Machian Inertia and the Isotropic Universe

This paper addresses the origin of the forces of inertia. It proposes a Newton-Mach particle interaction force between all pairs of particles that depends on their relative acceleration and is proportional to the gravitational force between them. The motion of all objects therefore becomes directly influenced by all of the matter in the universe, as prescribed by Mach's principle. The effect of the observed hierarchical structure of the universe is considered and is used to ensure that the inertial force on an object is finite and isotropic. The instantaneous matter interaction force is justified and both Einstein's and Mach's objections to a Newtonian framework are discussed and shown to be absorbed by the proposed universal law of inertia.     

Effects of large amplitude and transverse shear on vibrations of triangular plates

In this paper an analytical investigation of large amplitude free flexural vibrations of isotropic and orthotropic moderately thick triangular plates is carried out. The governing equations are expressed in terms of the lateral displacement, w, and the stress function, F, and are based on an improved non-linear vibration theory which accounts for the effects of transverse shear deformation and rotatory inertia. Solutions to the governing equations are obtained by using a single-mode approximation for w, Galerkin's method and a numerical integration procedure. Numerical results are presented in terms of variations of non-linear frequency ratios with amplitudes of vibrations. The effects of transverse shear, rotatory inertia, material properties, aspect ratios, and thickness parameters are studied and compared with available solutions wherever possible. Present results are in close agreement with those reported for thin plates. It is believed that all of the results reported here that are applicable for moderately thick plates are new and therefore, no comparison is possible.     

Field equation for the transverse motion of a two-layered plate

An approximate theory is developed for the transverse motion of a two-layered plate. The two layers are assumed to be elastic, isotropic, homogeneous and welded to each other. The theory is similar to the Timoshenko-Mindlin model for a single-layered plate in which corrections are included for rotary inertia and shear deformation. A single equation of transverse motion is derived that predicts the first four antisymmetric modes and is applicable to practical problems. Phase velocities of these modes are numerically analyzed for a plate consisting of a copper layer and a steel layer.     

Equilibrium theory of molecular fluids: Structure and freezing transitions

In this article we review equilibrium theory of molecular fluids which includes structure and freezing transitions. The application of the theory to evaluate the pair correlation functions using Integral Equation methods and Computer Simulations have been discussed. Freezing of classical complex fluids based on the density functional approach is also discussed and compare a variety of its versions. Transitions discussed are sensitive to the value of direct correlation functions of the effective liquid which is required as an input information in the theory. Accurate evaluation of pair correlation functions is emphasized. Calculation of these correlation functions which pose problems in the case of ordered phases is discussed. The pair correlation functions of the ordered phase, which are supposed to be made up of two contributions, one that preserves the symmetry of the isotropic phase and a second that breaks it, are discussed. A new free-energy functional developed for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function is discussed. The most useful three dimensional reference interaction site model (3D-RISM) and its extension done recently by many workers is discussed. Application of this theory to a large variety of complex systems in combination with the density functional theory method implemented in the Amsterdam density functional software package is discussed. Coupling of the 3D-RISM salvation theory with molecular dynamics in the Amber molecular dynamics package is also given.     

The Hubbard model at high dimensions: some exact results and weak coupling theory

Recently it was shown that the theory of systems of correlated fermions on a lattice is greatly simplified in the limit of high dimensions as compared to lattice systems of dimensions 2 or 3 or to isotropic systems. We discuss here the implications of the limit of high dimensions on the single particle propagator of the Hubbard model. It is shown that all the typical Fermi liquid features are retained at high dimensions. Some exact results are obtained for infinite dimension: the shape of the Fermi surface as well as the density of states at the Fermi surface are not renormalized at all by the Coulomb interaction as long as the symmetry of the system is not broken. The self-consistent weak coupling theory is cast into a form which is solved numerically with very little effort.Research performed within the program of the Sonderforschungs-bereich 341 supported by the Deutsche Forschungsgemeinschaft     

Free vibration of antisymmetric,angle-ply laminated plates including transverse shear deformation by the finite element method

A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented. The theory is a generalization of Mindlin's theory for isotropic plates to laminated anisotropic plates and includes shear deformation and rotary inertia effects. Finite element solutions are presented for rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of a highly anisotropic composite material. Two sets of material properties that are typical of high modulus fiber-reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. The numerical results are compared with the closed form results of Bert and Chen. As a special case, numerical results are presented for thick isotropic plates, and are compared with those for 3-D linear elasticity theory and Mindlin's thick plate theory.     

Properties of magnetically dilute alloys

Recently it has been shown by analysing Mössbauer spectra of dilute alloys of iron in gold that the anisotropic part of the exchange interaction between iron near neighbours determines the direction of magnetisation of such iron moments at low temperatures. Estimates of the important interactions between moments, which are here identified as the isotropic and anisotropic parts of the near neighbour exchange, and the isotropic exchange between further neighbours via the conduction electrons, have been obtained from available experimental data. The near neighbour exchange causes spins within random clusters linked as near neighbours to align parallel (the isotropic part) and to prefer certain directions in the cluster (the anisotropic part). The further neighbour exchange is responsible for the cooperative magnetic transition shown in Mössbauer and small field susceptibility results. The final model leads to qualitative interpretations of the temperature and field dependence of the susceptibility, and is able to reproduce the hysteresis loops observed at low temperatures for samples cooled in different fields. The effects of the interactions on the entropy and specific heats are discussed, and it is shown that the linear specific heat contributions at low temperatures occur because of the anisotropic interactions.     

希土金属中的s-f相互作用

本文利用量子力学中角动量理论的代数方法,对希土金属的s-f相互作用模型作了比较仔细的讨论,导出了s-f电子间相互作用的哈密顿量的一般形式。用算符形式的微扰论方法,求得了通过s-f相互作用而导致的f电子间f-f间接作用的有效哈密顿量的一般表达式。在保留到二极小项的情况下,除各向同性的交换作用以外,还得到了赝偶极矩作用。在所得结果的基础上,初步讨论了希土金属铁磁相的磁晶各向异性。指出了以上的结果可能解释的一些实验事实。     

Cosmic Structure Formation with Kinetic Field Theory

Kinetic field theory (KFT) is a statistical field theory for an ensemble of classical point particles in or out of equilibrium. Its application to cosmological structure formation is reviewed. Beginning with the construction of a generating functional, it is described in detail how the theory needs to be adapted to an expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, three approaches are developed to nonlinear cosmic structures, which rest either on expanding an interaction operator, averaging the interaction term, or resumming perturbation terms. An analytic, parameter‐free equation for the nonlinear cosmic power spectrum is presented. It is explained how density profiles of bound structures and velocity power spectra can be derived from the theory. It is clarified how KFT relates to the BBGKY hierarchy. Kinetic field theory is then applied to fluids, reformulating KFT in terms of macroscopic quantities. The resulting resummation scheme is used to describe mixtures of gas and dark matter. Finally, it is discussed how KFT can be combined with modified theories of gravity. As an example for a noncosmological application, results are shown on the spatial correlation function of cold Rydberg atoms derived from KFT.     

Isotropic acoustooptic Bragg diffraction in paratellurite by a slow shear wave

An analysis is made of acoustooptic Bragg diffraction in a paratellurite crystal in the case of a slow shear acoustic wave. It is shown that the isotropic acoustooptic interaction in crystals has characteristic physical features, which distinguish it from the well-known anisotropic interaction. The isotropic interaction under study is shown to be a more complicated process than diffraction in optically isotropic media. A theoretical and experimental study of the dependences of Bragg angle of incidence on the ultrasound frequency was made. Expressions for the calculation of this dependence are presented, which give results that agree well with the experimental data. The dependences of the isotropic-diffraction efficiency on the acoustic power were studied. For the first time, it was found that the corresponding dependences for anisotropic and isotropic interactions are substantially different. It is shown that the isotropic interaction under study is weaker than the anisotropic interaction. However, the isotropic-diffraction efficiency has a noticeable value and can reach tens of a percent.     

Vibrations of annular plates including the effects of rotatory inertia and transverse shear deformation

An investigation of the natural vibrations of isotropic annular plates of uniform thickness has been made by considering the effects of rotatory inertia and shear deformation. The frequency determinantal equations are derived in explicit form for nine sets of common boundary conditions. Numerical results for the frequency parameters of annular plates having various thickness ratios and inner to outer radii ratios have been obtained. The results are compared with those given by the classical plate theory wherever possible. Among the effects of transverse shear deformation and rotatory inertia, the effect of shear deformation has been found to be more prominent.     

Vibrations in cylindrical shells with transverse elastic isotropy: Application to III-V nitride nanotubes

The vibrational modes of cylindrical shells with transverse elastic isotropy and arbitrary thickness are calculated in the framework of the elasticity theory and a comparison with the isotropic approach is presented. Cylindrical shells are a good model for nanotubes and here an application for nanotubes of transversely isotropic elastic materials is given. We have obtained the expression for the frequency of the radial breathing mode and it is shown that calculated frequencies coming from that expression compare fairly well with those obtained from different ab initio, force constant model calculations and experimental results. Further, the dispersion relations depend on all the elastic coefficients and therefore they are quite different for nanotubes with hexagonal or wurtzite structure. This demonstrates the need to go beyond the isotropic model to investigate the vibrational spectrum of transversely isotropic elastic material nanotubes and nanowires.     

The analysis of the impact response of a thin plate via fractional derivative standard linear solid model

The impact of a rigid body upon an infinite isotropic plate is investigated for the case when the viscoelastic features of the plate represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives. Thus, the problem concerns the shock interaction of the dropping mass and the target, wherein instead of the Hertz contact law the generalized fractional derivative standard linear solid law is employed as a law of interaction. The part of the plate beyond the contact domain is assumed to be elastic, and its behaviour is described by the equations of motion which take rotary inertia and shear deformations into account. It is assumed that transient waves generate in the plate at the moment of impact, the influence of which on the contact domain is considered using the theory of discontinuities. To determine the desired values behind the transverse shear wave front, one-term ray expansions are used, as well as the equations of motion of the falling mass and the contact region. As a result, we are led to a set of two linear differential equations, the solution of which is found analytically by the Laplace transform and by the Euler substitution method. This allows the contact force to be determined as a function of time.     

热惯性对热弹性行为影响的渐近分析

当热作用时间或受热器件结构尺寸呈现微尺度特征时, 热流运动的惯性效应将对热量的传递过程产生显著地影响. 基于热质的概念, 依据牛顿力学原理引入用于描述热质运动的热波方程, 结合各向同性材料的本构关系, 构建了计及热流运动惯性效应的广义热弹性动力学模型. 利用超常传热的微尺度特征, 采用解析的方法对半无限大体外表面受热冲击作用的一维问题进行了渐近求解. 通过对热波、热弹性波的传播和各物理场分布的分析以及与已有广义热弹性理论预测结果的对比, 揭示了热流运动的惯性效应对热弹性行为的影响. 结果表明：热量的传递除了受到热流加速的时间惯性影响之外, 热流运动的空间惯性也对传热行为产生影响, 当计及空间惯性时, 热波、热弹性波的波速、波前位置, 各物理场的建立时间、阶跃峰值及阶跃间隔均受到不同程度的影响. 关键词： 热惯性 热质运动 广义热弹性动力学模型 渐近分析     

Inclusion of the Full Electromagnetic Interaction in Correlations and Physical Quantities

Density-density correlations in a homogeneous, isotropic, classical plasma are calculated with inclusion of the full electromagnetic interaction. This leads to isotropic homogeneous field limits, contrary to the electrostatic approximation, that is consequently not valid for small wavenumbers. Application of the theory of generalized functions, combined with Kramer Kronig relations makes it possible to deal with the integrals that occur in the transverse part, provided a nonrelativistic approximation has been applied. As a side result Kubo's formula, applied to the electric conductivity, and generally derived under restriction to the electrostatic approximation, reappears for the case that the full electromagnetic interaction is included.     

Vibration of thick plates carrying concentrated masses

The method for obtaining the natural frequencies and orthogonality relation for combined dynamical systems in which the Green functions of the vibrating subsystems are used is applied to a thick plate carrying concentrated masses. The effects of transverse shear and rotary inertia of each mass is accounted for. It is demonstrated that as the plate thickness goes to zero the results of thin plate analysis are obtained. The Green functions for both thin and thick vibrating plates are derived by modal analysis in the form of infinite series. The advantages and disadvantages of this representation are discussed. An example involving a simply supported isotropic square plate carrying a single concentrated mass at its center is provided.     

Specific heat of the quadratic antiferromagnetic CuCl2

An attempt has been made to test the cluster theory of Muramatsu and Oguchi by applying it to the case of anhydrous cupric chloride. The magnetic specific heat which has been derived from experimental measurements is shown to fit the theory if the exchange interaction is close to isotropic, with anisotropy parameter η=0.927, showing the Néel point at 23.9 K and a broad maximum around 40 K.     

Inertia and Gravity: a New Approach to Dynamical Theory in General Relativity

A new approach to gravitational field dynamics is proposed, as an alternative to the standard formulation of General Relativity. The spacetime metric tensor is split, into an externally fixed background geometry (inertia) and a local dynamical field (gravity); and a dynamical theory of matter and gravity in the inertial background is developed. The physical origin of inertia (Mach's Principle), and its observable properties, are discussed. The coordinate representations of inertia and gravity are found to have an internal gauge degree of freedom, due to the Equivalence Principle; the transformation properties of these fields, and the notion of covariant gauge conditions, are discussed. The dynamics of matter and gravitic fields is then investigated, using: (i) The group of motion of the inertial background, appearing as an externally fixed Lie symmetry in the matter and gravity action principles, which yields weakly conserved energy-momentum-like objects; and (ii) an internal symmetry gauge group, yielding strongly conserved “internal currents”. A fully covariant field-theoretical formalism is used, in which all quantities and operations are tensorial; the well-known difficulties of “coordinate effects” in the standard nontensorial formulation are thus avoided. The physical significance of various types of conservation laws is discussed; and a complete family of energy-momentum tensors of gravity, covariantly conserved together with the matter energy-momentum, is deduced from a tensorial action principle. Treating gravity as an independent dynamical interaction, on an equal footing with other (matter) interactions, we are then finally led to the conclusion that the gravitic energy-momentum of a system is fully determined by the matter energy-momentum; various physical implications of this are discussed in some detail.     

The effect of a magnetic field on a 2D problem of fibre-reinforced thermoelasticity rotation under three theories

In the present paper,we introduce the coupled theory(CD),Lord-Schulman(LS) theory,and Green-Lindsay(GL) theory to study the influences of a magnetic field and rotation on a two-dimensional problem of fibre-reinforced thermoelasticity.The material is a homogeneous isotropic elastic half-space.The method applied here is to use normal mode analysis to solve a thermal shock problem.Some particular cases are also discussed in the context of the problem.Deformation of a body depends on the nature of the force applied as well as the type of boundary conditions.Numerical results for the temperature,displacement,and thermal stress components are given and illustrated graphically in the absence and the presence of the magnetic field and rotation.