L'equació de les plantes invasores

Els fenòmens naturals poden ser analitzats amb models teòrics, molts dels quals es poden plasmar amb unes equacions matemàtiques més o menys sofisticades. Aquest és el repte que ha afrontat un equip de físics teòrics amb les plantes invasores: elaborar un model matemàtic que permeti descriure i predir la capacitat d'invasió d'una planta en un ecosistema estrany i la velocitat d'ocupació dels nous territoris. El model contempla el cicle de vida de la planta, el seu ritme de creixement, la maduració de les seves llavors... Els resultats han estat confirmats per a vàries plantes invasores en diferents ecosistemes.Los fenómenos naturales pueden ser analizados con modelos teóricos, muchos de los cuales se pueden plasmar con unas ecuaciones matemáticas más o menos sofisticadas. Este es el reto que ha afrontado un equipo de físicos teóricos con las plantas invasoras: elaborar un modelo matemático que permita describir y predecir la capacidad de invasión de una planta en un ecosistema extraño y la velocidad de ocupación de los nuevos territorios. El modelo contempla el ciclo de vida de la planta, su ritmo de crecimiento, la maduración de sus semillas... Los resultados han sido confirmados para varias plantas invasoras en diferentes ecosistemas

Irreversible thermodynamics of Poisson processes with reaction

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics

Matemàtiques per millorar les estratègies de cerca

Els processos pels quals es realitza una cerca, quan es busquen persones desaparegudes per exemple o quan els animals busquen aliments, han de ser el més eficients possible per a reduir al màxim el temps i l'energia necessaris. En aquest sentit, un grup d'investigadors del Departament de Física ha estudiat matemàticament les millors estratègies de cerca. Aquest treball ha contribuït a fer més realistes aquests càlculs matemàtics incloent la possibilitat de que l'objectiu estigui amagat i que, per tant, qui realitza la cerca pugui no trobar-lo quan estigui aprop. Aquest grup de la UAB segueix treballant en trobar models matemàtics que s'acostin cada vegada més a la realitat.Los procesos por los cuales se realiza una búsqueda, cuando se buscan personas desaparecidas por ejemplo o cuando los animales buscan alimentos, deben ser lo más eficientes posible para reducir al máximo el tiempo y la energía necesarios. En este sentido, un grupo de investigadores del Departamento de Física ha estudiado matemáticamente las mejores estrategias de búsqueda. Este trabajo ha contribuido a hacer más realistas estos cálculos matemáticos incluyendo la posibilidad de que el objetivo esté escondido y que, por tanto, quien realiza la búsqueda pueda no encontrarlo cuando este cerca. Este grupo de la UAB sigue trabajando en encontrar modelos matemáticos que se acerquen cada vez más a la realidad

Reaction-subdiffusion front propagation in a comblike model of spiny dendrites

Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions along dendrites are considered. In the framework of fractional subdiffusive comb model, we develop a Hamilton-Jacobi approach to estimate the overall velocity of the reaction front propagation. One of the main effects observed is the failure of the front propagation for both scenarios due to either the reaction inside the spines or the interaction of the reaction with the spines. In the first case the spines are the source of reactions, while in the latter case, the spines are a source of a damping mechanism

Population extinction and survival in a hostile environment

We study the conditions for extinction and survival of populations living in a patch surrounded by a hostile environment. We find analytic expressions for the steady states when population dynamics is described by diffusion and reaction is driven by compensation, depensation, or critical depensation growths. The role of initial population density is studied, and the complete bifurcation diagrams are constructed and validated numerically for the three cases studied

Continuous-time random walks and traveling fronts

We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher-Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processe

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Nonuniversality and the role of tails in reaction-subdiffusion fronts

Recently there has been a certain controversy about the scaling properties of reaction-subdiffusion fronts. Some works seem to suggest that these fronts should move with constant speed, as do classical reaction-diffusion fronts, while other authors have predicted propagation failure, i.e., that the front speed tends asymptotically to zero. In the present work we confirm by Monte Carlo experiments that the two situations can actually occur depending on the way the reaction process is implemented. Also, we present a general analytical model that includes these two different behaviors as particular cases. From our analysis, we reach two main conclusions. First, the differences found in the scaling properties show the lack of universality of reaction-subdiffusion fronts. Second, we prove that, contrary to the widespread belief, the tail of the waiting time distributions is not always decisive to determine the speed of these fronts, but sometimes it plays just a marginal role in the front dynamics

Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Front propagation in hyperbolic fractional reaction-diffusion equations

From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition, we find fronts exhibiting an unphysical behavior: they travel faster in the subdiffusive than in the diffusive regime