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This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1+1)-dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport...
We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.
The primary objective of this work is to develop coarse-graining
schemes for stochastic many-body microscopic models and quantify their
effectiveness in terms of a priori and a posteriori error analysis. In
this paper we focus on stochastic lattice systems of
interacting particles at equilibrium.
The proposed algorithms are derived from an initial coarse-grained
approximation that is directly computable by Monte Carlo simulations,
and the corresponding numerical error is calculated using the...
This paper describes the extension of a
recently developed numerical solver for the Landau-Lifshitz
Navier-Stokes (LLNS) equations to binary mixtures in three
dimensions. The LLNS equations incorporate thermal fluctuations into
macroscopic hydrodynamics by using white-noise fluxes. These
stochastic PDEs are more complicated in three dimensions due to the
tensorial form of the correlations for the stochastic fluxes and in
mixtures due to couplings of energy and concentration fluxes (e.g.,
Soret...
In this paper, we discuss advanced
thermostatting techniques for sampling molecular systems in the canonical ensemble.
We first survey work on dynamical thermostatting methods, including the Nosé-Poincaré method, and generalized bath methods which introduce a more complicated extended model to obtain better ergodicity. We describe a general controlled temperature model, projective thermostatting molecular dynamics
(PTMD) and demonstrate that it flexibly accommodates existing alternative
thermostatting...
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute
filament solutions. In the dilute case, we use a probabilistic model of microtubule
interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules
are modeled as polar rods interacting through fully inelastic, binary collisions. Our
model indicates that initially disordered systems of interacting rods exhibit an
orientational instability...
We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus "light waves" are somewhat supressed, which in turn allows thenumerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step. We construct a numerical scheme based on semi-Lagrangian...
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
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