human factors in teams. Our previous study developed an agent-based simulation ofteam cooperation using a team cognition model based on mutual beliefs. We modified thatsimulation model in the current study to appropriately reflect the meta-cognition behind teamcooperation and conducted simulations to examine the effect of mutual beliefs on team performance. Besides, we examined the impact of domain dependence caused by the knowledge
structure. The results revealed that regardless of the knowledge structure, communication
generated by mutual beliefs improves team performance.
Keywords: Situation Awareness, Agent-based simulation, Team communication

1. Introduction
Several human factor studies explored the cognitive and behavioral factors that affect teamperformance. Primarily, these studies used verbal protocol analysis and behavior analysis tomeasure cooperative behavior in team processes. For example, Kiekel et al. [1] developed
several automated methods to analyze communication data for measuring team cognition.
However, these measurements focus only on observable data, making the precise and efficient extraction of underlying cognitive mechanisms challenging. A promising alternative for
exploring cognitive aspects of team cooperation is a computer simulation that can test various
hypotheses regarding team cognition. However, the computational approach for team cognitive studies is still in its infancy. Yojima et al. [2] developed an agent-based simulation forcooperative behavior analysis based on a team cognition model proposed by Kanno et al. [3].
It uses the concept of mutual beliefs, explaining the cognitive mechanisms behind dyadic
team cooperation. Though the study is yet to conduct multiple simulations with various parameter settings, the simulation was performed with only one domain-specific knowledge.
Besides, there was room for improvement in the simulation model as the meta-cognitive operations after communication were inappropriate.

293

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Therefore, in this study, we modified the previous simulation model to investigate the effectof team cognition on team performance and established a new comparative analysis methodof the simulation results. Further, we examined the dependence on the knowledge structure.

2. Simulation Model in the Previous Research
Kanno et al. suggest a three-layered structure in their team cognition model: self-cognition,
belief about the partner's cognition, and belief about the partner's self-cognition. The previous
simulation model [2] used a car diagnosis with two agents collaboratively diagnosing a car’s
failures. Each agent could see only part of the car; thus, they need cooperation to acquire thecorrect and complete situation awareness (SA). Each layer of the model is implemented usinga Bayesian Belief Network (BBN), representing the agent’s domain knowledge structure
along with cognitive and inference mechanisms. In the simulation model, agents perform
three types of actions: observation (look at) and two types of communication (inform/query).
Observation involves obtaining an SA by perceiving the environment, while communication
includes resolving contradictions between layers. A “query” is a communicative action to notify the partner about his/her SA of "Unknown" and requesting his/her SA, while “inform” isan action showing the agent's SA to the partner. Table 2 summarizes the conditions for performing each type of communication and action. While taking action, metacognitive operations modeled as interlayer interactions in the simulation model initiate cognition and inference. We evaluate team performance through team accuracy formulated in Equation (1),where 𝑈! represents a set of states of all nodes in the BBN of the car model, and 𝑈"# represents a set of states of all nodes in the BBN of agent A’s first layer. Table 1 lists the model
parameters used in a previous study [2].
𝑈! ∩ 𝑈"# 𝑈! ∩ 𝑈$#
1
𝑇𝑒𝑎𝑚 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = ,
+
0×
𝑈!
𝑈!
2

(1)

Table 1 Parameter Setting of Simulation.
Parameter

Definition

Value

ThresholdThreshold of occurrence recognition of an event

0.75

Inter-Layer-Effect

The effect of the inter-layer interaction

0.95

Human Error

Do the agents have wrong SA at the start of the simulation?

Referenced Layers

The layers the agent refers to when choosing an action

True/False
L1/L12/L13/L123

3. Model Modifications
The previous study had an issue of metacognitive processes in communication not being reflected properly in the model. Specifically, whenever agents conduct “inform,” there is excessive interlayer interaction, and the second layer is updated almost every time. To fix this294

JSST2021
problem, we divided “inform” into two types based on the motivation to tell the partner
his/her SA. Type 1 is notifying when the partner does not seem to have the correct SA, andType 2 is activated when the partner appears to misunderstand his/her SA. The modified
communication rules are also shown in Table 2. According to this reconfiguration, the interlayer interactions for each type of “inform” were modified. We also performed simulations
using different BBNs to examine the dependence of cooperative behavior on knowledge
structure. Using the two types of knowledge structures and the parameter settings shown in
Table 1, we performed a simulation with the modified model and conducted a comparative
analysis of the simulation results. Specifically, we repeated the simulation 100 times under
the same conditions, sorting the obtained team accuracy in ascending order and making ascatter plot of Team Accuracy with the same rank against those obtained when referencing theL1 layers. The new comparative analysis by removing the effect of parameters other than thereference layers helps in observing whether communication generated by the mutual belief
improves team performance and to what extent.
Table 2 Communication Rules.
Let 𝑆! , 𝑆" and 𝑆# be the states of corresponding nodes in the first, second, and third layer of an agent.
The first row represents the case of a conflict in the states between the first (Unknown) and second layer. When this case occurs, the agent will observe the car parts first, and then, if the conflict is not resolved, will query the partner about the state of the node in his/her first layer.
Action (In Previous Research)

Action (After Modification)

𝑆! ≠ 𝑆" 𝑎𝑛𝑑 𝑆! = 𝑈𝑛𝑘𝑛𝑜𝑤𝑛

Condition

Look at → Query

Look at → Query

𝑆! ≠ 𝑆" 𝑎𝑛𝑑 𝑆" = 𝑈𝑛𝑘𝑛𝑜𝑤𝑛

InformInform (Type 1)

𝑆! ≠ 𝑆"

Look at → Query

Look at → Query

𝑆! ≠ 𝑆# 𝑎𝑛𝑑 𝑆! = 𝑈𝑛𝑘𝑛𝑜𝑤𝑛

Look at → Query

Look at → Query

𝑆! ≠ 𝑆# 𝑎𝑛𝑑 𝑆# = 𝑈𝑛𝑘𝑛𝑜𝑤𝑛

InformInform (Type 2)

𝑆! ≠ 𝑆#

InformInform (Type 2)

4. Results and Discussions
Fig. 1 shows the results of the simulation with the modified model. The horizontal axis represents team accuracy when referring only to the first layer, and the vertical axis represents the teamaccuracy obtained when referring to the first and second layers (L12), first and third layers(L13), and all three layers (L123). A plot above the dotted line indicates an improvement in teamperformance by mutual beliefs and inter-layer interactions triggered by meta-cognition. Table 2
shows the rate of the plot above the dotted line and the average number of actions taken by thetwo agents before and after model modifications. Team accuracy showed improvement whencommunication was generated by referring to the second layer or/and the third layer. Using
different BBNs in the simulation showed similar improvement. A comparison of the results
obtained by different layer combinations revealed that the team performance obtained with
L123 was slightly better than that with other combinations. These findings suggested that mutual belief is one of the major factors and driving force for better team cooperation. Moreover, we observed that the number of actions increased after the model modification, suggestingthat this modification realized appropriate interlayer interactions to generate constructive actions

295

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for enhancing team performance.

Fig. 1. Comparative Analysis of Results
Table 1. The Number of Total Actions and Rate of Improvement in Team Accuracy
Before Model Modifications
After Model Modifications

The Total Number of Actions
L1
L12
L13
L123
2.20
5.17
10.24
6.47
2.20
7.91
15.01
11.31

L1
-

Rate of Improvement
L12
L13
L123
1.000
0.994
0.984
1.000
0.946
1.000

5. Conclusion
To investigate the effect of cooperative behavior generated by mutual beliefs on team performance, we modified the simulation model of the previous study and conducted a comparative
analysis of the simulation results under different layer combinations and knowledge structures. We found that mutual beliefs played an important role in improving team performance
regardless of domain knowledge and structure. Although further improvements and sophistication are necessary, we believe that our simulation is a promising method to compensate forthe limitations of conventional human factor methods and exploring cognitive aspects of teamcooperation.

References[1] Kiekel, P. A., Cooke, N. J., Foltz, P. W., Gorman, J. C., & Martin, M. J.: Some Promising Results of Communication-Based Automatic Measures of Team Cognition, Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 46:3(2002),
298–302.
[2] Yojima, S., Kanno, T., Furuta, K.: Simulation of Team Communication and Shared Situation Awareness, 18th Asia Simulation Conference Kyoto, Japan/October, (2018), 2729
[3] Kanno, T., Furuta, K., & Kitahara, Y.: A model of team cognition based on mutual beliefs, Theoretical Issues in Ergonomics Science, 14:1(2013), 38-52.

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Agent-based simulation of consumer panic buying:feasible measures for mitigating its effect
Sotaro Kawanishi1*, Rithika Dulam1, Kazuo Furuta1, Taro Kanno2
1Technology Management for Innovation, School of Engineering, The University of Tokyo
2

System Innovation, School of Engineering, The University of Tokyo*kawanishi-sotaro718@g.ecc.u-tokyo.ac.jp

Abstract. Consumer panic buying in disasters makes supplies unavailable to many people andcauses supply chain disruption. Our previous research has analyzed the effect of consumer
panic buying on the supply chain by conducting agent-based simulation, but there are someproblems with the realism of the model and the limited proposed measures. Therefore, the objective of this research is to develop an agent-based simulation model based on our previous
research and devise effective/feasible measures that mitigate the effect of consumer panic buying. The results showed that implementing sales restriction, holding additional inventory, andtransmitting information are feasible measures that have significant effect, and the disruptionof the supply chain could be prevented by combining those measures. Results obtained in thisresearch could help the government and industry take appropriate measures when a disasteroccurs.
Keywords: Consumer panic buying, supply chain disruption, agent-based simulation

1. Introduction
Japan is prone to natural disasters such as typhoons, earthquakes, and tsunamis due to its
natural conditions. These natural disasters could cause serious damages by not only directly
resulting casualty and property loss, but also by causing secondary disasters such as panic buying of food and daily necessities. Typical examples of this secondary disaster are the buying up
of toilet paper during the Covid-19 pandemic and the buying up of bottled drinking water after
the Great East Japan Earthquake. Under such circumstances, it is necessary to guarantee thestability of supply chain to avoid shortage of necessities. Against this background, Dulamet al. conducted an agent-based simulation to analyze the effect of consumer panic buying on
supply chain disruption due to a disaster, and investigated what measures taken by retailers are
effective (hereinafter referred to as the previous study) [1]. In the previous study, two measures
were considered: sales restriction and rationing. The results showed that the implementation ofsales restriction did not have a significant impact on preventing the disruption of the supply
chain, and the implementation of rationing was considered very effective. From these results,
the implementation of rationing was recommended. However, rationing requires extensive

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government intervention and is impractical at present in Japan. Therefore, it is necessary todevise new measures that are both effective and feasible. In addition, the scale of the model
used in the previous study is too small and is too simple, so the model should be extended.

2. Method
2.1 Overview of the model
The model based on the previous study consists of
two parts: the supply chain model and the consumer
model. The target product assumed in the model is bottled water. The supply chain model includes five typesof supply chain agents (SCAs): manufacturers, distributors, individual retailers, chain heads, and chain stores.
These SCAs take a hierarchical structure, as shown in
Figure 1. The basic actions of the SCAs are placing orders and selling to the customers down the hierarchy,
managing their inventory to maximize their revenue efficiently. In the consumer model, each consumer agent
represents a household, and they each make purchaseaction to maintain their stock at a certain level. The variables of each consumer agent, such as the amount ofdaily water consumption and the frequency of purchase,are distributed based on a questionnaire survey.

Figure 1: Model structure

2.2 Model improvements
The model used in the previous study is very simple, consisting of 2,000 consumer agents,
four retailers, and other SCAs. There are no limitations put to the purchase action of the consumer agents, and consumer agents were able to visit every store in each timestep, in the orderof their preference. To increase the scale, the number of consumer agents and retail stores wasincreased tenfold. Since the number of stores increased, it is unrealistic for consumer agents tobe able to visit every store. Thus, the consumer agents’ purchase action was restricted. Morespecifically, a distance-based constraint was set to the consumer agents, and each agent could
only visit three retail stores in one timestep. By making this modification, the supply chain
model was more complicated, enabling more sophisticated strategies that could be taken toprevent the disruption of the supply chain.
2.3 Measures
Three measures that could be taken simultaneously with sales restriction proposed. The firstmeasure was holding emergency safety stock. The more inventory there is, the easier it is forthe supply chain to respond to sudden increases in demand. Therefore, holding extra inventory
was considered based on the study conducted by Nahleh et al. [2] The second measure is sharing
inventory information among SCAs. Since SCAs order (or produce) inventories based on theiraverage sales, there will be a lead time between the time retailers run out of stock and the time
SCAs in higher tiers increase their orders (or production). To eliminate this lead time, the average sale of a certain SCA is compared with the total sales of the related retailers, and thelarger number was used as the order (manufacturing) quantity. The third measure is provision298

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of retail store inventory information to consumers. Consumer agents provided with information
on inventory of nearby retailers, consumer agents will change their store preference, and willvisit the retailers in the order of their inventory. This will prevent situations in which consumers
could not purchase products while some retail stores within their distance limit are not stockout.
2.4 Simulation settings
To evaluate the effectiveness of the proposed methods, simulations were conducted for fivedifferent scenarios: normal case, disaster case, sales restriction case, rationing case, and sales
restriction combined with the three proposed measures case (hereinafter referred as the combination case). Same random numbers were used to compare the results under the same
conditions. The simulation was run for 100 timesteps where one timestep is a day, and thedisaster was set to occur in the 70th timestep. Countermeasures were taken from the 71sttimestep, right after the disaster occurred. The two main objectives of the measures are toprevent supply chain disruption and make supplies available to more consumers. The former
could be evaluated by reviewing the changes in inventory ratio to sales in each supply tier. If
the ratio > 1, the supply tire has sufficient inventory, and if the ratio < 1, the supply tier could
be considered stock out. If multiple supply tiers are continuously stock out, the supply chain isdeemed disrupted. The effect to consumer satisfaction could be evaluated by reviewing thechanges in the number of satisfied consumers. Consumer satisfaction for each consumer agent
is the average of inventory satisfaction (one if satisfied, and zero if not satisfied) and purchasesatisfaction (purchase quantity divided by required purchase quantity). By dividing the consumers into five categories according to the size of the satisfaction level, the overall consumer
satisfaction level could be shown by counting the number of agents in each category.

3. Results
Figure 2 shows the changes in the inventory sales ratio in the sales restriction case,rationing case, and the combination case. The results show that the supply chain is
disrupted and does not recover in the sales restriction case, while the supply chain
recovers around the 90th timestep in the rationing case and the combination case. In
addition, the supply chain is recovered from disruption around the 75th timestep inthe combination case. This positive effect is attributed to the increase in the amountof inventory in circulation due to the immediate increase in manufacturing quantity
and stockpiling of emergency safety stock.

Figure 2: Inventory sales ratio of SCAs

Figure 3 shows the changes in the number of consumer agents in each satisfaction category.
In the sales restriction case, consumers with zero satisfaction continue to exist until the 85th299

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timestep. In the rationing case, the number of unsatisfied consumers is smaller than in the sales
restriction case, but they do not disappear. However, there are no consumers with zero satisfaction in the combination case, excluding the 70th timestep when the disaster occurs. In addition,
consumers with medium satisfaction decreases, and consumers with high satisfaction increases
compared to the rationing case. From this result, the combination case is clearly superior to therationing case from the consumers’ perspective. This is because the amount of inventory incirculation increased as mentioned above, and consumer agents were able to access to themefficiently due to the provision of retailers’ inventory information.

Figure 3: Consumer satisfaction

To conclude, it can be said that combining sales restriction with the proposed methods issuperior to rationing in terms of effectiveness from both consumer and supply chain perspectives.

4. Conclusion
This research focused on analyzing the effect of consumer panic buying, which is a major
issue in recent years. A simulation model based on previous studies was developed, and feasible
measures were devised to mitigate the effects of consumer panic buying. Simulation results
showed that the impact of panic buying could be effectively mitigated by combining sales restriction with emergency safety stock, share inventory information among SCAs, and provisionof retail store inventory information to consumers. These simulation results could be used tohelp the government take appropriate measures when a disaster occurs. In the future, the model
could be developed by considering price and transportation time.

References[1] R. Dulam, K. Furuta, T. Kanno: Development of an agent-based model for the analysisof the effect of consumer panic buying on supply chain disruption due to a disaster, Journal of Advanced Simulation in Science and Engineering, Volume 7 (2020), Issue 1, 102116.
[2] Y. Nahleh, A. Hakimi, A. Kumar, F. Daver: Improving Order Quantity Model with Emergency Safety Stock (ESS), International Journal of Mechanical, Industrial Science andEngineering, Volume 7 (2013), Issue 12, 688-693.

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Comprehending and mitigating the implications ofconsumer panic buying
Rithika Dulam1*, Kazuo Furuta2, Taro Kanno3
1,2Technology Management for Innovation, School of Engineering, University of Tokyo
3

Systems Innovation, School of Engineering, University of Tokyo*rithika.dulam@gmail.com

Abstract. Consumer panic buying has been seen to occur frequently with the increasing number of disasters in recent years. Panic buying during the COVID-19 pandemic has seen the
disruption of even the most efficient supply chains. In order to develop optimal mitigation
measures, it is important to understand consumer behavioral changes and their implications. In
our effort, we have developed a model to assess the impact of panic buying on the supply chain
and consumer satisfaction. The current work focuses on the application of this model while
examining the effectiveness of popular mitigation measures, such as the quota policy.
Keywords: Decision-making, Agent-based model, Panic buying, Consumer behavior, Disaster1. Introduction
Supply chain (SC) management has come a long way from the traditional techniques to the
optimized and efficient ones with the help of advanced technology. However, they are often
susceptible to several risks, such as natural disasters, inaccurate forecast. The recent COVID19 pandemic exposed the drawbacks that led the organizations to reassess their risk management approaches. Severe movement restrictions, transportation disruptions, and panic buying
led to shortages of products in almost every sector, with panic buying being a major cause. The
incompetency of SC to cope with the situation during the pandemic has explicitly put forward
a lack of expertise and research to mitigate the risk of panic buying during emergencies.
Human nature is guided by emotions; especially with a sense of anxiety during disasters.
Performing some action over the risk provides a sense of control over the situation. Likewise,a consumer also undertakes the precautionary action of stockpiling as a safety measure against
having no stock. A large number of people indulging in stockpiling leads to panic buying, inturn disrupting SC, initiating further panic buying, which converts into a vicious circle. Essential commodities, such as food or water are typically at higher risk and might lead to chaotic
situations. Given the study on panic buying is meagre, there is a lack of a predictive consumer
model in disaster or SC disruption due to consumer behavior [1]. To bridge the gap, we aimed
to build a model that can support in predicting and mitigating the various consequences oflarge-scale panic buying. Dulam et. al. [2] developed a model to analyze both the consumer
panic buying of bottled water and the response of the SC in the disaster aftermath using anagent-based model. The enhanced consumer model assesses the panic purchase intention of aconsumer in an uncertain situation based on the factors that play a significant role during crises[3]. This model can help to understand the aftereffects, such as expected panic buying, the301

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possible SC disruption, and the outcomes of the mitigation measures, which could help industries and the government. The current paper discusses the application and usefulness of themodel to elevate the importance and benefits of such tools.

2. Methodology
The model (Fig.1) mainly comprises of a consumer model and an SC model, influenced by theconsequences of the Great East Japan Earthquake. Panic buying of food and drinking water
occurred, following the noticefrom the government due to radiation contamination. Analysis
of such situations helps us identify potential problems associated with panic buying. Hence,
we used the consequences of theFig 1. An overview of the model.
triple disaster as a reference for
identifying the key parameters of the model.
The consumer model involves the process leading to the purchase of essential commodities in disaster aftermath, influenced by several factors, such as personal, social, individual,
psychological, and situational. The model is built using a six-step decision-making process viz.,need recognition, information search and processing, factor valuation, decision, purchase, andpurchase evaluation. The household agent (consumer) makes the purchase decision based on
its available resources. The decision-making criteria are different in the pre-and post-disaster
phases. Pre-disaster decision-making is based on the available inventory and the consumptionof the household. However, the post-disaster scenario unveils a multitude of psychological andsituational factors as a consequence of the disaster. Hence, post-disaster decision-making wasdeveloped based on a logistic transformation model, using a multiple regression analysis of aquestionnaire survey. The SC model implements the key functions of the SC members required
for sustaining their businesses. The main action of the SC agents (SCAs) is to maintain sufficient inventory and satisfy the customer demand in every interval.

3. Results and Analysis
We conducted simulations by varying several key parameters of the model in a virtual 100x100
grid, with 2000 households and 4 stores. The simulation is run for 60 intervals, with the disasterin the 30th interval and the strategy is initiated in the 31st interval. The following four disasterand mitigation cases have been considered. Normal scenario; Disaster without strategy; Disaster with sales restrictions; Disaster with rationing. In the sales restrictions strategy, the consumers can make multiple purchases, while the consumer’s purchase is limited to one purchase perinterval in the rationing strategy.
3.1 Effect of strategy on consumer satisfaction:
Consumer satisfaction (Sf) is calculated based on product sufficiency and outcome of the purchase action with equal weightage to both factors, to measure the impact of the disaster or
strategy on consumers. Fig.2 shows the number of consumers in each category for the fourcases. It can be seen that 100% of consumers have been satisfied in the normal case. While, inthe disaster without strategy case, the number of zero satisfaction consumers have increased.

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The implementation of restrictions can be seen to reduce both the number of zero satisfaction
consumers andDisaster caseNormal casethe number of intervals with thepresence of suchconsumers. It canbe seen that the
number of zerosatisfaction conRationing case
Sales restriction casesumers has reduced
drastically, indicatingthat rationing canhelp increase theproduct reach.
Fig 2. Consumer satisfaction in the four scenarios.

3.2 Effect on supply chain performance:
SC performance (SCP), which is one of the key outcomes indicating the efficiency of the SCA,
can be evaluated using Inventory–Sale ratio (RIS). It is a ratio of inventory to sale, where thesale is the sum ofsale and lost sale(after stockout).
If RIS > 1, theDisaster caseNormal casewhite region in
Fig.3, the SCA ina safe condition,and if RIS < 1, thered region, the
SCA is in thestockout zone.
In Fig.3, allSales restriction case
Rationing case
SCAs are in thesafe zone in norFig 3. SCP in the four scenarios.
mal case. However, in the disaster case, due to high demand, all the SCAs are in the stockout zone, indicating
an SC crash. The sales restrictions have helped in averting the SC crash but could not avoid the
disturbances, while rationing was effective in avoiding the SC disruption.
Stockoutness: This parameter indicates the stockout
condition of the agent. It is a cumulative RIS in thestockout zone as shown below.
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = � 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖

1 − 𝑅𝑅𝐼𝐼𝐼𝐼𝐼𝐼 ,𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖 = �0,𝑖𝑖𝑖𝑖 𝑅𝑅𝐼𝐼𝐼𝐼𝐼𝐼 < 1𝑖𝑖𝑖𝑖 𝑅𝑅𝐼𝐼𝐼𝐼𝐼𝐼 > 1

Fig 4. Stockoutness of the SC tiers

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The SC stockoutness in the four cases is depicted in Fig.4. It can be observed that the strategies
have allowed the stockoutness of the SC to reduce, while rationing brings the stockoutness toalmost zero. Stockoutness can be used to compare the SCP among the scenarios.
3.3 Effect of time variation of the strategy:
We have conducted simulations to understand theeffect on SCP by varying the interval in which thestrategy is initialized, useful for disasters that canbe known beforehand, such as typhoons. Five cases
were considered with the strategy initialized in different intervals with respect to the disaster interval:
D-3 (three intervals before the disaster), D-1, D+1,
D+5, and D+10.
The stockoutness, for the five cases and the casewithout any strategy, was calculated and is shown
here. Fig.5 shows that stockoutness increases as theinitialization of the strategy is delayed. This indicates that the early employment of sales restrictions
by stores could avoid a possible SC disruption. The
SCP is improved immediately with the help of rationing at any point in time, as can be seen in Fig.6;
the effectiveness of rationing is evident, as stockoutness is greatly reduced in all cases when compared with the case without any strategy.

Fig 5. Stockoutness of the SC tiers when
initialization of sales restrictions is varied.

Fig 6. Stockoutness of the SC tiers when
initialization of rationing is varied.

4. Conclusions
We developed a multi-agent model of consumer panic buying and supply chain in the disaster
aftermath that can be used to study consumer panic buying consequences and its mitigation
approaches. The paper shows the application of the simulation model to test various scenariosand strategies that might be beneficial in avoiding SC disruptions. Rationing was found to bea more effective measure than sales restrictions. Similarly, several other scenarios can be studied to understand the outcomes and identify the solutions. The tool could be useful in helping
industries and government to analyze consumer behavioral changes and guiding them in developing optimal measures for a resilient SC and in tackling chaotic post-disaster situations.

References[1] K. F. Yuen, X. Wang, F. Ma, and K. V. Li: The psychological causes of panic buying following
a health crisis, International Journal of Environmental Research and Public Health, Volume
14, Issue 1:3513, 2020.
[2] R. Dulam, K.Furuta, T.Kanno: Development of an agent-based model for the analysis of theeffect of consumer panic buying on supply chain disruption due to a disaster. Journal of Advanced Simulation in Science and Engineering, Vol. 7, No. 1, 102-116, 2020.
[3] R. Dulam, K. Furuta, T. Kanno: Quantitative decision-making model to analyze the post-disaster consumer behavior, International Journal of Disaster Risk Reduction, 2021, 102329.

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Visualization of dose rate distribution around
Fukushima Daiichi Nuclear Power Plant using
artiﬁcial neural networks
Miyuki Sasaki1,* and Yukihisa Sanada1
1 Sector of Fukushima Research and Development, Japan Atomic Energy Agency∗ sasaki.miyuki@jaea.go.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.30

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Estimation of distribution of Uranium as shielding
body using machine learning
Yamazaki Haruka*, Kondo Yuto, Yamaguchi Katsuhiko
Faculty of Symbiotic Systems Science, Fukushima University*s2070027@ipc.fukushima-u.ac.jp

Abstract. Using machine learning, the position of shielding body and radiation source distribution are estimated from gamma-ray energy spectrum. In this study, Cs-137 was set up asradiation source and uranium as shielding body. Training data was made by simulation, insteadof time-consuming actual survey, because a large quantity of training data is required for machine learning. As a result, position of shielding body was estimated roughly, although estimation of distribution of source was not carried out well.
Keywords: Machine Learning, Monte Carlo method, Fukushima Daiichi Nuclear Power Station

1. Introduction
Fukushima Daiichi Nuclear Power Station accident happened in 2011, and it brings necessary for decommissioning work and decontamination. In order to advance theseworks, it is helpful to estimate the radiation source and some material aroundsource. We have studied estimation of radiation source and shielding body using
machine learning[1]. Using this method, a large amount of gamma-rays energy
spectra data and various condition such as position of radiation source and shielding body are used as training data, and estimation is carried out.
In this study, uranium and Cs-137 is treated. Uranium is one of radioactive material that is included in fuel debris, but there are few radiation dose from uranium.
So uranium was treated as shielding body. And Cs-137, one of the fission products,
was set up as radiation source.

2. Simulation Method
To make training data we used PHITS(ver.3.220)[2]. PHITS (Particle and Heavy Ion
Transport code System) is a general purpose Monte Carlo particle transport simulation codedeveloped by JAEA. A scheme is a 10cm square plane separated by a 1 cm x 1 cm mesh was
set up for simulation to create training data for machine learning. The sources were randomly
placed on the plane. The uranium block was randomly placed too. A plane with a height of 1
cm was set as a detection surface, and the γ rays with energy that passed through the detection
surface were recorded. This detection surface was divided into a 10×10 mesh, and each of the308

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count number and the energy distribution are recorded. Recorded energy spectra are divided
into 14 parts and all data are normalized.
Fig.1 shows the schema of the machine learning. The spectra input to Input layer as training
data, and they are multiplied by the weight and input to the Output layer via Hidden layer. Afterthat the value that output from Output layer are compared to the answer data, namely, distribution of Cs-137 and uranium. Then weight were corrected to approximate output value to answer
value. As a result, if spectra which is not learnt by the network are used as input data, output
value will be almost the same as answer data.

Fig.1 Schema of machine learning

3. ResultFig.2 shows the dependence of epoch for loss function. The value of loss is calculated one by one when training data are input. The loss means the error when
input the training data. On the other hand, the valloss means one when input thedata that is not used as training data. In this study, the value of loss was less than
0.1 and one of valloss was about 0.3. Fig.3 shows one of the estimation result. As
a result of estimation of radiation source, the value of error was 1.10× 10−1 . When
we estimate position of uranium, the value of the error was 2.88× 10−2.
Our previous study was estimate the position of lead block. That result of error
was about 10 times less than that one when we estimate the position of uranium.
Possible cause is covering most of γ ray with uranium, because the density of uranium is higher than that of uranium.

Fig.2 dependence of epoch for loss function309

Fig.3 example of the result of estimation

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References[1] Takero Uemura, Katsuhiko Yamaguchi: Estimation of radiation source distribution using
machine learning with γ ray energy spectra, J. Adv. Simulat. Sci. Ecg. Vol. 7, No. 1, 7181(2020)[2] Tatsuhiko Sato et al.: Features of Particle and Heavy Ion Transport code
System (PHITS) version 3.02, J. Nucl. Sci. Technol. 55(5-6), 684-690 (2018)

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Application of Multilayered Division Method
to Scattering by Slanted Gratings
Hideaki Wakabayashi1,* , Masamitsu Asai2 , Jiro Yamakita1
1 Faculty of Computer Science and Systems Engineering, Okayama Prefectural University
2 Faculty of Biology-Oriented Science and Technology, Kindai University∗ waka@c.oka-pu.ac.jp

Abstract. In the analysis of electromagnetic scattering by slanted gratings, the multilayer
division method has been often used. The method has a disadvantage of high computational cost to keep a high accuracy of approximation for the proﬁle. This paper presents the
improvements to reduce the computational cost.
Keywords: slanted grating, electromagnetic scattering, matrix eigenvalues method, multilayer division method

1. Introduction
In the electromagnetic analysis, slanted gratings have often been treated by dividing a grating layer into stratiﬁed thin grating layers [1] and by transforming the coordinates [2]. The
former is called the multilayer division method (MDM). The MDM has a big advantage thatit can be applied to any proﬁled grating, but has a disadvantage of high computational costto keep a high accuracy of approximation for the proﬁle. Authors have treated a slanted
grating as a grating having a tilted grating vector where the MDM is not used, and haveformulated the matrix eigenvalues method (MEM) in consideration of a grating vector [3].
The formulation starts with Maxwell’s equations, derives the ﬁrst-order matrix differential
equation directly, and reduces it into the eigenvalue problem for a coefficient matrix.
This paper incorporates the MDM into the MEM without using a grating vector forthe analysis of electromagnetic scattering by a slanted grating. The slanted region is approximated by dividing into stratiﬁed thin layers. When the division number increases, thenumber of times to calculate the eigenvalues and eigenvectors increases. Moreover, thedimension of a linear equation to be solved becomes large. In order to reduce the computational cost, we present two improvements of calculation procedure in the MEM to which
the MDM is applied. From some numerical examples, we show the effectiveness.

2. Analytical Theory
Let us consider the three-dimensional scattering problem of a slanted grating illuminated bya plane wave having an incident angle θ from the −x direction, an azimuthal angle φ from311

the +y direction. The slanted region having the thickness d is tilted at a slant angle ψ andis divided into K stratiﬁed thin layers with the relative permittivities ε1 and ε2 , as shown in
Fig. 1. The grating has the width W and the periodicity Λ in the tilted direction. The relative
permittivities in the incidence and substrate regions are denoted by εa and εs , respectively.
From Maxwell’s equations, we obtain the differential equation for the tangential ﬁelds as
h
iT
d
(1)
Ft (x) = j [C] Ft (x), Ft (x) = ey (x) ez (x) hy (x) hz (x)dxwhere [C] is the coefficient matrix, and ey(z) and hy(z) have (2M +1) spatial harmonics. Usingan eigenvectors matrix [T] and a diffraction amplitude vector g(x), the solution of Eq. (1) is"#[δ e− jξl (x− ẋ) ]0]
Ft = [T][U(x)] g(x), [U(x)] = ln
(2)[0][δln e jξl (x− ẍ) ]with l, n = 1, 2, . . . , 2(2M + 1). δln is the Kronecker’s delta, ∓ξl is the l th eigenvalue,
and ẋ and ẍ are the phase reference positions. Putting [Ak ] = [Tk ][Uk (xk )] and [Bk+1 ] =−[Tk+1 ][Uk+1 (xk )], we have the boundary condition at x = xk as
h i "g+ (xk−1 )# hi " g+ (xk ) # "0#kAk+ Bk+1 −k+1=
(3)
g−k (xk )gk+1 (xk+1 )0with k = 1, 2, . . . , K. The symbol ± denotes for the waves traveling in the ±x directions. We
rewrite Eq. (3) using a matrix form as  g0 
[A0 ] [B1 ]





[A1 ] [B2 ]  g1   




  .  0

···
···
···
···
  ..   . 
[Ak−1 ] [Bk ](4)  .  =  ..  .
  ..   

·
·
·
·
·
·
·
·
·
·
·
·

 
0  gK 

[A
]
[B
]
K−1
K



 

[AK ] [BK+1 ] gK+100

It is high computational cost to solve Eq. (4) directly to obtain the mth diffraction amplitudes
hn a− o n a− oiT
hn s+ o n s+ oiT
g−0 = E gm M gm
and g+K+1 = E gm M gm . The superscripts E and M denote TE
and TM waves, respectively. We present the following two improvements to reduce the cost.
z

0

εa

y

1
2
3

ε2

ε1

k

0
1
2
3
k

d

ψ

Λ

W
K−1
K

K
εs

K +1
x

Figure 1: Multilayer division for a slanted grating.

312

The procedure to calculate eigenvalues and eigenvectors
For the slanted case, the matrix [Ck ] of the kth layer can be expressed by

 

 nK  h i 
h i−1
h i
n
K
 , n  = he jm nk zk δ i (5) [Ck ] = N K [C1 ] N K ,N K = 
K
mn

nK

 
nK with nK = λ/Λz and Λz = Λ/ cos ψ. the diagonal matrix κk of eigenvalues is the same as[κ1 ] in the 1st layer, and [Tk ] is derived by shifting the phase of [T1 ] ash i[κk ] = [κ1 ], [Tk ] = N K [T1 ] .
(6)
1

0

0

We can get [κk ] and [Tk ] in all stratiﬁed layers by numerical calculation only once.
2 Successive elimination to solve linear equation
We solve Eq. (4) without using inverse matrix. Using forward elimination successively, we
eliminate the unknown amplitudes g1 ，g2 , . . . , gK as follows :#" (k−1)#" (k)  [P
] [Q(k−1) ][0][C(k) ]
[A0 ]
(7)
=⇒
[0]
[Ak ]
[Bk+1 ]
[P(k) ] [0] [Q(k) ]where k = 1, 2, . . . , K, [P(0) ] = [A0 ] and [Q(0) ] = [B1 ]. Comparing with Eq. (4), the working
memory for Eq. (7) becomes small. We ﬁnally have the two medium boundary problems as
" +#
" + #
(K) g0(K) gK+1[P ] − + [Q ] −
=0.
(8)
g0
gK+1

3. Numerical examples and discussions
This section considers the effectiveness of the above two improvements for a slanted gratingcase. First, we compare the computational times using the improvements 1 , 2 and the
combination of 1 and 2 with the case 0 without using these improvements. Figure 2
shows the required time to calculate a set of diffraction efficiencies against the division
number K by PC (CPU : Intel Xeon W-2145 3.70 GHz, Memory : 128 GB, OS : Windows
64 bit) under 2M + 1 = 31. We can see that the effect of 2 is large. It is worth noting that
2 can be applied not only to a slanted grating but also to surface proﬁled gratings.

CPU time [s]

30

20

0

1

10

2

0
0

20

40

60

80

1+2

100

The division number K

Figure 2: The calculation time against division number.

313

Next, Fig. 3 compares the numerical results by the MDM and by the method of Ref. [3]using a tilted grating vector for TE and TM incidences having θ = 60◦ and φ = 90◦ inplanar mounting case. Calculation parameters were chosen as 2M + 1 = 31, Λ/λ = 0.4,
W/Λ = 0.5, εa = ε1 = 1.0, ε2 = εs = 1.52 and d/Λ x = 3.0 with Λ x = Λ/ sin ψ. Figurer against the division number K at slant(a) plots the −1st reﬂected diffraction efficiencies η−1◦◦angles ψ = 45 and 75 . When the division number K increases, the results by the MDM arerby the method of Ref. [3], which are the dotted lines
in good agreement with the results η−1in the ﬁgure. So, we conﬁrmed the validity of the MDM. Figure (b) calculates the relativer − η r /η r . As ψ becomes large, the error increases. This means that applying
errors η−1−1−1
the MDM to the analysis of surface proﬁled gratings, a division size should be determinedaccording to the gradient of the grating shape.
−1

1.0
0.8

r
η−1

0.6

TM
TE

45◦

TE

75◦

Relative errors

10ψ = 45◦

0.4

75◦

TM
0.2

TE

−2

10

TM

75◦

TE

−3

10

TM

ψ = 45◦

−4

10

1+2

The method of Ref. [3]
0.0
0

−5

50

100

150

200

The division number K

10

0

50

100

150

200

The division number K(a) The diffraction efficiencies(b) The relative errors

Figure 3: The comparisons of results by the MDM and the method of Ref. [3].

4. Conclusions
This paper has targeted the analytical method of electromagnetic scattering by slanted gratings. In order to reduce the computational cost, we have improved calculation procedurein the MEM that incorporates the MDM. Some numerical results have shown that our proposed improvements are successful. Using the successive elimination and the division size
according to the grating shape, it is expected that the computational cost can be reduced in
the analysis of scattering by various surface proﬁled gratings.

References[1] S. Campbell, L. C. Botten, R. C. Mcphedran and C. Martijn de Sterke, Modal method forclassical diffraction by slanted lamellar gratings, Journal of the Optical Society of America A,
25 (2008), pp. 2415–2426.
[2] G. Granet, M. H. Randriamihaja and K. Raniriharinosy, Polynomial modal analysis of slanted
lamellar gratings, Journal of the Optical Society of America A, 34 (2017), pp. 975–982.
[3] H. Wakabayashi, M. Asai and J. Yamakita, Three-dimensional analysis of structural coloration by a slanted dielectric grating, Journal of the Optical Society of America A, 37 (2020),
pp. 1539–1547.

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On the Regular Tetrahedral Layout of Helices
for a Quasi-Isotropic Chiral Particle
Masamitsu Asai1*, Hideaki Wakabayashi2, Jiro Yamakita2
1

Department of Computational Systems Biology, Kindai University
2
Okayama Prefecture University*asai@waka.kindai.ac.jp

Abstract. The regular tetrahedral layout of thin-wire conducting helices is presented as the
structure of a quasi-isotropic chiral particle. This work is done as part of pursuit of particle
structure under the trade-off between the simplification of structure and the quality of isotropy
and chirality. Effective constitutive parameters of the medium composed of the particles withthe presented structure are analyzed by the quasi-static Lorentz theory combined with themethod of moments to investigate the quality of isotropy and chirality. The extent of cancellation of electric quadrupole moments is also checked as a criterion for isotropic chirality.
Keywords: Artificial medium, chiral medium, electromagnetic theory, medium design.

1. Introduction
Metamaterials for electromagnetic waves have been of great interest in the fields of radio
science, optics, and acoustics etc. They are composed of artificially-fabricated particles inbackground matrices or are fabricated by working matrices into fine mosaics. They are designed to show required macroscopic characteristics. The size and spacing of each particle orroughness is to be much smaller than the wavelength. The Pasteur medium i.e. a reciprocal
isotropic chiral medium was first developed as a metamaterial. It was considered as the magnified scale model of the organic compounds by which K. F. Lindman investigated the opticalactivity in the microwave frequency in 1914 through 1922. Artificial bi-isotropic and bi-anisotropic media and artificial magnetic and dielectric media also have been studied [1]. The term
‘metamaterials’ has been given to those artificial media since the negative index of refraction
in a left-hand material was realized by J. B. Pendry, D. R. Smith et al. in around 2000 [2].
Research on the artificial chiral medium has been intensively reported not only on the opticalactivity but on the biomimetic functions and the medical effects such as suppression of cancer
proliferation etc. [3],[4]. Convensional isotropic chiral media are composed of random or homogeneous distributions of randomly-oriented chiral particles. In the practical design however,
it is actually very hard to have the orientations and positions of particles perfectly random, thenthe isotropy with high accuracy is hard to realize. It is on the other hand more realistic andpractical to design a three-dimensional periodic array of quasi-isotropic chiral particles. Eachparticle should be close to electromagnetically isotropic and should be downsized to around a315

JSST2021

tenth of wavelength that is known to be adequate granularity for chiral media. Authors havepresented the cubic layout of helices that has twelve helical or double-helical thin wires considering rotational symmetry and granularity. The resultant medium has shown high quality ofisotropy and chirality [5]. Although it is still necessary to pursue optimal structure of particles,
it is also important to simplify the structure for cost reduction and simplicity of fabrication
under the trade-off with the quality of isotropy and chirality.
In this work, the regular tetrahedral layout of thin-wire conducting helices is presented as
the structure of a quasi-isotropic chiral particle. Compared to the cubic layout, the number ofhelical or double-helical wires is reduced by half that is likely to sacrifice the quality of isotropic chirality. To investigate the quality of isotropy and chirality of the medium composed ofthe particles with the presented structures, the effective constitutive parameters are numericallyanalyzed by the quasi-static Lorentz theory [7] combined with the method of moments for thinwire approximation [5],[6]. The electric and magnetic dipole moments and the electric quadrupole moments are taken into account in the analyses [8],[9]. The extent of cancellation of theelectric quadrupole moments is also checked as a criterion for the isotropic chirality.

2. Structure and Analysis
The regular tetrahedron with edge length L is shown in Fig. 1. The center of gravity is on

Fig. 1

Regular tetrahedron

Fig. 2

Particle structure

the origin of Cartesian coordinate. One of the apices is on z-axis that is a perpendicular line andone of the edges is parallel to x-axis. A right-handed single or a double helix is located at thecenter of each edge of the regular tetrahedron to form a particle and each helical axis is on eachedge as shown in Fig. 2. The single helix (that also composes a double helix) is a five-turn
perfectly-conducting helical thin wire with wire radius r, wire length l, and axis length h. The
particle can be rotated clockwise in the order of toward x, and toward z-axis forθandφdegrees
respectively. The medium is composed of three-dimensional periodic array of the particles
along the coordinates in free space. The periodicity along each coordinate axis is identically d.
Fig. 3 shows the normalized chirality constant at frequencies of 8.0 through 11.0 GHz where
double helix is used for each element, and l=18.75mm, r=0.03mm, h/l=0.14, L/h=1.8, d=2L,
θ=27°, φ=0°. Three diagonal elements of the chirality tensor, averaged absolute valuesof non-diagonal elements, and the averaged absolute values of the electric quadrupole components of each element are plotted. It can be seen that at around 8.5 through 9.0 GHz and higher

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than around 10.5 GHz, three diagonal elements have almost the same values, and non-diagonal
elements and the quadrupole components are very small compared to the diagonal elements,that shows almost perfect isotropic chirality.

Fig. 3Chirality constant for the case of double heilx

3. Conclusion
The number of helices was reduced at the present particle structure by half compared tothat of our previous work i.e. the cubic case. The present simplified particle turned out to beavailable as an almost isotropic chiral one for the limited requirements of frequency region andmagnitude of chiral constant. Pursuing the simpler structures that can coexist with the highquality of isotropy and chirality will be our future work.

References[1] I. V. Lindell el al., Artech House, (1994), pp. 1-18, 193-243.
[2] D. R. Smith et al., Physical Review Letters, Vol. 84, No. 18 (2000), pp. 4184-4187.
[3] M. Asai et al., Materials Integrations, Vol. 25, No. 12 (2012), pp. 31-37.
[4] S. Motojima et al., Applied Physics Letters, Vol. 56, No. 4 (1995), pp.321[5] M. Asai et al., Proc. of JSST Int. Conf. Sim. Tech, Vol. 1 (2019)[6] M. Asai et al., Proc. of ISAP, Vol. 1, (2016), pp. 2C2-20584.
[7] A. Ishimaru et. al., IEEE Trans. Antennas Propag., Vol. 51, No. 10, (2003),
pp. 2550-2557.
[8] A. D. Buckingham et al., J. Chem. Soc.A, (1971), pp. 1988-1991.
[9] I. P. Theron et al., J. Electromag. Waves App. Vol. 10, No. 4 (1996), pp. 539-561.

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An investigation of deflated ICCG method for finite
element analysis of eddy current problem
Kota Watanabe*, Wataru Kotani
Graduate School of Engineering, Muroran Institute of Technology*

k-wata@muroran-it.ac.jp

Abstract. A fast liner solvers for Finite Element Analysis (FEA) using a deflation technique isdiscussed. A deflated Incomplete Cholesky Conjugate Gradient (ICCG) method is introduced
so as to reduce the cost of FEA for electromagnetic devices such as motors. The deflation technique decomposes the solution into fast and slowly components. The slowly components canbe solved by direct methods with low computational cost due to small dimensions. Therefore,
the deflated ICCC method can improve the convergence. The deflated method is applied to a
FEA of eddy current problem as well as magnetostatic problem. Numerical results show thatthe present method can reduce the computational cost of FEA of a synchronous motor.
Keywords: Conjugate gradient method, Deflation method, Eddy current problem

1. Introduction
Finite Element Analyses (FEA) is widely used to evaluate performance of electromagnetic
devices such as motors. Fast linear solvers are an important factor to reduce computational costof FEA. Therefore, it is important to reduce the computational cost in solver process by introducing fast linear solvers.
The deflation technique that replaces small eigenvalues with zeros in the system matrix can
improve the convergence of incomplete Cholesky conjugate gradient (ICCG) method [1][2].
The deflated ICCG requires eigenvectors that have high computational cost to obtain. To solve
this difficulty, simple quasi vectors instead of eigenvectors are introduced. The authors haveapplied the present method to FEA of magnetstatic problem. The numerical results show thatthe present method has good convergence property in comparison with the conventional ICCG
method. In this study, the present method is applied to a eddy current problem.

2. Formulation
Let us consider a system of linear equations Ax = b with n DoF (Degree of Freedom) obtainedby a FEA where A is coefficient matrix, x and b are solution and right hand side vector respectively. The solution x is decomposed into slowly and fast components as

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𝒙 = 𝑊𝒚 + (𝒙 − 𝑊𝒚)where W = [w1 w2 ... wk]ℜ ∈𝑛×𝑘 , 𝒘𝑖 (𝑖 = 1,2, … , 𝑘) ∈𝑛×𝑘 is the eigenvector corresponding
to the i-th eigenvalue. A-orthogonality is imposed on the vectors 𝒘𝑖 to x – Wy results in
WtAWy = WtAx. The slowly converging component Wy can be expressed as
Wy = W(WtAW)-1WtAx≡ 𝑄𝒙(2)where𝑄 ∈𝑘×𝑛 . Moreover, let us introduce the matrix P given by, P = I – Q = I – W(WtAW)-1WtA.
Consequently, the solution x can be expressed as x = Px + Qx. The fast converging component
Px can be obtained by solving APx = PtAx = Ptb. The slowly component Qx is obtained from
Qx = W(WtAW)-1Wtb. The huge computational cost is requires to obtain the eigenvectors 𝒘𝑖 .
To solve this difficulty, quasi eigenvectors 𝒘∗𝑖 which are similar to 𝒘𝑖 are introduced [1].

3. Results
The present method is applied to an Interior Permanent Magnet (IPM) motor based on the
IEEJ D model. The FEA of non-linear magnetstatic problem is performed on a 1/4 model due
to symmetry. A Newton-Raphson method is used to solve non-linear equation. Table I shows aresult for convergence of present method. The result show that the present method has good
convergence in comparison with ICCG method. Results in the eddy current problem are shownin the conference.
Table I Comparison of convergence in magnetostatic problem
deflated ICCG
MethodICCG
with k = 4
Number of total iterations
446
283

References[1] H. Igarashi, K. Watanabe: Deflation Techniques for Computational Electromagnetism:
Theoretical Considerations, IEEE Trans. Magn., 47:5 (2011), 1438-1441.
[2] Y. Saad, M. Yeung, J. Erhel, F. Guyomarch: A deflated version of the conjugate gradientalgorithm, SIAM J. Sci. Comput., 21:5 (2000), 1909-1926.

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JSST 2021

Eulerian coupling simulation methodfor dynamics of air and shock-absorbing structure
Ryohei Katsumata1,* , Koji Nishiguchi1 , Tokimasa Shimada2,3 , Hiroya Hoshiba1 ,Junji Kato1
1 Department of Civil Engineering, Graduate School of Engineering, Nagoya University
2 Department of Computational Science, Graduate School of System Informatics, Kobe

University
3 RIKEN Center for Computational Science, RIKEN∗ katsumata.ryohei@k.mbox.nagoya-u.ac.jp

Abstract. The purpose of this study is to analyze the large deformation of a fractureprevention ﬂoor with a shock-absorbing structure made of rubber-resin mixtures. However,to analyze the coupled phenomena between the structure with large deformation and the air,
it is necessary to consider the interface discontinuity of the mass density and velocity ﬁeld at
the interface between the solid and the ﬂuid. This paper proposes an Eulerian ﬂuid-structureinteraction analysis method that can be used stably even in a ﬁeld where the interface isdiscontinuous and verify its validity and eﬀectiveness.
Keywords: Eulerian ﬂuid-structure interaction, Finite volume method, Large deformation

1.

Introduction

To reduce the number of bone fractures caused by falls among the elderly, which has become a major social problem in recent years, ﬂoor structures that absorb the impact of falls
made of rubber-resin mixtures are being explored. To design a more eﬀective structure forabsorbing the impact of falls, it is necessary to consider the dynamic structural analysis oflarge deformations and the interaction with air. However, conventional structural analysis
using the ﬁnite element method suﬀers from the failure of the Lagrangian mesh due to large
deformations, the time and cost of mesh generation and computation, and the diﬃculty of
ﬂuid-structure interaction analysis considering the eﬀect of air.
In this study, ﬂuid-structure interaction analysis is performed using the Eulerian ﬁnite
volume method based on the Building Cube Method (BCM) [1]-[4], which has been developed by the authors. However, the problem of discontinuities in the mass density andvelocity ﬁelds at the interface between solid and ﬂuid has remained an open issue in previous studies.
Against this background, the purpose of this study is to develop and validate a uniﬁed
Eulerian ﬂuid-structure interaction analysis scheme that can take into account interfacial320discontinuities in the mass density and velocity ﬁelds and verify the eﬀectiveness of thismethod by massively parallel simulations of shock-absorbing structures for preventing fall
fractures.

2.

Numerical method

In this study, the governing equations are the continuity equation and the equation of motion, which are the basic equations in continuum mechanics, volume-averaged in the control
volume [1]. We assume an incompressible neo-Hooke solid as the constitutive equation fora solid and an incompressible Newtonian ﬂuid as the constitutive equation for a ﬂuid [3].
Deﬁne the velocity vector at the cell center and discretize it using the ﬁnite volume
method. In this case, the stress is divided into pressure and deviation stress, and the velocity
and pressure ﬁelds are computed separately using the fractional step method [2][3]. To
avoid numerical diﬀusion due to advection of the interface and internal variables of the solid,
Lagrangian marker particles are used, which not only represent the solid domain explicitly
but also serve to compute the physical quantities of the solid.
Previous studies have used the same mass density between solids and ﬂuids, but in thisstudy, we use an equation that smoothes out the discontinuity in mass density at the interface
by averaging it by volume fraction. In addition, while previous studies have used a secondorder central diﬀerence scheme for the spatial discretization of the advection term, in thisstudy, we use a ﬁfth-order WENO scheme, [5], which has higher accuracy to stably solve
the discontinuous velocity ﬁeld at the interface.

3.

Numerical examples

First, to verify the validity of the method, we analyze the two-dimensional push-in problem
shown in Figure 1. Push the upper rigid body into the deformed body in the plane strainstate without slipping. The physical properties of the solid and ﬂuid are given in Table 1.
A ﬁnite element solution using the commercial solid analysis code LS-DYNA with asuﬃciently ﬁne mesh to which the numerical solution has converged is prepared as a reference solution. Figure 2 compares the deformation diagram and Mises stress distribution at
t = 0.30 ms. From this ﬁgure, it can be conﬁrmed that the solution by the present method isin general agreement with the reference solution.

Table 1: Physical properties
in a two-dimensional
push-in problem.
Solid: incompressible neo-Hookean solid
Mass density ρs [kg/m3 ]1.0 × 103
Young’s modulus E [Pa]1.0 × 106
Viscosity µs [Pa · s]0

Figure 1: Two-dimensional
push-in problem
with rigid bodies.

Fluid: incompressible Newtonian ﬂuid
Mass density ρf [kg/m3 ]1.2
Viscosity µf [Pa · s]
1.8 × 10−5

321a) Reference
800 × 256
elementsb) Present
2048 × 1024
cells

Figure 2: Mises stress distribution
in a push-in problem.
(t = 0.30 ms)

Figure 3 is a graph showing the strain energy time history of the solutions by the present
method using meshes with diﬀerent spatial resolutions and the reference solution by theﬁnite element method. From this ﬁgure, it can be conﬁrmed that the solutions by the present
method have lower values than the reference solution. The stresses and strains were lower
than the actual values due to the overlap of deformed particles in the rigid region.
The next is to analyze the deformation of the fracture prevention ﬂoor shown in Figure
4. Push the upper rigid body into the deformed body without slipping. The solid is assumed
to be a rubber-resin mixture and the ﬂuid is assumed to be air at 20◦ C. The properties shownin Table 2 are given. A hierarchical Cartesian mesh with a minimum cell size of about 0.35mm and a total cell number of 11,190,272 is used, and the analysis time is up to 1.8 ms.

Strain energy [J]3.0

Reference

512×256 cells

128×64 cells

1024×512 cells

256×128 cells

2048×1024 cells

Table 2: Physical properties
in the analysis of
fracture prevention ﬂoor.

2.0

Solid: incompressible neo-Hookean solid
Mass density ρs [kg/m3 ]1.0 × 103
Young’s modulus E [Pa]3.0 × 107
Viscosity µs [Pa · s]
1.8 × 10−5

1.0

0.0
0

0.1

0.2

0.3

Time [ms]Figure 3: Time history of strain energy.

Figure 4: Analysis of
fracture prevention ﬂoor.

Fluid: incompressible Newtonian ﬂuid
Mass density ρf [kg/m3 ]1.2
Viscosity µf [Pa · s]
1.8 × 10−5

Figure 5 shows the deformation and Mises stress distribution in the deformation analysis
of a fracture prevention ﬂoor. It can be conﬁrmed that the coupled problem between the air
and the structure, which undergoes large deformation, can be computed stably. Figure 6
is the distribution of the velocity ﬁeld. It can be conﬁrmed that air with a velocity about
10 times faster than the pushing velocity of the rigid body is ﬂowing out from the gap of
the deformed body. Figure 7 is the distribution of the pressure ﬁeld. It can be conﬁrmedthat there are areas where high pressure of more than 1 MPa is generated. Considering the
thickness of the structure (about 2-3 mm) and Young’s modulus (30 MPa), these eﬀects
cannot be neglected, suggesting that the interaction between the structure and the air is astrong phenomenon.

Figure 5: Deformation andMises stress distribution.
(t = 1.8 ms)(a) t = 0.9 ms(a) t = 0.9 ms(b) t = 1.4 ms(b) t = 1.4 ms(c) t = 1.8 ms(c) t = 1.8 ms

Figure 6: Distribution of
the velocity ﬁeld.

322

Figure 7: Distribution of
the pressure ﬁeld.

4.

Conclusion

In this study, we proposed a uniﬁed Eulerian ﬂuid-structure interaction analysis method thattakes into account the interfacial discontinuities in the mass density and velocity ﬁelds bymodifying the volume averaging of the mass density and the spatial discretization schemeof the advection terms. Then, the validity of this method was veriﬁed through a twodimensional push-in problem, and the eﬀectiveness of this method was veriﬁed throughthe analysis of a fracture prevention ﬂoor. Future work includes modiﬁcation of the velocity
boundary condition with a rigid body and quantitative comparison of the load-displacement
curves with experiments.

References[1] Nishiguchi, K., Okazawa, S., Tsubokura, M.: Multimaterial Eulerian ﬁnite element
formulation for pressure-sensitive adhesives, International Journal for Numerical
Methods in Engineering, 114:13 (2018), 1368-1388.
[2] Nishiguchi, K., Okazawa, S., Tsubokura, M.: Fully Eulerian solid-ﬂuid interaction
analysis using hierarchical Cartesian mesh method for large-scale parallel computing,
Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics), 73:2 (2017),
153-163.
[3] Nishiguchi, K., Bale, R., Okazawa, S., Tsubokura, M.: Full Eulerian deformablesolid-ﬂuid interaction scheme based on building-cube method for large-scale parallel computing, International Journal for Numerical Methods in Engineering, 117:2(2019), 221-248.
[4] Nishiguchi, K., Okazawa, S., Tsubokura, M.: Implicit particle-in-cell formulation
for incompressible solid-ﬂuid interaction problem, Journal of Japan Society of Civil
Engineers, Ser. A2 (Applied Mechanics), 74:2 (2018), 253-263.
[5] Liu, X.D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes, Journalof Computational Physics, 115:1 (1994), 200-212.

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Coupled analysis for active control and energy
harvesting from ﬂow-induced vibration
Shigeki Kaneko1,* and Shinobu Yoshimura1
1 Department of Systems Innovation, School of Engineering, The University of Tokyo∗ s kaneko@save.sys.t.u-tokyo.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.1

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Finite element approach to
fluid-structure interaction with contact
Tomohiro Sawada1*, Junichi Matsumoto1
Continuum Simulation Team, Research Center for Computational Design of Advanced Func-

1

tional Materials, National Institute of Advanced Industrial Science and Technology*tomohiro-sawada@aist.go.jp

Abstract. Fluid-structure interaction with contact of structures is one of the challenging issues
in computer simulation. We present a direct numerical simulation method for the FSI withcontact based fully on a finite element method. Two applications to the sedimentation and mixing of elastic capsules are shown.
Keywords: Computer simulation, Finite element method, Fluid-structure interaction, Contact

1. Introduction
Fluid-structure interaction (FSI) that involves contact of structures is one of the challenging
issues in computer simulation. It is still good if there are few structures, but if there are many,
it is necessary to compute multiple contacts between structures while computing fluid flow
between the structures. Furthermore, structures may be deformed by fluid and contact forces.
This paper presents a method based on a finite element method (FEM) that can handle all ofthese problems. The present method is a method that incorporates implicit contact computation
into the interface-reproducing capturing (IRC) method for FSIs proposed in [1-4]. Section 2
briefly describes the computational method. Section 3 shows two examples of computing thesedimentation and mixing of elastic particles/capsules by the method.

2. Method
The present method is summarized as follows:
Motion of the structures including deformation is computed with Lagrangian meshes thattrack the structures. Flow of the fluid is computed with a Eulerian mesh fixed in space.

By applying the extended finite element method (XFEM [5,6]) to the fluid elements atinterface between fluid and structures, requisite discontinuities at the interface are reproduced, and thus the overall spatial convergence is enhanced [1-4].
Equilibrium at the fluid-structure interfaces is computed by a novel stabilized Lagrangemultiplier method embedded on surface of the structures with a stabilization term.
Contacts of the structures in the fluid are computed by a two-pass approach based on apenalty method that inserts nonlinear springs at structural elements near contact.
After finite element discretization, a nonlinear monolithic matrix equation is obtained. We

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solve the monolithic equation as monolithic. The Newmark-β method is employed to theequation for a time integration scheme, and the Newton-Raphson method is employed tofind a numerical solution of the nonlinear equation [3,4].
We adopted the completely implicit and monolithic method so that it can solve hard contact
problems.

3. Applications
Figure 1(a) shows a two-dimensional application to finite element simulation of sedimentationof eighteen very soft capsules under gravity in a usual incompressible viscous water [7]. Figure1(b) shows another application to mixing of nine very soft capsules in a shear flow of a very
thick Bingham fluid [7].

(a) Sedimentation of eighteen elastic capsules.
(b) Mixing of nine elastic capsules.
Fig.1 Two applications of the proposed method to fluid-structure interaction with contact.

Reference[1] T. Sawada, A. Tezuka: High-order Gaussian quadrature in X-FEM with the Lagrangemultiplier for fluid-structure coupling, Int. J. Numer. Meth. Fluids, 64 (2010), 1219-1239.
[2] T. Sawada, A. Tezuka: LLM and X-FEM based interface modeling of fluid-thin structureinteractions on a non-interface-fitted mesh, Comput. Mech., 48 (2011), 319-332.
[3] T. Sawada: Interface-Reproducing Capturing (IRC) Technique for Fluid-Structure Interaction: Methods and Applications, In: T. Tezduyar (eds), Frontiers in Computational
Fluid-Structure Interaction and Flow Simulation, Modeling and Simulation in Science,
Engineering and Technology, Birkhäuser, Cham, (2018).
[4] T. Sawada, M. Kondo, J. Matsumoto: Computation of Fluid Inertial Term in XFEM for
Fluid-Structure Interaction, Transactions of JSCES, Paper No. 20200004 (2020), 1-15
(in Japanese Language).
[5] N. Moës, J. Dolbow, T. Belytschko: A finite element method for crack growth without
remeshing, Int. J. Numer. Meth. Engng., 46:1 (1999), 131-150.
[6] T. Belytschko, N. Moës, S. Usui, C. Parimi: Arbitrary discontinuities in finite elements,
Int. J. Numer. Meth. Engng., 50:4 (2001), 993-1013.
[7] T. Sawada: Direct Numerical Simulation Techniques for Fluid-Structure Interactions,
Journal of Japanese Society of Tribologists, 65:11 (2020), 672-677 (in Japanese Language).

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Locomotion Control of Snake-like Robot utilizing
Friction Forces: Feasibility Veriﬁcation via Two
Wheeled Robot
Shunsuke Nansai1,* and Hiroshi Itoh1
1 Department of Advanced Machinery Engineering, School of Engineering, Tokyo Denki

University∗ nansai@mail.dendai.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.113

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Degradation diagnosis of Lithium-ion batteriesconsidering operation temperature
TODA Kousuke1 , ODAGAKI Yuuki1,* , KAMAMICHI Norihiro1 , IWASE
Masami1 , SATOH Yasuyuki1
1 Department of Simulation, School of Technology, Tokyo Denki University∗ odagaki@ctrl.fr.dendai.ac.jp

Abstract. This paper proposes a simulation method for a fractional derivative system representing the dynamics of lithium-ion batteries. The transfer function of the general lithiumion battery dynamics has non-integer derivative terms. Therefore the fractional calculus is
introduced for the simulation method. As a result, a fractional-order state-space representation is derived reducing the modeling approximation. In the representation, the systemorder may change according to the batteries’ operation, and it causes the system matrix sizechange. Therefore we propose a method to determine α that reduces the size of the system
matrix when deriving a fractional state-space model.
Keywords: Computer simulation, Li-ion-Battery, temperature, State-Of-Charge

1.

Introduction

Lithium-ion batteries have a risk of accidents due to ignition as they deteriorate, so it isnecessary to predict and diagnose deterioration in advance in a non-destructive manner.
However, since the characteristics of LIB change depending on the temperature, it has a great
influence on the deterioration diagnosis. Therefore, in this study, the change characteristics
due to temperature are evaluated using a detailed LIB model. At the same time, the eﬀect
on deterioration is analyzed.
Fractional calculus is an extension of integer calculus to real calculus, and the expression of
fractional calculus can be used to give solutions to actual physical problems, or conventional
calculus can be modeled. It is known that it is possible to model what was diﬃcult [1]. The
electrical response of LIB is aﬀected by the ion diﬀusion phenomenon as a concentration
overvoltage, and the model derived from this equivalent circuit can also be modeled by afractional derivative system.
Zhang et al. Confirmed that the parameters of the equivalent circuit model change withtemperature [2]. From this, the fractional model changes depending on the temperature,
which may aﬀect the time response.

334

2.

Real time respnse simulation

The real-time response simulation method and results for a temperature of LIB are described.

2.1.

Fractional derivative system

Frequency transfer function of LIB contains Constant Phase Elements(CPE) index α, which
is non-integer number and Warburg impedance √1jω , which is fractional value. From this,it sure that transfer function of LIB is expressed as fractional derivative system instead ofusual diﬀerentiation system.
In order to simulate the real-time response of this fractional derivative system, in the previous research, LIB was represented by a fractional state-space model using Caputo’s fractional calculus. The fractional state-space model is represented
1

D m x(t) = Ax(t) + Bu(t)(1)y(t) = Cx(t) + Du(t).

(2)

And this solution orbit is1mx(t) = E 1 ,1 (At )x(0) +
m

∫ t
0

(t − τ) m −1 E 1 , 1 (A(t − τ) m )u(τ)dτ.
1

1

m m

(3)

Next, in order to consider the exogenous input, consider a spreading system that adds astate to the input, and let it be1

D m = Ā x̄(t).
Satisfy the following conditions. x̄, Ā are
[
]
[
]
x(t)
A B
x̄(t) =, Ā =
.
u(t)
0 0

(4)

(5)

The solution orbit of this expansion system isρ1x̄(t) = E 1 (Āt m ) x̄(0).
m ,1

(6)

However, Eα,β (z) is a 3-parameter Mittag-Leﬄer function. The function is a generalizationof the exponential function. That function can be expressed asρEα,β (z) =∞∑(ρ)k zk.
Γ(αk + β) k!
k=0

(7)

It is necessary to apply the 3-parameter matrix Mittag-Leﬄer function after transforming it
into the Jordan normal form since this system has duplicate eigenvalues.The function is
Eα,β (z) = Pdiag(Eα,β (J 1 )), (Eα,β (J 2 )), · · · , (Eα,β (J s ))P−1 .

(8)

It is possible to simulate without divergence by the exact calculation of the infinite series ofEα,β (J k ).

335

2.2.

Derivate a fractional state-space model of LIB

We derivate a fractional state-space model of LIB. The fractional order is determined fromthe least common multiple of CPE index α and √1jω , which is the denominator of Warburg
impedance. The CPE index α at 10 degrees Celsius and the value when approximated to a
fraction are as α = 0.572 ≒ 35 .

2.3.

Simulation

It was confirmed that the calculation time changed significantly because the system matrix
changed due to the change in the diﬀerential structure. The size of the system matrix andthe simulation time for the value of α are as follows. Under condition α = 34 , 1 hour and 6
minutes or more. 37 hours or more under condition α = 23 . The execution did not end andthe simulation did not complete under condition α = 35 .
In this study, in order to solve this problem, we propose a method to fix the diﬀerential
structure. The fractional order is determined by approximating the CPE index, which is adecimal, to some extent. Therefore, we think that the same diﬀerential structure can be usedby expanding the allowable range of approximation. This time, in order to reduce the sizeof the system matrix, the real-time response is simulated with the CPE index α = 34 . The
fractional state-space model can be derived as 0 0
A =  0
 0

0

2.4.

1
0
0
0
0

0
1
0
0
1
T R1

0
0
1
0
0

 √2σ T  T R 
0 
0


 
1

 0 0 
 0 
[
]


 

0  , B =  0  , C =  1  , D = R0 .
 
 √T  0 1 
 2σ 
 



0
1
0

(9)

Simulation results at 10 degrees Celsius

The real-time response simulation results of the state x and the output y at 10 degrees Celsius
are shown in Fig. 1, Fig. 2. The simulation time was 0.5 s and the sampling time was 0.025
s.

Figure 1: Real-time response simulation of Figure 2: Real-time response simulation of
output ystate x336

From Fig. 1, it can be confirmed that the input is 1, so it is a step response. It was
confirmed that the change in state x5 was the largest among the states. From Fig. 2, it canbe confirmed that the step response can be output. Here, we compare the real-time response
obtained in the previous section with the simulation. A comparison is shown in Fig. 3.

Figure 3: Real-time response and simulation of output voltage
As shown in Fig. 3, it can be confirmed that the real-time response and the rise timeof the simulation are similar. However, there is a diﬀerence of about 0.05 V for the steadystate value, which shows that the simulation is higher. It can also be confirmed that there isa diﬀerence of about 0.01V from the steady value of α = 34 .

3.

conclusion

It was confirmed that the size of the system matrix of the fractional derivative system of
LIB changes depending on the value of α. It was confirmed that there is a problem that thecalculation time becomes long when the size of the system matrix is large. As a solution tothis problem, we proposed a method of deriving a fractional state-space model by deciding
on α to reduce the size of the system matrix. As a result of simulating the real-time response,
the steady-state deviation was larger than that of the previous research method. Let us
consider the cause of this.
The possible cause is that the initial values of the fractional terms are diﬀerent from theactual model. The initial values of the fractional-order terms of the current fractional-orderstate-space model are all set to 0 for simulation. The reason is that it is possible to give
physical meaning to terms of integer order, but it is diﬃcult to give physical meaning toterms of fractional order. Although this problem has not been solved, we think that we canderive an integer derivative system from the real-time response of LIB and identify the initialvalue of the fractional state-space model from that system.

References[1] Igor Podlubny: Fractional Diﬀerential Equations, 198:1 (1999), 41-75.
[2] S.S.Zhang, K.Xu,T.R.Jow: Electrochemical impe-dance study on the low temperatureof Li-ion batteries, 49:Issue 7 (2004), 1057-1061.

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Analysis of electrostatically induced current in
humans when in contact with a stepladder underpower transmission lines
Yuta Ishida1*、Shoji Hamada1
Kansai University

1

k616258@kansai-u.ac.jp

Abstract. We numerically analyzed the short-circuit current flowing from the bare feet of avoxel human model to the ground when standing under power transmission lines and in contact
with an ungrounded conductive stepladder model with its left hand. A 50 Hz AC electric fieldof 3 kV/m was vertically applied to the model, and the short-circuit current was analyzed for
different heights of the stepladder, ranging from 2–10 m. In addition, the stepladder height wasestimated when the short-circuit current exceeded the reference levels specified in the international guidelines for the general public and occupational workers.
Keywords: Electrostatically induced current, Voxel model, Human model, Short-circuit current

1. Introduction
When a human body is in close proximity with high-voltage equipment such as power transmission lines, short-circuit currents are electrostatically induced in the body from exposure tocommercial frequency AC electric fields [1], [2]. The induced currents could cause anxiety anddiscomfort in the general public, and health issues in occupational workers. Therefore, to prevent such situations, the International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines have specified reference levels of such as contact currents [3]. To maintain thecurrents below the specified reference levels, induced currents have been widely studied
through numerical analysis using numerical human models. We have previously analyzed thecurrent induced in simple human voxel models holding a conductive umbrella, bat, plate, fishing rod, and so on [4]. In this study, we analyzed the currents induced in a human model standing
under power transmission lines in contact with an ungrounded conductive stepladder with its
left hand. To estimate the maximum short-circuit current value, we assumed the human model
to be standing barefoot on the ground. The short-circuit current was analyzed for different
heights of the stepladder, varying from 2–10 m. Furthermore, we estimated the stepladderheights when the short-circuit current reached the reference levels specified in the ICNIRP
guidelines. Note that we only investigated the steady-state AC currents and not transient currents.

2. Methods
Figures 1 (a) and (b) show the two analysis models of this study. The 165.6 cm tall humanvoxel model is grounded and in contact with the stepladder voxel model with its left hand, andis exposed to a uniform electric field of 3 kV/m (= regulation value of the electric field undertransmission lines in Japan) generated by the transmission lines present several tens of meters
above the ground. The voxel size was set to 0.9 cm, and the model shapes were expressed in

338

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spheres, cylinders, and partial cylinders. Further details are listed in Table 1. The shape of the
top board of the stepladder is shown in Figure 1 (c), and a three-view drawing of the stepladderin Figure 1 (a) is shown in Figure 1 (d). The stepladder voxel model was a combination ofcylinders with a diameter of 5.4 cm, excluding the top board. The stepladder was assumed to
be floating 9 cm (= 10 voxels) above the ground to simulate ungrounded conditions. The heightof the stepladder (from the ground to the top board) was changed from 2 m to 10 m in 1 m
increments, and the corresponding short-circuit current values were calculated. The 10 m tall
stepladder had a width and depth of 1.75 m and 5.50 m, respectively, and the vertical separation
between the rungs was 28.8 cm for all stepladders. The short-circuit current was calculatedusing the voxel-based fast multipole surface charge simulation method [2], [5]. The reference
level of the 50 Hz contact current is 500 µA and 1000 µA for the general public and occupational workers, respectively [3].

Fig. 1. (a) The human model next to a 10 m stepladder, (b) The human model next toa 2 m stepladder, (c) The dimensions of the top board of the stepladder, and (d) The
three-view of the stepladder in (a).

Table 1. Shape of body parts, dimensions, and coordinates of the human voxel model.

339

JSST2021

3. Results

The calculated electric field distribution, and short-circuit currents versus the height of the
stepladder, H, are shown in Figures 2 and 3, respectively. The distribution of the absolute electric field |E| is depicted on the x-z cross-section at y = 3.6 m, and on the y-z cross-section at x
= 2.34 m. The red region indicates a strong electric field, and the upper section of the stepladderfalls under this region, owing to the electric charges induced on the upper surface of the stepladder and the human model. Conversely, the electric field distribution under the stepladder ornear the ground becomes weaker than the applied electric field. In Figure 3, the black circles
represent the currents calculated using the surface charge simulation method, and the solid
curve represents the currents calculated by the quadratic function obtained from the leastsquares fitting, represented as
I[µA] = 22.64 + 17.14H + 11.16H 2. ・・・(1)The difference between the numerical analysis and the fitting curve, indicated by black dots
and solid lines in Figure 3, respectively, ranged from -1.13% to 0.54%. It is known that theFig. 2. Electric field distribution around the 10m stepladder.

Fig. 3. Short-circuit current versus the heightof the of the stepladder.

340

Fig. 4. Half-reduced rungs model.

JSST2021
short-circuit current running through the human model is proportional to the square of the human’s height when the model is exposed to a vertical uniform electric field [1]. Therefore, asimilar relationship appears in the stepladder model, as seen in Figure 3. According to the fitting
equation (1), the ground current reaches 500 µA and 1000 µA when H is 5.81 m and 8.62 m,
respectively. Futhermore, we calculated the short-circuit current when the spacing of stepladderrungs was doubled as shown in Figure 4. The calculated short circuit currents are plotted as whitecircles and a dashed line in Figure 3. The white circles are 1.06% to 2.20% smaller than the black
circles. Similar to the fitting equation (1), the dashed line is represented as
I[µA] = 22.62 + 17.22H + 10.87H 2. ・・・(2)The fluctuation of the short circuit current at the actual rung spacing would be smaller than thesefluctuation levels. Therefore, the dependence of the short circuit current on the rung spacing is muchless than its dependence on the height.

4. Summary
In this study, we quantitatively calculated the short-circuit current of a grounded human modelin contact with an ungrounded conductive stepladder model with its left hand when exposed toa 50 Hz uniform AC electric field of 3 kV/m under transmission lines. The calculated shortcircuit current was approximated by a quadratic equation of the stepladder height H, and thefitting coefficient was calculated using the least squares method. The quadratic equation could
express the short-circuit current within a difference of -1.13% to 0.54%. The height of the
stepladder was 5.81 m and 8.62 m when the short-circuit current reached the reference levelsof contact current for the general public and occupational workers, respectively, specified by
ICNIRP. The estimated short-circuit currents can be proportionally altered in different frequencies and applied electric fields. In future research, we plan to consider the non-uniformity ofthe electric field distribution and to use detailed anatomical human models to analyze the shortcircuit current.

References[1] H. Tarao, N. Hayashi, K. Isaka, Estimation of short-circuit current induced by ELF uniform electric fields in grounded humans with different body shapes based on a semiellipsoidal model, Biomed. Phys. Eng. Express, 6 (2020), 055012.
[2] S. Hamada, Calculation of electrostatically induced electric fields in human models using a two-step process method of voxel-based fast multipole surface charge simulation
method, IEEJ Trans. FM, 140:10 (2020), 481-490 (in Japanese).
[3] International Commission on Non-Ionizing Radiation Protection Guidelines for limiting
exposure to time-varying electric and magnetic fields (1 Hz to 100 kHz), Health Phys.,
99 (2010), 818-836.
[4] Y. Ishida, S. Hamada, Short-circuit current analysis of simple human voxel model holding conductive plate and rod, 2020 annual conference of FM IEEJ, 2-C-p2-3 (2020), (inJapanese).
[5] S. Hamada, T. Kobayashi, Analysis of electric field induced by ELF magnetic field utilizing fast-multipole surface-charge-simulation method for voxel data, IEEJ Trans. FM,
126:5 (2006), 355-362 (in Japanese).

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Eﬀects of the number of observations on 4D-Var data
assimilation: preliminary experiments
Yasuyoshi Horibata
Faculty of Science and Engineering, Hosei University∗ horibata@hosei.ac.jp

Abstract. This paper presents preliminary numerical experiments for eﬀects of the numberof observations on 4D-Var data assimilation. A simple equation of thermal conduction isconsidered. The source program which simulates the heat conduction is diﬀerentiated inreverse mode by automatic diﬀerentiation tool to generate the adjoint program. In optimization, the gradient of a cost function is computed by the adjoint program.
Keywords: Variational data assimilation, Automatic diﬀerentiation, Adjoint program, Optimization

1.

Introduction

Four-dimensional variational (4D-Var) data assimilation is an extension of the three-dimensionalvariational (3D-Var) data assimilation; it allows for observations distributed within a time interval. The cost function is a summation over time of the cost function for each observational
increment computed with respect to the model integrated to the time of the observation. The
control variable (the variable with respect to which the cost function is minimized) is theinitial state of the model. The optimization algorithm requires the gradient of the cost function with respect the control variable. The adjoint program is used in order to compute thegradient eﬃciently.
In [1], we considered 4D-Var meteorological data assimilation. We improved the differentiability of the source program that simulates the three-dimensional atmospheric flow,
and diﬀerentiated it by the automatic diﬀerentiation tool TAPENADE [2]. The generated
tangent and adjoint program were validated by the dot product test. Numerical experiments
ware presented for data assimilation for a downburst; the downburst is a strong downdraft
which induces an outburst of damaging winds on or near the ground.
In the present paper, we present preliminary numerical experiments for eﬀects of thenumber of observations on 4D-Var data assimilation. We deal with a simple heat equation
where temperature varies only in one space dimension. For the sake of simplicity, we assume
no observation and background errors.

342

2.

Heat equation

We consider the heat equation
∂T
∂2 T
=α 2
(0 < x < L, t > 0)
(1)
∂t
∂x
This governs the time-dependent temperature distribution in a homogeneous constant property solid under conditions where the temperature varies only in one space dimension. Consider a large wall of thickness L. The faces of the wall continue to be held as 0◦ C.
The spatial derivative is approximated using the central-diﬀerence scheme and the gridis uniform in x-direction. The explicit Euler method is used in order to integrate it. The newtemperature value, T in+1 , is:
where

n
n
T in+1 = dT i−1+ (1 − 2d)T in + dT i+1

d=α

∆t
(∆x)2

(2)
(3)

Let L = 1m, α = 0.02m2 /h. We use ∆x = 5 × 10−3 m and ∆t = 2.25 sec. Figure 1 shows theobtained evolution of the temperature field.
We use some values of the temperature field as observations.

Figure 1: Evolution of the temperature field.

3.

Data assimilation

We generate the adjoint program of the simulation program by using TAPENADE.
We use 8 time levels as observation times: 37.5 min (1000∆t), 75 min (2000∆t), 112.5
min (3000∆t), 150 min (4000∆t), 187.5 min (5000∆t), 225 min (6000∆t), 262.5 min (7000∆t),
and 300 min (8000∆t). Using the observations T i,1000∗k, the cost function is defined as
o
8

J=

#2
1 ! !" 1000∗kTi− T i,1000∗ko
2 k=1 i343

(4)

Three cases are considered for the number of observation points: 199 (i = 1, 2, . . . , 199), 9(i = 20, 40, 60, 80, 100, 120, 140, 160, 180), and 2 (i = 65, 135) grid points.
Usually, in 4D-Var data assimilation, the optimization problem has thousand or millions
control variables [1]. Hence, we use the modified L-BFGS-B algorithm [3] in order to solve
the problem. Stating from the initial guess, the algorithm repeats search until it reaches
the optimal point. Figure 2 shows the initial guess. Figures 3, 4, and 5 show the convergence histories of the optimization and the estimated fields for 199, 9, and 2 grid points,
respectively.

Figure 2: The temperature field of the starting point used for the optimization.

4.

Conclusions

We use observations at 8 time levels and 199, 9, 2 grid points. The estimate obtained fromobservations at 199 grid points is almost identical with the truth. The estimates obtained
from observations at 9 and 2 grid points agree reasonably with the truth. The cost functions
decrease unsatisfactorily in both cases. More eﬃcient algorithm is required for solving large
optimization problems.

References[1] Yasuyoshi Horibata, Y.: Validation of diﬀerentiated programs and their application todata assimilation, Proceedings of the 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics(ECFD 7), June 11-15, 2018, Glasgow, UK, Edited by: Roger Owen, René de Borst,
Jason Reese and Chris Pearce (2018), 1325-1339.
[2] Laurent Hascoet, Valerie Pascual: TAPENADE 2.1 user’s guide, INRIA, France, 2004.
[3] J. L. Morales, J. Nocedal: Remark on Algorithm 778: L-BFGS-B: Fortran subroutines
for large-scale bound constrained optimization, ACM Transactions on Mathematical
Software, 38 (2011), Article 7.

344

Figure 3: Convergence history of the optimization (left) and the estimated temperature field(right) for 199 grid points.

Figure 4: Convergence history of the optimization (left) and the estimated temperature field(right) for 9 grid points.

Figure 5: Convergence history of the optimization (left) and the estimated temperature field(right) for 2 grid points.

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JSST 2021

Rate of double strand breaks of genome-sized DNA intritiated water: dependence on tritium concentration,water temperature, and DNA concentration
Yuji Hatano1,* , Hiroto Shimoyachi2 , Tatsya Asano2 , Takahiro Kenmotsu3 ,Takuro Wada4 , Yasuhisa Oya4 , Hiroaki Nakamura5 , Susumu Fujiwara6
1 Hydrogen Isotope Research Center, University of Toyama
2 Graduate School of Science and Engineering, University of Toyama
3 Faculty of Life and Medical Sciences, Doshisha University
4 Graduate School of Integrated Science and Technology, Shizuoka University
5 National Institute for Fusion Science
6 Faculty of Materials Science and Engineering, Kyoto Institute of Technology∗ hatano@ctg.u-toyama.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.198

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Tritium-induced damage on polymers and biopolymers: Molecular dynamics simulations and theoretical calculations
Susumu Fujiwara1*, Haolun Li1, Ryuta Kawanami1,2, Kazushi Terakawa1,
Tomoko Mizuguchi1, Hiroaki Nakamura3,4, Yoshiteru Yonetani2, Kazumi Omata5,6,
Seiki Saito7, Takuo Yasunaga8, Ayako Nakata9, Tsuyoshi Miyazaki9, Takao Otsuka10,
Takahiro Kenmotsu11, Yuji Hatano12, Shinji Saito13
1

2

Kyoto Institute of Technology
National Institute for Quantum and Radiological Science and Technology
3
National Institute for Fusion Science
4
Nagoya University
5
National Center for Global Health and Medicine
6
Kumamoto University
7
Yamagata University
8
Kyushu Institute of Technology
9National Institute for Materials Science
10
RIKEN Center for Biosystems Dynamics Research
11
Doshisha University
12
University of Toyama
13
Institute for Molecular Science*fujiwara@kit.ac.jp

Abstract. Molecular dynamics (MD) simulations and theoretical calculations are carried out
to study the tritium-induced damage of polymers and biopolymers. We deal with several topics
related to the tritium-induced damage: (i) MD simulations of structural change of polymers andDNA by decay effect in which chemical bonds break by beta decay of substituted tritium tohelium-3, (ii) MD simulations of structural change of DNA by indirect action in which tritiuminduced or radiation-induced hydroxyl radicals damage DNA, and (iii) theoretical calculationsof structural change of polymers by decay effect based on the linear response theory. In thispaper, we briefly introduce these results.
Keywords: Molecular dynamics simulation, Polymer, Biopolymer, damaged DNA, Tritium

1. Introduction

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JSST2021
Tritium is a radioactive isotope of hydrogen and disintegrates to helium-3 by beta decay withemissions of a beta-ray and an antineutrino with a half-life of 12.323 years [1,2]. Beta rays may
cause damage on polymers and biopolymers both directly (known as direct action) and indirectly (known as indirect action). Moreover, if substituted tritium in polymers and biopolymers
decays to helium-3, their structure may be changed by breaking chemical bonds, which is called
decay effect. Tritium-induced damage on polymers and biopolymers include the damage byindirect action of free radicals or active oxygen generated by the tritium beta decay and that by
decay effect of substituted tritium of polymers and biopolymers.

2. Our research topics
Our research topics cover several ones related to the tritium-induced damage on polymers andbiopolymers:(i)

MD simulations of structural change of polymers and DNA by decay effect in which
chemical bonds break by beta decay of substituted tritium to helium-3 [3-6],(ii)

MD simulations of structural change of DNA by indirect action in which tritium-induced or radiation-induced hydroxyl radicals damage DNA,(iii)

theoretical calculations of structural change of polymers by decay effect based on thelinear response theory.

In the talk, we give a brief introduction to these results.

References[1] Tritium: Fuel of Fusion Reactors, edited by T. Tanabe (Springer Japan, 2017).
[2] P. C. Souers, Hydrogen Properties for Fusion Energy (University of California Press,
California, 1986).
[3] S. Fujiwara, H. Nakamura, H. Li, H. Miyanishi, T. Mizuguchi, T. Yasunaga, T. Otsuka,
Y. Hatano, S. Saito, Computational strategy for studying structural change of tritiumsubstituted macromolecules by a beta decay to helium-3, J. Adv. Simul. Sci. Eng., 6:1(2019), 94-99.
[4] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, T. Yasunaga, T. Otsuka, T.
Kenmotsu, Y. Hatano, and S. Saito, Structural change of tritium-substituted polymeric materials by a beta decay: A molecular dynamics study, Plasma FusionRes., 14 (2019), 3401106.
[5] H. Nakamura, H. Miyanishi, T. Yasunaga, S. Fujiwara, T. Mizuguchi, A. Nakata, T.
Miyazaki, T. Otsuka, T. Kenmotsu, Y. Hatano, S. Saito: Molecular dynamics study on
DNA damage by tritium disintegration, Japanese J. Appl. Phys., 59 (2019), SAAE01.

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JSST2021[6] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, A. Nakata, T. Miyazaki and S.
Saito, Structural change of damaged polyethylene by beta-decay of substituted
tritium using reactive force field, Jpn. J. Appl. Phys., 60 (2021), SAAB06.

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Eﬀect of tritium β decay in deoxy-D-ribose on duplex
of telomeric DNA
Kento Ishiguro1,* , Hiroaki Nakamura1,2 , Takuo Yasunaga3 , Susumu fujiwara4 ,Tomoko Mizuguchi4 , Ayako Nakata5 , Tsuyoshi Miyazaki5 , Takahiro Kenmotsu6 ,Yuji Hatano7 , Shinji Saito8 , Yoshiteru Yonetani9
1 Department of Electrical Engineering, Nagoya University, 2 National Institute for Fusion

Science, 3 Kyushu Institute of Technology, 4 Kyoto Institute of Technology, 5 National
Institute for Materials Science, 6 Doshisha University, 7 University of Toyama, 8 Institute for
Molecular Science, 9 National Institutes for Quantum and Radiological Science andTechnology∗ naka-lab@nifs.ac.jp

Abstract. We conﬁrm the relationship between the number of tritium substitutions for hydrogen in DNA and the occurrence of double strand breaks (DSBs) by using MD simulation.
As the result, to induce DSB by the decay eﬀect, it is necessary to damage the DNA with alarge number of decays.
Keywords: Molecular dynamics simulation, Double strand break, Telomeric DNA, Tritium

1.

Introduction

Tritium is known as a fuel of nuclear fusion power generation. Tritium becomes helium-3(3 He) and β-electron (β-radiation) when it decays. The energy of β-ray, emitted from tritium,is small (≤ 18.6 keV), so there is little eﬀect on the human body from external exposure[1].
Therefore, the main problem is the damage caused by internal exposure.
One of the major damages that DNA suﬀers from internal exposure to radiation isdouble-strand breaks (DSBs). It can be repaired, but it can also lead to cell death or cell
cancer. In tritium’s β-decay, there is three diﬀerent processes damage DNA, called direct
eﬀect, indirect eﬀect, and disintegration eﬀect. In the research by a single molecule observation (SMO), the inﬂuence of the disintegration eﬀect has not been clariﬁed. We conﬁrm
the relationship between the number of tritium substitutions for hydrogen in DNA and theoccurrence of DSBs by using MD simulation[8, 9, 10, 11].

2.

Molecular dynamics simulation

By using telomeric DNA (d (TCTAGGGTTAGGGTTAG)2 ) in 3SJM[2], we prepared theinitial structure as (Fig. 1). The size of simulation box is 100 Å × 100 Å × 100 Å.

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Figure 1: Simulation model. A telomeric DNA structure is surrounded by water moleculesand charge neutralized by sodium and chloride ions.
We use Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)[3][5][6]as the MD code, and a kind of reactive force ﬁeld [4][7]. Under the conditions of 310 K and1 atm, DNA is shaken around in the box. The hydrogen at the 5’ and 5” positions of themain strand was replaced by tritium (Fig. 2), and the decay to helium-3 was simulated as if
the replaced hydrogen had been removed.

Figure 2: A part of DNA (the base is guanine). Two blue circles indicate the 5’ and 5”hydrogens, which are replaced by tritium.

3.

Results

As a result, in the case of hydrogen removal at seven bases each in both main strands, it was
divided into at least two fragments, and into at least three fragments in the case of removal
at all bases (Fig. 3). No cleavage occurred in the case where one base was removed fromeach of the two main chains, as in the case of removal at no base (Fig. 4).

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Figure 3: Simulation results. The left ﬁgure is the case of hydrogen removal at seven basesin each strand (total 28 hydrogen are removed). DSBs occurs with the red dotted line. The
right ﬁgure is the case of removal at all bases (total 68 hydrogen are removed). DSBs occur
with the red and white dotted line.

Figure 4: Simulation results. The left ﬁgure is the case of hydrogen removal at one base ineach strand (total 2 hydrogen are removed). The right ﬁgure is the case that no hydrogen isremoved. In both cases, DSBs does not occur.

4.

Conclusion

In order to induce DSBs by the decay eﬀect, it is necessary to damage the DNA with a large
number of decay pairs.

Acknowledgments
The research was supported by Grants-in-Aid for Scientiﬁc Research (C), Nos.18K11416,
19K03800 and 21K19845 from the Japan Society for the Promotion of Science, and by the354

NIFS Collaborative Research Programs NIFS20KNTS066, NIFS20KNTS070, NIFS20KNSS149,
NIFS20KNSS150 and NIFS21KKGS030. The computations were performed using Research Center for Computational Science, Okazaki, Japan.

References[1] H. Tauchi, T. Umata, and A. Tachibana, J. Plasma Fusion Res. Vol. 88, No. 2, p.
119,2012.
[2] S.K. Nair, S.K. Sliverman, J.H. Chen, and Y. Xiao, Crystal structure analysis of TRF2Dbd-DNA complex. 2012.
[3] Steve Plimpton, Fast parallel algorithms for short-range molecular dynamics, Journalof Computational Physics, Vol. 117, No. 1, pp. 1–19, 1995.
[4] H. M. Aktulga, J. C. Fogarty, S. A. Pandit, and A. Y. Grama. Parallel reactive molecular
dynamics: Numerical methods and algorithmic techniques, Parallel Computing, Vol.
38, pp. 245–259, 2012.
[5] H. M. Aktulga, C. Knight, P. Coﬀman, K. A. OHearn, T. R. Shan, and W. Jiang, Optimizing the performance of reactive molecular dynamics simulations for multi-core architectures, International Journal of High Performance Computing Applications, toappear.
[6] Adri C. T. van Duin, Siddharth Dasgupta, Francois Lorant, and William A. Goddard.Reaxﬀ: A reactive force ﬁeld for hydrocarbons, The Journal of Physical Chemistry A, Vol. 105, No. 41, pp. 9396–9409, 2001.
[7] Sung-Yup Kim and Adri C. T. van Duin. Simulation of titanium metal/titanium dioxide etching with chlorine and hydrogen chloride gases using the reaxﬀ reactive force
ﬁeld, The Journal of Physical Chemistry A, Vol. 117, No. 27, pp. 5655–5663, 2013.
PMID:23750609.
[8] H. Nakamura, H. Miyanishi, T. Yasunaga, S. Fujiwara, T. Mizuguchi, A. Nakata, T.
Miyazaki, T. Otsuka, T. Kenmotsu, Y. Hatano, and S. Saito, Jpn. J. Appl. Phys. 59,
SAAE01 (2020). [DOI: 10.7567/1347-4065/ab460d][9] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, A. Nakata, T. Miyazaki and S. Saito,
Jpn. J. Appl. Phys. 60, SAAB06 (2021). [DOI: 10.35848/1347-4065/abbdc8][10] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, T. Yasunaga, T. Otsuka, T. Kenmotsu, Y. Hatano, and S. Saito, Plasma Fusion Res. 14, 3401106 (2019). [DOI:
10.1585/pfr.14.3401106][11] S. Fujiwara, H. Nakamura, H. Li, H. Miyanishi, T. Mizuguchi, T. Yasunaga, T. Otsuka, Y. Hatano and S. Saito, J. Adv. Simulat. Sci. Eng. 6(1), 94-99 (2019). [DOI:
10.15748/jasse.6.94]

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Examination of Coil Resistance Measurement during
Wireless Power Transfer and Comparison with Finite
Element Analysis
Daigo Yonetsu1,* , Yuji Nakano1 , Naoya Hamano1
1 Department of Electrical and Electronics Engineering, Kansai University∗ yonetsu@kansai-u.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.40

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Study on Parallel Coupled Analysis ofHigh-Frequency Electromagnetic Field andHeat Conduction Problemsof Numerical Human Body Model
Shin-ichiro Sugimoto1*, Amane Takei2, Masao Ogino3
Department of Mechanical Engineering, Faculty of Engineering,
Hachinohe Institute of Technology

12Department of Electrical and System Engineering, Faculty of Engineering,
University of Miyazaki

3

Department of Information Systems, Faculty of Informatics, Daido University*sugimoto@hi-tech.ac.jp

Abstract. This paper deals with a high-frequency electromagnetic field - heat conduction coupled analysis of a numerical human body model in a parallel environment. The iterative substructuring method has been considered to be an efficient parallel computing method.
Keywords: High-Frequency Electromagnetic Field - Heat Conduction Coupled Analysis, Parallel
Computing, Finite Element Method, Hierarchical Domain Decomposition Method, Numerical Human Body Model

1. Introduction
In order to evaluate an effect of cancer treatment by hyperthermia quantitatively, we have been
studying its high-frequency electromagnetic field – heat conduction coupled analysis in a parallel environment. In our study, the NICT numerical human body model [1] is analyzed. Thismodel uses a binary data format wherein types of organs are encoded using voxels with a sizeof 2 mm. However, the boundaries of its different materials are not smooth; thus, unwanted
reflection and scattering of electric fields has been observed in numerical simulator results. To
reduce this numerical noise, some mesh smoothing techniques with tetrahedral elements havebeen developed [2]. Furthermore, the diameters of cancers treated with hyperthermia are several millimeters. Therefore, elements must be refined to obtain sufficient accuracy. However,there are approximately 130 billion degrees of freedom (DOFs) provided that the element sizes
are 0.25 mm. In addition, smoothing techniques increase the DOFs further.
The efficient parallel computing method for large-scale finite element analysis (FEA) that we360

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have been studying is the iterative substructuring method in the form known as the domain
decomposition method (DDM) based on the iterative method [3]. It is expected to obtain scalable parallel efficiency on distributed memory parallel computers with the implementation ofa Hierarchical Domain Decomposition Method (HDDM) [4].
The HDDM has been applied to the large-scale FEA of structural mechanics [5], and heat transfer [6]. In structural analysis, the problem with 100 billion DOFs has been analyzed [7]. In
addition, the HDDM has been applied to the large-scale FEA of electromagnetics [8]-[9], too.
In recent years, it has been clarified that the conjugate orthogonal conjugate residual (COCR)
method [10] is very effective for problems that involve symmetric systems with complex numbers and ill-conditioned systems [11]-[12]. Thus, in the electromagnetic field analysis, highfrequency electromagnetic field problems have been solved with 30 billion DOFs [11] and 130
billion DOFs [13]. These achievements have been implemented as a parallel electromagnetic
field analysis module called ADVENTURE_Magnetic [14].
In order to analyze large-scale problems, the parallel analysis of the electromagnetic field problem has been mainly studied. As the next step, a parallel coupled analysis of the high-frequency
electromagnetic field and the heat conduction problems is considered. In this paper, the numerical human body model involving 30 million DOFs is analyzed in the parallel environment.

2. High-frequency electromagnetic field– heat conduction coupled problem
Since the hyperthermia heats the human body from normal body temperature (36-37 degrees
Celsius) to the temperature at which the cancer dies (42-43 degrees Celsius), the temperaturechange is only about 5 degrees; thus, changes in physical quantities related to the electromagnetic field analysis due to temperature are negligible. Therefore, in this paper, a one-way coupled analysis using the results of the electromagnetic field analysis for the heat conduction
analysis is performed.
The numerical human body model is composed of voxels generated from tomographic images
obtained by CT or MRI. Therefore, the boundaries of its different materials are not smooth;thus, unwanted reflection and scattering of electric fields has been observed in numerical simulator results. To reduce this numerical noise, some mesh smoothing techniques with tetrahedral elements will be used in the future; thus, the HDDM based on the finite element method
is used for the numerical analysis, in this paper. Since the one-way coupled problem is considered, separate solvers are used for the electromagnetic field and heat conduction analyses. In
this paper, ADVENTURE_Magnetic is used for the electromagnetic field analysis, and a parallel heat conduction analysis module called ADVENTURE_Thermal [14] is used for the heat
conduction analysis.
In the coupled analysis, 𝐸ℎ which is the electric field approximated by the edge elements is
obtained by the high-frequency electromagnetic field analysis, first. Then, the eddy current
density 𝐽𝑒ℎ [A/m2] for each element is obtained as follows:(1)

𝐽𝑒ℎ = 𝜎𝐸ℎ .

where 𝜎[S/m] is the conductivity. Here, 𝐽𝑒ℎ is a complex number (= 𝐽𝑟 + 𝑖𝐽𝑖 ), and its amplitude 𝐽𝑚 and effective value 𝐽𝐸 are obtained as follows:(2)

𝐽𝑚 = √𝐽𝑟2 + 𝐽𝑖2 ,361

JSST2021
1

𝐽𝑚 .
(3)
√2
Then, the heat generation density 𝑓̃[W/m3] for each element due to heating is obtained asfollows:
𝐽𝐸 =2
𝐽𝐸2 𝐽𝑚
𝐽𝑟2 + 𝐽𝑖2(4)𝑓̃ = ==.
𝜎 2𝜎
2𝜎
In the heat conduction analysis, the temperature distribution in the body is obtained using 𝑓̃,and the heat production by muscles.

3. Hierarchical Domain Decomposition Method (HDDM)
In the HDDM, an original domain Ω is divided without overlapping elements. Furthermore,
the original domain is hierarchically divided into parts, which are further decomposed into
smaller domains called subdomains.
𝑁𝑝 −1 𝑁𝑠 −1(5)Ω = ⋃ ⋃ Ω(𝑖,𝑗) ,𝑖=0 𝑗=0(𝑖,𝑗)where Ωdenotes the subdomain 𝑗 in the part 𝑖, the superscript (𝑖, 𝑗) corresponds to thesubdomain Ω(𝑖,𝑗) . 𝑁𝑝 and 𝑁𝑠 are the number of parts and that of subdomains in each part,respectively. 𝑁𝑠 is equal for all parts. In Fig. 1, the original domain is first divided into twoparts, and then further decomposed into two subdomains within each part (𝑁𝑃 = 𝑁𝑠 = 2). The
solid circles in the figure are the DOFs shared between parts and subdomains, which are calledinterface DOFs.
In the HDDM, the interface problem which is obtained by statically reducing DOFs to theinterface DOFs is solved by the parallel iterative methods such as the Conjugate Gradientmethod and COCR method.
part 0subdomain 0

DomainDecomposition subdomain 1: DOF

part 1
subdomain 0

subdomain 1: Interface DOF

Fig. 1. Hierarchical domain decomposition.

4. Numerical example
The NICT numerical human body model involving 30 million DOFs provided that the element
sizes are 4 mm (Fig. 2) is analyzed in parallel environment. Assumption of the treatment of thechest, the electromagnetic waves are emitted from the antenna in front of the chest. The physical quantities of each organ are quoted from [15] and [16].
Fig. 3 and Fig. 4 show the eddy current density and temperature distribution, respectively. It

362

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can be confirmed that the eddy current density around the heart near the antenna is strong, andtemperature around the heart is rising.

Fig. 2. Numerical human body modelwith 30 million DOFs.

Fig. 3. Result of the electromagnetic field analysis.
Eddy current density (real part) [A/m2]

Fig. 4. Results of the heat conduction analysis (body temperature (degrees Celsius)).
Left: without heating, Right with heating.

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5. Conclusions
In this paper, the high-frequency electromagnetic field – heat conduction coupled analysis of
the numerical human body model involving 30 million DOFs provided that the element sizes
are 4 mm has been attempted in the parallel environment. In the future, the analysis of larger
models and the analysis considering the influence of blood flow will be tried.

Acknowledgment
This work is partially supported by Takahashi Industrial and Economic Research Foundation,
JSPS KAKENHI Grant Number 17H02829, and Aomori foundation for promotion of technological education.

References[1] Electromagnetic Compatibility Laboratory, Applied Electromagnetic Research Institute, National Institute of Information and Communications Technology HP:
http://emc.nict.go.jp/index_e.html[2] A. Takei, K. Murotani, S. Sugimoto, M. Ogino, H. Kawai: High-Accuracy Electromagnetic Field Simulation using Numerical Human Body Models, IEEE Transaction on
Magnetics, Vol.52, Issue 3, 7402704 (2016), 4p.
[3] A. Quarteroni, A. Valli: Domain Decomposition Methods for Partial Differential Equations, Clarendon Press, Oxford (1999).
[4] R. Shioya, G. Yagawa: Iterative domain decomposition FEM with preconditioning
technique for large scale problem, ECM’99 Progress in Experimental and Computational Mechanics in Engineering and Material Behaviour (1999), pp.255-260.
[5] S. Yoshimura, R. Shioya, H. Noguchi, T. Miyamura: Advanced general-purpose computational mechanics system for large-scale analysis and design, Journal of Computational and Applied Mathematics, Vol.149, Issue 1 (2002), pp.279-296.
[6] A.M.M. Mukaddes, M. Ogino, M, H. Kanayama, R. Shioya: A scalable balancing domain decomposition based preconditioner for large scale heat transfer problems, JSMEInternational Journal Series B Fluids and Thermal Engineering, Vol,49, No.2 (2006),
pp.533-540.
[7] M. Ogino, R. Shioya: Scalable non-overlapping domain decomposition method for finite element simulations with 100 billion degrees of freedom model, Proceedings ofthe 1st International Conference on Computational Engineering and Science for Safety
and Environmental problems (2014), pp.96-99.
[8] H. Kanayama, S. Sugimoto: Effectiveness of A- method in a parallel computing withan iterative domain decomposition method, IEEE Transactions on Magnetics, Vol.42,
Issue 4 (2006), pp.539-542.
[9] A. Takei, S. Yoshimura, H. Kanayama: Large-scale parallel finite element analyses ofhigh frequency electromagnetic field in commuter trains, Computer Modeling in Engineering & Sciences, Vol.31, No.1 (2008), pp.13-24.

364

JSST2021[10] T. Sogabe, S.L. Zhang: A COCR method for solving complex symmetric linear systems,
Journal of Computational and Applied Mechanics, Vol.199, No.2 (2007), pp.297-303.
[11] S. Sugimoto, A. Takei, M. Ogino: Finite Element Analysis with Tens of Billions ofDegrees of Freedom in A High-Frequency Electromagnetic Field, Mechanical Engineering Letters, Vol.3, p.16-0067 (2017), 10p.
[12] M. Ogino, A. Takei, H. Notsu, S. Sugimoto, S. Yoshimura: Finite element analysis ofhigh frequency electromagnetic fields using a domain decomposition method based on
the COCR method, Theoretical and Applied Mechanics Japan, Vol.61 (2013), pp.173181.
[13] S. Sugimoto, A. Takei, M. Ogino: High-Frequency Electromagnetic Field Analysis
with 130 Billion of Degrees of Freedom, The 38th JSST Annual Conference, International Conference on Simulation Technology, (2017), pp.290-295.
[14] ADVENTURE Project HP: https://adventure.sys.t.u-tokyo.ac.jp/[15] Human organs property Database for Computer simulation, RIKEN:
http://cfd-duo.riken.go.jp/cbms-mp/index.htm[16] Tissue Properties Database V4.0:
https://itis.swiss/virtual-population/tissue-properties/downloads/database-v4-0/

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Analysis of electrostatically induced short-circuit current in a human body on a 500 kV transmission tower
Shoji Hamada1*
1Department of Electrical Electronic and Information Engineering, Kansai University*shamada@kansai-u.ac.jp

Abstract. We performed the numerical analysis of electrostatically induced steady-state ACshort-circuit currents running through a human model on a transmission tower model. The
transmission tower model was 80.22 m tall with 500 kV double-circuit three-phase overhead
conductors and two ground wires. The NICT TARO model was used for the human model after
modifying the posture and resolution. The toe of the left foot of the human model was in directcontact with the bottom cross arm of the tower model, and we analyzed the short-circuit current
flowing through the contact point. The model comprised of cubic voxels with a side length of
2 cm, and the overall rectangular region occupied by the model was 27.5 m × 270 m × 165 m,
including the mirror image under the ground plane. A voxel-based fast multipole surface charge
simulation method was used for the analysis. By applying a single-circuit three-phase voltage
of 50Hz, short-circuit AC currents of 441 µA and 500 µA flowed in the standard posture andleft-arm-raised posture models, respectively. These currents were about half the reference levelof the contact current specified in the international guidelines for occupational workers.
Keywords: Electrostatically induced AC current, Voxel model, Transmission tower, Human body

1. Introduction
High-voltage power equipment electrostatically induces AC electric fields and currents in humans in close proximity [1]-[3]. The induced fields and currents could cause
anxiety and discomfort in the general public, and health issues in occupational workers. Therefore, international guidelines have specified basic restrictions of internal electricfields and reference levels of flowing currents [4]. Electrostatically induced electric fields andcurrents have been widely researched using numerical human models to prevent the fields andcurrents from exceeding the specified values [2], [3]. In this study, we quantitatively investigated
the induced short-circuit contact current flowing through the occupational workers working on
a transmission tower through numerical analysis.

2. Numerical calculation method
A two-step process method is known as a method for calculating the electrostatically induced
AC current density distribution inside the human body [3], [5]. In the first stage, we calculate theinduced electric charge distribution on the body surface while assuming that the human body366

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is a perfect conductor. This assumption is based on the fact that the electric field inside
the body is about 6 to 7 orders of magnitude smaller than the applied electric fieldoutside the body [3], [5]. We can convert this induced charge distribution into the induced
conductive current density distribution on the body surface. In the second stage, we calculate
the internal body current distribution on the basis of the continuity of the conductive current.
Since the short-circuit current flowing through the grounded human body part equals the sumof the current injected through the body surface, we can calculate the short-circuit current using
the first stage calculation alone. The first stage requires electrostatic field analysis of the systemof conductors, which was performed by the voxel-based fast multipole surface charge simulation method in this study [3], [6]. The voxel surface that forms a boundary between the conductor
and the air is regarded as a square surface element, and the surface charge densities on thesurface elements are treated as unknown variables. We construct simultaneous linear equations
based on the Dirichlet condition of electric potential, which is solved using an iterative solver
with the fast multipole method. The amount of calculation required for one step of the iterativesolver is O(N), where N is the number of unknowns. Note that N = O(D2), where D is a representative value of the number of divisions per dimension in the three-dimensional model.

3. Specifications of calculation model
Figure 1 shows a voxel model composed of a human, a transmission tower, six bundled conductors, and two ground wires. The tower was a 500 kV three-phase doublecircuit transmission tower. The tower was 80.22 m tall, and the supporting points of theoverhead conductors in the A, B, and C phases were 71.52 m, 58.32 m, and 45.12 m tall, respectively. The conductor distance between two-circuits was 18.72 m. The bundled conductors consist of four sub-conductors. The span length, the sag, the bundle spacing, and theradius of the conductor were 400 m, 10 m, 40cm, and 2 cm, respectively. The conductor shapewas expressed by a quadratic function. Figure 2 shows the close-up view of the human modelon the tower model, simulating a worker who accidentally strays into the live line side. The
NICT TARO model was used as the human model, and the posture deformation and smoothresampling were performed using a software tool provided by the NICT [7], [8]. A standard posture model and a left-arm-raised posture model were used in this study. The human model wasplaced upright with the toe of the left foot in direct contact with the bottom cross arm of thetower. The human body, tower, conductors, and ground wires were regarded as perfect

Fig. 1. A model composed of a human, a tower, 6 conductors, and 2 ground wires.

367

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conductors. However, the insulators were ignored, or their relative permittivities were approximated to one. The angle steel of the tower was approximated to a rectangular or a cylinder
having cross-sectional width of 20 or 30 cm. To consider the image electric charges, the model
above the ground was mirror-inverted and duplicated underground. Cubic voxels with theside length of 2 cm were used. The dimensions of the entire region, including the image
model, were 27.5 × 270 × 165 m or 1375 × 13500 × 8250 voxels, and a lossless compression
technique was used to handle the voxel model [9]. The number of surface elements (= the number of unknowns in the numerical calculation) was approximately 15 million. A unit voltage
was applied to each phase to perform one numerical calculation, and a total of threecalculations were performed for the three phases. Then the phasors of all three phases
were combined to obtain the maximum value of the induced current.

4. Calculation result
Figure 3 shows the normalized potential distribution when the voltages were –0.5,
1.0, and –0.5 V for phases A, B, and C, respectively, in the standard and left-armraised postures. The computer used for the analysis had the following specifications:
CPU: AMD Ryzen Threadripper 3990X; main memory: 256 GB. Approximately 27 min
were required to generate the model. Whereas the field calculation took approximately
8 min for a single voltage energization and required 6.7GB of memory. A rated voltage
of 500 kV means the root mean square value of the line voltage, thus the short-circuitcurrent was also calculated as the root mean square value. When the three-phase
50Hz voltage was applied, short-circuit currents of 441 µA and 500 µA were inducedin the standard and the left-arm-raised posture models, respectively. Raising one arm
increased the current by 13.4%. The reference level of the contact current in occupational workers specified in the ICNIRP guidelines [4] is 1000 µA. Therefore, the calculated values are approximately half the reference level value. Furthermore, the rms
current of 500 µA corresponds to the peak body-surface charge amount of 2.25 µC,

Fig. 2. Close-up view of human models.

368

Fig. 3. Potential distribution.

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which is approximately 10 times greater than the perception threshold value of 0.2–
0.3 µC when stimulated by the transient discharge current due to electrification [10].

5. Summary
We performed the numerical analysis of the 50Hz short-circuit currents electrostatically induced in the voxel human model on the 500 kV transmission tower model. The
voxel human model NICT TARO was used after posture deformation and resolution
resampling. The model comprised of voxels with a side length of 2 cm and occupied arectangular region of 27.5 m × 270 m × 165 m. On applying a three-phase voltage, ashort-circuit current of 500 µA (rms) was observed when using the left-arm-raised posture model. This current was half the reference level value of the contact current for
occupational workers specified in the ICNIRP guidelines. In the future, we plan toreduce the voxel size and analyze the electric field and current in the human body.

References[1] D. W. Deno: Current induced in the human body by high voltage transmission line electric field - measurement and calculation of distribution and dose, IEEE Trans. on PAS,
PAS-96:5 (1977), 1517-1527.
[2] H. Tarao, N. Hayashi, and K. Isaka: Estimation of short-circuit current induced by ELF
uniform electric fields in grounded humans with different body shapes base on a semiellipsoidal model, Biomed. Phys. Eng. Express, 6 (2020) 1-12.
[3] S. Hamada: Calculation of electrostatically induced electric fields in human models using a two-step process method of voxel-based fast multipole surface charge simulation
method, IEEJ Trans. FM, 140:10, (2020) 481-490 (in Japanese).
[4] ICNIRP: Guidelines for limiting exposure to time-varying electric and magnetic fields(1 Hz to 100 kHz), Health Phys., 99:6 (2010) 818-836.
[5] K. Chen, H. Chuang, C. Lin: Quantification of interaction between ELF-LF electricfields and human bodies, IEEE Trans. on Biomedical Engineering, BME-33:8 (1986)
746-756.
[6] S. Hamada and T. Kobayashi: Analysis of electric field induced by ELF magnetic field
utilizing fast-multipole surface-charge-simulation method for voxel data, IEEJ Trans.
FM, 126:5, (2006) 355-362 (in Japanese).
[7] T. Nagaoka, S. Watanabe, K. Sakurai, E. Kunieda, S. Watanabe, M. Taki, Y. Yamanaka:
Development of realistic high-resolution whole-body voxel models of Japanese adultmales and females of average height and weight, Phys. Med. & Biol., 49 (2004) 1-15.
[8] T. Nagaoka, and S. Watanabe: Postured voxel-based human models for electromagnetic
dosimetry, Phys. Med. & Biol., 53 (2008) 7047-7062.
[9] S. Hamada: Surface charge simulation method based on lossless compression voxel
models, 2021 annual meeting record IEEJ, 1-024 (2021) 34 (in Japanese).
[10] JNIOSH: Recommendations for requirements for avoiding electrostatic hazards in industry 2007, JNIOSH-TR-NO. 42, (2007) (in Japanese)369

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Comparative Study of Strongly Coupled Fluid andStructure Systems With Computational Control
Vinay Shankar1 and Daisuke Ishihara2,*
1,2,* Department of Intelligent and Control Systems, Kyushu Institute of Technology, 680-4

Kawazu, Iizuka, Fukuoka, 820-8502, Japan∗ ishihara.daisuke399@mail.kyutech.jp

Abstract. Fluid-structure interaction (FSI) is a typical multi-physics coupled system. Theinteraction affects the vibration characteristics of coupled system and thus such complex
system must be controlled taking into account the interaction. This paper proposes computational control based on the finite element method for strongly coupled analysis of FSI.
The vibration characteristics and the effect of direct velocity and displacement feedback(DVDFB) control in FSI for soft and stiff structure will be investigated and the stability of
two types of structures will be compared. The results for a soft material show a reduction in
displacement and amplitude and more stability compared to the stiff material.
Keywords: Finite element method, Direct velocity and displacement feedback control, Active control, Fluid-structure interaction

1.

Introduction

A lot of researches is ongoing for development of insect-like flapping wings based on
MEMS technology for micro and nano air vehicles. There are many challenges regarding the design and implementation of the flight mechanism due to coupled systems, suchas FSI. Such complex system requires proper control of flapping wings. In computational
control, multi-field system interaction with control is simulated [1]. This paper proposes
computational control based on the finite element method (FEM) for the coupled analysis
of FSI for the stiff and soft structures. Active DVDFB control [2] is employed to investigate
the vibration characteristics and the stability of soft and stiff structures is compared.
In this study, FSI is implemented using a monolithic approach. The projection method is
employed to solve FSI [3]. Active DVDFB control is incorporated with FSI. Few researchers
have applied active control to FSI [2], [4], [5]. Here, we use active DVDFB control toinvestigate the vibration characteristics and compare the stability of soft and stiff structures.
FSI with active control have potential application in sensors and actuators such as energy
harvesters which control the flapping of wings to fly freely.

370

2.

Methodology

A FEM for FSI with DVDFB control is proposed. The monolithic equations for the FSI
system is split into its subsystem algebraically [3].
t+∆t (k)a + Ct+∆t v(k) + N + qt+∆t ut (k) − Gt+∆t p(k) = g,LM

TGt+∆t (k)v= 0,(1a, 1b)where M is the mass matrix, C is the diffusion matrix, N is the convective term vector,
G is the divergence operator matrix, g is the external force vector, q is the internal force
vector, a, v, u and p are the acceleration, velocity, displacement and pressure vectors at timet + ∆t, respectively. Control force will be added to the translational degree of freedom of thestructural external force in Eq. (1a). The control force equation can be written as [2],Fc = −Kd u − Kv u̇,(2)where Fc is the control force, Kd is the displacement proportional gain, Kv is the velocity
proportional gain, t u and t u̇ are the displacement and velocity at previous time step, respectively. Kv adds damping and Kd adds stiffness to the system. By varying Kv and Kd , we cancontrol the damping and stiffness to stabilize the system.

3.

Numerical control of soft and stiff structures with FSI

3.1. Soft structurea.

Problem setup

In Fig.1, we perform a numerical simulation of the suppression of vibration characteristics
and compare the stability of soft and stiff structures by active DVDFB control. Mok and Wallproposed a flexible flap in a fluid channel which is also regarded as a benchmark problem[6]. The material properties of soft structure can be referred from [3].

Figure 1: Flexible flapping in converging
Figure 2: Displacement
fluid channel with control
without controlb.

Results and discussion

Figure 2 shows the displacement result obtained using rubber in [3] without DVDFB control.
When the control force is applied to the soft structure, there is a significant reduction in371

displacement with kd , as shown in Fig.3. A larger kd does not produce instability. In previous
research [2], when kd was over 10, it led to numerical instability.

Figure 3: Displacement feedback control kd Figure 4: Velocity feedback control andfor rubber structure
control force kv for rubber structureWith kv , there is a significant reduction in amplitude, as shown in Fig. 4. When kv > 1.5,
it produces instability. The response of the control force is also shown in Fig. 4. The
instability can be removed by using a finer time step.

3.2.
a.

Stiff structure
Problem setup

In this problem setup, PVDF is used as a stiff structure and the piezoelectric effect of PVDF
is neglected. The flexible solid beam in Fig. 1 is replaced with a stiff material, for which thematerial density, Young’s modulus, and Poisson’s ratio are ρs = 1800kg/m3 , Es = 2.0GPa,
and vs = 0.29, respectively. DVDFB control is applied at the tip of the stiff structure.
b.

Results and discussion

We performed a numerical simulation of a stiff structure with DVDFB control. The resultsin Fig. 5 show a reduction in displacement because of kd . When kd > 27.5, the large control
force produces instability.
In another simulation, kv is used. The results in Fig. 6 show no reduction in displacement. When kv > 4.9, the control fails and produces instability. The control force is also
shown in Fig. 6. There is no instability and no reduction in amplitude because PVDF is a
stiff structure. A comparison of the results for PVDF and rubber indicates that better systemstability is obtained with rubber. PVDF has a very high stiffness and thus the control force
cannot act properly. Rubber is soft and flexible and thus the DVDFB control is more stable.

372

Figure 6: Velocity feedback control andFigure 5: Displacement feedback control kd
control force kv for PVDF structure
for PVDF structure

4.

Conclusions

This paper proposed a computational control based on FEM for the FSI of stiff and soft
structures. The vibration characteristics were investigated and stability of system with stiffand soft structures were compared with DVDFB control. For a stiff material, namely PVDF,
there was a reduction in displacement due to kd but kv had no effect. A large control force
led to instability. For a soft material, namely rubber, there was a reduction in displacement
and amplitude. A larger control force also led to instability, but it was less than that for
PVDF. The results show that the proposed computational control algorithm is more stablecompared with previous studies.

5.

Acknowledgements

This research was supported by the Japan Society for the Promotion of Science under KAKENHI Grant Nos. 19F19379, and 20H04199.

References[1] A. Mini et al.: PAMM, (2016), 15–18.
[2] S. Kaneko et al.: Computational Mechanics, (2017), 49–558.
[3] D. Ishihara, T. Horie: CMES, 101 (2014), 421–440.
[4] L. Chirco and S. Manservisi: Fluids, (2020), 87–102.
[5] A. Mehmood et al. J. Vib. Control, (2014), 1137–1147.
[6] D. P. Mok et al.: Trends in Computational Structural Mechanics, (2001), 689–698.

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Passive motions and aerodynamic performance ofinsect’s flapping wings simulated using the pixel wingmodel and the strong coupling method
Minato Onishi 1*, Daisuke Ishihara 2
Department of Computer Science and Systems Engineering, Kyushu Institute of Technology

1

Department of Intelligent and Control Systems, Kyushu Institute of Technology

2*oonishi-m@solid.mse.kyutech.ac.jp

Abstract. In this study, the relationship between the passive motions and the aerodynamic
performance in insect’s flapping wings is investigated. For this purpose, the pixel wing model
flapped in air is analyzed by the strong coupling method for the fluid-structure interaction(FSI). The pixel wing model can deform due to the aerodynamic pressure to produce the passive feathering and cambering motions. Hence, the FSI analysis simulates the aderodynamic
forces produced by these passive motions. The aerodynamic force coefficients are evaluatedfor a variety of wing parameters, and the aerodynamic performance enhancement due to thesepassive motions is demonstrated.
Keywords: Fluid-structure interaction, Insect’s flapping wing, Passive motion, Feathering, Cambering, Pixel wing model, Strong coupling method

1. Introduction
The elastic deformations observed in insect flapping wings are generated by the aerodynamic
force from the surrounding air, because insect’s wings lack interior muscle [1]. Especially,
the feathering and the cambering contribute to the improvement of the aerodynamic performance. As far as we know, there is no study that simulates the feathering and the cambering
passively, whose magnitudes are close to those of actual insects. Therefore, the relationshipbetween these passive motions and the aerodynamic performance is still unclear. Hence, inthis study, this relationship is investigated using the fluid-structure interaction (FSI) analysisof the pixel wing model flapped in air.

2. Modeling of the insect flapping wing
Fig. 1 shows the employed pixel wing model. The fundamental concept of this model is basedon the Ref. [2]. The complicated network of veins is simplified by the leading edge, the cen-374

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ter vein, and the root vein using the structured shell element. The different mechanical role ofthe membrane and veins are represented using the different set of the pseudo-elastic material
properties. The Young’s modulus of the leading edge and root vein are determined based on
the flexural ridgidity along the span-wise direction Gs and the chord-wise direction Gc, respectively. The Young’s modulus of the center vein is determined such that the flexural rigidity is equal to that of a most significant vein in the center domain of an actual insect’s wing.
The Young’s modulus of the wing membrane Em is determined from an actual insect’s cuticle.
Fig. 2 shows the schematic of the flapping motion.  and  are the stroke angle and the angular displacement of flapping motion, respectively. The time history for d/dt based on an observation as shown in Fig. 3 is applied to the leading edge. Tφ is the flapping period, and theacceleration and deceleration time tφ is set to Tφ/8, which is a typical value. The featheringand the cambering can be simulated from the interaction between the wing and surrounding
fluid. The feathering motion can be described using the feathering angular displacement θ asshown in Fig. 4, which is positive in the counter-clockwise direction about the torsional axis.
The magnitude of the camber is defined as the ratio of the wing’s height Ch to the wing’s
chord length Cl as shown in Fig. 4, and the sign of the camber is positive if the shape of thecamber is concave along the direction of the flapping translation [3].

xStrokeangle O

Strokeplane
Stroke direction

Figure 1: Employed pixel wing model.
+4Time history of stroke anglularvelocity ddt [deg/sec]

0z

Leading edge

2

−2

Axis oftorsionFeathering
angle 𝜃Figure 2: Schematic of flapping motion.

[10 ]

0Angulardisplacement of
flapping motion tWing chord



t
t



Cl

y

f = 1/T
0.5



Ch

t

Stroke directionz

1Time [cycle]x

Figure 3: Time history of angular flapping Figure 4: Definition of the feathering angle
velocity.
and the camber.

3. Fluid-structure interaction analysis of the pixel wing model
The finite element discretized equation of the incompressible viscous fluid and the equilibrium equation of the elastic body are combined using the interface conditions, and the monolithic equation systems of FSI is derived as follows:L

Ma  Cv  N  q  u   Gp  g ,  Gv  0 ,375(1a, b)

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where the matrices M, C, and G are the mass, diffusive, and divergence operator, respectively, the vectors a, v, N, q, u, p, and g are the acceleration, velocity, convective term, elastic
inertial force, displacement, pressure, and external force, respectively. The subscripts L and 
denote lumping and transpose, respectively. Eq. (1) is solved using a projection method [4].

4. Numerical result
The parameters used in this study are given based on actual insect’s data [5-10] as follows:
The wing span length Rw = 0.0113m, the wing chord length cw = 0.00311 m, the wing’s thickness t = 2.0 μm, the flexural rigidity of along the wing’s span-wise direction Gs = 4.0 μNm2,
the flexural rigidity of along the wing’s chord-wise direction Gc = 0.35 μNm2, the flexural rigidity of the most significant center vein = 0.26 nNm2, Poisson’s ratio ν = 0.49,  = 71°, theflapping frequency f (= 1/T) = 148 Hz, the fluid mass density f = 1.205 kg/m3, the fluid
viscosity f = 1.82210-5 Pa s, the time increment t = T/150000. For the purpose of evaluating the relationship between passive deformation and the aerodynamic performance, theYoung’s modulus of wing membrane Em was varied from 7.0 to 13.0 GPa. The normalized
position r/Rw is defined, where r is the distance from the wing base.
Fig. 5 shows the comparison of the lift coefficient CL for various Em. Fig. 6 shows the relationship between the Em and average lift coefficient. Fig. 7 shows the the comparison of thecross section for r/Rw = 0.5 at 0.25 cycle. Fig. 8 shows the distribution of the camber along
the wing’s span-wise direction for the various Em. CL increases as Em decreases and the average lift coeficient are monotonically proportional to Em as shown in Fig. 5 and 6. This is because that the passive feathering and cambering increases as Em decreases as shown in Fig. 7
and 8. Therefore passive deformations such the feathering and cambering can improove theaerodynamic performance.


1.1  Pa

1.3  Pa

Em = 7.0  Pa

Average lift coefficient

Lift coefficient CL2



9.0  Pa
4

2

0

1.9

1.8

8

0

0.5

Time [cycle]

1012Young's modulus ofwing membrane Em [GPa]1Figure 5: Time history of the lift coefficient Figure 6: Relationship between the Em
for various Em.
and average lift coefficient.
Em = 7.0  Pa
9.0  Pa
1.1  Pa
1.3  Pa

8

Camber [%]y coordinate

0−0.0010.25 cycle
r/Rw = 0.5−0.002yx−0.0030Strokedirection

0.00020.00046Em = 7.0  Pa
9.0  Pa

1.1  Pa
1.3  Pa

4
0.25 cycle
2
0.25
0.5

0.75

1

Distance from the base along the wing's
span wise direction r/Rw
0.0006x coordinate

Figure 7: Comparison of the cross section Figure 8: The distribution of the camber
for r/Rw = 0.5 at 0.25 cycle.
along the wing’s span-wise direction.

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5. Concluding remarks
The relationship between the passive motions and the aerodynamic performance is investigated using the FSI analysis of the pixel wing model flapped in air. The lift coefficient increases
as the Young’s modulus of the wing membrane decreases. This is because the passive feathering and cambering increase as the Young’s modulus of wing membrane decreases. Therefore,
these passive motions enhance the aerodynamic performance. In our future work, the passive
mechanism of the feathering and cambering will be revealed.

Acknowledgments
This work was supported by JSPS KAKENHI Grant number 20H04199.

References[1] R. J. Wooton, R. C. Herbert, P. G. Young, K. E. Evans: Approaches to the structuralmodeling of insect wings. Philosophical Transactions of the Royal Society of London B,
358, pp. 1577-1587, 2003.
[2] M. Onishi, D. Ishihara: Modeling the cambering of the flapping wings of an insect using rectangular shell finite elements, Journal of Advance Simulation in Science andEngineering, 7, 1, pp. 181-188, 2020.
[3] S. M. Walker, A. L. R. Thomas, G. K. Taylor: Deformable wing kinematics in freeflying hoverfly, Journal of the Royal Society Interface, 7, pp. 131–142, 2010.
[4] D. Ishihara and T. Horie: “A projection method for the monolithic interaction system of
an incompressible fluid and a structure using a new algebraic splitting”, Computer
Modeling in Engineering and Sciences, 101, pp. 421-440, 2014.
[5] H. Tanaka, R. J. Wood: Fabrication of corrugated artificial insect wings using laser micromachined molds, Journal of Micromechanics and Microengineering, 20, 075008,
2010.
[6] S. A. Combes, T. L. Daniel: Flexural stiffness in insect wings I. Scaling and the influence of the wing venation. The Journal of Experimental Biology, 206, pp. 2979-2987,
2003.
[7] S. A. Wainwright, W. D. Biggs, J. D. Currey, J. M. Gosline: Mechanical Design in Organism, Princeton University Press, 1982.
[8] J. F. V. Vincent and U. G. K. Wegst: “Design and mechanical properties of insect cuticle”, Arthropod Structure & Development, 33, pp. 187-199, 2004.
[9] C. P. Ellington: The aerodynamics of hovering insect flight III. Kinematics, Philosophical Transactions of the Royal Society of London B, 305, 1122, pp. 41-78, 1984.
[10] A. R. Ennos: The kinematics and aerodynamics of the free flight of some Diptera. The
Journal of Experimental Biology, 142, pp. 49-85, 1989.

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Comparative study on partitioned iterativealgorithms for coupled multiple phenomena
in piezoelectric energy harvesters
Naoto Takayama1*, Daisuke Ishihara2*, Prakasha C Ramegowda2, Shunsuke Nozaki1
Department of Computer Science and Systems Engineering, Kyushu Institute of Technology

1

Department of Intelligent and Control Systems, Kyushu Institute of Technology

2*ishihara.daisuke399@mail.kyutech.jp

Abstract. Various coupled algorithms are possible for the structure-piezoelectric-circuit interaction in piezoelectric bimorph energy harvesters. Hence, in this study, we propose a partitioned iterative algorithm using an explicit time marching method for the electric circuit, andcompare it to that using an implicit time marching method for solving the electric circuit interms of accuracy, computational cost, and numerical stability in a typical benchmark problemof piezoelectric energy harvesters.
Keywords: Piezoelectric Bimorph, Direct Piezoelectric Effect, Inverse Piezoelectric Effect, Electric Circuit, Partitioned Iterative Method, Block Gauss-Seidel Method, Finite Element Method

1. Introduction
In the piezoelectric energy harvesters, direct and inverse piezoelectric effects and electric circuit are strongly coupled, and this interaction determines the frequency response characteristics.
Hence, the accurate prediction of this coupled problem using the numerical approaches is necessary for the design process of these devices. In Ref. [1], the monolithic approach was used
for the direct numerical modeling of the structure–piezoelectric–circuit interaction in the piezoelectric energy harvester. The partitioned approach has been also used to simulate this coupled problem. However, the majority of previous studies on this approach used simplified numerical modeling such as the one-way coupling, the structural elements, and the circuit elements. On the contrary, we have been developing the partitioned approach using the direct
numerical modeling [2], where the fully implicit algorithm was used. However, various algorithms are possible because of multiple and hierarchical natures of this coupled problem. Hence,the purpose of this study is to propose a new hybrid approach using hierarchical decomposition

378

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for the coupled multiple phenomena. Some partitioned iterative algorithms given by this approach are compared to each other in terms of accuracy, computational cost, and numericalstability, and the effectiveness of this approach is demonstrated.

2. Materials and Methods
The spatially discretized equations of motion of linear piezoelectricity in the global coordinate
system are derived using the variation principle with the standard procedure of the finite element method as  K uu u  K uφφ  F , K Tuφu  K φφφ  qext  qc ,M uu u(1a, b)where Muu is the global mass matrix of the structure, Kuu is the global mechanical stiffness
matrix of the structure, Kuφ is the global piezoelectric stiffness matrix of the piezoelectric continuum, Kφφ is the global dielectric stiffness matrix of the piezoelectric continuum, u is thenodal global vector of the mechanical displacement, φ is the nodal global vector of the electric
potential, F is the global equivalent vector of the mechanical external force, qext is the global
equivalent vector of the external surface charge, qc is the global equivalent vector of the surface
charge supplied from the integrated electric circuit, and the right-hand superscript T denotes
the transpose of the matrix. We consider the electrical resistance load as the circuit. A SDOF
governing equation of this circuit can be derived using Kirchhoff’s law as

RQ  Vp  Ve ,(2)

where R, Q, Vp, and Ve are the electrical resistance, the electric charge, the electric potential
difference given by the piezoelectric oscillator, and the electric voltage given by the external
electric power supply, respectively. The continuities of the electric potential and the electriccharge are satisfied at the interface between the piezoelectric continuum and the electric circuit.
The electric circuit is connected to the piezoelectric oscillator via electrodes. Here, let S+c and
S-c denote the areas of the electrodes where the electric circuit is connected with the subscripts+ and − corresponding to the positive and negative poles defined in the general circuit expression. Then, the continuity conditions imposed on the interface can be formulated asVp  *  * ,q c   c N φ  Q / S c  dS   c N φ  Q / S c  dS
SS(3a, b)where φx* (x is + or −) denotes the electric potential at the point in Sxc where the circuit isconnected and Nφ is the global assemblage of the interpolation functions used for the electric
potential. Note that the formulation of Eq. (3a) assumes that the charge from the electric circuit
is distributed uniformly and instantaneously throughout each electrode.

References[1] Ravi S, Zilian A. Time and frequency domain analysis of piezoelectric energy harvesters
by monolithic finite element modeling. Int J Numer Meth Eng 2017;112:1828–47.
[2] Ishihara D, Takata R, Ramegowda PC, Takayama N. Strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction using hierarchical decomposition, Comput Struct 2021;253:106572.

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Simulation of Cable-Laying Snake-like Robot
Locomotion on Cable Rack
Hayato Nagae1* , Junta takarabe1 , Koji Uchiyama1 , Yasuyuki Sato1 , Masami Iwase1
1 Department of Robot Mechatronics, School of Science and Technology for Future Life,

Tokyo Denki University∗ nagae17@ctrl.fr.dendai.ac.jp

Abstract. We aim to develop a snake-like robot towing a lead cable for reducing the workload in cable laying. For the purpose, it is essential that the snake-like robot can propel
while towing the lead cable on a cable rack. Therefore, in this paper, we develop a simulator which mimics the motion of the snake-like robot moving on a cable rack toward laying
a cable. Then, on the simulator, we design a motion pattern of the snake-like robot propelling on the cable rack, and verify its eﬀectiveness. We propose two patterns of motion
for propulsion, spiral and longitudinal wave. Evaluating the two patterns on a simulator
using MATLAB Simscape, it is conﬁrmed that the longitudinal wave motion is eﬀective for
propulsion on the cable rack.
Keywords: Snake-like robot, Cable rack, Pitch angle serpenoid motion, Spiral motion,
Computer simulation, MATLAB Simscape1.

Introduction

Cable laying is one of the interior works at building construction, and as buildings has
more IT devices and apparatus, the number of cables to be laid increases. It leads toenhance research and development on labor-saving methods. In the general cablelaying, cables should be laid on a rack which hangs from the ceiling. It is common forworkers to ride on stepladders or aerial platforms for manually laying cables. However,the number of aged workers increases, and the total number of workers is decreasingfrom the peak [1]. Therefore, it is expected that cable laying is automated by robots to savelabor.
We propose a snake-like robot that has a long and slender body without limbs for the
purpose. The robot is possible to promote a narrow space such as inside a pipe [2]. The
locomotive ability is expected to adapt to cable-laying on a cable rack or on the narrow space
between laid cables. Also, the ability of the robot to move while pulling a thin lead-in wireis required for cable laying. A snake-like robot can be expected to meet two requirements.
In previous our research, the authors have developed a prototype snake-like robot formoving on a rack and towing a lead cable [3]. The robot has compact passive wheels on

380

each body segment. The wheels play a important role in locomotion on rough terrain suchas sandy and gravel roads. Each joint of the robot is driven by a servomotor. Also, each
body segment is composed of alternating pitch-rotating joint and yaw-rotating joint driven
by the servomotor. Since the robot is designed having joints with a range of motion of ±90
deg, it can realize various movement even in a narrow space. So, we use the robot with somemodiﬁcation, and design propelling motion of the robot that can move on a cable rack.
As a related study of the movement algorithm, there is a spiral motion of a snake-likerobot at Carnegie Mellon University [5]. The spiral motion gives the robot propulsion overcylinders that overhang in a comb shape. We compare mobility eﬃciency of the spiralmotion and the proposed longitudinal wave motion on a cable rack in a simulator. The
simulator including a snake-like robot reproduces the precise shape and motion of the robot
by importing its CAD data. The simulator is eﬀective to verify the proposed motion to moveon the cable rack towing the lead-cable.

2. Robot Conﬁguration
The conﬁguration of the snake-like robot used in this research is shown. Our robot ispresented in Fig. 1, and each parameter of the robot is shown in Table 1. The robot consistsof 16 links and 15 joints. The coordinates of the robot is set as shown in Fig. 2.The pitch istaken around the x-axis. The body axis is around the y-axis. The yaw is around the z-axis.
Each link consists of two passive wheels and two servomotors. The servo motors can rotate
in the pitch or yaw directions with the range of motion of ±90 deg. A web camera is built
into the robot’s head to watch the target environment.
Table 1: Parametersy ĂǆŝƐz ĂǆŝƐ ĂǆŝƐ

,ĞĂĚ

Figure 1: Snake-like robot

3.

Figure 2: Coordinate axes

parameters
Link number[-]
1 link length[m]Yaw angle[rad]Pitch angle[rad]Amplitude[m]Phase[rad]Number of motors[-]

variable
i
li
ψj
θj
A
P
j

Pitch Angle Serpenoid Motion Simulation

We simulate a movement of the snake-like robot, and try to design a motion for moving
on a cable rack, which is considered as a pitch-angle serpenoid motion. In the previous
research, we have demonstrated the serpenoid motion on the ﬂat ﬂoor generated by the yawaxis servomotors. The serpenoid motion is represented by (2).
ϕi = Asin(t − P(i − 1))

381

(1)

By controlling the pitch angle according to (2), the snake-like robot can realize the pitchangle serpenoid motion. We set A = π/2 m, and P = 2π/3 rad in (2). The result is shown in
Fig. 3. It can be conﬁrmed that the snake-like robot is moving on the cable rack due to the
motion of pitch angle serpenoid. The motion is easily implemented to the robot forcontrolling the corresponding servomotors.

Figure 3: Pitch angle serpenoid motion on the cable rack4.

Comparison with Spiral Motion

We compare and verify the eﬀectiveness of the proposed pitch-angle serpenoid motion
by comparing it with the spiral motion by CMU. For the comparison and veriﬁcatoin, we
ﬁrst need to design the attitude angle to give the spiral shape of the serpentine robot.
Assuming that x, y, z is each coordinate axis respectively, we set and a, b are constants
which decide the shape of the normal spiral. The relationship is represented by (2) [5].
(x(t), y(t), z(t)) = (asint, acost, bt)(2)

A normal spiral can be formed by shifting the phases in the yaw and pitch direction by ±90
deg. Based on (2), the attitude angles determined to form a spiral shape in consideration of
the period and phase are given in (3) and (4) as shown in [6].
)
( j
− jπ
−( −1)πψ j = Asin 2P− Asin P2(3)( j)−( 2 −1)π
− jπ
2
+
Acos
(4)
θ j = −Acos
P
P
Next, in the simulator developed by using Simscape, we input (3) in the yaw direction of theservomotor and (4) in the pitch direction as commands. The result is shown in Fig. 4. It canbe conﬁrmed that the snake-like robot cannot propel on the cable rack by the spiral motion.
The fact leads to a conclusion where pitch-angle serpenoid motion is more eﬀective than the
spiral motion for propulsion on the cable rack.

5.

Concludion

We developed a simulator for developing a snake-like robot towing a thin lead-wire
toward cable laying. In the simulator, the propulsion of a serpentine robot by pitch angle

382

Figure 4: Spiral motion on the cable rack

serpenoid motion on a cable rack model was investigated. As a result, it was found that thesnake-like robot can move by the proposed motion. After that, we also simulated the
movement of the snake-like robot on the rack due to the spiral motion, and compared it withpitch angle serpenoid motion. The comparison result said that the snake-like robot could notpropel on the cable rack in the spiral motion. Therefore, it was conﬁrmed that pitch angle
serpenoid motion is more eﬀective than spiral for propulsion of the snake-like robot on thecable rack. We will verify the actual propulsion on the cable rack by the pitch angle
serpenoid motion of the snake-like robot.

References[1] Japanese Statistics Bureau: Labor force survey, (2021).
[2] Selvarajan, A.; Kumar, A.; Sethu, D.; bin Ramlan, M. A.: Design and Developmentof a Snake-Robot for Pipeline Inspection, 2019 IEEE Student Conference on Researchand Development (SCOReD), (2019), 237-242.
[3] Dal Corso Francesco, Zini Stefano, Takumi Yamato, Masami Iwase: Design modelingand control of a snake-like robot, 2019 MSCS, (2019).
[4] CMU Biorobotics Lab: Modular Snake Robots,(2020),
http://biorobotics.ri.cmu.edu/projects/modsnake/pipes.html[5] Keener, James P. , Tyson, John J.: Spiral waves in the Belousov-Zhabotinskii reaction,
Physica D: Nonlinear Phenomena , Vol. 21, No. 2-3 Elsevier, (1986), 320-322.
[6] Takumi Yamato, Dal Corso Francesco, Zini Stefano, Shoshiro Hatakeyama, Masami
Iwase: Helical Rotary Propulsion of Snake-like Robot on Gravel Road, 2020 MSCS,(2020).

383

JSST 2021

Path tracking ﬂight of engine-driven multicopter forforest inventory
Yuto Terada1,* , Kazuya Sato1 , Naoki Masuda1 , Masami Iwase1 , Yasuyuki Sato1
1 Department of Simulation, School of Technology, Tokyo Denki University∗ terada17@ctrl.fr.dendai.ac.jp

Abstract. The purpose of this study is to conduct a highly accurate and eﬃcient forest
inventory using a multicopter equipped with a laser sensor. To achieve this purpose, we solve
three problems. The ﬁrst is to realize an altitude maintenance control of the multicopter. The
second is to realize long ﬂight of the multicopter. The third is to achieve collision avoidanceby the multicopter with standing rees. For the purpose, we develop a simulator for the ﬂight
control of a multicopter to avoid obstacles. Using the simulator an algorithm is designed to
ﬂy in the forest, and is conﬁrmed for the autonomous ﬂight.
Keywords: Forestry, Drone, Forest survey, Trajectory generation

1.

Introduction

About two-thirds of Japan’s land area is covered forest. The forest has multiple functions;such as forest conservation of national land, prevention of global warming, forest including
wood product supply. In order to keep these functions sustainably, people hope that forest
operations become more eﬃcient. Therefore, it is important to accurately grasp the condition of forest and evaluate the value of forest correctly. In the direction, it is necessary
to survey forest in detail and to measure each tree conditions; height, stem circumference,
bend of each tree and so on. Current general survey method is a kind of sample plot surveys.
However, since the sample survey takes only a part sample of a standard land representing
the interest forest, it does not provide an understanding of the topography of the entire forest. It sometimes leads to additional survey is required to perform forest management. For
these reasons, decline in proﬁtability for forestry become a problem. In order to solve theproblems, we propose to develop an engine-driven multicopter equipped with a laser sensor ﬂying and scanning forest. It can be used toward a substitute ﬁeld surveys by workers[1]-[2].
This method enables safe surveying even on steep slopes because users only operate thedrone far from the survey area. In addition, the multicopter ﬂies for long time during forest
suvey. Using the laser sensors eﬃciently measuring single-tree unit data, the multicopter
provides well-rich information for forest management planning. To realizethis system, it
is necessary to develop a ﬂight control system of the multicopter. Toward the purpose, we384

Figure 1: Engine-driven multicopter
should solve the following three problems. The ﬁrst is to realize an altitude maintenancecontrol of the multicopter. Because the measurement of each tree by laser sensors requires
stable hovering. The second is to extend the continous ﬂight time of the multicopter. The
multicopter in this system uses a gasoline engine as the power source because it is required
for the multicopter to have both a high payload to carry the laser sensors and the long ﬂight
time. The third is to achieve collision avoidance of multicopter with standing trees Whenthe multicopter ﬂies in the forest, there is a possibility that the multicopter will collide withtrees. Therefore a collision avoidance system is needed to enable non-professional operators
to ﬂy multicopters in the forest. To realize collision avoidance, we implement Simultaneous
Localization and Mapping, and generate the trajectory for collision avoidance.
In this paper，We aim to develop simulator that takes the ﬂight path into account.

2.

trajectory generation

In this section, we describe simulation of the ﬂight path of a multirotor ﬂying in a forest.
The multicopter is able to follow the generated ﬂight path by position control.In this study,
the Lidar mounted on a multicopter is used to measure standing trees, and the speed of
the Lidar is kept constant to facilitate the measurement. As shown in the Figure 3, theFigure 2: velocity

Figure 3: Path tracking ﬂight

multicopter ﬂies over a ﬁeld of trees randomly placed at intervals of 2.0 m or more. If there
is a tree in the middle of the ﬂight path, it is necessary to avoid the collision between the tree
and the multicopter, so the multicopter ﬂy as shown in Figure 3. As this time, the distance385

between the tree and the multicopter was set to 0.3 m or more. However in this algorithm, a
new target value is set and the ﬂight is performed when the target value reached each time.
Therefore, the trajectory when avoiding the trees became irregular. So, we propose a newalgorithm for collision avoidance ﬂight.

Figure 4: New collision avoidance ﬂight proposal
As shown in Figure 4, the multicopter ﬂies along the trajectory interpolated from theWaypoints set on the generated ﬂight path. When an obstacle on this path is detected by
Lidar during ﬂight, the path is changed appropriately. We think we can change the routeby hypothetically assuming that the line connecting the waypoints has a spring-like elastic
force, and that there is a repulsive force between the point cloud detected by Lidar and the
waypoints. We denote by F p ( j, i) the repulsion force that the i-th Waypoint receives fromthe j-th point group, Fw (i, i − 1) the force that the i-th Waypoint receives from the previous
Waypoint, and Fw (i, i + 1) the force that the i-th Waypoint receives from the subsequent
Waypoint. F p ( j, i), Fw (i, i − 1) and their combined force are represented by the following
equations.
F p ( j, i) =Xh·wi − p j(1)

wi − p j
wi − p j
Fw (i, i − 1) = k (wi−1 − wi )(2)

F p ( j, i) + Fw (i, i − 1) + Fw (i, i + 1) = 0

(3)

2

j

We use the Newton-Raphson method to search for waypoints where these resultant forces
are zero. We deﬁne a vector X with the coordinates of the waypoint to be changed aligned
vertically.
 w2 
 . X =  .. 
(4)


wN−1
In this case, the waypoints at both ends to be changed are ﬁxed. Therefore, if w1 and wN are
ﬁxed as Waypointw1 , w2 , ·, wN , the Waypoint that can be changed is w2 , ·, wN−1 . The vector
X is updated according to the Newton-Raphson method with the initial value of X 0 as shownin the following equation.
X k+1 = X k −∂H(X k )× H(X k )
∂X

386

(5)

By moving the waypoints to these equilibrium points, the appropriate ﬂight path is generated
to avoid collisions between the multicopter and each trees. We have veriﬁed the proposed
algorithm by simulation.
The simulation is shown in Figure 5.

Figure 5: Path generation for collision avoidance ﬂight
As shown in Figure 5, the path that the multicopter is planning to ﬂy is indicated by theblue waypoints. When the multicopter is ﬂying at position (0,0), the Lidar detected half ofa tree. As a result, green Waypoints, which is a path that avoids collisions with the tree, wasgenerated. We conﬁrmed that a new ﬂight path that avoids collisions with the tree can begenerated from the point cloud detected by Lidar.

3.

Conclution

This study aims to develop a path-following ﬂight of an engine-driven multicopter for
surveying in forest. For this purpose, we conﬁrmed the ﬂight control of the multicopterand created simulation of the ﬂight path. The simulated ﬂight path was unstable due toirregular spacing when avoiding collisions between the multicopter and trees. Therefore,
we proposed an algorithm in which Lidar detects obstacles and generates a new route to
avoid collisions. The eﬀectiveness of the proposed algorithm was conﬁrmed by simulations,which generated a new ﬂight path that avoided collisions with trees based on the point clouddetected by Lidar.
In the future, we will conﬁrm the path generation in the forest considering the collision
avoidance algorithm by simulation and verify it on the actual machine of multicopter.

References[1] A. Masato KATOH, B. Songqiu DENG, C. Yuki TAKENAKA, D. kwaion CHEUNG,
E. Masahiro HORISAWA, F. Katsumasa OONO, G. Takaaki ITO: Smart Precision
Forestry Using Laser Sensing, 85:3 (2019), 232–235.
[2] A. Naoki Muroki, B. Takayuki I: Estimating a stand volume using UAV-aerial images
and terrestrial laser scanning, 52:2 (2019), 83–88.

387

JSST2021

Angular momentum of electromagnetic wave radiatedfrom a relativistic electron moving on a spiral orbit
Elham Salehi*
UVSOR, Institute for Molecular Science, National Institutes of Natural Sciences*elham@ims.ac.jp

Abstract. We give an analytic expression for the vector potential of the electromagnetic wave
radiated from a relativistic electron moving on a spiral orbit. Based on this expression, we showthat the electromagnetic wave has a spiral wave front and carries angular momentum which is
combined with spin and orbital angular momentum.
Keywords: Electromagnetic wave, Relativistic electron, Angular momentum, Optical vortex

1. Introduction
Twisted photon beams (optical vortices) have attracted enormous interests because of their applications [1, 2, 3]. A twisted beam forming an helical wave-front structure exhibits two intrinsic degrees of freedom associated angular momentum; an orbital angular momentum (OAM)
anda spin angular momentum (SAM).
In the helical undulator, electrons run on a spiral orbit. The spiral motion of the electrons canbe separated into a drift motion along the undulator axis and a circular motion around it. In themoving reference frame with the drift velocity, the radiation field should be that from the circular motion. Its Lorentz transformation to the laboratory frame is the helical undulator radiation. Therefore, the origin of the peculiar characteristics of the radiation field from helical undulators should be found in the radiation from the circular motion as shown in [4, 5]. In thispaper, we derive the analytic expression directly from the spiral electron motion and discuss
the spatial structure and angular momentum of the radiation emitted from this electron.

2. Analytic Expersion for Radiation Field and Angular Momentum
The vector potential of the radiation from an electron on a helical orbit in the spherical coordinate system may be expressed as follows [6];+∞𝐴⃗(𝑡) = ∫−∞ 𝐴(𝑡)𝑒 𝑖𝜔𝑡 𝑑𝑡 = 𝑒
(1)

𝜔
𝑖 𝑟

𝑒 𝑐
𝑟

⃗⃗⃗∙𝑟
⃗⃗
+∞ 𝑖𝜔(𝑡+𝑛
)

∫−∞ 𝑒

𝑐

1

(1)

1

𝑑𝑟⃗𝑒 + 𝑜 (𝑟2 ) ≡ 𝐴⃗𝜔 + 𝑜 (𝑟2 )(1)Here, 𝐴𝜔 shows the vector potential of the first order of 1⁄𝑟. By the vector potential we
can obtain the fourie components of the electric and magnetic fields. It should be noted thatthe non-zero terms of longitudinal component of the electromagnetic fields starts from the388

JSST2021
second order of 1/𝑟 which is usually neglected in the radiation field calculation, contributes
to angular momentum.
The number of photons carried by the m-th harmonic of the radiation can be obtained by dividing the energy of the radiation to the energy per photon, ℏ𝜔𝑚 (𝜃), as follows;𝑑𝑁 𝑚
11𝑚(1) 𝑚(1)∗𝑚(1) 𝑚(1)∗= ∫ 4𝜋ℏ𝑐 𝑟 2 𝑑𝛺𝜔𝑚 (𝜃) (𝐴𝜃 𝐴𝜃
+ 𝐴𝜑 𝐴𝜑) + 𝑜 (𝑟 )𝑑𝑡

(2)

The angular momentum component parallel to the axis of the helical motion carried by m-th
harmonic of the radiation field may be expressed as follows:𝑑𝐽𝑧𝑚𝑚 𝜔 (𝜃)1𝑚(1) 𝑚(1)∗𝑚(1) 𝑚(1)∗= ∫ 𝑐𝑟 2 𝑗𝑧𝑚 𝑑Ω = 4𝜋 ∫ 𝑚𝑐 (𝐴𝜑 𝐴𝜑+ 𝐴𝜃 𝐴𝜃) 𝑟 2 𝑑Ω + 𝑜 (𝑟)𝑑𝑡(3)Eqs. (2) and (3) may be summarized as follows;
𝑑𝐽𝑧𝑚
𝑑𝑁 𝑚
=
𝑚ℏ
𝑑𝑡
𝑑𝑡

(4)

which indicates that m-th harmonic component carries angular momentum, 𝑚ℏ per photon.
Here, we have obtained the same result as obtained in the previous work [4] which the angularmomentum was calculated for a circular motion. This work verifies the treatment in the previous work.
Here, we present the numerical results to show typical spatial structures of the phase and intensity of the radiation emitted from an electron in a spiral motion for the positive helecity ofthe second harmonic 𝑚 = 2 in Fig. 1. The donut-shaped of intensity (left) and phase structure(right) of the radiation show that the radiation carries OAM, (𝑚 − 1)ℏ = ℏ. The degree ofcircular polarization indicates 100% circular polarization with positive helicity.

Figure 1: Spatial structure of the 2nd harmonic component

3. Conclusion
We have shown analyticaly and numerically that the electromagnetic field radiated from a freeelectron running on a spiral orbit carries angular momentum and possesses a helical phasestructure, depending on the harmonic number and the helicity. Such a physical situation, in
which relativistic free electron are running on spiral orbits, can be found in laboratories andnature, such as in particle accelerators, nuclear fusion plasma, astrophysical objects and so on.

References[1] e.g. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3 (2007), 305-310.
[2] e.g. R. W. Bowman, M. J. Padgett, Nat. Photon., 5 (2011), 343-348.
[3] e.g. Y. Shen et al.: Optical vortices 30 years on, Light: Sci. & Appl., 8:90 (2019) (29 Pages).
[4] M. Katoh et al., Phys. Rev. Lett. 118:9 (2017), 094801 (5 Pages).
[5] H. Kawaguchi, M. Katoh, Prog. Theor. Exp. Phys. 2019 (2019), 083A02 (18 Pages).
[6] E. Salehi, M. Katoh, J. Adv. Simulat. Sci. Eng., 8:1 (2021), 87-97

389

JSST 2021

Structure formation of chiral needles
by modeled force fields with helical phaseusing molecular dynamics simulation
Shu Habu1* and Hiroaki Nakmaura1,2
1 Department of Electrical Engineering, Graduate School of Engineering, Nagoya

University
2 National Institute for Fusion Science, National Institute of National Sciences∗ naka-lab@nifs.ac.jp

Abstract. We fabricate the helical nano-scaled metal needle (nanoneedle) structure of tantalum using classical molecular dynamics simulation. Since the force on atoms due to theexternal field is too complex, we simplified it so that the force is proportional to the external
electric field. It was found that the nanoneedle structure depends on the topological structureof the external field.
Keywords: Orbital angular momentum, Molecular dynamics simulation, chiral structure

1.

Introduction

Laguerre-Gaussian (LG) beams carry orbital angular momentum (OAM) around its beamaxis [1]. The component of angular momentum flux in the direction of the EM-wave propagation is J = ε0 ω(l + σz )/2, where l (= 0, ±1, · · · ) is the azimuthal mode index, andσz (= 0, ±1) is the polarization of the beam.
Omatsu group demonstrated that when the polished tantalum (Ta) target which was ∼2
mm in thickness was irradiated with LG beam, the helical nanoneedle was fabricated on thesurface of the Ta target [2]. According to their result [2], on the surface of the target Ta
irradiated with the LG beam, which has the non-zero orbital angular momentum (l , 0), thehelical needle structures were observed.
Therefore, we investigate the mechanism of the helical nanoneedle structural formationby the EM-wave with the OAM using molecular dynamics (MD) [3, 4].

2.

Molecular dynamics simulation

As the MD code, we adopted Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) code [5]. In this classical MD simulation, the body-centered cubic (BCC) Ta390

crystal at 300 K was prepared as the initial structure of the target. We used the interatomic
potential, embedded atom method (EAM) potential force field of Ta [6]. The canonicalensemble with the Langevin thermostat [7] was also used to control the temperature of thesystem T . Assuming that the LG beam is irradiated to Ta during 30 ps, we set the external
force field to the target instead of calculating the interaction between the EM-wave andthe material. This external force described by Eq. 1 depends on the l (the azimuthal mode
index of the beam), and σz (the polarization of the beam). In the case of l , 0, it has thehelical phase distribution. Then, we continued the simulation with no external force to get
the target in the equilibrium state at 300 K. We carried out the above procedure in the ninecases, l = 0, ±1 and σz = 0, ±1, respectively.

Figure 1: Simulation model. The tantalum BCC crystal was prepared as the initial structureof the target. Assuming that the EM-wave is irradiated from the −z direction to the target,
the external force field described by Eq. 1 was set to the target. The nanoneedle structure
was generated on the surface of the target.
The external force Fl,σz set to the target is proportional to the electric field of LG beamin the simple form (radial mode index is 0) ELG
0,l,σz , which has the following form:
Fl,σz (r, ϕ, z, t) ∝ ELG
0,l,σz (r, ϕ, z, t)

iπσ

E0 
 e x + ey e 2 z LGe=u0,l (r, ϕ, z)
√


2 
2

 LG
LG (r, ϕ, z) u0,l (r, ϕ, z)
∂e
u0,l

π
i  ∂e i(kz−ωt)+ ei 2 σze+ c.c.,+ez √ 




∂x
∂y
2k

(1)

where the k direction of the EM-wave propagation is set to the −z direction, and the unit
vector of the z axis is defined by ez . The x and y axes are set in the transverse plane, andLG is defined in thetheir unit vectors are defined by e x and ey . The function of LG beam eu0,lcylindrical coordinate (r, ϕ, z) as follows:
√
(
)|l|
[
]
2 w0
r
r2
LG
e
u0,l (r, ϕ, z) :=exp − 2
π|l|! w(z) w(z)
w (z)
[
( )]
2
r z
−1 z
− i(|l| + 1)tan,(2)
× exp ilϕ + i 2zRw (z)zR391

where the Rayleigh length zR and the radius of the beam w(z) are given by zR = kw20 /2 and√w(z) = w0 1 + (z/zR )2 . The constant w0 is set to unity.

3.

Results

We succeeded in the helical nanoneedle fabrication in the cases of (l, σz ) = (1, 1) and(−1, −1) shown in Fig. 2. Furthermore, we found that the direction of the helical needle
structure turns on l. However, the nanoneedle was not fabricated in other cases of l , 0
that the external force field has the helical phase distribution. The problem may exist in theenergy transfer from EM-wave to the material (Ta). we also need to improve the modelingof the external force field. It is said that the optical force of the radial and azimuthal components of the external force field are significant to the helical needle fabrication, which collectthe Ta particles to the center of the axial core and produce the orbital motion of the particles
about the axial core [2, 8, 9].

Figure 2: Simulation results. The twisted nanoneedle structure is fabricated in silico by MD
simulation. In the bellow figures, the red lines show the helical structures of the nanoneedle,
the directions of the helical structures are opposite.

4.

Conclusion

In this paper, we have demonstrated the fabrication of the chiral needle using the MD withthe modeled external force. In the future work, we will introduce the radiation force formula
to improve this model [10].

Acknowledgments
The research was supported by Grants-in-Aid for Scientific Research (C), Nos.18K11416
and 19K03800 from the Japan Society for the Promotion of Science, and by the NIFS Collaborative Research Programs NIFS20KNTS066, NIFS20KNSS150 and NIFS20KKGS028.

392

The computations were performed using the JFRS-1 supercomputer system at Computational Simulation Centre of International Fusion Energy Research Centre (IFERC-CSC) in
Rokkasho Fusion Institute of QST (Aomori, Japan) , Research Center for Computational
Science (Okazaki, Aichi, Japan) , and ”Plasma Simulator”(NEC SX-Aurora TSUBASA) of
NIFS (Toki, Gifu, Japan) .

References[1] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman. Orbital angularmomentum of light and the transformation of laguerre-gaussian laser modes. Phys.
Rev. A, Vol. 45, pp. 8185–8189, Jun 1992.
[2] Kohei Toyoda, Fuyuto Takahashi, Shun Takizawa, Yu Tokizane, Katsuhiko Miyamoto,Ryuji Morita, and Takashige Omatsu. Transfer of light helicity to nanostructures. Phys.
Rev. Lett., Vol. 110, p. 143603, Apr 2013.
[3] Hiroaki Nakramura, Shu Habu, Seiki Saito, and Shin Kubo. Molecular dynamics simulation on structural formation of chiral nanoneedle by optical vortex. In The 38th
JSST Annual International Conference on Simulation Technology, Miyazaki, Japan,
11 2019. The Japan Society for Simulation Technology.
[4] Shu Habu and Hiroaki Nakmaura. MD Simulation on Chiral Needle Fabrication in
Radiation Force Field of Laguerre-Gaussian Beams. In The 29th International Toki
Conference on Plasma and Fusion Research, Gifu, Japan, 10 2020. National Institutefor Fusion Science.
[5] Fast parallel algorithms for short-range molecular dynamics. Journal of Computational
Physics, Vol. 117, No. 1, pp. 1–19.
[6] R. Ravelo, T. C. Germann, O. Guerrero, Q. An, and B. L. Holian. Shock-induced
plasticity in tantalum single crystals: Interatomic potentials and large-scale moleculardynamics simulations. Phys. Rev. B, Vol. 88, p. 134101, Oct 2013.
[7] T. Schneider and E. Stoll. Molecular-dynamics study of a three-dimensional onecomponent model for distortive phase transitions. Phys. Rev. B, Vol. 17, pp. 1302–
1322, Feb 1978.
[8] Takashige Omatsu, Keisuke Chujo, Katsuhiko Miyamoto, Masahito Okida, Kazuki
Nakamura, Nobuyuki Aoki, and Ryuji Morita. Metal microneedle fabrication using
twisted light with spin. Opt. Express, Vol. 18, No. 17, pp. 17967–17973, Aug 2010.
[9] Kohei Toyoda, Katsuhiko Miyamoto, Nobuyuki Aoki, Ryuji Morita, and Takashige
Omatsu. Using optical vortex to control the chirality of twisted metal nanostructures.
Nano Letters, Vol. 12, No. 7, pp. 3645–3649, 2012. PMID: 22690654.
[10] James P. Gordon. Radiation forces and momenta in dielectric media. Phys. Rev. A,
Vol. 8, pp. 14–21, Jul 1973.

393

JSST 2021

The study on the stability of DNA structure by steered
molecular dynamics simulations
Tomoko Mizuguchi1,* , Naoto Fukushima1 , Takashi Aoki2 , Masato Hashimoto1 ,Susumu Fujiwara1
1 Faculty of Materials Science and Engineering, Kyoto Institute of Technology
2 Department of Biobased Materials Science, Kyoto Institute of Technology∗ mizuguti@kit.ac.jp

The full paper of this paper has been published in Journal of Advanced Simulation in
Science and Engineering (JASSE).
DOI: https://doi.org/10.15748/jasse.9.160

394

JSST2021

Reactive molecular dynamics study on damaged
polyethylene after hydrogen abstraction by radiation
Haolun Li1*, Susumu Fujiwara2, Hiroaki Nakamura3,4, Tomoko Mizuguchi1,
Ayako Nakata5, Tsuyoshi Miyazaki5, Shinji Saito6, Wataru Sakai1
12Graduate School of Science and Technology, Kyoto Institute of Technology

Faculty of Materials Science and Engineering, Kyoto Institute of Technology
3
National Institute for Fusion Science
4
Nagoya University
5
National Institute for Materials Science
6
Institute for Molecular Science*d0871005@edu.kit.ac.jp

Abstract. One of the effects that radiation causes on polymeric materials is the hydrogen abstraction reaction, which induces radicalization and the subsequent structural changes such as
de-crystallization, cross-link and chain scission. However, at a nanoscale, the changes of theentire chain and the reaction paths on local segments are difficult to be completely caught byexperiment. In this research, we investigate the structural change of hydrogen-removed polyethylene by means of reactive molecular dynamics simulations using two kinds of ReaxFF
force field parameter sets, called CHO-2006 and CHO-2016. And to compare the two parameter sets, atomic forces of the final configurations are calculated by density functional theory.
Our results suggest that CHO-2006 is a better parameter set for treating damaged hydrocarbons.
Furthermore, during simulations using the CHO-2006 parameter set, de-crystallization, formation of C=C double bond, cyclic structure and conjugated bond and chain scission wereobserved.
Keywords: Molecular dynamics simulation, Polyethylene, Structural change, Reactive force field

1. Introduction
After exposure to radiation within a high energy or for a long time, polymeric materials areradicalized from the surface to the interior, leading to structural changes and chemical bondrearrangements. Among the effects caused by radiation on polymeric materials, hydrogen abstraction (H-abstraction) reaction is one of the most possibly occurred effect. For the reason
that H-abstraction reaction occurs on random position of polymer chains, it is difficult to study
the structural change of polymers induced by H-abstraction at a nanoscale through experiment.
In our former research, coarse-grained molecular dynamics (MD) simulations were employed
to treat a hydrogen-removed polyethylene chain with a folding structure and the results showsthat if more hydrogen atoms are removed from polyethylene chain, the crystallinity decreases

396

JSST2021
more [1-2]. However, it is extremely possible that losing hydrogen on the polyethylene cause
chemical bond rearrangements, but the classical MD methods are not able to treat chemical
reactions. Thus, we introduce a reactive force field, ReaxFF, which is developed by van Duinand able to treat the break and the formation of chemical bonds. In this research, we predict thestructural change of hydrogen-removed polyethylene by MD simulations using ReaxFF force
field. As there are two parameter sets (called CHO-2006 [3] and CHO-2016 [4]) available fortreating damaged hydrocarbons, we also employed density functional theory (DFT) calculations to compare the appropriateness of the two parameter sets.

2. Simulation models and methods
Hydrogen-removed polyethylene models were made by the following steps. In step (i), an allatom polyethylene model (C300H602) was cooled in 100 K by classical force field and formed achain-folding structure (Fig. 1(a)). In step (ii), we randomly removed hydrogen atoms from themodel. The ratio of removed hydrogen atoms to carbon atoms (fH) is set to 0, 0.01, 0.05, 0.1,
0.2, and the number of removed hydrogen atoms is 0, 3, 15, 30, 60, respectively. In step (iii),
the models of each fH with the same initial configuration were kept 100 K for 1.3 ns (13,000,000
time steps, 1 fs per time step) in a vacuum simulation box by ReaxFF MD simulations using
two parameter sets, CHO-2006 and CHO-2016 respectively. After the simulations, DFT calculations were done to calculate atomic forces of the final configuration. Furthermore, to study
the structural change in a high temperature, the models were heated from 100 K to 400 K at aheating rate of 100 K/ns for 3 ns (30,000,000 time steps). In all simulations, NVT ensemble isemployed and the size of the vacuum simulation box is set to 400 Å × 400 Å × 400 Å. The
Nosé–Hoover method is applied to control the temperature. The simulation software used is
LAMMPS.

3. Results and discussions
For the step (a) in ReaxFF MD simulations, the structures of models at 100 K visualized areshown in Fig. 1. To quantify the time dependence of structural change, we also calculate theglobal orientational order parameter and the root mean square deviation of the carbon atoms.
The results suggest that during simulations using either parameter set, the models of fH = 0 keepa chain-folding crystal structure and the models of fH = 0.2 become less ordered after thesimulations of 1.3 ns at 100 K.
To compare the two used parameter set CHO-2006 and CHO-2016, DFT calculations are introduced as a reference and classical force field calculations are also employed for a comparison. In DFT calculations, ReaxFF MD simulations and classical force field calculations, theatomic forces of all atoms of the final configuration (CHO-2006 model and CHO-2016 model,
respectively) are calculated. The magnitude of forces (F) calculated by different methods iscompared in Tables I and II. In Table I and II, the average F in CHO-2006 case and CHO-2016
case derived by ReaxFF MD simulations and DFT calculations is in the same level. However,
the average F derived by both classical force field calculations is much higher in CHO-2016
case than in CHO-2006 case and higher than those derived by ReaxFF MD simulations and
DFT calculations. It means that the structure configured by CHO-2006 is more stable for classical MD simulations, while that by CHO-2016 is unstable and not in an equilibrium state forclassical MD simulations. By this reason, the CHO-2006 is suggested to be the more suitableparameter set to treat damaged polyethylene than CHO-2016.

397

JSST2021↓D1-CH2-CH-CH2—CH2-CH-CH2D3↑↑D2 ↓-CH2-CH=CH2 + CH2=CH-CH2-

CHO-2006

(b)

(c)
(

𝒇𝐇 = 𝟎𝒇𝐇 = 𝟎. 𝟐

(a)

(Å)

Initial Structure

CHO-2016(d)(e)

𝒇𝐇 = 𝟎𝒇𝐇 = 𝟎. 𝟐

Fig. 1 Snapshots of the structure of polyethylene
chains: (a) initial structure before simulation, (b) and(c) structures of 𝑓! = 0 and 0.2 after simulation using CHO-2006, respectively, (d) and (e) structures of
𝑓! = 0 and 0.2 after simulation using CHO-2016,
respectively, where hydrogen atoms are not shown.

Fig. 2 The reaction formula of chain scission and temperature dependence of the distance of different C-C pairs. At
about 348 K, the unstable blue bond breaks, violet C-C single bond becomes stable, and the brown one changes froma unstable C-C single bond to a stable C=C double bond.

Table I. The average F (unit: a.u.) of all atoms for all fH’s derived from four kinds of calculations where the models
are configured by CHO-2006.

fH

0

0.01

0.05

0.1

0.2

DFT

0.02584

0.025390.024810.024240.02316

CHO-2006

0.018160.01832

0.01786

0.01901

0.01850

OPLS-AA

0.02107

−

−

−

−

DREIDING-AA

0.02317

−

−

−

−

Table II. The average F (unit: a.u.) of atoms for all fH’s derived from four kinds of calculations where the models
are configured by CHO-2016.

fH

0

0.01

0.05

0.1

0.2

DFT

0.026240.026990.02709

0.02651

0.02580

CHO-2016

0.01859

0.01805

0.018290.017620.01788

OPLS-AA

0.03510

−

−

−

−

DREIDING-AA

0.05008

−

−

−

−

During the simulations using CHO-2006, several kinds of chemical reactions were observedon specific segments. Chain scissions (C-C bond break) occur at a high temperature. The temperature dependence of one chain scission is shown as Fig. 2. A unstable bond breaks at about
348 K. And at the same time, the adjacent four C-C bonds changes to be stable or form a C=C
double bond, respectively. During simulations at 100 K, formations of C=C double bonds, cyclic bonds and conjugated bonds were also found in specific positions. The reaction formulas
are shown in Fig. 3.

398

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Fig. 3 The reaction formulas (a)-(d) corresponding to situations (1)-(4), respectively. In formula (a), the average
length of new C-C bond is 1.51 Å. In formulas (b) and (c), the average length of new C=C double bond is 1.35Å. In formula (d), the average length of conjugated bond is 1.40 Å. Red parts represent newly formed bonds.

4. Conclusions
In this research, structural change of hydrogen-removed polyethylene is studied by ReaxFF
MD simulations using two kinds of parameter sets and DFT calculations are employed tocompare the two used parameter sets. Based on our simulation results, we found that losing
more hydrogen atoms leads to a higher decrease of crystallinity. After the comparison of atomic
forces, the CHO-2006 is suggested to be more suitable to treat damaged hydrocarbons. And
during the simulations, chemical reactions at specific segments occurred, including formationsof C=C double bonds, cyclic bonds and conjugated bonds at 100 K and chain scissions at ahigh temperature.

References[1] S. Fujiwara, H. Nakamura, H. Li, H. Miyanishi, T. Mizuguchi, T. Yasunaga, T. Otsuka,
Y. Hatano, S. Saito: Computational Strategy for Studying Structural Change of TritiumSubstituted Macromolecules by a Beta Decay to Helium-3, J. Adv. Simulat. Sci. Eng., 61 (2019), 94-99[2] H. Li, S. Fujiwara, H. Nakamura, T. Mizuguchi, T. Yasunaga, T. Otsuka, T. Kenmotsu,
Y. Hatano, S. Saito: Structural Change of Tritium-Substituted Polymeric Materials by a
Beta Decay: A Molecular Dynamics Study, Plasma Fusion Res., 14 (2019), 3401106[3] K. Chenoweth, A. van Duin, W. A. Goddard: ReaxFF Reactive Force Field for Molecular Dynamics Simulations of Hydrocarbon Oxidation, J. Phys. Chem. A, 112 (2008),
1040-1153.
[4] C. Ashraf, A. van Duin: Extension of the ReaxFF Combustion Force Field toward
Syngas Combustion and Initial Oxidation Kinetics, J. Phys. Chem. A, 121 (2017), 10511068.

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Comparison of beam-wall interaction models using
boundary element method
Kazuhiro Fujita1*
Department of Information Systems, Faculty of Engineering, Saitama Institute of Technology

1*

kfujita@sit.ac.jp

Abstract. The electromagnetic interaction of a relativistic particle beam with resistive pipes isof great interest in accelerator physics. There are perturbative and nonperturbative models forthis beam-wall interaction. We present direct comparison of frequency domain simulations forboth models in the context of boundary element method.
Keywords: Accelerator beam pipe, resistive wall, perturbation theory, boundary element method

1. Introduction
The electromagnetic interaction of a relativistic charged particle beam with vacuum chamberbeam pipes with walls of finite conductivity is of great interest in accelerator physics [1]. As aresult of this interaction, electromagnetic fields, known as wake fields [1], can be excited dueto the existence of resistive wall. The boundary element method (BEM) [2].[3] is one of promising numerical approaches for this subject. The so-called perturbative theory [1], where it isassumed that the magnetic field on the wall is the same as in the case of perfect conductivity,
is often used. However, no comparison of perturbative and nonperturbative models in theframework of BEM is shown in [2],[3]. The main purpose of this work is to show direct comparison of perturbative and nonperturbative simulations using the 2-D BEM [4].

2. ModelingIn the nonperturbative model, a boundary integral representation of magnetic field H for infinitely long resistive pipe with the cross-section C can be derived as [4]1

𝐇 = 𝐇𝑠 − 𝑗𝜔𝑭 + 𝜇 ∇ × 𝐀, 𝐀 = 𝜇 ∫𝐶 𝐺(𝐫, 𝐫 ′ )𝐊(𝐫 ′ )𝑑𝐫 ′ , 𝐅 = 𝜀 ∫𝐶 𝐺(𝐫, 𝐫 ′ )𝐌(𝐫 ′ )𝑑𝐫 ′ (1)1𝐺(𝐫, 𝐫 ′ ) = 2𝜋 𝐾0 (𝑘𝑟 |𝐫 − 𝐫 ′ |),𝐧 × 𝐇 = 𝐊,

𝐌 = 𝑍𝑠 𝐊 × 𝐧(2)

where Hs is the self-field of a relativistic charged particle beam moving with constant velocity
vez in the z direction and the beam current I, G is the Green function, K and M are the electricand magnetic surface current on the pipe wall, respectively, Zs is the surface impedance, K0 is
the modified Bessel function, kr=k/γ, k=ω/v, γ is the Lorentz factor and ω=2πf is the angular400

JSST2021
frequency. According to the conventional BEM procedure, Eq.(1) is solved for K. After K isgiven as boundary values, the longitudinal electric field Ez is obtained from M.
In the perturbative model, it is assumed that the magnetic field on the wall is the same asin the case of perfect conductivity. Eq.(1) is solved with Zs=0, and then Ez is obtained from M.

3. Numerical result
We assume here that a particle is highly relativistic (γ=10000) and moves in the center of an
infinitely long resistive pipe, for comparison with the perturbation theory [1],[5]. Using bothmodels, we numerically calculate “coupling impedances” Z=−Ez/I for round and square pipes
with wall conductivity σ=5.8×107 S/m and a=2.5mm as in Fig.1. For the round pipe, the theory
is valid for (|Zs|ωa)/(2cZ0)<<1 with c=1/(μ0ε0)1/2 and Z0=(μ0/ε0)1/2, Zs=(1+j)(Z0ω/2cσ)1/2, i.e.
f<<11 THz. Fig.1 shows comparison of the nonperturbative (black) and perturbative (red) coupling impedances (real part) for both pipes. As expected, for low frequencies f<1 THz, bothmodels are in good agreement. Larger discrepancies are observed as f increases.

(a) Circular pipe(b) Square pipe
Figure 1: Comparisons of perturbative and nonperturbative coupling impedances (a=2.5mm)

4. Conclusion
The nonperturbative and perturbative beam-wall interaction simulations using BEM have beenpresented. Direct comparisons of the nonperturbative and perturbative coupling impedances
for the round resistive pipe and the square one are clearly shown in the BEM context. A limitation of the perturbation theory is confirmed in our simulations.

References[1] G. Stupakov, Wake and impedance, SLAC-PUB-8683, 2000.
[2] K. Yokoya, Resistive wall impedance of beam pipes of general cross section, Part. Accel.,vol.41(1993), pp.221-248.
[3] A. Macridin, et al., Nonperturbative algorithm for the resistive wall impedance of general cross-section beam pipes, Phys. Rev. ST Accel. Beams, vo.16 (2013), 121001.
[4] K. Fujita, A study on boundary element analysis of accelerator beam pipes with walls offinite conductivity, IEICE Technical Report, EMT2021-27 (2021), pp.105-108.
[5] K. Bane et al., The short-range resistive wall wake fields, SLAC-PUB-95-7074,1995.

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Design study of BiCG-Stab matrix solver circuit for
FIT scheme based on dataflow architecture
Chenxu Wang, Seiya Ota, Hideki Kawaguchi
Division of Information and Electronic Engineering, Graduate School of Engineering,
Muroran Insititute of Technology, Japan*kawa@mmm.muroran-it.ac.jp

Abstract. In order to achieve high-performance computation for the Finite Integration Technique (FIT) based on the BiCG-Stab method for 2D magnetostatic field simulation, this paper
discusses a method of dedicated computer with dataflow architecture for magnetostatic field
simulations. In particular, we design the integer arithmetic circuit of the BiCG-Stab matrix
solver for FIT scheme based on the dataflow architecture.
Keywords: Dedicated computer, Dataflow architecture, BiCG-Stab matrix solver

1. Introduction
In the last half century, computer performance has progressed remarkably and now performance of the highest-end supercomputer reaches to 400 petaflops. However, such the highperformance computation is achieved by vary large supercomputer system based on von Neumann architecture with over 10 millions cores, and 10 megawatts power consumption. Authors
have been working in a development of dedicated computers based on the dataflow architecture,
to aim to achieve a portable, low power consumption, low cost and green high-performancecomputing for electromagnetic field simulations[1]. In this work, we propose the dedicated hardware circuit based on the dataflow architecture of finite integration technique (FIT) scheme formagnetostatic fields.

2. Design of BiCG-Stab matrix solver circuit
Two dimensional magnetostatic field is described by the vector Poisson equation for z-component of the magnetic vector potential 𝐀.FIT discretization of the vector Poisson equation canbe expressed as follows:
(0)

(1)

(2)

(3)

(4)

𝑐𝑖,𝑗 𝐴𝑖,𝑗 − 𝑐𝑖,𝑗 𝐴𝑖,𝑗−1 − 𝑐𝑖,𝑗 𝐴𝑖+1,𝑗 − 𝑐𝑖,𝑗 𝐴𝑖,𝑗+1 − 𝑐𝑖,𝑗 𝐴𝑖−1,𝑗 = 𝐼𝑖,𝑗
(0)

(1)

(2)

(3)

(4)

(1)

𝑐𝑖,𝑗 = 𝑐𝑖,𝑗 +𝑐𝑖,𝑗 +𝑐𝑖,𝑗 +𝑐𝑖,𝑗 , 𝑐𝑖,𝑗 = 2𝜇

1

𝑖,𝑗−1

(2)

𝑐𝑖,𝑗 = 2𝜇

1

𝑖,𝑗−1

1

(3)

1

1

𝑖,𝑗

𝑖−1,𝑗

+ 2𝜇 , 𝑐𝑖,𝑗 = 2𝜇 + 2𝜇
𝑖,𝑗

402

+ 2𝜇

1

𝑖−1,𝑗−1(4), 𝑐𝑖,𝑗 = 2𝜇

,

1

𝑖−1,𝑗

+ 2𝜇

1

𝑖−1,𝑗−1(1)

JSST2021
where 𝐴𝑖,𝑗 , 𝐼𝑖,𝑗 and 𝜇𝑖,𝑗 are the magnetic vector potential, externally applied current and permeability at the i-th, j-th grid in the 2D grid space. We can obtain the distribution of the magnetic vector potential 𝐴𝑖,𝑗 to construct a matrix equation of (1) for all grid point and to solve
the marix equation. Accordingly, in the development of the dedicated computer for the 2D
magnetostatic field computation, a main task is a design of the hardware circuit of the matrix
solver for (1). Then, the use of floating-point calculations in the hardware circuit requires large
size hardware, in addition, large numbers of clock cycles. In order to achieve hardware circuitsof the matrix solver with a smaller size hardware and shorten clock cycle, we consider to use
fixed-point arithmetic with integer format instead of floating-point arithmetic for matix solver
hardware circuits. In the implementation of the matrix solver scheme such as the BiCG-Stabmethod using the fixed-point arithmetic with integer format, we need to carefully treat individual arithmetic operation between unknown values to avoid truncations and accuracy degrations[2]. Figure 1 depicts a conceptual design of hardware circuits for a single unit grid of the
FIT sheme which include the BiCG-Stab matrix solver circuit based on multiple precision
fixed-point arithmetic with integer format. All of unknown values are stored in registers at eachgrid. These registers are connected each other via arithmetic circuits which execute the BiCGStab matrix solver scheme. By allocating this unit circuit all over grid space, the magnetostatic
field can be simulated automatically.

References[1] H. Kawaguchi et.al, IEEE Trans. Magn, Vol.51, Issue 3, 7202404, 2015.
[2] T. Kuroki et.al, Trans. IEEJ, vol.129, No.10, pp.687-692, 2009.

Figure 1. BiCG-Stab matrix solver unit grid circuit for FIT shceme of 2D magnetostatic field

403

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Importance of 3-D piezoelectric coupled analysis inevaluation of thin piezoelectric bimorph deformation
Shoichi Aikawa1, Daisuke Ishihara2*, Naoki Iwamaru1, Prakasha C. Ramegowda 2
Department of Computer Science and Systems Engineering, Kyushu Institute of Technology

1

Department of Intelligent and Control Systems, Kyushu Institute of Technology

2*ishihara.daisuke399@mail.kyutech.jp

Abstract. Thin piezoelectric bimorphs are often used as actuators and sensors in advanced
electromechanical systems. Therefore, it is necessary to accurately evaluate their electromechanical behavios. In this study, the finite element analysis results for the deflection of piezoelectric bimorphs are compared with the analytical solutions based on the beam theory, and it isshown that three-dimensional piezoelectric-inverse piezoelectric coupled analysis is important
if the electromechanical coupling coefficient and the width of the bimorph are large.
Keywords: Piezoelectric Bimorph, Finite Element Analysis, Coupled Analysis

1. Introduction
Piezoelectric materials can work as sensors using the accumulation of electric charge in response to mechanical strain or the direct-piezoelectric effect, while as actuators using thechange in the size in response to an applied electrical potential or the inverse-piezoelectriceffect. Most recently, piezoelectric devices are increasingly employed throughout the field ofvibration control, energy harvesting, and nano-aerial vehicles [1]. These piezoelectric devices
are usually fabricated as thin cantilevered composite structures with one or more piezoelectric
layers, typically, thin cantilevered piezoelectric bimorphs. Their electromechanical behavior
has been extensively studied using a variety of numerical approaches [2-5].
This study considers the thin cantilevered piezoelectric bimorph. As seen in the previous studies, this configuration allows various simplified models including closed-form solutions. However, as shown in Ref. [3], the thin cantilevered piezoelectric bimorph beam operating in thesensor mode can present the complicated three-dimensional electric field, which requires the
direct numerical modeling for the accurate prediction of the electrical behavior. Similarly, inthe thin cantilevered piezoelectric bimorph actuator, a correct understanding of the cases that
require the direct numerical modeling is very important. Hence, for the purpose of this understanding, the direct and inverse piezoelectric interaction and the three-dimensional (3-D) geometrical configuration are investigated quantitatively in the mechanical behavior of the thincantilevered piezoelectric bimorph actuator. Their direct numerical modeling is necessary forthe accurate prediction of the thin cantilevered piezoelectric bimorph actuator deformation.

404

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2. Materials and Methods
The spatially discretized equilibrium equations of linear piezoelectricity in the global coordinate system are derived using the variation principle with the standard procedure of the finite
element method as

K uuu  K uφφ  F , K Tuφu  K φφφ  q ,(1a, b)where Kuu is the global mechanical stiffness matrix of the structure, Kuφ is the global piezoelectric stiffness matrix of the piezoelectric continuum, Kφφ is the global dielectric stiffness matrix of the piezoelectric continuum, u is the nodal global vector of the mechanical displacement,
φ is the nodal global vector of the electric potential, F is the global equivalent vector of themechanical external force, q is the global equivalent vector of the external surface charge, andthe right-hand superscript T denotes the transpose of the matrix.
In the strong coupling method, u and φ that satisfy Eqs. (1a, b) accurately are obtained using
the block Gauss-Seidel method, while, in the weak coupling method, as the first step, Eq. (1b)with u = 0 is solved to get φ, and, as the next step, Eq. (1a) with φ obtained in the first step issolved to get u. The strength of coupling is measured using the electromechanical coupling
coefficient k31 = d31/(ε33 sE11)0.5, where d31 is the piezoelectric strain constant, ε33 is the dielectric
constant, and sE11 is the elastic compliance constant. The relative difference between the weak
coulpling analysis result and the theoretical solution is less than 0.1% iresspective of k31 for theactual PZT materials considered here. On the contrary, the relative difference between thestrong coulpling analysis result and the theoretical solution reaches 8% for the maximum k31.

References[1] Ishihara D, Ohira N, Takagi M, Horie T. Fluid-structure interaction design of insect-likemicro flapping wing. Proceeding of the VII International Conference on Computational
Methods for Coupled Problems in Science and Engineering 2017:870–5.
[2] Ramegowda PC, Ishihara D, Niho T, Horie T. A novel coupling algorithm for the electricfield-structure interaction using a transformation method between solid and shell elements
in a thin piezoelectric bimorph plate analysis. Finite Elem Anal Des 2019;159:33–49.
[3] Ramegowda PC, Ishihara D, Takata R, Niho T, Horie T. Finite element analysis of thinpiezoelectric bimorph with a metal shim using solid direct-piezoelectric and shell inversepiezoelectric coupling with pseudo-piezoelectric evaluation. Compos Struct
2020;245:112284.
[4] Ramegowda PC, Ishihara D, Takata R, Niho T, Horie T. Hierarchically decomposed finite
element method for a triply coupled piezoelectric, structure, and fluid fields of a thin piezoelectric bimorph in fluid. Comput Meth Appl Mech Eng 2020;365:113006.
[5] Ishihara D, Takata R, Ramegowda PC, Takayama N. Strongly coupled partitioned iterative
method for the structure–piezoelectric–circuit interaction using hierarchical decomposition. Comput Struct 2021;253:106572.

405

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Comparative study on linear and quadratic solid
direct-piezoelectric solvers with shell
inverse-piezoelectric solver to analyze a thinpiezoelectric bimorph device
P.C. Ramegowda1,* and D. Ishihara1
1 Department of Intelligent and Control Systems, Kyushu Institute of Technology, Iizuka,

Fukuoka, Japan∗ prakasha@solid.mse.kyutech.ac.jp

Abstract. The successful design of a thin piezoelectric bimorph device for sensor and actuator applications requires an efficient and accurate finite element modeling (FEM) of direct
and inverse piezoelectric effects. In this work, a partitioned iterative method utilizing thebest features of the solid elements for the direct-piezoelectric field and MITC shell elements
for the inverse-piezoelectric field is employed. A comparative study of linear and quadraticelements for the approximation of the electrical potentials in the solid direct-piezoelectricsolver is presented. Numerical results are compared with analytical results. Quadratic solid
piezoelectric elements significantly outperform linear solid piezoelectric elements in termsof solution accuracy and computational efficiency.
Keywords: Linear solid piezoelectric element, quadratic solid piezoelectric element, MITC4
shell inverse-piezoelectric solver, partitioned iterative method, thin piezoelectric bimorph.

1.

Introduction

Piezoelectric materials exhibits two types of electromechanical coupling effects, namely,
direct-piezoelectric effect and inverse-piezoelectric effect. Authors in their early works[1, 2] had proposed a novel FE method wherein the combination of 3D solid and MITC
shell elements are employed to solve direct-piezoelectric and inverse-piezoelectric fields,
respectively, to overcome the demerits of these elements to solve both the direct and inversepiezoelectric effects in a single framework reported in the works of Benjeddou [3]. Shellelements are efficient for analyzing the deformation of a thin-layered piezoelectric device.
However, the electric potential distribution within the piezoelectric continuum is still significantly three-dimensional even though the structure is thin [1, 4] and it is quadratic throughthickness [5]. Therefore, 3D solid elements are necessary for analyzing the electric potential
distribution in the piezoelectric material. The electromechanical coupling is only partial if
the potential is assumed to vary linearly through the thickness [3]. Quadratic variation of
the electric potential through the thickness direction can be achieved using linear 3D solid406

elements by increasing the density of the mesh in the thickness direction which leads to anincrease in the computational cost. Therefore, this work presents a comparative study oflinear and quadratic elements for the approximation of the electrical potentials to solve thedirect-piezoelectric field. Numerical results are compared with analytical results. Quadraticsolid piezoelectric elements significantly outperform linear solid piezoelectric elements interms of solution accuracy and computational efficiency.

2.

Finite element equations and coupling strategy

Eqs.(1) and (2) represents the general FE coupled inverse-piezoelectric and direct-piezoelectriceffect of a piezoelectric material.
Muu ü + Kuu u + Kuφ φ = F,

(1)

Kφu u + Kφφ φ = q,(2)

where Muu is the constant mass matrix, Kuu is the mechanical stiffness matrix, Kuφ is thepiezoelectric coupling matrix, Kφφ is the dielectric stiffness matrix, F is the external force
vector, and q is the external electric charge vector. Employing shell elements for inversepiezoelectric equation (1) and solid elements for direct-piezoelectric equations (2), ignoring
the inertial effect (Muu = 0), we obtain Eqs.(3) and (4). The kinematic coupling between
the shell and solid is done using a transformation method [1] in a Block Gauss-Seidel (BGS)
iterative loop [4]. The Eqs.(3) and (4) can be written as Eqs.(5) and (6).
shell
solid
+ Ksolid= FshellKshell
uu u
uφ φ
solid
solid
Ksolid+ Ksolid= qsolid
φu u
φφ φ

(3)

shell
Kshell= Fshell + e Fshell
uu u

(5)

(4)

solid
Ksolid= qsolid + e qsolid
φφ φ

(6)

The transformation of the quantities from shell to solid and solid to shell are represented
using the transformation matrix e T and u T, respectively. Eqs.(7) and (8) represents the nodal
electric force and the nodal electric charge given by the solid direc-piezoelectric solver,
respectively.
e solidFsolid= −Ksoliduφ φe solidsolid= −Ksolid
φu uqe shell

(7)

F

h
i
= e Fshell , e Mshell = e Te Fsolid(9)u e shell(10)

usolid = T u(8)e Fsolid is transformed to the equivalent forces e Fshell and moments e Mshell acting on the shellmesh from the solid mesh. Eqs.(11) and (12) represents the equivalent force and momentson the shell from linear solid mesh, while Eqs.(13) and (14) represents the equivalent force
and moments on the shell from quadratic solid mesh [1].

e shell

F

=

Nr
X
nr =1

e

Mshell =e shelle solid
Fnr

Nr 
X
nr =1

F

(11)


dnr × e Fsolid
(12)
nr

=

Nr
X
nr =1

e

Mshell =e solid
Fnr +

Nr 
X
nr =1

Ns
X
n s =1e solid
Fns /2

(13)

Ns 
 X

dnr × e Fsolid+
dns × e Fsolid
ns /2nr
n s =1

(14)

407

3.

Piezoelectric bimorph sensor analysis

3.1. Problem setup

Figure 1: a) Short circuit bimorph sensor with external force Fext = 1.0mN. b) Solid meshfor the piezoelectric analysis. c) Shell mesh for the inverse-piezoelectric analysis.
Fig. 1(a) shows the short circuit sensor mode of the piezoelectric bimorph. The length andthe width of the bimorph are 250mm and 20mm, respectively, the thicknesses of the piezoelectric and shim layers are 5mm and 0.5mm, respectively. The materials of the piezoelectricand shim layers are PVDF and brass, respectively. Fig. 1(b) shows the solid mesh used in the
direct-piezoelectric analysis. Fig. 1(c) shows the shell mesh used in the inverse-piezoelectric
analysis. The solid elements are hexahedral elements (8-node element for linear and 20-nodeelement for quadratic), while the shell elements are MITC4 elements [6].

3.2.

Results and Discussions

Fig. 2 shows the electric potential distribution at the fixed end of the bimorph through the
thickness for various mesh densities. As shown in Fig. 2(a), the red curve shows a smoothquadratic variation than the blue curve. On the contrary, a smooth quadratic distribution
through the thickness is achieved using 20-node solid elements, as shown in the magenta
curve in Fig. 2(b). The solution obtained with the 20-node solid is very close to that of
the theory. The theoretical solution is 3.524 × 10−1 V. The error is 1.61%. The solution
accuracy in Fig. 2(a) are very bad. The green curve shows a solution accuracy (6.64%) close
to that of the magenta curve in Fig. 2(b). This indicates that quadratic solid-piezoelectricsolver is computationally efficient and solutions are very accurate than linear solid-direct
piezoelectric solvers

4.

Conclusions

A comparative study of linear and quadratic elements for the approximation of the electrical potentials in the solid direct-piezoelectric solver, while shell elements for inversepiezoelectric solver are presented. Numerical results are compared with analytical results.
Quadratic solid piezoelectric elements significantly outperform linear solid piezoelectric elements in terms of solution accuracy and computational efficiency.

408

(a)

(b)

Figure 2: Induced electric potentials through the thickness: blue curve (8-node solid; meshdivision along the length, width, and thickness are 50,1, 10 respectively), red curve (8-node
solid; mesh division along the length, width, and thickness are 50,1, 20 respectively), green
curve (8-node solid; 4646 number of nodes; mesh division along the length, width, andthickness are 100, 1, and 22, respectively), magenta curve (20-node solid; 3803 number ofnodes; mesh division along the length, width, and thickness are 50, 1, and 10, respectively.)

Acknowledgments
The present study was supported by JSPS KAKENHI Grant No. 19F19379

References[1] P.C. Ramegowda, D. Ishihara, T. Niho, T. Horie: A novel coupling algorithm forthe electric field–structure interaction using a transformation method between solidand shell elements in a thin piezoelectric bimorph plate analysis, Finite Elements inAnalysis and Design, 159 (2019), 33–49.
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