相关论文: Persistence in nonequilibrium surface growth
The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears.…
We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $\zeta_c$ of the particle…
In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
We present results of numerical simulations to estimate scaling exponents associated with driven surface growth in two spatial dimensions. We have simulated the restricted solid--on--solid growth model and used the time and system size…
A review is provided of our current theoretical understanding of dynamic scaling in nonequilibrium interface growth as, for example, in MBE growth under ultrahigh vacuum deposition conditions.
We explore the dynamical stabilities of a quasi-one dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed $N$ atoms with time-independent external potential. For the stationary states with zero flow density the general…
We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d=7+1. To this end, we study the restricted solid - on - solid growth model,…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
We define a new model of interface roughening which has the property that the minimum of interface height is conserved locally during the growth. This model corresponds to the limit $q \to \infty$ of the q-color dimer deposition-evaporation…
In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium in which the periodicity is such that at long distances the behavior is always in the random-substrate universality class. This contrasts with the models with an…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by periodic driving of the interatomic interaction. We show that this modulation generically leads to a stable square grid density pattern, due to…
Local and global persistence exponents associated with zero temperature quenched dynamics of two dimensional XY model and three dimensional Heisenberg model have been estimated using numerical simulations. We have used the method of block…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
The properties of a wide variety of growing models, generically called $X/RD$, are studied by means of numerical simulations and analytic developments. The study comprises the following $X$ models: Ballistic Deposition, Random Deposition…
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),…
As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the…