Showing papers by "Lorenzo Pareschi published in 2004"
01 Jan 2004
TL;DR: The Fokker-Planckck-Landau Equation on Multipole Approximations of the Fokkers-Plankck Landau Operator Traffic Flow was used in this article.
Abstract: Preface Part I: Rarefied Gases Macroscopic Limits of the Boltzmann Equation: A Review Moment Equations for Charged Particles: Global Existence Results Monte-Carlo Methods for the Boltzmann Equation Accurate Numerical Methods for the Boltzmann Equation Finite-Difference Methods for the Boltzmann Equation for Binary Gas Mixtures Part II: Applications Plasma Kinetic Models: The Fokker-Planck-Landau Equation On Multipole Approximations of the Fokker-Planck-Landau Operator Traffic Flow: Models and Numerics Modelling and Numerical Methods for Granular Gases Quantum Kinetic Theory: Modelling and Numerics for Bose--Einstein Condensation On Coalescence Equations and Related Models
124 citations
TL;DR: In this article, a simple kinetic model of economy involving both exchanges between agents and speculative trading is considered and a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals.
Abstract: 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.
35 citations
01 Jan 2004
TL;DR: For the Boltzmann equation, the authors presented a hybrid Monte Carlo method that is robust in the fluid dynamic limit, based on representing the solution as a convex combination of a non-equilibrium particle distribution and a Maxwellian.
Abstract: For the Boltzmann equation, we present a hybrid Monte Carlo method that is robust in the fluid dynamic limit. The method is based on representing the solution as a convex combination of a non-equilibrium particle distribution and a Maxwellian. The hybrid distribution is then evolved by Monte Carlo with an unconditionally stable and asymptotic preserving time discretization. Some computational simulations of spatially homogeneous problems are presented here and extensions to spatially non homogeneous situations discussed.
15 citations
01 Jan 2004
TL;DR: In this paper, the authors review some modelling and numerical aspects in quantum kinetic theory for a gas of interacting bosons and explain what makes Bose-Einstein condensation in a dilute gas mathematically interesting and numerically challenging.
Abstract: We review some modelling and numerical aspects in quantum kinetic theory for a gas of interacting bosons and we try to explain what makes Bose-Einstein condensation in a dilute gas mathematically interesting and numerically challenging. Particular care is devoted to the development of efficient numerical schemes for the quantum Boltzmann equation that preserve the main physical features of the continuous problem, namely conservation of mass and energy, the entropy inequality and generalized Bose-Einstein distributions as steady states. These properties are essential in order to develop numerical methods that are able to capture the challenging phenomenon of bosons condensation. We also show that the resulting schemes can be evaluated with the use of fast algorithms. In order to study the evolution of the condensate wave function the Gross-Pitaevskii equation is presented together with some schemes for its efficient numerical solution.
15 citations
TL;DR: A general relaxation system which yields compressible and incompressible Euler and Navier-Stokes equations in the limit is presented and can be used to set up relaxation schemes that work uniformly in the above limits.
13 citations
TL;DR: Methods for the development of fast numerical schemes for the Boltzmann collision integral based on a combination of a Carleman-like representation together with a suitable angular approximation for the hard spheres model in dimension three are presented.
12 citations
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TL;DR: This note considers the problem of constructing suitable hydrodynamic approximations for linear dissipative models of the Boltzmann equation and its application to hard spheres.
Abstract: Recently linear dissipative models of the Boltzmann equation have been introduced. In this work, we consider the problem of constructiing suitable hydrodynamic approximations for such models where the mean velocity and the temperature of inelastic particles appear as independent variables.
9 citations
06 Jun 2004
TL;DR: The method presented in this paper is simple to formulate and to implement, and can be straightforwardly extended to higher dimensional conservation laws.
Abstract: We present a Monte Carlo method for approximating the solution of conservation laws A relaxation method is used to transform the conservation law to a kinetic form that can be interpreted in a probabilistic manner A Monte Carlo algorithm is then used to simulate the kinetic approximation The method we present in this paper is simple to formulate and to implement, and can be straightforwardly extended to higher dimensional conservation laws Numerical experiments are carried out using Burgers equation subject to both smooth and nonsmooth initial data
8 citations
01 Jan 2004
TL;DR: In this paper, the cooling process of dilute granular systems of spheres with dissi- pative collisions and variable coefficient of restitution is studied under the assumption of weak inelasticity.
Abstract: We discuss certain kinetic models of dilute granular systems of spheres with dissi- pative collisions and variable coefficient of restitution. Under the assumption of weak inelastic- ity the cooling process of the system is studied and some hydrodynamical models are derived. Accurate numerical methods based on a spectral representation in velocity are also presented and the development of fast algorithms is considered.
6 citations
TL;DR: Pareschi et al. as mentioned in this paper considered a fourth order degenerate parabolic equation modeling the evolution of the interface of a spreading droplet and derived numerical approximations that preserve positivity of the solution and the main relevant physical properties.
5 citations
TL;DR: The relaxed Burnett system, recently introduced in as a hydrodynamical approximation of the Boltzmann equation, is numerically solved and a parallel stiff ODE solver based on 4-stage Radau IIA IRK is applied to reduce computing time.
Abstract: The relaxed Burnett system, recently introduced in as a hydrodynamical approximation of the Boltzmann equation, is numerically solved. Due to the stiffness of this system and the severe CFL condition for large Mach numbers, a fully implicit Runge-Kutta method has been used. In order to reduce computing time, we apply a parallel stiff ODE solver based on 4-stage Radau IIA IRK. The ODE solver is combined with suitable first order upwind and second order MUSCL relaxation schemes for the spatial derivatives. Speedup results and comparisons to DSMC and Navier-Stokes approximations are reported for a 1D shock profile.
TL;DR: This paper proves convergence of this quadrature formula together with other theoretical estimates on the integral approximation for the evaluation of the stress intensity factor for convex planar cracks.
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TL;DR: In this article, a simple kinetic model of economy involving both exchanges between agents and speculative trading is considered and a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals.
Abstract: 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.