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Stationary mass distribution and non-locality in models of coalescence and shattering
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Connaughton, Colm, Dutta, Arghya, Rajesh, R., Siddharth, Nana and Zaboronski, Oleg V. (2018) Stationary mass distribution and non-locality in models of coalescence and shattering. Physical Review E, 97 (2). 022137. ISSN 1539-3755.
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Official URL: https://doi.org/10.1103/PhysRevE.97.022137
Abstract
We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the large and small mass asymptotic behavior of the mass distribution depend on whether the collision kernel is local (the aggregation mass flux is essentially generated by collisions between particles of similar masses) or nonlocal (collision between particles of widely different masses give the main contribution to the mass flux). We show that the nonlocal regime is further divided into two subregimes corresponding to weak and strong nonlocality. We also observe that at the boundaries between the local and nonlocal regimes, the mass distribution acquires logarithmic corrections to scaling and calculate these corrections. Exact solutions for special kernels and numerical simulations are used to validate some nonrigorous steps used in the analysis. Our results show that for local kernels, the scaling solutions carry a constant flux of mass due to aggregation, whereas for the nonlocal case there is a correction to the constant flux exponent. Our results suggest that for general scale-invariant kernels, the universality classes of mass distributions are labeled by two parameters: the homogeneity degree of the kernel and one further number measuring the degree of the nonlocality of the kernel.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Kernel functions | ||||||
| Journal or Publication Title: | Physical Review E | ||||||
| Publisher: | American Physical Society | ||||||
| ISSN: | 1539-3755 | ||||||
| Official Date: | 21 February 2018 | ||||||
| Dates: |
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| Volume: | 97 | ||||||
| Number: | 2 | ||||||
| Article Number: | 022137 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 12 February 2018 | ||||||
| Date of first compliant Open Access: | 20 June 2018 |
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