Related papers: Gelation for Marcus-Lushnikov process
The coagulation (or aggregation) equation was introduced by Smoluchowski in 1916 to describe the clumping together of colloidal particles through diffusion, but has been used in many different contexts as diverse as physical chemistry,…
Giant molecular clouds (GMCs) are the primary reservoirs of cold, star-forming molecular gas in the Milky Way and similar galaxies, and thus any understanding of star formation must encompass a model for GMC formation, evolution, and…
To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are…
If reheating of the Universe takes place via Planck-suppressed decay, it seems that the thermalization of produced particles might be delayed, since they have large energy/small number densities and number violating large angle scatterings…
Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium…
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…
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…
The possible occurrence of instantaneous gelation to Oort-Hulst-Safronov (OHS) coagulation equation is investigated for a certain class of unbounded coagulation kernels. The existence of instantaneous gelation is confirmed by showing the…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
We consider patchy gold nanoparticles decorated by liquid crystalline ligands. The cases of two, three, four and six symmetrically arranged patches of ligands are discussed, as well as the cases of their equatorial and uniform arrangement.…
Colloidal gels are widely applied in industry due to their rheological character -- no flow takes place below the yield stress. Such property enables gels to maintain uniform distribution in practical formulations; otherwise, solid…
We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the…
Circumgalactic gas around massive galaxies generally has a volume-filling component -- an atmosphere -- with a temperature determined by the potential-well depth of the galaxy's halo. If the atmosphere is near hydrostatic equilibrium and is…
The standard treatment of cooling in Cold Dark Matter halos assumes that all of the gas within a ``cooling radius'' cools and contracts monolithically to fuel galaxy formation. Here we take into account the expectation that the hot gas in…
Attractive colloidal particles can form a disordered elastic solid or gel when quenched into a two-phase region, if the volume fraction is sufficiently large. When the interactions are comparable to thermal energies the stress-bearing…
Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of non-uniqueness is constructed. The stochastic…
We consider Smoluchowski's coagulation equation in the case of the diagonal kernel with homogeneity $\gamma>1$. In this case the phenomenon of gelation occurs and solutions lose mass at some finite time. The problem of the existence of…
Astrophysical gases such as the interstellar-, circumgalactic- or intracluster-medium are commonly multiphase, which poses the question of the structure of these systems. While there are many known processes leading to fragmentation of cold…
We investigate the thermal and dynamical evolution of primordial gas clouds in the universe after decoupling. Comparing the time-scale of dynamical evolution with that of fragmentation, we can estimate the typical fragmentation scale. We…
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…