Unwinding Scaling Violations in Phase Ordering

The one-dimensional $O(2)$ model is the simplest example of a system with topological textures. The model exhibits anomalous ordering dynamics due to the appearance of two characteristic length scales: the phase coherence length, $L \sim t^{1/z}$, and the phase winding length, $L_{w} \sim L^{\chi}$. We derive the scaling law $z=2+\mu\chi$, where $\mu=0$ ($\mu=2$) for nonconserved (conserved) dynamics and $\chi=1/2$ for uncorrelated initial orientations. From hard-spin equations of motion, we consider the evolution of the topological defect density and recover a simple scaling description. (please email [email protected] for a hard copy by mail)Comment: 4 pages, LATeX, uuencoded figure file appended: needs epsf.sty, [resubmitted since postscript version did not work well], M/C.TH.94/21,NI9402

Triangular anisotropies in Driven Diffusive Systems: reconciliation of Up and Down

Deterministic coarse-grained descriptions of driven diffusive systems (DDS) have been hampered by apparent inconsistencies with kinetic Ising models of DDS. In the evolution towards the driven steady-state, ``triangular'' anisotropies in the two systems point in opposite directions with respect to the drive field. We show that this is non-universal behavior in the sense that the triangular anisotropy ``flips'' with local modifications of the Ising interactions. The sign and magnitude of the triangular anisotropy also vary with temperature. We have also flipped the anisotropy of coarse-grained models, though not yet at the latest stages of evolution. Our results illustrate the comparison of deterministic coarse-grained and stochastic Ising DDS studies to identify universal phenomena in driven systems. Coarse-grained systems are particularly attractive in terms of analysis and computational efficiency.Comment: 6 pages, 7 figure

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

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

Stress-free Spatial Anisotropy in Phase-Ordering

We find spatial anisotropy in the asymptotic correlations of two-dimensional Ising models under non-equilibrium phase-ordering. Anisotropy is seen for critical and off-critical quenches and both conserved and non-conserved dynamics. We argue that spatial anisotropy is generic for scalar systems (including Potts models) with an anisotropic surface tension. Correlation functions will not be universal in these systems since anisotropy will depend on, e.g., temperature, microscopic interactions and dynamics, disorder, and frustration.Comment: 4 pages, 4 figures include

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

Stuttering Min oscillations within E. coli bacteria: A stochastic polymerization model

We have developed a 3D off-lattice stochastic polymerization model to study subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding, and fragmentation of MinD filaments due to MinE. Each of processivity, protection, and fragmentation reduces stuttering, speeds oscillations, and reduces MinD filament lengths. Neither processivity or tip-protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations are consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization in experimental conditions.Comment: 21 pages, 7 figures, missing unit for k_f inserte

Heterocyst placement strategies to maximize growth of cyanobacterial filaments

Under conditions of limited fixed-nitrogen, some filamentous cyanobacteria develop a regular pattern of heterocyst cells that fix nitrogen for the remaining vegetative cells. We examine three different heterocyst placement strategies by quantitatively modelling filament growth while varying both external fixed-nitrogen and leakage from the filament. We find that there is an optimum heterocyst frequency which maximizes the growth rate of the filament; the optimum frequency decreases as the external fixed-nitrogen concentration increases but increases as the leakage increases. In the presence of leakage, filaments implementing a local heterocyst placement strategy grow significantly faster than filaments implementing random heterocyst placement strategies. With no extracellular fixed-nitrogen, consistent with recent experimental studies of Anabaena sp. PCC 7120, the modelled heterocyst spacing distribution using our local heterocyst placement strategy is qualitatively similar to experimentally observed patterns. As external fixed-nitrogen is increased, the spacing distribution for our local placement strategy retains the same shape while the average spacing between heterocysts continuously increases.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version will be available onlin