منابع مشابه
Coagulation Equations with Gelation
Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel Kij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the preand postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation to, and give a...
متن کاملInstantaneous gelation in coagulation dynamics
The formation of a distribution of cluster sizes is a common feature in a wide variety of situations. Examples include astrophysics, atmospheric physics and polymer science, [2, 3, 8]. In this paper we discuss some mathematical aspects of the Smoluchowski coagulation equation which is a model for the dynamics of cluster growth. This model involves a coupled infinite system of ordinary different...
متن کاملInstantaneous gelation in Smoluchowski's coagulation equation revisited.
We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initia...
متن کاملInduced gelation in a two-site spatial coagulation model
A two-site spatial coagulation model is considered. Particles of masses m and n at the same site form a new particle of mass m + n at rate mn . Independently, particles jump to the other site at a constant rate. The limit (for increasing particle numbers) of this model is expected to be non-deterministic after the gelation time, namely, one or two giant particles randomly jump between the two s...
متن کاملPost-gelation behavior of a spatial coagulation model
A coagulation model on a finite spatial grid is considered. Particles of discrete masses jump randomly between sites and, while located at the same site, stick together according to some coagulation kernel. The asymptotic behavior (for increasing particle numbers) of this model is studied in the situation when the coagulation kernel grows sufficiently fast so that the phenomenon of gelation is ...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 1983
ISSN: 0022-4715,1572-9613
DOI: 10.1007/bf01019497