Updated on 2022/05/17

写真a

 
YANAO, Tomohiro
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2020
    -
    2022

    理工学術院総合研究所   兼任研究員

Education

  •  
    -
    2003

    University of Tokyo   Graduate School of Arts and Sciences   Multidisciplinary Science  

  •  
    -
    2003

    University of Tokyo   Graduate School of Arts and Sciences   Multidisciplinary Science  

Degree

  • University of Tokyo   Ph.D.

Research Experience

  • 2011
    -
     

    Waseda University, Associate Professor

  • 2011
    -
     

    Waseda University, Associate Professor

  • 2009
    -
     

    Waseda University, Assistant Professor

  • 2008
    -
     

    California Institute of Technology, JSPS Fellow for Research Abroad

  • 2006
    -
     

    Fukui Institute for Fundamental Chemistry, Research Fellow

  • 2004
    -
     

    California Institute of Technology, Postdoctoral Scholar

  • 2003
    -
     

    Nagoya University, JSPS Fellow (PD)

  • 2003
    -
     

    Nagoya University, JSPS Fellow (PD)

  • 2001
    -
     

    University of Tokyo, JSPS Fellow (DC2)

  • 2001
    -
     

    University of Tokyo, JSPS Fellow (DC2)

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Professional Memberships

  •  
     
     

    Japan Society for Molecular Science

  •  
     
     

    Physical Society of Japan

  •  
     
     

    American Physical Society

  •  
     
     

    Society for Industrial and Applied Mathematics

 

Research Areas

  • Biophysics, chemical physics and soft matter physics

  • Mathematical physics and fundamental theory of condensed matter physics

Research Interests

  • statistical mechanics, nonlinear dynamics, geometric mechanics, applied mathematics, molecular science, biophysics, celestial mechanics

Papers

  • Geometric somersaults of helical chains through twist propagation

    Shiori Uda, Mengyun Li, Tomohiro Yanao

    Artificial Life and Robotics   23 ( 1 ) 28 - 33  2018.03

     View Summary

    This study is concerned with the rotary motions of helical chains that play essential roles in the functions of molecular motors in biological systems. While the standard pictures for the rotary motions of molecular motors may be more or less like the rotations of rigid bodies, this study explores a qualitatively different mechanism for the rotary motions. We take a simple model of a helical chain and highlight its geometric angle shifts induced by internal twist propagation. Such angle shifts, which we call geometric somersaults, can generally arise even under the conditions of zero total angular momentum, and are thereby analogous to the somersault of a falling cat. Helical chirality of the chain and the direction of twist propagation are the decisive factors that determine the direction of the resulting somersaults. As an application, we argue that the geometric somersaults of the helical chain may serve as a prototypical model for the rotary motions of the central shaft of ATP synthase.

    DOI

  • Analysis of medium-energy transfers to the Moon

    Kenta Oshima, Francesco Topputo, Stefano Campagnola, Tomohiro Yanao

    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY   127 ( 3 ) 285 - 300  2017.03  [Refereed]

     View Summary

    This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth-Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun-Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions.

    DOI

  • Global search for low-thrust transfers to the Moon in the planar circular restricted three-body problem

    Oshima, Kenta, Campagnola, Stefano, Yanao, Tomohiro

    Celestial Mechanics and Dynamical Astronomy     1 - 20  2017.02  [Refereed]

     View Summary

    © 2017 Springer Science+Business Media DordrechtThis paper globally searches for low-thrust transfers to the Moon in the planar, circular, restricted, three-body problem. Propellant-mass optimal trajectories are computed with an indirect method, which implements the necessary conditions of optimality based on the Pontryagin principle. We present techniques to reduce the dimension of the set over which the required initial costates are searched. We obtain a wide range of Pareto solutions in terms of time of flight and mass consumption. Using the Tisserand–Poincaré graph, a number of solutions are shown to exploit high-altitude lunar flybys to reduce fuel consumption.

    DOI

  • Geometric somersaults of a polymer chain through cyclic twisting motions

    Yanao, Tomohiro, Hino, Taiko

    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics   95 ( 1 )  2017.01

     View Summary

    © 2017 American Physical Society.This study explores the significance of geometric angle shifts, which we call geometric somersaults, arising from cyclic twisting motions of a polymer chain. A five-bead polymer chain serves as a concise and minimal model of a molecular shaft throughout this study. We first show that this polymer chain can change its orientation about its longitudinal axis largely, e.g., 120, under conditions of zero total angular momentum by changing the two dihedral angles in a cyclic manner. This phenomenon is an example of the so-called "falling cat" phenomenon, where a falling cat undergoes a geometric somersault by changing its body shape under conditions of zero total angular momentum. We then extend the geometric somersault of the polymer chain to a noisy and viscous environment, where the polymer chain is steered by external driving forces. This extension shows that the polymer chain can achieve an orientation change keeping its total angular momentum and total external torque fluctuating around zero in a noisy and viscous environment. As an application, we argue that the geometric somersault of the polymer chain by 120 may serve as a prototypical and coarse-grained model for the rotary motion of the central shaft of ATP synthase (FOF1-ATPase). This geometric somersault is in clear contrast to the standard picture for the rotary motion of the central shaft as a rigid body, which generally incurs nonzero total angular momentum and nonzero total external torque. The power profile of the geometric somersault implies a preliminary mechanism for elastic power transmission. The results of this study may be of fundamental interest in twisting and rotary motions of biomolecules.

    DOI

  • Jumping mechanisms of Trojan asteroids in the planar restricted three- and four-body problems

    Kenta Oshima, Tomohiro Yanao

    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY   122 ( 1 ) 53 - 74  2015.05  [Refereed]

     View Summary

    We explore minimal dynamical mechanisms for the transport of Trojan asteroids between the vicinities of the stable Lagrange points and within the framework of the planar restricted three- and four-body problems. This transport, called "jumping" of Trojan asteroids, has been observed numerically in the sophisticated Solar System models. However its dynamical mechanisms have not been fully explored yet. The present study shows that invariant manifolds emanating from an unstable periodic orbit around the unstable Lagrange point mediate the jumping of Trojan asteroids in the Sun-Jupiter planar restricted three-body problem. These invariant manifolds form homoclinic tangles and lobes when projected onto the configuration space through a discrete mapping. Thus the resulted lobe dynamics explains the mechanism for the jumping of Jupiter's Trojan asteroids. In the Sun-Earth planar restricted three-body problem, on the other hand, invariant manifolds of an unstable periodic orbit around do not exhibit clear homoclinic tangles nor lobes, indicating that the jumping is very difficult to occur. It is then shown that the effect of perturbation of Venus is important for the onset of the jumping of Earth's Trojan asteroids within the framework of the Sun-Earth-Venus planar restricted four-body problem. The results presented here could shed new insights into the transport mechanism as well as trajectory design associated with L-3, L-4 and L-5.

    DOI

  • Roles of dynamical symmetry breaking in driving oblate-prolate transitions of atomic clusters

    Yurie Oka, Tomohiro Yanao, Wang Sang Koon

    JOURNAL OF CHEMICAL PHYSICS   142 ( 13 )  2015.04  [Refereed]

     View Summary

    This paper explores the driving mechanisms for structural transitions of atomic clusters between oblate and prolate isomers. We employ the hyperspherical coordinates to investigate structural dynamics of a seven-atom cluster at a coarse-grained level in terms of the dynamics of three gyration radii and three principal axes, which characterize overall mass distributions of the cluster. Dynamics of gyration radii is governed by two kinds of forces. One is the potential force originating from the interactions between atoms. The other is the dynamical forces called the internal centrifugal forces, which originate from twisting and shearing motions of the system. The internal centrifugal force arising from twisting motions has an effect of breaking the symmetry between two gyration radii. As a result, in an oblate isomer, activation of the internal centrifugal force that has the effect of breaking the symmetry between the two largest gyration radii is crucial in triggering structural transitions into prolate isomers. In a prolate isomer, on the other hand, activation of the internal centrifugal force that has the effect of breaking the symmetry between the two smallest gyration radii is crucial in triggering structural transitions into oblate isomers. Activation of a twisting motion that switches the movement patterns of three principal axes is also important for the onset of structural transitions between oblate and prolate isomers. Based on these trigger mechanisms, we finally show that selective activations of specific gyration radii and twisting motions, depending on the isomer of the cluster, can effectively induce structural transitions of the cluster. The results presented here could provide further insights into the control of molecular reactions. (C) 2015 AIP Publishing LLC.

    DOI

  • Chiral symmetry breaking of a double-stranded helical chain through bend-writhe coupling

    Tomohiro Yanao, Kenichi Yoshikawa

    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics   89 ( 6 )  2014.06

     View Summary

    This paper explores asymmetric elasticity of a double-stranded helical chain, which serves as a minimal model of biopolymers. The model consists of two elastic chains that mutually intertwine in a right-handed manner, forming a double-stranded helix. A simple numerical experiment for structural relaxation, which reduces the total elastic energy of the model monotonically without thermal fluctuations, reveals possible asymmetric elasticity inherent in the helical chain. It is first shown that a short segment of the double-stranded helical chain has a tendency to unwind when it is bent. It is also shown that a short segment of the helical chain has a tendency to writhe in the left direction upon bending. This tendency gives rise to a propensity for a longer segment of the chain to form a left-handed superhelix spontaneously upon bending. Finally, this propensity of the helical chain to form a left-handed superhelix is proposed to be a possible origin of the uniform left-handed wrapping of DNA around nucleosome core particles in nature. The results presented here could provide deeper insights into the roles and significance of helical chirality of biopolymers. © 2014 American Physical Society.

    DOI PubMed

  • Dynamical Characteristics of Helical Polymers : Spontaneous Symmetry Breaking(Essay)

    Yanao Tomohiro, Yoshikawa Kenichi

    Journal of the Japan Society for Simulation Technology   33 ( 1 ) 55 - 58  2014.03

    CiNii

  • The falling cat problem and shape effects in small molecules in a random environment: A case study

    Carsten Hartmann, Tomohiro Yanao

    Molecular Physics   111 ( 22-23 ) 3534 - 3545  2013.12

     View Summary

    We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo non-trivial conformational transitions we consider a planar four-atomic molecule, with underdamped dynamics of Langevin-type. In this simplified setting, we can extend the available gauge theory of semi-flexible molecules to the stochastic setting which allows us to analyse and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperature-dependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equation, i.e., friction coefficient, atomic masses, temperature and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g., to the overdamped limit or optimal control. © 2013 Taylor &amp
    Francis.

    DOI

  • Control of a model of DNA division via parametric resonance

    Wang Sang Koon, Houman Owhadi, Molei Tao, Tomohiro Yanao

    CHAOS   23 ( 1 )  2013.03  [Refereed]

     View Summary

    We study the internal resonance, energy transfer, activation mechanism, and control of a model of DNA division via parametric resonance. While the system is robust to noise, this study shows that it is sensitive to specific fine scale modes and frequencies that could be targeted by low intensity electro-magnetic fields for triggering and controlling the division. The DNA model is a chain of pendula in a Morse potential. While the (possibly parametrically excited) system has a large number of degrees of freedom and a large number of intrinsic time scales, global and slow variables can be identified by (1) first reducing its dynamic to two modes exchanging energy between each other and (2) averaging the dynamic of the reduced system with respect to the phase of the fastest mode. Surprisingly, the global and slow dynamic of the system remains Hamiltonian (despite the parametric excitation) and the study of its associated effective potential shows how parametric excitation can turn the unstable open state into a stable one. Numerical experiments support the accuracy of the time-averaged reduced Hamiltonian in capturing the global and slow dynamic of the full system. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790835]

    DOI

  • Intramolecular energy flow and the mechanisms for dissociation of atomic clusters

    Tomohiro Yanao, Yurie Oka, Wang Sang Koon

    Journal of Thermal Science and Technology   8 ( 2 ) 423 - 434  2013

     View Summary

    This paper explores the mechanisms for dissociation of atomic clusters in terms of internal energy flow and driving forces. We employ the hyperspherical coordinates to investigate internal dynamics of atomic clusters. The hyperspherical coordinates consist of three gyration radii and 3n - 9 hyperangular degrees of freedom that parameterize the shape of an n-atom system in the three-dimensional physical space. The latter 3n - 9 hyperangular degrees of freedom are further classified into three twisting modes and 3n-12 shearing modes. We numerically characterize the patterns of energy flow among the internal degrees of freedom leading to dissociations. It is shown that a large amount of kinetic energy tends to accumulate in the largest gyration radius upon dissociations of the cluster. We also identify some of the twisting and shearing modes that are active right at the instant of dissociation. These modes may be regarded as the triggers that drive dissociation of the cluster by pumping energy into the largest gyration radius. Physically, this pumping of energy is mediated by the internal centrifugal forces that originate from twisting and shearing motions of the system. These results are consistent with theoretical expectations from the equations of motion for gyration radii, and could be an initial step towards the control of large-amplitude collective motions of complex molecular systems. © 2013 by JSME.

    DOI

  • Chiral selection in supercoiling and wrapping of DNA

    Tomohiro Yanao, Kenichi Yoshikawa

    POLYMER SCIENCE SERIES C   54 ( 1 ) 11 - 20  2012.09  [Refereed]

     View Summary

    This paper gives an account of our recent studies on the mechanisms for chiral selection in super-coiling and wrapping of DNA. We first present a compact model of double-stranded DNA (Model 1), which consists of two elastic chains that mutually intertwine in a right-handed manner to form a double-stranded helix. Numerical analysis of this model suggests an intrinsic propensity of DNA to writhe in the left direction upon bending. Based on this asymmetric elasticity of DNA, we present a further simplified model of DNA (Model 2), which is a single-chained homopolymer with the propensity to writhe in the left direction upon bending. This simplified model is incorporated into a Langevin dynamics study to explore the origin of the uniform left-handed wrapping of DNA around a nucleosome core particle in nature. We finally show that the propensity of DNA to writhe in the left direction upon bending gives rise to the selective left-handed wrapping, provided that the size of the core particle is appropriate. This result suggests the fundamental significance of the asymmetric elasticity of helical biopolymers in their structural dynamics and functions.

    DOI

  • Dynamical Mechanisms for Collective Motions of Nanostructures (Geometric Mechanics)

    Yanao Tomohiro

    RIMS Kokyuroku   1692   46 - 56  2010.06

    CiNii

  • A nonequilibrium rate formula for collective motions of complex molecular systems

    T. Yanao, W. S. Koon, J. E. Marsden

    American Institute of Physics Conference Proceedings   1281   1597 - 1600  2010  [Refereed]

  • Nonlinear dynamics and geometry of collective motions of complex molecular systems

    T. Yanao

    American Institute of Physics Conference Proceedings   1281   1571 - 1573  2010  [Refereed]

  • Intramolecular energy transfer and the driving mechanisms for large-amplitude collective motions of clusters

    T. Yanao, W. S. Koon, J. E. Marsden

    The Journal of Chemical Physics   130   144111 - 20  2009  [Refereed]

  • Elastic origin of chiral selection in DNA wrapping

    T. Yanao, K. Yoshikawa

    Physical Review E   77   021904 - 11  2008  [Refereed]

  • Collective coordinates and the mechanism for conformational transitions of complex molecules

    T. Yanao, W. S. Koon, J. E. Marsden, I. G. Kevrekidis

    Proceedings in Applied Mathematics and Mechanics   7   1080503 - 2  2007

  • Gyration-radius dynamics in structural transitions of atomic clusters

    T. Yanao, W. S. Koon, J. E. Marsden, I. G. Kevrekidis

    The Journal of Chemical Physics   126   124102 - 17  2007  [Refereed]

  • Application of tube dynamics to non-statistical reaction processes

    F Gabern, WS Koon, JE Marsden, SD Ross, T Yanao

    FEW-BODY SYSTEMS   38 ( 2-4 ) 167 - 172  2006.06  [Refereed]

     View Summary

    A technique based on dynamical systems theory is introduced for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. In particular, we merge invariant manifold tube dynamics with Monte Carlo volume determination for accurate rate calculations. This methodology is applied to a three-degree-of-freedom model problem and some ideas on how it might be extended to higher-degree-of-freedom systems are presented.

    DOI

  • Mass-related dynamical barriers in triatomic reactions

    T Yanao, WS Koon, JE Marsden

    FEW-BODY SYSTEMS   38 ( 2-4 ) 161 - 166  2006.06  [Refereed]

     View Summary

    A methodology is given to determine the effect of different mass distributions for triatomic reactions using the geometry of shape space. Atomic masses are incorporated into the non-Euclidean shape space metric after the separation of rotations. Using the equations of motion in this non-Euclidean shape space, an averaged field of velocity-dependent fictitious forces is determined. This force field, as opposed to the force arising from the potential, dominates branching ratios of isomerization dynamics of a triatomic molecule. This methodology may be useful for qualitative prediction of branching ratios in general triatomic reactions.

    DOI

  • Mass effects and internal space geometry in triatomic reaction dynamics

    T. Yanao, W. S. Koon, J. E. Marsden

    Physical Review A   73   052704 - 11  2006  [Refereed]

  • EFFECTS OF AN INTRINSIC METRIC OF MOLECULAR INTERNAL SPACE ON CHEMICAL REACTION DYNAMICS

    Tomohiro Yanao, Kazuo Takatsuka

    GEOMETRIC STRUCTURES OF PHASE SPACE IN MULTIDIMENSIONAL CHAOS: APPLICATIONS TO CHEMICAL REACTION DYNAMICS IN COMPLEX SYSTEMS, PT B   130   87 - 128  2005  [Refereed]

  • (解説)ネコの宙返りと形空間のリーマン幾何学

    柳尾朋洋

    生物物理   45   66 - 71  2005

  • Kinematic effects associated with molecular frames in structural isomerization dynamics of clusters

    T. Yanao, K. Takatsuka

    The Journal of Chemical Physics   120   8924 - 8936  2004

  • Collective coordinates and an accompanying metric force in structural isomerization dynamics of molecules

    T. Yanao, K. Takatsuka

    Physical Review A   68   032714 - 16  2003  [Refereed]

  • Microcanonical temperature and its Arrhenius relation to lifetimes in isomerization dynamics of clusters

    K Takatsuka, T Yanao

    JOURNAL OF CHEMICAL PHYSICS   113 ( 7 ) 2552 - 2562  2000.08  [Refereed]

     View Summary

    In a previous study of isomerization dynamics of clusters as a chaotic conservative system, we proposed a temperature, called the microcanonical temperature [C. Seko and K. Takatsuka, J. Chem. Phys. 104, 8613 (1996)], which is expected to characterize a phase space distribution on a constant energy plane. In contrast to the standard view of equal a priori distribution in phase space, we note a fact that this distribution usually becomes sharply localized with a single peak, if projected onto the potential energy coordinate. The microcanonical temperature is defined as a kinetic energy at which this projected distribution takes the maximum value. Then the most probable statistical events should be dominated by those components in vicinity of the peak, provided that the projected distribution is singly and sharply peaked and the associated dynamics is ergodic. The microcanonical temperature can be similarly redefined in the individual potential basins. Here in the present article a numerical fact is highlighted that the inverse of the lifetime of an isomer bears an Arrhenius-type relation with thus defined local microcanonical temperature assigned to the corresponding potential basin. We present an analysis of how the Arrhenius relation can arise. (C) 2000 American Institute of Physics. [S0021-9606(00)50831-9].

  • Timescale of isomerization reactions and isotropic inflation model of basin boundaries in cluster dynamics

    T Yanao, K Takatsuka

    CHEMICAL PHYSICS LETTERS   313 ( 3-4 ) 633 - 638  1999.11  [Refereed]

     View Summary

    We present a theoretical treatment that accounts for the internal-energy dependence of the rate of geometrical isomerization of Ar-7-like clusters in the so-called liquid-like phase (high-energy region). Since many trajectories representing this reaction pass through a broad range of basin boundaries other than the transition state and since there are many channels involved, the reaction rate is not determined by a few local characteristics of the potential surfaces such as the transition state or the reaction coordinates. We therefore propose a reaction rate model which is based on the isotropic inflation of the density of states at the global basin boundaries. (C) 1999 Elsevier Science B.V. All rights reserved.

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Research Projects

  • 複雑な流体現象のモデリング,マルチスケール構造の解明と数理解析

    Project Year :

    2016.07
    -
    2019.03
     

     View Summary

    キャビテーション,衝撃波の伝播,多成分流体,大気の循環などの流体解析では,ミクロとマクロの境界で発生するマルチスケール現象や非平衡系の数学的解析が重要である.本研究では,複雑流体のモデリング,マルチスケール構造の解明と数学解析手法の確立を目的とする.2016年度は,モデリング,数学解析と応用に分けて研究を推進した.流体のモデリングについては,有限自由度の離散的な非平衡熱力学系についての変分的な定式化を行った.また,キャビテーション気泡と気泡クラウドに関する実験,レイリー・ベナール対流の解析を中心に行った.数学解析としては,ナビエ・ストークス方程式,オイラー方程式,非線型シュレディンガー方程式をはじめとする非線型発展方程式の初期値問題の時間大域解の存在を保障する先験評価に重要な役割を果たす対数型ソボレフ埋蔵に就いて研究し,放物型方程式に対してはその散逸構造に因り通常のソボレフ埋蔵の枠組で閉じている事を明らかにした.また,非圧縮粘性流体の自由境界問題を有界領域の場合に考察し、時間局所解の一意存在と時間大域解の一意存在及び解の漸近挙動を示した.さらに,複数の保存量を持つ微視的な系から非線形流体力学揺動理論を経て導かれると予想される,多成分 KPZ 方程式について考察し,殆ど全ての初期値に対し方程式は大域的適切性を持つことを示した.また,質量保存アレン-カーン方程式にノイズを加えて得られる確率偏微分方程式について,極限で確率的摂動を持つ質量保存平均曲率運動が導かれることを示した.数値解析として,準離散化方程式の対称性と保存則を研究し,ネーター定理を導き,高階の場の理論のために,マルチシンプレクティック構造の研究を行った.非線形力学の応用として,ミクロスケールでの高分子鎖の捩れ運動から生じる幾何学的位相を見出し,回転型分子モーターの回転軸運動の粗視化モデルに適用した.概ね順調に進んでいるが,研究代表者と分担者4名で研究内容が多岐に渡るため,全体のまとまりを考えて,本来の研究目的に沿って組織的に研究を遂行する必要があると考えている.複雑流体のモデリングについては,連続的な非平衡系としての変分的定式化の確立,レリー・ベナール対流の解析,気泡クラウドのマクロモデルの構築,確率的な気泡ダイナミクスの変分的定式化と解析を中心に進める.数学解析では,部分積分に依る時間発散型の高次繰り操みエネルギーとブレジス・ガルエの論法を駆使し,半相対論的方程式の高次相互作用が数学的に実現されるかどうか,検討する.また,2相流問題の考察を行い,まずは非圧縮・非圧縮の2相問題についての有界領域で外側の境界条件が自由境界条件の場合を考える.つづいて,一方が有界領域、外側がその補集合である全空間での2相問題を考え,この時間局所解,時間大域解、解の漸近挙動を示す.さらに,多成分KPZ方程式について,カップリング定数が3重線形性を満たさない場合の不変測度の研究,大規模相互作用系からのKPZ方程式の導出を目指した研究,ノイズ項が空間変数にも依存する確率アレン-カーン方程式や確率的平均曲率運動に関する研究などを進める.数値解析については,マルチシンプレクティック構造の研究を続け,流体力学への応用,特に拘束を含む系への応用を考え,離散的ディラック構造の研究も進行する予定である.非線形力学の応用として,高分子鎖の捩れ運動から生じる幾何学的位相の効果を,ベン毛微生物の遊泳機構の解明に応用する.できるだけ,分担者からの使用ができるだけ均一になるように早めの確認と連絡をしたい.また,大学院生による研究調査や協力のための謝金にも利用したい

  • Study on the mechanisms for collective motions of molecular and astronomical systems based the methods of many-body problems

    Project Year :

    2014.04
    -
    2017.03
     

     View Summary

    Understanding the fundamental mechanisms for collective motions of many-body systems, ranging from the microscopic molecular systems to macroscopic astronomical systems, is a significant challenge in modern science and technology. In this study, we have tackled this issue utilizing the methodologies of nonlinear dynamics, statistical mechanics, and differential geometry. As a result, we have developed novel dynamical models for the rotary motions of biological molecular motors and the formation of higher-order structures of DNA. We have also uncovered a dynamical mechanism for driving the dissociation of atomic clusters in terms of the competition between collective internal forces. As to the macroscopic astronomical systems, we have designed fuel-efficient transfer trajectories for space missions between the Earth and the Moon by using resonant gravity assists and invariant manifolds of periodic orbits

  • Study on collective motions and functions of complex molecular systems based on the geometry of shape and rotational dynamics

    Project Year :

    2011.04
    -
    2014.03
     

     View Summary

    In this project, we have investigated the mechanisms for collective motions, reactions, and functions of complex molecular systems on the basis of statistical mechanics, nonlinear dynamics, and geometry. We have clarified the driving mechanisms for oblate-prolate structural transitions and dissociations of atomic clusters. We have also clarified asymmetric elasticity of biomolecules such as DNA and its significance in the formation of higher-order structures. Moreover, we have studied the mechanisms for the transport of asteroids between local equilibria based on the dynamical analogy between molecular systems and planetary systems

  • Elucidation of the mechanisms for collective motions of complex molecular systems with hierarchical structures

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    This study focused on the mechanisms for large-amplitude collective motions of complex molecular systems with highly-organized hierarchical structures and functions. We found that specific mode coupling and energy transfer among internal (vibrational) modes govern the onset and rates of structural transitions of atomic/molecular clusters. We also scrutinized elastic properties of DNA and clarified the mechanisms for the spontaneous selection of chirality of higher-order structures of DNA

Presentations

  • Mode-specific effects in structural transitions of atomic clusters with multiple channels

    SIAM Conference on Applications of Dynamical Systems 

    Presentation date: 2015.05

  • Collective motions of complex molecular systems driven by spontaneous symmetry breaking

    Workshop on Energy Landscapes 

    Presentation date: 2014.08

  • Chaotic state transitions in molecular and astronomical systems

    Workshop on Lagrangian Coherent Structures and Dynamical Systems 

    Presentation date: 2014.03

  • Geometric effects in shape dynamics of complex molecular systems

    International Symposium on Computational Materials and Biological Sciences 

    Presentation date: 2013.09

  • Intramolecular Energy Flow and the Mechanisms for Collective Motions of Complex Molecular Systems

    International Conference on Flow Dynamics 

    Presentation date: 2012.09

  • A nonequilibrium rate formula for collective motions of complex molecular systems

    International Conference of Numerical Analysis and Applied Mathematics 

    Presentation date: 2010.09

  • Dynamical mechanisms for collective motions of nanostructures

    Conference on Geometric Mechanics 

    Presentation date: 2009.12

  • Intramolecular energy transfer, driving mechanisms, and reaction rates for collective motions of clusters

    American Physical Society March Meeting 

    Presentation date: 2009.03

  • A novel mechanism for molecular reactions

    Oberwolfach Workshop 

    Presentation date: 2008.07

  • Collective coordinates and dynamic reaction barriers in conformational transitions of clusters and biopolymers

    Telluride Workshop on the Complexity of Dynamics 

    Presentation date: 2007.08

  • Collective coordinates and the mechanism for conformational transitions of complex molecules

    International Congress on Industrial and Applied Mathematics 

    Presentation date: 2007.07

  • Geometric effects in structural isomerization dynamics of atomic clusters

    Third Pacific Rim Conference on Mathematics 

    Presentation date: 2005.08

  • Reduction of phase space structure and identification of dynamical barriers in molecular reaction dynamics

    Telluride Workshop on Energy Landscapes 

    Presentation date: 2005.07

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Specific Research

  • 自然界における捩れ・渦・回転の協同運動の解明と予測

    2018  

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    本研究では,ミクロからマクロまで,自然の各階層で生じる捩れ,渦,回転の協同現象を,非線形力学,統計力学,幾何学の観点から理論的に解明し,予測することを目的とした.特に,らせん構造を基本モチーフとする生体高分子の「回転」機構の新たなモデルの構築を目指して,らせん型フィラメントの上を捩れの波動が伝播することによって生じる幾何学的な角度変位の機構を明らかにした.また,分子系および天体系の基本モデルとして重要な3体問題に着目し,3体系の周期的な変形運動から生じる幾何学的な角度変位を,慣性主軸のキネマティクスの観点から定量化した.また,時間遅れ座標の手法を用いて,原子集合体の協同的かつ突発的な構造変化の前兆を捉え,この前兆が原子集合体の捩れ運動から生じる構造変化の駆動力の振る舞いと対応していることを明らかにした.

  • 多体系の非線形ダイナミクスから生じる集団運動の理解と応用

    2009  

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    本研究の目的は、非線形力学および幾何学の手法を応用することで、原子・分子集合体のミクロスケールな運動から、天体・宇宙探査機のようなマクロスケールの運動までを「多体系の集団運動」という普遍的な観点から理解し、工学的に応用することにある。特に、ミクロとマクロ、および速い運動と遅い運動というスケール間の相互作用に注目し、多重スケールを有する複雑システムの集団運動の統一的な理解と制御を目指してきた。 本年度はまず、原子・分子スケールの興味深い現象として、オゾン分子の解離反応、アルゴンクラスターの構造異性化運動、水クラスターの構造変化運動を取りあげた。これらの現象は、どれも分子内の多くの自由度が協同的に関与することによって発生する集団運動である。このような集団運動の動的な機構を明らかにするために、我々は、近年開発した超球モード解析という多体系の振動回転運動の解析法を上述の系に応用した。その結果、上述の系において集団運動が発生する際には,系の内部モード間で特定のエネルギーの受け渡しが生じることが明らかになった。さらに、これらのエネルギーの受け渡しのパターンを解析することで、集団運動に直接的に関与する集団モードと、集団モードにエネルギーを注入する役割を果たす駆動モードが存在することが分かった。現在は、これらの集団モードと駆動モードを用いることで原子分子系の集団運動をコントロールする方法論を開発中である。また、この方法論を宇宙探査機の軌道計算へと応用する研究も開始している。 本研究ではまた、ナノメートルからマイクロメートルのスケールに渡る興味深い階層性システムとして真核生物のDNAを取り上げ、その折り畳みの機構の一端を探る研究を行った。まず右巻き2重らせん構造をもつDNAを弾性体のネットワークとしてモデル化し、その基本的な弾性特性を探った。その結果、DNAの曲げと捩れのカップリングの機構が明らかになり、DNAが折り畳み構造をとる際に右巻きと左巻きの間のカイラル対称性が破れる仕組みを明らかにした。

 

Syllabus

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