Showing papers on "Scalar potential published in 1977"

Three-dimensional magnetic field determination using a scalar potential--A finite element solution

Abstract: A novel procedure of formulating the three-dimensional magnetic field problem in heterogeneous materials in terms of the unknown scalar potential φ and a known analytical solution for a vector potential which is caused by the specified current densities in a homogeneous domain is presented. The analytical solution to the auxiliary problem is easily determined, and the resulting scalar formulation presents considerable economies against the more obvious but costly direct solution with a three-component vector potential A. Two-and three-dimensional examples assuming linear behavior of the material are given to assess the accuracy of the process, and indication is given of the nature of iterations required for nonlinear properties.

Quantum mechanics of charged particles near a plasma surface

Abstract: The interaction between a quantized model of a semi-infinite plasma and a charged non-relativistic particle outside it is considered allowing fully for relativistic retardation in the electromagnetic field. The choice of gauge, which in the past has occasioned difficulty and imprecision, is elucidated. The Hamiltonian is written down in the strict Coulomb gauge having div A=0 everywhere. It is then transformed canonically to a more popular gauge where div A has a delta -function singularity on the interface, and where the scalar potential is zero in absence of the particle. The effective interaction ('dynamic image potential') is evaluated to second order in nu / omega pZ but exactly in omega pZ/c; (v is the particle velocity, Z is distance to interface, omega p is the plasma frequency) and the results discussed.

Theory of flux penetration into laminated iron and associated losses

Abstract: The penetration of leakage flux into a laminated machine or transformer core is governed by the currents induced in the steel, and poses an anisotropic and 3-dimensional field problem which is also severely nonlinear. It is shown that the differential equations can be formulated in terms of an electric vector potential T, and magnetic scalar potential Ω, and that the solution can be expressed in the form of three different characteristic modes, two associated with the core surfaces and the third describing the flux penetration into the interior. This form of solution provides both a qualitative and quantitative picture of the 3-dimensional flux paths, and eddy current loss distribution, and also a practicable means of allowing for saturation. The result can be expressed in the form of a simple network model that is well suited to numerical solution by computer.

Low-energy properties of a relativistic quark model with linear scalar potential

Abstract: A simple quark model with a linear rising scalar confining potential and an additional Coulomb potential is discussed. The eigenvalues of the appropriate Dirac equation are studied with respect to variations of the quark bare mass and to the potential parameters. The model is able to account for the static properties of the nucleon.

Magnetic fields of active regions and their zero points

Abstract: The possibility of a potential approximation for the description of magnetic fields in the chromosphere and the corona is discussed. The introduction of a scalar potential allows one to investigate the overall geometrical properties of the field. On the basis of the results of the general theory of differential equations, it is shown that the number of singular (zero) points of a magnetic field above the plane of the photosphere is determined by the number of maxima and minima in the potential at the photosphere. The arrangement of the singular points determines the overall topological structure of the field. The Neumann problem is solved for the fields of active regions. The results of a numerical solution of the boundary problem for the active region McMath No. 11,693 are given as an example of the application of the proposed methods. The structure of the magnetic field of this region and the singular points found for it are described.

Wave operators for oscillating potentials

Abstract: We consider the Schrodinger operator with magnetic vector potential and static scalar potential We show the existence of the wave operators under considerations which allow strong oscillations of the potentials

Numerical Analysis on Isotropic Elastic Waveguides by Mode-Matching Method - I. Analytical Foundations and General Algorithms

Abstract: A new method for computer-aided calculation, the mode- motching merhod, based on the Rayleigh expansion theorem, is pro- posed in order to analyze the boundary condition problem of elastic fields, and its analytical foundations and general algorithms are dis- cussed. The alastic fields are represented by scalar potential functions which are solutions of Helmholtz equations and expanded by the well- known separated solutions. Introducing the formal Green functions, the integral representations of the potentials are derived. The Rayleigh expansion theorem assures the existence of the infinite sequence of the truncated modal expansions which uniformly converges to the true field in arbitrarily shaped cross section. Through this theorem and the integral representations, the procedure of the mode-matching method is described simply so that the truncated modal expansions are made to fit for the boundary conditions in the least squares sense. Conse- quently this new method may ensure more precise analyses not only on the dispersion characteristics, but also on the field distributions of the particle velocity or the stress by small amount of computational efforts, than the other numerical methods reported so far. The general algo- rithm for the mode-matching method is described in the cases of forced and free vibrations of the homogeneous isotropic elastic waveguide with arbitrarily shaped cross section.

Localized solutions of a nonlinear scalar field with a scalar potential

Abstract: The exact localized solutions for a nonlinear scalar field with a scalar potential are studied In particular, we compare the stability of the above solutions and those obtained by Rosen in absence of the scalar potential

Magnetic Field Diffusion in Fast Discharging Homopolar Machines

Abstract: The unusually high mechanical and thermal stresses occuring in fast discharging homopolar machines require accurate prediction of high magnetic fields accompanying their operation. Linear methods and ideal configurations are no longer acceptable as simplifying assumptions in designing such devices used in controlled thermonuclear fusion experiments, laser applications, etc. A finite element method - Galerkin technique is used for solution of Maxwell's equations for a moving medium. The transient skin effect in the system is described in terms of a magnetic vector potential and an electric scalar potential. Lagrange multipliers are used to impose the necessary constraint on the vector potential Ā. The formulation for the steady-state magnetic fields in nonlinear media results as a particular case of the method. This approach was used for predicting the parameters for the very fast discharging homopolar machine (FDX) designed by the Center for Electromechanics at The University of Texas at Austin. ...

Multipole structure of static continuous matter distributions in general relativity

Abstract: A mass skeleton is defined for a static extended body in a gravitational field. It is a scalar-valued distribution on a tangent space, and is equivalent to that part of the reduced multipole moment structure which describes the mass density of the body. An explicit form is given for this distribution in terms of the mass density and the scalar potential of the field. It is deduced that the mass skeleton and the scalar potential are not completely independent. The smoothness of the mass distribution imposes certain weak restrictions on those scalar potentials which are compatible with a given mass skeleton.

Finite-element solutions for geothermal systems

Abstract: Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.

A field analysis of nonlinear irreversible thermodynamic processes

Abstract: The generalized thermodynamic potential analysis of nonlinear irreversible processes precludes the analysis of rotational processes. The nonexistence of scalar potential functions necessitates a thermodynamic analysis of the system forces. A field analysis in the phase space of the generalized displacements and velocities treats the force components as tensors of second order that tend to deform and rotate the irreversible process, which is viewed as an elastic material. The analysis of chemical oscillatory processes involves the introduction of the thermodynamic vector potential, which is subsequently used in the formulation of a variational principle and to define an energy flux vector. The direction of energy flow elucidates the mechanism by which steady motion is maintained and it is a characteristic property of open systems. Field analyses of systems that are described by half and single degrees of freedom are contrasted.

Event Horizon and Scalar Potential

Abstract: The introduction of a scalar potential with a more general schema than general Relativity eliminates the “event horizon.” Among possible solutions, the Schwarzschild one represents a singular case. A study of the geodesic properties of the matching with an approximated interior Solution are given. A new definition of the gravitational mass and χ function is deduced.

Symmetry Properties of the Macroscopic Scalar Potential.

Abstract: Abstract This Communication examines the group properties of the macroscopic scalar potential of an alkali halide derived previously by Ritter and Markham. The potential has the form σ i f i ( r ) q i , where f i is a function of space and q i is a normal coordinate. It does not consider in detail the properties of the potential at a site, since Ritter and Markham omit all higher order terms in an expansion. This makes the origin arbitrary. The potential has space group symmetry. One desires point group symmetry when working with point imperfections. Hence, here we consider the point group symmetry of the σ i f i 2 ( r ) without regards to the q i 's. We believe that f 2 i is more appropriate than just the f i . Our interest is limited to the Φ + 1 , Φ + 3 , Φ - 4 and Φ + 5 irreducible representations of O h , and the lengthy calculations were made only for KCl. The γ + 1 part of the potential dominates, especially near the arbitrary origin where the other parts of the potential go to zero.