Displaying similar documents to “Stochastic Lagrangian method for downscaling problems in computational fluid dynamics”

An introduction to probabilistic methods with applications

Pierre Del Moral, Nicolas G. Hadjiconstantinou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This special volume of the ESAIM Journal, , contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics. In this preface, we provide...

Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process

Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We study a free energy computation procedure, introduced in [Darve and Pohorille, (2001) 9169–9183; Hénin and Chipot, (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre , (2008)...

Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation

François Bolley, Arnaud Guillin, Florent Malrieu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation ...

Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example,...