Seminarios 2011

De Cadedif

Contenido 1 (Jueves 25-XI-2011) Roberto Rodríguez del Río, UCM 2 (Jueves 10-III-2011) Peter Kloeden (Johann Wolfgang Goethe-Universita ̈t Frankfurt am Main, Alemania) 3 (Jueves 17-III-2011) Peter Kloeden (Johann Wolfgang Goethe-Universita ̈t Frankfurt am Main, Alemania) 4 (Jueves 28-IV-2011) Leandro del Pezzo (Universidad de Buenos Aires, Argentina) 5 (Martes 5-VII-2011) María Vela-Pérez (UCM)

(Jueves 25-XI-2011) Roberto Rodríguez del Río, UCM

Título: La Ecuación de la Naturaleza.

Resumen: Uno de los grandes retos que se plantea la Ciencia actualmente es la unificación de las teorías de la Física. Se trata de buscar modelos matemáticos que se ajusten a las leyes de la Naturaleza. En esta charla se abordarán algunas de estas cuestiones desde un punto de vista no técnico.

de 13:00 a 14:00, Aula QB65 (planta 6 del pabellón B, Facultad de Ciencias Químicas, UCM)

(Jueves 10-III-2011) Peter Kloeden (Johann Wolfgang Goethe-Universita ̈t Frankfurt am Main, Alemania)

Título: Semihiperbolicity and conjugacy in Dynamical Systems.

de 15:00 a 16:00, Aula QB64 (planta 6 del pabellón B, Facultad de Ciencias Químicas, UCM)

(Jueves 17-III-2011) Peter Kloeden (Johann Wolfgang Goethe-Universita ̈t Frankfurt am Main, Alemania)

Título: Taylor expansions and numerical approximation of stochastic PDEs.

de 15:00 a 16:00, Aula QB64 (planta 6 del pabellón B, Facultad de Ciencias Químicas, UCM)

(Jueves 28-IV-2011) Leandro del Pezzo (Universidad de Buenos Aires, Argentina)

Título: Método de Galerkin discontinuo para el p(x)-Laplaciano.

de 12:30 a 13:30, Aula QB66 (planta 6 del pabellón B, Facultad de Ciencias Químicas, UCM)

(Martes 5-VII-2011) María Vela-Pérez (UCM)

Título: Geodesic paths in simple graphs and the plane for some social insects.

Resumen: Social insects are an important example of complex collective behavior. In particular, ant colonies develop different tasks as foraging, building and allocation [1]. While they search for food they deposit a pheromone that it is considered as a crucial element in the mechanism for finding minimal paths. The experimental observations suggest that the model should include the presence of pheromone and the persistence (tendency to follow straight paths in the absence of other effects). In our study, we will consider ants as random walkers where the probabil- ity to move in one or another direction is influenced by the concentration of pheromone near them (reinforced random walks). We are mainly interested not in an individual random walker but rather on a large number of random walkers, their collective behavior, and the possibility for them to aggregate forming geodesic paths between two points in some simple networks. We investigate the behavior of ants in a two node network and in a three node network (with and without directionality constraint). Our analytical and computational results show that in order for the ants to follow shortest paths between nest and food, it is necessary to superimpose to the ants’ random walk the chemotactic reinforcement. It is also needed a certain degree of persistence so that ants tend to move preferably without changing their direction much. Another important fact is the number of ants, since we will show that the speed for finding minimal paths increases very fast with it. Furthermore, we investigate numerically the behavior of ants in some general graphs and the plane. We develop several simulations to see that ants follow geodesic paths taking into account both reinforcement and persistence.

de 13:00 a 14:00, Aula QB66 (planta 6 del pabellón B, Facultad de Ciencias Químicas, UCM)