東京大学 竹内研究室 公式ウェブページ

Kinetic roughening is the process by which interfaces develop a self-affine roughness in non-equilibrium systems. The interfaces can represent domain walls, the surface of a growing crystal, the edge of a bacterial colony, etc. We present two consequences of non-equilibrium kinetic roughening in two dimensions.

Our first story reports on the non-equilibrium diffusion of two-dimensional cluster. These clusters can represent e.g. an Ising droplet driven by a field, a monolayer island growing on a facet during crystal growth or dissolution, or an expanding bacterial colony. We find that the mean square displacement of the center of mass of clusters exhibit a transition from superdiffusive to subdiffusive diffusion during growth, with exponents controlled by the kinetic roughening of the cluster edge.

The second story focuses of the collision between growth fronts. We here aim to model e.g. the process by which grain boundaries form in graphene, or by which different expanding bacterial films collide. We claim that this process can be seen as non-trivial generalization of first passage processes. We show that the spatio-temporal roughness of the collision is controlled by the roughness accumulated before the collision. The distribution of times of collision, and the roughness of interface after collision are shown to obey dynamic scaling, and combine linearly the distributions of the two fronts before collision.

REFERENCES
1. Non-equilibrium cluster diffusion during growth and evaporation in two dimensions (editor's suggestion), Y. Saito, M. Dufay, O. Pierre-Louis, Phys Rev. Lett. 108, 245504 (2012)
2. Non-equilibrium interface collisions, F.A. Reis, O. Pierre-Louis, preprint (2016)

Adult tissues undergo rapid turnover as mature cells are continuously lost, and new cells arise through cell division. The balance between gain and loss of cells must be finely orchestrated to maintain tissues, but how this balance is achieved remains largely unknown. For the skin, it had been assumed that the fate choices of stem cells (division or differentiation) are made strictly cell-autonomously. Here we recorded every stem cell fate choice within mouse skin epidermal regions over one week and found that, far from being cell-autonomous, stem cell loss by differentiation was compensated by direct neighboring division[1]. Furthermore, division events were triggered by neighbor differentiation and not vice versa, showing differentiation-dependent division as the core feature of homeostatic control.

In this presentation, we will formalize the problem of tissue homeostasis using a macroscopic nonequilibrium model setup[2]. Starting from an interacting particle system with Brownian motion, we show how the coarse-graining of our model will lead to the effective dynamics of the Voter model (DP2). We will then explain the pitfall in two-dimensions of using scaling relations of the type used before for the clonal fate trace of cells, and illustrate the workaround used in the new data analysis to definitively show the existence of cell-to-cell fate correlation.

[1] Mesa, Kawaguchi et al., Biorxiv (2017) doi: https://doi.org/10.1101/155408
[2] Yamaguchi, Kawaguchi, and Sagawa, Phys. Rev. E 96, 012401 (2017)

Ageing phenomena may arise in systems quenched, from some initial state, either (i) into a coexistence phase with more than one stable equilibrium state or else (ii) onto a critical point of the stationary state. Studies of dynamical critical properties, in the same way that the steady state properties, are neccesarily limited to samples of finite size. For this reason it is important to explore computational alternatives to obtain reliable results. In this work we explain how the critical dynamic can be implemented correctly in the Majority voter model, an non-equilibrium Ising-like model, using CUDA. By means of Monte Carlo simulations of the critical Ising and Majority voter models with Glauber dynamics on two dimensional honeycomb lattices we found that the dynamic critical exponents for the Majority voter model are in good agreement with the reported values of the Ising model.

Anomalous transportation is characterized by a scale dependent transportation coefficient. It has been conjectured that such behavior is effectively described by a stochastic model. However, the parameter values of the model are determined only by measurements, and it is not established to connect the parameter value of such effective models with microscopic descriptions. It may be obvious that this can be studied by the renormalization group (RG) method. However, standard RG analysis, in which a fixed point and scaling exponents are studied, cannot determine the effective model for scale-dependent parameters.

In this talk, we propose a new theoretical framework to determine parameter values of an effective stochastic model for anomalous transportation [1]. We discuss that the model is determined by identifying ''a specific trajectory'' of solutions of the RG equation. The trajectory represents the minimum flow from an effective model to an infrared universal behavior. Specifically, we determine the Kardar-Parisi-Zhang equation that effectively describes the universal behavior of the Kuramoto-Sivashinsky equation. Furthermore, we discuss an application of our theory to other systems that have anomalous transportation.

Reference:
[1] Y. Minami, S. Sasa, arXiv:1703.08946 [cond-mat.stat-mech].

Collective motion of self-propelled elements, as seen in bird flocks, fish schools, bacterial swarms, etc., is so ubiquitous that it has driven physicists to search for its possibly universal properties. Evidence for such universality has been provided by many theoretical and numerical studies using simple flocking models such as Vicsek-style models and hydrodynamic theories [1-2]. However, no experiments so far have been fully convincing in demonstrating the existence of this universality.

In this seminar, after introducing standard models of collective motion and giving state-of-the-art interpretations on previous experimental studies, I show our experiments on elongated bacteria swimming in a quasi-two-dimensional fluid layer [3]. Strong confinement and the high aspect ratio of bacteria induce weak nematic alignment upon collision, which gives rise to spontaneous breaking of rotational symmetry and global nematic order at sufficiently high density of bacteria. This homogeneous but fluctuating ordered phase has turned out to exhibit true long-range orientational order, non-trivial giant number fluctuations, and algebraic correlations associated with Nambu-Goldstone modes, which verifies the existence of an active phase predicted to emerge in standard flocking models. Such properties contrast our system with usual bacterial experiments that end up with turbulent states without any global orientational order.

Through our experiments, I will also discuss (i) what might be crucial for the emergence of such universality in reality and (ii) possible discrepancy between our experiments and theoretical predictions with approximations.

[1] F. Ginelli, “The Physics of the Vicsek model”, Eur. Phys. J.: Special Topics, 225, 2099 (2016).
[2] J. Toner, Y. Tu, and S. Ramaswamy. “Hydrodynamics and phases of flocks”, Ann. Phys. (N.Y.), 318, 170 (2005).
[3] D. Nishiguchi, K. H. Nagai, H. Chaté, and M. Sano, “Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria”, Phys. Rev. E, 95, 020601(R) (2017).

A reversible-irreversible (RI) transition of particle trajectories was first investigated in a low density periodically driven colloidal system and it was found to be a continuous absorbing state transition [1,2]. It has been also discussed that the transition might belong to the directed percolation universality class [2]. In the higher density systems, on the other hand, a RI transition is observed but the nature of the transition has not been clarified yet.

In this seminar, we present our recent studies on the RI transitions for various densities especially near the jamming transition by using oscillatory sheared molecular dynamics simulations. Here it is revealed that the transition behaviors are dramatically changed at the jamming transition density. In particular, above the transition density, we observe only the discontinuous RI transition and find that it is clearly correlated with the yielding transition [3]. On the other hand, below the jamming transition density, we find that there exist several distinct transitions depending on the density and strain amplitude, i.e., (i) continuous, (ii) reentrant, and (iii) weakly discontinuous RI transitions. We show that these transition behaviors are strongly correlated to the number of the contacts among the particles. This implies that these distinct transitions are explained in the context of the contact percolation and mechanical stability [4].

Refs:
[1] D. J. Pine, J. P. Gollub, J. F. Brady, and A. M. Leshansky, Nature 438, 997 (2005).
[2] L. Cort?, P. M. Chaikin, J. P. Gollub, and D. J. Pine, Nat Phys 4, 420 (2008).
[3] T. Kawasaki and L. Berthier, Phys. Rev. E 94, 022615 (2016).
[4] K. Nagasawa, K. Miyazaki, and T. Kawasaki (in preparation).

Entropy is a fundamental concept in physics. It appears in thermodynamics, statistical mechanics, information theory, computation theory, and thermodynamics of black holes. Recently, the inter-relations between different types of entropy have been discovered. By synthesizing various aspects of entropy, we thus obtain a deeper understanding of fundamental laws in physics. Now, there is a paper [1], which claims that black hole entropy is obtained as the Noether charge associated with the horizon Killing field. We are then naturally led to ask whether thermodynamic entropy of standard materials is also characterized by a Noether invariant.

In this seminar, we study a classical many-particle system with an external control represented by a time dependent parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal non-uniform time translation, where trajectories in the phase space are restricted to those consistent with quasi-static processes in thermodynamics [2]. The most remarkable result of our theory is the emergence of a universal constant of the action dimension, while our theory stands on classical mechanics, classical statistical mechanics, and thermodynamics.

Furthermore, we study a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. From unitary time evolution of quantum pure states, we derive an effective action for trajectories in a thermodynamic state space. In the action, the entropy appears with its conjugate variable. Especially, for saddle-point trajectories, the conjugate variable provides a time coordinate called thermal time. Then, the symmetry for the uniform translation of the thermal time emerges, which leads to the entropy as a Noether invariant [3].

[1] R. M. Wald, Phys. Rev. D 48 R3427 (1993).
[2] S. Sasa and Y. Yokokura, Phys. Rev. Lett. 116, 140601 (2016).
[3] S. Sasa, S. Sugiura, and Y. Yokokura, in preparation.

At the nanoscale, the morphological evolution of solid films and islands under annealing is strongly influenced by wetting properties. Inspired by analogies with recent advances in the wetting behavior of liquids, we explore two situations where solid-state wetting plays a crucial role.

In a first part, we discuss the dewetting dynamics of a thin solid film based on 2D Kinetic Monte Carlo (KMC) simulations and analytical models. We focus on the role of the faceting of the dewetting rim, which changes the asymptotic behavior of the dewetting velocity. In addition, we analyze the instability of the dewetting front, which leads to the formation of fingers. We also discuss the consequences of the wetting potential on the dewetting process and on the triple-line dynamics.

In a second part, we will present some results on the wetting statics and dynamics of islands (or nanoparticles) on surface with topographical structures of large aspect ratio, such as pillars or trenches using 3D KMC simulations including elastic effects.

In his landmark 1883 paper, Osborne Reynolds studied qualitatively different kinds of motion of fluid in a straight pipe. His aim was to demonstrate the transition to “sinuous”, in current terminology turbulent, motion as the flow rate increases. As it turns out, he had picked a set up that is practically simple but mathematically very complicated. The flow state that is void of any turbulence remains asymptotically stable for any experimentally reachable flow rate, and swirling flows occur suddenly and intermittently. Their onset is hysteretic and strongly depends on the way the flow rate is varied. Intrigued by this result, A. N. Kolmogorov introduced a more abstract model of fluid motion, restricting it to two spatial dimensions and discarding material boundaries. However, it soon turned out to be overly restrictive and exclude transitions like the one Reynolds had observed. In this presentation, I will show that extending Kolmogorov’s model to three spatial dimensions places it in the same category as elementary shear flows such as that of fluids in pipes and channels. I will study the hysteretic onset of turbulence and the structure of phase space by numerical bifurcation analysis as well as energy methods. This is joint work with Susumu Goto of Osaka University.

In most granular media, interactions between grains are dominated by contact events: either dissipative collisions in diluted granular media or friction in denser ones. I consider grains that carry a magnetic dipole and interact through dipole-dipole interactions. I will discuss how these long range interactions modify the behavior of the granular medium. In particular I will present several instabilities such as the formation of peaks at the surface of a dense granular layer or a transition similar to the liquid-gas phase transition.