Fluctuations in coagulating systems |
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Authors: | P G J van Dongen M H Ernst |
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Institution: | (1) Institute for Theoretical Physics, State University, 3508 TA Utrecht, The Netherlands;(2) Physics Department, University of Florida, 32611 Gainesville, Florida;(3) Present address: Institut für theoretische Physik C, RWTH-Aachen, Templergraben 55, D-5100 Aachen, Germany |
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Abstract: | Time-dependent fluctuations in a system of coagulating particles are studied, using the master equation for the probability distributionsP(m,t) for the occupation numbersm={m
k} (k=1,2,...) of thek-cluster states. Van Kampen's -expansion is used to determine the deterministic (order
0) and fluctuating part (order
–1/2) of the solution. We calculate the time-dependent behavior of the fluctuations in the cluster size distribution. The model under consideration is of special interest since it exhibits a phase transition (gelation). For monodisperse initial states we give explicit expressions for the probability distribution of the fluctuations and for the equal-time and two-time correlation functions also near the phase transition. For general initial conditions we study the fluctuations (1) for large cluster sizes, (2) in the scaling limit (near the critical point), and (3) for large times. Our results show that the deterministic approach to coagulation processes (Smoluchowski theory) is invalid very close to the gelpointt
c and at large times (t t
M), where the distance from the gelpoint and the timet
M depend upon the size of the system. |
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Keywords: | Van Kampen's -expansion" target="_blank">gif" alt="OHgr" align="BASELINE" BORDER="0">-expansion fluctuations in aggregation kinetics fluctuations near a gelation transition Smoluchowski's coagulation equation master equation |
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