Related papers: Domain wall propagation and nucleation in a metast…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
The characteristic size for spatial structure, that emerges when the bifurcation parameter in model partial differential equations is slowly increased through its critical value, depends logarithmically on the size of added noise. Numerics…
In the domain growth process, small structures gradually vanish, leaving behind larger ones. We investigate spectral energy transfers in two standard models for domain growth: (a) the {\it Cahn-Hilliard} (CH) equation with conserved…
Domain walls formed during a phase transition in a simple field theory model with $\mathbb{Z}_2$ symmetry in a periodic box have been demonstrated to annihilate as fast as causality allows and their area density scales $\propto t^{-1}$. We…
We study some properties of a multi-species degenerate Ginzburg-Landau energy and its relation to a cross-diffusion Cahn-Hilliard system. The model is motivated by multicomponent mixtures where crossdiffusion effects between the different…
The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the…
We investigate the geometric evolution of elastic domain-wall loops in two dimensions. Assuming an instantaneous, isotropic, and homogeneous arc-velocity response of the domain wall to external pressure and local signed curvature, we derive…
We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the…
The interaction of electric field with charged domain walls in ferroelectrics is theoretically addressed. A general expression for the force acting per unit area of a charged domain wall carrying free charge is derived. It is shown that, in…
We study the dynamics of the equation obtained by Schryer and Walker for the motion of domain walls. The reduced equation is a reaction diffusion equation for the angle between the applied field and the magnetization vector. If the hard…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
We propose a mathematical model for describing propagating confined modes in domain walls of intermediate angle between domains. The proposed model is derived from the linearised Bloch equations of motion and after reasonable assumptions,…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
We consider a nonequilibrium reaction-diffusion model on a finite one dimensional lattice with bulk and boundary dynamics inspired by Glauber dynamics of the Ising model. We show that the model has a rich algebraic structure that we use to…
This article presents a phenomenological dynamic phase transition theory -- modeling and analysis -- for superfluids. As we know, although the time-dependent Ginzburg-Landau model has been successfully used in superconductivity, and the…
Time-dependent Ginzburg-Landau model with noise for neutral s-wave superconductor is derived from real-time finite-temperature quantum field theory by integrating over fermions in the density matrix propagator. Quantum decoherence due to…
We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of…
The environment of a quantum dot, which is connected to two leads, is modeled by telegraph noise, i.e. random Markovian jumps of the (spinless) electron energy on the dot between two levels. The temporal evolutions of the charge on the dot…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…