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第110回現象数理セミナー
日時：12月9日(月)
会場：W1-C-716
15:15〜15:45
Speaker 1:
Dr. Daurenbek Serikbaev
(Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan)
Title:
Inverse problem of determining time-dependent leading coefficient in the time-fractional
heat equation
Abstract:
In this work, we consider direct and inverse problems
for the time-fractional heat equation with a time-dependent leading coefficient for positive
operators.
First, we consider the direct problem, and the unique existence of the generalized solution
is established.
We also deduce some regularity results. Second, we study the inverse problem of
determining the
leading coefficient, and the well-posedness of this inverse problem is proved.
16:00〜17:30
Speaker 2:
講演者:Prof. Michael Vynnycky
(University of Limerick, Ireland)
Title:
Beyond the Richards equation: two-phase flow in an unsaturated porous medium
Abstract:
Flow in an unsaturated porous medium is typically modelled using the
Richards equation, which is unquestioningly believed to be an accurate
enough approximation when the viscosity of the fluid being displaced,
e.g. air, is much smaller than that of the infiltrating fluid, e.g. oil
or water. Here, we apply asymptotic and numerical methods to a
one-dimensional problem when this is not the case. With the viscosity
ratio as a small parameter, we find that the Richards equation gives a
leading-order solution that is not uniformly valid over the whole domain
of interest. Instead, whilst the Richards equation holds for the bulk
flow, the problem has a derivative (or one-sided corner) layer for the
saturation function at the infiltration boundary, i.e. there is a
boundary layer in the spatial derivative of the saturation, but not in
saturation itself. Although seemingly insignificant, this has a dramatic
effect on the time taken to fill the porous medium: instead of filling
exponentially quickly, it fills algebraically slowly. As a consequence,
using the Richards equation will dramatically underestimate the time
taken to fill a porous medium. Numerical computations are provided to
underscore these asymptotic predictions.
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第109回現象数理セミナー
日時：11月29日(金) 16:00-17:30
会場：九州大学伊都キャンパス ウエスト1号館7階C棟 C-715
講演者：Prof. David Wood
(The University of Calgary, Canada)
題目: Consistent boundary conditions for computational fluid dynamics
modelling in steady, incompressible, two-dimensional flow
要旨:
A good choice of far-field boundary conditions (BCs) for the simulation
of airfoil and other aerodynamic flows, allows the minimization of the
domain size for a given level of error or the converse. Simulations of a
NACA 0012 airfoil for a range of angles up to 45 degrees using OpenFOAM,
show the need for consistency with the Kutta-Joukowsky (KJ) equation for
the lift in the form of a point vortex boundary condition. This is not
surprising, given that the KJ equation is well-known. What is less
well-known is that consistency with the drag requires a point source
BC. A combined point source, point vortex BC is easy to implement, but
still may be inconsistent with the moment equation for the body. This
may adversely affect the accuracy of the torque computed for, say,
vertical axis turbines which are often simulated in
two-dimensions. Methods of achieving consistency with the moment
equation will be discussed and a surprisingly simple correction for the
use of commonly-used, but inconsistent BCs, will be described.
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第108回現象数理セミナー
日時：8月28日(月) 14:30-16:00
場所：「C513中講義室」
1つ目：14:30-16:00
講演者：Prof. Yi Zhang
[Zhejiang Normal University (浙江師範大学), 中国]
題目: Bidifferential calculus approach to N-component NLS equations and their solutions
要旨:
In this talk, in the framework of bidifferential calculus, we investigate the N-component NLS equations via a matrix version of the binary Darboux transformation, which involves a Lyapunov equation. When the spectral matrix is in the form of diagonal or Jordan block, the corresponding matrix solution of the Lyapunov equation is given. From vanishing and nonvanishing seed solutions, abundant soliton solutions, including breathers, positon solutions, semi-rational rogue waves, and dark solitons, are provided.
2つ目：16:00-17:30
講演者：Prof. Alex Klimenko
[The University of Queensland, オーストラリア]
題目: Why time has an arrow?
要旨:
The physical mechanisms enacting the direction of time remain one of nature's most guarded secrets. The two principal factors --- evident profound outcomes and physical mechanisms deeply hidden somewhere in the quantum world --- create a sense of “time flow”, which, in fact, is a powerful illusion. This illusion is very useful in day-to-day life and even in most scientific explorations but creates numerous difficulties when we try to analyse time. When dealing with such a complex issue as the direction of time it is important to ask the right questions before correct answers can be found. In this presentation, we will try to answer the following three questions:
1. Does entropy increase forward in time or does time “flow” in the direction of entropy increase?
2. Is the low entropy origin of the Universe sufficient to explain the temporal asymmetry?
3. Can asymmetry of the directions of time and matter/antimatter asymmetry be related?
We will consider alternative answers to these questions, their implications and opinions expressed by prominent scientists and intellectuals (Boltzmann, Reichenbach, Popper, Hawking, Penrose, Price,…). We will illustrate these questions through thought experiments and discuss the possibility of testing the answers by experiments from the real world. We will conclude by presenting the fundamental alternatives that can shape our understanding of the world around us.
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第107回現象数理セミナー
講演者：谷口 伸隆 氏（東京大学大学院工学系研究科D1）
1/17（火）15:30 - 17:00
九州大学伊都キャンパスウエスト1号館 C-512中講義室
題目
渦運動に対する圧縮性の作用と推定軌道の安定性に着目した安定性解析手法の開発に関する研究
アブストラクト (Abstract)
In this seminar, study on the development of the stability analysis method of compressible flow is reported. Compressible flow is a complex flow involving sound propagation and changes of internal energy. Thus, the effect of compressibility on incompressible vortex dynamics is an essential problem. In this research, we investigated the compressibility effect on incompressible steady and unsteady vortex movement using global stability analysis. The calculation results show the layer distribution around velocity shear layer and mode separation of vortex and sound propagation especially for low Mach number. In the latter section of this seminar, we report the development of novel stability analysis based on estimated orbital stability as an extension of nonlinear global optimal disturbance method. In this analysis, the entropy production relating to orbital stability is focused on and the calculation results of flow around a 2D square cylinder are presented.
The 107th Seminar on Nonlinear Phenomena and Analysis
（Contact: K. Matsue kmatsue@imi.kyushu-u.ac.jp）
Speaker: Mr. Nobutaka Taniguchi (Univ. of Tokyo, D1)
Jan. 17th (Tue), 15:30 - 17:00
Venue: Lecture Room C-512, West 1, KU
(In person only.)
Title: Effect of compressibility to vortex dynamics and the development of stability analysis method based on estimated flow field stability
Abstract: See above.
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第106回現象数理セミナー
日時：7月26日(火) 16:00-17:30
場所： C-502 (九州大学伊都キャンパス・ウエスト1号館)
講演題目：
Electromagnetic stirring and the continuous casting of steel
講演者：
Prof. Michael Vynnycky (University of Limerick, Ireland)
要旨：
Electromagnetic stirring (EMS) has been used in the continuous casting of steel since as early
as the 1970s as a way to control solidification structures, thereby increasing yield and productivity.
In tandem, mathematical modelling has played an important role in the implementation of EMS, as regards providing
understanding of exactly what effect stirring has. In this talk, we consider some anomalies in the earlier work, which arise as a
consequence of incorrectly-posed boundary conditions. After that, a combination of asymptotic and numerical techniques is used to provide accurate but rapid computation of the Lorentz stirring forces for this three-dimensional transient problem.
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第105回現象数理セミナー
日時：7月21日(木) 15:00-16:00
場所： C-512 (九州大学伊都キャンパス・ウエスト1号館)
講演題目：
Inverse source problems for wave equations on Lorentzian manifolds
講演者：
髙瀬裕志
（九州大学マス・フォア・インダストリ研究所 ）
要旨：
We consider an inverse problem of the wave equation on a Lorentzian manifold, a
type of semi-Riemannian manifold. This kind of equation is obtained by linearizing
the Einstein equation and is known as the equation satisfied by gravitational waves.
In this talk, we prove a global Lipschitz stability for the inverse source problem of
determining a source term in the equation. Sobolev spaces on manifolds, semigeodesic
coordinates, and Carleman estimates, which are important tools in geometric analysis,
will also be discussed.
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第104回現象数理セミナー
日時：2月20日(木) 14:30-17:30
場所： C-512 (九州大学伊都キャンパス・ウエスト1号館)
終了後に、天神-中州あたりで懇親会を行う予定です。
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講演1 14:30-16:00
題目： New Frontiers in Non-Equilibrium Thermodynamics
講演者： Tommaso Ruggeri (Research Center on Applied Mathematics, University
of Bologna and Accademia dei Lincei, Italy)
講演2 16:00-17:30
題目： Shock Waves in Non-Equilibrium Thermodynamics
講演者： Andrea Mentrelli (Department of Mathematics & Alma Mater Research
Center on Applied Mathematics, University of Bologna, Italy)
** 講演要旨 **
講演 1: Tommaso Ruggeri
There are differences between the approach of continuum mechanics,
kinetic theory and the particle description. This is a main part of the
Hilbert Sixth Problem. Through concrete examples, we will explain these
difference and the main idea of Extended Thermodynamics.
講演 2: Andrea Mentrelli
We shall introduce the problem of shock waves and shock structures with
an emphasis on Extended Thermodynamics. After a general introduction, we
shall focus on the open problems in the study of shock waves in Extended
Thermodynamics and outline the most recent advancement in this field.
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第103回現象数理セミナー
日時：8月26日(月)16:00から17:30
場所： C513 (九州大学伊都キャンパス・ウエスト1号館)
終了後に懇親会を開催します。
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講演題目：
層流―乱流遷移に現れる動的渦群の機械学習による挙動解析
講演者：
松浦一雄
(愛媛大学大学院理工学研究科)
要旨：
ヘアピン渦は，層流―乱流遷移および乱流流れで共通して見られ，乱流の主要な基本構造であると考えられている。一方で，時々刻々と複雑に変化する境界層流れの中にあって，その形態は多彩であり，同一あるいは異なる乱流間での普遍性，不安定性やスケールは必ずしも明確ではない。本研究は，還元論的視点に基づく，ヘアピン渦挙動の理解と法則性の発見を目指している。まず，圧縮性Navier-Stokes方程式の直接シミュレーションを行い，渦の循環強度や壁面からの立ち上がり角といった渦の特徴量が渦挙動に与える影響を調べた。次に，流れ場に現れる個々の渦を個別に分析しながらも，多数の渦を扱うため，渦の点群－スケルトン化・方程式の細分化・スケルトン点の局所近傍における基礎式の簡易化に基づく新たな渦データマイニング手法の提案を行った。さらに，これまで開発した手法を発展させた，機械学習に基づく新手法についても発表する。
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第102回現象数理セミナー
日時：1月29日(火)16:00から17:30
場所： C512 (九州大学伊都キャンパス・ウエスト1号館)
終了後に懇親会を開催します。
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講演題目：
Paradox of multiple plasmonic resonances at light scattering by a
cylinder of infinitesimal radius
講演者：
Michael I. Tribelsky
(Lomonosov Moscow State University, Russia
＆山口大学時間学研究所)
要旨：
The paradox of the divergence of the resonant scattering cross section
of a cylinder with the permittivity equals minus unity and vanishing
radius (R) irradiated by a monochromatic electromagnetic wave is
discussed. Within the framework of the exact solution of the Maxwell
equations, the divergence at the specified conditions is caused by the
overlap of all but one multipolar resonances. It is shown that the
origin of the paradox is in the essential singularity of the cross
section as a function of the permittivity and R at the given point. To
resolve the paradox one must generalize the problem formulation, taking
into account a final linewidth of the incident wave, and then perform
the correct sequence of limit transitions. The application of this
approach gives rise to the vanishing cross section at the vanishing R.
It ruins the expectations to employ such a cylinder as a superscatterer
but simultaneously open a door to counterintuitive effects both in far
and near field zones related to unusual size dependences of the
scattered fields at small but finite R.
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第101回現象数理セミナー
日時：1月10日(木)16:00から17:30
場所： C512 (九州大学伊都キャンパス・ウエスト1号館)
終了後に懇親会を行う予定です。
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講演題目：
Three dimensional Tayler instability of Hall MHD
講演者：
Rong ZOU
(Zhejiang Normal University, 中国)
要旨：
The Tayler instability of Hall MHD is studied by calculating the energy
of disturbances. A static equilibrium in an azimuthal magnetic field is
considered. Both the axisymmetric and nonaxisymmetric disturbances are
discussed. By the energy principle, the positivity of potential energy
is sufficient for the stability of flows. We obtain the sufficient
condition for the stability of Hall MHD, which is weakened to the
condition for MHD stability when the Hall effect is neglected as shown
by R. J. Tayler.
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第100回現象数理セミナー
日時：6月7日(木)16:00から17:30
場所： C512 (九州大学伊都キャンパス・ウエスト1号館)
終了後に懇親会を行う予定です。
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講演題目：
普遍数理構造としてのトポロジー理工学
講演者：
丹田 聡
(北海道大・工学研究科・応用物理学部門
・トポロジー理工学教育研究センター)
要旨：
そもそもトポロジーとは「ちぎったり貼ったりせずに構造（見方によっては空間、物体、システムなど）を連続変形したときの不変的性質を探る」学問として数学の幾何学分野で生まれた。 その応用成功例として20世紀前半にEinsteinが導入したように曲がっている時空という実空間多様体に対してリーマン幾何学やそのリーマン代数を用いて表す一般相対性理論、複素数場として表される量子力学、場の量子論などの基礎物理分野において自然な形で数学から輸入され応用研究として育まれてきた。また古くはオイラーの時代からダイナミクスを語る流体分野においても、連続変形を許してもなお残る保存量として、解析力学やラグランジュアンを通してボルティシティ（渦度）が論じられてきている。さらに流体ヘリシティ（渦巻度）が物理量として着目され1960年代に提唱されるに至り、それぞれ数学用語に対応するワインディング数、リンキング数というトポロジカル不変量として表されるようになっている。20世紀後半にはいり、比較的自由に変形可能な場を扱う高分子分野においても、ヘリックスとしてリンキング数で表されるトポロジカルな2重螺旋構造DNAの発見や超伝導体・液晶・結晶などの種々の秩序場におけるトポロジカル欠陥、トポロジカルソリトンの発見に伴い物性分野においても応用されるようになっている。現在では熱相転移（古典相転移）や量子相転移などの臨界現象、非平衡場におけるダイナミックな相転移を扱う複雑系分野や、システムとしての関係性を重んじる生命科学、カーボンナノチューブ、グラフェンシートなどの電子場・ゲージ場、断熱的にパラメーター空間を動かすことによりベリー位相を利用した光渦場、や各種ネットワーク場、量子情報科学とも密接な関係があることが明らかになってきている。それはまさに種々の場を連続変形、連続写像しても変わらない本質的な性質を抽出し特徴づける幾何学的な量としてトポロジカル不変量があり、「場の本質を不変量として、摂動では扱えないほど大胆な変化を伴う場のダイナミクスを不変量の変化として表現していくこと」が理に適っているためである。そしてトポロジー理工学は、トポロジーがもつ「局所的な性質（部分）と大局的な性質（全体）の相関を解明する」という極めて一般的な科学的手法の確立を目的とした学問であるため、単に数学や物理学に留まらず、自然科学・社会科学・先端工学分野に対して、幅広く適用可能な新しいアプローチ手法として注目されてきている (図１)．このようなトポロジー理工学であるが学問形態としての位置づけをもう少しはっきりと表したい。 要素還元論の対極にある普遍数理構造論ということになる。 多種多様な自然界における種々の現象を探索していくには要素に普遍性を求める方法（要素還元論）と、類推により発見していく方法 (普遍数理構造論)と二種類ある。トポロジー理工学はアナロジーを使った広げる学問であり普遍数理構造を追及する科学である。
例えばヘリシティは多種多様な分野で巨視的現象、微視的現象として出現しており、普遍数理構造を通して自然を理解していく上では応用も含め非常にいいテーマだと考えられる。北大のトポロジー理工学センターでは、ヘリシティがトポロジカル不変量であるチャーン数で表されることもあって早くから着目して研究を行ってきた。これまで以下のような発見がなされてきた。結晶場、電荷密度場、波動関数場、超格子場、ゲージ場、時空においてヘリシティが新たに発見されてきたのである。 これらは、素粒子の場10－１５mのサイズ、人間規模のサイズから宇宙の場1025mも含めかなりの広い範囲に渡ってヘリシティ構造が出ている。 学問のすすめ方の提案も含め多くの系でヘリシティがなぜ出現するのかを中心に議論したい。
また最近の応用例としてリング系の量子時間結晶を提案します。時間が許せば普遍数理構造をもつ素粒子分野への応用としてのガロア体を論じます。
[1] S. Tanda, et al., Nature (2002): Helicity(CS) in Crystal, Mobius Crystals
[2] J. Ishioka et al., PRL (2010), PRB(2013): Helicity(CS) in Chiral Charge Density Waves
[3] H. Nobukane et al PRB(2011): Helicity(CS) in Chiral Superconductors.
[4] K. Konno et al., PRD (2008): Helicity(CS) in Space-Time
[5] T.Matsuyama, PTP(1987): Helicity(CS) in Gauge fields
[6]K.Nakatsugawa, PRB(2017):Topological Quantum Time Crystals
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第99回現象数理セミナー
日時：1月25日(木) 16:00-
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
終了後に懇親会を行う予定です。
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講演題目：
Helical vortices: theory and applications
講演者：
Valery L. Okulov
(Department of Wind Energy, Technical University of Denmark)
要旨：
The main applications of 2D dynamics of helical vortices embedded
in flows with helical symmetry are addressed.
The fundamentals of the 2D helical vortex dynamics lie in
(i) 2D algebraical expression of Biot-Savart law for helical filament;
(ii) analytical solution for self-induced motion of the helical vortex cores;
(iii) Goldstein’s solution for circulation of equilibrium of helical vortex sheets;
(iv) Generalization of Kelvin’s problem on point vortex N-gon stability to helix etc.
The primary assumption of the 2D theory is the hypothesis of helical symmetry
that has been carefully tested in swirling flows in different kinds of swirlers
and vortex generators. Both right- and left-handed helical symmetries were
found in these real flows and hypothesis of existence of possible transitions
between the different types of the vortex structures have been put forward.
The change in axial velocity distribution from a jet-like profile to a wake-like
during vortex breakdown has been investigated from this point of view and
the associated transition from right- to left-handed helical symmetry of the
vorticity field has been confirmed from experimental data and numerical simulations.
Various vortex models for far wakes behind rotors are analyzed.
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第98回現象数理セミナー
日時：12月12日(火) 14:30-17:30
場所： D710(九州大学伊都キャンパス・ウエスト1号館)
講演1 14:30-16:00
題目：Transient effects at resonant light scattering by particles
講演者：Michael I. Tribelsky (Lomonosov Moscow State University)
講演2 16:00-17:30
題目：Quantum simulation of atom coupled to Bose field(s)
講演者：廣川真男 (広島大・工学研究科)
夕方には、天神-中州あたりで懇親会を行う予定です。
** 講演要旨 **
講演 1: Michael I. Tribelsky
Transient effects at excitation of high-Q resonant modes at a leading
edge of a laser pulse and their decomposition at its trailing edge
during the pulse scattering by a particle are discussed. The main
attention is paid to the nonradiating (anapole) mode excited in a
high-index cylinder. The problem is studied both analytically and
numerically. It is shown that the anapole is a steady but essentially
non-equilibrium mode, which can exist if and only if the host particle
is irradiated by a continuous incident wave. As soon as the incident
wave is switched off, the anapole becomes a radiating mode and
collapses very fast owing to extensive radiative losses. It ruins
the hopes to employ the anapole-like excitations as storages
for the “frozen light.”
講演 2: 廣川真男
We consider quantum simulations for the following 3 subjects:
1. the duality between a dark state and a quasi-dark state for
an atom coupled to both the 1-mode photon and 1-mode phonon
in cavity optomechanics;
2. the dressed photon and the Schr oedinger-cat-like entangled
ground state of the generalized quantum Rabi model;
3. the possibility of the conversion from virtual photon to real
photon in a ground state of the generalized quantum Rabi model.
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第97回現象数理セミナー
日時：6月22日(木)16:00から17:30
場所： C501 (九州大学伊都キャンパス・ウエスト1号館)
（部屋が普段と違いますので、ご注意ください）
（終了後に懇親会を開催します）
講演題目：
Integrable discrete models for one-dimensional soil water infiltration
講演者：
Dimetre Triadis
(Kyushu University)
要旨：
I will describe some integrable discrete models for one-dimensional soil water infiltration, developed through collaborative research at the IMI Australia Branch. The discrete models are based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection-diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct discrete models parallel to the continuum model and preserving the underlying integrability. These take the form of self-adaptive moving mesh schemes. The discretizations are based on linearizability of the Burgers equation to the linear diffusion equation, however the naive Euler discretization that is often used in the theory of discrete integrable systems does not necessarily produce a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model with reasonable stability and accuracy.
（今回のセミナーは可積分系セミナーと合同で行われます）
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第96回現象数理セミナー
日時：3月28日(火)16:00から17:30
場所： C512 (九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
講演題目：
Molecular Extended Thermodynamics of a Rarefied Polyatomic Gas
講演者：
Tommaso Ruggeri
(University of Bologna, Italy)
要旨：
Extended Thermodynamics can be considered as a theory of continuum
with structure because there are new field variables with respect to
the classical approach and they are dictated at mesoscopic level
by the kinetic theory. In this talk I present some recent results
on so-called Molecular Extended Thermodynamics (MET) in which
the macroscopic fields are related to the moments of a distribution function
that for polyatomic gas contains an extra variable taking into account
the internal degrees of freedom of a molecule. The closure is obtained
via the variational procedure through the Maximum Entropy Principle.
Particular attention will be paid on the simple model of MET
with six independent fields, i.e., the mass density, the velocity,
the temperature and the dynamic pressure, without adopting
near-equilibrium approximation. The model obtained is the simplest
example of non-linear dissipative fluid after the ideal case of Euler.
The system is symmetric hyperbolic with the convex entropy density
and the K-condition is satisfied. Therefore, in contrast to the Euler case,
there exist global smooth solutions provided that the initial data are
suffficiently smooth.
References
[1] I. Muller and T. Ruggeri: Rational Extended Thermodynamics
(Springer, New York, 1998) 2nd ed.
[2] T. Ruggeri and M. Sugiyama: Rational Extended Thermodynamics
beyond the Monatomic Gas (Springer, Cham, Heidelberg,
NewYork, Dordrecht, London, 2015).
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第95回現象数理セミナー
日時：3月16日(木)16:00から17:30
場所： C512 (九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
講演題目：
形状最適化問題による流れ場の安定性制御
講演者：
中澤 嵩
(東北大学理学研究科)
要旨：
講演者はこれまで，低速流体を想定した場合において，線形安定性解析を
考慮することで，流れ場の線形安定性を直接的に制御可能な形状最適化問題
を構築してきた．しかし，乱流場のような複数の擾乱が発達している流れ場
において，その適用は困難であり，従来の方法では乱流場の安定性制御は
不可能であった．そこで，現在，統計的手法手法の一つである
Proper Orthogonal Decomposition(POD)とNavier-Stokes方程式の数値解析，
形状最適化問題を融合させることで，乱流場の安定性制御を試みている．
講演当日には，2次元Cavity流れに対して当該最適化問題を適用し結果
を紹介する．
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第94回現象数理セミナー
日時：3月8日(水)15:30から17:00
場所： C512 (九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
講演題目：
Simulating fracture propagation and damage evolution in 3D isotropic and
anisotropic, heterogeneous rock with a pre-existing surface flaw.
講演者：
Sanjib Mondal
(School of Earth and Environmental Sciences
The University of Queensland, Australia)
要旨：
Fracture propagation and damage evolution is extremely important for
many industrial application including mining industry, composite
materials, earthquake simulations, hydraulic fracturing. In this project
a numerical damage model is applied to an isotropic sandstone specimen
containing a pre-existing 3-D surface flaw in different configurations
under uniaxial compression. The heterogeneity of rock is considered by
assuming the material properties in rock can be represented by a Weibull
distribution. We investigate the effect of parameters including the
heterogeneity of the elastic moduli and geometry of the single flaw on
the stress strain response. The generation of three typical surface
cracking patterns, called wing cracks, anti-wing cracks and far-field
cracks were identified and these depend on the geometry of the pre-
existing surface flaw. The numerical fracture simulation of rock
specimen by using eScript software and finite element method is
presented. This project will also develop anisotropic damage models for
fracture propagation which will be coupled to porous media flow models
to build hydraulic fracture simulators that include key factors such as
the cleated nature of the coal seam, pre-existing joints and faults, in-
situ stress and surrounding stratigraphy of the coal seams. Completion
of the model will advance our understanding of fracture growth in
heterogeneous cleated coal and help to develop fracture simulators that
can be applied to both unconventional and conventional oil and gas
reservoirs.
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第93回現象数理セミナー
日時：2月13日(月)16:00から17:30
場所： C715(九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
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講演題目：
Navier-Stokes flow in an exterior domain in a half space
講演者：
Zhengguang Guo
(College of Mathematics and Information Science, Wenzhou University)
要旨：
We consider the problem of a body moving within an incompressible fluid
at constant speed parallel to a wall, in an otherwise unbounded domain.
This situation is modeled by the incompressible Navier-Stokes equations
in an exterior domain in a half space, with appropriate boundary conditions
on the wall, the body, and at infinity.
In this talk, we show the existence of solution and asymptotic behavior
of 3D incompressible exterior Navier-Stokes equations.
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第92回現象数理セミナー
日時：12月8日(木)16:00から17:00
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
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講演題目：
Laser heating of dielectric particles for medical and biological
applications
講演者：
Michael I. Tribelsky
(Lomonosov Moscow State University &
National Research Nuclear University MEPhI (Moscow Engineering Physics
Institute))
要旨：(添付file にあります)
We consider the general problem of laser pulse heating of a spherical
dielectric particle embedded in a liquid. The discussed range of the
problem parameters is typical for medical and biological applications.
We focus on the case, when the heat diffusivity in the particle is of
the same order of magnitude as that in the fluid. We perform
quantitative analysis of the heat transfer equation based on interplay
of four characteristic scales of the problem, namely the particle radius,
the characteristic depth of light absorption in the material of the
particle and the two heat diffusion lengths: in the particle and in the
embedding liquid. A new quantitative characteristic of the laser action,
namely the cooling time, describing the temporal scale of the cooling
down of the particle after the laser pulse is over, is introduced and
discussed. Simple analytical formulas for the temperature rise in the
center of the particle and at its surface as well as for the cooling
time are obtained. We show that at the appropriate choice of the problem
parameters the cooling time may be by many orders of magnitude larger
the laser pulse duration. It makes possible to minimize the undesirable
damage of healthy tissues owing to the finite size of the laser beam and
scattering of the laser radiation, simultaneously keeping the total
hyperthermia period large enough to kill the cancer cells. An example of
application of the developed approach to optimization of the therapeutic
effect at the laser heating of particles for cancer therapy is presented.
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第91回現象数理セミナー
日時：9月15日(水)16:00から17:00
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
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講演者：
David Wood
(University of Calgary, Canada)
講演題目：
Application of helical vortex solutions to determine wind turbine tip loss
要旨：
The talk will discuss two related problems of Blade-Element-Momentum-Theory (BEMT) for horizontal axis wind turbines, both connected to the analytical solution for the flow induced by helical vortices. For many years, it was believed that this solution was first derived by the American scientist Hardin in 1982, but recently the work of the Japanese aerodynamicist Kawada in 1935 was rediscovered. The first problem is the determination of the tip loss, used in BEMT to account for the finite number of blades on a real turbine. Currently, tip loss is approximated by a simple expression due to Prandtl, but this formulation is not accurate over the full operating range of a wind turbine. In 1939 Kawada made two important contributions to this problem which were subsequently forgotten for nearly 80 years. Kawada's work will be used to develop a more accurate alternative to Prandtl's formula that is almost as simple to implement. The second problem is the effect of the azimuthal variation of the flow in the wake of the rotor which give rise to nonlinear terms in the equations for axial and angular momentum. Kawada's contributions allow these terms to be accurately determined for the first time. It will be shown that they contribute significantly at some operating conditions.
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第90回現象数理セミナー
日時：4月6日(水)16:00から17:00
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
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講演題目：
Classification of Electron Energy Level Crossings in terms of the Theory
of Singularities and Analysis of Non-Adiabatic Transitions around the
Crossings
講演題目：
寺本 央
(北海道大学電子科学研究所)
要旨：（数式の表示がおかしくなっている部分があります）
Electron energy level crossings play important roles in photochemistry. For example, conical intersections, ones of the representative electron energy level crossings, provide efficient gateways for non-radiative decay of photo-excited states of molecules. To understand the photochemistry and to control it by applying external fields, like, electric and magnetic fields, it is crucial to understand electron energy level crossings and how they are modulated by these external fields. Classification of electron energy level crossings is done by Hagedorn [1] and it was shown that there are 11 types of electron energy level crossings (Type A-K) under the setting in which there is no accidental degeneracy other than the crossings. Two of them, Type A and B, can occur when the system does not have a time-reversal symmetry and the other nine types, Type C-K, can occur otherwise. Among these types, Type I is the most important one in the following sense. First of all, magnitudes of non-adiabatic interactions in neighborhoods of Type A, C-H are of order ( ) 4 1 M ε = m where m is the mass of electrons whereas M is a typical mass of nuclei. Contrastingly, magnitudes of non-adiabatic interactions in neighborhoods of Type B, I, J, K are of order 0 ε . Regarding the order of the non-adiabatic interactions, Type B, I, J, K should be more important than the others. Next, in general case, Type B, I, J, and K crossings have codimension 3, 2, 3, and 5, respectively, where a manifold of codimension n is a manifold having n dimension less by that of the ambient space. Therefore, regarding the order of the non-adiabatic interactions and the codimension, Type I should be the most important one among all. In what follows, we focus on Type I crossing but our analysis applies to the other cases as well. Hagedorn [1] also derived a normal form in neighborhoods of all the types of crossings in general cases. However, if the system is under external fields, these electron energy level crossings are going to be modulated by external fields and it is vital to understand not only the general cases but also less general cases, like, cases on the verge of bifurcations. In this talk, we provide a theoretical framework to classify electron energy level crossings including these less general cases, their bifurcations, and investigate dynamics of wave packets in a vicinity of them. References [1] G. Hagedorn, Mem. Amer. Math. Soc. Vol. 111 (1994).
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第89回現象数理セミナー
日時：3月8日(火)16:00から17:00
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
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講演題目：
細胞集団運動におけるソリトン現象の発見
Biological Soliton in Multicellular Movement
講演者：
講演者：桑山秀一(筑波大学生命環境系生物科学専攻)
要旨：
ソリトンとはぶつかっても互いに通りぬける不思議な性質をもつ波のことで、数学や物理学において非常に重要な現象・概念です。これまで細胞運動のレベルにおいてソリトン現象は観察されていませんでしたが、私のグループでは、多細胞運動としては世界で初めて、細胞性粘菌の突然変異株においてソリトン現象を観察しました(Kuwayama and Ishida, Scientific Reports, 3, Article number: 2272, 2013)。
細胞性粘菌は真核アメーバの単細胞生物ですが、餌がなくなると走化性運動により集合して子実体を形成します。独自に分離したある突然変異株は走化性運動ができず、子実体を形成しません。しかしながら、その細胞運動を観察したところ、子実体は形成しない代わりに、波紋様の塊を形成することを発見しました。この波紋様の塊は細胞が集まった細胞集団で、形を崩さずに一定の速度で運動し、ぶつかり合っても形を崩すことなく互いに通り抜けてしまうソリトンの性質を示すことを明らかにしました（Fig. 1）。このソリトン様細胞運動の性質を調べると、①ソリトン様細胞集団の形成と維持は、走化性などによる外部からの化学信号によるものではなく、細胞間の接着によって形成・維持されている。②ソリトン様細胞集団の運動は、進行方向前部にある細胞を取り込みながら前進すると同時に、取り込んだ分に相当する細胞を後方に残していくことで、一定の大きさを保っている。つまりその形状は、動的平衡によって一定に維持されている。③ソリトン様細胞集団どうしが衝突すると、細胞のシャッフリングが起こるが、分離する際にそれぞれが衝突前と同様なソリトン様細胞集団を再形成する。これにより、あたかも一見通り抜けたような現象に見える。④大きさの違うソリトン様細胞集団が衝突すると分離後もそれぞれ大きな波と小さな波を形成した。これらは、波状の細胞集団の大きさや運動量は集団として記憶され、個々の細胞に依存していないこと
を意味しています。
本セミナーでは、細胞性粘菌の生物としての性質と細胞運動のソリトン現象の特徴についてお話します。
Solitons have been observed in various physical phenomena mainly in physical fields. We showed that the distinct characteristics of solitons are present in the mass cell movement of non-chemotactic mutants of the cellular slime mould Dictyostelium discoideum (Kuwayama and Ishida, Scientific Reports, 3, Article number: 2272, 2013).
During starvation, D. discoideum forms multicellular structures that differentiate into spore or stalk cells and, eventually, a fruiting body. The non-chemotactic mutant cells do not form multicellular structures; however, they exhibited a characteristic structure with the features of a self-reinforcing solitary wave, or soliton. Under starvation conditions, the mutants do not aggregate but form an arc-shape multicellular structure, named the Soliton-Like-Structure (SLS). SLS movement continues much longer than the developmental cycle, moves at constant speed without changing shape, and does not obey the superposition principle. Even after collisions, waves pass through each other, conserving their physical qualities (Fig.1). They do undergo mass cell movement in the form of a pulsatile soliton-like structure (SLS). It was also found that SLS induction is mediated by adhesive cell-cell interactions. These observations provided novel insights into the mechanisms of biological solitons in multicellular movement.
In this seminar, the nature of the cellular slime mould and the feature of the biological soliton will be introduced.
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第88回現象数理セミナー
日時：2月4日(木)16:00から
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
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講演題目：
磁気圏サブストームに伴う2-null, 2-separator構造の崩壊
講演者：
吉岡大樹
(九州大学大学院理学府地球惑星)
要旨：
現代社会においてサブストームの研究は必要不可欠なものとなっている。実際にサブストームによる 様々な被害が報告されているため、現在では宇宙天気の研究が進められており将来的に宇宙天気の予報 につなげる必要がある。そのための基礎研究として本研究では、グローバル MHD シミュレーションを 用いて、IMF が北向きから南向きに変わっていく過程で、磁気圏がどのように反応し、その磁場トポロ ジーがサブストームとどのように関係しているのかを解明する。本研究で磁場トポロジーというグロー バルな視点からサブストームを理解することにより、各々のローカルな現象理解の深化につなげられる。
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第87回現象数理セミナー
日時：1月14日(木)16:00から
場所： C512(九州大学伊都キャンパス・ウエスト1号館)
（終了後に懇親会を開催します）
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講演題目：
Giant resonances and other peculiarities of light scattering by
particles with high refractive index
講演者：
Michael Tribelsky
(Lomonosov Moscow State University & Moscow State Institute of
Radioengineering)
要旨：
A detailed inspection of light scattering by a particle with high refractive index m+iκ and small dissipative constant κ is presented. It is shown that there is a dramatic difference in the behavior of the electromagnetic field within the particle (inner problem) and the scattered field outside it (outer problem). With an increase in m at fix values of the other problem parameters the field within the particle asymptotically converges to a periodic function of m. The electric and magnetic type Mie resonances of different orders overlap substantially. It may lead to a giant concentration of the electromagnetic energy within the particle. At the same time, it is demonstrated that identical transformations of the solution to the outer problem allow to present each partial scattered wave as a sum of two partitions. One of them corresponds to the m-independent wave, scattered by the perfectly reflecting particle, while the other is associated with the excitation of a sharply-m-dependent resonant Mie mode. The interference of the partitions brings about a typical asymmetric Fano profile. At an increase in m, in contrast to the inner problem, the resonant modes of the outer problem die out, and the scattered field converges to the universal, m-independent profile. The behavior of the resonances at a fixed m and varying particle size parameter (x) is also examined in detail. The similarities and differences of the two cases (fixed x – varying m and fixed m – varying x) are disclosed. The relevant experiments are discussed.
（添付ファイル”Tribelsky_Abstract_2.pdf”より転載）
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第86回現象数理セミナー
日時：11月19日(木)15:30-17:00
場所： C５１２室(九州大学伊都キャンパス・ウエスト1号館)
（終了後に地下鉄沿線にて懇親会を開催します）
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講演者：深川宏樹 九州大学大学院工学研究院機械工学部門
タイトル：変分原理による非一様温度場中の界面のある散逸流体の定式化
要旨：
非一様温度場中にある二成分流体、液晶などの複雑な内部構造を持つ界面のある散逸流体の運動方程式を知るのは難しい。我々はこの問題を解決すべく、変分原理による定式化を提案した。
一般に、散逸による系の履歴依存性は非ホロノミック拘束条件として与えられる。変分原理を用いれば、散逸系の運動方程式は作用汎関数を非ホロノミック拘束条件の下で停留値を与える必要条件として得られる。つまり、作用汎関数の被積分関数であるラグランジアン密度と散逸を表す非ホロノミック拘束条件が分かれば、流体の運動方程式が導出できる。
ラグランジアン密度は運動エネルギー密度と内部エネルギー密度の差で与えられる。一方、非ホロノミック拘束条件は複雑な系だと分からないことが多い。そこで我々は非ホロノミック拘束条件を課した変分原理に次の2つを満たすことを要求した。
１ 物理系は対称性とそれに関連する保存則を持つ。(ネーターの定理)
２ 物理系は良設定問題である。つまり解が存在する。
これにより、ラグランジアン密度が与えられた時に非ホロノミック拘束条件のクラスが決まり、散逸系の運動方程式が得られる。我々はこの定式化を界面のある粘性流体、二成分流体、液晶に適用し、これらの運動方程式を得た。
本講演では、主に理論を紹介し、最後に数値計算について議論したい。
参考文献
Hiroki Fukagawa, Chun Liu, and Takeshi Tsuji. A variational formulation for dissipative fluids with interfaces in an inhomogeneous temperature field.
arXiv:1411.6760
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第85回現象数理セミナー
日時：9月14日(月) 10:30-12:00
場所： ２０４室(数理学研究教育棟１階)
（今回は懇親会は行いません。）
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講演者：
Prof. Luis A. Davalos-Orozco
Departamento de Polimeros
Instituto de Investigaciones en Materiales
Universidad Nacional Autonoma de Mexico
タイトル：
"Thermocapillary instability of a thin film falling down a thick and deformed cooled wall with finite thermal conductivity"
要旨：
The stability of thin liquid films is of importance in problems of coating solid surfaces. Mainly, when the goal is to have a smooth free surface after the film solidifies. Sometimes the wall has small deformations which have to be taken into account. The goal of this talk is to present recent results on the non linear stability of the free surface of liquid films flowing down smoothly deformed vertical walls. It is also of interest to show the important influence on the stability of the finite thickness and thermal conductivity of the wall.
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第84回現象数理セミナー
日時：3月4日(水)15:30から
場所： 中セミナー室３(数理学研究教育棟)
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講演題目：
Thermocapillary manipulation of thin liquid films using traveling thermal waves
講演者：
Alexander Oron
(Technion - Israel Institute of Technology)
要旨：
Using long-wave theory and direct numerical solutions of the Navier-Stokes equations, we investigate nonlinear dynamics of thermocapillary flows arising in a two-layer system consisting of a thin liquid film and an overlying gas layer with the liquid film covering a heated solid substrate with a non-uniform temperature in the form of traveling thermal waves. Our results indicate that unidirectionally propagating interfacial waves are formed in the liquid film. The interfacial waves transport liquid, thereby creating a net pumping effect. We show that the frequency of thermal waves leading to the most efficient pumping is defined by their wave length and weakly depends on other system parameters.
In the case of a stationary thermal wave with sufficiently large amplitude and Marangoni number, liquid film rupture takes place with a flattish wide trough. For moderately small frequencies of the thermal wave, a periodic structure consisting of localized drops interconnected by thin liquid bridges emerges with virtually no mass exchange between the adjacent drops. This train of drops travels along the heated substrate following the thermal wave. For larger thermal wave frequencies, the thickness of the bridges increases enabling fluid flow between the neighboring drops. The drop-train regimes may be utilized in microfluidic applications for directed transport of liquid content enclosed in drops formed by thermocapillary forces.
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第83回現象数理セミナー
日時：2月19日(木)15:00から
場所： 中セミナー室３(数理学研究教育棟)
講演題目：
Fano resonances: What is it?
講演者：
Michael Tribelsky
(Lomonosov Moscow State University & Moscow State Institute of
Radioengineering)
要旨：
The Fano resonances are one of the “hottest” topics of the modern physics and technology. There are numerous publications devoted to these resonances. Unfortunately, the level of complexity of these publications usually does not allow an average undergraduate student to understand them. In contrast, in the present talk a comprehensive discussion of the Fano resonances is presented. To understand the discussion no preliminary knowledge in Quantum Mechanics and just basic knowledge in Math, corresponding to the general undergraduate curriculum, are required. The discussion includes the history of the phenomenon, explains why the phenomenon is so important and elucidates the main features of it. Then, the simplest mechanical model exhibiting the Fano resonances (the forced oscillations of two coupled pendulums) is introduced and analyzed. Based upon this analysis certain general conclusions are obtained.
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第82回現象数理セミナー
日時：11月27日(木)15:30から
場所： 中セミナー室３(数理学研究教育棟)
講演題目：
A Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver for
Electrostatics of Solvated Proteins
講演者：
Robert Krasny
(Department of Mathematics, University of Michigan)
要旨：
Electrostatic effects play an important role in determining protein
structure and function. Here we present a treecode-accelerated boundary
integral (TABI) solver for the electrostatic potential of a solvated
protein described by the linear Poisson-Boltzmann equation. In this
model the solvent is a continuum dielectric material with ionic
screening. The treecode reduces the computational cost from $O(N^2)$ to
$O(N\log N)$, where $N$ is the number of faces in the triangulated
molecular surface. We compare TABI results to those obtained using the
grid-based APBS code. The TABI solver exhibits good serial and parallel
performance, with relatively simple implementation, efficient memory
usage, and geometric adaptability. This is joint work with Weihua Geng
(Southern Methodist University).
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第８１回現象数理セミナー
日時：５月２９日(木)15:30-17:00
場所：伊都キャンパス 数理学研究院 ３階 中セミナー室３
講演題目：
Linear instability of moving phase boundaries at heat transfer problems in solids: Exact results
講演者：
Michael Tribelsky
(Lomonosov Moscow State University)
講演要旨：
Two problems of stability of a moving phase boundary at heat transfer
problems:
(i) at a plane wave of laser-sustained evaporation of solids and
(ii) at self-similar crystal growth from an undercooled liquid
are considered. Both the problems may exhibit instabilities breaking
the initial high (plane, or spherical) symmetry. In both the cases
the exact expressions for the spectrum of unstable modes are obtained.
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第８０回現象数理セミナー
日時：2月3日(月)13:00-16:15
伊都キャンパス 数理学研究院 ３階 中セミナー室７
講演1 13:00-14:30
題目：Recent Mathematical Results in Classical and Relativistic Extended
Thermodynamics
講演者：Tommaso RUGGERI (University of Bologna)
講演2 14:45-15:30
題目：濃密気体に対する拡張された熱力学 -その理論と応用-
講演者：有馬隆司 (名工大・産学官連携センター )
講演3 15:30-16:15
題目：「拡張された熱力学」に基づく多原子分子希薄気体中の衝撃波構造
講演者：谷口茂 (名工大・工)
** 講演要旨 **
講演1: T. RUGGERI
Newton流体の構成式と、熱伝導に対する Fourier則を用いた流体方程式は
Navier-StokesStokes Fourier理論と呼ばれている。この理論は、Eckart,
Meixner, Prigogine達による「不可逆過程の熱力学（TIPTIP）」により基礎付け
られる。TIP は、局所平衡の仮定に基づいている。最近、この仮定が成り立たな
い強い非平衡な現象にも適用できる理論として「拡張された熱力学(ET)」[1] が
発展してきている。本講演において、ET理論の基本的考え方を、非相対論な場合
および相対論的な場合について、 数理的な観点を強調しながら概説する。さら
に、気体分子運動論との関連[2] についても述べる。ただし、ここでの講演は、
主として、希薄な単原子分子気体の場合に限定し、濃密気体および多原希薄気体
のET理論については、次の講演 に譲る。
[1] I. Muller and T. Ruggeri: Rational Extended Thermodynamics
(Springer, New York, 1998) 2nd ed.
[2] M. Pavic, T. Ruggeri and S. Simic, Physica A 392, 1302-1317 (2013).
講演2: 有馬隆司
拡張された熱力学(ET)[1]は、物理量の急激な時間・空的変化を伴う非平衡現象
に適用可能な理論であり、局所平衡の仮定に基づく Navier-Stokes Fourier理論
（NSF）よりも広い適用範囲を持つ。本講演では、最近提案した濃密気体および
多原子分希薄気体に適用可能なET理論[2]を紹介す る。さらに、その応用として
音波を解析し、NSFによる理論予測が実験からずれるような高振動数領域でも、
ETによる理論予測が実験をうまく再現 できること示す[3] 。
[1] I. Muller and T. Ruggeri: Rational Extended Thermodynamics
(Springer, New York, 1998) 2nd ed.
[2] T. Arima, S. Taniguchi, Ruggeri and M. Sugiyama, Cont. Mech.
Thermodyn, 24, 271-292 (2012).
[3] T. Arima, S. Taniguchi, Ruggeri and M. Sugiyama, Cont. Mech.
Thermodyn. 25, 727-737 (2013).
講演3: 谷口茂
多原子分希薄気体中を伝播する垂直衝撃波の衝撃波構造(衝撃波面内部の強い非
平衡状態における物理量の空間分布)について、「拡張された熱力学」 (ET)理論
を用いて解析した結果報告する[1, 2]。多原子分子希薄気体中の衝撃波構造は、
マッハ数の増加ともに、(A)対称的な衝撃波構造から、(B) 非対称な衝撃波構造
に変化し、さらには(C) 薄い層と厚い層の二層からなる衝撃波構造に変化すると
いう特徴を持つ。本講演では、(i)ET理論は(A)-(C)の衝撃波構造を統一的に説明
できるこ と、(ii)ETによる理論予測は実験データと定量的によく一致すること
を示す。さらに、従来のBethe-Teller理論について、ETの観 点から批判的に検
討を行う。
[1] S. Taniguchi, T. Arima, Ruggeri and M. Sugiyama: “Thermodynamic
theory of the shock wave structure in a rarefied polyatomic gas: Beyond
the Bethe-Teller theory", Phys. Rev. E, in press.
[2] S. Taniguchi, T. Arima, Ruggeri and M. Sugiyama: Phys. Fluids, Vol.
26, 016103 (2014).
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第７９回現象数理セミナー&院生プロジェクト
日時：11月9日(土) 14:00-15:30
場所：中セミナー室7 (数理学研究教育棟)
講演題目：
Incorporating Native Hawaiian Culture into High School Mathematics
講演者：
Aaron Tamura-Sato
(University of Hawaii at Manoa）
講演要旨：
The School and University Partnership for Educational Renewal
in Mathematics (SUPER-M) Fellowship is a GK-12 program at the
University of Hawaii at Manoa which sends UH graduate students
to schools throughout Hawaii. I will share some of the work
that we do and present several math activities created by
the program inspired by native Hawaiian culture and sports,
such as he'e holua (Hawaiian lava surfing), 'ulu maika
(stone disk bowling), and 'ahu 'ula (featherwork capes).
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第７８回現象数理セミナー
日時 : 2013 年 6月6日(木)15:30
場所 : 九州大学伊都キャンパス数理学研究院／IMI３階 中セミナー室3
講演題目：
Nonlinear Phenomena Induced by fs Laser Pulses on Silicon Surface and
their Simulation
講演者：
Stjepan Lugomer
(Rudjer Boskovic Institute, Zagreb, Croatia）
講演要旨：
Interaction of ultraviolet femtosecond laser pulses with silicon and generation of surface structures has been studied at two energy densities, E1 ~ Ethr ~ 0.17 J/cm2, (near the ablation threshold) and E2 ~ 0.42 J/cm2 >> Ethr, much above the ablation threshold. In both cases the number of pulses, N, is the external control parameter that controls the formation and transformation of structures.
E1 ~ Ethr: For N < 200, the «carpet-like» pattern of nano-, and micro-spikes is generated by the bubble explosion in a silicon foam-layer. The accumulation of nanobubbles due to repetition of laser pulses and their explosion cause damped membrane-like oscillation of the foam-layer. For N ≥ 200, bifurcation of surface morphology takes place: (i) In the peripheral region of the spot, the surface tension waves with L1 ~ 180 mm, have been formed. The change of their wavelength into L2 ~ 40 mm with propagation distance indicates the Eckhaus instability caused by the phase modulation with increasing N. The simulation of the left and the right propagating waves can be based on the complex Landau-Ginzburg equation.(ii) In the central region of the spot, a rough irregular morphology appears caused by the fast spinodal decomposition and fragmentation of superheated silicon layer.
E2 >> Ethr: The train of 120 ≤ N ≤ 190 pulses establishes the 2D unidirectional cnoidal-like waves as well as the Y- and X-type configurations. In the region of high laser intensity, the interaction of stable line solitary-like waves give rise to the complex network structure. The network of line-solitons was shown to be decomposed into segments with more simple configurations which can be simulated by the Kadomtsev-Petviashvili (KP-II) equation with negative dispersion as 2-soliton solutions. For the sequence of pulses 200 ≤ N < 220, the transition from stable into unstable waves takes place. The unstable wiggling cnoidal and decaying line-soliton waves were shown to be reproduced by using the KP-I equation with positive dispersion. The sequence of pulses approaching the critical value, Ncritical ( ≥ 230), destruction of unstable cnoidal and solitary waves into localized lump solitons, takes place.