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Rajesh R, Das D, Chakraborty B, et al. Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;66(5):056104doi: 10.1103/PhysRevE.66.056104.
Rajesh, R., Das, D., Chakraborty, B., & Barma, M. (2002). Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates. Physical review. E, Statistical, nonlinear, and soft matter physics, 66(5), 056104. https://doi.org/10.1103/PhysRevE.66.056104
Rajesh, R, et al. "Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 66,5 (2002): 056104. doi: https://doi.org/10.1103/PhysRevE.66.056104
Rajesh R, Das D, Chakraborty B, Barma M. Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates. Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5):056104. doi: 10.1103/PhysRevE.66.056104. Epub 2002 Nov 07. PMID: 12513553.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5):056104. doi: 10.1103/PhysRevE.66.056104. Epub 2002 Nov 07.

Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates.

Physical review. E, Statistical, nonlinear, and soft matter physics

R Rajesh, Dibyendu Das, Bulbul Chakraborty, Mustansir Barma

Affiliations

  1. Department of Physics-Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom. [email protected]

PMID: 12513553 DOI: 10.1103/PhysRevE.66.056104

Abstract

The effect of introducing a mass-dependent diffusion rate approximately m(-alpha) in a model of coagulation with single-particle breakup is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all alpha>0 in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite-size scaling implications of this are characterized. The exponents characterizing the steady-state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean-field approximation and found to compare well with the results from numerical simulations in one dimension.

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