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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

The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…

Statistical Mechanics · Physics 2018-02-21 Agata Fronczak , Anna Chmiel , Piotr Fronczak

The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…

Probability · Mathematics 2009-11-13 Jean Bertoin , Vladas Sidoravicius

We establish nearly optimal rates of convergence to self-similar solutions of Smoluchowski's coagulation equation with kernels $K = 2$, $x + y$, and $xy$. The method is a simple analogue of the Berry-Ess\'een theorem in classical…

Adaptation and Self-Organizing Systems · Physics 2011-04-26 Ravi Srinivasan

Ice-templating is a well-established processing route for porous ceramics. Because of the structure/properties relationships, it is essential to better understand and control the solidification microstructures. Ice-templating is based on…

Soft Condensed Matter · Physics 2017-12-22 Dmytro Dedovets , Sylvain Deville

We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion…

Probability · Mathematics 2010-09-30 Inés Armendáriz

We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal…

Analysis of PDEs · Mathematics 2014-04-17 Oleh Krehel , Adrian Muntean , Peter Knabner

Multicomponent gel systems have garnered much interest due to their compelling mechanical properties in the past decade. Yet, some mechanisms associated with multicomponent gels, such as sequential gelation, have been explored primarily in…

Soft Condensed Matter · Physics 2026-03-31 Alexander Kaltashov , Safa Jamali

In this article, the uniqueness of weak solutions to the continuous coagulation and multiple fragmentation equation is proved for a large range of unbounded coagulation and multiple fragmentation kernels. The multiple fragmentation kernels…

Analysis of PDEs · Mathematics 2013-03-26 Ankik Kumar Giri

In this work, we study the long time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision…

Analysis of PDEs · Mathematics 2024-11-19 Iulia Cristian , Juan J. L. Velázquez

Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…

Probability · Mathematics 2016-11-22 Nathanael Hoze , David Holcman

Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…

Analysis of PDEs · Mathematics 2024-09-27 Jiwoong Jang , Hung V. Tran

The present paper deals with the existence and uniqueness of global classical solutions to the continuous coagulation and nonlinear multiple fragmentation equations for large classes of unbounded coagulation, collision and breakup kernels.…

Analysis of PDEs · Mathematics 2018-02-27 Prasanta Kumar Barik , Ankik Kumar Giri

This work outlines an exact combinatorial approach to finite coagulating systems through recursive equations and use of generating function method. In the classic approach the mean-field Smoluchowski coagulation is used. However, the…

Statistical Mechanics · Physics 2021-04-16 Michał Łepek , Paweł Kukliński , Agata Fronczak , Piotr Fronczak

We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modelling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem.…

Analysis of PDEs · Mathematics 2016-10-04 Toyohiko Aiki , Adrian Muntean

The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…

Statistical Mechanics · Physics 2014-08-19 M. Horváth , T. S. Biró

We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels $K(x,y)=2$, $x+y$ and $xy$. In addition to the known self-similar solutions with exponential tails, there…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Govind Menon , Robert L. Pego

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski…

Analysis of PDEs · Mathematics 2014-09-17 Oleh Krehel , Adrian Muntean , Toyohiko Aiki

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…

Statistical Mechanics · Physics 2009-11-13 Andrea Gabrielli , Michael Joyce

We define a Markov process on the partitions of $[n]=\{1,\ldots,n\}$ by drawing a sample in $[n]$ at each time of a Poisson process, by merging blocks that contain one of these points and by leaving all other blocks unchanged. This…

Probability · Mathematics 2018-09-03 Sophie Lemaire