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The kinetic limit of a system of coagulating Brownian particles. To appear in Arch. Rational Mech. Anal. Available at www.arxiv.org/math.PR/0408395. 29 Alan Hammond and Fraydoun Rezakhanlou. The kinetic limit of a system of coagulating planar Brownian par
"... Understanding the evolution in time of macroscopic quantities such as pressure or temperature is a central task in nonequilibrium statistical mechanics. We study this problem rigorously for a model of massbearing Brownian particles that are prone to coagulate when they are close, where the macrosc ..."
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Understanding the evolution in time of macroscopic quantities such as pressure or temperature is a central task in nonequilibrium statistical mechanics. We study this problem rigorously for a model of massbearing Brownian particles that are prone to coagulate when they are close, where the macroscopic quantity in this case is the density of particles of a given mass. Brownian motion
Kinetic limit for a system of coagulating planar Brownian particles
 J. Stat. Phys
"... We study a model of massbearing coagulating planar Brownian particles. Coagulation occurs when two particles are within a distance of order ε. We assume that the initial number of particles N is of order log ε. Under suitable assumptions of the initial distribution of particles and the microscopi ..."
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Cited by 9 (6 self)
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We study a model of massbearing coagulating planar Brownian particles. Coagulation occurs when two particles are within a distance of order ε. We assume that the initial number of particles N is of order log ε. Under suitable assumptions of the initial distribution of particles and the microscopic coagulation propensities, we show that the macroscopic particle densities satisfy a Smoluchowskitype equation. 1
Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE
, 2012
"... The Smoluchowski coagulationdiffusion PDE is a system of partial differential equations modelling the evolution in time of massbearing Brownian particles which are subject to shortrange pairwise coagulation. Presented here are the notes of a graduate class given by the author at the University of ..."
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The Smoluchowski coagulationdiffusion PDE is a system of partial differential equations modelling the evolution in time of massbearing Brownian particles which are subject to shortrange pairwise coagulation. Presented here are the notes of a graduate class given by the author at the University of Geneva in the autumn of 2012 in which a detailed overview is given of the derivation of the Smoluchowski PDE from microscopic models of coagulating Brownian particles in the limit of high particle number. These notes are an informal but fairly detailed exposition of the kinetic limit derivation of the Smoluchowski PDE undertaken in [2]. The proof in its overall structure is not new, but there is some novelty in the use of probabilistic approaches in obtaining certain key steps.
Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE
, 2013
"... The Smoluchowski coagulationdiffusion PDE is a system of partial differential equations modelling the evolution in time of massbearing Brownian particles which are subject to shortrange pairwise coagulation. This survey presents a fairly detailed exposition of the kinetic limit derivation of the ..."
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The Smoluchowski coagulationdiffusion PDE is a system of partial differential equations modelling the evolution in time of massbearing Brownian particles which are subject to shortrange pairwise coagulation. This survey presents a fairly detailed exposition of the kinetic limit derivation of the Smoluchowski PDE from a microscopic model of many coagulating Brownian particles that was undertaken in [10]. It presents heuristic explanations of the form of the main theorem before discussing the proof, and presents key estimates in that proof using a novel probabilistic technique. The survey's principal aim is an exposition of this kinetic limit derivation, but it also contains an overview of several topics which either motivate or are motivated by this derivation.
Measure solutions for the Smoluchowski coagulationdiffusion equation
, 2014
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