Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $\Theta$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the Boltzmann constant), except in the linear response regime, where the fluctuation dissipation theorem holds. In order to elucidate the physical meaning of $\Theta$ far from equilibrium, we analyze a modulated system with a slowly varying potential. We derive a large scale description of the probability density for the modulated system by use of a perturbation method. The expressions we obtain show that $\Theta$ plays the role of the temperature in the large scale description of the system and that $\Theta$ can be determined directly in experiments, without measurements of the diffusion constant and the differential mobility

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 $\delta$ in the Ising model.Comment: 8 pages, 2 figure

Exact transformation of a Langevin equation to a fluctuating response equation

We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time dependent perturbation. This transformation is constructed on the basis of an operator formulation originally used in nonlinear perturbation theory for differential equations by extending it to stochastic analysis. We find that the obtained expression is useful for the calculation of fundamental quantities of the system, and that it provides a physical basis for the decomposition of the forces in the Langevin description into effective driving, dissipative, and random forces in a large-scale description.Comment: 14 pages, to appear in J. Phys. A: Math. Ge

A universal form of slow dynamics in zero-temperature random-field Ising model

The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial condition, we derive exactly an evolution equation for an order parameter. Through a bifurcation analysis of the obtained equation, we reveal a new class of cooperative slow dynamics with the determination of critical exponents.Comment: 4 pages, 2 figure

Effects of Surface Soil Removal on Dynamics of Dissolved Inorganic Nitrogen in a Snow-Dominated Forest

To clarify the effect of vegetation and surface soil removal on dissolved inorganic nitrogen (N) dynamics in a snow-dominated forest soil in northern Japan, the seasonal fluctuation of N concentrations in soil solution and the annual flux of N in soil were investigated at a treated site (in which surface soil, including understory vegetation and organic and A horizons, was removed) and control sites from July 1998 to June 2000. Nitrate (NO3–) concentration in soil solution at the treated site was significantly higher than that of the control in the no-snow period, and it was decreased by dilution from melting snow. The annual net outputs of NO3– from soil at the treated site and control sites were 257 and –12 mmol m–2 year–1, and about 57% of the net output at the treated site occurred during the snowmelt period. NO3– was transported from the upper level to the lower level of soil via water movement during late autumn and winter, and it was retained in soil and leached by melt water in early spring. Removing vegetation and surface soil resulted in an increase in NO3– concentration of soil solution, and snowmelt strongly affected the NO3– leaching from treated soil and the NO3– restoration process in a snow-dominated region

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.Comment: 12page

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.Comment: 16 pages, 4 figure

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.Comment: 11 pages (Revtex) + 5 figures (postscript