Related papers: Cahn-Hilliard Equations on Lattices: Dynamic Trans…
Fast-slow systems are studied usually by "geometrical dissection". The fast dynamics exhibit attractors which may bifurcate under the influence of the slow dynamics which is seen as a parameter of the fast dynamics. A generic solution comes…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling…
The system of mixed hexagonal and square lattices on a spherical surface is examined, with an emphasis on the exploration of the disclination patterns that form in the square-rich regime. To demonstrate the possible outcomes, the Hertzian…
Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
Based on the mean-field method applied either to the extended single-band Hubbard model or to the single-band Peierls-Hubbard Hamiltonian we study the stability of both site-centered and bond-centered charge domain walls. The difference in…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time…
A combination of cellular contractility and active phase separation in cell-matrix composites is thought to be an enabler of spatiotemporal patterning in multicellular tissues across scales, from somitogenesis to cartilage condensation. To…
Using extensive particle-based simulations, we investigate out-of-equilibrium pattern dynamics in an oppositely driven binary particle system in two dimensions. A surprisingly rich dynamical behavior including lane formation, jamming,…
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity…
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform,…
We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one and two dimensional systems. The model describes the lattice system…
In this thesis, we consider some spin effects in QCD and recurrence lattices with multi-site exchanges. Main topic of our manuscript are critical phenomena in spin systems defined on the recurrence lattices. Main tool of our approach is the…