The Experts below are selected from a list of 248685 Experts worldwide ranked by ideXlab platform

Christoph Walker - One of the best experts on this subject based on the ideXlab platform.

  • A Parabolic Free Boundary Problem Modeling Electrostatic MEMS
    Archive for Rational Mechanics and Analysis, 2014
    Co-Authors: Joachim Escher, Philippe Laurençot, Christoph Walker
    Abstract:

    The Evolution Problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary Problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.

  • a parabolic free boundary Problem modeling electrostatic mems
    arXiv: Analysis of PDEs, 2012
    Co-Authors: Joachim Escher, Philippe Laurençot, Christoph Walker
    Abstract:

    The Evolution Problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary Problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.

Joachim Escher - One of the best experts on this subject based on the ideXlab platform.

  • A Parabolic Free Boundary Problem Modeling Electrostatic MEMS
    Archive for Rational Mechanics and Analysis, 2014
    Co-Authors: Joachim Escher, Philippe Laurençot, Christoph Walker
    Abstract:

    The Evolution Problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary Problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.

  • a parabolic free boundary Problem modeling electrostatic mems
    arXiv: Analysis of PDEs, 2012
    Co-Authors: Joachim Escher, Philippe Laurençot, Christoph Walker
    Abstract:

    The Evolution Problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary Problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.

Andreas Kugi - One of the best experts on this subject based on the ideXlab platform.

  • stability of an euler bernoulli beam with a nonlinear dynamic feedback system
    IEEE Transactions on Automatic Control, 2016
    Co-Authors: Maja Miletic, Dominik Sturzer, Anton Arnold, Andreas Kugi
    Abstract:

    This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a finite-dimensional nonlinear dynamic feedback system. The latter comprises dynamic systems satisfying the nonlinear KYP lemma, which may represent the closed-loop dynamics of subordinate controlled actuators, as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability is rigorously proven for the resulting closed-loop partial differential equation–ordinary differential equation (PDE–ODE) system. The analysis is based on semigroup theory for the corresponding first order Evolution Problem. For the large-time analysis, precompactness of the trajectories is shown by deriving uniform-in-time bounds on the solution and its time derivatives.

  • stability of an euler bernoulli beam with a nonlinear dynamic feedback system
    arXiv: Analysis of PDEs, 2015
    Co-Authors: Maja Miletic, Dominik Sturzer, Anton Arnold, Andreas Kugi
    Abstract:

    This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers satisfying the nonlinear KYP lemma as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability is rigorously proven for the resulting closed-loop PDE-ODE system. The analysis is based on semigroup theory for the corresponding first order Evolution Problem. For the large-time analysis, precompactness of the trajectories is shown by deriving uniform-in-time bounds on the solution and its time derivatives.

Anthony Nouy - One of the best experts on this subject based on the ideXlab platform.

  • Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods
    ESAIM: Mathematical Modelling and Numerical Analysis, 2019
    Co-Authors: Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern, Anthony Nouy
    Abstract:

    We devise a space-time tensor method for the low-rank approximation of linear parabolic Evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual formulation of the Evolution Problem in Hilbert--Bochner spaces. The discrete solution is sought in a linear trial space composed of tensors of discrete functions in space and in time and is characterized as the unique minimizer of a discrete functional where the dual norm of the residual is evaluated in a space semi-discrete test space. The resulting global space-time linear system is solved iteratively by a greedy algorithm. Numerical results are presented to illustrate the performance of the proposed method on test cases including non-selfadjoint and time-dependent differential operators in space. The results are also compared to those obtained using a fully discrete Petrov--Galerkin setting to evaluate the dual residual norm.

  • low rank approximation of linear parabolic equations by space time tensor galerkin methods
    arXiv: Numerical Analysis, 2017
    Co-Authors: Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern, Anthony Nouy
    Abstract:

    We devise a space-time tensor method for the low-rank approximation of linear parabolic Evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual formulation of the Evolution Problem in Hilbert--Bochner spaces. The discrete solution is sought in a trial space composed of tensors of discrete functions in space and in time and is characterized as the unique minimizer of a discrete functional where the dual norm of the residual is evaluated in a space semi-discrete test space. The resulting global space-time linear system is solved iteratively by a greedy algorithm. Numerical results are presented to illustrate the performances of the proposed method on test cases including non-selfadjoint and time-dependent differential operators in space. The results are also compared to those obtained using a fully discrete Petrov--Galerkin setting to evaluate the dual residual norm.

Philippe Laurençot - One of the best experts on this subject based on the ideXlab platform.

  • A Parabolic Free Boundary Problem Modeling Electrostatic MEMS
    Archive for Rational Mechanics and Analysis, 2014
    Co-Authors: Joachim Escher, Philippe Laurençot, Christoph Walker
    Abstract:

    The Evolution Problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary Problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.

  • a parabolic free boundary Problem modeling electrostatic mems
    arXiv: Analysis of PDEs, 2012
    Co-Authors: Joachim Escher, Philippe Laurençot, Christoph Walker
    Abstract:

    The Evolution Problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary Problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.