Related papers: Cluster size distribution in the autocatalytic gro…
We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: I) Growth: Clusters grow indefinitely; II) Gelation: All mass is…
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…
We survey our research on modeling the mechanisms of control of uniformity in growth of nanosize and colloid particles. The former are produced as nanocrystals, by burst-nucleation from solution. The latter, colloid-size particles, are…
Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely…
This paper presents a comprehensive analysis of simple models useful to analyze the growth of nanostructures obtained by cluster deposition. After detailing the potential interest of nanostructures, I extensively study the first stages of…
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…
The continuous generalized exchange-driven growth model (CGEDG) is a system of integro-differential equations describing the evolution of cluster mass under mass exchange. The rate of exchange depends on the masses of the clusters involved…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains…
Reactions in solution require "contact" between the reagents. We can predict the rate at which reagents come into "contact" (at least in dilute conditions), but if the initial collision does not lead to reaction, what happens then? The…
The continuous generalized exchange-driven growth model (CGEDG) is a coagulation-fragmentation equation that describes the evolution of the macroscopic cluster size distribution induced by a microscopic dynamic of binary exchanges of masses…
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…
We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nano- or micro-cluster phases. We predict the distribution of cluter sizes with respect to interaction parameters and colloid…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
In this paper we prove that the time dependent solutions of a large class of Smoluchowski coagulation equations for multicomponent systems concentrate along a particular direction of the space of cluster compositions for long times. The…
Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities with constant rate coefficients, the temperature-dependent…
We show that models for homogeneous and heterogeneous nucleation of D-dimensional droplets in a d-dimensional medium are described in mean-field by a modified Smoluchowski equation for the distribution N(s,t) of droplets masses s, with…
The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may…
We show, in this report, how a population balance model differential equation describing batch crystal growth from solution can be solved in closed form for the case of diffusion limited growth with and without modeling the effects of…
We investigate the kinetics of particle aggregation within the framework of the Smoluchowski coagulation equation, extending it to account for electrostatic interactions among charged clusters. Using a stochastic Monte Carlo implementation,…