Related papers: Spherical model of growing interfaces

We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on…

We propose a simple effective model for the description of interfaces in 2d statistical models, based on the first-order treatment of an action corresponding to the length of the interface. The universal prediction of this model for the…

Two canonical models of statistical mechanics, the fully-connected voter and Glauber-Ising models, are modified to incorporate growth via the addition or replication of spins. The resulting behaviour is examined in a regime where the…

We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…

We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and…

We present a comprehensive study of non-equilibrium phenomena in the low temperature phase of the Edwards-Anderson Gaussian spin glass in 3 and 4 spatial dimensions. Many effects can be understood in terms of a time dependent coherence…

We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of phase field and a Cahn-Hilliard…

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy…

The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions,…

We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in four dimensions under the influence of a non-hamiltonian perturbation. We find that for small asymmetry the model behaves as the hamiltonian one, while for large…

We study the interface representation of the contact process (CP) at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a…

We consider a version of a Glauber dynamics for a p-spin Sherrington--Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the N-dimensional hypercube. We show that, for any p>2 and any inverse…

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes…

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…

The shape of large on-lattice Eden clusters grown from a single seed is ruled by the underlying lattice anisotropy. This is reflected on the linear growth with time of the interface width ($w\sim t$), in contrast with the KPZ universality…

We analyze by means of extensive computer simulations the out of equilibrium dynamics of Edwards-Anderson spin glasses in d=4 and d=6 dimensions with +-J interactions. In particular, we focus our analysis on the scaling properties of the…

This lecture deals with glassy dynamics and aging in disordered systems. Special emphasis is put on dynamic mean field theory. In the first part I present some of the systems of interest, in particular spin-glasses, supercooled liquids and…

We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…

We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface,…