The Experts below are selected from a list of 237 Experts worldwide ranked by ideXlab platform

Dominique Lépingle - One of the best experts on this subject based on the ideXlab platform.

  • A NON-LINEAR STOCHASTIC Differential Equation INVOLVING THE HILBERT TRANSFORM
    Journal of Functional Analysis, 1999
    Co-Authors: Aline Bonami, François Bouchut, Emmanuel Cépa, Dominique Lépingle
    Abstract:

    We consider a non-linear stochastic Differential Equation which involves the Hilbert transform, Xt=σ·Bt+2λ ∫t0 Hu(s, Xs) ds. In the previous Equation, u(t, ·) is the density of μt, the lax of Xt, and H represents the Hilbert transform in the space variable. In order to define correctly the solutions, we first study the associated non-linear second-order Integro-Partial Differential Equation which can be reduced to the holomorphic Burgers Equation. The real analyticity of solutions allows us to prove existence and uniqueness of the non-linear diffusion process. This stochastic Differential Equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity. More precisely, it has been show that the empirical measure process tends to the unique solution μ=(μt)t⩾0 of the non-linear second-order Integro-Partial Differential, Equation studied here.

  • A non linear stochastic Differential Equation involving Hilbert Transform
    Journal of Functional Analysis, 1999
    Co-Authors: Aline Bonami, François Bouchut, Emmanuel Cépa, Dominique Lépingle
    Abstract:

    We consider a non-linear stochastic Differential Equation which involves the Hilbert transform, Xt=σ·Bt+2λ ∫t0 Imageu(s, Xs) ds. In the previous Equation, u(t, ·) is the density of μt, the lax of Xt, and Image represents the Hilbert transform in the space variable. In order to define correctly the solutions, we first study the associated non-linear second-order Integro-Partial Differential Equation which can be reduced to the holomorphic Burgers Equation. The real analyticity of solutions allows us to prove existence and uniqueness of the non-linear diffusion process. This stochastic Differential Equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity. More precisely, it has been show that the empirical measure process tends to the unique solution μ=(μt)tgreater-or-equal, slanted0 of the non-linear second-order Integro-Partial Differential, Equation studied here.

Li-qun Chen - One of the best experts on this subject based on the ideXlab platform.

  • Asymptotic solutions of coupled Equations of supercritically axially moving beam
    Nonlinear Dynamics, 2016
    Co-Authors: Yuanbin Wang, Hu Ding, Li-qun Chen
    Abstract:

    In supercritical regime, the coupled model Equations for the axially moving beam with simple support boundary conditions are considered. The critical speed is determined by linear bifurcation analysis, which is in agreement with the results in the literature. For the corresponding static equilibrium state, the second-order asymptotic nontrivial solutions are obtained through the multiple scales method. Meantime, the numerical solutions are also obtained based on the finite difference method. Comparisons among the analytical solutions, numerical solutions and solutions of Integro-Partial-Differential Equation of transverse which is deduced from coupled model Equations are made. We find that the second-order asymptotic analytical solutions can well capture the nontrivial equilibrium state regardless of the amplitude of transverse displacement. However, the Integro-Partial-Differential Equation is only valid for the weak small-amplitude vibration axially moving slender beams.

  • Supercritical vibration of nonlinear coupled moving beams based on discrete Fourier transform
    International Journal of Non-Linear Mechanics, 2012
    Co-Authors: Hu Ding, Guo-ce Zhang, Li-qun Chen
    Abstract:

    Abstract Natural frequencies of nonlinear coupled planar vibration are investigated for axially moving beams in the supercritical transport speed ranges. The straight equilibrium configuration bifurcates in multiple equilibrium positions in the supercritical regime. The finite difference scheme is developed to calculate the non-trivial static equilibrium. The Equations are cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for non-trivial equilibrium configuration. Under fixed boundary conditions, time series are calculated via the finite difference method. Based on the time series, the natural frequencies of nonlinear planar vibration, which are determined via discrete Fourier transform (DFT), are compared with the results of the Galerkin method for the corresponding governing Equations without nonlinear parts. The effects of material parameters and vibration amplitude on the natural frequencies are investigated through parametric studies. The model of coupled planar vibration can reduce to two nonlinear models of transverse vibration. For the transverse Integro-Partial-Differential Equation, the equilibrium solutions are performed analytically under the fixed boundary conditions. Numerical examples indicate that the Integro-Partial-Differential Equation yields natural frequencies closer to those of the coupled planar Equation.

  • Supercritical equilibrium solutions of axially moving beams with hybrid boundary conditions
    Mechanics Research Communications, 2011
    Co-Authors: Hu Ding, Guo-ce Zhang, Li-qun Chen
    Abstract:

    Abstract In this paper supercritical equilibria and critical speeds of axially moving beams constrained by sleeves with torsion springs are deduced. Transverse vibration of the beams is governed by a nonlinear Integro-Partial-Differential Equation. In the supercritical regime, the corresponding static equilibrium Equation for the hybrid boundary conditions is analytically solved for the equilibria and the critical speeds. In the view of the non-trivial equilibrium, comparisons are made among the Integro-Partial-Differential Equation, a nonlinear partial-Differential Equation for transverse vibration, and coupled Equations for planar motion under the hybrid boundary conditions.

  • Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams
    Shock and Vibration, 2011
    Co-Authors: Hu Ding, Li-qun Chen
    Abstract:

    Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steady-state periodical response are numerically investigated. An Integro-Partial-Differential Equation and a partial-Differential Equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steady-state response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steady-state response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the Integro-Partial-Differential Equation gives results more closely to the coupled planar vibration.

  • A Numerical Investigation into Equilibria of Axially Moving Beams
    2010
    Co-Authors: Hu Ding, Li-qun Chen
    Abstract:

    Equilibria of axially moving beams with the fixed boundary conditions are computationally investigated in the supercritical transport speed ranges. The governing Equations of coupled planar is reduced to a partial‐Differential Equation and an integro‐partial‐Differential Equation of transverse vibration. The numerical schemes are respectively presented for the governing Equations and the corresponding static equilibrium Equation of coupled planar and the two governing Equations of transverse motion for non‐trivial equilibrium solutions via the finite difference method. A steel beam is treated as example to demonstrate the non‐trivial equilibrium solutions of three nonlinear Equations. It exhibits a symmetric pitchfork bifurcation as the axial velocity of the beam is varied beyond a critical value. Numerical results indicate that the three models predict qualitatively the same tendencies of the pitchfork bifurcation with the changing parameters and the integro‐partial‐Differential Equation yields results q...

Aline Bonami - One of the best experts on this subject based on the ideXlab platform.

  • A NON-LINEAR STOCHASTIC Differential Equation INVOLVING THE HILBERT TRANSFORM
    Journal of Functional Analysis, 1999
    Co-Authors: Aline Bonami, François Bouchut, Emmanuel Cépa, Dominique Lépingle
    Abstract:

    We consider a non-linear stochastic Differential Equation which involves the Hilbert transform, Xt=σ·Bt+2λ ∫t0 Hu(s, Xs) ds. In the previous Equation, u(t, ·) is the density of μt, the lax of Xt, and H represents the Hilbert transform in the space variable. In order to define correctly the solutions, we first study the associated non-linear second-order Integro-Partial Differential Equation which can be reduced to the holomorphic Burgers Equation. The real analyticity of solutions allows us to prove existence and uniqueness of the non-linear diffusion process. This stochastic Differential Equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity. More precisely, it has been show that the empirical measure process tends to the unique solution μ=(μt)t⩾0 of the non-linear second-order Integro-Partial Differential, Equation studied here.

  • A non linear stochastic Differential Equation involving Hilbert Transform
    Journal of Functional Analysis, 1999
    Co-Authors: Aline Bonami, François Bouchut, Emmanuel Cépa, Dominique Lépingle
    Abstract:

    We consider a non-linear stochastic Differential Equation which involves the Hilbert transform, Xt=σ·Bt+2λ ∫t0 Imageu(s, Xs) ds. In the previous Equation, u(t, ·) is the density of μt, the lax of Xt, and Image represents the Hilbert transform in the space variable. In order to define correctly the solutions, we first study the associated non-linear second-order Integro-Partial Differential Equation which can be reduced to the holomorphic Burgers Equation. The real analyticity of solutions allows us to prove existence and uniqueness of the non-linear diffusion process. This stochastic Differential Equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity. More precisely, it has been show that the empirical measure process tends to the unique solution μ=(μt)tgreater-or-equal, slanted0 of the non-linear second-order Integro-Partial Differential, Equation studied here.

Kouroush Sadegh Zadeh - One of the best experts on this subject based on the ideXlab platform.

  • An Integro-Partial Differential Equation for modeling biofluids flow in fractured biomaterials.
    Journal of theoretical biology, 2010
    Co-Authors: Kouroush Sadegh Zadeh
    Abstract:

    A novel mathematical model in the framework of a nonlinear Integro-Partial Differential Equation governing biofluids flow in fractured biomaterials is proposed, solved, verified, and evaluated. A semi-analytical solution is derived for the Equation, verified by a mass-lumped Galerkin finite element method (FEM), and calibrated with two in vitro experimental datasets. The solution process uses separation of variables and results in explicit expression involving complete and incomplete beta functions. The proposed semi-analytical model shows reasonable agreements with the finite element simulator as well as with two in vitro experimental time series and can be successfully used to simulate biofluids (e.g. water, blood, oil, etc.) flow in natural and synthetic porous biomaterials.

Emmanuel Cépa - One of the best experts on this subject based on the ideXlab platform.

  • A NON-LINEAR STOCHASTIC Differential Equation INVOLVING THE HILBERT TRANSFORM
    Journal of Functional Analysis, 1999
    Co-Authors: Aline Bonami, François Bouchut, Emmanuel Cépa, Dominique Lépingle
    Abstract:

    We consider a non-linear stochastic Differential Equation which involves the Hilbert transform, Xt=σ·Bt+2λ ∫t0 Hu(s, Xs) ds. In the previous Equation, u(t, ·) is the density of μt, the lax of Xt, and H represents the Hilbert transform in the space variable. In order to define correctly the solutions, we first study the associated non-linear second-order Integro-Partial Differential Equation which can be reduced to the holomorphic Burgers Equation. The real analyticity of solutions allows us to prove existence and uniqueness of the non-linear diffusion process. This stochastic Differential Equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity. More precisely, it has been show that the empirical measure process tends to the unique solution μ=(μt)t⩾0 of the non-linear second-order Integro-Partial Differential, Equation studied here.

  • A non linear stochastic Differential Equation involving Hilbert Transform
    Journal of Functional Analysis, 1999
    Co-Authors: Aline Bonami, François Bouchut, Emmanuel Cépa, Dominique Lépingle
    Abstract:

    We consider a non-linear stochastic Differential Equation which involves the Hilbert transform, Xt=σ·Bt+2λ ∫t0 Imageu(s, Xs) ds. In the previous Equation, u(t, ·) is the density of μt, the lax of Xt, and Image represents the Hilbert transform in the space variable. In order to define correctly the solutions, we first study the associated non-linear second-order Integro-Partial Differential Equation which can be reduced to the holomorphic Burgers Equation. The real analyticity of solutions allows us to prove existence and uniqueness of the non-linear diffusion process. This stochastic Differential Equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity. More precisely, it has been show that the empirical measure process tends to the unique solution μ=(μt)tgreater-or-equal, slanted0 of the non-linear second-order Integro-Partial Differential, Equation studied here.