On stress/strain state in a rotating disk

In the framework of mechanics of continuum bodies, the problem of stress/strain state in a high-speed rotating disk of constant thickness has been considered. The material of the disk is assumed to be homogeneous, elastic/perfectly-plastic. In the plastic zone, the stresses and plastic strains are related by some associated law similar to the one employed in deformation theory of plasticity. The general algorithm of the solution covers any smooth plasticity function. At some steps of the algorithm, it is possible to get analytical expressions, particularly, for the quadratic Mises yield criterion. For the given model, the notion of control parameters (external and internal) has been introduced. The allowable boundaries of external parameters have been defined as well. For some states of the disk, the coherent values of external parameters have been obtained. The results are represented graphically to show various states of the disk. The usage of piecewise plasticity functions has been briefly discussed. The results obtained can be used in preliminary engineering design and related numerical codes.info:eu-repo/semantics/publishedVersio

Coulomb gap in the one-particle density of states in three-dimensional systems with localized electrons

The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D, higher stability criteria, including two or more electrons, were predicted to exponentially deplete the 1P-DOS at energies close enough to the Fermi level. In this paper we show that there is a range of intermediate energies where this depletion is strongly compensated by the excitonic interaction between single-particle excitations, so that the crossover from quadratic to exponential behavior of the 1P-DOS is retarded. This is one of the reasons why such exponential depletion was never seen in computer simulations.Comment: 6 pages, 1 figur

Interacting quantum rotors in oxygen-doped germanium

We investigate the interaction effect between oxygen impurities in crystalline germanium on the basis of a quantum rotor model. The dipolar interaction of nearby oxygen impurities engenders non-trivial low-lying excitations, giving rise to anomalous behaviors for oxygen-doped germanium (Ge:O) below a few degrees Kelvin. In particular, it is theoretically predicted that Ge:O samples with oxygen-concentration of 10$^{17-18}$cm$^{-3}$ show (i) power-law specific heats below 0.1 K, and (ii) a peculiar hump in dielectric susceptibilities around 1 K. We present an interpretation for the power-law specific heats, which is based on the picture of local double-well potentials randomly distributed in Ge:O samples.Comment: 13 pages, 11 figures; to be published in Phys. Rev.

Exact Solutions to the Navier–Stokes Equations with Couple Stresses

This article discusses the possibility of using the Lin–Sidorov–Aristov class of exact solutions and its modifications to describe the flows of a fluid with microstructure (with couple stresses). The presence of couple shear stresses is a consequence of taking into account the rotational degrees of freedom for an elementary volume of a micropolar liquid. Thus, the Cauchy stress tensor is not symmetric. The article presents exact solutions for describing unidirectional (layered), shear and three-dimensional flows of a micropolar viscous incompressible fluid. New statements of boundary value problems are formulated to describe generalized classical Couette, Stokes and Poiseuille flows. These flows are created by non-uniform shear stresses and velocities. A study of isobaric shear flows of a micropolar viscous incompressible fluid is presented. Isobaric shear flows are described by an overdetermined system of nonlinear partial differential equations (system of Navier–Stokes Equations and incompressibility equation). A condition for the solvability of the overdetermined system of equations is provided. A class of nontrivial solutions of an overdetermined system of partial differential equations for describing isobaric fluid flows is constructed. The exact solutions announced in this article are described by polynomials with respect to two coordinates. The coefficients of the polynomials depend on the third coordinate and time. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Density of States and Conductivity of Granular Metal or Array of Quantum Dots

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are dropped. Some small changes are given to improve the organizatio

On dispersive energy transport and relaxation in the hopping regime

A new method for investigating relaxation phenomena for charge carriers hopping between localized tail states has been developed. It allows us to consider both charge and energy {\it dispersive} transport. The method is based on the idea of quasi-elasticity: the typical energy loss during a hop is much less than all other characteristic energies. We have investigated two models with different density of states energy dependencies with our method. In general, we have found that the motion of a packet in energy space is affected by two competing tendencies. First, there is a packet broadening, i.e. the dispersive energy transport. Second, there is a narrowing of the packet, if the density of states is depleting with decreasing energy. It is the interplay of these two tendencies that determines the overall evolution. If the density of states is constant, only broadening exists. In this case a packet in energy space evolves into Gaussian one, moving with constant drift velocity and mean square deviation increasing linearly in time. If the density of states depletes exponentially with decreasing energy, the motion of the packet tremendously slows down with time. For large times the mean square deviation of the packet becomes constant, so that the motion of the packet is ``soliton-like''.Comment: 26 pages, RevTeX, 10 EPS figures, submitted to Phys. Rev.

Coulomb gap in a model with finite charge transfer energy

The Coulomb gap in a donor-acceptor model with finite charge transfer energy $\Delta$ describing the electronic system on the dielectric side of the metal-insulator transition is investigated by means of computer simulations on two- and three-dimensional finite samples with a random distribution of equal amounts of donor and acceptor sites. Rigorous relations reflecting the symmetry of the model presented with respect to the exchange of donors and acceptors are derived. In the immediate neighborhood of the Fermi energy $\mu$ the the density of one-electron excitations $g(\epsilon)$ is determined solely by finite size effects and $g(\epsilon)$ further away from $\mu$ is described by an asymmetric power law with a non-universal exponent, depending on the parameter $\Delta$.Comment: 10 pages, 6 figures, submitted to Phys. Rev.

Effect of inter-wall surface roughness correlations on optical spectra of quantum well excitons

We show that the correlation between morphological fluctuations of two interfaces confining a quantum well strongly suppresses a contribution of interface disorder to inhomogeneous line width of excitons. We also demonstrate that only taking into account these correlations one can explain all the variety of experimental data on the dependence of the line width upon thickness of the quantum well.Comment: 13 pages, 8 figures, Revtex4, submitted to PR

Problems of Development and Application of Metal Matrix Composite Powders for Additive Technologies

The paper considers the problem of structure formation in composites with carbide phase and a metal binder under self-propagating high-temperature synthesis (SHS) of powder mixtures. The relation between metal binder content and their structure and wear resistance of coatings was studied. It has been shown that dispersion of the carbide phase and volume content of metal binder in the composite powders structure could be regulated purposefully for all of studied composites. It was found that the structure of surfaced coating was fully inherited of composite powders. Modification or coarsening of the structure at the expense of recrystallization or coagulation carbide phase during deposition and sputtering does not occur

Transport of magnetoexcitons in single and coupled quantum wells

The transport relaxation time $\tau (P)$ and the mean free path of magnetoexcitons in single and coupled quantum wells are calculated ($P$ is the magnetic momentum of the magnetoexciton). We present the results for magnetoexciton scattering in a random field due to (i) quantum well width fluctuations, (ii) composite fluctuations and (iii) ionized impurities. The time $\tau(P)$ depends nonmonotonously on $P$ in the case (ii) and in the cases (i), (iii) for $D/l$ smaller than some critical value ($D$ is the interwell separation, $l=\sqrt{\hbar c/eH}$ is the magnetic length). For $D/l\gg 1$ the transport relaxation time increases monotonously with $P$. The magnetoexciton mean free path $\lambda (P)$ has a maximum at $P\ne 0$ in the cases (i), (iii). It decreases with increasing $D/l$. The mean free path calculated for the case (ii) may have two maxima. One of them disappears with the variation of the random fields parameters. The maximum of $\lambda (P)$ increases with $H$ for types (i,iii) of scattering processes and decreases in the case (ii).Comment: 13 pages, 8 figures in EPS format; Physica Scripta (in print