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Substances such as chemical compounds are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Though spectra of pure chemicals can be identified by visual inspection, the spectra of…

We often encounter a situation that black hole solutions can be regarded as continuous deformations of simpler ones, or modify general relativity by continuous parameters. We develop a general framework to compute high-order perturbative…

A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…

We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…

The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally…

We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…

This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over the random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for…

This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of…

Model-based computational elasticity imaging of tissues can be posed as solving an inverse problem over finite elements spanning the displacement image. As most existing quasi-static elastography methods count on deterministic formulations…

Rotating modulation is a technique for indirect imaging in the hard x-ray and soft gamma-ray energy bands, which may offer an advantage over coded aperture imaging at high energies. A rotating modulator (RM) consists of a single mask of…

When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…

The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…

Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…