Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

Time-delayed fronts from biased random walks

We generalize a previous model of time-delayed reaction–diffusion fronts (Fort and Méndez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

La UdG, centre neuràlgic del món del turisme

La xarxa dels Centres de Recerca de Catalunya implica una aposta decidida del govern català per fer aflorar, dotar de contingut i expandir totes aquelles àrees de coneixement que, d’una manera o altra, representen un punt i a part en el panorama de la investigació a Catalunya. Girona disposa en l’actualitat de dos d’aquests centres: l’Institut Català de Recerca en Patrimoni Cultural i l’Institut Català de Recerca de l’Aigua; i s’està a l’expectativa sobre la destinació final de l’IRTUCA (Institut de Recerca en Turisme de Catalunya)

Anisotropic dispersion, space competition, and the slowdown of the Neolithic transition

The front speed of the Neolithic (farmer) spread in Europe decreased as it reached Northern latitudes, where the Mesolithic (huntergatherer) population density was higher. Here, we describe a reaction diffusion model with (i) an anisotropic dispersion kernel depending on the Mesolithic population density gradient and (ii) a modified population growth equation. Both effects are related to the space available for the Neolithic population. The model is able to explain the slowdown of the Neolithic front as observed from archaeological data

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Aproximació hermenèutica al "tolle, lege" agustinià. Per una lectura al·legòrica de Confessions VIII, 6-12

Aquest treball gira entorn a la controvèrsia que, des de finals del segle XIX, va generar el passatge de les Confessions (VIII, 6-12) on Agustí relata la seva crisi decisiva, viscuda a Milà l'estiu de l'any 386, que l'acabaria portant a l'aparent definitiva conversió al cristianisme. Els motius de fons de la controvèrsia són dos de clars. En primer lloc, i a la llum del que nosaltres entenem per gènere autobiogràfic, s'imposa aclarir si un relat com el de les Confessions s'hi pot adscriure, i per tant si ens relata una sèrie d'esdeveniments viscuts per Agustí històricament, o bé si cal interpretar els elements que l'autor desplega al llarg de la narració com a símbols d'un missatge que supera la narració que es troba a la superfície. La segona qüestió, directament vinculada a la primera, és el sentit que cal donar a aquesta conversió en relació a la noció de forma de vida filosòfica, i la influència que tindrà aquesta noció en la biografia i el pensament d'Agustí.