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Published July 1993 | Published
Journal Article Open

Asymptotic Behavior for a Coalescence Problem

Abstract

Consider spherical particles of volume x having paint on a fraction y of their surface area. The particles are assumed to be homogeneously distributed at each time t, so that one can introduce the density number n (x, y, t). When collision between two particles occurs, the particles will coalesce if and only if they happen to touch each other, at impact, at points which do not belong to the painted portions of their surfaces. Introducing a dynamics for this model, we study the evolution of n (x, y, t) and, in particular, the asymptotic behavior of the mass x n (x, y, t) dx as t → ∞.

Additional Information

© 1993 American Mathematical Society. Received by the editors March 7, 1991. We would like to thank David Ross from Eastman Kodak for suggesting the problem studied in this paper and for several useful conversations. The first author is partially supported by ARO Contract DAAL-03-88-K-0110; the second author is partially supported by National Science Foundation Grant DMS-86-12880; the third author is supported by N.I.S.T. Grant No. DOC/60NANBOD1027.

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