International Mathematical Science Workshop
in Yamaguchi 2019
Presented by RITS
1.

Purpose
We will hold a workshop on mathematical science. The research topic is not
restricted and may or may not be directly related to Time Studies, but it must
be mathematical science. Even not so mathematical study is welcome.
The aim is for participants to get inspiration. Conversely, we do not rush to seekpractical applications. Emphasis will be on a free atmosphere. Prominent andactive researchers will be invited, while students are also encouraged toparticipate actively.

2.

Date / Venue / Language
Date2019 November 7 - 8

Venue

Yamaguchi University (Yoshida Campus)
Yoshida Research and Education Building, 3F Forum Space

Language

English (Japanese maybe ok)

Presentation

Invited talks

Proceeding

not producedProgram<Nov. 7th>
14:00-14:40

M. I. Tribelsky

Non-Steady Resonant Wave Scattering by an Obstacle

14:40-15:20

H. Matano

Propagation of bistable fronts through a perforated wall

15:20-16:00

S. KajiTime evolution of Kaleidocycles

16:00-16:20

Coffee break

16:20-17:00

K. Matsue

Premixed Flame Dynamics: Modeling, Numerical andMathematical Studies

17:00-17:40Y. Kuramoto

Dynamical Reduction of Coupled Oscillators
Banquet<Nov. 8th>
09:30-10:10

H. UenoPerception of time-dependent environmental change: A
toy model with photo-coupled electronic oscillatorscomposing frustrated network

10:10-10:50

T. Narumi

Tagged-particle dynamics in Nikolaevskii turbulence

10:50-11:30

A. Miroshnichenko

On redundant poles of the S-matrix

11:30-13:30

Lunch break

13:30-14:10

T. Makino

On Mathematical Models of Gaseous Stars

14:10-14:50

S. A. Tishchenko

N-separator and its application in the degree-diameterproblem

Non-Steady Resonant Wave Scattering by an Obstacle
Michael I. Tribelsky1,2,3
1M. V. Lomonosov Moscow State University, Moscow, Russia
2National Research Nuclear University MEPhI (Moscow Engineering Physics Institute),

Moscow, Russia
3RITS Yamaguchi University, Yamaguchi, Japan

A survey of the recent results of the author in the unsteady high-Q resonant scattering of ultrashortpulses by a particle, whose size is comparable or smaller than the wavelength of the incident
radiation at the carrier frequency is presented. It is shown that the unsteadiness of the scattering
process may result in qualitative changes in the manifestation of the phenomenon both in the nearfield and in far-field wave zones. Most attention is paid to the dynamics of the nonradiating anapolemodes and dynamic Fano resonances, which are discussed in detail. Simple, analytically tractablemodels are proposed to describe the transient processes. Their comparison with the results of thedirect numerical integration of the complete set of the Maxwell equations shows that the models
exhibit high accuracy in the quantitative description of the phenomenon.
The financial support of the Russian Foundation for Basic Research (Grant No. 17-02-00401) andthe Russian Science Foundation (Project No. 19-72-30012) is acknowledged.

1

Propagation of bistable fronts througha perforated wall
Hiroshi MatanoMeiji University

We consider a bistable reaction-diffusion equation in the presence of an obstacle, which
can be regarded as a wall of infinite span with periodically arrayed holes. Our goal is tostudy what happens when a planar traveling front coming from infinity meets the wall .
We first show that there is clear dichotomy between `propagation' (or invasion) and`blocking', and that there is no intermediate behavior. This dichotomy result is provedby what we call a De Giorgi type lemma.
Next we discuss sufficient conditions for blocking, and those for propagation. Roughlyspeaking, blocking occurs if the holes are small.
As for propagation, we present three types of walls that allow the front to propagate,
namely (a) walls with large holes; (b) small-capacity wall; (c) skeleton walls. This is
joint work with Henri Berestycki (EHESS Paris) and Francois Hamel (Univ. AixMarseile).

2

Time evolution of Kaleidocycles
Kaji Shizuo
Institute of Mathematics for Industry Kyusyu UniversityKaleidocycle is an origami toy which can be folded from a sheet of paper.
Unlike usual origami, it has some mobility; in fact, it can be seen as an example of linkage
mechanisms which consists of hinges.
We model (a generalisation of) Kaleidocycles as discrete space curves with constanttorsions.
In particular, we see that the motion of a Kaleidocycle is governed by a semi-discrete(discrete space, continuous time) integrable system.
The origami piece demonstrates visually how different fields of mathematics, topology,
algebraic geometry, and analysis meet as well as art.
This is joint work with K. Kajiwara and H. Park.

3

Premixed Flame Dynamics:
Modeling, Numerical and Mathematical Studies
Kaname Matsue
Institute of Mathematics for Industry, Kyushu University
International Institute for Carbon-Neutral Energy Research, Kyushu University
University of Illinois at Urbana-Champaign
Combustion is the oldest technology for energy generation in human history.
Recently, renewable energy and related technology are coming into the mainstream ofenergy generation or new infrastructure towards creating the carbon-neutral society.
Nevertheless, combustion is still important for balancing energy generation andefficiency to maintain our daily lives.
One of the important issues in combustion research is to understand the mechanism offlame dynamics related to energy generation and realistic combustion processes.
In the present study, we study the dynamics of hydrodynamical unstable, premixed planar
flame fronts based on a fully nonlinear, hydrodynamic model obtained by a multi-scale
analysis that exploits the distinct length scales associated with such problems.
In particular, we focus on the composite effects of thermal expansion, differential
diffusion, and gravity on flame dynamics.
The flame dynamics based on the model with finite thermal expansion is the main issue,
while the problem in the weak thermal expansion setting, where numerical bifurcation
theory and mathematical methodology for describing rigorous solutions can be applied,is also considered to extract mathematically intrinsic feature in flame dynamics in thepresence of gravity.

4

Perception of time-dependent environmental change:
A toy model with photo-coupled electronic oscillatorscomposing frustrated network
H. Ueno, M. Matsushima, Y. Kamiya, H. Kawakami, and K. Yoshikawa.
Lab. Biol. Phys., Dep. Med. Info.,
Grad. Sch. Life Med. Sci., Doshisha Univ.
We adapted a very simple experimental model on the coupling of excitable/oscillatory
element, by using opto-electronic circuit known as multi-vibrator composed of resistor,
capacitor, Op-Amp. The circuit exhibits periodic ON/OFF rhythmic oscillation by a LED
in a dark environment, whereas this synchronizes its blinking with environmental
event, detecting light by photo-transistor.
A simple network of three oscillators composing a triangle connection performs thetime-dependent processing of information; each neighbouring pair exhibit anti-phasesynchronization; i.e., frustrated network. In this system, multi-stability is embedded,
where each mode is generated from specific time-sequential input. Certain history ofinput evokes corresponding mode of entrainment in these simple oscillators. Suchspecificity of time-dependent mode selection will be discussed in relation to thepotentiality of perception with coupled oscillators.

5

Tagged-particle dynamics in Nikolaevskii turbulence
Narumi Takayuki
Yamaguchi University Graduate School of Sciences
and Technology for Innovation
We have studied the Nikolaevskii turbulence, which is a mathematical model of weakturbulence. To clarify it from the Lagrangian description, we calculated the velocity fieldof the turbulence assuming convective structure and carried out tagged-particle
simulations in the flow. The particle diffuses in the disturbed flow, and the diffusion wassuperdiffusive in an intermediate timescale. A simplified model we proposed has revealeda hierarchy in the Nikolaevskii turbulence. The diffusive feature of the slow structure ischaracterized by the power-law for the control parameter near the transition point of theNikolaevskii turbulence, implying that the diffusive characteristics of the slow structure
hold scale-invariance.

6

On redundant poles of the S-matrix
Andrey Miroshnichenko
School of Engineering and Information Technology
University of New South Wales Canberra, Australia, ACT 2600

A fundamental property of the S-matrix is that any boundstate corresponds to a pole of the S-matrix on the physicalsheet of the complex energy plane. For a repulsive
exponentially decaying potential, none of infinite number ofpoles of the s-wave S-matrix on the physical sheet
corresponds to any physical state. On the 2nd sheet of thecomplex energy plane, the S-matrix has infinite number ofpoles corresponding to virtual states and a finite number ofpoles corresponding to complementary pairs of resonances
and anti-resonances. The origin of redundant poles andzeros is confirmed to be related to peculiarities of analytic
continuation of a parameter of two linearly independent
analytic functions. The overall contribution of redundantpoles to the asymptotic completeness relation, provided that the residuum theorem can beapplied, is determined to be an oscillating function.

78

N-separator and its application in the degree-diameter problem

Serge A. Tishchenko (Moscow State University)

We study N-separators the divide and conquer method in weighted (vertices, edges and faces)
planar graph (an N-separator of a connected graph G is a subgraph G whose deletion
decomposes G into N connected components). A number of papers were inspired by the original
paper by Lipton and Tarjan on 2-separators in weighted (only vertices and edges) planargraphs. Their separator construction is very important issue in many graph applications suchas VLSI modelling, communication networks, parallel computing. The most complete andrecent survey on graph separators was made by Rosenberg and Heath.
One of the possible applications of the separator method is the degree-diameter problem inplanar graphs. In this case, the separator method is used for planar graph characterization.
The largest graphs in the degree-diameter problem are very dense. Therefore, the simplest
Lipton and Tarjan separator which is a cycle obtained by addition of an edge to some edges of aspanning tree becomes an e cient tool in the degree-diameter problem. Each of two separated
subsets is either the interior or the exterior of the cycle. Further progress can be achieved in
the degree-diameter problem increasing the number of separated subsets. In general, anN-separator is needed consisting of several cycles.
We optimize the separator construction in plane graphs with weighted vertices, faces andedges. Such generalization is important for practical applications. We consider the problem ofexistence of an N-separator in a planar graph and give optimal bounds to the minimum weightcomponent.

TitlesN-separator and its application in the degree-diameter problem

AuthorSerge A. Tishchenko

9ParticipantsMichael I. TRIBELSKY

MSU／MEPhI／RITS

Serge A.TISHCHENKOMSU／RITS

Andrey MIROSHNICHENKO

Kyoto University／RITSKURAMOTO Yoshiki
MATANO Hiroshi
KAJI Shizuo

UNSW Canberra

MIMS, Meiji University

IMI, Kyushu University

MATSUE Kaname

IMI, Kyushu University

MIIKE Hidetoshi

Yamaguchi Gakugei University

MAKINO Tetsu

Yamaguchi University

UENO Hiroshi

Doshisha University

HIROSAWA Fumihiko
NARUMI TakayukiYamaguchi University
Yamaguchi University

FUJISAWA Kenta

RITS, Yamaguchi University

NOZAKI Takayuki

Yamaguchi University

HOSHINAGA Shota

Yamaguchi University

HORIKAWA Yuka

Yamaguchi University