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Recent progress on KPZ equation for higher dimensions

Speaker: Dr. Shuta Nakajima (Meiji University)
Date : Jan. 26 (Thu) 2023, JST 10:30-12:00
Place : hybrid (register here)

In recent years, the analysis of diffusion phenomena, including computer viruses and pathogens, has become increasingly important. Among the various diffusion phenomena, one of the most physically exciting and long-studied subjects is the penetration of liquids, which appears, for example, when water is spilled on a towel. Experimental and numerical studies have led to several predictions, such as the existence of specific laws for the fluctuations in the permeation area and the fact that its boundary can be described by a new framework of stochastic partial differential equations called the KPZ equation. Surprisingly, experiments and numerical calculations have confirmed that various diffusion phenomena, such as paper burning and bacterial growth, behave like a solution to the KPZ equation. In (space) dimension one, much work has been concentrated in the past years, and they have succeeded in making sense of the solution to the KPZ equation. Moreover, several works have recently studied the KPZ equation in dimensions two and higher, though many significant problems remain to be solved. In this talk, I will talk about recent work around the KPZ equation for higher dimensions, both from microscopic and macroscopic viewpoints.

How does the surface roughness of colloids affect the behavior upon compression at liquid interfaces?

Speaker: Dr. Airi N. Kato (Wenzhou Institute)
Date : Jan. 24 (Tue) 2023, JST 13:30-15:00
Place : hybrid (register here)

Shapes of colloidal particles matter the interparticle interaction at liquid interfaces. In this study, the effect of surface roughness was investigated experimentally and numerically in terms of isotherms and particle configuration changes upon compression. Sufficiently rough particles exhibit an intermediate state between gas-like and solid-like states due to roughness-induced capillary attraction, forming a percolated network. Moreover, the surface roughness decreases the jamming point, attributed to the friction and interlocking due to the particles’ surface asperities. Furthermore, the tangential contact force owing to surface asperities can cause a gradual off-plane collapse of the compressed monolayer. Our study on rough colloids at interfaces will also benefit the development of functional materials. At the end of the talk, I will share possible future directions related to active matter.

The signal in the noise: size and dynamics of topological domains from DNA fluctuations

Speaker: Prof. Enrico Carlon (EU Leuven)
Date : Oct. 11 (Tue) 2022, JST 10:30-12:00
Place : hybrid (register here)

In the cell, long DNA molecules carry the genetic information and must be stored yet remain accessible to interact with various biomolecules which control for read out and processing. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here we present a methodology to determine the size and dynamics of topological domains using the analysis of fluctuations: a protein-binding event causes a drop in the variance in the end-end distance of a stretched over-wound DNA molecule. Using a combination of high-speed magnetic tweezers experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We demonstrate how transient (partial) dissociation of DNA bridging proteins results in dynamic sampling of different topological states. Our work highlights how considering DNA extension fluctuations, in addition to the mean extension, provides additional information and enables the investigation of protein-DNA interactions that are otherwise not detectable.


1. E. Skoruppa, E. Carlon, "Equilibrium Fluctuations of DNA Plectonemes" Phys. Rev. E 106, 024412 (2022)
2. W. Vanderlinden, E. Skoruppa, P. Kolbeck, E. Carlon, J. Lipfert, "DNA fluctuations reveal the size and dynamics of topological domains" biorXiv:2021.12.21.473646

Polarization-Density Patterns of Active Particles in Motility Gradients

Speaker: Dr. Sven Auschra (formerly at Institute for Theoretical Physics, University of Leipzig)
Date : Sep. 8 (Thu) 2022, JST 10:30-12:00
Place : hybrid (register here)

The colocalization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. I employ the active-Brownian-particle model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step. The analysis allows for an optional (but not necessary) orientation-dependent propulsion speed, as often employed in force-free particle steering. The results agree well with measurement data for a thermophoretic microswimmer, which can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind these formal results is robustly captured and elucidated by a schematic two-species “run-and-tumble” model.

Dynamics of replisome along bacterial genome

Speaker: Dr. Deepak Bhat (OIST)
Date : Mar. 8 (Tue), JST 10:00-11:30
Place : online

Replisomes are multi-protein complexes that replicate genomes with remarkable speed and accuracy. In bacteria, two replisomes initiate replication at a well-defined origin site on the circular genome, progress in opposite directions, and complete replication upon encountering each other in a terminal region. Precise features of replisome dynamics, such as whether their speed is approximately constant or varies along the genome, are important to determine the location of their encounter point and the distribution of replication errors on the genome. But this detailed information is hard to obtain. We developed a mathematical model to infer the replisome dynamics from the DNA abundance in a growing bacterial population. I will discuss our findings in detail in this seminar.

Knotted Matter

Speaker: Prof. Ivan I. Smalyukh (University of Colorado)
Date : Jan. 11 (Tue) 2022, JST 10:30-12:00
Place : hybrid

Topological order and phases represent an exciting frontier of modern research [1]. Starting with Gauss and Kelvin, knots in fields, like the magnetic field, were postulated to behave like particles. However, experimentally they were found only as transient features and could not self-assemble into three-dimensional crystals. I will describe energetically stable solitonic knots that emerge in the physical fields of chiral liquid crystals and magnets [2,3]. While spatially localized and freely diffusing in all directions, they behave like colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures, as well as forming low-symmetry mesophases and gas- or liquid-like states [2]. A combination of energy-minimizing numerical modeling and nonlinear optical imaging uncovers the internal structure and topology of individual solitonic knots and the various hierarchical crystalline and other organizations that they form. Being classified as the elements of the third homotopy group of two-spheres, these solitonic knots are robust and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli like electric or magnetic fields. I will show how low-voltage electric fields can switch between the heliknoton [2,3] and hopfion [4] embodiments of such knot solitons while preserving their topology. Finally, I will discuss how this emergent paradigm of knotted solitonic matter could allow for imparting new designable material properties and for realizing phases of matter that so far could not be found in naturally occurring materials [5-7].

1. I. I. Smalyukh. Rep. Prog. Phys. 83, 106601 (2020).
2. J.-S. B. Tai and I. I. Smalyukh. Science 365, 1449 (2019).
3. R. Voinescu, J.-S. B. Tai and I. I. Smalyukh. Phys Rev Lett 125, 057201 (2020)
4. P. J. Ackerman and I. I. Smalyukh. Nature Materials 16, 426 (2017)
5. H. Mundoor, S. Park, B. Senyuk, H. Wensink and I. I. Smalyukh. Science 360, 768 (2018).
6. Y. Yuan, Q. Liu, B. Senyuk and I.I. Smalyukh. Nature 570, 214 (2019).
7. H. Mundoor, J.-S. Wu, H. Wensink and I.I. Smalyukh. Nature 590, 268 (2021).


Speaker: 作道 直幸 氏 (東京大学)
Date : Mar. 25 (Thu), 10:30-12:00
Place : online

ゴムや高分子ゲルは、鎖状高分子の(永続的な)三次元網目構造からなるやわらかい物質である。この内、大量の溶媒を含むものを高分子ゲル、含まないものをゴムという。熱力学や統計力学の学部講義や教科書において、ゴムの弾性は熱力学第二法則に由来する「エントロピー的な力」の代表例として登場する [1,2]。現実のゴムの弾性において「エントロピー的な力」が支配的であることは、体積一定の条件下における、ずり弾性率(G)の絶対温度(T) 依存性の測定から確かめられる。なぜなら、熱力学の一般論から、エントロピー変化由来の弾性(エントロピー弾性)が、TG'(T)となるからである[1,3,4]。天然ゴムや合成ゴムにおいては、それらの弾性がほとんどエントロピー変化由来であることが実験的に確かめられている [3,4]。一方、高分子ゲルにおいては、実験的検証なしに、その弾性がエントロピー変化由来であると仮定して、ゴム弾性論が慣習的に使用されてきた [5]。

本研究は、高分子ゲルにおいて、この仮定が誤りであることを発見した [6]。高分子ゲルは、エントロピー弾性に加えて、内部エネルギー変化由来の「負のエネルギー弾性」を持ち、その合計で弾性が決まる。我々は、50種類以上の相異なる網目構造を持つゲルを作り分けたが、その全てに無視できないほど大きな負のエネルギー弾性が存在した。さらに、負のエネルギー弾性には、現象論的な支配法則があることも明らかになった。ゲルの含む溶媒を減らす(ゴムに近づける)と、負のエネルギー弾性はゼロに近づくため、ゴム弾性の実験結果とも整合的である。逆に言えば、溶媒由来の「負のエネルギー弾性」が、ゴム弾性とゲル弾性の本質的な違いである。セミナーでは、時間が許せば、ゲルの浸透圧における普遍法則 [7] についても軽く触れる。二つの研究 [6,7] を合わせると、高分子ゲルの「完全な熱力学関数」は比較的シンプルな構造を持つことがわかる。

[1] 前野昌弘『よくわかる熱力学』(東京図書, 2020) 10.5節
[2] 田崎晴明『統計力学1』(培風館, 2008) 5.6.4節
[3] 久保亮五『ゴム弾性論』(河出書房1947、裳華房1996)
[4] P.J.フローリ『高分子化学(上・下)』(丸善1955)
[5] 例えば、M. Zhong, et al., Science (2016)
[6] Yoshikawa, Sakumichi, Chung, Sakai, PRX (2021)
[7] Yasuda, Sakumichi, Chung, Sakai, PRL (2020)

Dynamic self-organization and collective chemotaxis of migrating cells through contact communication

Speaker: Dr. Tetsuya Hiraiwa (Mechanobiology Institute, National University of Singapore)
Date : Feb. 9 (Tue), 15:00-16:30
Place : online

Migration is a ubiquitous kind of eukaryotic cell behavior. Some cells migrate around on a substrate according to intracellular signals that localize at their front or back, even without extracellular cues. In light of this, we theoretically investigated single eukaryotic cell migration with such intrinsic polarity [1,2] and recently applied the theory to the multicellular case where cells communicate with each other [3,4,5].
In this talk, I will address what forms of multicellular dynamic patterns, or dynamic self-organization, can be formed through intercellular contact communication of migrating cells. I plan to explain the concept and the results of our numerical simulations based on an individual cell-based model in which migrating cells perform contact following and inhibition/attraction of locomotion [3,5]. In particular, I would like to present the results showing that (i) tuning those strengths causes varieties of dynamic self-organization, and (ii) this includes a novel form of collective migration, snake-like dynamic assembly [5]. I will compare some of our results with experimental observations of a social cellular slime mold, Dictyosteloum discoideum, and its mutant, showing the traveling density wave formation [4]. I may also talk about how such dynamic self-organization can contribute to the accuracy of taxis behaviour in population [3,5].
[1] T. Hiraiwa et al., “Relevance of intracellular polarity to accuracy of eukaryotic chemotaxis” Physical Biology 11, 056002 (2014).
[2] T. Hiraiwa, A. Baba and T. Shibata, “Theoretical model for cell migration with gradient sensing and shape deformation” Euro. Phys. J. E 36, 32 (2013).
[3] T. Hiraiwa, “Two types of exclusion interactions for self-propelled objects and collective motion induced by their combination” Phys. Rev. E 99, 012614 (2019).
[4] M. Hayakawa, T. Hiraiwa, Y. Wada, H. Kuwayama and T. Shibata, “Polar pattern formation induced by contact following locomotion in a multicellular system” eLife 9: e53609 (2020).
[5] T. Hiraiwa, “Dynamic self-organization of idealized migrating cells by contact communication”, Phys. Rev. Lett. 125, 268104 (2020).


Speaker: 足立 景亮 氏 (理研BDR)
Date : Oct. 8 (Thu), 10:30-12:00
Place : online

外部エネルギーを用いて自己駆動する粒子系はアクティブマターと呼ばれ、フロッキング転移、モティリティ誘起相分離、ミクロ相分離といった非平衡特有の相転移現象が生じることが知られている [1]。このような相転移の性質は、古典モデルのシミュレーションや人工粒子系の観察などにより、近年理解が進んできた。一方、量子系に目を向けると、冷却原子系に代表される人工量子系の制御技術の発展に伴い、エネルギー流入や散逸を伴う開放量子系の研究が盛んに進められている。特に、非エルミートハミルトニアンによる有効記述を用いて、特有の臨界現象やトポロジカル相などが議論されてきた [2]。

このような背景のもと我々は、量子多体系におけるアクティブマターモデルを初めて提案し、古典系での自己駆動力が量子系では非エルミート性として表現されることを明らかにした [3]。このモデルでは、自己駆動力に起因した量子相転移が生じ、フロッキング状態やモティリティ誘起相分離状態の量子対応物が現れることがわかった。さらに、量子相転移が古典確率過程モデルにおける動的相転移に対応することを見出し、この対応を相図の解釈に利用した。また、このモデルは散逸を導入した光格子中の冷却原子気体によって実現できると考えられ、その実装方法も提案した。


[1] G. Gompper et al., J. Phys. Condens. Matter 32, 193001 (2020).
[2] Y. Ashida, Z. Gong, and M. Ueda, arXiv:2006.01837.
[3] K. Adachi, K. Takasan, and K. Kawaguchi, arXiv:2008.00996.


Speaker: 藤本 和也 氏 (名古屋大学)
Date : Aug. 6 (Thu), 10:30-12:00
Place : online


[1] M. Prüfer et al., Nature 563, 217 (2018).
[2] S. Erne et al., Nature 563, 225 (2018).
[3] J. A. P. Glidden et al., arXiv:2006.01118.
[4] K. Fujimoto, R. Hamazaki, and Y. Kawaguchi, Phys. Rev. Lett. 124, 210604 (2020).

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