Related papers: Interface pinning and slow ordering kinetics on in…
In a convex domain $\O\subset\R^3$, we consider the minimization of a 3D-Ginzburg-Landau type energy $E_\v(u)=1/2\int_\O|\n u|^2+\frac{1}{2\v^2}(a^2-|u|^2)^2$ with a discontinuous pinning term $a$ among $H^1(\O,\C)$-maps subject to a…
Orbitally ordered states exhibit unique features which make them a promising platform for exploring the ultrafast dynamics of long-range order in solids: Their free energy typically has multiple discrete minima, and electric laser fields or…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness, at any scale, of the…
We study a model for the pinning of vortices in a two-dimensional, inhomogeneous, Type-II superconductor in its mixed state. The model is based on a Ginzburg-Landau (GL) free energy functional whose coefficients are determined by the…
The non equilibrium relaxational dynamics of the solid on solid model on a disordered substrate and the Sine Gordon model with random phase shifts is studied numerically. Close to the super-roughening temperature $T_g$ our results for the…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…
A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized…
We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of…
We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…
We model the isotropic depinning transition of a domain-wall using a two dimensional Ginzburg-Landau scalar field instead of a directed elastic string in a random media. An exact algorithm accurately targets both the critical depinning…
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…
We derive an analytical approximation for the linear scaling evolution of the characteristic length $L$ and the root-mean-squared velocity $\sigma_v$ of standard frictionless domain wall networks in Friedmann-Lema\^itre-Robertson-Walker…
Phase field evolutions are obtained by means of time discrete schemes, providing (or selecting) at each time step an equilibrium configuration of the system, which is usually computed by descent methods for the free energy (e.g.staggered…
In this paper, we perform a detailed study of the scaling properties of a ferromagnetic thin film model. Recently, interest has increased in the scaling properties of the magnetic domain wall (MDW) motion in disordered media when an…
We studied a Lorentz-violating inspired Ginzburg-Landau model for superconductivity where we considered a CPT-odd contribution given by $(k_{AF})^{\mu}$, also known as the Carroll-Field-Jackiw term. In the static limit of the equations, we…
We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau-de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model…
Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…
Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…
We study domain growth kinetics in a random-field system in the presence of a spatially correlated disorder $h_{i}(\vec r)$ after an instantaneous quench at a finite temperature $T$ from a random initial state corresponding to $T=\infty$.…