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Flow past an obstacle in one dimension of a fluid described by a driven and dissipative non-linear Schroedinger equation| old_uid | 20076 |
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| title | Flow past an obstacle in one dimension of a fluid described by a driven and dissipative non-linear Schroedinger equation |
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| start_date | 2022/02/10 |
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| schedule | 16h-18h |
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| online | no |
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| details | - séance technique (formation en mathématiques ou physique recommandée). |
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| summary | It has been predicted long time ago by Lev Landau that the flow of a superfluid past an obstacle, a localized repulsive potential, is stationary below a critical velocity or a critical amplitude of the potential, and become time-dependent above. This phenomenon has beenim studied in several works by describing the dynamics of superfluids with the help of the nonlinear Schroedinger equation. It has also been experimentally studied using Bose condensates in cold atomic vapors. A new type of condensate has been recently studied ( an "exciton-polariton fluid") which needs to be modeled by a generalized nonlinear Schroedinger equation (GNLSE). The GNLSE wiithout a localized potential admits in the regime of interest, two coexisting stable constant solutions and one unstable constant solutions, with two different density (the square modulus of the solution).
We have studied the question of a flow past an obstacle in one-dimension for the GNLSE in this bistable regime with the injected fluid in the high density state. We have found by computer simulations that there are bifurcations of the flow, when the fluid velocity or the amplitude of the localized potential are increased but that they differ from the classical Landau bifurcation. Instead of a bifurcation towards a time-dependent solution, the bifurcations take place between stationary solutions. The solutions below and above the transition tend towards different stable constant solutions in the wake of the obstacle. At the bifurcation point, the solution is stationary and tends toward the unstable constant solution of the GNLE in the far wake of the obstacle. We will provide some explanations of these phenomena by an asymptotic analysis in the double limit of an obstacle varying on a long length scale and a large fluid velocity.
Work performed in collaboration with Amandine Aftalion (CNRS, CAMS) and Simon Pigeon (CNRS, LKB). |
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| oncancel | Nouveau - ! Horraire |
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| responsibles | Berestycki, Nadal |
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