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Effects of fluctuations on propagating fronts
 Physics ReportsReview Section of Physics Letters
, 2004
"... Propagating fronts are seen in varieties of nonequilibrium pattern forming systems in Physics, Chemistry and Biology. In the last two decades, many researchers have contributed to the understanding of the underlying dynamics of the propagating fronts. Of these, the deterministic and meanfield dyna ..."
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Propagating fronts are seen in varieties of nonequilibrium pattern forming systems in Physics, Chemistry and Biology. In the last two decades, many researchers have contributed to the understanding of the underlying dynamics of the propagating fronts. Of these, the deterministic and meanfield dynamics of the fronts were mostly understood in late 1980s and 1990s. On the other hand, although the earliest work on the effect of fluctuations on propagating fronts dates back to early 1980s, the subject of fluctuating fronts did not reach its adolescence until the mid 1990s. From there onwards the last few years witnessed a surge in activities in the effect of fluctuations on propagating fronts. Scores of papers have been written on this subject since then, contributing to a significant maturity of our understanding, and only recently a full picture of fluctuating fronts has started to emerge. This review is an attempt to collect all the works on fluctuating (propagating) fronts in a coherent and cogent manner in proper perspective. It is based on the idea of making our knowledge in this field available to a broader audience, and it is also expected to help to collect
Microscopic models of traveling wave equations
 Computer Physics Communications
, 1999
"... Reactiondiffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or KolmogorovPetrovskyPiscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. B ..."
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Reactiondiffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or KolmogorovPetrovskyPiscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. By simulating systems of size up to N = 10 16 particles at the microscopic scale, where particles react and diffuse according to some stochastic rules, we show that a single velocity is selected for the front. This velocity converges logarithmically to the solution of the FKPP equation with minimal velocity when the number N of particles increases. A simple calculation of the effect introduced by the cutoff due to the microscopic scale allows one to understand the origin of the logarithmic correction.
The critical wave speed for the Fisher–Kolmogorov–Petrowskii–Piscounov equation with cutoff
, 2007
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Series Expansions of Lyapunov Exponents and Forgetful Monoids
, 2000
"... We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memoryloss property which holds generically for random products of matrices over the maxplus semiring, and in particular, for ..."
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We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memoryloss property which holds generically for random products of matrices over the maxplus semiring, and in particular, for Tetrislike heaps of pieces models, we give a series expansion formula for the Lyapunov exponent, as a function of the probability law. In the case of rational probability laws, we show that the Lyapunov exponent is an analytic function of the parameters of the law, in a domain that contains the absolute convergence domain of a partition function associated to a special "forgetful" monoid, defined by generators and relations.
Series Expansions of Lyapunov Exponents and
, 2000
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
École Doctorale de Physique de la Région Parisienne ED 107 Thèse de doctorat
"... Sujet de la thèse: Dynamique quantique horséquilibre et systèmes désordonnés pour des atomes ultrafroids bosoniques présentée par Bruno Sciolla pour obtenir le grade de Docteur de l’Université Parissud 11 Directeur de thèse: Henri Orland Thèse préparée sous la direction de Giulio Biroli ..."
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Sujet de la thèse: Dynamique quantique horséquilibre et systèmes désordonnés pour des atomes ultrafroids bosoniques présentée par Bruno Sciolla pour obtenir le grade de Docteur de l’Université Parissud 11 Directeur de thèse: Henri Orland Thèse préparée sous la direction de Giulio Biroli
Dynamique quantique horséquilibre et systèmes désordonnés pour des atomes ultrafroids bosoniques
, 2012
"... ..."
LIMIT THEOREM FOR SUMS OF RANDOM PRODUCTS
, 2008
"... We study asymptotic behavior of the sums ZN,m(β) determined by the formula N∑ λ ZN,m(β) = ..."
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We study asymptotic behavior of the sums ZN,m(β) determined by the formula N∑ λ ZN,m(β) =
Computer Physics Communications 121–122 (1999) 376–381 www.elsevier.nl/locate/cpc Microscopic models of traveling wave equations
"... Reactiondiffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov–Petrovsky–Piscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. B ..."
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Reactiondiffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov–Petrovsky–Piscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. By simulating systems of size up toN D 1016 particles at the microscopic scale, where particles react and diffuse according to some stochastic rules, we show that a single velocity is selected for the front. This velocity converges logarithmically to the solution of the FKPP equation with minimal velocity when the number N of particles increases. A simple calculation of the effect introduced by the cutoff due to the microscopic scale allows one to
Shift in the velocity of a front . . .
, 1997
"... We consider the effect of a small cutoff ε on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff ε is to select a single velocity which converges when ε→0to the o ..."
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We consider the effect of a small cutoff ε on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff ε is to select a single velocity which converges when ε→0to the one predicted by the marginal stability argument. For small ε, the shift in velocity has the form K(log ε) −2 and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the FisherKolmogorov or similar equations.