arXiv subjects

S. J. Cornell

Publications and source records attributed to S. J. Cornell.

3 recordsLinked to original sources

arXiv1997

Corrections to Scaling in Phase-Ordering Kinetics

The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form C(r,t) = f_0(r/L) + L^{-ω} f_1(r/L) + ..., where L is a characteristic length scale extracted from the energy. The correction-to-scaling exponent ωhas the value ω=4 for the d=1 Glauber model, the n-vector model with n=\infty, and the approximate theory of Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, ωhas a non-trivial value: omega = 3.8836... for d=2, and ω= 3.9030... for d=3. The correction-to-scaling functions f_1(x) are also calculated.

cond-mat.stat-mech↗

arXiv1997

Non-Markovian Persistence and Nonequilibrium Critical Dynamics

The persistence exponent θfor the global order parameter, M(t), of a system quenched from the disordered phase to its critical point describes the probability, p(t) \sim t^{-θ}, that M(t) does not change sign in the time interval t following the quench. We calculate θto O(ε^2) for model A of critical dynamics (and to order εfor model C) and show that at this order M(t) is a non-Markov process. Consequently, θis a new exponent. The calculation is performed by expanding around a Markov process, using a simplified version of the perturbation theory recently introduced by Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].

cond-mat.stat-mech↗

arXiv1996

Global Persistence Exponent for Critical Dynamics

A `persistence exponent' $θ$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t) \sim t^{-θ}$, 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 $n=\infty$ limit of the $O(n)$ model, to first order in $ε= 4-d$, and for the 1-d Ising model. Numerical results are obtained for the 2-d Ising model. We argue that $θ$ is a new independent exponent.

cond-mat↗