Showing papers on "Scalar potential published in 2009"
TL;DR: A full-wave solver to model large-scale and complex multiscale structures using the augmented electric field integral equation (A-EFIE), which includes both the charge and the current as unknowns to avoid the imbalance between the vector potential and the scalar potential in the conventional EFIE.
Abstract: We describe a full-wave solver to model large-scale and complex multiscale structures. It uses the augmented electric field integral equation (A-EFIE), which includes both the charge and the current as unknowns to avoid the imbalance between the vector potential and the scalar potential in the conventional EFIE. The formulation proves to be stable in the low-frequency regime with the appropriate frequency scaling and the enforcement of charge neutrality. To conquer large-scale and complex problems, we solve the equation using iterative methods, design an efficient constraint preconditioning, and employ the mixed-form fast multipole algorithm (FMA) to accelerate the matrix-vector product. Numerical tests on various examples show high accuracy and fast convergence. At last, complex interconnect and packaging problems with over one million integral equation unknowns can be solved without the help of a parallel computer.
201 citations
TL;DR: In this article, a modified dilaton profile and a quartic term in the bulk scalar potential were used to separate the dependence on spontaneous and explicit chiral symmetry breaking in the soft-wall version of the anti-de Sitter/QCD model.
Abstract: We show how to incorporate chiral-symmetry breaking in the soft-wall version of the anti-de Sitter/QCD model by using a modified dilaton profile and a quartic term in the bulk scalar potential. This allows one to separate the dependence on spontaneous and explicit chiral-symmetry breaking. Moreover, our 5D model automatically incorporates linear trajectories and non chiral-symmetry restoration for highly excited radial states. We compare our resulting mass spectra in the scalar, vector, and axial-vector sectors with the respective QCD resonances and find reasonable agreement using the known values for the pion mass and decay constant.
162 citations
TL;DR: In this paper, different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced.
Abstract: Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and some differences highlighted.
119 citations
TL;DR: In this paper, a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integrals of motion is considered.
Abstract: We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integrals of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.
87 citations
TL;DR: In this article, the authors reformulate N = 2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7) by combining the Ramond-Ramond scalar degrees of freedom together with O(6,6) pure spinors.
Abstract: In this paper we reformulate N = 2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7). In particular we combine the Ramond-Ramond scalar degrees of freedom together with the O(6,6) pure spinors which govern the Neveu-Schwarz sector by considering an extended version of generalised geometry. We give E7(7)-invariant expressions for the Kahler and hyperkahler potentials describing the moduli space of vector and hypermultiplets, demonstrating that both correspond to standard E7(7) coset spaces. We also find E7(7) expressions for the Killing prepotentials defining the scalar potential, and discuss the equations governing N = 1 vacua in this formalism.
78 citations
TL;DR: In this article, the non-Gaussianity induced by a pseudo Nambu-Goldstone boson with a cosine-type scalar potential was studied, and it was shown that the resultant non-gaussianity is similar to that obtained in the quadratic potential.
Abstract: We study non-Gaussianity induced by a pseudo Nambu-Goldstone boson with a cosine-type scalar potential. We focus on how the non-Gaussianity is affected when the pseudo Nambu-Goldstone boson rolls down from near the top of the scalar potential where the deviation from a quadratic potential is large. We find that the resultant non-Gaussianity is similar to that obtained in the quadratic potential, if the pseudo Nambu-Goldstone boson accounts for the curvature perturbation; the non-Gaussianity is enhanced, otherwise.
77 citations
TL;DR: In this paper, the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the 3 + 1 -dimensions for spinless bosonic particles was studied.
Abstract: We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3 + 1 -dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are directly proportional and inversely proportional to the distance from the force center. The exact bound-state energy eigenvalues and the corresponding wave functions of the Klein-Gordon equation for mixed scalar-vector and pure scalar Coulomb-like field potentials are obtained by means of the Nikiforov-Uvarov (NU) method. The energy spectrum is discussed for different scalar-vector potential mixing cases and also for the constant-mass case.
77 citations
TL;DR: In this article, the model of the holographic Chaplygin gas has been extended to two general cases: first the case of a modified variable Chuggin gas and second case of the viscous generalized CHG.
Abstract: In this paper, the model of the holographic Chaplygin gas has been extended to two general cases: first the case of a modified variable Chaplygin gas and second the case of the viscous generalized Chaplygin gas. The dynamics of the model is expressed by the use of scalar fields and scalar potentials.
69 citations
TL;DR: In this article, a three-dimensional approach based on the Coulombian model is presented for the calculation of the magnetic field components created by ring permanent magnets. But the results presented in this paper clearly show that the two-dimensional studies dealing with the optimization of ring permanent magnet dimensions cannot be treated with the same precisions as 3D studies.
Abstract: This paper presents an improvement of the calculation of the magnetic field components created by ring permanent magnets. The three-dimensional approach taken is based on the Coulombian Model. Moreover, the magnetic field components are calculated without using the vector potential or the scalar potential. It is noted that all the expressions given in this paper take into account the magnetic pole volume density for ring permanent magnets radially magnetized. We show that this volume density must be taken into account for calculating precisely the magnetic field components in the near-field or the far-field. Then, this paper presents the component switch theorem that can be used between infinite parallelepiped magnets whose cross-section is a square. This theorem implies that the magnetic field components created by an infinite parallelepiped magnet can be deducted from the ones created by the same parallelepiped magnet with a perpendicular magnetization. Then, we discuss the validity of this theorem for axisymmetric problems (ring permanent magnets). Indeed, axisymmetric problems dealing with ring permanent magnets are often treated with a 2D approach. The results presented in this paper clearly show that the two-dimensional studies dealing with the optimization of ring permanent magnet dimensions cannot be treated with the same precisions as 3D studies.
55 citations
TL;DR: In this article, a nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields.
52 citations
TL;DR: In this article, the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, was studied.
Abstract: We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov–Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.
TL;DR: In this paper, a method for obtaining the critical state in 3D was described using an extension of a previous 1D model based on flux line motion in which the equations are not based on an E-J curve, which leads to time dependence.
Abstract: A method for obtaining the critical state in three dimensions is described. This uses an extension of a previous 1D model based on flux line motion in which the equations are not based on an E–J curve, which leads to time dependence. In order to make clear the connection between the scalar potential, the particular vector potential derived and the electrostatic surface charges, it has proved necessary to start from eddy currents in a normal conductor. The eddy current solutions for a normal conductor are the same as those for a London superconductor in a DC field, except that although a scalar potential is needed there are no electrostatic charges. The problem of a superconducting puck in a field parallel to the faces is solved. It is assumed that the electric field is parallel to the current density which is quite probable for high Tc superconductors, but other criteria could be used. Like other 3D solutions the computation takes a long time; even this relatively simple case takes 7 h with a 1.3 GHz PC. However this was using a standard PC with default parameters in the finite element package so there is room for optimization. All the results were obtained with FlexPDE.
TL;DR: In this article, the attractor properties of the simplest chaotic model of inflation were reviewed, in which a minimally coupled scalar field is endowed with a quadratic scalar potential and the equations of motion in a flat Friedmann-Robertson-Walker universe were written as an autonomous system of equations.
Abstract: We review the attractor properties of the simplest chaotic model of inflation, in which a minimally coupled scalar field is endowed with a quadratic scalar potential. The equations of motion in a flat Friedmann–Robertson–Walker universe are written as an autonomous system of equations, and the solutions of physical interest appear as critical points. This new formalism is then applied to the study of inflation dynamics, in which we can go beyond the known slow-roll approximation.
TL;DR: In this paper, the authors compute fourth sound for holographic superfluids dual to a charged scalar and a gauge field in an AdS4 background, and show that conformal invariance can be enforced at low temperatures.
Abstract: We compute fourth sound for superfluids dual to a charged scalar and a gauge field in an AdS4 background. For holographic superfluids with condensates that have a large scaling dimension (greater than approximately two), we find that fourth sound approaches first sound at low temperatures. For condensates that a have a small scaling dimension it exhibits non-conformal behavior at low temperatures which may be tied to the non-conformal behavior of the order parameter of the superfluid. We show that by introducing an appropriate scalar potential, conformal invariance can be enforced at low temperatures.
TL;DR: In this article, the notions of mass and range of a Brans-Dicke-like scalar field in scalar-tensor and f(R) gravity are defined.
Abstract: The notions of mass and range of a Brans–Dicke-like scalar field in scalar–tensor and f(R) gravity are subject to an ambiguity that hides a potential trap. We spell out this ambiguity and identify a physically meaningful and practical definition for these quantities. This is relevant when giving a mass to this scalar in order to circumvent experimental limits on the PPN parameters coming from solar system experiments.
TL;DR: In this paper, Euclidean three-space and Minkowski four-space identities and uniqueness theorems are reviewed and extended, and a time-dependent extension of the Helmholtz identity is also derived.
Abstract: Euclidean three-space and Minkowski four-space identities and uniqueness theorems are reviewed and extended. A Helmholtz identity is used to prove two three-vector uniqueness theorems in Euclidean three-space. The first theorem specifies the divergence and curl of the vector, and the second is a Helmholtz type theorem that sums the irrotational and solenoidal parts of the vector. The second theorem is shown to be valid for three-vector fields that are time dependent. A time-dependent extension of the Helmholtz identity is also derived. However, only the three-vector and scalar components of a Minkowski space four-vector identity are shown to yield two identities that lead to a uniqueness theorem of the first or source type. Also, the field equations of this latter theorem appear to be sufficiently general such that the field equations naturally divide into two distinct classes, a four-solenoidal electromagnetic type class in a relativistic transverse gauge and a four-irrotational class in a relativistic longitudinal gauge.
Journal Article•
TL;DR: In this article, scalar potential scattering and spin-orbit scattering on the warped hexagonal isoenergy contour are considered through the T-matrix formalism, and the characteristic scattering wavevectors found in their analysis agree well with recent experiment results.
Abstract: through the T-matrix formalism. Both the scalar potential scattering and the spin-orbit scattering on the warpedhexagonal isoenergy contour are considered. While backscatterings are forbidden by time-reversalsymmetry, other scatterings are allowed and exhibit strong dependence on the spin configurations ofthe eigenfunctions at ~k points over the isoenergy contour. The characteristic scattering wavevectorsfound in our analysis agree well with recent experiment results.
TL;DR: In this article, a return mapping algorithm for a rather general class of phenomenological rate-independent models for ferroelectroelastic materials is presented, based on the operator splitting methodology, which employs the closest point projection scheme to obtain an efficient and robust integration of the constitutive model.
Abstract: Return mapping algorithms for a rather general class of phenomenological rate-independent models for ferroelectroelastic materials are presented. The fully coupled thermodynamically consistent three-dimensional constitutive model with two internal variables (remanent polarization vector and remanent strain tensor) proposed by C. M. Landis in 2002 is used for the simulation of electromechanical hysteresis effects in polycrystalline ferroelectric ceramics. Based on the operator splitting methodology, the return mapping algorithm employs the closest point projection scheme to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is obtained in closed form by linearizing the return mapping algorithm, and is found to be non-symmetric in the general case due to the dependence of the switching criterion on internal variables. Conditions that provide the symmetry of the consistent tangent matrix are analyzed. The compactness and generality of the received relations are achieved by means of using the thermodynamically based compact notations combining mechanical and electrical values. Both the cases scalar potential finite element (FE) formulation (primary variables: strain and electric field) and vector potential FE formulation (primary variables: strain and electric displacement) are considered. The accuracy and robustness of the algorithms are assessed through numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.
TL;DR: In this paper, a characterization program for the supersymmetric configurations and solutions of the supergravity theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugings is presented.
Abstract: We perform the characterization program for the supersymmetric configurations and solutions of the supergravity theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugings. By using the conditions yielded by the characterization program, new exact supersymmetric solutions are found in the SO(4, 1)/SO(4) model for the hyperscalars and with SU(2) × U(1) as the gauge group. The solutions contain also non-trivial vector and massive tensor fields, the latter being charged under the U(1) sector of the gauge group and with self-dual spatial components. These solutions are black holes with AdS2 × S3 near horizon geometry in the gauged version of the theory and for the ungauged case we found naked singularities. We also analyze supersymmetric solutions with only the scalars x of the vector/tensor multiplets and the metric as the non-trivial fields. We find that only in the null class the scalars x can be non-constant and for the case of constant x we refine the classification in terms of the contributions to the scalar potential.
TL;DR: This paper introduces central force optimisation, a novel, nature-inspired, deterministic search metaheuristic for constrained multidimensional optimisation in highly multimodal, smooth, or discontinuous decision spaces.
Abstract: This paper introduces central force optimisation, a novel, nature-inspired, deterministic search metaheuristic for constrained multidimensional optimisation in highly multimodal, smooth, or discontinuous decision spaces. CFO is based on the metaphor of gravitational kinematics. The algorithm searches a decision space by 'flying' its 'probes' through the space by analogy to masses moving through physical space under the influence of gravity. Equations are developed for the probes' positions and accelerations using the gravitational metaphor. Small objects in our universe can become trapped in close orbits around highly gravitating masses. In 'CFO space' probes are attracted to 'masses' created by a user-defined function of the value of an objective function to be maximised. CFO may be thought of in terms of a vector 'force field' or, loosely, as a 'generalised gradient' methodology because the force of gravity can be computed as the gradient of a scalar potential. The CFO algorithm is simple and easily implemented in a compact computer program. Its effectiveness is demonstrated by running CFO against several widely used benchmark functions. The algorithm exhibits very good performance, suggesting that it merits further study.
TL;DR: In this article, the authors studied the propagation of scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field.
Abstract: We study the propagation of the scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total four degrees of freedom. Two of these degrees will have a superluminal propagation--with k-dependent speed of propagation--whereas the other two will travel with the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed. Comment: 13 pages, 1 figure, uses RevTeX
TL;DR: The list of 6 previously known nontrivial stationary points in the scalar potential of N=8, D=4 supergravity with gauge group SO(8) is extended by fourteen new entries, whose properties have been obtained numerically using the sensitivity backpropagation technique as mentioned in this paper.
Abstract: The list of six previously known nontrivial stationary points in the scalar potential of N=8, D=4 supergravity with gauge group SO(8) is extended by fourteen new entries, whose properties have been obtained numerically using the sensitivity backpropagation technique. Eight of the new solutions break the gauge group completely, while three have a residual symmetry of U(1). Three further ones break the gauge group to U(1)xU(1), and while the approximate numerical data are somewhat inconclusive, there is evidence that one of these may have a residual N=1 supersymmetry, hence correspond to a stable vacuum. It must be pointed out that this list of new solutions most likely is not exhaustive.
TL;DR: In this article, the authors derived a scalar potential in the recently proposed N = 1 supersymmetric generalization of f(R) gravity in four spacetime dimensions, which is classically equivalent to the standard n = 1 supergravity coupled to a chiral superfield via a Legendre-Weyl transform in superspace.
Abstract: We derive a scalar potential in the recently proposed N = 1 supersymmetric generalization of f(R) gravity in four spacetime dimensions. Any such higher-derivative supergravity is classically equivalent to the standard N = 1 supergravity coupled to a chiral (matter) superfield, via a Legendre–Weyl transform in superspace. The Kahler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function. We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine tuning, which define a no-scale F(R) supergravity. The F(R) supergravities are suitable for physical applications in the inflationary cosmology based on supergravity and superstrings.
TL;DR: In this article, an inverse vector Preisach hysteresis model has been developed and identified by applying the measured data and inserted into a finite element procedure through the fixed point technique and the reduced magnetic scalar potential formulation.
Abstract: This paper presents a Preisach model of ferromagnetic hysteresis to simulate the vector hysteresis properties of ferromagnetic materials. Vector behavior has been studied using a single sheet tester with a round shaped specimen at low frequency, and the magnetic flux density vector has been controlled by a digital measurement system. Circular magnetic flux density pattern has been measured. An inverse vector Preisach hysteresis model has been developed and identified by applying the measured data. Finally, the inverse model has been inserted into a finite element procedure through the fixed point technique and the reduced magnetic scalar potential formulation. The applicability of the measurement system as well as the developed model has been proven by comparing measured and simulated results.
TL;DR: In this paper, a modified-potential theory of gravity is proposed, where the MOND potential phi produced by a mass distribution rho is a solution of the Poisson equation for the modified source density rho(1/4 pi G)divergence(g), where g is the Newtonian acceleration field of rho.
Abstract: A new formulation of MOND as a modified-potential theory of gravity is propounded. In effect, the theory dictates that the MOND potential phi produced by a mass distribution rho is a solution of the Poisson equation for the modified source density rho*=-(1/4 pi G)divergence(g), where g=nu(|gN|/a0)gN, and gN is the Newtonian acceleration field of rho. This makes phi simply the scalar potential of the algebraic acceleration field g. The theory thus involves solving only linear differential equations, with one nonlinear, algebraic step. It is derivable from an action, satisfies all the usual conservation laws, and gives the correct center-of-mass acceleration to composite bodies. The theory is akin in some respects to the nonlinear Poisson formulation of Bekenstein and Milgrom, but it is different from it, and is obviously easier to apply. The two theories are shown to emerge as natural modifications of a Palatini-type formulation of Newtonian gravity, and are members in a larger class of bi-potential theories.
TL;DR: In this paper, a brane model using two interacting scalar fields in 7D and 8D gravity was considered and a special choice of potential energy was used to obtain numerically regular asymptotically flat vacuum solutions.
Abstract: We consider a thick brane model using two interacting scalar fields in 7D and 8D gravity. Using a special choice of potential energy, we obtain numerically regular asymptotically flat vacuum solutions. The possibility of obtaining the similar solutions for an arbitrary number of extra spatial dimensions is being estimated.
TL;DR: In this article, the authors reformulate N = 2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7).
Abstract: In this paper we reformulate N=2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7). In particular we combine the Ramond--Ramond scalar degrees of freedom together with the O(6,6) pure spinors which govern the Neveu-Schwarz sector by considering an extended version of generalised geometry. We give E7(7)-invariant expressions for the Kahler and hyperkahler potentials describing the moduli space of vector and hypermultiplets, demonstrating that both correspond to standard E7(7) coset spaces. We also find E7(7) expressions for the Killing prepotentials defining the scalar potential, and discuss the equations governing N=1 vacua in this formalism.
TL;DR: In this article, a class of scalar field potentials for which w = const was derived in the framework of the loop cosmology with holonomy corrections, and the model was analyzed analytically for the whole parameter space.
TL;DR: Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopolelike field as mentioned in this paper.
Abstract: Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopolelike field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere, and Wilczek, a conserved angular momentum is constructed, despite the nonconservation of the electric charge. No Runge-Lenz vector has been found.
TL;DR: In this article, the SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms, and the new scalar potential is obtained.
Abstract: We consider the most general SU(3) singlet space of gauged N=8 supergravity in four-dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we eventually obtain the new scalar potential. For the two extreme limits, we reproduce the previous results found by Warner in 1983. In particular, for the N=1 G_2 critical point, we find the constraint surface parametrized by three scalar fields on which the cosmological constant has the same value. We obtain the BPS domain-wall solutions for restricted scalar submanifold. We also describe the three-dimensional mass-deformed superconformal Chern-Simons matter theory dual to the above supersymmetric flows in four-dimensions.