Studying nonlinear effects on the early stage of phase ordering using a decomposition method

Nonlinear effects on the early stage of phase ordering are studied using Adomian's decomposition method for the Ginzburg-Landau equation for a nonconserved order parameter. While the long-time regime and the linear behavior at short times of the theory are well understood, the onset of nonlinearities at short times and the breaking of the linear theory at different length scales are less understood. In the Adomian's decomposition method, the solution is systematically calculated in the form of a polynomial expansion for the order parameter, with a time dependence given as a series expansion. The method is very accurate for short times, which allows to incorporate the short-time dynamics of the nonlinear terms in a analytical and controllable way.Comment: 11 pages, 1 figure, to appear in Phys Lett

Numerical analysis of a quasi-static contact problem for a thermoviscoelastic beam

AbstractIn this paper we revisit a quasi-static contact problem of a thermoviscoelastic beam between two rigid obstacles which was recently studied in [1]. The variational problem leads to a coupled system, composed of an elliptic variational inequality for the vertical displacement and a linear variational equation for the temperature field. Then, its numerical resolution is considered, based on the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Error estimates are proved from which, under adequate regularity conditions, the linear convergence is derived. Finally, some numerical simulations are presented to show the accuracy of the algorithm and the behavior of the solution

Numerical analysis of a model for phase separation of a multicomponent alloy.

We consider a fully discrete implicit finite-element approximation of a model for the phase separation of a multi-component alloy. We prove existence, uniqueness and stability of the numerical solution for a sufficiently small time step. We prove convergence to the solution of the associated continuous problem. We perform a linear stability analysis of the equation and describe some numerical experiments

Numerical analysis of a dual-phase-lag model with microtemperatures

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGIn the last twenty years, the analysis of problems involving dual-phase-lag models has received an increasing attention. In this work, we consider the coupling between one of these models and the microtemperatures effects. In order to overcome the infinite speed paradox, two relaxation parameters are introduced for each evolution equation related to the temperature and the microtemperatures, leading to a system of linear hyperbolic partial differential equations. Its variational formulation is written in terms of the temperature acceleration and the microtemperatures acceleration. An energy decay property is proved. Next, fully discrete approximations are introduced by using the finite element method and the Euler scheme, proving a stability property and a discrete version of the energy decay, obtaining a priori error estimates and performing one- and two-dimensional numerical simulationsConselho Nacional de Desenvolvimento Científico e Tecnológico, Brasil | Ref. 304709 / 2017-4Ministerio de Ciencia, Innovación y Universidades | Ref. PGC2018-096696-B-I00Ministerio de Ciencia, Innovación y Universidades | Ref. PID2019-105118GB-I0