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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B. Ycart, W. A. Woyczynski, J. Szulga, S. Reazor, J. A. Mann, Jr. (1988)
Applicationes Mathematicae
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Pablo A. Ferrari, Patricia Gonçalves, James B. Martin (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate ∈(1/2, 1] and to the left at rate 1−, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose...
E. Tirapegui (1972)
Annales de l'I.H.P. Physique théorique
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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...
Dolan, P., Zenios, A.C. (1984)
International Journal of Mathematics and Mathematical Sciences
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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.
Pierre Degond, Amic Frouvelle, Jian-Guo Liu, Sebastien Motsch, Laurent Navoret (2012-2013)
Séminaire Laurent Schwartz — EDP et applications
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In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss...
Manuel Baumgartner, Peter Spichtinger (2017)
Mathematics of Climate and Weather Forecasting
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Diffusion ofwater vapor is the dominant growth mechanism for smallwater droplets and ice crystals in clouds. In current cloud models, Maxwell’s theory is used for describing growth of cloud particles. In this approach the local interaction between particles is neglected; the particles can only grow due to changes in environmental conditions, which are assumed as boundary conditions at infinity. This assumption is meaningful if the particles are well separated and far away from each other....
Márton Balázs (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Yiran Xue, Peng Liu, Ye Tao, Xianglong Tang (2017)
International Journal of Applied Mathematics and Computer Science
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In the field of intelligent crowd video analysis, the prediction of abnormal events in dense crowds is a well-known and challenging problem. By analysing crowd particle collisions and characteristics of individuals in a crowd to follow the general trend of motion, a purpose-driven lattice Boltzmann model (LBM) is proposed. The collision effect in the proposed method is measured according to the variation in crowd particle numbers in the image nodes; characteristics of the crowd following...
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.