Related papers: Distributed source identification for wave equatio…
Partial Wave Analysis has traditionally been carried out using a set of tools handcrafted for each experiment. By taking an object-oriented approach, the design presented in this paper attempts to create a more generally useful, and easily…
This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first show that the point sources in both $\mathbb{R}^2$ and…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
This work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated…
For the wave and the Schr\"odinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.
We approach wave particle duality, the role of the observer and implications on Retrocausality, by starting with the results of a well verified quantum experiment. We analyze how some current theoretical approaches interpret these results.…
We establish boundary observability and control for the fractional heat equation over arbitrary time horizons $T > 0$, within the optimal range of fractional exponents $s \in (1/2, 1)$. Our approach introduces a novel synthesis of…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a…
We establish sharp regional observability results for solutions of the wave equation in a bounded domain of $\Omega \subset \mathbb{R}^n$, in case where the geometric control condition is not satisfied. Assuming that the waves are observed…
Uncertain differential equations have a wide range of applications. How to obtain estimated values of unknown parameters in uncertain differential equations through observations has always been a subject of concern and research, many…
Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is…
We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…
This paper proposes a determined blind source separation method using Bayesian non-parametric modelling of sources. Conventionally source signals are separated from a given set of mixture signals by modelling them using non-negative matrix…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…