5,143 research outputs found
Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models
A ``persistence'' exponent theta has been extensively used to describe the
nonequilibrium dynamics of spin systems following a deep quench: for
zero-temperature homogeneous Ising models on the d-dimensional cubic lattice,
the fraction p(t) of spins not flipped by time t decays to zero like
t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because
of ``blocking'' (but perhaps still like a power). What are the effects of
disorder or changes of lattice? We show that these can quite generally lead to
blocking (and convergence to a metastable configuration) even for low d, and
then present two examples --- one disordered and one homogeneous --- where p(t)
decays exponentially to p(infinity).Comment: 8 pages (LaTeX); to appear in Physical Review Letter
Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape
A simplified form of the time dependent evolutionary dynamics of a
quasispecies model with a rugged fitness landscape is solved via a mapping onto
a random flux model whose asymptotic behavior can be described in terms of a
random walk. The statistics of the number of changes of the dominant genotype
from a finite set of genotypes are exactly obtained confirming existing
conjectures based on numerics.Comment: 5 pages RevTex 2 figures .ep
Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence
We study analytically the statistics of multiple sign changes in a discrete
non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's
are independent and identically distributed random variables each drawn from a
symmetric and continuous distribution \rho(\phi). We show that the probability
P_m(n) of m sign changes upto n steps is universal, i.e., independent of the
distribution \rho(\phi). The mean and variance of the number of sign changes
are computed exactly for all n>0. We show that the generating function {\tilde
P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where
the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial
formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le
p\le 1. We also show that in the natural scaling limit when m is large, n is
large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large
deviation function \Phi(x) is computed. The implications of these results for
Ising spin glasses are discussed.Comment: 4 pages revtex, 1 eps figur
On the Inelastic Collapse of a Ball Bouncing on a Randomly Vibrating Platform
We study analytically the dynamics of a ball bouncing inelastically on a
randomly vibrating platform, as a simple toy model of inelastic collapse. Of
principal interest are the distributions of the number of flights n_f till the
collapse and the total time \tau_c elapsed before the collapse. In the strictly
elastic case, both distributions have power law tails characterised by
exponents which are universal, i.e., independent of the details of the platform
noise distribution. In the inelastic case, both distributions have exponential
tails: P(n_f) ~ exp[-\theta_1 n_f] and P(\tau_c) ~ exp[-\theta_2 \tau_c]. The
decay exponents \theta_1 and \theta_2 depend continuously on the coefficient of
restitution and are nonuniversal; however as one approches the elastic limit,
they vanish in a universal manner that we compute exactly. An explicit
expression for \theta_1 is provided for a particular case of the platform noise
distribution.Comment: 32 page
Influence of environmental factors on sweating rate of sedentary subjects
Results of a comparative study on the influence of various thermal indices on the sweating rate of sedentary subjects have been reported in this paper. Superiority of dry-bulb temperature of air over other indices for rough assessment of water requirement in relatively dry heat has been demonstrated, and a simple prediction chart for the same has been worked out. The results have thus been found to lend support to the idea that sweating rate alone cannot serve as an index of comfort. Limitations of such field trials have also been discusse
Cold Stress at High Altitudes
The problem of cold at high altitudes has been analysed from a purely physical standpoint. It has been shown that Siple's Wind-Chill Index is not reliable because (i) it does not make use of the well established principles governing the physical processes of heat transfer by convection and radiation, and (ii) it assumes that the mean radiant temperature of the surroundings is the same as the ambient dry bulb temperature. A Cold Stress Index has been proposed which is likely to be a more reliable guide for assessing the climatic hazards of high altitude environments. The Index can be quickly estimated with the help of two nomograms devised for the purpose
Record statistics and persistence for a random walk with a drift
We study the statistics of records of a one-dimensional random walk of n
steps, starting from the origin, and in presence of a constant bias c. At each
time-step the walker makes a random jump of length \eta drawn from a continuous
distribution f(\eta) which is symmetric around a constant drift c. We focus in
particular on the case were f(\eta) is a symmetric stable law with a L\'evy
index 0 < \mu \leq 2. The record statistics depends crucially on the
persistence probability which, as we show here, exhibits different behaviors
depending on the sign of c and the value of the parameter \mu. Hence, in the
limit of a large number of steps n, the record statistics is sensitive to these
parameters (c and \mu) of the jump distribution. We compute the asymptotic mean
record number after n steps as well as its full distribution P(R,n). We
also compute the statistics of the ages of the longest and the shortest lasting
record. Our exact computations show the existence of five distinct regions in
the (c, 0 < \mu \leq 2) strip where these quantities display qualitatively
different behaviors. We also present numerical simulation results that verify
our analytical predictions.Comment: 51 pages, 22 figures. Published version (typos have been corrected
Global Persistence Exponent for Critical Dynamics
A `persistence exponent' is defined for nonequilibrium critical
phenomena. It describes the probability, , that the
global order parameter has not changed sign in the time interval following
a quench to the critical point from a disordered state. This exponent is
calculated in mean-field theory, in the limit of the model,
to first order in , and for the 1-d Ising model. Numerical
results are obtained for the 2-d Ising model. We argue that is a new
independent exponent.Comment: 4 pages, revtex, one figur
Persistence in nonequilibrium surface growth
Persistence probabilities of the interface height in (1+1)- and
(2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface
growth are studied using kinetic Monte Carlo simulations, with emphasis on
models that belong to the molecular beam epitaxy (MBE) universality class. Both
the initial transient and the long-time steady-state regimes are investigated.
We show that for growth models in the MBE universality class, the nonlinearity
of the underlying dynamical equation is clearly reflected in the difference
between the measured values of the positive and negative persistence exponents
in both transient and steady-state regimes. For the MBE universality class, the
positive and negative persistence exponents in the steady-state are found to be
and ,
respectively, in (1+1) dimensions, and and
, respectively, in (2+1) dimensions. The noise
reduction technique is applied on some of the (1+1)-dimensional models in order
to obtain accurate values of the persistence exponents. We show analytically
that a relation between the steady-state persistence exponent and the dynamic
growth exponent, found earlier to be valid for linear models, should be
satisfied by the smaller of the two steady-state persistence exponents in the
nonlinear models. Our numerical results for the persistence exponents are
consistent with this prediction. We also find that the steady-state persistence
exponents can be obtained from simulations over times that are much shorter
than that required for the interface to reach the steady state. The dependence
of the persistence probability on the system size and the sampling time is
shown to be described by a simple scaling form.Comment: 28 pages, 16 figure
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