相关论文: Generic equations for pattern formation in evolvin…
We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the…
In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species $N \ge 8$. We use…
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a…
Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competition between nonlinear and nonlocal processes in various…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can…
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
General features of the formalism describing hydrodynamic evolution of transversally thermalized matter possibly produced at the very early stages of ultra-relativistic heavy-ion collisions are presented. Thermodynamical consistency of the…
Common envelope evolution, the key orbital tightening phase of the traditional formation channel for close binaries, is a multistage process that presents many challenges to the establishment of a fully descriptive, predictive theoretical…
We establish universal relations between pattern formation and dissipation with a geometric approach to nonequilibrium thermodynamics of deterministic reaction-diffusion systems. We first provide a way to systematically decompose the…
The formalism of local maximization for entropy gradient producing the evolution and dynamical equations for closed systems. It eliminates the inconsistency between the reversibilty of time in dynamical equations and the strict direction of…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
We study the evolution of coherent structures in arbitrary turbulence phenomena, developing some tools, from non-archimedean analysis and algebraic geometry, in order to model its display. We match the scale-dependent, topological structure…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…