On a kinetic model for a simple market economy

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 distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.Econophysics;Boltzmann equation;wealth and income distributions;Fokker Planck model; Monte Carlo simulations; Pareto distribution

One dimensional Fokker-Planck reduced dynamics of decision making models in Computational Neuroscience

We study a Fokker-Planck equation modelling the firing rates of two interacting populations of neurons. This model arises in computational neuroscience when considering, for example, bistable visual perception problems and is based on a stochastic Wilson-Cowan system of differential equations. In a previous work, the slow-fast behavior of the solution of the Fokker-Planck equation has been highlighted. Our aim is to demonstrate that the complexity of the model can be drastically reduced using this slow-fast structure. In fact, we can derive a one-dimensional Fokker-Planck equation that describes the evolution of the solution along the so-called slow manifold. This permits to have a direct efficient determination of the equilibrium state and its effective potential, and thus to investigate its dependencies with respect to various parameters of the model. It also allows to obtain information about the time escaping behavior. The results obtained for the reduced 1D equation are validated with those of the original 2D equation both for equilibrium and transient behavior

Mesoscopic modelling of financial markets

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investments alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model under a suitable scaling we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis.wealth distribution, power-law tails, stock market, self-similarity, kinetic equations.

A limitation of the hydrostatic reconstruction technique for Shallow Water equations

Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical flux, allows to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid unstabilities when dealing with dry zones. In this note, we prove that this method exhibits an abnormal behavior for some combinations of slope, mesh size and water height.Comment: 7 page

An analytical solution of Shallow Water system coupled to Exner equation

In this paper, an exact smooth solution for the equations modeling the bedload transport of sediment in Shallow Water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter & Muller. One of the main interest of this solution is the derivation of numerical benchmarks to valid the approximation methods

An asymptotic preserving scheme for Hydrodynamics Radiative Transfert Models

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 transfert models. Some numericalresults are shown

Novel Ternary Oxobromides with Ta6 Clusters and Rare Earths: The Synthesis of (RE)Ta6Br13O3 (RE = Rare Earth) and the Crystal Structure of LuTa6Br13O3

Crystallochemistry of the novel oxobromides (RE)TagBr1803 with RE = Sm to Lu (except Eu and Yb) is reported. All these compounds, which exhibit 14 valence electrons per Tag cluster, are isotypic with ScNbgCl^Og with the space group 74x22. The structure of LuTagBrxgOg has been determined from single crystal X-ray diffraction: a = 9.383(1) Å and c = 54.60(1) Å, R = 0.050 and Rw = 0.054 for 755 symmetry-independent reflections. For this compound, the (TagL18) units (L = Br and O), in which the Tag cluster is very distorted, are linked together by four bridging bromines to form pseudo-helices of units. The lutetium is five-coordinated at a small site formed by three oxygen and two bromine atoms belonging to three adjacent units. The formula developed for this compound is Lu(TagBr91031)Br2aBr4/2a_a. These structural results allow discussion of the influence of interatomic distances on the potential properties of these novel ternary tantalum oxobromides in relation to the oxidation state of the cluster

Over-populated Tails for conservative-in-the-mean Inelastic Maxwell Models

We introduce and discuss spatially homogeneous Maxwell-type models of the nonlinear Boltzmann equation undergoing binary collisions with a random component. The random contribution to collisions is such that the usual collisional invariants of mass, momentum and energy do not hold pointwise, even if they all hold in the mean. Under this assumption it is shown that, while the Boltzmann equation has the usual conserved quantities, it possesses a steady state with power-like tails for certain random variables. A similar situation occurs in kinetic models of economy recently considered by two of the authors [24], which are conservative in the mean but possess a steady distribution with Pareto tails. The convolution-like gain operator is subsequently shown to have good contraction/expansion properties with respect to different metrics in the set of probability measures. Existence and regularity of isotropic stationary states is shown directly by constructing converging iteration sequences as done in [8]. Uniqueness, asymptotic stability and estimates of overpopulated high energy tails of the steady profile are derived from the basic property of contraction/expansion of metrics. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t goes to infinity to the steady solution in these distances, which metricizes the weak convergence of measures. These results show that power-like tails in Maxwell models are obtained when the point-wise conservation of momentum and/or energy holds only globally

FullSWOF_Paral: Comparison of two parallelization strategies (MPI and SKELGIS) on a software designed for hydrology applications

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 approach uses Parallel Algorithmic Skeletons and more precisely a library named SkelGIS (Skeletons for Geographical Information Systems). The first results presented in this article show that the two approaches are similar in terms of performance and scalability. The two implementation strategies are however very different and we discuss the advantages of each one.Comment: 27 page

Constraints on the injection energy of positrons in the Galactic centre region

Recent observations of the 511 keV positron-electron annihilation line in the Galactic centre region by the INTEGRAL/SPI spectrometer have stirred up new speculations about the origin of the large corresponding positron injection rate. Beyond astrophysical candidates, new mechanisms have been put forward. We focus on the annihilation of light dark matter particles and review the various gamma-ray radiation components related to such a source of mono-energetic positrons in addition to the 511 keV line itself. We study the influence of the degree of ionisation of the bulge on this radiation, and its possible effects on the observational constraints on the mass of the hypothetical light dark matter particle or the injection energy of a mono-energetic source of positrons in general.Comment: 4 pages, 7 figures, 1 table. Accepted for publication in the proceedings of the 6th INTEGRAL Workshop on the Obscured Universe (ESA SP-622). 2-8 July 2006, Moscow, Russi