Table of contents

In relation to the recently intensified search for new superconducting systems, it is interesting to study the properties of metal nanoclusters containing ≈10²–10³ free carriers. It is essential that the spectra of delocalized electrons in many clusters form energy shells similar to those in atoms and nuclei. The superconducting pairing can be very strong if the cluster parameters satisfy certain conditions. Such clusters constitute a new family of high-temperature superconductors (with T_c ≥ 150 K). Transition into the superconducting state is manifested in an essential rearrangement of the energy spectrum. Pair correlation affects the optical, magnetic, and thermodynamic properties of clusters; corresponding changes can be detected in specific experiments. Clusters can form high-temperature superconducting tunneling networks, and this leads to macroscopic high-temperature superconductivity. In principle, higher values of T_c, up to room temperature, may be achieved.

While silicon and gallium arsenide are dominant materials in modern micro- and nanoelectronics, devices fabricated from them still use Si and GaAs substrates only separately. Integrating these materials on the (highest effeciency) substrate of Si has been the subject of much research effort for more than twenty years. This review systematizes and generalizes the current understanding of the fundamental physical mechanisms governing the epitaxial growth of GaAs and its related III–V compounds on Si substrates. Basic techniques avilable for improving the quality of such heterostructures are described, and recent advances in fabricating device-quality A^IIIB^V/Si heterostructures and devices on their bases are also presented.

An analytic solution methodology for general relativity (GR) equations describing the hypothetical phenomenon of wormholes is presented and the analysis of wormholes in terms of their physical properties is discussed. An analytic solution of the GR equations for static and dynamic spherically symmetric wormholes is given. The dynamic solution generally describes a 'traversable' wormhole, i.e., one allowing matter, energy, and information to pass through it. It is shown how the energy–momentum tensor of matter in a wormhole can be represented in a form allowing the GR equations to be solved analytically, which has a crucial methodological importance for analyzing the properties of the solution obtained. The energy–momentum tensor of wormhole matter is represented as a superposition of a spherically symmetric magnetic (or electric) field and negative-density dust matter, serving as exotic matter necessary for a 'traversable' wormhole to exist. The dynamics of the model are investigated. A similar model is considered (and analyzed in terms of inflation) for the Einstein equations with a Λ term. Superposing enough dust matter, a magnetic field, and a Λ term can produce a static solution, which turns out to be a spherical Multiverse model with an infinite number of wormhole-connected spherical universes. This Multiverse can have its total energy positive everywhere in space, and in addition can be out of equilibrium (i.e., dynamic).

This article deals with the linear ordinary differential equations for one or several coupled oscillators. Emphasis is placed on the separate notions of the frequency matrix (as a kinematic entity) and the impedance matrix. The latter matrix is explicitly introduced in this article, and its time dependence is shown to be responsible for parametric excitation and for nonconcervation of adiabatic invariants.

The mixing formulas for calculating the effective parameters of composite materials with inclusions having a negative permeability or permittivity are analyzed. The problems appearing when various formulas are utilized were outlined, and the computation algorithms yielding physically meaningful solutions were described. The problem of the calculation of a refractive index for media with arbitrary values of permittivity and permeability is discussed.

Plasma reactors and ion sources whose operation relies on a low-pressure radio-frequency (RF) inductive discharge have been an important constituent of modern ground and space technologies for several decades already. However, the steadily toughening and varying requirements of plasma technologies call for improving the old models of devices and developing novel prospective models. Of vital importance in the development of inductive plasma sources is the provision of conditions whereat the plasma efficiently absorbs the RF power. In recent years it has become evident that in a low-pressure RF inductive discharge the RF-generator power is distributed between the active resistance of the external circuit and the plasma. In the latter case, the power is delivered to the plasma via two channels: an inductive channel, which exists due to the current flowing through an inductor or an antenna, and a capacitive one, which is due to the antenna–plasma capacitive coupling. RF inductive discharge properties related to the RF-power redistribution between the channels are considered and the mechanisms of RF-power absorption are analyzed. The feasibilities of optimizing RF inductive plasma sources are also discussed.

The article traces the way Einstein formulated the relation between energy and mass in his work from 1905 to 1955. Einstein emphasized quite often that the mass m of a body is equivalent to its rest energy E₀. At the same time, he frequently resorted to the less clear-cut statement of the equivalence of energy and mass. As a result, Einstein's formula E₀=mc² still remains much less known than its popular form, E=mc², in which E is the total energy equal to the sum of the rest energy and the kinetic energy of a freely moving body. One of the consequences of this is the widespread fallacy that the mass of a body increases when its velocity increases and even that this is an experimental fact. As wrote the playwright A N Ostrovsky "Something must exist for people, something so austere, so lofty, so sacrosanct that it would make profaning it unthinkable."