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We analyze a two-dimensional spring network model comprising breakable and unbreakable springs. Computer simulations showed this system to exhibit intermittent stress drops in a larger strain regime, and these stress drops resulted in ductile-like behavior. The scaling analysis reveals that the avalanche size distribution demonstrates a cut-off, depending on its internal structure. This study also investigates the relationship between cluster growth and stress drop, and we show that the amount of stress drop increases in terms of power law, corresponding to crack growth. The crack length distribution also demonstrates a cut-off depending on its internal structure. The results show that both the cluster growth-stress drop relationship and the crack size distribution are scaled by the quantity related to the internal structure, and the relevance of the exponent that scales the cluster growth-stress drop relationship to the exponent that scales crack size distribution is verified., Comment: 6 pages, 9 figures

In this study, we experimentally investigated the time dependence of the statistical properties of two-dimensional drying crack patterns to determine the functional form of fragment size distribution. Experiments using a thin layer of a magnesium carbonate hydroxide paste revealed a "dynamical scaling" property in the time series of the fragment size distribution, which has been predicted by theoretical and numerical studies. Further analysis results based on Bayesian inference show the transition of the functional form of the fragment size distribution from a log-normal distribution to a generalized gamma distribution. The combination of a statistical model of the fragmentation process and the dynamics of stress concentration of a drying thin layer of viscoelastic material explains the origin of the transition.

We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical results indicate that size distributions at different times can be collapsed into a single time-invariant curve by scaling size by average fragment size (i.e., the distribution obeys the dynamical scaling law). If lifetime is determined by a logarithmic function of fragment size, the distribution does not obey the scaling law. The necessary and sufficient condition that the scaling law is obeyed is obtained by a scaling analysis of the master equation.

We reproduce patterns of drying paste by means of smoothed particle hydrodynamics which is the one of methods for solving the equations of continuum in the Lagrangian description. In addition to reproduce a realistic pattern, we find that average size of fragments decays in proportion to inverse time in the case of a linear drying process. Distributions of the size of the fragments are obtained depending on the time. We find a universal scaling distribution by scaling analysis with the average size of the fragment., Comment: 7 pages, 6 figures

A nonequilibrium distribution function of microscopic thermal current is studied by a direct numerical simulation in a thermal conducting steady state of particle systems. Two characteristic temperatures of the thermal current are investigated on the basis of the distribution. It is confirmed that the temperature depends on the current direction; Parallel temperature to the heat-flux is higher than antiparallel one. The difference between the parallel temperature and the antiparallel one is proportional to a macroscopic temperature gradient., Comment: 4 pages

We study non-linear rheology of a simple theoretical model developed to mimic layered systems such as lamellar structures under shear. In the present work we study a 2-dimensional version of the model which exhibits a Kosterlitz-Thouless transition in equilibrium at a critical temperature Tc. While the system behaves as Newtonain fluid at high temperatures T > Tc, it exhibits shear thinning at low temperatures T < Tc. The non-linear rheology in the present model is understood as due to motions of edge dislocations and resembles the non-linear transport phenomena in superconductors by vortex motions., Comment: 10 pages, 5 figures, contribution to the conference proceeding of International Conference on Science of Friction, Irago Aichi, Japan Sept 9-13 2007

Heat conduction in three-dimensional nonlinear lattices is investigated using a particle dynamics simulation. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in which the interparticle potential has a biquadratic term together with a harmonic term. The system size is $L\times L\times 2L$, and the heat is made to flow in the $2L$ direction the Nose-Hoover method. Although a linear temperature profile is realized, the ratio of enerfy flux to temperature gradient shows logarithmic divergence with $L$. The autocorrelation function of energy flux $C(t)$ is observed to show power-law decay as $t^{-0.98\pm 0,25}$, which is slower than the decay in conventional momentum-cnserving three-dimensional systems ($t^{-3/2}$). Similar behavior is also observed in the four dimensional system., Comment: 4 pages, 5 figures. Accepted for publication in J. Phys. Soc. Japan Letters

Nonequilibrium behaviors of positional order are discussed based on diffusion processes in particle systems. With the cumulant expansion method up to the second order, we obtain a relation between the positional order parameter $\Psi$ and the mean square displacement $M$ to be $\Psi \sim \exp(- {\bf K}^2 M /2d)$ with a reciprocal vector ${\bf K}$ and the dimension of the system $d$. On the basis of the relation, the behavior of positional order is predicted to be $\Psi \sim \exp(-{\bf K}^2Dt)$ when the system involves normal diffusion with a diffusion constant $D$. We also find that a diffusion process with swapping positions of particles contributes to higher orders of the cumulants. The swapping diffusion allows particle to diffuse without destroying the positional order while the normal diffusion destroys it., Comment: 4 pages, 4 figures. Submitted to Phys. Rev. E

Vulcanian explosive eruption, which is a nonlinear and nonequilibrium abrupt dynamics of magma-gas mixture, is modeled by a two-component Lennard-Jones particle system. Molecular-dynamics simulation of a shock-tube experiment gives consistent results with a explosive eruption picture of volcanology; Shock wave and expansion wave are reproduced. In addition bubble nucleation of a gas component in the magma melt and spinodal-like decomposition are observed in the simulation. The result is also compared with a continuum hydrodynamic model; Qualitative features of continuum dynamics are reproduced by the present model. We find that the particle description of dynamics is an effective method in such kind of abrupt dynamics., Comment: 4 pages, 4 figures

The second law of ordinary thermodynamics and the second law of steady state thermodynamics, as proposed by Oono and Paniconi, are investigated from the microscopic point of view for the open quantum system. Based on the H-theorem of Lindblad, we show that both second laws are consistent with the quantum dynamics generated by the completely positive map. In addition, microscopic expressions of entropy production and ``housekeeping heat'' are obtained for some classes of dynamical quantum systems., Comment: 4 pages, revtex4; corrected typo

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To confirm its validity in a practical situation, we also investigate an open quantum system that is a spin 1/2 system with a scanning magnetic field interacting with a thermal heat bath. As a result, we find that the quantum analogue functions well., Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000)

Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional system of the size of $L_x\times L_y\times L_z(L_z\gg L_x,L_y)$ is simulated. Heat baths are put in both end: one has higher temperature than the other. In the crystal case, the interaction potential $V$ has fourth-order non-linear term in addition to the harmonic term, and Nose-Hoover method is used for the heat baths. In the fluid case, stochastic boundary condition is charged, which works as the heat baths. Fourier-type heat conduction is reproduced both in crystal and fluid models in three-dimensional system, but it is not observed in lower dimensional system. Autocorrelation function of heat flux is also observed and long-time tails of the form of $\sim t^{-d/2}$, where $d$ denotes the dimensionality of the system, are confirmed., Comment: 4 pages including 3 figures

Quantum mechanical motion of a particle in a periodic asymmetric potential is studied theoretically at zero temperature. It is shown based on semi-classical approximation that the tunneling probability from one local minimum to the next becomes asymmetric in the presence of weak oscillating field, even though there is no macroscopic field gradient in average. Dissipation enhances this asymmetry, and leads to a steady unidirectional current, resulting in a quantum ratchet system., Comment: 12 pages, 2 Figures, submitted to J. Phys. Soc. Jpn

The concept of thermal ratchets is extended to the system governed by quantum mechanics. We study a tight-binding model with an asymmetric periodic potential contacting with a heat bath under an external oscillating field as a specific example of quantum ratchet. Dynamics of a density operator of this system is studied numerically by using the quantum Liouville equation. Finite net current is found in the non-equilibrium steady state. The direction of the current varies with parameters, in contrast with the classical thermal ratchets., Comment: 7 pages, Latex, 4 ps figures; No change in the text by this replacement. only the figures are replaced with higher quality ones (but smaller size)

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle properly, and the maps are coupled to each other through the headway distance. By simulating the model, we obtain a plot of the flow against the concentration similar to the observed data in real traffic flows. Realistic traffic jam regions are observed in space-time trajectories., Comment: 5 postscript figures available upon request