Mass Exchange Processes with Input
arXiv:1503.02112 · doi:10.1088/1751-8113/48/20/205003
Abstract
We investigate a system of interacting clusters evolving through mass exchange and supplemented by input of small clusters. Three possibilities depending on the rate of exchange generically occur when input is homogeneous: continuous growth, gelation, and instantaneous gelation. We mostly study the growth regime using scaling methods. An exchange process with reaction rates equal to the product of reactant masses admits an exact solution which allows us to justify the validity of scaling approaches in this special case. We also investigate exchange processes with a localized input. We show that if the diffusion coefficients are mass-independent, the cluster mass distribution becomes stationary and develops an algebraic tail far away from the source.
arXiv comment14 pages, 2 figs
References in corpus (15)
- Theory of Phase Ordering Kinetics
- Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
- Wealth Distributions in Models of Capital Exchange
- Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
- Scaling Theory for Migration-Driven Aggregate Growth
- Exchange Driven Growth
- Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term
- Influence of Island Diffusion on Submonolayer Epitaxial Growth
- Explosive condensation in a mass transport model
- Cluster-Cluster Aggregation as an Analogue of a Turbulent Cascade : Kolmogorov Phenomenology, Scaling Laws and the Breakdown of self-similarity
- Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions
- Instantaneous Gelation in Smoluchowski's Coagulation Equation Revisited
- Logarithmic Clustering in Submonolayer Epitaxial Growth
- Driven Brownian coagulation of polymers
- Unusual features of coarsening with detachment rates decreasing with cluster mass