%0 Book Section %1 statphys23_0157 %A Babovsky, H.K. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K diffusion gelation numerical simulation statphys23 topic-11 %T Gelation in a diffusive environment: Algorithmic aspects %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=157 %X Gelation is the merging of aerosol particles to ``macroparticles''. Mathematically it can be described by the Smoluchowski equation. Numerically it is usually simulated by stochastic systems. To this aim, efficient variants of the socalled Marcus-Lushnikov process have been derived (see 1,2 and the literature cited there). However, the simulation of the transition to the gel phase turned out to be a time and resource consuming problem leaving open a number of questions. Recently, a hybrid code has been derived coupling a (deterministic) numerical scheme with a stochastic component simulating the critical phase of the approach to the gelation time. As shown in 3, it combines high accuracy with efficiency. In our presentation we use this to investigate the approach of the gelation phase in a diffusive environment. Several modelling aspects concerning the spreading of the gel are discussed. Special attention is paid to the effect of random fluctuation. In particular, we demonstrate how stochasticity may turn stable, non gelating systems with sink and source into metastable ones running eventually into gelation. ACKNOWLEDGEMENTS. This work was supported by the German Research Foundation (DFG). References 1) H. Babovsky. The impact of random fluctuations on the gelation process. Talk presented at the 6th International MAFPD-Workshop, Kyoto, 2004 (to appear in Bull. Inst. Math. Acad. Sinica, 2007).\\ 2) H. Babovsky. Gelation of stochastic diffusion-coagulation systems. Physica D, 222, 54--62 (2006)\\ 3) H. Babovsky. Approximations to the gelation phase of an aerosol. Preprint 11/06, Inst. f. Math., TU Ilmenau, 2006. Submitted.

@incollection{statphys23_0157, abstract = {Gelation is the merging of aerosol particles to ``macroparticles''. Mathematically it can be described by the Smoluchowski equation. Numerically it is usually simulated by stochastic systems. To this aim, efficient variants of the socalled Marcus-Lushnikov process have been derived (see [1,2] and the literature cited there). However, the simulation of the transition to the gel phase turned out to be a time and resource consuming problem leaving open a number of questions. Recently, a hybrid code has been derived coupling a (deterministic) numerical scheme with a stochastic component simulating the critical phase of the approach to the gelation time. As shown in [3], it combines high accuracy with efficiency. In our presentation we use this to investigate the approach of the gelation phase in a diffusive environment. Several modelling aspects concerning the spreading of the gel are discussed. Special attention is paid to the effect of random fluctuation. In particular, we demonstrate how stochasticity may turn stable, non gelating systems with sink and source into metastable ones running eventually into gelation. ACKNOWLEDGEMENTS. This work was supported by the German Research Foundation (DFG). References 1) H. Babovsky. {\em The impact of random fluctuations on the gelation process.} Talk presented at the 6th International MAFPD-Workshop, Kyoto, 2004 (to appear in {\sl Bull. Inst. Math. Acad. Sinica}, 2007).\\ 2) H. Babovsky. Gelation of stochastic diffusion-coagulation systems. {\sl Physica D}, {\bf 222}, 54--62 (2006)\\ 3) H. Babovsky. {\sl Approximations to the gelation phase of an aerosol.} Preprint 11/06, Inst. f. Math., TU Ilmenau, 2006. Submitted.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Babovsky, H.K.}, biburl = {https://www.bibsonomy.org/bibtex/25a104652312888a71023e56818177aba/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {14b0c3eb2e5a52165cd96558e3ab0ded}, intrahash = {5a104652312888a71023e56818177aba}, keywords = {diffusion gelation numerical simulation statphys23 topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:13.000+0200}, title = {Gelation in a diffusive environment: Algorithmic aspects}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=157}, year = 2007 }