arXiv subjects

Alan J. Bray

Publications and source records attributed to Alan J. Bray.

43 records · Page 3Linked to original sources

arXiv1998

Persistence with Partial Survival

We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $θ(p)$ changes continuously with $p$, $θ(0)$ being the usual persistence exponent. We compute $θ(p)$ exactly for a one-dimensional deterministic coarsening model, and approximately for the diffusion equation. Finally we develop an exact, systematic series expansion for $θ(p)$, in powers of $ε=1-p$, for a general Gaussian process with finite density of zero crossings.

cond-mat.stat-mech↗

arXiv1998

Pattern Dynamics of Rayleigh-Benard convective rolls and weakly segregated diblock copolymers

We consider the pattern dynamics of the lamellar phases observed in Rayleigh-Benard convection, as described by the Swift-Hohenberg equation, and in the weak segregation regime of diblock copolymers. Both numerical and analytical investigations show that the dynamical growth of the characteristic length scale in both systems is described by the same growth exponents, thus suggesting that both systems are members of the same universality class.

cond-mat.stat-mech↗

arXiv1998

Inelastic collapse of a randomly forced particle

We consider a randomly forced particle moving in a finite region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r_c\equiv e^{-π/\sqrt{3}}, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r_c is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.

cond-mat.stat-mech↗

arXiv1997

Scaling of the Random-Field Ising Model at Zero Temperature

The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal models behave distinctly in 4 dimensions with the latter apparently having a discontinuous jump in the magnetization. A finite-size scaling analysis is presented for this transition.

cond-mat.dis-nn↗

arXiv1996

Nontrivial Exponent for Simple Diffusion

The diffusion equation \partial_tϕ= \nabla^2ϕis considered, with initial condition ϕ( _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 ϕ( _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_1,t_2) \sim [\ln(t_2/t_1)]^n(t_1/t_2)^{-θ}. The exponent θhas predicted values 0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with simulation results.

cond-mat↗

arXiv1996

Phase ordering dynamics of cosmological models

The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of topological defects in the early universe. The common feature of these different physical processes is scaling. A fully analytical approximate scheme -- the linear-gaussian approach -- is proposed to evaluate 1-point, 2-point, etc.\ scaling functions for the ordering dynamics of the $O(n)$-symmetric Higgs-field models.

hep-ph↗

arXiv1996

Domain Growth in a 1-D Driven Diffusive System

The low-temperature coarsening dynamics of a one-dimensional Ising model, with conserved magnetisation and subject to a small external driving force, is studied analytically in the limit where the volume fraction μof the minority phase is small, and numerically for general μ. The mean domain size L(t) grows as t^{1/2} in all cases, and the domain-size distribution for domains of one sign is very well described by the form P_l(l) \propto (l/L^3)\exp[-λ(μ)(l^2/L^2)], which is exact for small μ(and possibly for all μ). The persistence exponent for the minority phase has the value 3/2 for μ\to 0.

cond-mat↗