Persistence in systems with algebraic interaction

Persistence in coarsening 1D spin systems with a power law interaction $r^{-1-\sigma}$ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent $\sigma$ ($\sigma\geq 1/2$ in our simulations), persistence decays as an algebraic function of the length scale $L$, $P(L)\sim L^{-\theta}$. The Persistence exponent $\theta$ is found to be independent on the force exponent $\sigma$ and close to its value for the extremal ($\sigma \to \infty$) model, $\bar\theta=0.17507588...$. For smaller values of the force exponent ($\sigma< 1/2$), finite size effects prevent the system from reaching the asymptotic regime. Scaling arguments suggest that in order to avoid significant boundary effects for small $\sigma$, the system size should grow as ${[{\cal O}(1/\sigma)]}^{1/\sigma}$.Comment: 4 pages 4 figure

Scaling state of dry two-dimensional froths: universal angle deviations and structure

We characterize the late-time scaling state of dry, coarsening, two-dimensional froths using a detailed, force-based vertex model. We find that the slow evolution of bubbles leads to systematic deviations from 120degree angles at three-fold vertices in the froth, with an amplitude proportional to the vertex speed, v ~ sqrt(t), but with a side-number dependence that is independent of time. We also find that a significant number of T1 side-switching processes occur for macroscopic bubbles in the scaling state, though most bubble annihilations involve four-sided bubbles at microscopic scales.Comment: 7 pages, 7 figure

Steady-state MreB helices inside bacteria: dynamics without motors

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasi-static evolution of the helical pitch with cell growth, as well as timescales of helix turnover and denovo establishment. We find that while the body of a polarized MreB helix treadmills towards its slow-growing end, the fast-growing tips of laterally associated protofilaments move towards the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.Comment: 7 figures, 1 tabl

Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional XY Model

The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that governs the equilibrium dynamics. We show that, for the 2D XY model, the rate of approach to equilibrium depends on the initial condition. In particular, $\xi(t) \sim t^{1/2}$ if no free vortices are present in the initial state, while $\xi(t) \sim (t/\ln t)^{1/2}$ if free vortices are present.Comment: 4 pages, 3 figure

Determination of the Critical Point and Exponents from short-time Dynamics

The dynamic process for the two dimensional three state Potts model in the critical domain is simulated by the Monte Carlo method. It is shown that the critical point can rigorously be located from the universal short-time behaviour. This makes it possible to investigate critical dynamics independently of the equilibrium state. From the power law behaviour of the magnetization the exponents $\beta / (\nu z)$ and $1/ (\nu z)$ are determined.Comment: 6 pages, 4 figure

Dynamical Scaling: the Two-Dimensional XY Model Following a Quench

To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly compare various length-scales. All of our results are consistent with dynamical scaling and an asymptotic growth law $L \sim (t/\ln[t/t_0])^{1/2}$, though with a time-scale $t_0$ that depends on the length-scale in question. We then reconstruct correlations from the minimal-energy configuration consistent with the vortex positions, and find them significantly different from the ``natural'' correlations --- though both scale with $L$. This indicates that both topological (vortex) and non-topological (``spin-wave'') contributions to correlations are relevant arbitrarily late after the quench. We also present a consistent definition of dynamical scaling applicable more generally, and emphasize how to generalize our approach to other quenched systems where dynamical scaling is in question. Our approach directly applies to planar liquid-crystal systems.Comment: 10 pages, 10 figure

Comment on ``Theory of Spinodal Decomposition''

I comment on a paper by S. B. Goryachev [PRL vol 72, p.1850 (1994)] that presents a theory of non-equilibrium dynamics for scalar systems quenched into an ordered phase. Goryachev incorrectly applies only a global conservation constraint to systems with local conservation laws.Comment: 2 pages LATeX (REVTeX macros), no figures. REVISIONS --- more to the point. microscopic example added, presentation streamlined, long-range interactions mentioned, to be published in Phys. Rev. Let

Non-equilibrium Phase-Ordering with a Global Conservation Law

In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density, $\rho \sim L^{-1}$. For $T>0$, activated kinetics recovers the standard asymptotic growth-law, $L \sim t^{1/2}$. However, at all temperatures, infinite-range energy-transport is allowed by the spin-exchange dynamics. A better implementation of global conservation, the microcanonical Creutz algorithm, is well behaved and exhibits the standard non-conserved growth law, $L \sim t^{1/2}$, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st

Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence

We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of grain sizes different from isotropic theories. As an application of our results, we show that the persistence decay exponent depends on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure