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Turbulence in growth of rain droplets and rain formation is studied under an approximating particle system representing aggregation at the level of individuals, depending on their volume and distance in space, of the Smoluchowski…

Probability · Mathematics 2021-11-25 Andrea Papini

We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and its collision kernel K is…

Statistical Mechanics · Physics 2009-10-30 Stephane Cueille , Clement Sire

In this paper, a partial integro-differential equation modeling of coagulation and multiple fragmentation events is studied. Our purpose is to investigate the global existence of gelling weak solutions to the continuous coagulation and…

Analysis of PDEs · Mathematics 2019-11-05 Prasanta Kumar Barik

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$…

Adaptation and Self-Organizing Systems · Physics 2013-05-16 Govind Menon , Robert L. Pego

Existence of global weak solutions to the continuous Oort-Hulst-Safronov (OHS) coagulation equation is investigated for coagulation kernels capturing a singularity near zero and growing linearly at infinity. The proof mainly relies on a…

Analysis of PDEs · Mathematics 2020-05-13 Prasanta Kumar Barik , Pooja Rai , Ankik Kumar Giri

The multicomponent coagulation equation is a generalisation of the Smoluchowski coagulation equation in which size of a particle is described by a vector. As with the original Smoluchowski equation, the multicomponent coagulation equation…

Mathematical Physics · Physics 2024-01-24 Jochem Hoogendijk , Ivan Kryven , Camillo Schenone

Simple toy models are often not sufficient to cover the complexity of the dust coagulation process, and a number of numerical approaches are therefore used, among which integration of the Smoluchowski equation and various versions of Monte…

Earth and Planetary Astrophysics · Physics 2014-09-05 Joanna Drazkowska , Fredrik Windmark , Cornelis P. Dullemond

A notion of measure solution is formulated for a coagulation-diffusion equation, which is the natural counterpart of Smoluchowski's coagulation equation in a spatially inhomogeneous setting. Some general properties of such solutions are…

Analysis of PDEs · Mathematics 2014-08-25 James Norris

Binary coagulation is an important process in aerosol dynamics by which two particles merge to form a larger one. The distribution of particle sizes over time may be described by the so-called Smoluchowski's coagulation equation. This…

Mathematical Physics · Physics 2021-06-25 Marina A. Ferreira

Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of…

Computational Physics · Physics 2023-12-11 M. A. Larchenko , R. R. Zagidullin , V. V. Palyulin , N. V. Brilliantov

We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when aggregations occur. Loosely speaking, this imposes…

Mathematical Physics · Physics 2015-05-13 Jean Bertoin

We study multicomponent coagulation via the Smoluchowski coagulation equation under non-equilibrium stationary conditions induced by a source of small clusters. The coagulation kernel can be very general, merely satisfying certain power law…

Analysis of PDEs · Mathematics 2021-03-25 Marina A. Ferreira , Jani Lukkarinen , Alessia Nota , Juan J. L. Velázquez

The processes of simultaneous coagulation and Ostwald ripening of particles in the concluding stage of phase transformation are considered. We solve the integro-differential system of Smoluchowski-type kinetic and mass balance equations…

Numerical Analysis · Mathematics 2026-01-21 Robert T. Zaks , Sergey A. Matveev , Margarita A. Nikishina , Dmitri V. Alexandrov

In the present article we introduce a variant of Smoluchowski's coagulation equation with both position and velocity variables taking a kinetic viewpoint arising as the scaling limit of a system of second-order (microscopic) coagulating…

Analysis of PDEs · Mathematics 2022-11-15 Franco Flandoli , Ruojun Huang , Andrea Papini

We place additional constraints on the three parameters of the dark matter halo merger rate function recently proposed by Parkinson, Cole & Helly by utilizing Smoluchowski's coagulation equation, which must be obeyed by any binary merging…

Astrophysics · Physics 2022-10-12 Andrew J. Benson

We introduce and study a discrete random model for Smoluchowski's equation with limited aggregations. The latter is a model of coagulation introduced by Bertoin which may exhibit gelation. In our model, a large number of particles are…

Probability · Mathematics 2015-09-04 Mathieu Merle , Raoul Normand

We characterize the long-time behaviour of solutions to Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $\gamma < 1$. Due to the property of the diagonal kernel, the value of a solution depends only on a discrete…

Analysis of PDEs · Mathematics 2016-08-11 Philippe Laurençot , Barbara Niethammer , Juan J. L. Velázquez

We derive a satisfying rate of convergence of the Marcus-Lushnikov process toward the solution to Smoluchowski's coagulation equation. Our result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in…

Probability · Mathematics 2011-03-10 Eduardo Cepeda , Nicolas Fournier

Researchers have employed variations of the Smoluchowski coagulation equation to model a wide variety of both organic and inorganic phenomena and with relatively few known analytical solutions, numerical solutions play an important role in…

Numerical Analysis · Mathematics 2013-12-30 Dustin D. Keck , David M. Bortz

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…

Statistical Mechanics · Physics 2007-12-05 P. Horvai , S. V. Nazarenko , T. H. M. Stein