Related papers: Dipole density instead of potentials in electrocar…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we can solve inverse problems for the plate equation…
Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
Focal arrhythmias, which arise from delayed afterdepolarizations (DADs), are observed in various pathophysiological heart conditions; these can lead to sudden cardiac death. A clear understanding of the electrophysiological factors of…
The electric and magnetic fields are investigated on the basis of quantum vacuum. The analysis of the electromagnetic energy and force indicates that an electric field is a polarized distribution of the vacuum virtual dipoles, and that a…
We prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The leading idea is to reduce the problem to an abstract parabolic…
This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of…
We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results…
We investigate the zero-temperature quantum phases of a quasi-one-dimensional zigzag chain of dipoles that are polarized in a plane by an external electric field. Since the Hamiltonian contains nearest-neighbor (NN) and…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
Density functional theory (DFT) remains the most widely used electronic structure method. Although exact in principle, in practice, it relies on approximations to the exchange-correlation (XC) functional, which is known to be a unique…
Herein, we study an inverse problem for detecting unknown obstacles by the enclosure method using the Dirichlet--to--Neumann map for measurements. We justify the method for an penetrable obstacle case involving a biharmonic equation. We use…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
We consider the problem of identifying possibly discontinuous doping profiles in semiconductor devices from data obtained by\,stationary voltage-current maps. In particular, we focus on the so-called unipolar case, a system of PDE's derived…
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 study the inverse dynamic problem of recoverying the potential in the one-dimensional dynamical system with memory. The Gelfand--Levitan equations are derived for the kernel of the integral operator which is inverse to the control…
We study the aggregation of insulating electrically charged spheres suspended in a nonpolar liquid. Regarding the van der Waals interaction as an irreversible sticking force, we are especially interested in the charge distribution after…
We study relationships between a set-valued map and its inverse limits about the notion of periodic point set, transitivity, sensitivity and Devaney chaos. Density of periodic point set of a set-valued map and its inverse limits implies…
We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well…