Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $b$ located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any $a,b>0$. When $a$ and $b$ tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure

Possibility of the treatment effects on the dynamics of apoptosis processes in tissues of kidneys in acute pyleonephritis and comparative diabetes mellitus in the experiment

Programmed cell death under conditions of an infectious-inflammatory process plays a biologically exclusively positive role in the elimination of cells. Acute inflammatory process is a phenomenon capable of excessive concentration of aggressive effectors of inflammation. The aim of the work was to assess the dynamics of ultrastructural changes and early signs of apoptosis in the kidney tissues in experimental modeling of acute pyelonephritis (AP) and concomitant diabetes mellitus (DM) of type II and II when conducting complex drug correction. The work was performed on 300 adult Wistar rats, divided into 6 groups. Fragments of the kidneys were studied and photographed in the electron microscope PEM-100-01. In the kidneys of animals of the group, where traditional medical correction was used after the friendly modeling of pyelonephritis and type I diabetes, it was found that the glomerular ultrastructure was more preserved, but part of the capillaries of the glomerulus remained deformed with a narrowed lumen, there are signs of insufficient restoration of the glomerular capillary network. In the group of animals using the proposed complex drug correction, the renal structure was preserved, the capillaries of the glomerular network with unchanged architectonics. It has been established that the traditional medical correction did not sufficiently contribute to the restoration of damaged kidney tissue ultrastructure. After carrying out the complex medical correction proposed by us after a friendly simulation of an OP of DM type II, the ultrastructure of the kidney tissue in form and structure approached that of control animals, signs of a compensatory-restorative process appeared: most of the podocytes were hyperplastic and hypertrophied. The podocytes of the outer leaflet were in the active phase of activity, as evidenced by an increase in contractile function and, possibly, the release of urine from the cavity into the lumen of the proximal tubules. The structure of the tubules and interstitial tissue is close to the structure of the group of control animals, only in the cytoplasm of the podocytes of the proximal tubules there is an increased content of lysosomes. The ultrastructure of the glomeruli was normalized; the number of hypertrophic podocytes of the inner leaflet with signs of enhanced protein synthesis increased. Changes in the structures of the cortical and medulla are similar except for the state of cytotrabeculae, where their size decreased in the medulla and signs of deformation of the plasmolemma appeared. In experimental modeling of PD and DM of types I and II, pronounced ultrastructural changes in the kidney tissues were established, and manifestations of early apoptosis processes are significantly limited. The use of the complex drug correction proposed by us stimulates the development of the reparative processes of the kidney and moderately activates apoptosis. The addition of multi-vector preparations (Armadin and Nuklex) to the complex of treatment intensifies compensatory-restorative changes in the kidneys and apoptosis, which contributes to the elimination from the renal microstructures of excess damaged cells and aggressive effectors of inflammation

A small-angle neutron scattering study of sodium dodecyl sulfate-poly(propylene oxide) methacrylate mixed micelles

cited By 3International audienceMixed micelle of protonated or deuterated sodium dodecyl sulfate (SDS and SDSd25, respectively) and poly(propylene oxide) methacrylate (PPOMA) are studied by small-angle neutron scattering (SANS). In all the cases the scattering curves exhibit a peak whose position changes with the composition of the system. The main parameters which characterize mixed micelles, i.e., aggregation numbers of SDS and PPOMA, geometrical dimensions of the micelles and degree of ionisation are evaluated from the analysis of the SANS curves. The position qmax of the correlation peak can be related to the average aggregation numbers of SDS-PPOMA and SDSd25-PPOMA mixed micelles. It is found that the aggregation number of SDS decreases upon increasing the weight ratio PPOMA/SDS (or SDSd25). The isotopic combination, which uses the "contrast effect" between the two micellar systems, has allowed us to determine the mixed micelle composition. Finally, the SANS curves were adjusted using the RMSA for the structure factor S(q) of charged spherical particles and the form factor P(q) of spherical core-shell particle. This analysis confirms the particular core-shell structure of the SDS-PPOMA mixed micelle, i.e., a SDS "core" micelle surrounded by the shell formed by PPOMA macromonomers. The structural parameters of mixed micelles obtained from the analysis of the SANS data are in good agreement with those determined previously by conductimetry and fluorescence studies. © 2005 Elsevier Inc. All rights reserved

Profession loss crisis at an old age: Specific features, factors, and mechanisms of coping

This article discusses the specific characteristics of profession loss crisis at an old age. Profession loss crisis is the last normative crisis of personal professional development that is caused by the completion of one's professional biography after reaching a certain age. The research employs a psychobiographic method and a critical events method. These methods are based on the use of a formalized biographical questionnaire worked out by Norakidze V.G. and reconstructed by Zeer E.F. The authors have identified and provided a detailed description of the main factors that cause profession loss crisis: Random events, adverse circumstances while implementing professional plans, etc. The article outlines the main strategies for coping with this crisis: Changing jobs, re-training, the assistance of colleagues and administration, etc. The authors suggest technologies to minimize the effects of these factors and overcome profession loss crisis effectively. © 2019 by the authors

The Monte Carlo and Molecular Dynamics Simulation of Gas-surface Interaction

A testing procedure and a program product for modeling gas-surface scattering process have been developed. Using the developed product the numerical simulation of the thermal transpiration phenomenon at free molecular conditions of the gas flow in channels with the use of different scattering kernels has been carried out. The surface structure influence on energy and momentum exchange in a gas-surface system has been studied by the use of Molecular Dynamics method. © Springer-Verlag Berlin Heidelberg 2005.The research described in this publication was made possible by Awards No: 03-53-5117 of INTAS and No: REC-005 (EK-005-X1), Y2-P-05-15 of U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF)