Power-Law Fluctuations at the Order-Disorder Transition in Colloidal Suspensions under Shear Flow
AIP Conference Proceedings, 2008
We investigate order‐disorder transitions in non‐equilibrium systems. Specifically, we consider c... more We investigate order‐disorder transitions in non‐equilibrium systems. Specifically, we consider colloidal suspensions under shear flow by performing Brownian dynamics simulations. We characterize the order‐disorder transition in this system in terms of a statistical property of the time‐dependent maximum value of structure factor. We report that it exhibits power‐law fluctuations, which appears only in the ordered phase.
Biological system is unique in that component biomolecules are selforganized and emerge adaptable... more Biological system is unique in that component biomolecules are selforganized and emerge adaptable, stable and energy-saving functions. To understand the essential condition for reproducing the properties and constructing stable system from unstable flexible components, we are designing artificial muscle using myosin and DNA nanostructure. System size, spatial positioning, degree of intrinsic noise and the mechanical communication in the synthesized muscle can be modulated and we'll observe the internal dynamics and the system behavior at the single molecule resolution. We have developed several novel tools to modulate the system and monitor the internal dynamics with high precision.
A large number of interacting particles that obey a classical Hamiltonian equation may exhibit hy... more A large number of interacting particles that obey a classical Hamiltonian equation may exhibit hydrodynamic phenomena including turbulence. The equations describing the phenomena far from equilibrium are derived from Hamiltonian particle systems by formulating a simple perturbation theory with a scale separation parameter.
Oscillating interfaces are found in the one-dimensional complex Ginzburg-Landau equation subject ... more Oscillating interfaces are found in the one-dimensional complex Ginzburg-Landau equation subject to a periodic force. By introducing a suitable section in the phase space, it is shown that the oscillation starts with a Hopf bifurcation and that subsequent bifurcations lead to various motions of interface. Interfacial motion plays crucial roles in the long-time behavior of spatially extended systems with bistabiIity. Recent studies revealed the nature of interaction between interfaces,l),Z) universal scaling in the motion of random interfaces,3) and instability of interface associated with negative surface tension. 4 ) In one-dimensional systems, there is no curvature flow characteristic of higher dimensional systems. One may suspect that the interface is either stationary or steadily propagating and that complex motion like 'breathing' can only arise from the interaction between interfaces. 5
For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we fin... more For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities can be calculated using only one UPO sampled from the ensemble. Evidence to support this conclusion is obtained by generating the ensemble by Monte Carlo calculation for a statistical mechanical model described by a space-time Hamiltonian that is expressed in terms of Floquet exponents of UPOs. This result allows us to interpret the recent interesting discovery that statistical properties of turbulence can be obtained from only one UPO [G.
Publisher's Note: Microscopic description of the equality between violation of fluctuation-dissipation relation and energy dissipation [Phys. Rev. E 72, 060102 (2005)]
An extended ensemble Monte Carlo study of a lattice glass model
Journal of Physics: Conference Series, 2010
ABSTRACT The thermodynamic transition to a glass phase from a liquid phase is studied in a simple... more ABSTRACT The thermodynamic transition to a glass phase from a liquid phase is studied in a simple lattice glass model both on a random graph and in two dimensions by employing an extended ensemble Monte Carlo method, which enables us to explore its equilibrium behavior in a high density regime. The results for the random-graph case support the scenario of an equilibrium glass transition as predicted from one-step replica symmetry breaking schemes via the cavity method. Numerical evidence for the glass transition is also found for the system in two dimensions. The equation of state measured indicates a discontinuous change in the compressibility at the transition point and the overlap distribution function has a sharp double peak structure in the glassy phase. They suggest that this singularity originates from a one-step replica symmetry breaking.
A class of kinetically constrained models with reflection symmetry is proposed as an extension of... more A class of kinetically constrained models with reflection symmetry is proposed as an extension of the Fredrickson-Andersen model. It is proved that the proposed model on the square lattice exhibits a freezing transition at a non-trivial density. It is conjectured by numerical experiments that the known mechanism of the singular behaviors near the freezing transition in a previously studied model (spiral model) is not responsible for that in the proposed model. Lattice theory and statistics • Theory and modeling of the glass transition • Percolation
We propose an energetic interpretation of stochastic processes described by Langevin equations wi... more We propose an energetic interpretation of stochastic processes described by Langevin equations with non-uniform temperature. In order to avoid Itô-Stratonovich dilemma, we start with a Kramers equation, and derive a Fokker-Plank equation by the renormalization group method. We give a proper definition of heat for the system. Based on our formulations, we analyze two examples, the Thomson effect and a Brownian motor which realizes the Carnot efficiency.
Cooperative behaviors near the disorder-induced critical point in a random field Ising model are ... more Cooperative behaviors near the disorder-induced critical point in a random field Ising model are numerically investigated by analyzing time-dependent magnetization in ordering processes from a special initial condition. We find that the intensity of fluctuations of time-dependent magnetization, χ(t), attains a maximum value at a time t = τ in a normal phase and that χ(τ) and τ exhibit divergences near the disorder-induced critical point. Furthermore, spin configurations around the time τ are characterized by a length scale, which also exhibits a divergence near the critical point. We estimate the critical exponents that characterize these power-law divergences by using a finitesize scaling method.
When a stable phase is adjacent to a metastable phase with a planar interface, the stable phase g... more When a stable phase is adjacent to a metastable phase with a planar interface, the stable phase grows. We propose a stochastic lattice model describing the phase growth accompanying heat diffusion. The model is based on an energy-conserving Potts model with a kinetic energy term defined on a two-dimensional lattice, where each site is sparse-randomly connected in one direction and local in the other direction. For this model, we calculate the stable and metastable phases exactly using statistical mechanics. Performing numerical simulations, we measure the displacement of the interface R(t). We observe the scaling relation , where D is the thermal diffusion constant and L x is the system size between the two heat baths. The scaling function R(z) shows R(z) z 0.5 for z z c and R(z) z α for z z c , where the cross-over value z c and exponent α depend on the temperatures of the baths, and 0.5 ≤ α ≤ 1. We then confirm that a deterministic phase-field model exhibits the same scaling relation. Moreover, numerical simulations of the phase-field model show that the cross-over value R(z c ) approaches zero when the stable phase becomes neutral.
It has been known that epidemic outbreaks in the SIR model on networks are described by phase tra... more It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability one in the thermodynamic limit. We elucidate its mechanism by deriving a simple Langevin equation that captures an essential aspect of the phenomenon. We also calculate the probability of epidemic outbreaks near the transition point.
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Papers by Shin-ichi Sasa