Showing papers on "Scalar potential published in 1996"

Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence

Abstract: Mixing of a passive scalar in statistically homogeneous, isotropic, and stationary turbulence with a mean scalar gradient is investigated via direct numerical simulation, for Taylor‐scale Reynolds numbers, Rλ, from 28 to 185. Multiple independent simulations are performed to get confidence intervals, and local regression smoothing is used to further reduce statistical fluctuations. The scalar fluctuation field, φ(x,t), is initially zero, and develops to a statistically stationary state after about four eddy turnover times. Quantities investigated include the dissipation of scalar flux, which is found to be significant; probability density functions (pdfs) and joint‐pdfs of the scalar, its derivatives, scalar dissipation, and mechanical dissipation; and conditional expectations of scalar mixing, ∇2φ. A linear model for scalar mixing jointly conditioned on the scalar and v‐velocity is developed, and reproduces the data quite well. Also considered is scalar mixing jointly conditioned on the scalar and scalar...

Nonminimal coupling of the scalar field and inflation

Abstract: We study the prescriptions for the coupling constant of a scalar field to the Ricci curvature of spacetime in specific gravity and scalar field theories. The results are applied to the most popular inflationary scenarios of the universe; their theoretical consistency and certain observational constraints are discussed. \textcopyright{} 1996 The American Physical Society.

A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements

Abstract: An advanced A-V method employing edge-based finite elements for the vector potential A and nodal shape functions for the scalar potential V is proposed. Both gauged and ungauged formulations are considered. The novel scheme is particularly well suited for efficient iterative solvers such as the preconditioned conjugate gradient method, since it leads to significantly faster numerical convergence rates than pure edge element schemes. In contrast to nodal finite element implementations, spurious solutions do not occur and the inherent singularities of the electromagnetic fields in the vicinity of perfectly conducting edges and corners are handled correctly. Several numerical examples are presented to verify the suggested approach.

Comparison of magnetically induced elf fields in humans computed by FDTD and scalar potential FD codes

Abstract: This paper presents a comparison of the magnetically induced low frequency electric and current density fields within an anatomically realistic model of the full human body, as computed using two different numerical techniques. The first method is a full wave quasi-static finite-difference time-domain method. The second method is based on a representation of the first-order internal electric field in terms of a scalar conduction potential plus a vector potential for the lowest-order applied magnetic field. Each code was used to calculate the fields, induced by three orthogonal uniform magnetic fields, in a 7.2 mm-resolution human full-body model. Three-dimensional correlation coefficients of better than 99.8% were observed between results computed by the two methods. Individual edge electric fields typically agree to 3 significant digits.

Models for the integer quantum Hall effect: The network model, the Dirac equation, and a tight-binding Hamiltonian

Abstract: We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness in the mass, the scalar potential, and the vector potential. Separately, we show that the network model can also be associated with a nearest neighbour, tight-binding Hamiltonian.

Non-Gaussian scalar statistics in homogeneous turbulence

Abstract: Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.

Non-Gaussian scalar statistics in homogeneous turbulence

Abstract: Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.

Consequences of particle conservation along a flux surface for magnetotail tearing

Abstract: The energy principle for magnetotail tearing is reexamined using conservation of electron particle number along a flux surface as a means of calculating the volume-integrated perturbed number density 〈 n1 〉, where n1 is the perturbed electron number density and the angle brackets denote integration along a field line. It is shown that if the electron response is magnetohydrodynamic, then 〈 n1 〉 can be calculated as a function of the perturbation vector potential component A1y (assuming magnetotail coordinates) independent of the potential components A1x and A1z and independent of the scalar potential ϕ. This result holds as long as the equilibrium and the tearing perturbations are two-dimensional, independent of the y coordinate. In the case of a parabolic field model, the resulting 〈 n1 〉 exactly matches the results obtained previously by Lembege and Pellat [1982], who used the kinetic drift equation to calculate the electron response. Thus the compressional stabilization of the tearing mode is a direct consequence of, and can be completely calculated from, the conservation of electron particle number along the field line. Further, it is shown that 〈 n1 〉 is independent of By, the guide component of the magnetic field, so the inclusion of a guide field does not alter the tearing stabilization condition.

A generalized cable equation for magnetic stimulation of axons

Abstract: During magnetic stimulation, electric fields are induced both on the inside (intracellular region) and the outside (extracellular region) of nerve fibers. The induced electric fields in each region can be expressed as the sum of a primary and a secondary component. The primary component arises due to an applied time varying magnetic field and is the time derivative of a vector potential. The secondary component of the induced field arises due to charge separation in the volume conductor surrounding the nerve fiber and is the gradient of a scalar potential. The question, "What components of intracellular fields and extracellular induced electric fields contribute to excitation?" has, so far, not been clearly addressed. Here, the authors address this question while deriving a generalized cable equation for magnetic stimulation and explicitly identify the different components of applied fields that contribute to excitation. In the course of this derivation, the authors review several assumptions of the core-conductor cable model in the context of magnetic stimulation. It is shown that out of the possible 4 components, only the first spatial derivative of the intracellular primary component and the extracellular secondary component of the fields contribute to excitation of a nerve fiber. An earlier form of the cable equation for magnetic stimulation has been shown to result in solutions identical to three-dimensional (3D) volume-conductor model for the specific configuration of an isolated axon in a located in an infinite homogenous conducting medium. The authors extend and generalize this result by demonstrating that their generalized cable equation results in solutions identical to 3D volume conductor models even for complex geometries of volume conductors surrounding axons such as a nerve bundle of different conductivity surrounding axons. This equivalence in the solutions is valid for several representations of a nerve bundle such as anisotropic monodomain and bidomain models.

Path integral for Klein-Gordon particle in vector plus scalar Hulthén-type potentials

Abstract: The Green's function for a Klein-Gordon particle subjected to vector plus scalar Hulthen-type potentials is calculated in the path integral approach. The energy spectrum together with the normalized wave functions of the bound states are deduced. Special cases including the pure vector Hulthen potential, the pure attractive scalar Hulthen potential and the Coulomb potential are also analyzed.

The scalar contribution toτ →K πν τ

Abstract: We consider the scalar form factor inτ →Kπντ decays. It receives contributions both from the scalar resonanceK*0(1430) and from the scalar projection of off-shell vector resonances. We construct a model for the hadronic current which includes the vector resonancesK*(892) andK*(1410) and the scalar resonanceK*0(1430). The parameters of the model are fixed by matching to theO(p4) predictions of chiral perturbation theory. Suitable angular correlations of theKπ system allow for a model independent separation of the vector and scalar form factor. Numerical results for the relevant structure functions are presented.

N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map

Abstract: The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Lagrangians for rigid theories are also written in this general setting and the connection with local theories elucidated. The derivation of these results using geometrical techniques is briefly summarized.

3D eddy current analysis by the finite element method using double nodes technique

Abstract: There are several difficulties in calculating eddy currents in plates with thin slits by the finite element method (FEM). Under the influence of flat finite elements at slits, the accuracy of analysis decreases and the computation time increases. Using the A-/spl phi/ method, we propose a novel technique, which overcomes those defects. The feature of the method is to adopt double nodes for the electric scalar potential /spl phi/ at slits, but not to the magnetic vector potential A. Adopting this technique, slits are equivalent to current barriers that have infinitesimal width. Some numerical results, which show the validity of the proposed method, are also presented. We analyze the magnetic fields of a double-sided linear induction motor with slits in a secondary plate, as a suitable model for proving the validity of the proposed method.

Propagating torsion from first principles

Abstract: A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are written down for the vacuum and for various types of matter fields. Some of their properties are discussed. In particular, we show that gauge fields can interact minimally with the torsion without the breaking of gauge symmetry.

Reconstruction of fluid motion in acoustic diffraction tomography

Abstract: This paper shows how the technique of diffraction tomography can be applied for reconstructing the magnitudes and the directions of the velocity vectors as well as stationary sound‐speed perturbation in a fluid flow. The analysis is based on the wave equation describing the propagation of the sound in an inhomogeneous moving fluid medium. For plane‐wave irradiation and scattered field detection by a linear array of receivers, the Fourier diffraction theorem for the fluid vorticity has been obtained. Similar to the scalar case, the theorem relates the Fourier transform of the measured forward scattered data to the spatial spectrum of the vorticity and leads to the values of the two‐dimensional transform of the velocity vector curl along a semicircular arc in the frequency domain. Utilizing the nonreciprocity of sound scattering from moving fluid (as opposed to the reciprocity of the elastic scattering on the scalar potential), a procedure for the separation of scalar and moving components of the flow has b...

Validation of a scalar potential finite-difference code for extremely low frequency magnetic induction modelling using an analytical method

Abstract: This paper presents a comparison of numerical and analytical calculations of the low-frequency electric and current density fields, induced by an applied uniform axial magnetic field, in an equatorially stratified sphere having the conductivity distribution σ(ϕ) = σ 0 e−λ cos (pϕ) with p ∊ {1, 2} and λ > 0.

Three-dimensional magnetostatic field calculation using integro-differential equation for scalar potential

Abstract: An effective method for calculation of nonlinear three-dimensional magnetostatic fields is proposed. It is based on a numerical solution of the integro-differential equation for the total scalar potential. The main advantages of this method are that the problem has been formulated in terms of a scalar variable introduced only for regions filled with ferromagnetic materials and no artificial boundary conditions are required. The numerical algorithm which implements this method is described. Its application is illustrated with magnetostatic field calculation for C-magnets.

Renormalization of the charged scalar field in curved space.

Abstract: The DeWitt-Schwinger proper time point-splitting procedure is applied to a massive complex scalar field with arbitrary curvature coupling interacting with a classical electromagnetic field in a general curved spacetime. The scalar field current is found to have a linear divergence. The presence of the external background gauge field is found to modify the stress-energy tensor results of Christensen for the neutral scalar field by adding terms of the form (eF) 2 to the logarithmic counterterms. These results are shown to be expected from an analysis of the degree of divergence of scalar quantum electrodynamics.

`Critical' behaviour of weakly bound systems

Abstract: We consider the class of three-dimensional finite-range, or similar, potentials , depending on a strength constant . We study the behaviour of the eigenvalue E as a function of , where is the critical value at the transition from 0 1 bound state. For the case, we find , whereas the relationship is linear for . Treating as a continuous parameter in the radial Schrodinger equation, we give the evolution of the power law between and . Besides spherically symmetric scalar potentials, we also discuss the case of a repulsive scalar potential combined with a spin - orbit component of the Thomas form.

Exact scalar field cosmologies with a fluid

Abstract: Exact solutions for the scalar field and the potential function in an exponentially inflationary universe, whose source of the gravitational field is a classical scalar field plus an isotropic fluid, are found.

Analytical calculation of Boozer magnetic coordinates for axisymmetric magnetohydrodynamic equilibria

Abstract: A new analytical technique for extracting the Boozer magnetic coordinates in axisymmetric magnetohydrodynamic equilibria is described. The method is based upon the correspondence between the expansion of the flux function in toroidal multipolar moments and the expansion in toroidal axisymmetric harmonics of the magnetic scalar potential χ0, which appears in the covariant representation B=∇χ0+β ∇ψT of the magnetic field. An example of calculation of Boozer magnetic coordinates is given for an experimental highly shaped high β equilibrium of DIIID [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159].

Low-energy effective Lagrangian from nonminimal supergravity with unified gauge symmetry.

Abstract: From general supergravity theory with unified gauge symmetry, we obtain the low-energy effective Lagrangian by taking the flat limit and integrating out the superheavy fields in a model-independent manner. The scalar potential possesses some excellent features. Some light fields classified by using a supersymmetric fermion mass, in general, would get intermediate masses at the tree level after the supersymmetry is broken. We show that the stability of the weak scale can be guaranteed under some conditions. There exist extra nonuniversal contributions to soft supersymmetry-breaking terms which can give an impact on phenomenological study. \textcopyright{} 1996 The American Physical Society.

Numerical Simulation of Three-Dimensional Incompressible Flow by a New Formulation

Abstract: SUMMARY A new mathematical formulation, called the pseudovorticity-velocity formulation, of the three-dimensional incompressible NavierStokes equations is presented as an alternative to the vorticity-velocity approach. For the model lid-driven cavity flow problem in two and three dimensions, combined with an explicit mixed spectral/iinite different numerical scheme the proposed formulation is found to be efficient and very accurate as compared with the results available in the literature. In particular, the simulation results demonstrate an attractive feature of the present formulation compared with the vorticity-velocity approach, namely that the divergencefree condition of the velocity field can always be achieved on a non-staggered mesh. The mathematical formulations that are commonly used to simulate three-dimensional incompressible viscous flows include the primitive variables’ (velocity-pressure), vorticity-vector p~tential~,~ and vorticity-velocity4 formulations. As indicated in an overview of these formulations by Gresho: each formulation has its own advantages as well as shortcomings with respect to the others. Both the vorticity-vector potential formulations and the vorticity-velocity approach have a distinct advantage over the velocityTressure formulation in that the pressure need not be calculated explicitly. The vorticity-velocity method, similar to the velocityTressure formulation but unlike the velocity-vector potential approach, suffers from a major difficult in obtaining a solenoidal velocity field so that the continuity equation is satisfied explicitly. For the vorticity-velocity formulation the use of a staggered mesh or alternative boundary conditions for the vorticity has been proposed to provide a divergence-free velocity field.6 In the velocity-vector potential formulation, however, the vector potential is not uniquely defined and a scalar potential is further required for the non-enclosed flow configuration. It follows from the foregoing that it is highly desirable to develop a formulation having the advantages of the velocity-vorticity formulation but avoiding the difficulty of obtaining a divergencefree velocity field. Jia and Nakamura’ recently presented a new formulation in terms of velocity and a new variable q for two-dimensional incompressible flow. It has been demonstrated that their formulation can be applied to both steady and unsteady flow simulations on a non-staggered grid, yielding an essentially divergence-free velocity field. The present study represents a continuing effort in pursuit of this aspect. In this paper we present a new formulation, called the pseudovorticityvelocity formulation, and its application to three-dimensional incompressible viscous flow