Persistence of Manifolds in Nonequilibrium Critical Dynamics

We study the persistence P(t) of the magnetization of a d' dimensional manifold (i.e., the probability that the manifold magnetization does not flip up to time t, starting from a random initial condition) in a d-dimensional spin system at its critical point. We show analytically that there are three distinct late time decay forms for P(t) : exponential, stretched exponential and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d' and \eta, z are standard critical exponents. In particular, our theory predicts that the persistence of a line magnetization decays as a power law in the d=2 Ising model at its critical point. For the d=3 critical Ising model, the persistence of the plane magnetization decays as a power law, while that of a line magnetization decays as a stretched exponential. Numerical results are consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include

Global Persistence Exponent for Critical Dynamics

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 $n=\infty$ limit of the $O(n)$ model, to first order in $\epsilon = 4-d$, and for the 1-d Ising model. Numerical results are obtained for the 2-d Ising model. We argue that $\theta$ is a new independent exponent.Comment: 4 pages, revtex, one figur

Colloids in active fluids: Anomalous micro-rheology and negative drag

We simulate an experiment in which a colloidal probe is pulled through an active nematic fluid. We find that the drag on the particle is non-Stokesian (not proportional to its radius). Strikingly, a large enough particle in contractile fluid (such as an actomyosin gel) can show negative viscous drag in steady state: the particle moves in the opposite direction to the externally applied force. We explain this, and the qualitative trends seen in our simulations, in terms of the disruption of orientational order around the probe particle and the resulting modifications to the active stress.Comment: 5 pages, 3 figure

Phase Ordering Kinetics with External Fields and Biased Initial Conditions

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.Comment: 35 pages, latex, no figure

Phase Ordering of 2D XY Systems Below T_{KT}

We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length $L(t) \propto t^{1/2}$ at late times. The autocorrelation decay exponent, $\bar{\lambda} = (\eta_i+\eta_f)/2$, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, $C_{EQ}(r) \sim r^{-\eta}$. We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure

Non-equilibrium Dynamics Following a Quench to the Critical Point in a Semi-infinite System

We study the non-equilibrium dynamics (purely dissipative and relaxational) in a semi-infinite system following a quench from the high temperature disordered phase to its critical temperature. We show that the local autocorrelation near the surface of a semi-infinite system decays algebraically in time with a new exponent which is different from the bulk. We calculate this new non-equilibrium surface exponent in several cases, both analytically and numerically.Comment: revtex, 9 pages, 2 figures available from the author

Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim t^{1/(1+\sigma)}$ for all $\sigma >0$. Numerical results for $\sigma=0.5$, $1.0$, and $1.5$ demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki is asymptotically exact. For this case, the equal-time correlations scale, but the time-derivative correlations break scaling. The short-range solution also applies to systems with long-range interactions when $\sigma \rightarrow \infty$, and in that limit the amplitude of the growth law is exactly calculated.Comment: 19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 1549

Strong-coupling behaviour in discrete Kardar-Parisi-Zhang equations

We present a systematic discretization scheme for the Kardar-Parisi-Zhang (KPZ) equation, which correctly captures the strong-coupling properties of the continuum model. In particular we show that the scheme contains no finite-time singularities in contrast to conventional schemes. The implications of these results to i) previous numerical integration of the KPZ equation, and ii) the non-trivial diversity of universality classes for discrete models of `KPZ-type' are examined. The new scheme makes the strong-coupling physics of the KPZ equation more transparent than the original continuum version and allows the possibility of building new continuum models which may be easier to analyse in the strong-coupling regime.Comment: 21 pages, revtex, 2 figures, submitted to J. Phys.

Persistence at the onset of spatiotemporal intermittency in coupled map lattices

We study persistence in coupled circle map lattices at the onset of spatiotemporal intermittency, an onset which marks a continuous transition, in the universality class of directed percolation, to a unique absorbing state. We obtain a local persistence exponent of theta_l = 1.49 +- 0.02 at this transition, a value which closely matches values for theta_l obtained in stochastic models of directed percolation. This result constitutes suggestive evidence for the universality of persistence exponents at the directed percolation transition. Given that many experimental systems are modelled accurately by coupled map lattices, experimental measurements of this persistence exponent may be feasible.Comment: 7 pages, Latex, 6 Postscript figures, Europhysics Letters (to appear

Persistence in systems with conserved order parameter

We consider the low-temperature coarsening dynamics of a one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics in the domain representation. Domains diffuse with size-dependent diffusion constant, $D(l) \propto l^\gamma$ with $\gamma = -1$. We generalize this model to arbitrary $\gamma$, and derive an expression for the domain density, $N(t) \sim t^{-\phi}$ with $\phi=1/(2-\gamma)$, using a scaling argument. We also investigate numerically the persistence exponent $\theta$ characterizing the power-law decay of the number, $N_p(t)$, of persistent (unflipped) spins at time $t$, and find $N_{p}(t)\sim t^{-\theta}$ where $\theta$ depends on $\gamma$. We show how the results for $\phi$ and $\theta$ are related to similar calculations in diffusion-limited cluster-cluster aggregation (DLCA) where clusters with size-dependent diffusion constant diffuse through an immobile `empty' phase and aggregate irreversibly on impact. Simulations show that, while $\phi$ is the same in both models, $\theta$ is different except for $\gamma=0$. We also investigate models that interpolate between symmetric domain diffusion and DLCA.Comment: 9 pages, minor revision