Static spherically symmetric anisotropic fluid distribution in presence of electromagnetic field

Einstein’s field equations of general relativity corresponding to the anisotropic (principal stresses unequal) static fluid sphere in presence of electromagnetic field have been solved exactly. The integration constants are determined by matching the obtained solution with the Reissner-Nordström solution over the boundary. It has been found that the flaid model has non-negative expression for mass density and pressure. The mass density and stresses are everywhere regular and monotonically decreasing functions of the radial coordinate.     

Kirchhoff弹性直杆在力螺旋作用下的稳定性

研究受力螺旋作用的圆截面Kirchhoff弹性直杆在各种边界条件下的稳定性问题. 用直角坐标和Cardano角表示截面的形心位置和姿态. 由Kirchhoff方程得到弹性细杆的直线平衡特解,导出线性化扰动方程及其通解. 根据边界条件确定积分常数的非零解存在条件,讨论了各种边界条件,如两端铰支、两端固定、一端铰支一端固定以及一端固定一端自由的弹性细杆直线平衡状态的稳定性,导出了临界载荷的表达式,绘制了稳定域,将Greenhill公式推广到其他边界条件,并且使压杆的Euler 公式成为其特例. 关键词： Kirchhoff弹性杆 稳定性 力螺旋 Greenhill公式     

A spin-coefficient approach to Weyssenhoff fluids in Einstein-Cartan theory

The generalized Newman-Penrose formalism is used to analyze semiclassical aligned spin fluids satisfying the Weyssenhoff restriction in the framework of Einstein-Cartan theory. Some general properties are derived and the formalism is then used to obtain two classes of exact solution. One has a flat metric, but the fluid has in general nonzero acceleration, expansion, and shear. It is characterized by two arbitrary constants and two functions of two variables satisfying one partial differential equation. In the other class the fluid has nonzero acceleration and vorticity, and the free gravitational field is of typeD. It is characterized by three arbitrary constants and an arbitrary function of two spacelike coordinates.     

Plausible black hole solutions in higher-derivative gravity

Here we obtain explicit black hole solutions in Extension Gravity models with high-order derivative terms, while the Lichnerowicz-type theorem simplifies our analysis by vanishing Ricci's scalar curvature. We find out two explicit static, spherical solutions that satisfy the presented action: the first one is the same usual Schwarzschild solution and the other one is the new non-Schwarzschild solution. It means that Schwarzschild's solution following the no-hair theorem can describe any black hole object on each gravity theory. Without considering the first law of thermodynamics for it, we show that the non-Schwarzschild solution is depending on its set of constants, and then we consider its entropy and other thermodynamic parameters for specific values of the constants.     

A reduced dimensionality model of torsional vibrations in star molecules

The torsional vibrations of star molecules are studied with a reduced dimensionality model. In this model, the molecule is described by two equivalent sets of lumped inertial cylinders and vibrational frequencies are predicted by solution of the coupled equations of motion. Force constants are determined by including them as free parameters in the model and fitting the computed frequencies to their analogs as determined using full normal coordinate analysis at the HFSCF level of theory. Best agreement between the methods occurs when torsional force constants are included for the first two layers of the molecule. This reveals that non-bonded torsional interactions are important in the vibrational dynamics of these systems. Further insight is afforded by an analysis of why simple harmonic oscillator models are sufficient for modeling some related systems but fail to reproduce the trend in global mode frequencies for saturated aliphatic star molecules. The analysis reveals that the origin of this failure lies in backbone flexibility in these branched polymeric systems.     

Non-linear charged dS black hole and its thermodynamics and phase transitions

From solving the equations of the motion for a system of Einstein gravity coupled to a non-linear electromagnetic field in the dS spacetime with two integral constants, we derived a static and spherical symmetric non-linear magnetic-charged black hole. It is indicated that this black hole solution behaves like a dS geometry in the short-distance regime. And, thus this black hole is regular. The structure of the black hole horizons is studied in detail. Also, we investigated the thermodynamics and the thermal phase transition of the black hole in both the local and global views. By observing the discontinuous change of the specific heat sign and the swallowtail structure of the free energy, we showed that the black hole can undergo a thermal phase transition between a thermodynamically unstable phase and a thermodynamically stable phase.     

Dn+1(2) reflection K-matrices

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the D_n+1⁽²⁾ affine Lie algebra. We have classified them in terms of three types of K-matrices. The first one has n+2 free parameters and all the matrix elements are non-zero. The second solution is given by a block diagonal matrix with just one free parameter. It turns out that for n even there exists a third class of K-matrices without any free parameter.     

Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation

Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate and assuming a specific form of the vacuum stress-energy momentum tensor, a general solution of Møller's field equations in case of spherically symmetric nonsingular black holes is derived. The general solution is characterized by an arbitrary function and two constants of integration. The previously obtained solutions are verified as special cases of the general solution. The associated metric of the general solution gives no more than the spherically symmetric nonsingular black hole obtained before. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function, and is different from the standard one.     

Nonlinear fluctuation,frequency and stability analyses in free vibration of circular sector oscillation systems

In the present paper, the modified homotopy perturbation method (MHPM) is employed to investigate about both nonlinear swinging oscillation and the stability of circular sector oscillation systems. The sensitivity study performed for frequency analysis of the mentioned oscillatory circular sector body shows that frequency of nonlinear oscillation depends on some specific parameters and can be optimized. Furthermore onset of the instability is dependent to angle α and initial amplitude.Comparisons made among the results of the present closed-form analytical solution and the traditional numerical iterative time integration solution confirms the accuracy and efficiency of the presented analytical solution.In contrast to the available numerical methods, the present analytical method is free from the numerical damping and the time integration accumulated errors. Moreover, in comparison with the traditional multistep numerical iterative time integration methods, a much less computational time is required for the present analytical method. Responses of the dynamical systems to some extent are affected by the natural frequencies. Results reveal that for nonlinear systems, the natural frequency is remarkably affected by the initial conditions.     

Differential geometry of atomic structure and the binding energy of atoms

The geometric theory of partial differential equations due to E. Cartan is applied to atomic systems in order to solve the many-body problems and to obtain the binding energies of electrons in an atom. The procedure consists in defining a Schrödinger equation over an Euclidean patch which overlaps with other Euclidean patches in a specified way to form a manifold. If the energy of the system has to be a minimum, it is shown using the Dirichlet principle that the coordinate systems are related by the Cauchy-Riemann relations. The invariance of the Schrödinger equations in the overlapping region leads to a nonlinear second-order equation which is invariant to automorphic transformations and whose solutions are doubly periodic functions. There are only two possible single-valued solutions to this nonlinear partial differential equation and these correspond to lattices of points in the complex space, which are (a) corners of an array of equilateral triangles, and (b) corners of an array of isosceles right-angled triangles. The first solution was used in an earlier work to derive many static properties of nuclei. In this paper it is shown that the second solution gives binding energies of atoms in agreement of about 3% for the few experimental points that are available and also in good agreement with the binding energies of atoms obtained by the perturbation theory. It is also shown that this lattice under certain approximations is equivalent to a pure Coulomb law and the Bohr orbits of the hydrogen atom are correctly predicted. In obtaining the binding energies of atoms, no free parameters are required in the theory, except for the value of the binding energy of the He atom, as the theory is developed only for spinless systems. All other constants turn out to be fundamental constants.     

Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method

The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It’s found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy.     

Linearized superhairs on multi-black-hole backgrounds

It is shown that the linearized Rarita-Schwinger equation on a multi-black-hole background of the Majumdar-Papapetrou class admits time-independent and regular nongauge solutions that die off at infinity. The number of freely available real constants is supposed to be four, thus being independent of the number of black holes. As a consequence, the gravitino field seems to be uniquely determined by its supercharge. Moreover, each supercovariantly constant spinor corresponds to one gravitino solution.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P5259.     

Thermodynamic modelling of miscibility in (InAs) x (GaAs)1−x solid solutions

Current methods used to model the solution thermodynamics of III–V compound semiconductors involve the use of the valence force field as the molecular model and the regular solution model (with the temperature independent interaction parameter and underlying assumption of random mixing) as the engineering model. In this study, excess free energy models (with three or less adjustable parameters) are investigated to predict the solid–solid miscibility of (InAs) _x (GaAs)_{1? x} . The models investigated include the Porter/one-constant Margules (OCM) model, the two-constant Margules (TCM) model and the non-random two liquid (NRTL) model. These models are fit to excess free energy values derived from free energy change of mixing (variation with composition) data available from molecular simulations at different temperatures. The parameters in all the models have been found to be temperature dependent. The coexistence compositions are best predicted by the NRTL model, indicating the need to consider non-random mixing effects present in these solid solutions. The TCM model predicts better equilibrium composition data as compared to the OCM model.     

First-principles investigations on elastic,thermodynamic and lattice thermal conductivity of topological insulator LaAs

Topological insulators are always a hot topic owing to their various peculiar physical effects, which are useful in spintronics and quantum information processing. Herein, we systematically investigate the elastic, thermodynamic and lattice thermal conductivity of a new typical topological insulator LaAs by combining the first-principles approach and an iterative solution of the Boltzmann transport equation. The obtained elastic constants and other lattice structural parameters of LaAs are well consistent with the experimental and other theoretical results. For the first time, the lattice thermal conductivity (5.46 W/(m?K)) and mean free path (14.4 nm) of LaAs are obtained,which manifests that the LaAs is more likely to be a desirable thermoelectric material. It is noted that the obtained mode-averaged Grüneisen parameters by different ab initio simulation packages are very similar, suggesting that our results are rather responsible. From the phonon scattering rates of LaAs, we speculate that the reduction of acoustic-optical gap and the larger phonon scattering may jointly result in reduction of thermal conductivity for LaAs. Meanwhile, the temperature dependence curves of the lattice thermal conductivity, heat capacity and phonon mean free path are also presented. We expect our work can provide more information for further experimental studies.     

Thermal consequences of a regular black hole with cosmological constant and Einstein–Aether black hole

We discuss the thermodynamics of regular black hole (RBH) with cosmological constant and Einstein–Aether black hole (BH) with coupling constant in the presence of thermal corrections. For these BHs, we develop various thermodynamical quantities such as entropy, pressure, specific heats, Gibbs free energy and Helmholtz free energy. Thermal stability is also being analyzed through γ factor, Gibbs free energy and Helmholtz free energy. It is found that RBH with cosmological constant and Einstein–Aether show stable behavior with the increase of the values of cosmological and coupling constants.     

An approximate global solution of Einstein’s equations for a rotating finite body

We obtain an approximate global stationary and axisymmetric solution of Einstein’s equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find second-order approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic and quo-harmonic coordinates. In both cases, interior and exterior solutions are matched, in the sense of Lichnerowicz, on the surface of zero pressure to obtain a global solution. The resulting metric depends on three arbitrary constants: mass density, rotational velocity and the star radius at the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined by these three parameters. It is easy to check that Kerr’s metric cannot be the exterior part of that metric.     

Coupled flexural-longitudinal wave motion in a periodic beam

Periodic structure theory is used to study the interactions between flexural and longitudinal wave motion in a beam (representing a plate) to which offset spring-mounted masses (representing stiffeners) are attached at regular intervals. An equation for the propagation constants of the coupled waves is derived. The response of a semi-infinite periodic beam to a harmonic force or moment at the finite end is analyzed in terms of the characteristic free waves corresponding to these propagation constants. Computer results are presented which show how the propagation constants are affected by the coupling, and how the forced response varies with distance from the excitation point. The spring-mounted masses can provide very high attenuation of both longitudinal and flexural waves when no coupling is present, but when coupling is introduced the two waves combine to give very low (or zero) attenuation of the longitudinal wave. The influence of different damping levels on spatial attenuation is also studied.     

Local Operator Products and Field Equations in P(φ)2 Theories

In P(φ)₂ theories with small coupling constants, local fields exist which are obtained from normal ordering of Euclidean fields. Normal ordering with respect to the free measure and the physical measure leads to the same family of fields. The coefficients of the two resulting field equations are related by a fixed point problem. Conditions are exhibited under which there is a unique solution.     

Letter: A Twisting Electrovac Solution of Type II with the Cosmological Constant

An exact solution of the current–free Einstein–Maxwell equations with the cosmological constant is presented. It is of Petrov type II, and its double principal null vector is geodesic, shear–free, expanding, and twisting. The solution contains five constants. Its electromagnetic field is non–null and aligned. The solution admits only one Killing vector and includes, as special cases, several known solutions.