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We present results of numerical studies of the Landau-Ginzburg dynamics of the order parameter in one-dimensional models inspired by the condensed matter analogues of cosmological phase transitions. The main goal of our work is to show…
In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white…
We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schr\"odinger equation with…
Accurate prediction of damage and fracture evolution is critical for the safety design and preventive maintenance of engineering structures, however existing computational methods face significant limitations. On one hand, discrete damage…
We consider the problem of dynamical stability for the $n$-vortex of the Ginzburg-Landau model. Vortices are one of the main examples of topological solitons, and their dynamic stability is the basic assumption of the asymptotic ``particle…
We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies.The calculation is performed both to one-loop and in a…
We study the Landau model for uniaxial incommensurate-commensurate systems of the I class by keeping Umklapp terms of third and fourth order in the expansion of the free energy. It applies to systems in which the soft mode minimum lies…
We study electromigration in a driven diffusive lattice gas (DDLG) whose continuous Monte Carlo dynamics generate higher particle mobility in areas with lower particle density. At low vacancy concentrations and low temperatures, vacancy…
The differential conductivity for the out-of-plane transport in layered cuprates is calculated for Lawrence-Doniach model in the framework of time-dependent Ginzburg-Landau (TDGL) theory. The TDGL equation for the superconducting order…
We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a $d$-dimensional lattice. If the system is sufficiently localized, we show that, starting from a broad class of initial product…
The $\lambda \phi^4$ model in a finite volume is studied within a non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of equilibrium, with particular attention to the structure of the ground state and of certain…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
We investigate, via numerical simulations, the phase ordering kinetics of a two- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible mode cou- pling is included via the conserved conjugate momentum of the spin order parameter…
We present an analytical treatment of a three-dimensional variational model of a system that exhibits a second-order phase transition in the presence of dipolar interactions. Within the framework of Ginzburg-Landau theory, we concentrate on…
We explore dynamics of disordered and quasi-periodic interacting lattice models using a self-consistent time-dependent Hartree-Fock (TDHF) approximation, accessing both large systems (up to $L = 400$ sites) and very long times (up to $t =…
A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition.…
Ordering processes in fcc-alloys with composition A_3B (like Cu_3Au, Cu_3Pd, CoPt_3 etc.) are investigated by Monte Carlo simulation within a class of lattice models based on nearest-neighbor (NN) and second-neighbor (NNN) interactions.…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…