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# Documents  82D60 | enregistrements trouvés : 15

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## Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 1 Seppäläinen, Timo | CIRM H

Post-edited

Research School;Mathematical Physics;Probability and Statistics

Variational formulas for limit shapes of directed last-passage percolation models. Connections of minimizing cocycles of the variational formulas to geodesics, Busemann functions, and stationary percolation.

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## Topology and geometry of biopolymers.AMS special sessionBoston # April 21-22, 2018 Flapan, Erica ; Wong, Helen | American Mathematical Society 2020 Nouveau

Congrès

- ix; 234 p.
ISBN 978-1-4704-4840-0

Contemporary mathematics , 0746

Localisation : Collection 1er étage

topologie des biopolymères # géométrie de l'ADN # nouage des protéines # théorie des noeuds # théorie des graphes spatiaux # géométrie différentielle # simulation moléculaire # modèle aléatoire de nouage de l'ADN

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## Physical knots :knotting, linking, and folding geometric objects in R3#AMS special session on...#April 21-22 Calvo, Jorge Alberto ; Millett, Kenneth C. ; Rawdon, Eric J. | American Mathematical Society 2002

Congrès

- 340 p.
ISBN 978-0-8218-3200-4

Contemporary mathematics , 0304

Localisation : Collection 1er étage

théorie des noeuds # mathématique de la physique # variété # complexe cellulaire # noeud en dimension 3 # entrelacs # mathématique appliquée # biologie # ADN # entrelacement

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## Numerical methods for polymeric systemspapers from the workshop held at the University of Minnesota#May Whittington, Stuart G. | Springer 1999

Congrès

- 215 p.
ISBN 978-0-387-98557-2

The IMA volumes in mathematics and its applications , 0102

Localisation : Colloque 1er étage (MINN)

analyse numérique # mécanique statistique # structure de la matière # équilibre # méthode de Monte-Carlo # chaîne de Markov # polymère # somme de variables aléatoires indépendantes # marche aléatoire

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## Applications of knot theoryAmerican mathematical society short courseSan Diego # january 4-5, 2008 Buck, Dorothy ; Flapan, Erica | American Mathematical Society 2009

Congrès

- x; 186 p.
ISBN 978-0-8218-4466-3

Proceedings of symposia in applied mathematics , 0066

Localisation : Collection 1er étage

variétés # théorie des noeuds # ADN # biologie

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## Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 3 Seppäläinen, Timo | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

Kardar-Parisi-Zhang fluctuation exponent for the last-passage value of the two-dimensional corner growth model with exponential weights. We sketch the proof of the fluctuation exponent for the stationary corner growth process, and if time permits indicate how the exponent is derived for the percolation process with i.i.d. weights.

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## Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 2 Seppäläinen, Timo | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

Busemann functions for the two-dimensional corner growth model with exponential weights. Derivation of the stationary corner growth model and its use for calculating the limit shape and proving existence of Busemann functions.

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## The KPZ fixed point - Lecture 2 Remenik, Daniel | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion process (TASEP). Then I will present a Fredholm determinant formula for its distribution (at a fixed time) and show how all the main properties of the fixed point (including the Markov property, space and time regularity, symmetries and scaling invariance, and variational formulas) can be derived from the formula and the construction, and also how the formula reproduces known self-similar solutions such as the $Airy_1andAiry_2$ processes.
The second part of the course will be devoted to explaining how the KPZ fixed point can be computed starting from TASEP. The method is based on solving, for any initial condition, the biorthogonal ensemble representation for TASEP found by Sasamoto '05 and Borodin-Ferrari-Prähofer-Sasamoto '07. The resulting kernel involves transition probabilities of a random walk forced to hit a curve defined by the initial data, and in the KPZ 1:2:3 scaling limit the formula leads in a transparent way to a Fredholm determinant formula given in terms of analogous kernels based on Brownian motion.
Based on joint work with K. Matetski and J. Quastel.
In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion ...

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## The KPZ fixed point - Lecture 1 Remenik, Daniel | CIRM H

Multi angle

Research School;Mathematical Physics;Probability and Statistics

In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion process (TASEP). Then I will present a Fredholm determinant formula for its distribution (at a fixed time) and show how all the main properties of the fixed point (including the Markov property, space and time regularity, symmetries and scaling invariance, and variational formulas) can be derived from the formula and the construction, and also how the formula reproduces known self-similar solutions such as the $Airy_1andAiry_2$ processes.
The second part of the course will be devoted to explaining how the KPZ fixed point can be computed starting from TASEP. The method is based on solving, for any initial condition, the biorthogonal ensemble representation for TASEP found by Sasamoto '05 and Borodin-Ferrari-Prähofer-Sasamoto '07. The resulting kernel involves transition probabilities of a random walk forced to hit a curve defined by the initial data, and in the KPZ 1:2:3 scaling limit the formula leads in a transparent way to a Fredholm determinant formula given in terms of analogous kernels based on Brownian motion.
Based on joint work with K. Matetski and J. Quastel.
In these lectures I will present the recent construction of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class.
In the first part of the minicourse I will describe this process and how it arises from a particular microscopic model, the totally asymmetric exclusion ...

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## Multiscale modeling for soft matter - Perspectives and challenges Kremer, Kurt | CIRM H

Multi angle

Research talks;Numerical Analysis and Scientific Computing;Mathematical Physics

Material properties of soft matter are governed by a delicate interplay of energetic and entropic contributions. In other words, generic universal aspects are as relevant as local chemistry specific properties. Thus many different time and length scales are intimately coupled, which often makes a clear separation of scales difficult. This introductory lecture will review recent advances in multiscale modeling of soft matter. This includes different approaches of sequential and concurrent coupling. Furthermore problems of representability and transferability will be addressed as well as the question of scaling of time upon coarse graining. Finally some new developments related to data driven methods will be shortly mentioned. Material properties of soft matter are governed by a delicate interplay of energetic and entropic contributions. In other words, generic universal aspects are as relevant as local chemistry specific properties. Thus many different time and length scales are intimately coupled, which often makes a clear separation of scales difficult. This introductory lecture will review recent advances in multiscale modeling of soft matter. This includes ...

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## Annealed scaling for a charged polymer den Hollander, Frank | CIRM H

Multi angle

Research talks;Probability and Statistics

We study an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes an energy to the interaction Hamiltonian that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. We analyze the annealed free energy per monomer in the limit as the length of the polymer chain tends to infinity. We derive a spectral representation for the free energy and use this to show that there is a critical curve in the (charge bias, inverse temperature)-plane separating a ballistic phase from a subballistic phase. We show that the phase transition is first order, identify the scaling behaviour of the critical curve for small and for large charge bias, and also identify the scaling behaviour of the free energy for small charge bias and small inverse temperature. In addition, we prove a large deviation principle for the joint law of the empirical speed and the empirical charge, and derive a spectral representation for the associated rate function. This in turn leads to a law of large numbers and a central limit theorem. What happens for the quenched free energy per monomer remains open. We state two modest results and raise a few questions. Joint work with F. Caravenna, N. Petrelis and J. Poisat We study an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes an energy to the interaction Hamiltonian that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. We ...

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## The statistical mechanics of interacting walks, polygons, animals and vesicles Janse van Rensburg, E. J. | Oxford University Press 2000

Ouvrage

- x; 379 p.
ISBN 978-0-19-850561-7

Oxford lecture series in mathematics and its applications , 0018

Localisation : Ouvrage RdC (JANS)

mécanique statistique # homogénéisation # matériau composite

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## Stochastic processes in polymeric fluids :tools and examples for developing simulation algorithms Ottinger, Hans Christian | Springer-Verlag 1996

Ouvrage

- 362 p.
ISBN 978-3-540-58353-0

Localisation : Ouvrage RdC (OTTI)

mécanique des fluides # fluide visco-élastique # analyse stochastique # mécanique statistique # analyse numérique # polymer # dynamique des polymers # algorithme # simulation # FORTRAN # modélisation

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## Numerical solution of elliptic and parabolic partial differential equationsWith CD-ROM Trangenstein, John A. | Cambridge University Press 2013

Ouvrage

- xix; 635 p.
ISBN 978-0-521-87726-8

Localisation : Ouvrage RdC (TRAN)

analyse numérique # équation différentielle elliptique # équation différentielle parabolique

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## Modeling of soft matter Calderer, M. T. ; Terentjev, E. M. | Springer 2005

Ouvrage

- 99 p.
ISBN 978-0-387-29167-3

The IMA volumes in mathematics and its applications , 0141

Localisation : Ouvrage Rdc (Mode)

mécanique des solides déformables # mécanique des fluides # mécanique statistique # mécanique des solides # rhéologie # polymère # modélisation # structure de la matière

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