Cluster renormalization in the Becker-Döring equations
نویسندگان
چکیده
منابع مشابه
Cluster renormalization in the Becker-Döring equations
We apply ideas from renormalization theory to models of cluster formation in nucleation and growth processes. We study a simple case of the Becker-Döring system of equations and show how a novel coarsegraining procedure applied to the cluster aggregation space affects the coagulation and fragmentation rate coefficients. A dynamical renormalization structure is found to underlie the Becker-Dörin...
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The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we de...
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We introduce an infinite system of equations modeling the time evolution of the growth process of a network. The nodes are characterized by their degree k ∈ N and a fitness parameter f ∈ [0, h]. Every new node which emerges becomes a fitness f ′ according to a given distribution P and attaches to an existing node with fitness f and degree k at rate fAk, where Ak are positive coefficients, growi...
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We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker-Döring system of equations, using realistic expressions for the reaction constants fit to results from Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, subs...
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This paper continues the authors’ previous study (SIAM J. Math. Anal., 2016) of the trend toward equilibrium of the Becker-Döring equations with subcritical mass, by characterizing certain fine properties of solutions to the linearized equation. In particular, we partially characterize the spectrum of the linearized operator, showing that it contains the entire imaginary axis in polynomially we...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/41/308