COMPARISONS OF PHASE TIMES WITH TUNNELING TIMES BASED ON ABSORPTION PROBABILITIES

The times spent by an electron in a scattering event or tunnelling through a potential barrier are investigated using a method based on the absorption probabilities. The reflection and transmission times derived from this method are equal to the local Larmor times if the transmission and reflection probability amplitudes are complex analytic functions of the complex potential. The numerical results show that they coincide with the phase times except as the incident electron energy approaches zero or when the transmission probability is too small. If the imaginary potential covers the whole space the tunnelling times are again equal to the phase times. The results show that the tunnelling times based on absorption probabilities are the best of the various candidates.

Hierarchy of structure functions for passive scalars advected by turbulent flows

A hierarchical model is proposed for the joint moments of the passive scalar dissipation and the velocity dissipation in fluid turbulence. This model predicts that the joint probability density function (PDF) of the dissipations is a bivariate log-Poisson. An analytical calculation of the scaling exponents of structure functions of the passive scalar is carried out for this hierarchical model, showing a good agreement with the results of direct numerical simulations and experiments.

Peierls-Nabarro model of interfacial misfit dislocation: An analytic solution

We propose a method to treat the interfacial misfit dislocation array following the original Peierls-Nabarro's ideas. A simple and exact analytic solution is derived in the extended Peierls-Nabarro's model, and this solution reflects the core structure and the energy of misfit dislocation, which depend on misfit and bond strength. We also find that only with beta < 0.2 the structure of interface can be represented by an array of singular Volterra dislocations, which conforms to those of atomic simulation. Interfacial energy and adhesive work can be estimated by inputting ab initio calculation data into the model, and this shows the method can provide a correlation between the ab initio calculations and elastic continuum theory.

Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations.

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Scaling Functions In Conical Indentation Of Elastic-Plastic Solids

The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young's modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young's modulus E and Poisson's ratio nu are known.

Anisotropic, gradient and metal-like mechanical behaviors of teeth and their implications on tooth functions

The anisotropy and gradient of the elastic modulus and the hardness of teeth were investigated by means of instrumented indentation method. Such properties are attributed to the unique microstructures of teeth based on scanning electron microscopic analysis. By comparing the relationship between the ratio of hardness to the reduced elastic modulus and the ratio of elastic unloading work to the total work of teeth in course of indentation to those of other materials, we found that the material behaviors of teeth display metal-like characteristics rather than ceramics as considered traditionally. These material behaviors and relevant functions are discussed briefly.

Wave propagation and the frequency domain Green's functions in viscoelastic Biot/squirt (BISQ) media

In this paper, we examine the characteristics of elastic wave propagation in viscoelastic porous media, which contain simultaneously both the Biot-flow and the squirt-flow mechanisms (BISQ). The frequency-domain Green's functions for viscoelastic BISQ media are then derived based on the classic potential function methods. Our numerical results show that S-waves are only affected by viscoelasticity, but not by squirt-flows. However, the phase velocity and attenuation of fast P-waves are seriously influenced by both viscoelasticity and squirt-flows; and there exist two peaks in the attenuation-frequency variations of fast P-waves. In the low-frequency range, the squirt-flow characteristic length, not viscoelasticity, affects the phase velocity of slow P-waves, whereas it is opposite in the high-frequency range. As to the contribution of potential functions of two types of compressional waves to the Green's function, the squirt-flow length has a small effect, and the effects of viscoelastic parameter are mainly in the higher frequency range. Crown Copyright (C) 2006 Published by Elsevier Ltd. All rights reserved.

Traces of nonsmooth functions on polyhedral domains

introduced in this paper are the definitions of the traces for a class of nonsmooth functions on polyhedral domains. By analyzing their properties we get the structures of these traces.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Analytic expression of the diffraction of a circular aperture

Recurring to the characteristic of Bessel function, we give the analytic expression or the Fresnel diffraction by a circular aperture, thus the diffractions on the propagation axis and along the boundary of the geometrical shadow are discussed conveniently. Since it is difficult to embody intuitively the physical meaning from this series expression of the Fresnel diffraction, after weighing the diffractions on the axis and along the boundary of the geometrical shadow, we propose a simple approximate expression of the circular diffraction, which is equivalent to the rigorous solution in the further propagation distance. It is important for the measurement of the parameter or the beam, such as the quantitative analysis of the relationship of the wave error and the divergence of the beam, In this paper, the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is discussed too. (c) 2005 Elsevier GrnbH. All rights reserved.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.