A limit theorem for the position of a particle in the Lorentz model.
Vysotskiĭ, V.V. (2005)
Journal of Mathematical Sciences (New York)
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Vysotskiĭ, V.V. (2005)
Journal of Mathematical Sciences (New York)
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Benettin, G., Rondoni, L. (2001)
Mathematical Physics Electronic Journal [electronic only]
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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...
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...
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.
Dioşan, Laura, Dumitrescu, Dumitru, David, Delia (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
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P. Žáček, Vladimír Vanýsek (1981)
Acta Universitatis Carolinae. Mathematica et Physica
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P. A. Ferrari, C. Kipnis (1995)
Annales de l'I.H.P. Probabilités et statistiques
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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....
Mauro Mobilia, Tobias Reichenbach, Hauke Hinsch, Thomas Franosch, Erwin Frey (2008)
Banach Center Publications
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Nonequilibrium collective motion is ubiquitous in nature and often results in a rich collection of intriguing phenomena, such as the formation of shocks or patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase transitions. These stochastic many-body features characterize transport processes in biology, soft condensed matter and, possibly, also in nanoscience. Inspired by these applications, a wide class of lattice-gas models has recently been considered. Building on...