We study a system of hard-core particles sliding downwards on a fluctuating one-dimensional surface which is characterized by a dynamical exponent z. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale ∼ t 1/z . The structure factor deviates from the Porod law in some cases. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provides insight into the origin of this behaviour.PACS numbers: 05.70. Ln, 64.75.+g, 05.70.Jk How do density fluctuations evolve in a system of particles moving on a fluctuating surface? Can the combination of random vibrations and an external force such as gravity drive the system towards a state with large-scale clustering of particles? Such large-scale clustering driven by a fluctuating potential represents an especially interesting possibility for the behaviour of two coupled systems, one of which evolves autonomously but influences the dynamics of the other. Semi-autonomous systems are currently of interest in diverse contexts, for instance, advection of a passive scalar by a fluid [1], phase ordering in rough films [2], the motion of stuck and flowing grains in a sandpile [3], and the threshold of an instability in a sedimenting colloidal crystal [4].In this paper, we show that there is an unusual sort of phase ordering in a simple model of this sort, namely a system of particles sliding downwards under a gravitational field on a fluctuating one-dimensional surface. The surface evolves through its own dynamics, while the motion of particles is guided by local downward slopes; since random surface vibrations cause slope changes, they constitute a source of nonequilibrium noise for the particle system. The mechanism which promotes clustering is simple: fluctuations lead particles into potential minima or valleys, and once together the particles tend to stay together as illustrated in Fig. 1. The question is whether this tendency towards clustering persists up to macroscopic scales. We show below that in fact the particle density exhibits coarsening towards a phase-ordered state. This state has uncommonly large fluctuations which affect its properties in a qualitative way, and make it quite different from that in other driven, conserved, systems which exhibit coarsening [5].It is useful to state our principal results at the outset. (1) In an infinite system, an initially randomly distributed particle density exhibits coarsening with a characteristic growing length scale L(t) ∼ t 1/z where z is the dynamical exponent governing fluctuations of the surface. For some of the models we study, the scaled structure factor varies as |kL(t)| −(1+α) with α < 1, which represents a marked deviation from the Porod law (α = 1) for coarsening systems [6]. Further, a finite...

First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here we study the interplay between these two strategies, for a diffusing particle in an onedimensional trapping potential V (x), being randomly reset at a constant rate r. Stochastic resetting has been of great interest as it is known to provide an 'optimal rate' (r * ) at which the mean first passage time is a minimum. On the other hand an attractive potential also assists in first capture process. Interestingly, we find that for a sufficiently strong external potential, the advantageous optimal resetting rate vanishes (i.e. r * → 0). We derive a condition for this optimal resetting rate vanishing transition, which is continuous. We study this problem for various functional forms of V (x), some analytically, and the rest numerically. We find that the optimal rate r * vanishes with the deviation from critical strength of the potential as a power law with an exponent β which appears to be universal. PACS number(s): 05.40.-a,02.50.-r,02.50.Ey

We study an unconventional phase ordering phenomenon in coarse-grained depth models of the hill-valley profile of fluctuating surfaces with zero overall tilt, and for hard-core particles sliding on such surfaces under gravity. We find that several such systems approach an ordered state with large scale fluctuations which make them qualitatively different from conventional phase ordered states. We consider surfaces in the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ) and noisy surface-diffusion (NSD) universality classes. For EW and KPZ surfaces, coarse-grained depth models of the surface profile exhibit coarsening to an ordered steady state in which the order parameter has a broad distribution even in the thermodynamic limit, the distribution of particle cluster sizes decays as a power-law (with an exponent straight theta), and the scaled two-point spatial correlation function has a cusp (with an exponent alpha=1/2) at small values of the argument. The latter feature indicates a deviation from the Porod law which holds customarily, in coarsening with scalar order parameters. We present several numerical and exact analytical results for the coarsening process and the steady state. For linear surface models with a dynamical exponent z, we show that alpha=(z-1)/2 for z<3 and alpha=1 for z>3, and there are logarithmic corrections for z=3, implying alpha=1/2 for the EW surface and 1 for the NSD surface. Within the independent interval approximation we show that alpha+straight theta=2. We also study the dynamics of hard-core particles sliding locally downward on these fluctuating one-dimensional surfaces, and find that the surface fluctuations lead to large-scale clustering of the particles. We find a surface-fluctuation driven coarsening of initially randomly arranged particles; the coarsening length scale grows as approximately t(1/z). The scaled density-density correlation function of the sliding particles shows a cusp with exponents alpha approximately 0.5 and 0.25 for the EW and KPZ surfaces. The particles on the NSD surface show conventional coarsening (Porod) behavior with alpha approximately 1.

We study the coupled dynamics of the displacement fields in a one dimensional coupled-field model for drifting crystals, first proposed by R. S.Ramaswamy [Phys. Rev. Lett. 79, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model, for a special subspace in the parameter space, within the region where the model displays kinematic waves. We use these to construct the effective continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the long-time, large-distance properties of the correlation functions of the eigenmodes by using symmetry arguments, Monte Carlo simulations and self-consistent mode coupling methods. For most parameter values, the scaling exponents of the Kardar-Parisi-Zhang equation are obtained. However, for certain symmetry-determined values of the coupling constants the two eigenmodes, although nonlinearly coupled, are characterized by two distinct dynamic exponents. We discuss the possible application of the dynamic renormalization group in this context.