SOLUTION OF THE PROBLEM OF FREE FLOW OF ROUGH TWO-DIMENSIONAL WATER FLOW WHEN FLOWING OUT OF A PRESSURE-FREE PIPE

The authors improved the solution of the problem of free spreading of two-dimensional in terms of turbulent potential uniform flows obtained by I.A. Sherenkov. To obtain an analytical solution, the concept of a general flow is used. The conjugation of the solution in the physical plane and in the plane of the velocity hodograph (virtual plane) is used. This made it possible to determine the coordinates of the points of the extreme current line and determine the current parameters leading to an unambiguous analytical solution of the flow geometry.

AN ANALYSIS OF THE CONCEPT OF ULTIMATE REALITY FROM THE PERSPECTIVE OF VIVEKANANDA

Vivekananda is one of the Neo-Vedantin or contemporary Indian Philosophers who has got influenced by the Vedānta philosophy and used its philosophy in practical life for human welfare. Vivekananda considers the metaphysical question regarding the status of the Ultimate Reality as an important matter of discussion without which human life would be purposeless. Such metaphysical knowledge comes to man when he goes beyond the circle of reason or physical plane. Vivekananda’s Neo-Vedanta is a discussion of such metaphysical views. The concept of Ultimate Reality is here understood in the sense of both nirguṇa and saguṇa Brahman i.e., God without name and form and with name and form. However, in the present paper, the aim is to focus on the concept of Ultimate Reality both from the transcendental and empirical standpoint and to check whether the status of the nirguṇa Brahman and saguṇa Brahman are identical or different.

The Genesis of the Concept of Land

Various sources confirm that a human and the land have been connected through an exceptional link. However, an idealistic image of land has been getting weaker and a present individual has felt a changed connection with the land. The land is not the sole source of livelihood for people any more and its association with pagan rituals, deities and nature has become less and less frequent. The more formal understanding of land (earth) as a planet has prevailed in Lithuanian lexicography, whereas in other sources the land is associated only with hard work. The very concept of land is broad and complex, therefore, it is important to analyse the image that emerges at a subliminal level in the head of a Lithuanian, while he/she is thinking about the land. The whole concept LAND is analysed implementing the project “Bread. Land. Mother” financed by the State Commission of the Lithuanian Language (2018–2020). This article presents the lexicographic analysis and the data of students’ survey. The analysis of questionnaire revealed an obvious fact that the image of land is perceived by every individual in accordance with influence of the surrounding environment and the worldview constructed by an individual himself or herself. The concept is broad and every individual may have a significantly different understanding of it. Some people see it only as a physical plane, whereas others feel the link with land at a spiritual level because it is home or even more than this.

SPECIFIC FEATURES OF A PLANE SUPERSONIC FLOW

The purpose of this work is to study the characteristics of the flow with supersonic speed when using the tangential and radial components of convective acceleration and associated elements of the characteristic grid as parameters. Using input parameters allows to expand understanding of the zone of influence of disturbances and the nature of the forces contributing to isentropic acceleration (deceleration) of flow and one-to-one mapping between the physical plane and the hodograph of the velocity. The obtained results are proposed to be used in solving applied problems and analyzing experimental studies.

Gravitational waves in massive conformal gravity

First, we obtain the plane wave solution of the linearized massive conformal gravity field equations. It is shown that the theory has seven physical plane waves. In addition, we investigate the gravitational radiation from binary systems in massive conformal gravity. We find that the theory with large graviton mass can reproduce the orbit of binaries by the emission of gravitational waves.

Design and analysis microstrip antenna with reflector to enhancement gain for wireless communication

In this paper is presented the good solution to enhancement gain by using physical plane plate reflector with optimum distance by a reflector was used with the antenna and using a sweep parameter for the distance at which the reflector was placed at (, we found the best distance is when selected the bandwidth is 28GHz where . The gain at the bandwidth in 28GHz was improved from (5.48, 6.78, and 7.83) dB to 11.53 dB, while the gain without a reflector is 7.1 dB. The simulation results were obtained using CST which was more consistent with the practical results.

Explicit Form of Exact Analytical Solution for Calculating Ground Displacement and Stress Induced by Shallow Tunneling and Its Application

In urban environment, it is often unavoidable for shallow tunnels to be constructed adjacent to existing pile foundations. To obtain the ground displacements and stresses induced by shallow tunneling and existing pile foundation loads, the key procedure involves superimposing the analytical solution for shallow tunneling in green-field with the analytical solution for existing structure loads. In green-field, the complex variable method provides exact analytical solutions of ground displacements and stresses caused by shallow tunneling. However, the exact analytical solutions are not directly expressed as explicit functions of the coordinates (x, y) in the physical plane (called implicit form of exact analytical solutions), whereas the displacements and stresses induced by existing structure loads are explicit functions of the coordinates (x, y) in the physical plane, which makes it difficult to superpose the displacements and stresses induced by existing structure loads. In this paper, explicit form of exact analytical solutions of displacements and stresses induced by shallow tunneling in green-field is obtained by using the inverse conformal transformation and the Cauchy–Riemann equations. Comparison with implicit form of exact analytical solutions shows that the explicit form of exact analytical solutions is intuitional and easily used by engineers, and moreover, the calculation amount is much smaller than that for the implicit form of exact analytical solutions. Then, an application involving superimposing the explicit form of exact analytical solutions with Mindlin’s solution is implemented to analyze the secondary stress field and the related potential plastic zone caused by shallow tunneling adjacent to pile foundations. Moreover, the influences of pile foundation parameters on the ranges and shapes of the potential plastic zones induced by nearby tunneling are analyzed.

Maximally Spatial-Disjoint Lightpaths in Optical Networks

Lightpaths enable end-to-end all-optical transmission between network nodes. For survivable routing, traffic is often carried on a primary lightpath, and rerouted to another disjointed backup lightpath in case of the failure of the primary lightpath. Though both lightpaths can be physically disjointed, they can still fail simultaneously if a disaster affects them simultaneously on the physical plane. Hence, we propose a routing algorithm for provisioning a pair of link-disjoint lightpaths between two network nodes such that the minimum spatial distance between them (while disregarding safe regions) is maximized. Through means of simulation, we show that our algorithm can provide higher survivability against spatial-based simultaneous link failures (due to the maximized spatial distance).

New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

A numerical technique for linear elliptic partial differential equations in polygonal domains

Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is unknown. A new transform method for solving BVPs for linear and integrable nonlinear PDEs usually referred to as the unified transform ( or the Fokas transform ) was introduced by the second author in the late Nineties. For linear elliptic PDEs, this method can be considered as the analogue of Green's function approach but now it is formulated in the complex Fourier plane instead of the physical plane. It employs two global relations also formulated in the Fourier plane which couple the Dirichlet and the Neumann boundary values. These relations can be used to characterize the unknown boundary values in terms of the given boundary data, yielding an elegant approach for determining the Dirichlet to Neumann map . The numerical implementation of the unified transform can be considered as the counterpart in the Fourier plane of the well-known boundary integral method which is formulated in the physical plane. For this implementation, one must choose (i) a suitable basis for expanding the unknown functions and (ii) an appropriate set of complex values, which we refer to as collocation points, at which to evaluate the global relations. Here, by employing a variety of examples we present simple guidelines of how the above choices can be made. Furthermore, we provide concrete rules for choosing the collocation points so that the condition number of the matrix of the associated linear system remains low.