Related papers: The Time-Dependent Approach to Inverse Scattering

Coherent control of atomic and molecular scattering relies on the preparation of colliding particles in superpositions of internal states, establishing interfering pathways that can be used to tune the outcome of a scattering process.…

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been…

The inverse-scattering problem of an inhomogeneous material has been of interest for many years, and was generally addressed with various optimization techniques. In this paper, we suggest an optimization-free method for solving the…

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…

The synthesis of non-magnetic 2D dielectric cloaks as proper solutions of an inverse scattering problem is addressed in this paper. Adopting the relevant integral formulation governing the scattering phenomena, analytic and numerical…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…

Recent differentiable rendering techniques have become key tools to tackle many inverse problems in graphics and vision. Existing models, however, assume steady-state light transport, i.e., infinite speed of light. While this is a safe…

In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic…

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…

In this Perspective, we highlight several recent studies that illustrate how inverse strategies using appropriate physical models and computational methods can address complex materials design questions.

In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…

We study direct and inverse scattering problem for systems of interacting particles, having web-like structure. Such systems consist of a finite number of semi-infinite chains attached to the central part formed by a finite number of…

The problems we address in this paper are the spectral theory and the inverse problems associated with Laplacians on non-compact Riemannian manifolds and more general manifolds admitting conic singularities. In particular, we study the…

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…

We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…

The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…