Birth, death and diffusion of interacting particles

Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth dynamics is mediated by the local, within a given distance, density of particles. Groups of individuals are formed in the system and in this paper we concentrate on the study of the properties of these clusters (lifetime, size, and collective diffusion). In particular, in the limit of the interaction distance approaching the system size, a unique cluster appears which helps to understand and characterize the clustering dynamics of the model.Comment: 15 pages, 6 figures, Iop style. To appear in Journal of Physics A: Condensed matte

One-dimensional relativistic dissipative system with constant force and its quantization

For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.Comment: 11 pages, no figure

Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by L\'evy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.Comment: This version incorporates in the text the correction published as an Erratum in Europhysics Letters (EPL) 95, 69902 (2011) [doi: 10.1209/0295-5075/95/69902

Angular asymptotics for random walks

We study the set of directions asymptotically explored by a spatially homogeneous random walk in d-dimensional Euclidean space. We survey some pertinent results of Kesten and Erickson, make some further observations, and present some examples. We also explore links to the asymptotics of one-dimensional projections, and to the growth of the convex hull of the random walk

Estudio biométrico de la abeja melífera (Apis mellifera, Linneo 1758) (Hymenoptera, Apidae) de la isla de La Palma del Archipiélago Canario. II. Ángulos y longitudes de las alas.

The honey bees (A. mellifera L.) from the island of La Palma constitute a morphological group within which differences related to the geographical location of the apiaries are difficult to distinguish, probably due to the buying and selling of hives among beekeepers, and also to the migratory style of bee-keeping practised on the island. We have also studied the possible relationship of these bees with A. m. intermissa, which is distributed throughout the north of Africa, and with A. m. iberica in the Iberian Peninsula. Our results indicate that these bees are probably the result of a cross between these two races followed by selection of the best genotypes adapted to the environmental conditions.Las abejas meliferas (A. mellifera L.) oriundas de la isla de La Palma constituyen un grupo morfológico, en el que no podemos apreciar diferencias relacionadas con la localización geográfica de los colmenares; probablemente esto sea debido a las prácticas de compra-venta de colmenas entre los apicultores, y a la transhumancia practicada dentro de la isla. También hemos estudiado la posible relación de parentesco de estas abejas con la raza que se distribuye por el norte de África (A. m. intermissa), o con la que se localiza en la Península Ibérica (A. m. iberica). Los resultados obtenidos nos indican que probablemente estos animales sean el resultado de un proceso cruce entre las dos razas, y posterior selección de los genotipos mejor adaptados a unas determinadas condiciones ambientales