Exact solutions of temperature-dependent Smoluchowski equations

Abstract

We report a number of exact solutions for temperature-dependent Smoluchowski equations. These equations quantify the ballistic agglomeration, where the evolution of densities of agglomerates of different size is entangled with the evolution of the mean kinetic energy (partial temperatures) of such clusters. The obtained exact solutions may be used as a benchmark to assess the accuracy and computational efficiency of the numerical approaches, developed to solve the temperature-dependent Smoluchowski equations. Moreover, they may also illustrate the possible evolution regimes in these systems. The exact solutions have been obtained for a series of model rate coefficients, and we demonstrate that there may be an infinite number of such model coefficient which allow exact analysis. We compare our exact solutions with the numerical solutions for various evolution regimes; an excellent agreement between numerical and exact results proves the accuracy of the exploited numerical method.

References in corpus (14)

• Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
• Size distribution of particles in Saturn's rings from aggregation and fragmentation
• The Physics of Protoplanetesimal Dust Agglomerates. Vi. Erosion of Large Aggregates as a Source of Micrometer-Sized Particles
• Correlations in Ballistic Processes
• Exact solution of the one-dimensional ballistic aggregation
• Kinetics of Vapor-Solid Phase Transitions: Structure, growth and mechanism
• Ballistic aggregation: a solvable model of irreversible many particles dynamics
• Early-stage aggregation in three-dimensional charged granular gas
• Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics
• Dimension Dependence of Clustering Dynamics in Models of Ballistic Aggregation and Freely Cooling Granular Gas
• Electrification in granular gases leads to constrained fractal growth
• Anomalous aggregation regimes of temperature-dependent Smoluchowski equations
• Non-extensive super-cluster states in aggregation with fragmentation
• The role of energy in ballistic agglomeration

Cited by in corpus (2)

• Hydrodynamic equations for space-inhomogeneous aggregating fluids with first-principle kinetic coefficients
• A mini-review on combinatorial solutions to the Marcus-Lushnikov irreversible aggregation