Showing papers on "Scalar potential published in 1987"
TL;DR: In this article, a homogeneous isotropic cosmological model driven by a scalar field with an exponential potential is studied, and it is shown that there is a solution with power-law inflation, and this solution is an attractor.
443 citations
TL;DR: In this paper, a scalar potential formulation for three-dimensional problems is described, which avoids cancellation errors within ferromagnetic objects and discontinuities and non-uniqueness of a Scalar potential outside these objects.
Abstract: A new scalar potential formulation for three-dimensional problems is described. This formulation avoids cancellation errors within ferromagnetic objects and discontinuities and nonuniqueness of a scalar potential outside these objects. These deficiencies are peculiar to reduced and total scalar potential formulations, respectively. The finite-element discretization is applied to the new scalar potential formulation, and a novel approach to smoothing and extension of finite-element solutions is presented. Some numerical results obtained using the new scalar potential formulation are reported.
73 citations
TL;DR: In this paper, it was shown that one can choose the form of the magnetic vector potential to render the scalar potential of a single point charge associated with a horizontal, time-harmonic dipole in a layered medium identical to that associated with vertical dipole, provided that the source and observation points are within the same layer.
Abstract: It is demonstrated that one can choose the form of the magnetic vector potential to render the scalar potential of a single point charge associated with a horizontal, time-harmonic dipole in a layered medium identical to that associated with a vertical dipole, provided that the source and observation points are within the same layer. This proves the existence of the so-called mixed-potential electric field integral equation for objects of arbitrary shape in layered media.
66 citations
TL;DR: In this paper, the scalar potential of supergravity theories with arbitrary higher-derivative interactions was derived and the relevance of these results for the vacuum configurations of superstring theories was outlined.
51 citations
TL;DR: In this article, a set of coupled integral equations is derived to investigate the finite beta effects on the slab ion temperature gradient driven modes for a collisionless plasma in a sheared magnetic field.
Abstract: A set of coupled integral equations is derived to investigate the finite beta effects on the slab ion temperature gradient driven modes for a collisionless plasma in a sheared magnetic field. Low beta plasma is considered so that only the parallel component of perturbed vector potential A∥ and the perturbed scalar potential φ are involved. Comprehensive parametric studies show that finite beta of several percent could have significant stabilization effects on the slab modes under investigation.
36 citations
TL;DR: In this paper, a scalar potential is introduced to describe the magnetic field in the models constructed, where the current distribution is modeled by using a fictitious magnetization and only an equivalent charge distribution within the region considered.
Abstract: Given volume distributions of stationary or quasistationary electric current are replaced by equivalent distributions of fictitious magnetization and, eventually, of surface current, on the basis of the Amperian model for magnetized media. The fictitious magnetization is subsequently replaced by the equivalent distribution of fictitious magnetic charge. Consequently, the magnetic field due to given volume currents is determined from that produced by the corresponding charges and surface currents. This modeling method is also presented for generalized distributions of current. A scalar potential is introduced to describe the field in the models constructed. This scalar potential is a single‐valued function of position when the current distribution is modeled by using a fictitious magnetization and only an equivalent charge distribution within the region considered. The modeling procedure is flexible and the models proposed yield an easier physical interpretation and a substantially reduced amount of comput...
28 citations
TL;DR: In this paper, the effect of a scalar potential V (x, y) on a Landau level in two dimensions was considered and an exact effective Hamiltonian was derived which describes the effect on a single Landau-level, expressed as a power series in V/Ec, where Ec is the cyclotron energy.
Abstract: Considers the effect of a scalar potential V (x, y) on a Landau level in two dimensions. An exact effective Hamiltonian is derived which describes the effect of the potential on a single Landau level, expressed as a power series in V/Ec, where Ec is the cyclotron energy. The effective Hamiltonian can be represented as a function H (x, p) in a one-dimensional phase space. The function H (x, p) resembles the potential V (x, y): when the area of a flux quantum is much smaller than the square of the characteristic length scale of V, then H approximately=V. Also H (x, p) retains the translational and rotational symmetries of V(x, y) exactly, but reflection symmetries are not retained beyond the lowest order of the perturbation expansion.
27 citations
15 Aug 1987-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, the imaging properties of charged particle beams in arbitrary static magnetic fields are outlined starting from Hamilton's principle, and the magnetic scalar potential is expressed as a series of multipoles about an arbitrary space curve which need not necessarily coincide with a trajectory of the beam.
Abstract: Starting from Hamilton's principle, the imaging properties of charged particle beams in arbitrary static magnetic fields are outlined. The magnetic scalar potential is expressed as a series of multipoles about an arbitrary space curve which need not necessarily coincide with a trajectory of the beam. Appropriate power series expansions are given for the components of the magnetic vector potential where the expansion coefficients are related to the complex curvature of the axis and the strengths of the multipole components of the magnetic scalar potential. The general laws which govern the propagation of the charged particles are discussed by means of Hamilton's characteristic functions. It is shown that the Poisson and the Lagrange brackets are equivalent representations of the symplectic condition. The Poincare invariant is used for elucidating some characteristic imaging properties of magnetic fields. A perturbation eikonal is introduced which allows a systematic and simultaneous calculation of the geometrical and chromatic aberrations to any order. The method has the advantage that it reveals at the very beginning all interrelations between the aberration coefficients. The iteration procedure starts from the paraxial rays which are supposed to be known. The algorithm is especially suited for numerical calculation of the higher-order aberrations.
27 citations
TL;DR: In this article, the mechanism for generating radiative breaking of the gauge symmetry at an intermediate mass scale is analyzed in E 6 superstring-inspired models, which can be induced by large vacuum expectation values, which are developed along a flat direction of the scalar potential.
27 citations
TL;DR: In the continuum limit, the vanishing of the renormalized self-coupling is confirmed, and it is shown that the system can exist in one of two possible phases, both having a free particle of arbitrary mass.
Abstract: We study the \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ theory in 4 space-time dimensions in a Monte Carlo simulation on a ${10}^{4}$ lattice, through an especially simple and accurate way to calculate the effective potential. All renormalized parameters are obtained via the effective potential and the propagator. In the continuum limit we confirm the vanishing of the renormalized self-coupling, and show that the system can exist in one of two possible phases, both having a free particle of arbitrary mass. In one phase the vacuum expectation of the field vanishes, while in the other it is nonzero. This opens the possibility that, even though the self-coupling vanishes, the field can still be used to generate masses for gauge bosons and fermions.
21 citations
TL;DR: In this article, the bending wave equation for thin plates including some higher-order terms is obtained by this general method and compared to the corresponding equation of Timoshenko, and exact and approximate expressions for the ratio of parallel to perpendicular displacements at a plate surface are calculated.
TL;DR: In this article, a map θ: R → R such that, if G0 is the Kahler-invariant function of a standard flat model, G = θ∘G 0 is the corresponding function for the given higher-derivative flat potential model is constructed.
TL;DR: In this paper, the authors studied radiative corrections to an N = 1 supergravity model suggested by a particular compactification of superstring theories, including nonperturbative supersymmetry breaking effects.
TL;DR: In this article, the shifted 1/N expansion method has been applied to a linear scalar potential in the Dirac equation to obtain the relativistic energy eigenvalues.
Abstract: The shifted 1/N expansion method has been applied to a linear scalar potential in the Dirac equation to obtain the relativistic energy eigenvalues. The results are compared with those obtained by Rein (1977) and by Gunion and Li (1975).
TL;DR: Tanaka and Sato as mentioned in this paper presented two types of simulations of the kinetic Alfven wave using a macroscale particle simulation code, which enables individual particle dynamics to be followed in the MHD scales.
Abstract: Two types of simulations of the kinetic Alfven wave are presented using a macroscale particle simulation code (Tanaka and Sato, 1986) which enables individual particle dynamics to be followed in the MHD scales. In this code, low frequency electromagnetic fields are solved by eliminating high frequency oscillations such as the light modes, and the scalar potential electric field is solved by eliminating Lagrangian oscillations. The dependences of the frequency and the Landau damping on the perpendicular wavenumber were studied, and good agreement was found between simulation and theoretical predictions. Some fundamental nonlinear interactions of the kinetic Alfven wave with the particles (parallel acceleration of the electrons) were also noted.
TL;DR: It is found that for this model, in the absence of an ''external'' cosmological constant, the exterior geometry of the string approaches Minkowski space-time with a deficit angle, and it is shown that in the limit when the string becomes a line source, the deficit angle reduces to the well-known expression ..delta..theta = 8..pi mu.., withmore.
Abstract: We introduce a model for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. The properties of the geometry for the region exterior to the string are fully determined under the assumption that changes in the scalar and gauge field variables occur only at the cylindrical shell. This is consistent with a limiting form of the scalar potential V(phi) where a minimum at chemically bondphichemically bond = 0 is separated by a large barrier from a global minimum at chemically bondphichemically bond = etanot =0. The introduction of an approximately singular ''surface'' for the string allows the definition of a delta-function stress-energy density that characterizes discontinuities in the fields. We show consistency of the model with the full coupled equations for the metric, and the scalar and gauge fields in curved space-time. It is found that for this model, in the absence of an ''external'' cosmological constant, the exterior geometry of the string approaches Minkowski space-time with a deficit angle, and it is shown that in the limit when the string becomes a line source, i.e., its radius vanishes, the deficit angle reduces to the well-known expression ..delta..theta = 8..pi mu.., withmore » ..mu.. the proper mass per unit length of the string.« less
TL;DR: In this article, the quark-antiquark potential consists of two terms, one of which transforms like the time component of a Lorentz four-vector, and the other like a scalar.
TL;DR: In this article, a canonical representation of spacetime diffeomorphisms for parametrised Maxwell electrodynamics is found by turning the scalar potential into a canonical momentum pi conjugate to a supplementary scalar field psi and prescribing their dynamics by imposing the Lorentz gauge conditions.
Abstract: Using a recently developed schema of Isham and Kuchar (1985) a canonical representation of spacetime diffeomorphisms is found for parametrised Maxwell electrodynamics. Gauge invariance hampers the direct application of the schema because the scalar potential phi perpendicular to plays the role of a Lagrange multiplier which enforces the Gauss constraint and therefore lies outside the extended phase space. This difficulty is circumvented by turning the scalar potential into a canonical momentum pi conjugate to a supplementary scalar field psi and prescribing their dynamics by imposing the Lorentz gauge conditions. The super-Hamiltonian and supermomentum of this modified theory satisfy the Dirac closure relations and induce the correct behaviour of field projections under hypersurface shifts and tilts. These properties lead to the canonical representation of the generators of spacetime diffeomorphisms. The Maxwell theory is recovered at the end by imposing two additional constraints, the C(x):= psi (x)=0 constraint and the Gauss constraint, each of which is preserved by the generators of spacetime diffeomorphisms. The situation is compared with that arising in canonical geometrodynamics.
TL;DR: In this article, an efficient formulation for calculating all vector and scalar potential Green's functions for a thin, infinitely long waveguide with periodic excitation is described. But this method is not suitable for the case of Rotman lenses.
Abstract: An efficient formulation is described for calculating all vector and scalar potential Green's functions for a thin, infinitely long waveguide with periodic excitation. The Green's functions are represented by the first few terms of the modal expansion plus a quasi-static correction. This allows one to compute the Green's functions over a wide band of frequencies with little additional effort over that required for a single frequency. An attractive feature of the method is that the l/R free-space singularity exhibited by the potentials is explicitly extracted in the lowest order quasi-static term. Tfris is convenient for evaluating method-of-moments self-term contributions in closed form. The Green's functions have application for problems involving stripline structures such as Rotman lenses.
TL;DR: In this paper, the authors used a perturbation technique to obtain first-order toroidal corrections for the Advanced Toroidal Facility (ATF) torsatron, which is basically a pure system, augmented by an asymmetric broadening in the poloidal mode number spectrum because of toroidicity.
Abstract: Stellarator magnetic field configurations are analysed using a harmonic expansion of the scalar potential. Harmonic functions for fields due both to external coils (vacuum fields) and to plasma currents are derived from those for a straight stellarator, using a perturbation technique to obtain first-order toroidal corrections. In the case of the vacuum fields, the coefficients, or generalized multipole moments, are determined by a least-squares fit to the 'exact' fields, which are calculated from the coil geometry using the Biot-Savart method. The mode structure of the Advanced Toroidal Facility (ATF) torsatron, in particular, is basically that of a pure system, augmented by an asymmetric broadening in the poloidal mode number spectrum because of toroidicity. Configuration control in ATF is accomplished by varying the axisymmetric moments: the magnetic axis shift is most sensitive to the m = 1 moment and the central rotational transform is most sensitive to the m = 2 moment. These moments, in turn, are expressible simply as linear combinations of the coil currents, which allows them to be determined readily from experimental data.
TL;DR: In this paper, the authors derived general properties of the scalar potential and showed that the global positivity is not guaranteed: an extra condition on the Kahler potential is required, even if supersymmetry is broken by nonperturbative effects in the hidden sector.
TL;DR: In this article, it was shown that the problem of solving tensor equations can be reduced to the solution of a system of two coupled partial differential equations of second order for only two scalar potentials.
Abstract: Electromagnetic fields in anisotropic media can be represented in terms of dyadic Green's functions. The four dyadic Green's functions (Green's tensors) are solutions of systems of coupled tensor equations of first order which can be transformed to second-order tensor equations for each of the Green's tensors. For the special case of gyrotropic media (anisotropic media with a distinguished axis and electromagnetic parameters having a rotational invariance with respect to this axis, like a cold ionospheric electron plasma under the influence of earth's magnetic field) it is shown how the Green's tensors can be represented in terms of scalar Hertz potentials. So the problem of solving tensor equations can be reduced to the solution of a system of two coupled partial differential equations of second order for only two scalar potentials.
TL;DR: In this paper, the Dirac equation is shown to be exactly solvable with confining bound states with scalar-like potential V(z)=-Az, A)0.
Abstract: The author points out that the Dirac equation is exactly solvable giving confining bound states with the scalar-like potential V(z)=-Az, A)0.
TL;DR: In this paper, a generalization of no-scale supergravity models is presented where scale transformations and axion-like classical symmetries of the superstrings in four dimensions are explicitly realized as dilations and translations of the scalar fields in the Kahler manifold.
TL;DR: In this paper, a 3D analysis of a flux concentration model with two conducting plates placed in parallel between a pair of a.c.-excited coils is presented, where the flux concentration effect in the air-slit and flux reflection effect over a conducting plate are seen more clearly.
Abstract: This paper deals with the three dimensional analysis of a flux concentration model with two conducting plates placed in parallel between a pair of a.c.-excited coils. We have already presented an analysis for the model with a coarse mesh and volumeless plane coils, as well as newly developed iterative 3-D calculation method. [1] The model analyzed this time has total nodes and elements of about twice as those of the model previously calculated. The flux density distribution is compared with experimental data. Distributions of eddy currents and scalar potentials are also solved. Flux concentration effect in the air-slit and flux reflection effect over a conducting plate are seen more clearly. An inference about the role of scalar potential is obtained from our calculation results.
TL;DR: It is shown that the interaction between the electromagnetic field and an eventual scalar component of the gravitational force induces changes in the polarization state of a light wave traveling through a constant magnetic field, and it is suggested that using a laser beam one could obtain significant information on the scalar coupling strength.
Abstract: It is shown that the interaction between the electromagnetic field and an eventual scalar component of the gravitational force induces changes in the polarization state of a light wave traveling through a constant magnetic field, and it is then suggested that, using a laser beam, one could obtain significant information on the scalar coupling strength for ranges of the scalar interaction approximately 1 cm and smaller.
TL;DR: A formalism for calculating the rate of this particle creation is developed and applied to several model self-coupled scalar field theories and the application of the results to inflationary cosmology is discussed.
Abstract: The creation of the quanta of a self-coupled scalar field due to the time dependence of the classical scalar field is investigated. In general, a time-dependent solution of the classical field equation leads, in quantum field theory, to the creation of scalar particles. This effect tends to dissipate the energy of the classical field. A formalism for calculating the rate of this particle creation is developed and applied to several model self-coupled scalar field theories. The application of the results to inflationary cosmology is discussed.
TL;DR: In this article, a vector and scalar potential are represented in terms of a vector vector and a scalar vector, in a reference frame in which the sources are at rest.
Abstract: The moving sources are represented in terms of a vector and a scalar potential, in a reference frame in which the sources are at rest. Subsequently, Green's functions pertaining to the Fourier spectra of the radiated fields are found. The spectra of the fields detected by a stationary observer are given as space integrals over the volume occupied by the sources, of the product of these Green's functions with the source current density. The method is also applied to the spectra of the fields scattered by a two-dimensional moving body. In that case the scatterer is replaced by equivalent induced currents and/or charges which are the sources of the scattered field. For the scattering case, the theory is not developed in its full generality but the method is illustrated by the canonical case of a moving perfectly conducting circular cylinder immersed in an incident plane E wave.
TL;DR: In this paper, it was shown that the field equations force the scalar field to be independent of time, and that the trace-free energy-momentum tensor of a conformally invariant field can be used as the source.
Abstract: Recently, Innaiah and Reddy (1985) obtained a flat Robertson-Walker-type solution for the Einstein field equations with the trace-free energy-momentum tensor of a conformally invariant scalar field as source. Here we show that the field equations force the scalar field to be independent of time. Furthermore, we obtain open and closed Robertson-Walker-type solutions and observe that, once again, the scalar field has to be independent of time.
TL;DR: In this paper, an equation of state of the scalar field is derived by comparing the energy momentum tensors of the field and the perfect fluid, and the resulting equation depends essentially on the assumption whether the field is exactly homogeneous or only homogeneous in the mean.
Abstract: By a comparison of the energy momentum tensors of the scalar field and the perfect fluid, an equation of state of the scalar field is obtained. In connection with cosmological models, the resulting equation of state depends essentially on the assumption whether the scalar field is exactly homogeneous or only homogeneous in the mean.