Burnett, J;
Ford, IJ;
(2015)
Coagulation kinetics beyond mean field theory using an optimised Poisson representation.
Journal of Chemical Physics
, 142
(19)
, Article 194112. 10.1063/1.4921350.
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Abstract
Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable "gauge" transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.
| Type: | Article |
|---|---|
| Title: | Coagulation kinetics beyond mean field theory using an optimised Poisson representation. |
| Location: | United States |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1063/1.4921350 |
| Publisher version: | http://dx.doi.org/10.1063/1.4921350 |
| Language: | English |
| Additional information: | © 2015 AIP Publishing LLC. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Burnett, J; Ford, IJ; (2015) Coagulation kinetics beyond mean field theory using an optimised Poisson representation. Journal of Chemical Physics, 142 (19), Article 194112, and may be found at http://dx.doi.org/10.1063/1.4921350). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1472521 |
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