Stochastically perturbed Landau-Ginzburg equations |
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Authors: | Roberto Benzi Giovanni Jona-Lasinio Alfonso Sutera |
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Institution: | (1) Dipartimento di Fisica, Università di Roma Tor Vergata, I-00173 Rome, Italy;(2) Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Rome, Italy;(3) Department of Geology and Geophysics, Yale University, 06511 New Haven, Connecticut |
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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. |
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Keywords: | Stochastic P D E renormalization large (small) scale fluctuations atmospheric bimodality |
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