scholarly journals THE SPINOR WAVE FUNCTIONS AND OPERATORS IN THE LOCAL COORDINATE SYSTEM

1963 ◽  
Vol 19 (6) ◽  
pp. 341
Author(s):  
HOU BAI-YU
Keyword(s):  
Coordinate System ◽  
Local Coordinate System ◽  
Wave Functions ◽  
Spinor Wave

Establishment of local coordinate systems in the transition to the geodetic system of coordinates of GSK-2011

2017 ◽  
Vol 929 (11) ◽  
pp. 2-10
Author(s):  
A.V. Vinogradov
Keyword(s):  
Coordinate System ◽  
Small Businesses ◽  
Transition Period ◽  
Local Coordinate System ◽  
Initial Point ◽  
Central Meridian ◽  
Administrative District ◽  
Local Networks ◽  
Small Areas ◽  
Geodetic System

Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

scholarly journals MEASUREMENT OF VERTICALITY CONSTRUCTION OF BUSHINGS FOR LABORATORY CONSTRUCTION MATERIALS

2014 ◽  
Vol 40 (4) ◽  
pp. 171-174 ◽  
Author(s):  
Petr Jadviščok ◽  
Rostislav Dandoš ◽  
Tomaš Jiroušek
Keyword(s):  
Coordinate System ◽  
Building Materials ◽  
Civil Engineering ◽  
Local Coordinate System ◽  
Construction Materials ◽  
Polar Method ◽  
Standard Equipment ◽  
Final Number ◽  
Loading Tests ◽  
Design And Manufacture

This contribution describes process which was used for verticality measurement of the bushings for laboratory construction materials in the pavilion of testing. This pavilion is newly built in VŠB-TU Ostrava, Faculty of Civil Engineering, as part of the Testing house of the building materials. The requirement of the building investor was to determine the verticality of the bushings placed between the first aboveground and the first underground floor. After the building finishing, the bushings with the diameter 70 mm will be used for loading tests of various building materials. The final number of bushings is 169, and they are placed lengthwise and crosswise in the step of 750 mm. The centres of the bushings were measured by polar method in pavilion local coordinate system. The precision of the bushing centres determination was }5 mm according to the investor´s requirement. The precision would not be followed if the standard equipment for reflector fixing was used. In that case, it was necessary to design and manufacture special tool in the shape of truncated cone. On the top part was placed central pivot for reflector with additional plate bubble.

scholarly journals Computation of electrostatic fields in anisotropic human tissues using the Finite Integration Technique (FIT)

2005 ◽  
Vol 2 ◽  
pp. 309-313 ◽  
Author(s):  
V. C. Motresc ◽  
U. van Rienen
Keyword(s):  
Coordinate System ◽  
Electromagnetic Fields ◽  
Human Body ◽  
Local Coordinate System ◽  
Anisotropic Materials ◽  
The Body ◽  
Integration Technique ◽  
Data Set ◽  
Computer Data ◽  
Finite Integration Technique

Abstract. The exposure of human body to electromagnetic fields has in the recent years become a matter of great interest for scientists working in the area of biology and biomedicine. Due to the difficulty of performing measurements, accurate models of the human body, in the form of a computer data set, are used for computations of the fields inside the body by employing numerical methods such as the method used for our calculations, namely the Finite Integration Technique (FIT). A fact that has to be taken into account when computing electromagnetic fields in the human body is that some tissue classes, i.e. cardiac and skeletal muscles, have higher electrical conductivity and permittivity along fibers rather than across them. This property leads to diagonal conductivity and permittivity tensors only when expressing them in a local coordinate system while in a global coordinate system they become full tensors. The Finite Integration Technique (FIT) in its classical form can handle diagonally anisotropic materials quite effectively but it needed an extension for handling fully anisotropic materials. New electric voltages were placed on the grid and a new averaging method of conductivity and permittivity on the grid was found. In this paper, we present results from electrostatic computations performed with the extended version of FIT for fully anisotropic materials.

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

The Main Motivity Analysis of Deployment Process of Astromesh

2011 ◽  
Vol 71-78 ◽  
pp. 1554-1559
Author(s):  
Guo Hui Chen ◽  
Yong Xiao ◽  
Yan Ni Lei
Keyword(s):  
Coordinate System ◽  
Local Coordinate System ◽  
Action Principle ◽  
Basic Unit ◽  
Drive Mechanism ◽  
Synchronous Drive

The deployment process of Astromesh is analyzed and the basic unit is defines, based on which overall coordinate system of Astromesh and the units local coordinate system are established. The role of synchronous drive mechanism hinges and motor are analyzed in the unit local coordinate system, and whose action principle is stated in the form of parameter.

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