Boris Plamenevskii – författare

This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary.  The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

This volume studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach.

Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling.

Devices based on the phenomenon of electron resonant tunneling are widely used in electronics. Efforts are directed towards refining properties of resonance structures. There are prospects for building new nano size electronics elements based on quantum dot systems.

However, the role of resonance structure can also be given to a quantum wire of variable cross-section. Instead of an "electrode - quantum dot - electrode" system, one can use a quantum wire with two narrows. A waveguide narrow is an effective potential barrier for longitudinal electron motion along a waveguide. The part of the waveguide between two narrows becomes a "resonator" , where electron resonant tunneling can occur. This phenomenon consists in the fact that, for an electron with energy E, the probability T(E) to pass from one part of the waveguide to the other part through the resonator has a sharp peak at E = Eres, where Eres denotes a "resonant" energy. Such quantum resonators can find applications as elements of nano electronics devices and provide some advantages in regard to operation properties and production technology.

The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.