Sire, Clément

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length $L(t)\\sim t^{1/z}$, we find that for times $t\'$ and $t$ satisfying $L(t\')\\ll L(t)\\ll L(t\')^\\phi$ well inside the scaling regime, the autocorrelation function behaves like $\\sim L(t\')^{-(d-2+\\eta)...

Laval, Jean-Philippe Chavanis, Pierre-Henri Dubrulle, Bérengère Sire, Clément

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, as predicted by Carnevale et al., and it ...

Sire, Clément Chavanis, Pierre-Henri

In this paper, we introduce a numerical renormalization group procedure which permits long-time simulations of vortex dynamics and coalescence in a 2D turbulent decaying fluid. The number of vortices decreases as $N\\sim t^{-\\xi}$, with $\\xi\\approx 1$ instead of the value $\\xi=4/3$ predicted by a na\\\"{\\i}ve kinetic theory. For short time, we...

Cueille, Stéphane Sire, Clément

We define a block persistence probability $p_l(t)$ as the probability that the order parameter integrated on a block of linear size $l$ has never changed sign since the initial time in a phase ordering process at finite temperature T

Cueille, Stéphane Sire, Clément

We explore a new definition of the persistence exponent, measuring the probability that a spin never flips after a quench of an Ising-like model at a temperature 0

Yurke, B. Pargellis, A. N. Majumdar, S. N. Sire, Clément

Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $\\theta$ which characterizes the time evolution, $p(t) \\sim t^{-\\theta}$, of the probability p(t) that the local order parameter has not switched its state by the time t. For 0.4 seconds to 200 seconds following the phase q...

Majumdar, Satya N. Sire, Clément Bray, Alan J. Cornell, Stephen J.

The diffusion equation \\partial_t\\phi = \\nabla^2\\phi is considered, with initial condition \\phi( _x_ ,0) a gaussian random variable with zero mean. Using a simple approximate theory we show that the probability p_n(t_1,t_2) that \\phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between t_1 and t_2 has the asymptotic form p_n(t...

Majumdar, S. N. Bray, A. J. Cornell, S. J. Sire, Clément

A 'persistence exponent\' $\\theta$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t) \\sim t^{-\\theta}$, that the global order parameter has not changed sign in the time interval $t$ following a quench to the critical point from a disordered state. This exponent is calculated in mean-field theory, in the $n=\\i...

Majumdar, Satya N. Sire, Clément

We study the decay of the probability for a non-Markovian stationary Gaussian walker not to cross the origin up to time $t$. This result is then used to evaluate the fraction of spins that do not flip up to time $t$ in the zero temperature Monte-Carlo spin flip dynamics of the Ising model. Our results are compared to extensive numerical simulations...