A Mode I Crack Problem for a Thermoelastic Fibre-Reinforced Anisotropic Material Using Finite Element Method

In this article, the theory of generalized thermoelasticity with one relaxation time is used to investigate the thermoelastic fiber-reinforced anisotropic material with a finite linear crack. The crack boundary is due to a prescribed temperature and stress distribution. By using the finite element method, the numerical solutions of the components of displacement, temperature and the stress components have been obtained. Comparisons of the results in the absence and presence of reinforcement have been presented.     

Evolution of Crack Tip Constraint in a Mode II Elastic-Plastic Crack Problem

Numerous studies have shown that crack tip constraint has an important effect on the level of conservatism when crack extension is investigated in elastic-plastic fracture mechanics. Constraint effect has been explored extensively in the past but mainly for pure mode I problems. Very few researchers have dealt with the effects of crack tip constraint on mode II or mixed mode I/II fracture in metallic materials. In this paper, the evolution of mode II constraint parameter Q in terms of applied external load is determined numerically for a test specimen under pure mode II loading. The finite element method is utilized to model the specimen and to study the range of validity of mode II constraint parameter determined from a Q—T diagram. The parameter Q calculated from the finite element simulation (or from the full field solution) is compared with the values of Q determined from the Q—T diagram. For low levels of load, the results of full field solution are shown to be consistent well with the results obtained from the Q—T diagram. However, when the external load increases significantly, the results of Q—T diagram are no longer accurate and mode II constraint parameter Q should be calculated directly from finite element results.     

Power Flux along a Straight Crack in an Elastic Plate

Propagation of the edge waves along a straight crack in an elastic plate is studied. The power fluxes associated with these waves are calculated, and the modes of vibration are considered.     

V型三能级原子系统中电磁诱导各向同性的二维左手效应

研究被两正交光场耦合的V型三能级原子系统中电磁诱导下的左手效应.讨论了正交耦合光场强度、探测场失谐量和上能级间自发辐射耦合相干对该原子系统介电常数、磁导率和折射系数的影响.研究表明,在合适的参数条件下,该原子系统的介电常数、磁导率在二维相同的区域内同时为负值,且取值分布具有各向同性的特征;即产生了各向同性的二维左手效应.     

Spin Stiffness of 2D Isotropic Heisenberg Antiferrornagnet

The spin stiffness of spin-1/2 two-dimensional isotropic Heisenberg antiferromagnet is calculated by a perturbation method based on the extended Schwinger-Boson mean-field theory. We arrive at a value of the spin stiffness, p_s = 0.176J, which is in quite well agreement with experiments and the numerical results.     

A Relativistic Model of the Isotropic Oscillator

For a three-dimensional model of the harmonic oscillator in the relativistic configurational r-representation wave functions in the spherical coordinates r = (r, Θ, ?) are found. The generating function, orthogonality and various recurrence relations for the radial part of the wave function are obtained. The radial and orbital quantum numbers raising and lowering operators are defined and the dynamical symmetry group is constructed by means of the Infeld-Hull factorization method.     

Minisuperspace model of Machian resolution of Problem of Time. I. Isotropic case

It is well known that the three parameters that characterize the Kerr black hole (mass, angular momentum and horizon area) satisfy several important inequalities. Remarkably, some of these inequalities remain valid also for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this article recent results in this subject are reviewed.     

Stress-Strain State of Elastic Plate with a Crack

Russian Physics Journal - The paper considers an infinite plate with a crack in the form of a narrow hole with a certain curvature at the tip of the crack. The stress-strain state parameters of...     

A 2D Luttinger Model

A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is shown that the effective model thus obtained can be treated by exact bosonization methods. It is also discussed how this effective model can be used to obtain physical information about the corresponding lattice fermion system.     

S0 Lamb Wave Scattering from a Cylindrical Inhomogeneity in a Transversely Isotropic Composite Plate

An analytical model using the Poisson theory is proposed to predict the SO Lamb wave scattering from a cylindrical inhomogeneity in a transversely isotropic composite plate. Due to the anisotropic elastic properties of the plate, the suitability of the model is first examined by the dispersion curve of an SO wave by using approximate Poisson theory compared to the exact Lamb solution. It is found that the Poisson theory can accurately describe the behavior of the SO wave at low frequency when the incident SO wave is parallel or perpendicular to the fiber direction of the transversely isotropic composite plate. On this basis, making use of the wave function expansion technique and coupling conditions at the inhomogeneity defect boundary, the far field scattered patterns of various inhomogeneity sizes and properties are then explored. The present results reveal that the scattering patterns are strongly dependent on the size and stiffness of the cylindrical inhomogeneity.     

Mode-II Crack Problem for a Long Rectangular Slab of Superconductor under an Electromagnetic Force

We present a theoretical analysis to the fracture parameters of the large single domain YBCO superconductor with a tangential line crack under electromagnetic force. The mode-II fracture parameters are obtained due to coupled finite element and infinite element method, and the numerical results are conducted for two activation processes. For a zero-field cooling （ZFC） magnetization process, in the process of magnetic field descent, the larger the applied field is, the larger the stress intensity factors. In the case of field cooling （FC） magnetization process, the stress intensity factors have obvious differences between the two cases of bfc 〉 1 and bic ≤1. Additionally, J-integral characteristic is obtained, and according to these results, the mode-Ⅱ crack growth trend is predicted. These results are benefit for us to understand the fracture mechanism of superconductor both in theory and application.     

A General Solution of the Problem of Elastic-Wave Scattering by a Plane Crack

Doklady Physics - The 3D problem of elastic-wave scattering by cracks in a homogeneous isotropic medium is considered. Using the method of Green’s function and specially introduced auxiliary...     

Angular Momentum and Energy Structure of the Coherent State of a 2D Isotropic Harmonic Oscillator

The angular momentum structure and energy structure of the coherent state of a 20 isotropic harmonic oscillator were investigated. Calculations showed that the average values of angular momentum and energy (except the zero-point energy) of this nonspreading 20 wavepacket are identical to those of the corresponding classical oscillator moving along a circular or an elliptic orbit.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

Scattering of S0 Lamb Mode from a Blind Hole in a Plate Using Mindlin/Mindlin Plate Theory

An analytical model of Lamb wave scattering from a circular blind hole in isotropic plates is presented using the Mindlin plate theory for describing in-plane and flexural wave modes simultaneously. The model makes use of the wave function expansion technique and the boundary conditions at the hole edge to evaluate the scattered far fields of three fundamental guided wave modes. Comparisons are made to existing approximate models using Poisson/Kirchhoff theory and Poisson/Mindlin theory and a 3D model using the exact 3D equations. The results reveal that the present model is more consistent with the exact 3D model at higher frequencies than existing approximate models.     

A Fractal Model for Effective Thermal Conductivity of Isotropic Porous Silica Low-k Materials

We establish a new model based on fractal theory and cubic spline interpolation to study the effective thermal conductivity of isotropic porous silica low-k materials. A 3D fractal model is introduced to describe the structure of the silica xerogel and silica hybrid materials （such as methylsilsesquioxane, MSQ）. Combined with fractal structure, a more suitable medium approximation is developed to study the isotropic porous silica xerogel and MSQ materials. Cubic spline interpolation for fitting discrete predictions from the fractal model is used to obtain the continuous function of the effective thermal conductivity versus porosity. Compared with other common models, the effective thermal conductivity predicted by our model presents better agreement with the experimental data for all porosity. These results indicate that the proposed model is valid.     

Thermoelastic behavior of a thermoelectric thin-film attached to an infinite elastic substrate

Abstract

This paper examines the thermoelectric behaviour of a thermoelectric thin film bonded to an elastic substrate. A calculation model for thermoelectric thin films is developed based on the singular integral equation method. The interface shear stress is found to exhibit singular behaviour at the ends of the films. Numerical results for the thermal stress distribution in the film and the film/substrate interface are obtained. Effects of film thickness and the substrate to film stiffness ratio on the stress of the film and the stress intensity factor of the interface are identified. The effects of interface electricity conductivity and the elastic–plastic deformation of the film are discussed.     

A comparison of 2D and 3D PIV measurements in an oblique jet

A stereo PIV (SPIV) acquisition and analysis system was developed to measure three velocity components in planar flow fields. The analysis software is based on a third order mapping function method. The system was calibrated by imaging a square grid in three measurement planes with two Kodak Megaplus cameras oriented at 30 to the bisector between them. The camera images were dewarped into real coordinates by employing a set of transform matrices computed for each calibration plane. Bias and rms errors were determined by comparing displacements measured directly with displacements estimated from the dewarping and recombination algorithm. The bias errors in the directions parallel with the measurement plane were negligible while the bias in thez direction was about 0.6 pixel. The rms errors, 0.2–0.3 pixels, were largest in thez direction. These errors were thought to result from limitations in the calibration method. The SPIV system was tested in a two-dimensional oblique jet with Reynolds number of 1800. The three dimensional results were taken in a vertical (x, y) plane parallel with the jet span. The SPIV results were compared with LDV data and two-dimensional PIV data obtained in a vertical (y, z) plane of the same jet. The SPIV measurements yielded accurate values for the in-plane mean and rms velocity components. The measured out-of-plane mean component was underestimated due to the bias error mentioned above. The rms component was accurate in part of the field but overestimated in another part due to local variations in rms error. It is expected that in the future, the out-of-plane errors can be minimized by improving the calibration and transformation procedures.