Related papers: Dynamic exponent in Extremal models of Pinning
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…
Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104…
Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the homogeneous case (with velocity $v_0$) and deterministic…
We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion…
The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an…
We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition,…
Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\zeta$ of driven elastic strings at the depinning threshold in 1+1 dimensions for different functional forms of the (short-range)…
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
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…
We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…
The problem of random walk is considered in one dimension in the simultaneous presence of a quenched random force field and long-range connections the probability of which decays with the distance algebraically as p_l ~ \beta l^{-s}. The…
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…
We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are…
We study the susceptible-infected model with power-law waiting time distributions $P(\tau)\sim \tau^{-\alpha}$, as a model of spreading dynamics under heterogeneous human activity patterns. We found that the average number of new infections…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a…
We argue that while fluctuating fronts propagating into an unstable state should be in the standard KPZ universality class when they are {\em pushed}, they should not when they are {\em pulled}: The universal $1/t$ velocity relaxation of…
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…