On Schreier varieties of racks

We prove that a subrack of a free rack is free and suggest a method to prove a similar statement about involutory racks.Comment: 4 page

Quantum interference in exciton-Mn spin interactions in a CdTe semiconductor quantum dot

We show theoretically and experimentally the existence of a new quantum interference(QI) effect between the electron-hole interactions and the scattering by a single Mn impurity. Theoretical model, including electron-valence hole correlations, the short and long range exchange interaction of Mn ion with the heavy hole and with electron and anisotropy of the quantum dot, is compared with photoluminescence spectroscopy of CdTe dots with single magnetic ions. We show how design of the electronic levels of a quantum dot enable the design of an exciton, control of the quantum interference and hence engineering of light-Mn interaction.Comment: 11 pages, 4 figures, submitted to PR

The resistance law for stably stratified atmospheric planetary boundary layers

The resistance law for stably and neutrally stratified atmospheric planetary boundary layers (PBL) entered textbooks on boundary-layer meteorology but, until now, remains practically unused in modelling applications. This is not surprising. The law has been formulated and validated only for idealised cases, such as truly neutral PBL - implying neutral stratification across the entire atmosphere, nocturnal stable PBL - stably stratified near the surface but developed against the neutrally stratified free flow, and (more recently) conventionally neutral PBLs - neutrally stratified near the surface but developed against stable stratification in the free flow. We derive and validate the general formulation of the resistance law accounting for the integral effect on PBL of stable stratifications at the surface and in the free atmosphere. Such long-lived stable PBLs, typical of wintertime at high latitudes, were until recently overlooked in boundary-layer meteorology, not to mention weather and climate models. The proposed general formulation of the resistance law covers long-lived stable PBLs and opens up prospects for their improved modelling.Peer reviewe

Theory of exciton fine structure in semiconductor quantum dots: quantum dot anisotropy and lateral electric field

Theory of exciton fine structure in semiconductor quantum dots and its dependence on quantum dot anisotropy and external lateral electric field is presented. The effective exciton Hamiltonian including long range electron-hole exchange interaction is derived within the k*p effective mass approximation (EMA). The exchange matrix elements of the Hamiltonian are expressed explicitly in terms of electron and hole envelope functions. The matrix element responsible for the "bright" exciton splitting is identified and analyzed. An excitonic fine structure for a model quantum dot with quasi- two-dimensional anisotropic harmonic oscillator (2DLAHO) confining potential is analyzed as a function of the shape anisotropy, size and applied lateral electric field

Order out of chaos : Shifting paradigm of convective turbulence

Publisher Copyright: © 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).Turbulence is ever produced in the low-viscosity/large-scale fluid flows by velocity shears and, in unstable stratification, by buoyancy forces. It is commonly believed that both mechanisms produce the same type of chaotic motions, namely, the eddies breaking down into smaller ones and producing direct cascade of turbulent kinetic energy and other properties from large to small scales toward viscous dissipation. The conventional theory based on this vision yields a plausible picture of vertical mixing and has remained in use since the middle of the twentieth century in spite of increasing evidence of the fallacy of almost all other predictions. This paper reveals that in fact buoyancy produces chaotic vertical plumes, merging into larger ones and producing an inverse cascade toward their conversion into the self-organized regular motions. Herein, the velocity shears produce usual eddies spreading in all directions and making the direct cascade. This new paradigm is demonstrated and proved empirically; so, the paper launches a comprehensive revision of the theory of unstably stratified turbulence and its numerous geophysical or astrophysical applications.Peer reviewe

Реверсивное эндопротезирование плечевого сустава после оскольчатого перелома плечевой кости: клинический случай

Background. Fractures of the proximal humerus are common injury, especially among older age group patients. For the treatment of most cases, conservative tactics are required, some require surgery: osteosynthesis, arthroplasty. Proximal humerus fractures with extension to the metadiaphyseal and diaphyseal zones uncommon, and treatment of this type of injuries is complex for trauma surgeons. The aim of the study is to demonstrate successful experience of two-stage treatment of the proximal humerus fracture with extension to the diaphysis middle third in an older age group patient. Case presentation. The clinical case presents successful two-stage treatment of the proximal humerus fracture with extension to the middle third of the diaphysis in an older age group patient. The first stage was performed osteosynthesis of the humerus with the PHILOS Long plate, the second stage reverse shoulder arthroplasty. Conclusion. Consistent performing of osteosynthesis and total reverse shoulder arthroplasty allows to achieve satisfactory treatment results with restoration of the injured limb function and relief of pain syndrome.Актуальность. Переломы проксимального отдела плечевой кости распространенная травма, особенно среди пациентов старшей возрастной группы. Для лечения большинства данных повреждений применяется консервативная тактика, однако некоторым пациентам требуется хирургическое лечение: остеосинтез, эндопротезирование. Переломы проксимального отдела плечевой кости с распространением на метадиафизарную и диафизарную зоны встречаются значительно реже, и их лечение представляет сложную задачу для травматологов. Описание случая. Представлен успешный опыт двухэтапного лечения перелома проксимального отдела плечевой кости с распространением до средней трети диафиза у пациентки старшей возрастной группы. Первым этапом выполнен остеосинтез плечевой кости пластиной PHILOS Long, вторым этапом реверсивное эндопротезирование плечевого сустава. Заключение. Последовательное применение остеосинтеза и тотального реверсивного эндопротезирования плечевого сустава позволяет добиться удовлетворительных результатов лечения с восстановлением функции травмированной конечности и купированием болевого синдрома

Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motion. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and thus in modelling stably stratified turbulent flows. We obtain a theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE budget equation from atmospheric measurements of other components of the TKE budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science, and microphysics of clouds.Peer reviewe