Related papers: Boundary effects in extended dynamical systems
We present a general method of analyzing the influence of finite size and boundary effects on the dynamics of localized solutions of non-linear spatially extended systems. The dynamics of localized structures in infinite systems involve…
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
Chaotic pattern dynamics in many experimental systems show structured time averages. We suggest that simple universal boundary effects underly this phenomenon and exemplify them with the Kuramoto-Sivashinsky equation in a finite domain. As…
The effect of a finite geometry on the two-dimensional complex Ginzburg-Landau equation is addressed. Boundary effects induce the formation of novel states. For example target like-solutions appear as robust solutions under Dirichlet…
The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into…
We consider domain walls (DW's) between single-mode and bimodal states that occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and complex Ginzburg-Landau (CGL) equations with a spatially dependent coupling coefficient.…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We study a chaotic particle-conserving kinetically constrained model, with a single parameter which allows us to break reflection symmetry. Through extensive numerical simulations we find that the domain wall state shows a variety of…
New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of…
The role of boundary layers in conventional liquid crystals is commonly subsumed in their anchoring on confining walls. In the classical view, anchoring enslaves the orientational field of the passive material under equilibrium conditions.…
External fluctuations have a wide variety of constructive effects on the dynamical behavior of spatially extended systems, as described by stochastic partial differential equations. A set of paradigmatic situations exhibiting such effects…
We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
Pattern dynamics triggered by fixing a boundary is investigated. By considering a reaction-diffusion equation that has a unique spatially-uniform and limit cycle attractor under a periodic or Neumann boundary condition, and then by choosing…
We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a Time-Dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled…
The interaction between bulk and dynamic domain wall in the presence of a linear / non-linear electromagnetism make energy density, tension and pressure on the wall all variables, depending on the wall position. In [1] this fact seems to be…
Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and…