Применение неохлаждаемых микроболометров для регистрации импульсного терагерцового и инфракрасного излучения

Analytical relations for temperature response of the bolometer to periodic radiation pulses are obtained. It is theoretically shown and experimentally confirmed by the example of infrared bolometers that when detecting short radiation pulses, in contrast to the case of constant radiation, increasing the thermal conductivity of the bolometer and, accordingly, decreasing its thermal relaxation time, it is possible to significantly increase the response rate of the receiver, practically without reducing its sensitivity. The possibility of effective registration of pulsed terahertz radiation by microbolometers with a resistively coupled, thermally non-isolated antenna is considered. It is shown that such bolometers, which have increased thermal conductivity and, accordingly, reduced sensitivity to continuous-wave radiation, can be highly effective when detecting pulsed radiation with a duration shorter than the thermal relaxation time of the bolometer. On their basis, uncooled matrix detectors of pulsed terahertz radiation, characterized by a minimum detectable energy of less than 110-12 J and a frame rate of up to 1000 Hz, can be developed.

A hybrid algorithm for solving inverse boundary problems with respect to intermediate masses on a beam

The inverse problem of determining the weight of three intermediate masses on a uniform beam from the known three natural frequencies has been solved. The performed numerical analysis allows restoring the value of only the second mass in a unique way. The inverse problem of determining the weight of three intermediate masses is solved uniquely except in the case when the first and the third masses are located geometrically symmetric relative to the middle of the beam. The hybrid algorithm for the unique solving inverse problem of determining the weight of three intermediate masses has been developed. The first three natural frequencies of the beam are calculated numerically by using the Maple computer package. Analytical relations between the masses are found.

Uniaxially Strained Graphene: Structural Characteristics and G-Mode Splitting

The potential use of graphene in various strain engineering applications requires an accurate characterization of its properties when the material is under different mechanical loads. In this work, we present the strain dependence of the geometrical characteristics at the atomic level and the Raman active G-band evolution in a uniaxially strained graphene monolayer, using density functional theory methods as well as molecular dynamics atomistic simulations for strains that extend up to the structural failure. The bond length and bond angle variations with strain, applied either along the zigzag or along the armchair direction, are discussed and analytical relations describing this dependence are provided. The G-mode splitting with strain, as obtained by first principles’ methods, is also presented. While for small strains, up to around 1%, the G-band splitting is symmetrical in the two perpendicular directions of tension considered here, this is no longer the case for larger values of strains where the splitting appears to be larger for strains along the zigzag direction. Further, a crossing is observed between the lower frequency split G-mode component and the out-of-plane optical mode at the Γ point for large uniaxial strains (>20%) along the zigzag direction.

ANALYSIS OF MULTI-THREADED MARKOV SYSTEMS

Known technologies for analyzing Markov systems use a well-operating mathematical apparatus based on the computational implementation of the fundamental Markov property. Herewith the resulting systems of linear algebraic equations are easily solved numerically. Moreover, when solving lots of practical problems, this numerical solution is insufficient. For instance, both in problems of structural and parametric synthesis of systems, as well as in control problems. These problems require to obtain analytical relations describing the dependences of probability values of states of the analyzed system with the numerical values of its parameters. The complexity of the analytical solution of the related systems of linear algebraic equations increases rapidly along with the increase in the system dimensionality. This very phenomenon manifests itself especially demonstratively when analyzing multi-threaded queuing systems. Accordingly, the objective of this paper is to develop an effective computational method for obtaining analytical relations that allow to analyze high-dimensional Markov systems. To analyze such systems this paper provides for a decomposition method based on the idea of phase enlargement of system states. The proposed and substantiated method allows to obtain analytical relations for calculating the distribution of Markov system states. The method can be effectively applied to solve problems of analysis and management in high-dimensional Markov systems. An example has been considered

Analysis of the probability of connectivity of a telecommunications network based on the reduction of several non-connectivity events to a union of independent events

Introduction: For large and structurally complex telecommunication networks, calculating the connectivity probability turns out to be a very cumbersome and time-consuming process due to the huge number of elements in the resulting expression. The most expedient way out of this situation is a method based on the representation of a network connectivity event in the form of sums of products of incompatible events. However, this method also requires performing additional operations on sets in some cases. Purpose: To eliminate the main disadvantages of the method using multi-variable inversion. Results: It is shown that the connectivity event of a graph should be interpreted as a union of connectivity events of all its subgraphs, which leads to the validity of the expression for the connectivity event of the network in the form of a union of connectivity events of typical subgraphs (path, backbone, and in general, a multi-pole tree) of the original random graph. An iterative procedure is proposed for bringing a given number of connectivity events to the union of independent events by sequentially adding subgraph disjoint events. The possibility of eliminating repetitive routine procedures inherent in methods using multi-variable inversion is proved by considering not the union of connectivity events (incoherence) degenerating into the sum of incompatible products, but the intersection of opposite events, which also leads to a similar sum. However, to obtain this sum, there is no need to perform a multi-variable inversion for each of the terms over all those previously analyzed. Practical relevance: The obtained analytical relations can be applied in the analysis of reliability, survivability or stability of complex telecommunications networks.

Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

Load capacity of the board grillage with two stringers under ice loading

Снизить повреждаемость бортовых перекрытий при ледовых нагрузках можно за счет совершенствования расчетных зависимостей по оценке их несущей способности. Далеко не всегда такие зависимости, приводимые в справочных изданиях, дают верные рекомендации из-за не вполне ясного характера распределения нагрузок в сложных статически неопределимых системах. В справочнике по СМК приводится расчетная зависимость, позволяющая определить несущую способность регулярного перекрытия с двумя стрингерами при действиии локально распределенной нагрузки в пределах прямоугольника. Цель данной работы заключалась в оценке несущей способности реального бортового перекрытия ледокола типа Wind с помощью МКЭ при параметрах ледовой нагрузки, определяемой рекомендациями Морского Регистра РФ, и последующем сравнении полученных результатов с расчетами по теоретической зависимости, приведенной в справочнике. Полученные данные показали, что зависимость в справочнике для оценки несущей способности перекрытия дает удовлетворительно согласующиеся с МКЭ результаты после соответствующего уменьшения числового коэффициента в ней. При анализе несущей способности перекрытия варьировались шпация, толщина обшивки, высота стенок стрингеров и площадь приложения нагрузки. Установлено, что текучесть наблюдается в опорных сечениях шпангоутов и посредине их пролета, а из-за большой ширины присоединенного пояска обшивка у контура перекрытия практически никогда не течет. Полученные МКЭ результаты показали наличие обратно пропорциональной зависимости между предельной нагрузкой и шпацией при фиксированной площади нагружения. Отмечено, что увеличение толщины обшивки несущественно влияет на величину предельной нагрузки при остальных неизменных параметрах перекрытия. Выполненные расчеты позволяют кроме предельной нагрузки оценить также и величины прогибов при упругопластическом деформировании перекрытий, которые затруднительно подсчитать аналитически. To low damage of the board grillages under ice loading is possible by improving analytical relations on estimation of their load capacity. Not always such relations, bringing in manuals, give true recommendations because of complex character of the loads distribution in static indeterminate systems. Im manual on ship structural mechanics is giving analytical relation for determination of load capacity of regular grillage with two stringers under action of localy distributed load in rectangular area. Purpose of this study is to estimate load capacity of real board grillage of icebreaker of type Wind with help of FEM under parameters of ice load recommended in Maritime Register of RF, and following comparison of obtained results with calculation on analytical relation, given in manual. Obtained results show that relation in manual for estimation of load capacity of grillage give satisfactory results corresponding to FEM only after corresponding reducing of numerical coefficient in it. Under analysis of load capacity of grillage, it was changing frame space, thickness of plating, depth of stringers and area of application of load. It was estimated that most loaded zones of frames are their sections near supports and in the mid-span. Because of big width of associated plate the plating near contour of grillage is never yielding practically. Results obtained by FEM show existence of inversely proportional relation between the limit load and space framing under fixed area of loading. It was noticed that increasing of the plating thickness influent not essentially on value of the limit load under all other parameters of grillage unchangeable. Performed calculations allow to estimate limit load and value of deflections under elasto-plastic deformation of grillage, which is difficult to calculate analytically,

Analysis of vibration of beams with regularly located openings

В справочной литературе содержатся расчетные зависимости для частот свободных колебаний балок со сплошной стенкой, но отсутствуют данные по собственным колебаниям перфорированных балок. В то же время в судостроении и строительной практике широко распространены балки с перфорированной стенкой, содержащей вырезы круглой, овальной и прямоугольной формы. В статье проведен анализ влияния вырезов на частоту свободных колебаний перфорированных свободно опертых балок. При этом первоначально рассматривались балки со сплошной стенкой, а затем балки таких же размеров с вырезами. Для удобства практических вычислений известная зависимость была трансформирована к виду, позволяющему оценить частоту колебаний только по соотношению площадей полки и стенки и габаритным размерам балки без необходимости определения ее момента инерции и погонной массы. Аналогичные зависимости были получены и для перфорированных балок с круглыми и прямоугольными вырезами, в которых дополнительными факторами являлись параметры перфорации: относительная высота вырезов и относительная ширина перемычек. При отсутствии вырезов формулы для перфорированных балоксводятся к формуле для балки со сплошной стенкой.Сравнительный анализ частот проводился путем расчета по аналитическим зависимостям и методом конечных элементов с использованием программного комплекса ANSYS. На основе проведенного анализа сделан вывод, что наличие регулярно расположенных вырезов с высотой, не превышающей рекомендации Морского Регистра РФ, в зависимости от параметров перфорации приводит к разному повышению частот собственных колебаний однопролетных балок, хотя степень их повышения невелика. Предложенные аналитические зависимости для балок разного конструктивного оформления удовлетворительно согласуются с результатами расчетов МКЭ. In manual on the ship structural mechanics the analytical relations for determination of the natural frequencies of the beams with solid web are given, but there are no data about proper vibration of perforated beams. At the same time in shipbuilding and in structural industry the perforated beams with circular, rectangular and oval openings are widely used. In this article the analysis of influence of openings on the natural frequencies of the simply supported perforated beams is performed. Initially it was considered beams with solid web and then beams of the same dimensions with openings. For commodity of practical calculations, the well-known relation was transformed to the form allowing to appreciate frequency of vibration only with knowledge of ratio of areas of shelves and web without necessity of finding their moment of inertia and running mass of beam. Similar relations were obtained for perforated beams with circular and rectangular openings, in which additional arguments were such parameters of perforation as related depth of openings and related width of web-posts. In case of absence of openings, the formulas for perforated beams are reduced to formula for beam with solid web. Comparative analysis was performed by calculations according to analytical relations and with the finite element method using the program complex ANSYS. On base of performed analysis it was made conclusion that existence of regularly located openings with depth not extending recommendations of Russian Maritime Register, in dependence on parameters of perforation brings to different increasing of natural frequencies of vibration of one span beams, although degree of this increasing is not high. Suggested analytical relations for beams of different constructive design are in a good correlation with results obtained by the finite element method.

Precision of determination of thawing depth of the frozen rocks

An important quantity determining the choice of technical solutions in design of both surface and underground structures in the permafrost area is the thawing depth of the rocks. To obtain simple analytical relations to determine the thawing depth over time, a simple assumption is used: that the initial temperature of the rocks is equal to the melting temperature of ice. The aim of the present work was the assessment of impact of this assumption on the forecast precision. For a quantitative assessment, a simple typical formula recommended by construction norms was used. Functional dependence of the density of the rocks and their heat capacity on the fraction of ice content was considered in the formulas. A rock consisting of a combination of quartz sand and ice was used as an example.Multiple variant calculations were done according to the formulas and their results presented in the form of charts. It was shown that the relative error in determination of thawing depth depends solely on the Stefan criterion and is independent of the thawing duration, thermal conductivity coefficient of the thawing rocks and the air temperature during the thawing. A relation was obtained which allows to quickly assess at which initial values (temperature and ice content of the frozen rocks) it is possible to use the formulas obtained from the simplified calculation models with the assumption that the temperature of the rocks is equal to the melting temperature of ice.

Two Analytic Relations Connecting the Hot Gas Astrophysics with the Cold Dark Matter Model for Galaxy Clusters

Galaxy clusters are good targets for examining our understanding of cosmology. Apart from numerical simulations and gravitational lensing, X-ray observation is the most common and conventional way to analyze the gravitational structures of galaxy clusters. Therefore, it is valuable to have simple analytical relations that can connect the observed distribution of the hot, X-ray-emitting gas to the structure of the dark matter in the clusters as derived from simulations. In this article, we apply a simple framework that can analytically connect the hot gas empirical parameters with the standard parameters in the cosmological cold dark matter model. We have theoretically derived two important analytic relations, r s ≈ 3 r c and ρ s ≈ 9 β kT / 8 π Gm g r c 2 , which can easily relate the dark matter properties in galaxy clusters with the hot gas properties. This can give a consistent picture describing gravitational astrophysics for galaxy clusters by the hot gas and cold dark matter models.