相关论文: Nonequilibrium Growth problems

The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent…

We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise $f(t,{\bf x})$ is specified by the pair correlation function $\langle f(t,{\bf…

Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive…

Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…

Nonequilibrium phase transitions are discussed with emphasis on general features such as the role of detailed balance violation in generating effective (long-range) interactions, the importance of dynamical anisotropies, the connection…

We investigate the strong-coupling regime of the stationary Kardar-Parisi-Zhang equation for interfaces growing on a substrate of dimension d=1, 2, and 3 using a nonperturbative renormalization group (NPRG) approach. We compute critical…

Driven by breakthroughs in experimental and theoretical techniques, the study of non-equilibrium quantum physics is a rapidly expanding field with many exciting new developments. Amongst the manifold ways the topic can be investigated, one…

An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…

A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth…

In this paper we investigate the possibility of obtaining a measure representation for function- als arising in the context of optimal design problems under non-standard growth conditions and perimeter penalization. Applications to…

We present the formal geometric derivation of a nonequilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our…

Ballistic deposition (BD) is considered to be a paradigmatic discrete growth model that represents the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we question this connection by rigorously deriving a formal continuum…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

The steady state shock formation in processes like nonconserving asymmetric simple exclusion processes in varied situations is shown to be a nonequilibrium critical phenomenon. The diverging length scales and the quantitative description of…

This paper is concerned with the existence and uniqueness of weak solutions to the Cauchy-Dirichlet problem of backward stochastic partial differential equations (BSPDEs) with nonhomogeneous terms of quadratic growth in both the gradient of…

We study the dynamics of nonequilibrium instabilities in anisotropically expanding systems. The most prominent example of such a system is the 'Glasma' in the context of relativistic heavy-ion collision experiments, where the expansion is a…

In these lectures we give an overview of nonequilibrium stochastic systems. In particular we discuss in detail two models, the asymmetric exclusion process and a ballistic reaction model, that illustrate many general features of…

We study about order of growth and hyper order of growth of non trivial solutions of second order linear differential equations, having restrictions in the coefficients. These restrictions involve notions of Yang's inequality, Borel…

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the…

The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar Ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as…