The Casimir effect of Reissner-NordstrSm black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.     

电、磁场作用于扁球边界面上的力矩

本文研究电、磁场作用于扁球导体、磁导体上的力矩。根据基本解答和把体积力公式运用于扁球体面上后(包括平面上有半扁球形突面的边界问题〕,得出静电问题的较为普遍的解式。又由于静电、静磁张力公式的简单对应关系存在,故很容易把所得到的公式直接推广到对应的静磁问题上去,最后根据所得的解式,我们得到了若干有益的结论。     

Integrated photoelasticity for nondestructive residual stress measurement in glass

The paper gives a review of integrated photoelasticity and of its application for residual stress measurement in glass. By considering the basic theory of the method, two particular cases, the case of weak birefringence and that of constant principal stress axes, are picked up. It is shown that integrated photoelasticity is actually optical tensor field tomography. Its peculiarities in comparison with scalar field tomography are considered. Since directly integrated photoelasticity allows for the measurement of only some of the stress components, analytical or numerical methods are to be used for complete determination of the stress field. Nonlinear optical phenomena, interference blots and fringe bifurcation, are briefly considered. Several examples illustrate the application of the method.     

Stress Tensor Fluctuations and Passive Quantum Gravity

The quantum fluctuations of the stress tensor of a quantum field are discussed, as are the resulting space-time metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the space-time geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.     

引力场中的应力张量及其应用

根据引力场和静电场的相似性质，通过类比方法由静电场的麦克斯韦应力张量得出了引力场中的应力张量，并用它计算均质球体内部的万有引力。     

Smoothing regularization and particle creation in curved spacetime

A regularization procedure is given for the stress tensor of a quantized field in a background metric. This regularization is shown to be equivalent to a covariant renormalization of constants in the generalized Einstein equations. An example of the massive spinor field in Robertson-Walker universe is considered. Regular values of the stress tensor near the cosmological singularity are found.     

Electromagnetic solutions of the field equations in presence of zeromass mesons

The field equations of general relativity with electromagnetic stress tensor and zeromass scalar meson field are investigated. The metric coefficients are assumed to be functions of three variables only. It is then shown that, if one assumes a functional relation between some one of the metric coefficients and the electromagnetic potentials, that one can find a solution of the coupled Einstein-Maxwell equations in terms of a solution of the Einstein equations with zeromass scalar meson field as source.     

Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments

We obtain the singular asymptotic behavior of the stress field in the vicinity of a non-planar dislocation in three dimensions and the nearly singular behavior of the full self-force of the dislocation including both glide and climb forces, using asymptotic analysis. We also derive asymptotic formulas for the stress field in the vicinity of a curved dislocation segment. Numerical examples are presented to examine the asymptotic formulas. The obtained formulas can be used for qualitative understanding of the stress tensor associated with dislocations and efficient and accurate calculation of the stress tensor in dislocation dynamics simulations.     

Mechanical stress tensor for a fluid in a magnetostatic field

Summary Two constraints on the form of the mechanical stress tensor for an uncharged and linear dielectric fluid at rest in a magnetostatic field are determined. Moreover, it is shown that the stress tensor proposed by Helmholtz, that proposed by Einstein-Laub and that proposed by Liu-Müller are unacceptable as mechanical stress tensors for a dielectric fluid in the conditions stated above.     

Scaling behavior of semiclassical gravity

Using the idea of metric scaling we examine the scaling behavior of the stress tensor of a scalar quantum field in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. We view the process of renormalizing the stress tensor as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, we find that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant.     

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor,dislocation key-formulas and dislocation loops

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.     

Computation of aeolian tone from a circular cylinder using source models

The generation of aeolian tones from a two-dimensional circular cylinder situated in a uniform cross-flow is investigated. The major emphasis here is placed on identifying the important noise generation mechanisms. Acoustic-viscous splitting techniques are utilized to compute modelled acoustic source terms and their corresponding acoustic fields. The incompressible Reynolds averaged Navier-Stokes equation is used to compute the near-field viscous flow solution, from which modelled acoustic source terms are extracted based on an approximation to the Lighthill’s stress tensor. Acoustic fields are then computed with an acoustic solver to solve the linearized Euler equations forced by the modelled source terms. Computations of the acoustic field based on the approximated Lighthill’s stress tensor are shown to be in good agreement with those computed from the surface dipole sources obtained using Curle’s solution to the acoustic analogy. It is shown in this paper that the stress tensor source term in the streamwise direction makes a comparable, but slightly larger contribution to the overall radiated field, compared with that due to the stress tensor in the direction normal to the mean flow. In addition, it is shown that shear sources, which arise due to the interaction between the fluctuating velocity and the background steady mean velocity, make the greatest contribution to the acoustic field, while the self-noise sources, which represents the interaction between the fluctuating velocities, is shown to be comparably negligible.     

Electric charge systems moving with the velocity of light and associated with charge creation

A discussion is given of certain electromagnetic fields associated with charges moving with the velocity of light which are associated with zero magnetic field, and the creation of charge. The stress energy tensor associated with charge creation is also discussed and it is shown that the stress energy tensor includes a term which may be interpreted as a shear.     

Finite temperature field theory with boundaries: The photon field

We calculate the deviations from Planckian form of the photon field finite temperature stress tensor in a manifold with boundary, due to scattering from the boundary. Familiar non-integrable divergences are found in the photon stress tensor as the boundary is approached and these are shown to be an inescapable consequence of initial calculational assumptions. Modifications of these assumptions are discussed which serve to remove the divergences and to illustrate the importance of the role played by surface gravitational actions.     

〈Tab〉 for a two-dimensional Vaidya space-time

The expectation value of the stress tensor operator of a conformally invariant scalar field propagating in a two dimensional Vaidya space-time is investigated. It is shown that “Unruh vacuum” conditions allow the stress tensor to be completely determined.     

Casimir Energy in Hartle--Hawking State

We calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method, the approximate expressions of the Casimir effect in the low and high temperature limits are also discussed. Then employing some general properties of the renormalized stress tensor, we obtain the Casimir energy stress tensor in Hattie-Hawking state.     

Convective deformations of the matter tensor for the relativistic perfect magnetofluid

Maugin's Scheme for a relativistic perfect magnetofluid is used to study the convection-free stress and convective deformations of the matter tensor for the magnetofluid. It is proved that the convection-free stress of the magnetofluid implies the conservation of the pressure, the density, and the magnitude of the magnetic field along the flow vector. The relation between convective deformations of the matter tensor for the magnetofluid and deformation tensor is obtained.     

Equations of motion for an anisotropic nonlinear elastic continuum in a gravitational field

Equations of motion for an anisotropic nonlinear elastic continuum in the gravitational field are written in a form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors imbedded in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given.