Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations

We study the KPZ equation (in D = 2, 3 and 4 spatial dimensions) by using a RSOS discretization of the surface. We measure the critical exponents very precisely, and we show that the rational guess is not appropriate, and that 4D is not the upper critical dimension. We are also able to determine very precisely the exponent of the sub-leading scaling corrections, that turns out to be close to 1 in all cases. We introduce and use a {\em multi-surface coding} technique, that allow a gain of order 30 over usual numerical simulations.Comment: 10 pages, 8 eps figures (2 figures added). Published versio

Phase-ordering of conserved vectorial systems with field-dependent mobility

The dynamics of phase-separation in conserved systems with an O(N) continuous symmetry is investigated in the presence of an order parameter dependent mobility M(\phi)=1-a \phi^2. The model is studied analytically in the framework of the large-N approximation and by numerical simulations of the N=2, N=3 and N=4 cases in d=2, for both critical and off-critical quenches. We show the existence of a new universality class for a=1 characterized by a growth law of the typical length L(t) ~ t^{1/z} with dynamical exponent z=6 as opposed to the usual value z=4 which is recovered for a<1.Comment: RevTeX, 8 pages, 13 figures, to be published in Phys. Rev.

Variables and distance covered during the World Cup Southafrica'10

El objetivo de este trabajo fue relacionar las variables contextuales y la velocidad media de los desplazamientos realizados por los equipos que participaron durante la Copa del Mundo Sudáfrica 2010. Se estudiaron 128 registros, medidos a través de la velocidad media en metros por minuto (m∙min1), durante los 64 partidos celebrados. Las variables contextuales fueron: tipo de competición, continente, resultado del partido, ranking FIFA del equipo y ranking FIFA del rival. Únicamente se han encontrado diferencias significativas en las variables continente (F=3,861;p=0,005) y resultado del partido en interacción con tipo de competición (F=3,999;p=0,029). Los resultados de este trabajo permiten aumentar el conocimiento referente a la influencia de las diferentes variables contextuales en la intensidad de desplazamiento de los equipos mientras disputan un partido de competición y, en consecuencia, gestionar la importancia de estos requerimientos energéticos con relación a la evaluación del rendimiento físicoThe aim of this study was to determine whether there is any influence from different contextual variables on the physical performance of the teams during the South African World Cup 2010. The physical performances of 128 teams were studied, measured by distance travelled in meters per minute (m∙min-1), during the 64 matches played in South Africa 2010. The contextual variables were: type of competition, continent, match score, FIFA team ranking, and FIFA opponent ranking. Significant differences were found only in the continent variable (F=3.86,p=0.005) and match score in interaction with type of competition (F=3.999,p=0.029). The results of this study provide increasing knowledge concerning the influence of contextual variables on the physical demands on teams during a competition match and, therefore, will help to manage the importance of these energy requirements in relation to physical performanc

The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions

We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.Comment: 22 pages, 10 figures. To appear in Phys. Rev.

Statistical physics of the Schelling model of segregation

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics methods shed light on the rich phenomenology of this simple model, exhibiting static phase transitions typical of kinetic constrained models, nontrivial coarsening like in driven-particle systems and percolation-related phenomena.Comment: 4 pages, 3 figure

Routes to thermodynamic limit on scale-free networks

We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct dependence on the upper cutoff k_c of the degree distribution. Since the infinite network limit can be obtained by allowing k_c to diverge with the system size in an arbitrary way, this result implies that there are different routes to the thermodynamic limit in scale-free networks. The contact process (in its mean-field version) belongs to this second class and thus our results clarify the recent discrepancy between theory and simulations with different scaling of k_c reported in the literature.Comment: 5 pages, 3 figures, final versio

Solution of voter model dynamics on annealed small-world networks

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale $\tau$ separates a quasi-stationary disordered state with coexisting domains from a fully ordered frozen configuration. $\tau$ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.Comment: 11 pages, 4 figures, published version. Added section with extension to generic number of nearest neighbor