Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models Part I: The Thomas-Fermi-von Weizacker model. (arXiv:0909.1464v1 [math.NA])

We provide {it a priori} error estimates for the spectral and pseudospectral
Fourier (also called planewave) discretizations of the periodic
Thomas-Fermi-von Weizs"acker (TFW) model and of the Kohn-Sham model, within
the local density approximation (LDA). These models allow to compute
approximations of the ground state energy and density of molecular systems in
the condensed phase. The TFW model is stricly convex with respect to the
electronic density, and allows for a comprehensive analysis (Part I). This is
not the case for the Kohn-Sham LDA model, for which the uniqueness of the
ground state electronic density is not guaranteed. Under a coercivity
assumption on the second order optimality condition, we prove in Part II that
for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a
minimizer in the vicinity of any Kohn-Sham ground state, and that this
minimizer is unique up to unitary transform. We then derive optimal {it a
priori} error estimates for both the spectral and the pseudospectral
discretization methods.

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Original source : http://arxiv.org/abs/0909.1464...

Ayudantia 08092009 - Juego de vida de Conway 23/3

Un applet donde se implementa el Juego de Vida de Conway y otros mas...

link applet --- http://www.ibiblio.org/lifepatterns/

Codigo Fuente del Juego de Vida de Conway

codigo fuente 23/3 ---- http://adrigm.es/2008/12/otra-version-del-juego-de-la-vida/

Paper de 1970 con la definición de los primeros patrones

articulo original Conway --- http://www.ibiblio.org/lifepatterns/october1970.html

Investigador, Matematico, Programador, encontro los primeros patrones de crecimiento indefinido
Bill Gosper --- http://es.wikipedia.org/wiki/Bill_Gosper

Tarea: Implementar un Autómata Celular equivalente a una Máquina Universal de Turing (Turing-Completo) que genere números primos. En las proximas ayudantías se darán los detalles de la tarea, forma de entrega y los plazos.