Semiclassical inverse spectral problem for elastic Love waves in isotropic media

Optimal stability in the identification of a rigid inclusion in an isotropic Kirchhoff-Love plate

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of the plate. The plate is made by non-homogeneous, linearly elastic and isotropic material. Under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a constructive stability estimate of log type. Key mathematical tool is a recently proved optimal three spheres inequality at the boundary for solutions to the Kirchhoff-Love plat…

Semiclassical inverse spectral problem for elastic Rayleigh waves in isotropic media

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio is constant, we establish uniqueness and present a reconstruction scheme for the S-wave speed with multiple wells from the semiclassical spectrum of these waves.

线性弹性各向同性Cosserat材料中Love波的传播

Propagation of Love waves in linear elastic isotropic Cosserat materials

本研究提出基于代数Riccati方程的方法分析Cosserat材料中Love波传播，保证亚声速波速存在唯一性，并确认无需人为表面层。

Semiclassical states associated to isotropic submanifolds of phase space

We define classes of quantum states associated to isotropic submanifolds of cotangent bundles. The classes are stable under the action of semiclassical pseudo-differential operators and covariant under the action of semiclassical Fourier integral operators. We develop a semiclassical symbol calculus for them; the symbols are symplectic spinors. We outline various applications.

Semiclassical analysis of elastic surface waves

In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable to the wave length. Such a medium can also be thought of as a surficial layer (which can be thick) overlying a half space. The analysis is based on the work of Colin de Verdière on acoustic surface waves. The description is geometric in the boundary and locally spectral "beneath" it. Effective Hamiltonians of surface waves correspond with eigenvalues of ordi…

Optimal identification of cavities in the Generalized Plane Stress problem in linear elasticity

For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for the inverse problem of determining smooth cavities inside a thin isotropic cylinder {}from a single boundary measurement of traction and displacement. The result is obtained by reformulating the GPS problem as a Kirchhoff-Love plate-like problem in terms of the Airy's function, and by using the strong unique continuation at the boundary for a Kirchhoff-Love plate operator under homogeneous Dirichlet conditions, which has been recently obtained in \cite{l:arv}.