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Nonlinear least-squares method for the inverse droplet coagulation problem
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Jones, Peter P., Ball, Robin and Connaughton, Colm (2013) Nonlinear least-squares method for the inverse droplet coagulation problem. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Volume 88 (Number 1). Article number 012138 . doi:10.1103/PhysRevE.88.012138 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.88.012138
Abstract
If the rates, K(x,y), at which particles of size x coalesce with particles of size y is known, then the mean-field evolution of the particle size distribution of an ensemble of irreversibly coalescing particles is described by the Smoluchowski equation. We study the corresponding inverse problem which aims to determine the coalescence rates K(x,y) from measurements of the particle size distribution. We assume that K(x,y) is a homogeneous function of its arguments, a case which occurs commonly in practice. The problem of determining K(x,y), a function to two variables, then reduces to the simpler problem of determining a function of a single variable plus two exponents, μ and ν, which characterize the scaling properties of K(x,y). The price of this simplification is that the resulting least-squares problem is nonlinear in the exponents μ and ν. We demonstrate the effectiveness of the method on a selection of coalescence problems arising in polymer physics, cloud science, and astrophysics. The applications include examples in which the particle size distribution is stationary owing to the presence of sources and sinks of particles and examples in which the particle size distribution is undergoing self-similar relaxation in time.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Physics |
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| Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 1539-3755 | ||||
| Official Date: | 2013 | ||||
| Dates: |
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| Volume: | Volume 88 | ||||
| Number: | Number 1 | ||||
| Page Range: | Article number 012138 | ||||
| DOI: | 10.1103/PhysRevE.88.012138 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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