Browsing by Author "Escaff, Daniel"
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Item 33(33, 33) Rosas, Alexandre; Cisternas, Jaime; Escaff, Daniel; Pinto, Italo'Ivo Lima Dias; Lindenberg, Katja; 33It is well established that ensembles of globally coupled stochastic oscillators may exhibit a nonequilibrium phase transition to synchronization in the thermodynamic limit (infinite number of elements). In fact, since the early work of Kuramoto, mean-field theory has been used to analyze this transition. In contrast, work that directly deals with finite arrays is relatively scarce in the context of synchronization. And yet it is worth noting that finite-number effects should be seriously taken into account since, in general, the limits N?? (where N is the number of units) and t?? (where t is time) do not commute. Mean-field theory implements the particular choice first N?? and then t??. Here we analyze an ensemble of three-state coupled stochastic units, which has been widely studied in the thermodynamic limit. We formally address the finite-N problem by deducing a Fokker-Planck equation that describes the system. We compute the steady-state solution of this Fokker-Planck equation (that is, finite N but t??). We use this steady state to analyze the synchronic properties of the system in the framework of the different order parameters that have been proposed in the literature to study nonequilibrium transitions.Item 33(33, 33) Cisternas, Jaime; Escaff, Daniel; Clerc, Marcel G.; Lefever, René; Tlidi, Mustapha; 33Nonuniform spatial distributions of vegetation in scarce environments consist of either gaps, bands often called tiger bush or patches that can be either self-organized or spatially localized in space. When the level of aridity is increased, the uniform vegetation cover develops localized regions of lower biomass. These spatial structures are generically called vegetation gaps. They are embedded in a uniform vegetation cover. The spatial distribution of vegetation gaps can be either periodic or randomly distributed. We investigate the combined influence of the facilitative and the competitive nonlocal interactions between plants, and the role of crow/root allometry, on the formation of gapped vegetation patterns. We characterize first the formation of the periodic distribution of gaps by drawing their bifurcation diagram. We then characterize localized and aperiodic distributions of vegetation gaps in terms of their snaking bifurcation diagram.Item Arrays of stochastic oscillators : Nonlocal coupling, clustering, and wave formation /(Escaff, Daniel) Escaff, DanielConsideramos una serie de unidades, cada una de las cuales puede estar en uno de los tres estados.Las transiciones unidireccionales entre estos estados se rigen por procesos de velocidad de Markovian. Las interacciones entre unidades ocurren a través de una dependencia de las tasas de transición de una unidad en los estados de las unidades con las que interactúa. Este acoplamiento no es local, es decir, no es una interacción de todos a todos (denominada acoplamiento global), ni es una interacción de vecino más cercano (denominado acoplamiento local). El acoplamiento se elige para desfavorecer la aglomeración de unidades que interactúan en el mismo estado. Como resultado, no hay sincronización global. En cambio, la configuración espacio-temporal resultante es uno de los grupos que se mueven a una velocidad constante y que puede interpretarse como ondas de viaje. Desarrollamos una teoría de campo medio para describir la formación de conglomerados y analizar analíticamente este modelo. Las predicciones del modelo se comparan favorablemente con los resultados obtenidos por simulaciones numéricas directas.Item Item Fronts connecting stripe patterns with a uniform state: Zigzag coarsening dynamics, and pinning effectClerc, Marcel G.; Escaff, Daniel; Rojas, René G.Item Self-organized spiral patterns at the edge of an order-disorder nonequilibrium phase transitionLima Dias Pinto, Italo'Ivo; Escaff, Daniel; Rosas, Alexandre