382 research outputs found
Fluctuation dissipation ratio in the one dimensional kinetic Ising model
The exact relation between the response function and the
two time correlation function is derived analytically in the
one dimensional kinetic Ising model subjected to a temperature quench. The
fluctuation dissipation ratio is found to depend on time
through in the time region where scaling holds. The crossover from the nontrivial form
to takes place as the waiting
time is increased from below to above the equilibration time .Comment: 2 figure
Inverse design technique for cascades
A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided
Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model
The evolution of the structure factor is studied during the phase-ordering
dynamics of the kinetic Ising model with conserved order parameter. A
preasymptotic multiscaling regime is found as in the solution of the
Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is
always approached through a crossover from multiscaling to standard scaling,
independently from the nature of the microscopic dynamics.Comment: 11 pages, 3 figures, to be published in Europhys. Let
Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
We study analytically the probability distribution of the heat released by an
ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium
relaxation process following a temperature quench. We focus on the asymmetry
properties of the heat distribution in the nonstationary dynamics, in order to
study the forms taken by the Fluctuation Theorem as the number of degrees of
freedom is varied. After analysing in great detail the cases of one and two
oscillators, we consider the limit of a large number of oscillators, where the
behavior of fluctuations is enriched by a condensation transition with a
nontrivial phase diagram, characterized by reentrant behavior. Numerical
simulations confirm our analytical findings. We also discuss and highlight how
concepts borrowed from the study of fluctuations in equilibrium under symmetry
breaking conditions [Gaspard, J. Stat. Mech. P08021 (2012)] turn out to be
quite useful in understanding the deviations from the standard Fluctuation
Theorem.Comment: 16 pages, 7 figure
Energy and Heat Fluctuations in a Temperature Quench
Fluctuations of energy and heat are investigated during the relaxation
following the instantaneous temperature quench of an extended system. Results
are obtained analytically for the Gaussian model and for the large model
quenched below the critical temperature . The main finding is that
fluctuations exceeding a critical threshold do condense. Though driven by a
mechanism similar to that of Bose-Einstein condensation, this phenomenon is an
out-of-equilibrium feature produced by the breaking of energy equipartition
occurring in the transient regime. The dynamical nature of the transition is
illustrated by phase diagrams extending in the time direction.Comment: To be published in the Proceedings of the Research Program "Small
system non equilibrium fluctuations, dynamics and stochastics, and anomalous
behavior", Kavli Institute for Theoretical Physics China, July 2013. 40
pages, 9 figure
Off equilibrium response function in the one dimensional random field Ising model
A thorough numerical investigation of the slow dynamics in the d=1 random
field Ising model in the limit of an infinite ferromagnetic coupling is
presented. Crossovers from the preasymptotic pure regime to the asymptotic
Sinai regime are investigated for the average domain size, the autocorrelation
function and staggered magnetization. By switching on an additional small
random field at the time tw the linear off equilibrium response function is
obtained, which displays as well the crossover from the nontrivial behavior of
the d=1 pure Ising model to the asymptotic behavior where it vanishes
identically.Comment: 12 pages, 10 figure
Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
We present comprehensive numerical results for domain growth in the
two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber
kinetics. We characterize the evolution via the {\it domain growth law}, and
two-time quantities like the {\it autocorrelation function} and {\it
autoresponse function}. Our results clearly establish that the growth law shows
a crossover from a pre-asymptotic regime with "power-law growth with a
disorder-dependent exponent" to an asymptotic regime with "logarithmic growth".
We compare this behavior with previous results on one-dimensional disordered
systems and we propose a unifying picture in a renormalization group framework.
We also study the corresponding crossover in the scaling functions for the
two-time quantities. Super-universality is found not to hold. Clear evidence
supporting the dimensionality dependence of the scaling exponent of the
autoresponse function is obtained.Comment: Thoroughly revised manuscript. The Introduction, Section 2 and
Section 4 have been largely rewritten. References added. Final version
accepted for publication on Journal of Statistical Mechanics: Theory and
Experimen
Nonlinear susceptibilities and the measurement of a cooperative length
We derive the exact beyond-linear fluctuation dissipation relation,
connecting the response of a generic observable to the appropriate correlation
functions, for Markov systems. The relation, which takes a similar form for
systems governed by a master equation or by a Langevin equation, can be derived
to every order, in large generality with respect to the considered model, in
equilibrium and out of equilibrium as well. On the basis of the fluctuation
dissipation relation we propose a particular response function, namely the
second order susceptibility of the two-particle correlation function, as an
effective quantity to detect and quantify cooperative effects in glasses and
disordered systems. We test this idea by numerical simulations of the
Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure
Non trivial behavior of the linear response function in phase ordering kinetics
Drawing from exact, approximate and numerical results an overview of the
properties of the out of equilibrium response function in phase ordering
kinetics is presented. Focusing on the zero field cooled magnetization,
emphasis is on those features of this quantity which display non trivial
behavior when relaxation proceeds by coarsening. Prominent among these is the
dimensionality dependence of the scaling exponent which leads to
failure of the connection between static and dynamic properties at the lower
dimensionality , where . We also analyse the mean spherical
model as an explicit example of a stochastic unstable system, for which the
connection between statics and dynamics fails at all dimensionalities.Comment: 10 pages, 2 figures. Contribution to the International Conference
"Perspectives on Quantum Field Theory, Statistical Mechanics and Stochastics"
in honour of the 60th birthday of Francesco Guerr
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