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Register a new userAnalytical Solution for Wave Propagation in Stratified Poroelastic Medium. Part I: the 2D Case
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We are interested in the modeling of wave propagation in poroelastic media. We consider the biphasic Biots model in an infinite bilayered medium, with a plane interface. We adopt the Cagniard-De Hoops technique. This report is devoted to the calculation of analytical solutions in two dimensions. The solutions we present here have been used to validate numerical codes.
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We are interested in the modeling of wave propagation in poroelastic media. We consider the biphasic Biots model in an infinite bilayered medium with a plane interface. We adopt the Cagniard-De Hoops technique. This report is devoted to the calculation of analytical solution in three dimension.
We are interested in the modeling of wave propagation in an infinite bilayered acoustic/poroelastic media. We consider the biphasic Biots model in the poroelastic layer. The first part is devoted to the calculation of analytical solution in two dimensions, thanks to Cagniard de Hoop method. In this second part we consider the 3D case.
In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in order to prove $L^p$--$L^q$ decay rates for its solutions.
Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics.
We investigate the singularities of the trace of the half-wave group, $mathrm{Tr} , e^{-itsqrtDelta}$, on Euclidean surfaces with conical singularities $(X,g)$. We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author cite{Hil} and the two-dimensional case of the work of the first author and Wunsch cite{ForWun} as well as the seminal result of Duistermaat and Guillemin cite{DuiGui} in the smooth setting. As an intermediate step, we identify the wave propagators on $X$ as singular Fourier integral operators associated to intersecting Lagrangian submanifolds, originally developed by Melrose and Uhlmann cite{MelUhl}.
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