Existence, Uniqueness and Regularity for Solutions of the Conical Diffraction Problem

This paper is devoted to the analysis of two Helmholtz equations in ℝ2 coupled via quasiperiodic transmission conditions on a set of piecewise smooth interfaces. The solution of this system is quasi-periodic in one direction and satisfies outgoing wave conditions with respect to the other direction. It is shown that Maxwell's equations for the diffraction of a time-harmonic oblique incident plane wave by periodic interfaces can be reduced to problems of this kind. The analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for solutions corresponding to electromagnetic fields with locally finite energy. Special attention is paid to the regularity and leading asymptotics of solutions near the edges of the interface

Модернизация автоматизированной системы блока стабилизации давления магистрального насосного агрегата на нефтеперекачивающей станции

Объектом исследования является блок стабилизации давления магистрального насосного агрегата. Цель работы – модернизация автоматизированной системы блока стабилизации давления магистрального трубопровода нефтеперекачивающей станции с использованием ПЛК, на основе выбранной SCADA-системы. В данном проекте была разработана система контроля и управления технологическим процессом на базе промышленных контроллеров Modicon M340 BMXP34 2020, с применением SCADA-системы.The object of investigation is the pressure stabilization unit of the main pump unit. The purpose of the work is the modernization of the automated system for stabilizing the pressure of the main pipeline of the oil pumping station using PLCs, based on the SCADA system chosen. In this project, a system for monitoring and controlling the process was developed on the basis of industrial controllers Modicon M340 BMXP34 2020, using a SCADA system

Conical diffraction by multilayer gratings: A recursive integral equation approach

summary:The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in $\mathbb R^2$ coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with an arbitrary number of material layers we present the extension of a recursive procedure developed by Maystre for normal incidence, which transforms the problem to a sequence of equations with $2 \times 2$ operator matrices on each interface. Necessary and sufficient conditions for the applicability of the algorithm are derived

Transitions in effective scaling behavior of accelerometric time series across sleep and wake

We study the effective scaling behavior of high-resolution accelerometric time series recorded at the wrists and hips of 100 subjects during sleep and wake. Using spectral analysis and detrended fluctuation analysis we find long-term correlated fluctuations with a spectral exponent $\beta \approx 1.0$ ($1/f$ noise). On short time scales, β is larger during wake ($\approx 1.4$ ) and smaller during sleep ($\approx 0.6$ ). In addition, characteristic peaks at 0.2–0.3 Hz (due to respiration) and 4–10 Hz (probably due to physiological tremor) are observed in periods of weak activity. Because of these peaks, spectral analysis is superior in characterizing effective scaling during sleep, while detrending analysis performs well during wake. Our findings can be exploited to detect sleep-wake transitions