783 research outputs found
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 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 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 plays the role of the
temperature in the large scale description of the system and that 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 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
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