Spherical model of growing interfaces

Building on an analogy between the ageing behaviour of magnetic systems and growing interfaces, the Arcetri model, a new exactly solvable model for growing interfaces is introduced, which shares many properties with the kinetic spherical model. The long-time behaviour of the interface width and of the two-time correlators and responses is analysed. For all dimensions $d\ne 2$, universal characteristics distinguish the Arcetri model from the Edwards-Wilkinson model, although for $d>2$ all stationary and non-equilibrium exponents are the same. For $d=1$ dimensions, the Arcetri model is equivalent to the $p=2$ spherical spin glass. For $2<d<4$ dimensions, its relaxation properties are related to the ones of a particle-reaction model, namely a bosonic variant of the diffusive pair-contact process. The global persistence exponent is also derived.Comment: 33 pages, 4 figures, minor corrections. Final form, to appear in J.Stat.Mech. 05.40.-a, 05.70.Ln, 81.10.Aj, 02.50.-r, 68.43.D

La ville aujourd'hui entre public et privé

Notre communication consiste à montrer la perméabilité des espaces privés et publics dans la ville africaine, en insistant plus particulièrement sur la persistance des habitus communautaires, la précarité de l'existence et le rôle amplificateur de la crise qui sévit depuis plus d'une décennie. Pour le plus grand nombre, qui habite les quartiers populaires, se créer un chez-soi (un espace privé retranché de la sphère publique) est souvent impossible. Trois raisons essentielles à cela : le surpeuplement, le poids de la communauté et la fréquente utilisation de l'espace résidentiel comme lieu de travail. Si l'espace privé est ouvert sur l'extérieur, l'espace public est, en revanche, caractérisé par de multiples cloisonnements et tensions. Un examen géopolitique de la décennie 90 montre un espace public encore improbable ainsi qu'un ensemble de relations de concurrence et de connivence entre la culture publique et le sentiment communautariste : emergence du multipartisme, vagues de revendications ethnicistes et nouvelle constitution reconnaissant le droit du premier occupant émaillent cette situation politique très tendue. En cherchant à délimiter l'espace privé et l'espace public, on revient toujours à la communauté, ses logiques, ses obligations et ses systèmes de représentations. Dans le contexte africain, où l'espace public est de formation récente et les héritages autochtones conditionnent fortement le quotidien, la communauté reste un garant méta-social qui prend en charge les nombreux risques de la vie quotidienne. Le rapport à la mort et au deuil, illustre ce rôle primordial de la communauté et la centralité du village dans l'univers affectif des Camerounais. Les enterrements ont toujours lieu dans les villages et les cimetières urbains, communaux ou confessionnels, sont quasi inexistants... (D'après résumé d'auteur

Faster is More Different: Mean-Field Dynamics of Innovation Diffusion

Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally skewed in such a way that the fraction of innovators is substantially smaller than has been believed in conventional innovation-diffusion theory based on normality. Thus, the typical adoption pattern is predicted to be asymmetric with slow saturation in the ideal situation, which is compared with empirical data sets.Comment: 11 pages, 4 figure

Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process

The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe lattice. On a chain, this model is exactly solvable through the empty-interval method. This method can be extended to the Bethe lattice, in the ben-Avraham-Glasser approximation. On the Bethe lattice, the analysis of the Laplace-transformed time-dependent particle-density is analogous to the study of the stationary state, if a stochastic reset to a configuration of uncorrelated particles is added. In this stationary state logarithmic corrections to scaling are found, as expected for systems at the upper critical dimension. Analogous results hold true for the time-integrated particle-density. The crossover scaling functions and the associated effective exponents between the chain and the Bethe lattice are derived.Comment: 21 pages, 5 figures; v3: Scaling arguments at beginning of Section 4 were correcte

Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method

The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles meet. The exact two-time correlation and response function in the one-dimensional coagulation-diffusion process are derived from the empty-interval-particle method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the longtime ageing regime. A new generalised fluctuation-dissipation ratio with an universal and finite limit is proposed.Comment: 31 pages, submitted to J.Stat.Mec