The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.     

On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress

In this paper, the generalized thermoelasticity problem for an infinite fiber-reinforced transversely-isotropic thick plate subjected to initial stress is solved. The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading. The normal mode analysis is used to obtain the analytical expressions for the displacements, stresses and temperature distributions. The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags. Effect of phase-lags, reinforcement and initial stress on the field quantities is shown graphically. The results due to the coupled thermoelasticity theory, Lord and Shulman's theory, and Green and Naghdi's theory have been derived as limiting cases. The graphs illustrated that the initial stress, the reinforcement and phase-lags have great effects on the distributions of the field quantities.     

Connection Structures of Topological Singularity in Micromechanics from a Viewpoint of Generalized Finsler Space

Geometric structures of Cosserat or micropolar continuum are discussed based on geometric objects in a non-Riemannian space. A microrotation is described in a microscopic level than a macroscopic displacement level. In this case, a microscopic rotation can be expressed as a nonlocal internal variable attached to each point in a generalized Finsler space. Such non-local hierarchy is geometrically realized by using a second-order vector bundle viewpoint. Then, two kinds of torsion tensor in the second-order vector bundle are obtained. One is characterized by the macroscopic displacement. The other is characterized by the microscopic rotation. These torsion tensors are equivalent to nonintegrability conditions for multivalued macroscopic displacement and microscopic rotation. Especially, a path dependency of the displacement and the microscopic rotation is represented by a non-vanishing condition of torsion tensors. Moreover, the concept of non-locality of the Finsler geometry implies that the approach of higher-order geometry is applicable to a finite deformation in nonlinear mechanics. The singularity given by the multivalued function is also described as a boundary value problem. An application of the generalized Finsler geometry to a gradient theory is also discussed.     

The refined theory of deep rectangular beams based on general solutions of elasticity

The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity.     

Electro-optics of molecules. II

The formalism of polynomials of quantum numbers is generalized to the case of degenerate states and general recurrence relations are derived. A theorem of extraneous quantum numbers—the quantum numbers appearing in the anharmonic Hamiltonian as parameters—is formulated. With the help of this theorem the polynomial formalism is extrapolated to the case of rotation, and a simple and correct algorithm for deriving the coefficients of the Herman-Wallis factor is proposed. The expressions obtained for the first coefficients are more obvious than the conventional formulas and their application to the hydrogen iodide molecule leads to good agreement with modern experimental data. The necessity of taking into account the part of the magnetic dipole moment nonlinear in the spin variables—the magneto-optical anharmonicity—is shown for systems with the spin-spin interaction.     

The gauge theory of dislocations: Static solutions of screw and edge dislocations

We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations in terms of the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory, both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths ?₁, ?₂, ?₃ and ?₄, which are given explicitly. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length ?₁ = ?₄. For the problem of an edge dislocation, only two characteristic lengths ?₂ and ?₃ arise with one of them being the same ?₂ = ?₁ as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths ?₂ and ?₃ of an edge dislocation are equal, we obtain an edge dislocation, which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses, we recover well-known results obtained earlier.     

The generalized vectorial laws of reflection and refraction applied to the rotation problems in ray optics

This paper deals with the mirror rotation problem and the problem of rotation of refracting surface in ray optics. These two problems of rotation in ray optics have been dealt with on the basis of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. In addition to the development of many interesting physical insights to the aforesaid rotation problems in ray optics, the most remarkable fact that has been discovered in the present study is that the proposition ‘Velocity of light is unattainable’ is not correct. Rather, it is possible to have velocity exceeding the velocity of light - a result not in agreement with the special theory of relativity.     

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.     

Theory of solitary plastic waves

The paper deals with the dislocation dynamics of coherently propagating modes of plastic shear (Lüders bands) in single crystals oriented for single slip, in terms of a generalized Fisher-Kolmogorov equation. The role of (1) cross-slip and (2) non-axial stresses as propagation mechnisms is investigated, and the problem of propagation velocity selection is addressed. The phenomenon of slip band clustering which was observed in sufficiently thick tensile specimens is traced back to a propagative instability owing to non-axial stresses.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

The onset of rotational motion of dusty plasma structures in strata of a glow discharge in a magnetic field

An interpretation is given to the previously observed action of a magnetic field on the state of a dusty plasma structure in strata of a glow discharge. The conditions of previous experiments are analyzed, in which a nonuniform rotation and a change in the degree of order of a dusty plasma structure (the translational order), as well as a correlation between them, were revealed. Based on this analysis and on data in the literature on dusty plasmas in a magnetic field, a hypothesis is made that the reason for the rotation of the structure is the ion drag force. Additional experiments on the observation of the onset of rotational motion of a structure in “weak” and “strong” magnetic fields are conducted. It is shown that rotation reversal (and rearrangement of the order of the structure) is caused by changes in the direction of ionic flows—from internal regions of the structure to its periphery and vice versa—in the weak and strong magnetic fields. The results obtained agree qualitatively with the hypothesis adopted, as well as with the data of the two-dimensional theory of strata.     

Dislocation field theory in 2D: Application to graphene

A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material moduli. Two characteristic length scales are defined in terms of the four material moduli. Non-singular solutions of the stresses and elastic distortions of an edge dislocation are calculated. It has been pointed out that the elastic strain agrees well with experimental data found recently for an edge dislocation in graphene.     

Torsional-flexural waves in thin-walled open beams

A one-dimensional theory is developed for coupled torsional-flexural waves in thin-walled elastic beams of arbitrary open cross-section. Complex kinematical effects are fully taken into account with an emphasis on consistency. Exact equations of motion are obtained in terms of generalized stresses and generalized displacements defined by an averaging procedure. Constitutive relations accounting for flexural-torsional couplings are proposed. They include and generalize the static laws of strength of materials. General features of the dispersion are analyzed. This theory is applied to the case of a standard angle-section of which the dispersion curves are given.     

Cu3Nb2O8: a multiferroic with chiral coupling to the crystal structure

By combining bulk properties, neutron diffraction, and nonresonant x-ray diffraction measurements, we demonstrate that the new multiferroic Cu(3)Nb(2)O(8) becomes polar simultaneously with the appearance of generalized helicoidal magnetic ordering. The electrical polarization is oriented perpendicularly to the common plane of rotation of the spins-an observation that cannot be reconciled with the conventional theory developed for cycloidal multiferroics. Our results are consistent with coupling between a macroscopic structural rotation, which is allowed in the paramagnetic group, and magnetically induced structural chirality.     

Bethe-Salpeter Equation with Self-Energy Graphs I-Generalized Fredholm Theory,Parameter Imbedding Method

In this paper the classical Fredholm theory is generalized. The conceptions of the generalized fredholm denominator (GFD) and generalized Fredholm numerator (GFN) are defined. A set of parameter imbedding equations for GFD and GFN is deduced. In this way, the eigenvalue problem of the BS equation in ladder approximation with self-energy graphs, and the eigenvalue problem of nonlinear parameter integral equation, are carried over into an initial-value problem of a set of ordinary differential equations.     

Local instability of a plate with a circular nanohole under uniaxial tension

The problem of the influence of surface tension on the local instability of a plate under tension is investigated by the example of an infinite plate with a circular nanohole. The method for solving the problem under consideration is based on a previously developed approach for solving problems on local buckling of a thin uniaxially stretched elastic sheet with variously shaped macroholes. The critical (Euler) load, at which the instability occurs, is sought by the Ritz method in framework of the linearized Karman set of equations based on the principle of virtual motions as the smallest positive load giving the minimum of the potential energy of the plate deformation. The generalized plane stress state of the plate with a nanohole is found for its application taking into account surface stresses. The linearized Gurtin-Murdoch relationships for the surface elasticity, the generalized Young-Laplace law, and the Goursat-Kolosov complex potentials are used when deriving analytical dependences for the stress in this plane problem. The deflection of the plate is represented by a double row satisfying the damping condition at infinity and ensuring freedom of motion of hole edges. Numerical calculations are performed for the aluminum plate. Two variants of the elastic properties of a circular hole are considered. Zones of compressing circumferential tensions near the edges of the circular hole with radii 1, 2, and 4 nm under uniaxial tension are constructed. It is shown that the account of the surface stresses decreases the critical load, which has a tendency to decrease in both cases with a decrease in the cut radius in a nanometer variation range.     

Relativistic theory of superpotentials for a nonhomogeneous spatially isotropic medium

This work deals with the relativistic, coordinate invariant theory of electromagnetic wave propagation in a nonhomogeneous medium that is spatially isotropic with respect to the generalized 4-velocity. The existence of a new superpotential for the electromagnetic field is established. The governing field equation for the superpotential is derived via a generalized Lorentz gauge condition for the electromagnetic potential and two new tensor identities involving the curvature tensor. The new field equation takes a simple form which reveals the effect of non-rigidity, rotation, acceleration, and incomplete material isotropy with respect to the Fermi frames as well as curvature and nonhomogeneous material properties.     

Dynamics of current flow through the phase-boundary between a normal and a superconducting region

The time-dependent Bogoliubov Equations — which are derived in a slightly generalized form — are applied to the problem of quasiparticle reflection from the phaseboundary between a normal and a superconducting region. The momentum balance of current flow through the boundary is discussed. The supercurrent induced by a quasiparticle with excitation energy less than the maximum value of the pair-potential is calculated.     

谐振势阱中旋转广义玻色系统的热力学性质

以非广延Tsallis统计理论为基础,导出了广义玻色-爱因斯坦统计分布表达式,并用其分别讨论了三维和二维谐振势阱约束的旋转广义玻色气体的热力学性质.结合系统粒子数、玻色-爱因斯坦凝聚(BEC)临界温度、基态粒子占据率和比热等物理量的解析表达式,分析了非广延参数和势阱旋转频率等因素对系统热力学性质的影响.     

Bound Motion of Bodies and Paticles in the Rotating Systems

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton “feels” the Coriolis force caused by the rotation of the Earth.