Person: Tapiador Fernández, Bárbara
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Condiciones de contorno no reflectantes
En esta tesis hemos desarrollado condiciones de contorno no reflectantes en dos casos concretos. Por un lado, en modelos de crecimiento de burbujas de helio en plutonio, donde se produce un proceso de agregación molecular. Por otro, en sistemas de elasticidad discreta relacionados con la simulación de dinámica de defectos en nanocristales.
Nonreflecting boundary conditions for discrete waves
We introduce a new class of nonreflecting boundary conditions for lattice models, which minimizes reflections at artificial boundaries. Exact integrodifferential boundary conditions for finite chains and half-spaces are obtained by means of Green's functions for initial value problems. Truncating the resulting integrals in time, we obtain absorbing boundary conditions. Numerical tests illustrate the ability of these conditions to suppress reflections.
Analysis of helium bubble growth in radioactive waste
A discrete kinetic model for the growth of helium bubbles in plutonium is proposed and analyzed. This model captures some relevant qualitative features of the time behavior of the distribution of bubble sizes. Analytic formulae for the solutions are given, which agree reasonably well with the numerical solutions, and a rigorous existence theory is established for three different equivalent formulations.