Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

Evolving Planck Mass in Classically Scale-Invariant Theories

Abstract: We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

Design and Testing of a Superconducting Rotating Machine

Abstract: We have designed, constructed and tested an eight-pole superconducting rotating machine, based on an unconventional topology that could potentially lead to a significant increase in power density. Calculations have been carried out in two steps: estimation of the magnetic scalar potential from a Coulomb formulation using the Markov chain Monte Carlo (MCMC) method, and the calculation of the flux density by derivation of the potential using a regularization method. The use of the MCMC method enables the calculation of the magnetic scalar potential in selected regions of the discrete geometry, which is an important factor to minimize the computation time. The principle of the operation has been validated by a successful testing of the motor showing this novel configuration of an electrical motor as very promising

Return mapping algorithms and consistent tangent operators in ferroelectroelasticity

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.

Relating double field theory to the scalar potential of N = 2 gauged supergravity

Abstract: The double field theory action in the flux formulation is dimensionally reduced on a Calabi-Yau three-fold equipped with non-vanishing type IIB geometric and non-geometric fluxes. First, we rewrite the metric-dependent reduced DFT action in terms of quantities that can be evaluated without explicitly knowing the metric on the Calabi-Yau manifold. Second, using properties of special geometry we obtain the scalar potential of N = 2 gauged supergravity. After an orientifold projection, this potential is consistent with the scalar potential arising from the flux-induced superpotential, plus an additional D-term contribution.

New applications of pseudoanalytic function theory to the Dirac equation

Abstract: In the present work, we establish a simple relation between the Dirac equation with a scalar and an electromagnetic potential in a two-dimensional case and a pair of decoupled Vekua equations. In general, these Vekua equations are bicomplex. However, we show that the whole theory of pseudoanalytic functions without modifications can be applied to these equations under a certain nonrestrictive condition. As an example we formulate the similarity principle which is the central reason why a pseudoanalytic function and as a consequence a spinor field depending on two space variables share many of the properties of analytic functions. One of the surprising consequences of the established relation with pseudoanalytic functions consists in the following result. Consider the Dirac equation with a scalar potential depending on one variable with fixed energy and mass. In general, this equation cannot be solved explicitly even if one looks for wavefunctions of one variable. Nevertheless, for such Dirac equation, we obtain an algorithmically simple procedure for constructing in explicit form a complete system of exact solutions (depending on two variables). These solutions generalize the system of powers 1, z, z2, ... in complex analysis and are called formal powers. With their aid any regular solution of the Dirac equation can be represented by its Taylor series in formal powers.