Bruno, Oscar and Friedman, Avner and Reitich, Fernando (1993) Asymptotic Behavior for a Coalescence Problem. Transactions of the American Mathematical Society, 338 (1). pp. 133-158. ISSN 0002-9947 http://resolver.caltech.edu/CaltechAUTHORS:20120309-093931707
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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.|
|Subject Keywords:||Particles, collision, coalescence, asymptotic behavior.|
|Classification Code:||1991 MSC: Primary 35Q20, 35B40|
|Official Citation:||Asymptotic Behavior for a Coalescence Problem Oscar Bruno, Avner Friedman and Fernando Reitich Transactions of the American Mathematical Society , Vol. 338, No. 1 (Jul., 1993), pp. 133-158|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||12 Mar 2012 15:42|
|Last Modified:||26 Dec 2012 14:56|
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