arXiv subjects

Shin-ichi Sasa

Publications and source records attributed to Shin-ichi Sasa.

At least 109 records · Page 6Linked to original sources

arXiv2009

History dependence of mechanical properties in granular systems

We study the history dependence of the mechanical properties of granular media by numerical simulations. We perform a compaction of frictional disk packings in a two-dimensional system by controlling the area of the domain with various strain rates. We then find the strain rate dependence of the critical packing fraction above which the pressure becomes finite. The observed behavior makes a contrast with the well-studied jamming transitions for frictionless disk packings. We also observe that the elastic constants of the disk packings depend on the strain rate logarithmically. This result provides a experimental test for the history dependence of granular systems.

cond-mat.dis-nn↗

arXiv2009

Dynamics of k-core percolation in a random graph

We study the edge deletion process of random graphs near a k-core percolation point. We find that the time-dependent number of edges in the process exhibits critically divergent fluctuations. We first show theoretically that the k-core percolation point is exactly given as the saddle-node bifurcation point in a dynamical system. We then determine all the exponents for the divergence based on a universal description of fluctuations near the saddle-node bifurcation.

cond-mat.stat-mech↗

arXiv2008

Scale-free patterns at a saddle-node bifurcation in a stochastic system

We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation processes from a spatially homogeneous initial condition. We characterize the scale-free nature in terms of the spatial configuration of the exiting time from a marginal saddle where the pair annihilation of a saddle and a node occurs at the bifurcation point. Critical exponents associated with the scale-free patterns are determined by numerical experiments.

cond-mat.stat-mech↗

arXiv2008

Critical phenomena in globally coupled excitable elements

Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation are calculated theoretically. The calculated values appear to be in good agreement with those determined by numerical experiments. The relevance of our results to jamming transitions is also mentioned.

cond-mat.stat-mech↗

arXiv2008

Representation of nonequilibrium steady states in large mechanical systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.

cond-mat.stat-mech↗

arXiv2008

Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation

Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in the heat current. The associated Shannon-like microscopic expression of the entropy is suggestive. When the heat current is fixed, the extended Gibbs relation provides a unified treatment of thermodynamic forces in linear nonequilibrium regime.

cond-mat.stat-mech↗

arXiv2008

Critical fluctuations of time-dependent magnetization in a random-field Ising model

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 finite-size scaling method.

cond-mat.stat-mech↗

arXiv2007

A fluctuation-response relation of many Brownian particles under non-equilibrium conditions

We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In equilibrium cases, the linear response coefficient is related to the intensity of density fluctuations in a universal manner, which is called a fluctuation-response relation. We then report numerical evidence that this relation holds even in non-equilibrium cases. This result suggests that Einstein's formula on density fluctuations can be extended to driven diffusive systems when the slowly varying potential is applied in a direction transversal to the driving force.

cond-mat.stat-mech↗

arXiv2007

The order-disorder transition in colloidal suspensions under shear flow

We study the order-disorder transition in colloidal suspensions under shear flow by performing Brownian dynamics simulations. We characterize the transition in terms of a statistical property of time-dependent maximum value of the structure factor. We find that its power spectrum exhibits the power-law behaviour only in the ordered phase. The power-law exponent is approximately -2 at frequencies greater than the magnitude of the shear rate, while the power spectrum exhibits the $1 / f$-type fluctuations in the lower frequency regime.

cond-mat.stat-mech↗

arXiv2007

A perturbation theory for large deviation functionals in fluctuating hydrodynamics

We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the fluctuation theorem, we first relate the large deviation functional with a minimization problem. We then develop a perturbation method for solving the problem. In particular, by performing an expansion with respect to the average current, we derive the lowest order expression for the deviation from the local equilibrium part. This expression implies that the deviation is written as the space-time integration of the excess entropy production rate during the most probable process of generating the fluctuation that corresponds to the argument of the large deviation functional.

cond-mat.stat-mech↗

arXiv2007

A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions

We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time correlation function. Then, following the basic idea of Ginzburg-Landau theory for critical phenomena, we construct a phenomenological framework with which we can determine the critical statistical properties at saddle connection bifurcation points. Employing this framework, we analyze a model by considering the fluctuations of an instanton in space-time configurations of the order parameter. We then obtain the exponents characterizing the divergences of the length scale, the time scale and the amplitude of the fluctuations of the order parameter at the saddle connection bifurcation. The results are to be compared with those of previous studies of the four-point dynamic susceptibility at non-ergodic transitions in glassy systems.

cond-mat.stat-mech↗

arXiv2006

Fluctuations, Responses and Energetics of Molecular Motors

A novel equality relating the rate of energy dissipation to a degree of violation of the fluctuation-response relation (FRR) in nonequilibrium Langevin systems is described. The FRR is a relation between the correlation function of the fluctuations and the response function of macroscopic variables. Although it has been established that the FRR holds in equilibrium, physical significance of violation of the FRR in nonequilibrium systems has been under debate. Recently, the authors have found that an extent of the FRR violation is related in a simple equality to the rate of energy dissipation into the environment in nonequilibrium Langevin systems. In this paper, we fully explain the FRR, the FRR violation, and the new equality with regard to a Langevin model termed a Brownian motor model, which is considered as a simple model of a biological molecular motor. Furthermore, applications of our result to experimental studies of molecular motors are discussed, and, as an illustration, we predict the value of a new time constant regarding the motion of a KIF1A, which is a kind of single-headed kinesin.

cond-mat.stat-mech↗

arXiv2006

Criticality and Scaling Relations in a Sheared Granular Material

We investigate a rheological property of a dense granular material under shear. By a numerical experiment of the system with constant volume, we find a critical volume fraction at which the shear stress and the pressure behave as power-law functions of the shear strain rate. We also present a simple scaling argument that determines the power-law exponents. Using these results, we interpret a power-law behavior observed in the system under constant pressure.

cond-mat.stat-mech↗

arXiv2006

Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction

We study a non-ergodic transition in a many-body Langevin system. We first derive an equation for the two-point time correlation function of density fluctuations, ignoring the contributions of the third- and fourth-order cumulants. For this equation, with the average density fixed, we find that there is a critical temperature at which the qualitative nature of the trajectories around the trivial solution changes. Using a method of dynamical system reduction around the critical temperature, we simplify the equation for the time correlation function into a two-dimensional ordinary differential equation. Analyzing this differential equation, we demonstrate that a non-ergodic transition occurs at some temperature slightly higher than the critical temperature.

cond-mat.stat-mech↗

arXiv2006

An order parameter equation for the dynamic yield stress in dense colloidal suspensions

We study the dynamic yield stress in dense colloidal suspensions by analyzing the time evolution of the pair distribution function for colloidal particles interacting through a Lennard-Jones potential. We find that the equilibrium pair distribution function is unstable with respect to a certain anisotropic perturbation in the regime of low temperature and high density. By applying a bifurcation analysis to a system near the critical state at which the stability changes, we derive an amplitude equation for the critical mode. This equation is analogous to order parameter equations used to describe phase transitions. It is found that this amplitude equation describes the appearance of the dynamic yield stress, and it gives a value of 2/3 for the shear thinning exponent. This value is related to the mean field value of the critical exponent $δ$ in the Ising model.

cond-mat.soft↗

arXiv2006

Linear response theory in stochastic many-body systems revisited

The Green-Kubo relation, the Einstein relation, and the fluctuation-response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green-Kubo relation is a direct result of the local detailed balance condition, the fluctuation-response relation represents the dynamic extension of both the Green-Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.

cond-mat.stat-mech↗

arXiv2006

Systematic derivation of coarse-grained fluctuating hydrodynamic equations for many Brownian particles under non-equilibrium condition

We study the statistical properties of many Brownian particles under the We study the statistical properties of many Brownian particles under the influence of both a spatially homogeneous driving force and a periodic potential with period $\ell$ in a two-dimensional space. In particular, we focus on two asymptotic cases, $\ell_{\rm int} \ll \ell$ and $\ell_{\rm int} \gg \ell$, where $\ell_{\rm int}$ represents the interaction length between two particles. We derive fluctuating hydrodynamic equations describing the evolution of a coarse-grained density field defined on scales much larger than $\ell$ for both the cases. Using the obtained equations, we calculate the equal-time correlation functions of the density field to the lowest order of the interaction strength. We find that the system exhibits the long-range correlation of the type $r^{-d}$ ($d=2$) for the case $\ell_{\rm int} \gg \ell$, while no such behavior is observed for the case $\ell_{\rm int}\ll \ell$.

cond-mat.stat-mech↗

arXiv2006

Computation of the Kolmogorov-Sinai entropy using statistitical mechanics: Application of an exchange Monte Carlo method

We propose a method for computing the Kolmogorov-Sinai (KS) entropy of chaotic systems. In this method, the KS entropy is expressed as a statistical average over the canonical ensemble for a Hamiltonian with many ground states. This Hamiltonian is constructed directly from an evolution equation that exhibits chaotic dynamics. As an example, we compute the KS entropy for a chaotic repeller by evaluating the thermodynamic entropy of a system with many ground states.

cond-mat.stat-mech↗