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On the Growth of a Particle Coalescing in a Poisson Distribution of Obstacles

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Abstract

In this paper we consider the coalescence dynamics of a tagged particle moving in a random distribution of particles with volumes independently distributed according to a probability distribution (CTP model). We provide a rigorous derivation of a kinetic equation for the probability density for the size and position of the tagged particle in the kinetic limit where the volume fraction \({\phi}\) filled by the background of particles tends to zero. Moreover, we prove that the particle system, i.e., the CTP model, is well posed for a small but positive volume fraction with probability one as long as the distribution of the particle sizes is compactly supported.

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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Alessia Nota & Juan J. L. Velázquez

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  1. Alessia Nota
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  2. Juan J. L. Velázquez
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Correspondence to Alessia Nota.

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Communicated by H. Spohn

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Nota, A., Velázquez, J.J.L. On the Growth of a Particle Coalescing in a Poisson Distribution of Obstacles. Commun. Math. Phys. 354, 957–1013 (2017). https://doi.org/10.1007/s00220-017-2929-3

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  • DOI: https://doi.org/10.1007/s00220-017-2929-3

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