Babovsky, Hans Gelation of stochastic diffusion-coagulation systems. (English) Zbl 1104.60326 Physica D 222, No. 1-2, 54-62 (2006). Summary: We investigate aerosol systems diffusing in space and study their gelation properties. In particular we work out the role of fluctuations which turn stable configurations into metastable ones, and the influence of randomly distributed sources and sinks. Cited in 5 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C40 Kinetic theory of gases in time-dependent statistical mechanics Keywords:Smoluchowski equation; random perturbations PDFBibTeX XMLCite \textit{H. Babovsky}, Physica D 222, No. 1--2, 54--62 (2006; Zbl 1104.60326) Full Text: DOI References: [1] Aldous, D. J., Deterministic and stochastic models for coalescence (aggregation, coagulation): A review of the mean-field theory for probabilists, Bernoulli, 5, 3-48 (1999) · Zbl 0930.60096 [2] Anderson, P. W., Absence of diffusion in certain random lattices, Phys. Rev., 109, 1492-1505 (1958) [3] Babovsky, H., On a Monte Carlo scheme for Smoluchowski’s coagulation equation, Monte Carlo Methods Appl., 5, 1-18 (1999) · Zbl 0937.76058 [4] H. Babovsky, On the modeling of gelation rates by finite systems, Inst. f. Math., TU Ilmenau, 2001 (Preprint 11/01); H. Babovsky, On the modeling of gelation rates by finite systems, Inst. f. Math., TU Ilmenau, 2001 (Preprint 11/01) [5] H. Babovsky, The impact of random fluctuations on the gelation process, in: Talk presented at 6th International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics, Kyoto, 2004. Transport Theor. Statist. Phys. (in press); H. Babovsky, The impact of random fluctuations on the gelation process, in: Talk presented at 6th International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics, Kyoto, 2004. Transport Theor. Statist. Phys. (in press) [6] da Costa, F. P., A finite-dimensional dynamical model for gelation in coagulation processes, J. Nonlinear Sci., 8, 619-653 (1998) · Zbl 0915.34037 [7] Deaconu, M.; Fournier, N., Probabilistic approach of some discrete and continuous coagulation equations with diffusion, Stochastic Process. Appl., 101, 83-111 (2002) · Zbl 1075.60082 [8] Gärtner, J.; König, W., The parabolic Anderson model, (Deuschel, J.-D.; Greven, A., Interacting Stochastic Systems (2005), Springer: Springer Berlin), 153-179 · Zbl 1111.82011 [9] Guiaş, F., Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion, Stoch. Anal. Appl., 19, 254-278 (2001) · Zbl 1015.60094 [10] Guiaş, F., A stochastic numerical method for diffusion equations and applications to spatially inhomogeneous coagulation processes, (Niederreiter, H.; Talay, D., Monte Carlo and Quasi-Monte Carlo Methods 2004 (2006), Springer), 147-162 · Zbl 1097.65014 [11] Laurençot, P.; Mischler, S., The continuous coagulation-fragmentation equations with diffusion, Arch. Ration. Mech. Anal., 162, 45-99 (2002) · Zbl 0997.45005 [12] Mott, N. F.; Twose, W. D., The theory of impurity conduction, Adv. Phys., 10, 107-163 (1961) [13] Siegmund-Schultze, R.; Wagner, W., Induced gelation in a two-site spatial coagulation model, Ann. Appl. Probab., 16, 370-402 (2006) · Zbl 1102.60089 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.