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In this talk we will don't speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange's reception at the nineteenth Century. "Who read Lagrange at this Times?", "Why and How?", "What does it mean being a mathematician or doing mathematics at this Century" are some of the questions of our conference. We will give some elements of answers and the case Lagrange will be a pretext in order to explain what are doing historians of mathematics: searching archives and – thanks to a methodology – trying to understand, read and write the Past.
Lagrange - mathematical press - complete works - bibliographic index of mathematical sciences (1894-1912) - Liouville - Boussinesq - Terquem
[-] In this talk we will don't speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange's reception at the nineteenth Century. "Who read Lagrange at this Times?", "Why and How?", "What does it mean being a mathematician or doing mathematics at this Century" are some of the questions of our conference. We will give some elements of answers and the case Lagrange will be a pretext in order to explain what are doing historians of mathematics: ...
[+] 01A50 ; 01A55 ; 01A70 ; 01A74 ; 01A80
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y
Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.
[-] Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field ...
[+] 76F25 ; 35Q70 ; 70F99
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Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.
[-] Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field ...
[+] 76F25 ; 35Q70 ; 70F99
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y
Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.
[-] Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field ...
[+] 76F25 ; 35Q70 ; 70F99
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The spectral properties of a singularly perturbed self-adjoint Landau Hamiltonian in the plane with a delta-potential supported on a finite curve are studied. After a general discussion of the qualitative spectral properties of the perturbed Landau Hamiltonian and its resolvent, one of our main objectives is a local spectral analysis near the Landau levels.
This talk is based on joint works with P. Exner, M. Holzmann, V. Lotoreichik, and G. Raikov.
[-] The spectral properties of a singularly perturbed self-adjoint Landau Hamiltonian in the plane with a delta-potential supported on a finite curve are studied. After a general discussion of the qualitative spectral properties of the perturbed Landau Hamiltonian and its resolvent, one of our main objectives is a local spectral analysis near the Landau levels.
This talk is based on joint works with P. Exner, M. Holzmann, V. Lotoreichik, and G. ...
[+] 47A55 ; 47N50 ; 81Q10
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In this (hopefully) blackboard talk, we will discuss the spectral analysis of the Robin Laplacian on a smooth bounded two-dimensional domain in the presence of a constant magnetic field. In the semiclassical limit, I will explain how to get a uniform description of the spectrum located between the Landau levels. The corresponding eigenfunctions, called edge states, are exponentially localized near the boundary. By means of a microlocal dimensional reduction, I will explain how to derive a very precise Weyl law and a proof of quantum magnetic oscillations for excited states, and also how to refine simultaneously old results about the low-lying eigenvalues in the Robin case and recent ones about edge states in the Dirichlet case.
Joint work with R. Fahs, L. Le Treust and S. Vu Ngoc.
[-] In this (hopefully) blackboard talk, we will discuss the spectral analysis of the Robin Laplacian on a smooth bounded two-dimensional domain in the presence of a constant magnetic field. In the semiclassical limit, I will explain how to get a uniform description of the spectrum located between the Landau levels. The corresponding eigenfunctions, called edge states, are exponentially localized near the boundary. By means of a microlocal d...
[+] 81Q10 ; 35Pxx
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One-particle density matrix is the key object in the quantum-mechanical approximation schemes. In this talk I will give a short survey of recent regularity results with emphasis on sharp bounds for the eigenfunctions, and show how these bounds lead to the asymptotic formula for the eigenvalues of the one-particle density matrix. The argument is based on the results of M. Birman and M. Solomyak on spectral asymptotics for pseudo-differential operators with matrix-valued symbols.
[-] One-particle density matrix is the key object in the quantum-mechanical approximation schemes. In this talk I will give a short survey of recent regularity results with emphasis on sharp bounds for the eigenfunctions, and show how these bounds lead to the asymptotic formula for the eigenvalues of the one-particle density matrix. The argument is based on the results of M. Birman and M. Solomyak on spectral asymptotics for pseudo-differential ...
[+] 35J10 ; 47G10
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Let $\Omega \subset \mathbb{R}^3$ be a sheared waveguide, i.e., $\Omega$ is built by translating a cross-section (an arbitrary bounded connected open set of $\mathbb{R}^2$ ) in a constant direction along an unbounded spatial curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in $\Omega$. Under the condition that the tangent vector of the reference curve admits a finite limit at infinity, we find the essential spectrum of $-\Delta_{\Omega}^D$. After that, we state sufficient conditions that give rise to a non-empty discrete spectrum for $-\Delta_{\Omega}^D$. Finally, in case the cross section translates along a broken line in $\mathbb{R}^3$, we prove that the discrete spectrum of $-\Delta_{\Omega}^D$ is finite, furthermore, we show a particular geometry for $\Omega$ which implies that the total multiplicity of the discrete spectrum is equals 1.
[-] Let $\Omega \subset \mathbb{R}^3$ be a sheared waveguide, i.e., $\Omega$ is built by translating a cross-section (an arbitrary bounded connected open set of $\mathbb{R}^2$ ) in a constant direction along an unbounded spatial curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in $\Omega$. Under the condition that the tangent vector of the reference curve admits a finite limit at infinity, we find the essential spectrum of ...
[+] 49R05 ; 47A75 ; 47F05
English
