INTERNATIONAL WORKSHOP MSA-2019

Mathematical Sciences and Applications
November 07 - 08, 2019
RITS, Yamaguchi University, Yamaguchi, Japan
ChairsProfessor Kenta FUJISAWA
RITS, Yamaguchi University, Yamaguchi, Japan
Professor Michael I. Tribelsky
Lomonosov Moscow State University, Moscow, Russia
PurposeThe workshop is multidisciplinary. It covers a broad field of mathematical sciences with anemphasis on their applications to natural sciences and various technologies.
Venue: Yamaguchi University (Yoshida Campus), Yoshida Research and Education
Building, 3F Forum Space
Language: English/Japanese with slides and summary in EnglishPresentation: Oral
Program<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

17:00-17:40

Y. Kuramoto

Premixed Flame Dynamics: Modeling, Numerical andMathematical Studies
Dynamical Reduction of Coupled Oscillators
Banquet<Nov. 8th>
09:30-10:10

H. Ueno10:10-10:50

T. Narumi

Perception of time-dependent environmental change: Atoy model with photo-coupled electronic oscillatorscomposing frustrated network
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-diameter
problem

Abstracts of the talks

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 ofultrashort pulses 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 unsteadinessof the scattering process may result in qualitative changes in the manifestation of thephenomenon both in the near-field and in far-field wave zones. Most attention is paid to thedynamics of the nonradiating anapole modes and dynamic Fano resonances, which arediscussed in detail. Simple, analytically tractable models are proposed to describe thetransient processes. Their comparison with the results of the direct numerical integration of
the complete set of the Maxwell equations shows that the models exhibit high accuracy inthe quantitative description of the phenomenon.
The financial support of the Russian Foundation for Basic Research (Grant No. 17-02-00401)
and the Russian Science Foundation (Project No. 19-72-30012) is acknowledged.

Propagation of bistable fronts througha perforated wallHiroshi MatanoMeiji University
We consider a bistable reaction-diffusion equation in the presence of an obstacle, which canbe regarded as a wall of infinite span with periodically arrayed holes. Our goal is to study
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 proved bywhat we call a De Giorgi type lemma.
Next we discuss sufficient conditions for blocking, and those for propagation. Roughly
speaking, 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. Aix-Marseile).

Time evolution of Kaleidocycles
Kaji Shizuo
Institute of Mathematics for Industry Kyusyu University
Kaleidocycle 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 linkagemechanisms 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.

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 and efficiency
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, isalso considered to extract mathematically intrinsic feature in flame dynamics in thepresence of gravity.

Perception of time-dependent environmental change: A toymodel with photo-coupled electronic oscillators composing
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 the timedependent processing of information; each neighbouring pair exhibit anti-phasesynchronization; i.e., frustrated network. In this system, multi-stability is embedded, whereeach 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 the potentialityof perception with coupled oscillators.

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 field of
the turbulence assuming convective structure and carried out tagged-particle simulations in
the flow. The particle diffuses in the disturbed flow, and the diffusion was superdiffusive in
an intermediate timescale. A simplified model we proposed has revealed a hierarchy in theNikolaevskii turbulence. The diffusive feature of the slow structure is characterized by thepower-law for the control parameter near the transition point of the Nikolaevskii
turbulence, implying that the diffusive characteristics of the slow structure hold scaleinvariance.

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
bound state corresponds to a pole of the S-matrix
on the physical sheet of the complex energy plane.
For a repulsive exponentially decaying potential,none of infinite number of poles of the s-wave Smatrix on the physical sheet corresponds to any
physical state. On the 2nd sheet of the complex
energy plane, the S-matrix has infinite number ofpoles corresponding to virtual states and a finite number of poles 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 redundant poles to theasymptotic completeness relation, provided that the residuum theorem can be applied, isdetermined to be an oscillating function.

On Mathematical Models of Gaseous Stars
Tetu Makino
Prof. Emer. at Yamaguchi Univ.
The internal structure and its time evolution of stars are the major subject of astrophysics. On
this subject the study through observations and through numerical simulations have beenachieved marvelous progress, as well known, thanks to the efficiency of observational andcomputational devices. However the progress of mathematically rigorous theoretical study
on this subject isvery slow, and has not yet caught up with the observational and numerical performance.
The reason is that the underlying hydrodynamical equations are degenerated at the boundaryof the gaseous matter and the vacuum. Here the underlying equations are the Euler-Poisson
equations in the non-relativistic frame work, and the Einstein-Euler equations in therelativistic frame work, while the former is the limit of the latter as the speed of light tend toin_nity. Moreover the effect of self-gravitation is not yet well clari_ed. In this sense themathematics of the matter-vacuum boundary and self-gravitation should be more rapidly
developed.
Maybe some new theoretical paradigm is needed. In this talk the historical development of
the mathematically rigorous theory on the internal structure and time evolution of gaseous
star models is reviewed, and the open problems which confront us are introduced.

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 theoriginal paper by Lipton and Tarjan on 2-separators in weighted (only vertices and edges)
planar graphs. Their separator construction is very important issue in many graphapplications such as VLSI modelling, communication networks, parallel computing. The mostcomplete and recent 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 ofa spanning tree becomes an eﬃcient 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. Ingeneral, an N-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.

Titles N-separator and its application in the degree-diameter problem
Author Serge A. Tishchenko