General method for solving the self-consistent equations of motion and Maxwell equations

1982 ◽  
Vol 25 (11) ◽  
pp. 946-954
Author(s):  
Yu. G. Pavlenko
Keyword(s):  
Maxwell Equations ◽  
Equations Of Motion ◽  
The Self ◽  
Self Consistent ◽  
General Method

scholarly journals Computer models of spiral structure

1970 ◽  
Vol 38 ◽  
pp. 368-372 ◽  
Author(s):  
F. Hohl
Keyword(s):  
Motion Picture ◽  
Computer Model ◽  
Spiral Structure ◽  
Galactic Disk ◽  
Equations Of Motion ◽  
Computer Models ◽  
The Self ◽  
Large Numbers ◽  
Self Consistent

A computer model for isolated disks of stars is used to study the self-consistent motion of large numbers of point masses as they move in the plane of the galactic disk. The Langley Research Center's CDC 6600 computers are used to integrate the equations of motion for systems containing from 50000 to 200000 stars. The results are presented in the form of a motion picture.

Stability analysis of sheared non-neutral relativistic cylindrical electron beams in applied magnetic fields

1991 ◽  
Vol 45 (2) ◽  
pp. 191-201 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman
Keyword(s):  
Stability Analysis ◽  
Magnetic Fields ◽  
Maxwell Equations ◽  
Electron Beams ◽  
Radial Electric Field ◽  
The Self ◽  
Axial Motion ◽  
Axial Velocity Component ◽  
Self Consistent ◽  
Consistent Treatment

A self-consistent stability analysis of relativistic non-neutral cylindrical electron flows propagating along applied magnetic fields is considered within the framework of the macroscopic cold-fluid-Maxwell equations. The full influence of the equilibrium self-electric and self-magnetic fields is retained. Then the E x B drift (E being the radial electric field created by the uncompensated charge) generates a radial shear, vz(r) and v0(r). The effect of the shear in the axial velocity component, as reflected in the relative axial motion of adjacent concentric layers of beam particles, is investigated. The self-consistent treatment of the problem thus shows that the equilibrium state considered in this paper is unstable.

scholarly journals A generalization of the equations of the self-consistent field for two-electron configurations

1937 ◽  
Vol 160 (903) ◽  
pp. 588-604 ◽  
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Configuration Interaction ◽  
The Self ◽  
Angular Function ◽  
Radial Functions ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
General Method

The most successful general method so far devised for dealing with many- electron atoms is th a t of the self-consistent field (abbreviated in what follows to “ s. c. f.” ). If greater accuracy is required than is obtainable with the method as ordinarily used (either with or without exchange), either the so-called “ configuration interaction ” must be taken into account —usually a very laborious procedure—or else more complicated (varia­tional) methods must be used, which must be designed separately for each particular case, and in which the concept of each electron being assigned to its own “ orbit” is usually abandoned. It would seem desirable, therefore, to have, if possible, some general method which will increase the accuracy of the calculations without taking into account configuration interaction, and which will still allow the conceptual features of the s. c. f. method (i. e. the assignment of “ orbits” ) to be retained. In this paper such a method is developed for the case of two-electron configurations in Russell-Saunders coupling. The method consists in assuming a form for the wave function which is similar to that used in the s. c. f. method, except that the proper spatial symmetry is allowed for (which is not so in the case of the s. c. f. equations without exchange), and further, an adjustable function of Θ, the angle between the radii vectores to the two electrons, is inserted as a multiplying factor. The usual varia­tional method is then applied, and yields differential equations for the two radial functions which are similar to those of the ordinary theory, together with an equation for the angular function.

SCALE-SETTING WITHOUT THE HIGGS MECHANISM: NON-ABELIAN SYMMETRY

1992 ◽  
Vol 07 (01) ◽  
pp. 201-207
Author(s):  
J. T. ANDERSON
Keyword(s):  
Equations Of Motion ◽  
Mass Scale ◽  
Higgs Mechanism ◽  
The Self ◽  
Current Conservation ◽  
Coupled Equations ◽  
Consistent Field ◽  
Zero Current ◽  
Self Consistent ◽  
Self Consistent Field

For the non-Abelian Higgs model it is shown that the coupled equations of motion for Aμ, ϕ and ϕ* have nonanalytic singularities which must be removed if the equations are integrable. Current conservation is found to remove the singularities in the vector-field equation and give a mass scale independent of V and the Higgs mechanism. The self-consistent field solutions for Aμ and the ϕ fields give either (1) the Higgs mechanism, zero current and the pure-gauge solution, or (2) nonzero current, a gauge-covariant solution and the mass scale independent of V and the Higgs mechanism.

Modeling of the Plastic Behavior of Inhomogeneous Media

1984 ◽  
Vol 106 (4) ◽  
pp. 295-298 ◽  
Author(s):  
M. Berveiller ◽  
A. Zaoui
Keyword(s):  
Integral Equation ◽  
Strain Rate ◽  
The Self ◽  
Plastic Strain Rate ◽  
Plastic Behavior ◽  
Consistent Model ◽  
Self Consistent ◽  
Common Framework ◽  
Strain Rate Field ◽  
General Method

The general method which work for the case of linear properties are taken as a pattern for the derivation of the local total strain rate field of an inhomogeneous material (such as a polycrystal, a composite, or multiphase material) submitted to a uniform macroscopic elastic-plastic strain rate; the localization procedure leads to an integral equation, the solution of which is shown to yield the overall behavior. This method allows to locate within a common framework all the classical approaches, namely Taylor’s, Lin’s ones, the self-consistent scheme…and to suggest possible extensions. Some significant results are reported, concerning strain-hardening, yield stress, and texture devolopment of FCC polycrystals, according to simplified, one-site self-consistent model.

scholarly journals Crystal theory of metals: calculation of the elastic constants

1942 ◽  
Vol 180 (983) ◽  
pp. 451-476 ◽  
Keyword(s):  
Potential Energy ◽  
Perturbation Method ◽  
Elastic Constants ◽  
Equations Of Motion ◽  
The Self ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Set Up ◽  
Approximate Equations

The approximate equations of motion for the electrons in a cyclic lattice of a metal are set up with the help of the self-consistent field. The displacements of the ions are then considered as perturbations of the motion of the electrons. The change of the boundary is compensated by a co-ordinate transformation. The change of the potential energy of the lattice due to a homogeneous deformation is calculated by the perturbation method. The calculated values of the elastic constants are found to be in satisfactory agreement with the observed values.

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