INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS

This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.

Analysis of a Snowfall Process in North China during February 12-13, 2022

This research analyzed a snowfall process in north China during February 12-13, 2022. By using synoptic and numerical analysis, it is concluded that this snowfall process was mainly caused by trough, low-level vortex, shear line and Siberian High. Meanwhile, an easterly wind that transports water vapor from the Bohai to North China, was the water resource of the snowfall process. Relative humidity in the low atmosphere was above 80%, providing an excellent humidity condition for snowfall. Positive vorticity and convergence induced upward motion, which offered conditions for snowfall. Numerical reconstruction is also used to show the range and the intensity of the snowfall process.

NUMERICAL RECONSTRUCTION OF SMALL PERTURBATIONS IN THE ELECTROMAGNETIC COEFFICIENTS OF A DIELECTRIC MATERIAL

The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.

Identifiability and Stability of an Inverse Problem Involving a Fredholm Equation

The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.

Digital holographic shape measurement using Fizeau microscopy

We present a Fizeau interferometer using a microscopic objective as a tool for surface contouring without the need for a numerical lens for reconstruction. The interferometer is associated with a telescope system to feature the object with collimated light. The experiment is conducted on two objects possessing different step heights.The phase maps from the captured off-axis holograms are calculated numerically, which allows us to deduce the contours of the objects. The great advantages of the presented technique are that it can be done in real time and there is no need for numerical lenses for micro-objects reconstruction.