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Research School;Partial Differential Equations;Mathematical Physics;Mathematics in Science and Technology

Lecture 1. Collective dynamics and self-organization in biological systems : challenges and some examples.

Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions

Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.

35L60 ; 82C22 ; 82B26 ; 82C26 ; 92D50

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- x; 343 p.
ISBN 978-3-540-92795-2

Lecture notes in mathematics , 1970

Localisation : Collection 1er étage

modèle de treillis # mécanique statistique # méta-stabilité # transition de phase # géométrie stochastique

82B20 ; 82B26 ; 82C20 ; 60K35 ; 82C26 ; 82C35 ; 82B31 ; 82B41 ; 82B44 ; 82B10 ; 82C22 ; 60K05 ; 82B05 ; 82C05 ; 82-06 ; 00B25

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Research School;Mathematical Physics

In these three lectures steady states and dynamical properties of nonequilibrium systems will be discussed.
Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. This is very different from systems in thermal equilibrium where long-range correlations develop only at phase transition points. In some cases these correlations even lead to long-range order in d=1 dimension, of the type occurring in traffic jams. Simple examples of such correlations induced in the steady state of driven systems will be presented and discussed. Close correspondence of these nonequilibrium steady states to electrostatic potentials induces by charge distribution will be pointed out.
Another class which will be discussed is that of systems with boundary drive, such as in heat conduction problems, where anomalous heat conduction takes place in low dimensions. In addition some similarities between driven systems and equilibrium systems with long-range interactions will be elucidated.
In these three lectures steady states and dynamical properties of nonequilibrium systems will be discussed.
Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. This is very different from systems in thermal equilibrium where long-range correlations develop only at phase transition points. In some cases these correlations even lead to long-range order in d=1 ...

82C26 ; 82C22

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Research School;Mathematical Physics

In these three lectures steady states and dynamical properties of nonequilibrium systems will be discussed.
Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. This is very different from systems in thermal equilibrium where long-range correlations develop only at phase transition points. In some cases these correlations even lead to long-range order in d=1 dimension, of the type occurring in traffic jams. Simple examples of such correlations induced in the steady state of driven systems will be presented and discussed. Close correspondence of these nonequilibrium steady states to electrostatic potentials induces by charge distribution will be pointed out.
Another class which will be discussed is that of systems with boundary drive, such as in heat conduction problems, where anomalous heat conduction takes place in low dimensions. In addition some similarities between driven systems and equilibrium systems with long-range interactions will be elucidated.
In these three lectures steady states and dynamical properties of nonequilibrium systems will be discussed.
Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. This is very different from systems in thermal equilibrium where long-range correlations develop only at phase transition points. In some cases these correlations even lead to long-range order in d=1 ...

82C26 ; 82C22

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Research School;Partial Differential Equations;Mathematical Physics;Mathematics in Science and Technology

Lecture 1. Collective dynamics and self-organization in biological systems : challenges and some examples.

Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions

Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.

35L60 ; 82C22 ; 82B26 ; 82C26 ; 92D50

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Research School;Partial Differential Equations;Mathematical Physics;Mathematics in Science and Technology

Lecture 1. Collective dynamics and self-organization in biological systems : challenges and some examples.

Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions

Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.

35L60 ; 82C22 ; 82B26 ; 82C26 ; 92D50

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Research schools

For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one, the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such instability is the ice-albedo feedback. In a previous work, we defined the Melancholia states that sit between the two climates. Such states are embedded in the boundaries between the two basins of attraction and feature extensive glaciation down to relatively low latitudes. Here, we explore the global stability properties of the system by introducing random perturbations as modulations to the intensity of the incoming solar radiation. We observe noise-induced transitions between the competing basins of attractions. In the weak noise limit, large deviation laws define the invariant measure and the statistics of escape times. By empirically constructing the instantons, we show that the Melancholia states are the gateways for the noise-induced transitions. In the region of multistability, in the zero-noise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. At this regard, we relate our results to the debate around the prominence of contigency vs. convergence in biological evolution. Finally, we propose a new method for constructing Melancholia states from direct numerical simulations, thus bypassing the need to use the edge-tracking algorithm. For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one, the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such i...

82C26 ; 60Gxx ; 37D45 ; 85A20 ; 76E20

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- 486 p.

Pure and applied physics , 0017

Localisation : Ouvrage RdC (BLAT)

distribution de Bore-Einstein # distribution de Fermi- Dirrac # dynamique statistique # e nsemble canonique # effet Meissner # ensemble d'équilibre # entropie # gaz # mécanique statistique # perturbation # phase critique # super conductivité # équilibre

82Bxx ; 82C26 ; 82C27 ; 82C35 ; 82D55

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- 542 p.
ISBN 978-5-03-000648-2

Collection mir traduction francaise

Localisation : Ouvrage RdC (LAND)

approximation de la diffusion # champ magnétique # cinétique # cinétique des transitions de phases # diélectrique # diffusion # liquide quantique # métaux # physique théorique # plasma # propriété cinétique des systèmes hors d'équilibre # supraconducteur # théorie cinétique des gaz # théorie des instabilités

81-02 ; 82-02 ; 82C26 ; 82C27 ; 82Cxx

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- 483 p.
ISBN 978-981-02-3764-6

Localisation : Ouvrage RdC (KADA)

dynamique # dynamique aléatoire # hydrodynamique # moment # mécanique quantique # mécanique statistique # phase de transition # physique statistique # point critique # renormalisation # renormalisation de dimension un # système désordonné # technique de renormalisation d

82-02 ; 82Bxx ; 82C05 ; 82C10 ; 82C26 ; 82C27 ; 82C35 ; 82C41 ; 82C44 ; 82Cxx

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- xxi; 581 p.
ISBN 978-3-319-24775-5

Grundlehren der mathematischen wissenschaften , 0351

Localisation : Collection 1er étage

distribution # processus de Markov # théorie du potentiel # diffusion #équation différentielle stochastique # physique statistique # système de treillis

60K35 ; 60J45 ; 82C26 ; 60-02 ; 60Jxx

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