Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework
| Autor: | Michał Łepek, Piotr Fronczak, Paweł Kukliński, Agata Fronczak |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Chemical Physics (physics.chem-ph) Particle number Statistical Mechanics (cond-mat.stat-mech) Kinetics Time evolution FOS: Physical sciences Expression (computer science) 01 natural sciences 010305 fluids & plasmas Mathematics::Group Theory Product kernel Physics - Chemical Physics 0103 physical sciences Master equation Mass spectrum Coagulation (water treatment) 010306 general physics Condensed Matter - Statistical Mechanics Mathematical physics |
| DOI: | 10.48550/arxiv.1809.04172 |
| Popis: | 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. Comment: 10 pages, 3 figures. Original work. Figures changed from png to eps in this update |
| Databáze: | OpenAIRE |
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