A new model for the transport of particles in a thermostatted system.
Benettin, G., Rondoni, L. (2001)
Mathematical Physics Electronic Journal [electronic only]
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Benettin, G., Rondoni, L. (2001)
Mathematical Physics Electronic Journal [electronic only]
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Krzysztof Pilorz (2016)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of solutions of the corresponding kinetic equation are proved.
Vysotskiĭ, V.V. (2005)
Journal of Mathematical Sciences (New York)
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Márton Balázs (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Agnieszka Tanaś (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on Γ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions...
Jean Bertoin (2009)
Annales de l'I.H.P. Analyse non linéaire
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Bruno Sportisse, Jaouad Boutahar, Edouard Debry, Denis Quélo, Karine Sartelet (2002)
RACSAM
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In this article we discuss some issues related to Air Pollution modelling (as viewed by the authors): subgrid parametrization, multiphase modelling, reduction of high dimensional models and data assimilation. Numerical applications are given with POLAIR, a 3D numerical platform devoted to modelling of atmospheric trace species.
B. Ycart, W. A. Woyczynski, J. Szulga, S. Reazor, J. A. Mann, Jr. (1988)
Applicationes Mathematicae
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Miguel Escobedo (2002)
RACSAM
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We first present very elementary relations between climate and aerosols. The we introduce the homogeneous coagulation equation as a simple model to describe systems of merging particles like polymers or aerosols. We next give a recent result about gelation of solutions. We end with some related open questions.
Natalija Tumanova, Raimondas Čiegis, Mečislavas Meilūnas (2013)
Open Mathematics
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This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method...
Aline Lefebvre (2009)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model described in [B. Maury, ESAIM: Proceedings 18 (2007) 133–142]. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then,...
Nicolas Besse, Norbert J. mauser, Eric Sonnendrücker (2007)
International Journal of Applied Mathematics and Computer Science
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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...