We analyze several aspects of a reaction-diffusion equation in two space dimensions with cubic nonlinearity, stochastically perturbed by white noise in time and in space. This equation needs renormalization, and physical implications of this circumstance are discussed. In particular, for sufficiently large coupling constant the effective potential becomes a double well and rare transitions from one minimum to the other are possible. These, however, are revealed only by large-scale fluctuations which exhibit a bimodal distribution. Fluctuations below a critical scale have unimodal distribution and do not "see" the double well. This phenomenon is connected with the singular character of local fluctuations in two or more space dimensions. The theoretical results are confirmed by numerical simulations. The possible physical relevance of our results is illustrated in connection with the analysis of certain observations of atmospheric fields. © 1989 Plenum Publishing Corporation.

STOCHASTICALLY PERTURBED LANDAU-GINZBURG EQUATIONS / Roberto, Benzi; G., Jonalasinio; Sutera, Alfonso. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 55:3-4(1989), pp. 505-522. [10.1007/bf01041596]

STOCHASTICALLY PERTURBED LANDAU-GINZBURG EQUATIONS

SUTERA, Alfonso
1989

Abstract

We analyze several aspects of a reaction-diffusion equation in two space dimensions with cubic nonlinearity, stochastically perturbed by white noise in time and in space. This equation needs renormalization, and physical implications of this circumstance are discussed. In particular, for sufficiently large coupling constant the effective potential becomes a double well and rare transitions from one minimum to the other are possible. These, however, are revealed only by large-scale fluctuations which exhibit a bimodal distribution. Fluctuations below a critical scale have unimodal distribution and do not "see" the double well. This phenomenon is connected with the singular character of local fluctuations in two or more space dimensions. The theoretical results are confirmed by numerical simulations. The possible physical relevance of our results is illustrated in connection with the analysis of certain observations of atmospheric fields. © 1989 Plenum Publishing Corporation.
1989
atmospheric bimodality; large (small) scale fluctuations; renormalization; stochastic p.d.e.
01 Pubblicazione su rivista::01a Articolo in rivista
STOCHASTICALLY PERTURBED LANDAU-GINZBURG EQUATIONS / Roberto, Benzi; G., Jonalasinio; Sutera, Alfonso. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 55:3-4(1989), pp. 505-522. [10.1007/bf01041596]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/609
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