Related papers: The transmission problem on a three-dimensional we…
We have developed the technique of a quantum wave impedance determination for the sequence of not only constant potentials but also for potentials of forms for which the solution of a Shr\"{o}dinger equation exists at least in terms of…
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If…
We study time-harmonic Maxwell's equations in meta-materials that use either perfect conductors or high-contrast materials. Based on known effective equations for perfectly conducting inclusions, we calculate the transmission and reflection…
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
Inverse Laplace transform on the lattice spacing is introduced as a computational framework of the extrapolation of the strong coupling expansion to the scaling region. We apply the transform to the two-dimensional non-linear O(N) model at…
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…
Exactly solvable models are interesting for science and education, since they help in scientific search and in understanding of phenomena. Some exact solutions for simple quantum-mechanical models are considered. The models include two…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
In the reduced one-dimensional description of the adsorption on the wedge-shaped substrate the mid-point interface height serves as the order parameter. We point at the ambiguity which appears in the transfer-matrix approach to this…
We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning…
We study the spectrum and transmission coefficient of plane waves propagating along square ribbons of varying widths, containing a square-shaped, PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) and place a PT…
The transmission properties through a saturable cubic-quintic nonlinear defect attached to lateral linear chains is investigated. Particular attention is directed to the possible non-reciprocal diode-like transmission when the…
For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u, the shape derivative of the Dirichlet energy (with respect to u) is shown to be well-defined and is computed. The main…
The orthogonality of Hilbert spaces whose elements can be represented as simple and double layer potentials is determined. Conditions of well-posed solvability of integral equations for the sum of simple and double layer potentials…
The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…
Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
We prove that an $L^\infty$ potential in the Schr\"odinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace…
Formal Laplace operators are analyzed for a large class of resistance networks with vertex weights. The graphs are completed with respect to the minimal resistance path metric. Compactness and a novel connectivity hypothesis for the…