Effect of Oblateness of the Secondary up to J4 on L4,5 in the Photogravitaional ER3BP

In a synodic-pulsating dimensionless coordinate, with a luminous primary and an oblate secondary, we examine the effects of radiation pressure, oblateness (quadruple and octupolar i.e. ) and eccentricity of the orbits of the primaries on the triangular points in the ER3BP. have been shown to disturb the motion of an infinitesimal body and particularly has significant effects on a satellite’s secular perturbation and orbital precessions. The influence of these parameters on the triangular points of Zeta Cygni, 54 Piscium and Procyon A/B are highlighted in this study. Triangular points are stable in the range and their stability is affected by said parameters.

Стохастическая ячеистая модель очистки моторного масла от механических примесей объёмным фильтрованием

Приведено описание ячеистой модели фильтрования, которая создавалась на сочетании вероятностно-статистических методов с точным описанием на основе физических законов поведения дисперсной фазы при сложном взаимодействии её с дисперсионной средой. Выделены основные силы, действующие на частицу в потоке при фильтровании. Показано, что наибольшее воздействие на отсев оказывают силы Лондона-Ван-дер-Ваальса и электрокинетические, обусловленные полярными молекулами продуктов старения масла и моюще-диспергирующими присадками, которыми оно легируется. Выяснено, что в наименьшей степени на отсев влияют силы тяжести и Архимеда. Объединение детерминированных и случайных воздействий на дисперсную фазу осуществлено на базе уравнения Колмогорова Фоккера Планка. Показаны методы его формирования так, чтобы рассматриваемому случайному переносу частиц в поровом пространстве, идентифицированному совокупностью обобщенных координат и скоростей, соответствовало уравнение для многомерной плотности вероятности, отождествляемой с концентрацией дисперсной фазы. Приведены расчётные формулы для компонентов скорости частиц, по которым можно рассчитать граничную траекторию, определить безразмерную координату и фракционный коэффициент отсева. Определены краевые условия стохастической задачи фильтрования. Записаны интегралы для расчета фракционного отсева через паток вероятности. Проанализированы возможности детерминированной и стохастической ячеистых моделей фильтрования, показана их адекватность.A description is given of a cellular filtering model that was created using a combination of probabilistic and statistical methods with an accurate description based on the physical laws of the behavior of the dispersed phase during its complex interaction with the dispersion medium. The main forces acting on a particle in a stream during filtration are identified. It has been shown that the London-Van der Waals forces and electro kinetic forces caused by polar molecules of oil aging products and detergent-dispersant additives with which it is doped have the greatest impact on screening. It has been found that gravity and Archimedes force have the leas effect on screening. The combination of deterministic and random effects on the dispersed phase was carried out based on the Kolmogorov Fokker Planck equation. The methods of its formation are shown so that the equation for the multidimensional probability density, identified with the concentration of the dispersed phase, corresponds to the random particle transport in the pore space, identified by the set of generalized coordinates and velocities. Calculation formulas are given for the particle velocity components by which one can calculate the boundary trajectory and determine the dimensionless coordinate and fractional dropout coefficient. The boundary conditions of the stochastic filtering problem are determined. The integrals for calculating the fractional dropout through the molasses of probability are recorded. The possibilities of deterministic and stochastic cellular filtration models are analyzed, and their adequacy is shown.

Existence of Universal Phase Diagrams for Describing General Pore Shape Resulting From an Entrapped Bubble During Solidification

This study shows that there exist a pair of universal and unique phase diagrams to describe general development of the pore shape in solid, resulting from a bubble captured by a solidification front. Like thermodynamics, phase diagrams have advantages to generally identify the states and design processes of a system. Pore formation and its shape in solids influence not only microstructure of materials but also contemporary issues of biology, engineering, foods, geophysics, and climate change, etc. In this study, a pair of phase diagrams is thus found to be under dimensionless coordinate systems of dimensionless apex radius, contact angle, and base radius of the bubble cap, as well as solidification rate, contact angle, and growth rate of base radius. The computed results of the development of the pore shape agree with experimental data. The pore shape in solid thus can be optimistically predicted and controlled by choosing a desired path on phase diagrams.

Practical Techniques for Estimating the Accuracy of Finite-Difference Solutions to Parabolic Equations

A criterion is proposed which provides a priori means of choosing increments in the independent variables for effecting accurate finite-difference solutions to parabolic partial-differential equations. This is accomplished by relating the increments to the thickness of the diffusion layer. In this manner, the size of the increments is related to the magnitude of the derivatives which are known to influence strongly the accuracy. The fac- that the thickness of the diffusion layer is unknown is surmounted by relating the parameters of the discrete, physical plane to the diffusion variable and to the diffusion thickness. The diffusion variable is a dimensionless coordinate which governs the diffusion process. In similar problems, the diffusion variable is identical to the independent similarity variable. The thickness of the diffusion layer in terms of the diffusion coordinate is shown to be of the same order of magnitude for a wide variety of problems. The utility of the proposed criterion is demonstrated with numerous finite-difference solutions to problems in the areas of heat conduction and boundary-layer theory.