Новые поступления электронной библиотеки
2022-05-10
Получены новые точные решения волнового уравнения с нелинейными источниками. Построены уединенные бегущие волны и кинк-решения, формирующиеся при конкуренции двух источников. Определены условия возникновения аномального температурного отклика среды на тепловое воздействие («отрицательная теплоемкость»). Дан пример физической интерпретации одного из решений: вычислена скорость роста кристалла как функция переохлаждения расплава.
For a wave equation with sources, new running-wave type solutions are built. The results are expressed in terms of the heat transfer theory. We study two types of alternating volume energy sources qυ with a nonlinear temperature dependence T. Let qυ (T = Т1) = 0 where Т1 is the temperature of the source sign change. The source is positive at Т>Т1 (heat input) and negative at Т<Т1 (heat output) when is has technical origin. A source of biological origin differs from technical ones. It serves as a compensator: at Т>Т1 it takes the heat in; at Т<Т1, it gives the heat out. Three types of analytical solutions are obtained: the sole wave, the kink structure, and the wave chain. Subsonic and supersonic wave processes are studied with respect to the rate of heat perturbations. The examples for a non-classical phenomenon of "negative heat capacity" are given when heat input/output leads to a temperature decrease/increase. We have considered a nonlinear medium liable to an exact analytical description of a wave problem with a having a resonance type of the temperature dependence: its oscillations have a crescent amplitude. As an example of physical interpretation for one solution, the rate of crystal growth is calculated as a function of the melt undercooling.
2022-05-06
Построены точные частные решения уравнений Эйлера, определяющие стационарное сферическое движение несжимаемой невязкой жидкости. Даны примеры влияния структуры пространственной неоднородности силового поля на гидродинамические параметры течения: задача о протекании жидкости сквозь ядро сферического слоя; широтные и меридианные течения; поведение изобар и линий равных скоростей в потенциальном, соленоидальном и лапласовом силовых полях.
Exact particular solutions to Euler equations are obtained for a steady spherical flow of an incompressible inviscid fluid. The effect of the structure of the force field spatial nonuniformity on hydrodynamic parameters of the flow is studied. An exact solution to a flux problem is obtained. In this problem, the fluid flows in a spherical layer of finite thickness whose external boundary is impermeable. In the northern part of the layer, the fluid flows out of the core; in the southern part, into the core. There is no flowing at the equator. The peculiarities of the pressure gradient on the layer boundaries are discussed in detail. The intensity of mass force sources is calculated. Both exponential and power-law dependences of the flow velocity on the core surface temperature are proposed. The zonal and meridional flows occurring in potential, solenoidal, and Laplace force fields are considered. Examples of the conditions under which the velocity contours are or are not isobars are given. The behavior of these lines is shown to be mainly affected by a meridional component of the mass force. Physical models corresponding to the given solution sare presented. An example of the zonal flow inside an impermeable sphere is indicated. A zonal flow is considered in the external space of two impermeable cones. Arrangement of the cones has a sandglass-like shape. They have a common axis, a common vertex, and opposite bases. In a partial case, the impermeable boundaries are represented as a cone and an equatorial plane. The same arrangement of the cones is used for a hydrodynamic interpretation of the meridional flow, where the vertices of the cones are located in the center of the internal sphere, and the fluid flows out of the upper cone into the lower one through their permeable walls. The flow region is radially confined by external and internal impermeable spheres. In a specific case, the lower cone degenerates into a plane, and the fluid outflows from the spherical layer through a round ring located in the equatorial plane.
2022-05-06
Рассматривается проблема повышения практической подготовки студентов, привития им навыков анализа механических аппаратов и устройств. Для ее решения предлагается изучение студентами простых машин, известных с античности, и некоторых других объектов техники. Выбор тем для изучения базируется на классических курсах прикладной механики, разработанных Н. Е. Жуковским. Методикой изучения студентами этих тем выбрана самостоятельная управляемая работа студентов. Описаны организация такой работы, способы изложения теоретического материала и управления работой студентов.
There is considered the problem of improving the practical training of students, instilling for them the skills of mechanical apparatus and devices analyzing. To solve the mentioned problem it is proposed to teach students the simple machines, known from antiquity, and some other technical objects. The choice of topics for study is based on the classical courses in applied mechanics, developed by N. E. Zhukovsky. The methodology for studying these topics by students is an independent, guided work of students. The organization of such work, methods of presenting theoretical material and managing the work of students are described.
2022-05-05
Содержит семь тем практических работ с теоретическим материалом, необходимым для решения задач. Для студентов специальности 1-36 01 07 «Гидропневмосистемы мобильных и технологических машин» дневной формы обучения.
2022-05-05
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