相关论文: Time reversal methods in unknown medium and invers…
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
An approach for shielding an unwanted wave with a fixed frequency by generating a suitably controlled nontrivial wave with the same frequency is suggested. Unlike the well known surface potential approach, the source of the controlled wave…
We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…
The standard approach for photoacoustic imaging with variable speed of sound is time reversal, which consists in solving a well-posed final-boundary value problem for the wave equation backwards in time. This paper investigates the…
We study in this work the concept of instantaneous time mirrors that were recently introduced in the physics literature. Instantaneous time mirrors offer a new method for time reversal with a simplified experimental setup compared to…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
We propose a mathematical theory for the refocusing properties observed in time-reversal experiments, where classical waves propagate through a medium, are recorded in time, then time-reversed and sent back into the medium. The salient…
In this paper we analyze a time-reversal experiment in a random underwater acoustic channel. In this kind of waveguide with semi-infinite cross section a propagating field can be decomposed over three kinds of modes: the propagating modes,…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
We address the inverse problem of identifying a time-dependent potential coefficient in a one-dimensional diffusion equation subject to Dirichlet boundary conditions and a nonlocal integral overdetermination constraint reflecting spatially…
We revisit the problem of solving the one-dimensional wave equation on a domain with moving boundary. In J. Math. Phys. 11, 2679 (1970), Moore introduced an interesting method to do so. As only in rare cases, a closed analytical solution is…
We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
We introduce bounded generation as a generalized task to control video generation to synthesize arbitrary camera and subject motion based only on a given start and end frame. Our objective is to fully leverage the inherent generalization…
This paper presents a novel approach for steering the state of a stochastic control-affine system to a desired target within a finite time horizon. Our method leverages the time-reversal of diffusion processes to construct the required…
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…
The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…