400 research outputs found
The law of action and reaction for the effective force in a nonequilibrium colloidal system
We study a nonequilibrium Langevin many-body system containing two 'test'
particles and many 'background' particles. The test particles are spatially
confined by a harmonic potential, and the background particles are driven by an
external driving force. Employing numerical simulations of the model, we
formulate an effective description of the two test particles in a
nonequilibrium steady state. In particular, we investigate several different
definitions of the effective force acting between the test particles. We find
that the law of action and reaction does not hold for the total mechanical
force exerted by the background particles, but that it does hold for the
thermodynamic force defined operationally on the basis of an idea used to
extend the first law of thermodynamics to nonequilibrium steady states.Comment: 13 page
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.Comment: 4 pages, 3 figure
Derivation of Non-isotropic Phase Equations from a General Reaction-Diffusion Equation
A non-isotropic version of phase equations such as the Burgers equation, the
K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney
equation in the three-dimensional space is systematically derived from a
general reaction-diffusion system by means of the renormalization group method.Comment: 21pages,no figure
Anomalous time correlation in two-dimensional driven diffusive systems
We study the time correlation function of a density field in two-dimensional
driven diffusive systems within the framework of fluctuating hydrodynamics. It
is found that the time correlation exhibits power-law behavior in an
intermediate time regime in the case that the fluctuation-dissipation relation
is violated and that the power-law exponent depends on the extent of this
violation. We obtain this result by employing a renormalization group method to
treat a logarithmic divergence in time.Comment: 6 page
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
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.Comment: 27 pages, 3 figure
Thermodynamic relations in a driven lattice gas: numerical exprements
We explore thermodynamic relations in non-equilibrium steady states with
numerical experiments on a driven lattice gas. After operationally defining the
pressure and chemical potential in the driven lattice gas, we confirm
numerically the validity of the integrability condition (the Maxwell relation)
for the two quantities whose values differ from those for an equilibrium
system. This implies that a free energy function can be constructed for the
non-equilibrium steady state that we consider. We also investigate a
fluctuation relation associated with this free energy function. Our result
suggests that the compressibility can be expressed in terms of density
fluctuations even in non-equilibrium steady states.Comment: 4 pages, 4 figure
Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation
A Langevin equation whose deterministic part undergoes a saddle-node
bifurcation is investigated theoretically. It is found that statistical
properties of relaxation trajectories in this system exhibit divergent
behaviors near a saddle-node bifurcation point in the weak-noise limit, while
the final value of the deterministic solution changes discontinuously at the
point. A systematic formulation for analyzing a path probability measure is
constructed on the basis of a singular perturbation method. In this
formulation, the critical nature turns out to originate from the neutrality of
exiting time from a saddle-point. The theoretical calculation explains results
of numerical simulations.Comment: 18pages, 17figures.The version 2, in which minor errors have been
fixed, will be published in Phys. Rev.
Fracture driven by a Thermal Gradient
Motivated by recent experiments by Yuse and Sano (Nature, 362, 329 (1993)),
we propose a discrete model of linear springs for studying fracture in thin and
elastically isotropic brittle films. The method enables us to draw a map of the
stresses in the material. Cracks generated by the model, imposing a moving
thermal gradient in the material, can branch or wiggle depending on the driving
parameters. The results may be used to compare with other recent theoretical
work, or to design future experiments.Comment: RevTeX file (9 pages) and 5 postscript figure
Jarzynski equality for the transitions between nonequilibrium steady states
Jarzynski equality [Phys. Rev. E {\bf 56}, 5018 (1997)] is found to be valid
with slight modefication for the transitions between nonequilibrium stationary
states, as well as the one between equilibrium states. Also numerical results
confirm its validity. Its relevance for nonequilibrium thermodynamics of the
operational formalism is discussed.Comment: 5 pages, 2 figures, revte
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