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arXiv · 1809.04172

Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework

Agata Fronczak·Michał Łepek·Paweł Kukliński·Piotr Fronczak
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Abstract

The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability $W(Q,t)$ to find the system in a given mass spectrum $Q=\{n_1,n_2,\dots,n_g\dots\}$, with $n_g$ being the number of particles of size $g$. The exact expression for the average number of particles, $\langle n_g(t)\rangle$, at arbitrary time $t$ is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.

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Agata Fronczak, Michał Łepek, Paweł Kukliński, Piotr Fronczak. 2018-10-04. Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework. https://doi.org/10.1103/physreve.99.012104

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