scholarly journals HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES

2011 ◽  
Vol 20 (01) ◽  
pp. 59-75 ◽  
Author(s):  
EFRAIN ROJAS
Keyword(s):  
Ricci Tensor ◽  
General Structure ◽  
Extrinsic Curvature ◽  
Higher Order ◽  
Square Root ◽  
Auxiliary Variables ◽  
Field Equations ◽  
Alternative Description ◽  
Brane Models ◽  
Combined Matrix

The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions

1969 ◽  
Vol 36 (4) ◽  
pp. 757-762 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Structural Analysis ◽  
Legendre Polynomials ◽  
Direct Reduction ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Higher Order ◽  
Governing Equations ◽  
Field Equations ◽  
Displacement Boundary ◽  
Polynomial Expansions

Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.

Square-root-like higher-order topological states in three-dimensional sonic crystals

2021 ◽  
Author(s):  
Zhiguo Geng ◽  
Huanzhao Lv ◽  
Zhan Xiong ◽  
Yu-Gui Peng ◽  
Zhaojiang Chen ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Higher Order ◽  
Square Root ◽  
Root Lattice ◽  
Third Order ◽  
Topological Materials ◽  
Topological States ◽  
Sonic Crystal ◽  
Sonic Crystals

Abstract The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at the K-H direction induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in the z direction. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

Improved Thermal Stability of Gmr Spin Valve Films

1995 ◽  
Vol 384 ◽  
Author(s):  
R. D. Mcmichael ◽  
W. F. Egelhoff ◽  
Minh Ha
Keyword(s):  
Thermal Stability ◽  
Layer Thickness ◽  
Annealing Time ◽  
General Structure ◽  
Spin Valve ◽  
Square Root ◽  
Magnetic Multilayer ◽  
Valve Structure ◽  
Thermal Stability Of

ABSTRACTIn order to improve the thermal stability of magnetic multilayer “spin valve” structures, we have measured the magnetic and magnetoresistive properties of a number of samples with the general structure of NiO/Co/Cu/Co/Cu/Co/NiO as a function of annealing time at 250 °C. The magnetoresistance (MR) of the samples annealed in air decreases proportionally to the square root of the annealing time. For samples annealed in a vacuum, the decrease in magnetoresistance is reduced, but not eliminated. Magnetometry of a vacuum annealed NiO/Co/NiO sample shows a magnetization reduction and a coercivity increase which suggest oxidation of the NiO-biased “outer” Co layers of the spin valve structure. For increasing NiObiased Co layer thickness, we show enhanced thermal stability and even increasing MR with annealing time for samples with the thickest outer Co layers.

Vacuum polarization of generalized quantum electrodynamics in the Heisenberg picture

2020 ◽  
Vol 35 (04) ◽  
pp. 2050012
Author(s):  
David Montenegro
Keyword(s):  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
General Structure ◽  
Higher Order ◽  
Polarization Tensor ◽  
Induced Current ◽  
Heisenberg Picture ◽  
Qualitative And Quantitative ◽  
Physical Implication ◽  
Charge Renormalization

In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Källén methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme “à la” Källén is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory.

scholarly journals The nonlocal mean-field equation on an interval

2019 ◽  
Vol 22 (05) ◽  
pp. 1950028
Author(s):  
Azahara DelaTorre ◽  
Ali Hyder ◽  
Luca Martinazzi ◽  
Yannick Sire
Keyword(s):  
Field Equation ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mean Field ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Field Equations ◽  
Mean Field Equations ◽  
Blowing Up ◽  
Mean Field Equation

We consider the fractional mean-field equation on the interval [Formula: see text] [Formula: see text] subject to Dirichlet boundary conditions, and prove that existence holds if and only if [Formula: see text]. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.

The structure of Estonian personal values: a lexical approach

2002 ◽  
Vol 16 (3) ◽  
pp. 221-235 ◽  
Author(s):  
Toivo Aavik ◽  
Jüri Allik
Keyword(s):  
Principal Component Analysis ◽  
Personal Values ◽  
General Structure ◽  
Principal Component ◽  
Higher Order ◽  
The Self ◽  
The Other ◽  
Two Dimensional ◽  
Lexical Approach ◽  
Estonian Language

The main purpose of this paper is to investigate the variety of value describing words and interrelation of value categories in the Estonian language. To accomplish this aim, a psycholexical approach was adopted, during which a set of 560 value‐related words was selected from the Estonian Orthological Dictionary and the results were compared with the Schwartz Values Survey (SVS). When principal‐component analysis was applied on the self‐ratings of a reduced list of 78 value‐related words, six factors emerged and were labelled as benevolence, self‐enhancement, broadmindedness, hedonism, conservatism, and self‐realization. However, all these themes are interrelated and load on a singular secondary dimension. The constructs measured by SVS and the value categories in Estonian were only partially interchangeable; moderate correlations imply an imperfect correspondence: each theme was related to many categories on the other questionnaire. However, a significant general structure refers to the same two‐dimensional level of higher‐order values described by Schwartz in 1992. Copyright © 2002 John Wiley & Sons, Ltd.

Zur Schwarzschildschen Lösung in einer einheitlichen Feldtheorie

1964 ◽  
Vol 19 (9) ◽  
pp. 1032-1033
Author(s):  
G. Braunss
Keyword(s):  
Higher Order ◽  
Field Equations ◽  
The World

It is shown that the system of field equations1ϰGmn (Ф) ≡ 1ϰ (Rmn-½gmn R) =2k₀ [gmn(gab Φ,aΦ,b+ F (Φ)) -Φ, m Φ,n] ,in which the gmn are to be considered as functionals of the world field Φ. possesses a nonsingular static centralsymmetrical solution which, assuming F(Φ) ∼ — Φ6, is identical with the SCHWARZ-scHILD-solution up to terms of higher order for large values of r.

scholarly journals NEW GEOMETRIC FORMALISM FOR GRAVITY EQUATION IN EMPTY SPACE

2005 ◽  
Vol 14 (06) ◽  
pp. 1009-1022 ◽  
Author(s):  
XIN-BING HUANG
Keyword(s):  
Differential Equations ◽  
Gauge Field ◽  
Empty Space ◽  
Space Time ◽  
Gravity Theory ◽  
Spin Connection ◽  
Square Root ◽  
Field Equations ◽  
Complex Spin ◽  
Set Up

In this paper, a complex daor field which can be regarded as the square root of space–time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1, 3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and do not conflict with Einstein's gravity theory.

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