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Documents  Critères de recherche : "Dynamics" | enregistrements trouvés : 364

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I discuss several types of inverse problems for fluid dynamics such as Navier-Stokes equations. I prove uniqueness and conditional stability for the formulations by Dirichlet-to-Neumann map and Carleman estimates. This is a joint work with Prof. O. Imanuvilov (Colorado State Univ.)

35R30

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The aim of this two-hour lecture is to present the mathematical underpinnings of some common numerical approaches to compute average properties as predicted by statistical physics. The first part provides an overview of the most important concepts of statistical physics (in particular thermodynamic ensembles). The aim of the second part is to provide an introduction to the practical computation of averages with respect to the Boltzmann-Gibbs measure using appropriate stochastic dynamics of Langevin type. Rigorous ergodicity results as well as elements on the estimation of numerical errors are provided. The last part is devoted to the computation of transport coefficients such as the mobility or autodiffusion in fluids, relying either on integrated equilibrium correlations à la Green-Kubo, or on the linear response of nonequilibrium dynamics in their steady-states. The aim of this two-hour lecture is to present the mathematical underpinnings of some common numerical approaches to compute average properties as predicted by statistical physics. The first part provides an overview of the most important concepts of statistical physics (in particular thermodynamic ensembles). The aim of the second part is to provide an introduction to the practical computation of averages with respect to the Boltzmann-Gibbs ...

82B31 ; 82B80 ; 65C30 ; 82C31 ; 82C70 ; 60H10

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I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between shift to higher frequencies and escaping in the physical space. I will show meromorphic continuation of the resolvent of $X$; the poles, known as Pollicott-Ruelle resonances, describe exponential decay of correlations. As an application, I will prove that the Ruelle zeta function continues meromorphically for flows on non-compact manifolds (the compact case, known as Smale's conjecture, was recently settled by Giulietti-Liverani- Pollicott and a simple microlocal proof was given by Zworski and the speaker). Joint work with Colin Guillarmou. I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between ...

37D50 ; 53D25 ; 37D20 ; 35B34 ; 35P25

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These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb while controlling the dynamics: closing and connection of orbits, perturbation of the tangent dynamics... We derive various applications to the description of $C^1$-generic diffeomorphisms. These lectures will address the dynamics of vector fields or diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb ...

37C05 ; 37C29 ; 37Dxx

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The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by generation expansion (with the generation number corresponding to the number of times an individual became infected).
In joint work in progress with Wilfred de Graaf, Peter Teunis and Mirjam Kretzschmar we want to use either the generation expansion or an invariant/stable distribution as the starting point for the efficient computation of coarse statistics.
The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by ...

92D30 ; 60J75 ; 45D05

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Cubic surfaces in affine three space tend to have few integral points .However certain cubics such as $x^3 + y^3 + z^3 = m$, may have many such points but very little is known. We discuss these questions for Markoff type surfaces: $x^2 +y^2 +z^2 -x\cdot y\cdot z = m$ for which a (nonlinear) descent allows for a study. Specifically that of a Hasse Principle and strong approximation, together with "class numbers" and their averages for the corresponding nonlinear group of morphims of affine three space. Cubic surfaces in affine three space tend to have few integral points .However certain cubics such as $x^3 + y^3 + z^3 = m$, may have many such points but very little is known. We discuss these questions for Markoff type surfaces: $x^2 +y^2 +z^2 -x\cdot y\cdot z = m$ for which a (nonlinear) descent allows for a study. Specifically that of a Hasse Principle and strong approximation, together with "class numbers" and their averages for the ...

11G05 ; 37A45

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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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The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform analyticity for a large set of initial data, turbulence phenomenon for a dense set of smooth initial data in large Sobolev spaces.
From joint works with Patrick Gérard.
The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform ...

35B40 ; 35B15 ; 35Q55 ; 37K15 ; 47B35

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We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient.
We motivate our model in relation to experimental data and demonstrate how it correctly reproduces cut and graft experiments. In particular, our system improves on previous models by preserving polarity in regeneration, over orders of magnitude in body size during cutting experiments and growth phases. Our model relies on tristability in cell density dynamics, between head, trunk, and tail. In addition, key to polarity preservation in regeneration, our system includes sensitivity of cell differentiation to gradients of wnt-related signals measured relative to the tissue surface. This process is particularly relevant in a small tissue layer close to wounds during their healing, and modeled here in a robust fashion through dynamic boundary conditions.
We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient.
We motivate our model in relation to ...

92C15 ; 35B36 ; 35Q92 ; 37N25 ; 35K40

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Proceedings of symposia in applied mathematics , 0004

Localisation : Collection 1er étage

76-05 ; 76-06 ; 76Fxx ; 76JXX ; 76K05

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Proceedings of symposia in applied mathematics , 0018

Localisation : Collection 1er étage

76-06 ; 76Exx

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- 827 p.
ISBN 978-0-387-12336-3

Lecture notes in mathematics , 1007

Localisation : Collection 1er étage

58-06 ; 58-XX

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- 77 p.
ISBN 978-0-8218-1695-0

CBMS regional conference series in mathematics , 0003

Localisation : Collection 1er étage

34-02 ; 34C35 ; 54H20 ; 58F15 ; 70-02

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- 213 p.
ISBN 978-0-387-12705-7

Lecture notes in mathematics , 1031

Localisation : Collection 1er étage;Doubles

46Lxx ; 58Fxx ; 70Fxx ; 76Fxx

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ISBN 978-90-277-1390-2

Nato a.s.i. series

Localisation : Colloque 1er étage (CORT)

anneau # astrodynamique # astéroide # dynamique moderne # détermination # géodésique # mécanique céleste # mécanique statistique # nonlinéarité # planète # régularisation # résonance # satellite # variété # étoile

85-06 ; 85A04

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ISBN 978-0-12-302940-9

Academic press rapid manuscript reproduction

Localisation : Colloque 1er étage (MADI)

controle optimal # cours du système PLATO # diagramme d'age de mortalité # donnée censurée et risque de conception # dynamique de population # démographie # dépendance de durée # fonction de mariage # impact de la contraception # lactation sur post partum # lieu des 3 gènes # modèle d'attraction stochastique # modèle de mariage # onde de population # processus de migration # processus semi- Markov # processus stochastique doublement # structure des causes de décés controle optimal # cours du système PLATO # diagramme d'age de mortalité # donnée censurée et risque de conception # dynamique de population # démographie # dépendance de durée # fonction de mariage # impact de la contraception # lactation sur post partum # lieu des 3 gènes # modèle d'attraction stochastique # modèle de mariage # onde de population # processus de migration # processus semi- Markov # processus stochastique doublement # structure ...

92-06 ; 92A15

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- 187 p.
ISBN 978-0-387-12893-1

Lecture notes in mathematics , 1047

Localisation : Collection 1er étage

35D05 ; 35F25 ; 35L60 ; 76N10

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- 360 p.
ISBN 978-3-540-12549-5

Von karman institute book

Localisation : Ouvrage RdC (Comp)

76-04

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- 267 p.
ISBN 978-0-8218-1120-7

Lectures in applied mathematics , 0020

Localisation : Collection 1er étage

76-XX ; 85-XX ; 86-XX

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- 333 p.
ISBN 978-0-387-15225-7

Lecture notes in mathematics , 1127

Localisation : Collection 1er étage

49DXX ; 65Dxx ; 65Nxx

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