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Related papers: Gelation for Marcus-Lushnikov process

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Motivated by the recent results of Andreis-Iyer-Magnanini (2023), we provide a short proof, revisiting the one of Escobedo-Mischler-Perthame (2002), that for a large class of coagulation kernels, any weak solution to the Smoluchowski…

Analysis of PDEs · Mathematics 2025-01-08 Nicolas Fournier

The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers, or by positive…

Probability · Mathematics 2008-12-01 Mohammad Reza Yaghouti , Fraydoun Rezakhanlou , Alan Hammond

We construct a time-dependent solution to the Smoluchowski coagulation equation with a constant flux of dust particles entering through the boundary at zero. The dust is instantaneously converted into particles and flux solutions have…

Analysis of PDEs · Mathematics 2024-12-11 Marina A. Ferreira , Aleksis Vuoksenmaa

We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equation, and the fluctuations around this…

Probability · Mathematics 2026-03-30 Julian Amorim , Arturo Arellano , Milton Jara

The process of homogeneous crystal nucleation has been considered in a model liquid, where the interparticle interaction is described by a short-range spherical oscillatory potential. Mechanisms of initiating structural ordering in the…

Materials Science · Physics 2018-12-18 Bulat N. Galimzyanov , Dinar T. Yarullin , Anatolii V. Mokshin

We study a two-component model for gelation consisting of $f$-functional monomers (the gel) and inert particles (the solvent). After equilibration as a simple liquid, the gel particles are gradually crosslinked to each other until the…

Soft Condensed Matter · Physics 2009-11-07 Michael Plischke , D. C. Vernon , Bela Joos

We study a model of mass-bearing coagulating planar Brownian particles. Coagulation is prone to occur when two particles become within a distance of order $\epsilon$. We assume that the initial number of particles is of the order of $| \log…

Probability · Mathematics 2013-04-18 Alan Hammond , Fraydoun Rezakhanlou

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

Water usually contains dissolved gases, and because freezing is a purifying process these gases must be expelled for ice to form. Bubbles appear at the freezing front and are then trapped in ice, making pores. These pores come in a range of…

Soft Condensed Matter · Physics 2024-11-26 Virgile Thiévenaz , Jochem G. Meijer , Detlef Lohse , Alban Sauret

Smoluchowski's equation is a macroscopic description of a many particle system with coagulation and shattering interactions. We give a microscopic model of the system from which we derive this equation rigorously. Provided the existence of…

Probability · Mathematics 2018-04-26 Stefan Grosskinsky , Christian Klingenberg , Karl Oelschlaeger

We introduce a simple model, a binary mixture of patchy particles, which has been designed to form a gel upon heating. Due to the specific nature of the particle interactions, notably the number and geometry of the patches as well as their…

Soft Condensed Matter · Physics 2013-10-16 Sandalo Roldan-Vargas , Frank Smallenburg , Walter Kob , Francesco Sciortino

We present a simple unifying model for crystallization and melting temperatures by showing that homogeneous nucleation and phase transformations driven by thickening of pre-existing surface layers are limiting conditions of the more general…

Materials Science · Physics 2009-11-13 Sharon Cooper , Catherine Nicholson , Jian Liu

We consider in this work a model for aggregation, where the coalescing particles initially have a certain number of potential links (called arms) which are used to perform coagulations. There are two types of arms, male and female, and two…

Mathematical Physics · Physics 2009-11-09 Raoul Normand

The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general…

Statistical Mechanics · Physics 2018-02-14 Liangrong Peng , Yi Zhu , Liu Hong

A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid…

Soft Condensed Matter · Physics 2016-11-10 Nicholas B. Weingartner , Chris Pueblo , Flavio S. Nogueira , K. F. Kelton , Zohar Nussinov

We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…

Probability · Mathematics 2017-01-31 Andreas E. Kyprianou , Steven W. Pagett , Tim Rogers

We present a new model of homogeneous aggregation that contains the essential physical ideas of the classical predecessors, the Becker-Doring and Lifshitz-Slyovoz models. These classical models, which give different predictions, are…

Statistical Mechanics · Physics 2008-10-23 Yossi Farjoun

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

During their formation, nascent planetary systems are subject to FU Orionis outbursts that heat a substantial part of the disc. This causes water ice in the affected part of the disc to sublimate as the ice line moves outwards to several to…

Earth and Planetary Astrophysics · Physics 2024-06-19 Katrin Ros , Anders Johansen

The evolution of a turbulent tangle of quantum vortices in presence of finite-size active particles is studied by means of numerical simulations of the Gross-Pitaevskii equation. Particles are modeled as potentials depleting the superfluid…

Fluid Dynamics · Physics 2020-07-01 Umberto Giuriato , Giorgio Krstulovic