2009 年度


``A model for elastohydrodynamic collision of spheres in liquid'' (in English)
Abstract.We pursue a reduced-order model of normal “elastohydrodynamic” collision between two spheres in incompressible liquid (Wells 1993; Proc. Powders & Grains ’93, “W93”). The main analytical difficulty is the inverse-cube influence of local squeeze-film thickness on the pressure gradient. W93 assumed a “quasi-Hertzian” surface depression profile, yielding the first reduced-order model ODEs for this problem. Trajectories and coefficients of restitution agreed well with simulations ( Davis, Serayssol, & Hinch , 1986; J. Fluid Mech 201; “DSH86”). To avoid numerical integrations such as those in W93, Lian et al. (1996, J. Fluid Mech 311) assumed additionally that the gap inboard of a certain radius was constant, leaving only the centerline gap as an unknown. Then introducing an adjustable constant, they recovered coefficients of restitution close to DSH86. The present work extends W93 and Lian et al. to achieve, without adjustable constants, the analytical character that until now was only afforded by perturbation approaches (DSH86) wherein centerline deformation is assumed to be much smaller than the gap.
``Herds of mechanical circular sheep : an experimental reality'' (in English)
Abstract.For fifteen years, statistical physics try to understand the collective dynamics in living systems such as bacteria, fish shoals, flocks of birds or herds of sheep. They share specific characteristics : there is no leader and all individuals move in the preferred tail-head direction (the so-called polarity) interacting locally with each other. To figure out if these ingredients are enough for generating collective dynamics, we propose an experiment of vibrated circular self-propelled grains. Thanks to the balance between the energy input provided through the vibration and the dissipation of this energy by dissymetric grains, we have a system of circular grains moving along their own polarity, interacting only by contact. Such a non-equilibrium system reveals the signature of a transition towards collective motion by decreasing the angular noise on the self-propulsion of the grains. We will discuss the spatial ordering as well as the dynamical correlations of the polarity at a packing fraction close to 0.5. We will also give the first statistical properties of such a liquid which can flow without any external field !
``Stress transmission and incipient yield flow in dense granular materials'' (in English)
Abstract. Jammed granular materials transmit stresses non-uniformly unlike conventional solids, especially when it is on the verge of failure and immediately after yield. Jamming is caused by self-organization of granular matter under external loads, often giving rise to networks of force chains that support the loads non-uniformly. An ongoing debate in the literature concerns the correct way to model the static stress field in such media: good old elasticity theory or newcomer isostaticity theory. The two differ significantly and, in particular in 2D, isostaticity theory leads naturally to force chain solutions. More recently, it has been proposed that real granular materials are made of mixtures of regions, some behaving elastically and some isostatically. The theory to describe these systems has been named stato- elasticity [1,2]. In this talk, I first present the rationale for stato-elasticity theory. An important step towards the construction of this theory is a good understanding of stress transmission in the regions of pure isostatic states and new general solutions are presented for 2D isostatic regions. The solutions show that force chains is too simple a picture and that pure isostatic materials support generic solutions, where stresses along force chains attenuate, force chains branch, and stress 'leaks' away from main chains through secondary and tertiary chains into 'cones of influence' [3,4]. All these are direct solutions of the stress field equations with no need for additional modelling. I will then show how the static stress equations are related directly to incipient yield flow and derive the equations that govern yield and creep rheology of dense granular matter[5,6]. These equations are general and also describe the seemingly unrelated kinetics of auxetic materials [7].

1. R. Blumenfeld, Stresses in isostatic granular systems and emergence of force chains, Phys. Rev. Lett. 93, 118301 (2004).
2. R. Blumenfeld, Stresses in two-dimensional isostatic granular systems: Exact solutions, New Journal of Physics 9, 160 (2007).
3. M. Gerritsen, G. Kreiss, R. Blumenfeld, Stress chain solutions in two-dimensional isostatic granular systems: fabric-dependent paths, leakage and branching, Phys. Rev. Lett. 101, 098001 (2008).
4. M. Gerritsen, G. Kreiss, R. Blumenfeld, Analysis of stresses in two-dimensional isostatic
5. R. C. Ball and R. Blumenfeld, From Plasticity to a renormalisation group, Phil. Trans. R. Soc. Lond. 360 , 731 (2003).
6. R. Blumenfeld, S. F. Edwards and R. C. Ball, Granular matter and the marginal rigidity state, J. Phys.: Cond. Mat. 17, S2481 (2005).
7. R. Blumenfeld, Auxetic strains - insight from iso-auxetic materials, Molecular Simulation 31, 867-871 (2005).
``AdS/CFT対応と非平衡定常系''
Abstract. AdS/CFT対応とは、強く相互作用する共形場の量子論 を古典重力理論（一般相対性理論と古典場からなる理論） にマップする対応関係である。この対応を用いると共形場 （実際は、共形場以外にも拡張可能である）理論の 量子効果も含めた非摂動的物理が、重力側の古典的 計算により解析可能となる。系に有限温度や有限保存 電荷密度を導入することも可能であり、有限温度共形場 理論のある相状態は、重力理論側にブラックホールが 存在する系にマップされる。
ここでは、3+1次元（空間3次元、時間1次元）の、 ある特殊なゲージ理論のプラズマ中に一定の外部電場が 加えられ、保存電荷の定常電流が流れている、散逸の ある系を考える。この系は5次元のAdSブラックホール時空に D-braneと呼ばれる弦理論の非摂動的物体を挿入した系に マップされる。重力理論側でのD-brane作用の整合性等の 条件からプラズマの電気伝導度などの輸送係数が計算される。 また、単位時間あたりに熱浴に流出するエネルギー・運動量の 値も重力理論を用いて計算可能となる。従って、この セットアップは、量子効果も含めて物理量を具体的に 計算可能な「非平衡定常系」のモデルとなっている。 以上は既にM. Ammon et. al. arXiv:0908.2625等でなされた 仕事であるが、AdS/CFTの概略からはじめて、このセットアップ の解説を弦理論の非専門家向けに行う予定である。 さらに、可能であれば、この系における、非ゼロ電流存在下に おける電流の2点（2時間）相関関数等の計算も重力理論を 用いて試み、非平衡統計物理学の観点から意味のある計算・研究 へと発展させるための意見交換を行いたい。
``情報熱力学''
Abstract.情 報処理に必要な熱力学的エネルギーコスト（仕事）の限界については、マクスウェルのデーモンのパラドックスやランダウアー原理をはじめとして、古くから様 々な議論がなされてきた。我々は、フィードバック・測定・情報の消去といった情報処理に要する仕事の原理的な下限を、統計力学の観点から導いた [1,2]。その結果、ある特殊な場合を除いて、ランダウアー原理は破れうることが分かった。我々の結果においては熱力学変数と情報量が同等に扱われてお り、「情報熱力学」の第二法則とも呼ぶべきものになっている。また、我々の結果を検証した最近の実験についてもあわせて報告する。

[1] T. Sagawa and M. Ueda, Phys. Rev. Lett. 100, 080403 (2008).
[2] T. Sagawa and M. Ueda, Phys. Rev. Lett. 102, 250602 (2009).
``３次元非線形格子の熱伝導とその周辺の話題''
Abstract.熱 伝導現象において最も重要で基本的な法則は、フーリエ則である。その成立条件はパイエルスの問題提起以来、様々な角度から議論されてきた。最近はコン ピュータの性能が上がってきたため、数値計算によるアプローチが重要な寄与をしてきている。本研究では、数値計算的にも大変大がかりな計算になる３次元系 のフェルミ-パスタ-ウラム系で熱伝導の計算をしたので報告する。

``Slip avalanches in a fiber bundle model''(in English)
Abstract. A fiber bundle model will be presented to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can gradually increase their relaxed length with a stick-slip mechanism. We determine the constitutive equation of the system and show by analytical calculations that on the macro-scale a plastic response emerges followed by a hardening or softening regime. Releasing the load, an irreversible permanent deformation occurs which depends on the properties of slip events. We demonstrate that slips occur in avalanches triggered by small load increments. Slip avalanches can be characterized by the number of slipping fibers, by the total slip length, and by the triggering load increment. Our calculations revealed that all three quantities follow power law distributions. Varying the amount of disorder, a phase transition is obtained between regimes of different avalanche size exponents.
``牛乳の上にコーヒーが作るフラクタルパターン''
Abstract.フラクタルパターンはヴィスカスフィ ンガリングやバクテリアコロニー、電解析出といった実験で観察されてきた。これらのパターンは点や線から始まり、分岐を繰り返しながら面を覆いつくしフラ クタル構造を形成する。
今回、発表者は牛乳の上に濃いコーヒーの滴を置く実験で、牛乳表面にコーヒー溶液が描くフラクタルパターンを発見した。このフラクタルパターンは牛乳表面 に拡散したコーヒー溶液が次々と沈むことによってできる新しいタイプの消滅フラクタルである。密度相関関数法とボックスカウント法によるフラクタル解析か ら、パターンを特徴づけるフラクタル次元は時間経過、コーヒーの密度に依存せず、一定値1.88±0.06をとることが分かった。また、表面パターンの密 度は時間と共に指数関数的に減少し、その時定数はフラクタル解析が可能となる70秒と一致していたことから、表面に拡散したコーヒーが十分に沈み込むこと が消滅フラクタルの形成にとって重要であることがわかった。

``Single vesicle dynamics in various flows''
Abstract. Dynamics of deformable mesoscopic objects under hydrodynamic stresses determine rheology of many complex fluids, such as emulsions, suspensions of droplets or bubbles, solutions of vesicles, blood, biological fluids, etc. From a theoretical point of view this non-equilibrium problem is rather challenging due to the coupling between micro-scales of the object deformations and macro-scales of the flow, where the object shape is not given a priori but determined by interplay between flow, bending energy, and various physical constraints. A vesicle is an example of such deformable objects.
Dynamics of a single vesicle in a general flow is investigated experimentally. Phase diagram of three dynamical of a vesicle is obtained experimentally in both shear and general flows. The new control parameter, the ratio of the vorticity to the strain rate ω/s, allows following an experimental path, which scans across the whole phase diagram with a single vesicle. Surprisingly, all three states and transitions between them are obtained on the same vesicle and at the same viscosity of inner and outer fluids. We reveal the physical nature of the key dynamical state, coined by us trembling, which shows up in intrinsic shape instability on each cycle resulted in periodical bursting of higher order harmonics depending on the value of the control parameter proportional to ω/s. Depending on the value of this control parameter the regions with the dominated second, third, and higher harmonics in the trembling dynamics are identified. Agreement with theory is discussed.
``Force between colloidal particles in a nematic liquid crystal studied by optical tweezers''
Abstract. We measure the dependence of the interparticle force F on the distance R between two colloidal particles with hyperbolic hedgehog defects in a nematic liquid crystal using optical tweezers. The particle-defect pair can be regarded as an elastic "dipole" in the electrostatic analogy. In a parallel configuration, where the dipole vectors are parallel with each other, F is attractive and proportional to R^{-4}. However, F becomes repulsive at small R due to the existence of a defect between the particles. In an antiparallel configuration, where the particles directly face each other, F is repulsive over the whole range of R and proportional to R^{-3.6}. In another antiparallel configuration, where two hyperbolic hedgehog defects directly face each other, F is proportional to R^{-3.6} and F at small R turns out to be attractive upon tilting the dipoles. Furthermore, we yield the force between particles connected by a stringlike defect called a bubblegum defect.　
本研究は講演者が九州大学在籍時に高橋賢治氏、木村康之教授と共に取り組んだ ものである。
``微生物溶液のダイナミクス''
Abstract. Micro-organisms play a vital role in many biological, medical and engineering phenomena. Some recent research efforts have demonstrated the importance of biomechanics in understanding certain aspects of micro-organism behaviours such as locomotion and collective motions of cells. In particular, spatio-temporal coherent structures found in a bacterial suspension have been the focus of many research studies over the last few years. Recent studies have shown that macroscopic properties of a suspension, such as rheology and diffusion, are strongly affected by meso-scale flow structures generated by swimming microbes. Since the meso-scale flow structures are strongly affected by the interactions between microbes, a bottom-up strategy, i.e. from a cellular level to a continuum suspension level, represents the natural approach to the study of a suspension of swimming microbes. In this talk, we first provide a summary of existing biomechanical research on interactions between a pair of swimming micro-organisms, as a two-body interaction is the simplest many-body interaction. We show that interactions between two nearby swimming micro-organisms are described well by existing mathematical models. Then, collective motions formed by a group of swimming micro-organisms are discussed. We show that some collective motions of micro-organisms, such as coherent structures of bacterial suspensions, are satisfactorily explained by fluid dynamics. Lastly, we discuss how macroscopic suspension properties are changed by the microscopic characteristics of the cell suspension. The fundamental knowledge we present will be useful in obtaining a better understanding of the behaviour of micro-organisms.
``Time dependent correlations in a supercooled liquid from nonlinear fluctuating hydrodynamics.''
Abstract. We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH) for the supercooled liquid. The time correlation of the density fluctuations in equilibrium obtained　here shows quantitative agreement with molecular dynamics(MD) simulation data. We demonstrate numerically that the 1/ρ nonlinearity in the NFH equations of motion is essential in restoring the ergodic behavior in the liquid. Under nonequilibrium conditions the time　correlation functions relax in a manner similar to that observed in the molecular dynamics simulations in binary mixtures. The waiting time tw dependence of the non-equilibrium　response function follows a Modified Kohlrausch-Williams-Watts(MKWW) form similar to the behavior seen in dielectric relaxation data.
``弱電離プラズマ中での塵粒子の帯電と惑星形成理論へ の応用''
Abstract. 現在の標準的な惑星系形成シナリ オ（京都モデル）で は、 固体天体の形成ははじめにサブミクロンサイズの塵粒子（ダスト）の 付着成長（合体成長）を通じて進行するとされる。 ダストの合体成長の理論的モデル化は惑星形成理論において 最も未完成の作業の１つであり、進化経路を決定づける物理プロセス の洗い出しと詳細なモデル化が盛んに行われている。 本講演では、従来のダスト合体成長理論において無視されてきた 塵粒子の帯電に注目する。 電離ガス中に置かれたダストが帯電することは プラズマ物理の分野において良く知られた事実である。 一方、原始惑星系円盤は弱く電離していると考えられており、 ここでもダストは帯電しているはずである。 講演者は、弱電離ガス中でのダストの帯電状態を解析的に扱える 理論モデルをはじめて構築し、帯電と静電相互作用の効果を取り入れた ダストの合体成長シミュレーションを行った。 この結果、帯電するダストの合体成長はサイズ分布の２極分化を 引き起こすことを明らかにした。 この２極分化現象は、従来の惑星形成理論における ダスト合体成長の描像を定性的に変える可能性がある。
``Aggregation & Fragmentation Kinetics in Granular Gases''　(in English)
Abstract.Aggregation and fragmentation are important processes, which play a key role in many astrophysical systems. Formation of planets and planetesemals, evolution of interstellar dust clouds and planetary rings, such as Saturnian Rings, etc. may serve as representative examples. We discuss simplified theoretical models of ballistic of aggregation and fragmentation, which nevertheless describe the most salient properties of real systems. We study evolution of granular gases with fragmentation and aggregation along with the properties of the steady state. Analytical results are compared with the numerical solutions of the respective rate equations and with the results of the Monte-Carlo simulations. A good agreement between the theory and simulations is observed. Application of the theory to the experimental data for the planetary rings of Saturn is discussed.
``Quasi-Bound States in Continuum in Low Dimensional Nano-devise''　(in English)
Abstract.Bound states in continuum (BIC) predicted by von Neumann and Wigner long time ago are recently attracting many scientists, since modern technology now allows observing them. The BIC are possible because of some geometrical symmetry of the system. In addition to BIC we found quite similar phenomena called as quasi-bound states in continuum (QBIC) in a low dimensional nano electronic-device. However, QBIC are originated on a very different principle from BIC. The QBIC is associated to resonance states with time-symmetry braking with an extremely long lifetime. This anomalous long lifetime is a result of the presence of the divergent van Hove singularity of the electron density of states at the edge of the energy band. The QBIC appears when this edge is embedded inside the other band. In contrast to the BIC that may exist only in a special geometry of the system with a zero measure in a parameter space, the QBIC may exist for wide range (with non-zero measure) of variables in a parameter space. As a result, an experimental observation of the QBIC might be easier than the observation of BIC.
``Tumbling motion of a single chain in shear flow: Crossover between shear-dominant motion and fluctuation-dominant motion''

Abstract.We present numerical and analytical results for the dynamics of a single chain in linear shear flow. The tumbling motion is simulated and analyzed using a smoothed profile method that takes into account thermal fluctuations and hydrodynamic interactions accurately. The chain is represented by a bead-spring model in which each bead undergoes free rotation. It is observed that the dimensionless rotational frequency F depends only on the Peclet number Pe with a power law. The exponent of the power law changes clearly from 2/3 to 1 around the critical Peclet number reflecting a competition between contributions of thermal fluctuation and shear flow on the tumbling motion.
``Interfacial effects on Ising thermal transport''
Abstract. We investigate thermal transport in the two dimensional ferro Ising model with a magnetic interface by a nonequilibrium computer simulation. The interface enhances a thermal conductivity of the system, though an ordinary interface plays a thermal resistance in many heterogeneous systems like the Kapitza resistance. This enhancement causes by large fluctuations of the interface. Dynamics of the interface itself is also studied. We find that a distribution of the interface position is not flat, which is expected in an equilibrium state, in a nonequilibrium steady state.
``1 成分単純系のガラス転移とポリアモルフィズム''
Abstract.ガ ラス転移の理解を妨げている一つの要因として、ガラス形成物質の ほとんどが多成分で構成されているという事実がある。シミュレーション研究に おいてさえ、安定なガラス状態を作り出すためには２成分以上を必要とする。多 成分系を用いたシミュレーションの利点は、安定なガラス状態が形成できるこ と、それゆえにガラスのダイナミクスを調べることができるという点であるが、 問題点が二つ存在する。一つは、種類の異なる粒子による混合の効果が含まれて しまうために、幾何学的な配置の効果が見えにくいこと、もう一つは、現実の系 と違って結晶化が起こらないことである。一方で、単成分のモデル系では、結晶 化が起こる点は現実の系と対応するが、結晶化速度が速すぎて、ガラスのダイナ ミクスを十分に調べることができなかった。 本講演では、Lennard-Jones-Gauss (LJG)ポテンシャル[1]という新たなモデルを 導入し、分子シミュレーションによって、２次元単成分系で安定なガラス状態が 形成できることを示す。 LJGポテンシャルを用いる利点の一つは、単成分であり ながら低温で安定なガラス状態が形成できるため、緩和過程における幾何学的な 配置の効果を調べることが可能になる、という点である。もう一つの利点は、結 晶化に要する時間が長いため、結晶化の過程を詳しく調べることができる、とい うことである。 さらに、このシステムは低温でアモルファス・アモルファス転移を起こす。アモ ルファスとは、不規則な粒子配列を持った固体のことであり、ガラスもアモル ファスに含まれる。同一の構成要素でありながら、複数のアモルファス相が存在 することをポリアモルフィズム[2]と言う。これまで、粒子間相互作用が非等方 的であることが、ポリアモルフィズムの原因と考えられてきた。LJGポテンシャ ルは等方的な相互作用ポテンシャルであり、このシステムでポリアモルフィズム が発見されたことにより、これまでの説に疑問を投げかけることが可能である。

[1] M. Engel and H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007).
[2] H. W. Sheng, H. Z. Liu, Y. Q. Cheng, J. Wen, P. L. Lee, W. K. Luo, S. D. Shastri and E. Ma, Nature Mat. Lett. 6, 192 (2007).
[3] T. Mizuguchi and T. Odagaki, preprint (arXiv:0903.2728).
`` 厳密に解ける誕生・死滅過程''
Abstract.誕生・死滅過程 は，よく知られた1次元の定常マルコフ鎖で， ブラウン運動・ランダムウォークの離散化とも考えられる． 後者は，フォッカー・プランク方程式で記述され， シュレーディンガー方程式の（1次元量子力学）の解から， フォッカー・プランク方程式の解が得られることはよく知られている． そこで，厳密に解ける1次元の「離散量子力学」の解から，厳密に解ける誕 生・死滅過程の具体的な解を与えた．対応する固有関数系は， 離散直交測度を持つ超幾何直交多項式のすべてでMeixner, Charlier, Krawtchouk, Hahn 等の，既に知られているものも含まれる．(arXiv:0903.3097[math-ph])
``Heterogeneities, critical dynamics, and defect diffusion in 2D melting''
Abstract. ２ 次元粒子系の融解過程は、低次元系特有のゆらぎの増大に伴い、特異な性質の 相転移を示すことが知られている。主に単成分Lennard-Jones系の融解の相転移の 静的な性質、ならびに付随するダイナミクスについて、空間構造に焦点を当てて最 近調べた我々の結果を報告する[1]。具体的には以下の内容を扱う。a) 密度、構造の長距離不均一性、臨界熱揺らぎ
b) 欠陥のダイナミクスと動的不均一性
c) 中間状態(Hexatic相)の臨界減速
d) 粒径多分散性の効果
e) 剪断下の結晶のダイナミクス
参考文献：H. Shiba, A. Onuki, and T. Araki, preprint arXiv:0808.1453
``Size scaling and bursting activity in thermally activated breakdown''
Abstract.Subcritical rupture is one of the fracture phenomena, which occurs under a constant load below the fracture strength of materials. This fracture is of fundamental importance in a wide range of physical, biological, and geological systems, and has an enormous technological impact. We study subcritical fracture driven by thermally activated damage accumulation in the framework of fiber bundle models. We show that, in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect. We propose a modified form of the Arrhenius law which provides a comprehensive description of thermally activated breakdown. Thermal fluctuation triggers bursts of breakings which have a power law size distribution.