The Experts below are selected from a list of 136584 Experts worldwide ranked by ideXlab platform
Jérôme Kasparian - One of the best experts on this subject based on the ideXlab platform.
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Stabilization of uni-directional water wave trains over an uneven bottom
Nonlinear Dynamics, 2020Co-Authors: Andrea Armaroli, Alexis Gomel, Amin Chabchoub, Maura Brunetti, Jérôme KasparianAbstract:We study the evolution of nonlinear surface gravity water wave packets developing from modulational instability over an uneven bottom. A nonlinear Schrödinger equation (NLSE) with coefficients varying in space along propagation is used as a reference model. Based on a low-Dimensional Approximation obtained by considering only three complex harmonic modes, we discuss how to stabilize a one-Dimensional pattern in the form of train of large peaks sitting on a background and propagating over a significant distance. Our approach is based on a gradual depth variation, while its conceptual framework is the theory of autoresonance in nonlinear systems and leads to a quasi-frozen state. Three main stages are identified: amplification from small sideband amplitudes, separatrix crossing and adiabatic conversion to orbits oscillating around an elliptic fixed point. Analytical estimates on the three stages are obtained from the low-Dimensional Approximation and validated by NLSE simulations. Our result will contribute to understand the dynamical stabilization of nonlinear wave packets and the persistence of large undulatory events in hydrodynamics and other nonlinear dispersive media.
Koichi Suyama - One of the best experts on this subject based on the ideXlab platform.
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An internally stable realization of a finite-Dimensional Approximation of a delay element
International Journal of Control, 2004Co-Authors: Koichi SuyamaAbstract:Gain scheduling of the error of a finite-Dimensional Approximation of a delay element is an effective solution of an control problem for delay systems. In order to overcome the problem of a possible unstable pole-zero cancellation in the straightforward realization of the Approximation error, this paper presents a method for obtaining its internally stable realization using finite Laplace transforms.
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Internally stable realization of finite-Dimensional Approximation of a delay for gain scheduling
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 1Co-Authors: Koichi SuyamaAbstract:Gain scheduling of finite-Dimensional Approximation error of a delay is an effective solution of an H/sub /spl infin// control problem for a delay system. To overcome a possible unstable pole-zero cancellation in realizing directly the Approximation error, this paper presents a method for obtaining its internally stable realization using finite Laplace transforms.
Jens Eggers - One of the best experts on this subject based on the ideXlab platform.
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Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation
Journal of Fluid Mechanics, 1994Co-Authors: Jens Eggers, Todd F. DupontAbstract:We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-Dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.
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drop formation in a one Dimensional Approximation of the navier stokes equation
Journal of Fluid Mechanics, 1992Co-Authors: Jens Eggers, Todd DupontAbstract:We consider the viscous motion of a thin axisymmetric column of fluid with a free surface. A one-Dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare our results with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.
E Weinan - One of the best experts on this subject based on the ideXlab platform.
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ergodicity for the navier stokes equation with degenerate random forcing finite Dimensional Approximation
Communications on Pure and Applied Mathematics, 2001Co-Authors: E Weinan, Jonathan C MattinglyAbstract:We study Galerkin truncations of the two-Dimensional Navier-Stokes equation under degenerate, large-scale, stochastic forcing. We identify the minimal set of modes that has to be forced in order for the system to be ergodic. Our results rely heavily on the structure of the nonlinearity. c 2001 John Wiley & Sons, Inc.
Andrea Armaroli - One of the best experts on this subject based on the ideXlab platform.
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Stabilization of uni-directional water wave trains over an uneven bottom
Nonlinear Dynamics, 2020Co-Authors: Andrea Armaroli, Alexis Gomel, Amin Chabchoub, Maura Brunetti, Jérôme KasparianAbstract:We study the evolution of nonlinear surface gravity water wave packets developing from modulational instability over an uneven bottom. A nonlinear Schrödinger equation (NLSE) with coefficients varying in space along propagation is used as a reference model. Based on a low-Dimensional Approximation obtained by considering only three complex harmonic modes, we discuss how to stabilize a one-Dimensional pattern in the form of train of large peaks sitting on a background and propagating over a significant distance. Our approach is based on a gradual depth variation, while its conceptual framework is the theory of autoresonance in nonlinear systems and leads to a quasi-frozen state. Three main stages are identified: amplification from small sideband amplitudes, separatrix crossing and adiabatic conversion to orbits oscillating around an elliptic fixed point. Analytical estimates on the three stages are obtained from the low-Dimensional Approximation and validated by NLSE simulations. Our result will contribute to understand the dynamical stabilization of nonlinear wave packets and the persistence of large undulatory events in hydrodynamics and other nonlinear dispersive media.