Journal ArticleDOI
Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation
Reads0
Chats0
TLDR
The existence of self-similar solutions to Smoluchowski's coagulation equation has been conjectured for several years by physicists, and numerical simulations have confirmed the validity of this conjecture as mentioned in this paper.Abstract:
The existence of self-similar solutions to Smoluchowski’s coagulation equation has been conjectured for several years by physicists, and numerical simulations have confirmed the validity of this conjecture. Still, there was no existence result up to now, except for the constant and additive kernels for which explicit formulae are available. In this paper, the existence of self-similar solutions decaying rapidly at infinity is established for a wide class of homogeneous coagulation kernels.read more
Citations
More filters
Journal ArticleDOI
An introduction to mathematical models of coagulation–fragmentation processes: A discrete deterministic mean-field approach
TL;DR: In this paper, the authors summarise the properties and fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity (an integer multiple of some basic unit size).
Journal ArticleDOI
Simulating galactic dust grain evolution on a moving mesh
TL;DR: In this paper, a particle-based method for dust subject to dynamical forces including drag and gravity is employed, which is validated using several dust-hydrodynamical test problems.
Journal ArticleDOI
Dust and self-similarity for the Smoluchowski coagulation equation
TL;DR: In this paper, the authors consider l'equation de Smoluchowski for a classe de taux homogenes de degre λ set membership, variant[0,2] and propose a solution which conserves la masse lorsque λ less-than-or-equals, slant1 and perd de la masse en temps fini (phenomene de gelification).
Journal ArticleDOI
Self-similar Solutions with Fat Tails for Smoluchowski’s Coagulation Equation with Locally Bounded Kernels
TL;DR: The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable kernels and the diagonal one.
Journal ArticleDOI
Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels
TL;DR: In this article, the regularity of the scaling profiles ψ to Smoluchowski's coagulation equation was studied and the singular behaviour of ψ(x) as x → 0 was identified.
References
More filters
Journal Article
Drei Vortrage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen
Journal ArticleDOI
Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists
TL;DR: A wide-ranging survey of general kernels of the Marcus-Lushnikov model of stochastic coalescence and the underlying deterministic approximation given by the Smoluchowski coagulation equations is attempted.
Journal ArticleDOI
The self-preserving particle size distribution for coagulation by brownian motion
S.K Friedlander,Chiu-Sen Wang +1 more
TL;DR: In this paper, the authors reviewed the solutions to the kinetic equation of coagulation from the standpoint of their asymptotic behavior, and showed that the shape of the self-preserving spectrum is greatly influenced by the form of the collision frequency factor.
Related Papers (5)
Approach to self-similarity in Smoluchowski's coagulation equations
Govind Menon,Robert L. Pego +1 more