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In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the… (More)

This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the… (More)

In this paper, we shall propose a numerical scheme consisting of two steps: the first based relaxation method and the second on the so called well balanced scheme. The derivation of the scheme relies on the resolution of the stationnary Riemann problem with source terms. The obtained scheme is compatible with the diffusive regime of hydrodynamics radiative… (More)

- Stephane Cordier, Lorenzo Pareschi, Cyrille Piatecki
- 2010

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model [14, 15] using the methods of kinetic theory and consists of a linear Boltzmann equation for the… (More)

The aim of this note is to propose a definition of the scientific diversity and corollarly, a measure of the " interdisciplinarity " of collaborations. With respect to previous studies, the proposed approach consists of 2 steps : first, the definition of similarity between journals and second, these similarities are used to characterize the homogeneity (or,… (More)

In computational neuroscience, decision-making may be explained analyzing models based on the evolution of the average firing rates of two interacting neuron populations, e.g., in bistable visual perception problems. These models typically lead to a multi-stable scenario for the concerned dynamical systems. Nevertheless, noise is an important feature of the… (More)

In this paper, we propose two regularization approaches for the Boltz-mann collision operator. The constructed operators preserve the mass, momentum and energy; their equilibrium states are Maxwellians and they satisfy the H theorem. In the rst approach, the regularization consists in allowing microscopic collisions which do not exactly preserve energy and… (More)

In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D (http://www. univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for applications in hydrology) based on a domain decomposition strategy. The first approach is based on the classical MPI library while the second… (More)

We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem and holds on the whole phase space and not only locally around the spontaneous state. Macroscopic quantities, such as… (More)