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A quasi-variational inequality problem arising in the modeling of growing sandpiles

John W. Barrett, Leonid Prigozhin (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...

Dynamical critical exponent for two-species totally asymmetric diffusion on a ring.

Wehefritz-Kaufmann, Birgit (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...

Erdős-Renyi random graphs $+$ forest fires $=$ self-organized criticality.

Rath, Balazs, Toth, Balint (2009)

Electronic Journal of Probability [electronic only]

Random hysteresis loops

Gioia Carinci (2013)

Annales de l'I.H.P. Probabilités et statistiques

Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order $N^{- 2 / 3}$ , $N$ the size of the system, the “critical” hysteresis loop becomes random.