Related papers: Boundary effects in extended dynamical systems
Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, as opposed to static, boundary condition…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Interaction of a domain wall with boundaries of a system is studied for a class of stochastic driven particle models. Reflection maps are introduced for the description of this process. We show that, generically, a domain wall reflects…
In the Ginzburg-Landau equation, there are domain walls connecting two metastable states. The dynamics of domain walls has been intensively studied, but there remain still unsolved but crucial problems even for a single domain. We study the…
We study the onset of dynamo action of the Riga and Karlsruhe experiments with the addition of an external wall, the electro-magnetic properties of which being different from those of the fluid in motion. We consider a wall of different…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
We illustrate the effect of boundary conditions on the evolution of structure in Fuzzy Dark Matter. Scenarios explored include the evolution of single, ground-state equilibrium solutions of the Schr\"odinger-Poisson system, the relaxation…
Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase equation, the interaction of such walls is…
We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of…
In this work, we introduce two spatio-temporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. We then study and characterize the dependence of the defined bounded noises on both a temporal…
We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found,…
We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…
To study the onset of a stationary dynamo in the presence of inner or outer walls of various electromagnetic properties, we propose a simple 1D-model in which the flow is replaced by an alpha effect. The equation of dispersion of the…
We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…
Sticky diffusion processes on bounded domains spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on…