Related papers: Numerical schemes to reconstruct three dimensional…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
We propose the multi-frequency synthesis (MFS) algorithm with spectral correction of frequency-dependent source brightness distribution based on maximum entropy method. In order to take into account the spectral terms of n-th order in the…
We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
Localizing linearly moving sound sources using microphone arrays is challenging as the transient nature of the signal leads to relatively short observation periods. Commonly, a moving focus is used and most methods operate at least…
Recent frequency-modulated atomic force microscopy (FM-AFM) can measure three-dimensional force distribution between a probe and a sample surface in liquid. The force distribution is, in the present circumstances, assumed to be solvation…
Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…
Beamforming design for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging due to prohibitive computational complexity and complex near-field propagation effects. To address this, this paper introduces a…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…
In this paper, we consider the inverse problem of recovering a time-dependent nonlinearity for a third order nonlinear acoustic equation, which is known as the Jordan-Moore-Gibson-Thompson equation (J-M-G-T equation for short). This third…
We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…
Wall-bounded turbulent flows can be challenging to measure within experiments due to the breadth of spatial and temporal scales inherent in such flows. Instrumentation capable of obtaining time-resolved data (e.g., Hot-Wire Anemometers)…
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
We create virtual sources and receivers in a 3D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…