The onset of tree-like patterns in negative streamers

We present the first analytical and numerical studies of the initial stage of the branching process based on an interface dynamics streamer model in the fully 3-D case. This model follows from fundamental considerations on charge production by impact ionization and balance laws, and leads to an equation for the evolution of the interface between ionized and non-ionized regions. We compare some experimental patterns with the numerically simulated ones, and give an explicit expression for the growth rate of harmonic modes associated with the perturbation of a symmetrically expanding discharge. By means of full numerical simulation, the splitting and formation of characteristic tree-like patterns of electric discharges is observed and described

Evolution and breakup of viscous rotating drops

We study the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity $Omega$ or constant angular momentum L surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. The analysis is carried out by combining asymptotic analysis and full numerical simulation by means of the boundary element method. We pay special attention to the stability/instability of equilibrium shapes and the possible formation of singularities representing a change in the topology of the fluid domain. When the evolution is at constant $Omega$, depending on its value, drops can take the form of a flat film whose thickness goes to zero in finite time or an elongated filament that extends indefinitely. When evolution takes place at constant L and axial symmetry is imposed, thin films surrounded by a toroidal rim can develop, but the film thickness does not vanish in finite time. When axial symmetry is not imposed and L is sufficiently large, drops break axial symmetry and, depending on the value of L, reach an equilibrium configuration with a 2-fold symmetry or break up into several drops with a 2- or 3-fold symmetry. The mechanism of breakup is also describe

Resolucion de las ecuaciones de deriva-difusion mediante un método de difusion artificial. Aplicación a dispositivos semiconductores

En este artículo se propone un nuevo método de difusión artificial para la resolución del sistema de ecuaciones en derivadas parciales que representa el comportamiento de un dispositivo semiconductor en estado estacionario según el modelo clásico de deriva difusión. El método de difusión artificial consiste en añadir a dos de las ecuaciones del sitema términos difusivos provenientes de la discretización del problema transitorio a lo largo de las curvas características. Tras formular el sistema con estos nuevos términos, se compara su estabilidad con la del sistema inicial, para estudiar en qué situaciones es rentable aplicar el método. A continuación se aproxima numéricamente el sistema modificado, con el objetivo de obtener resultados que contrasten la comparación teórica anterior