Transmission time in the reflectionless complex potential

A phase time definition directly obtained from the Schr6dinger equation is used to investigate the time delay of a particle scattered by complex reflectionless potential. The artifacts introduced by truncating in the numerical simulation are clarified. The time delay of the transmitted wave packet is found to be equal to the reflection time of the truncated potential. Both time delays are the same as the traversal time in the free space, but shorter than the time taken by a classical particle to pass the same potential.

Quantum Mechanics of Complex Octic Potential in One Dimension

For gaining further insight into the nature of the eigenspectra of a complex octic potential [say], we investigate the quasi exact solutions of the Schr?dinger equation in an extended complex phase space characterized by . The analyticity property of the eigenfunction alone is found sufficient to throw light on the nature of eigenvalues and eigenfunction of a system. Explicit expressions of eigenvalues and eigenfunctions for the ground state as well as for the first excited state of a complex octic potential and its variant are worked out. It is found that imaginary part of the eigenvalue turns out to be zero for real coupling parameters, whereas it becomes non-zero for complex coupling parameters. However, the PT-symmetric version of a non-hermitian Hamiltonian possesses the real eigenvalue even if coupling parameters in the potential are complex.

A SCREW DISLOCATION IN A THREE-PHASE COMPOSITE CYLINDER MODEL WITH INTERFACIAL RIGID LINES

The problem of the elastic interaction between a screw dislocation and a three-phase circular inclusion with interracial rigid lines （anti-cracks） is investigated. An efficient and concise method for the complex multiply connected region is developed, with which explicit series form solutions of the complex potentials in the matrix, and the interphase layer and inclusion regions are derived. Based on the complex potentials, the image force on the screw dislocation is then calculated by using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, interphase layer thicknesses and material property combinations. The main results show that the interracial rigid lines exert a significant perturbation effect on the motion of the screw dislocation near the circular inclusion surrounded by an interphase layer.

The influence of jaw's curvature on the results of the Brazilian disc test

The general contact problem of a disc squeezed between jaws of arbitrary curvature is considered employing Muskhelishvili’s complex potentials.Taking advantage of the general solution introduced,the closed-form expressions for the stresses along strategic loci(loaded rim,loaded diameter,disc’s center)are obtained,in terms of the ratio r of the disc’s to the jaw’s curvature.Then,the effect of r(as well as that of the relative stiffness of the disc’s and jaw’s materials dictating the contact arc)on the stress distribution along these loci is explored.It is concluded that,for both smooth contact(zero friction)and contact with friction,the role of the jaw’s curvature is significant not only along the disc-jaw contact arc(as it could be expected),but also all along the loaded diameter.On the other hand,it is indicated that the stress field at the disc’s center is more or less insensitive to the jaw’s curvature assuming that r lies within the range(0,0.67)or in other words within the limits defined by the two standardized suggestions,i.e.that of American Society for Testing and Materials(ASTM)(plane loading platens with r ? 0)and that of International Society for Rock Mechanics(ISRM)(curved jaws with r ? 0.67).The upper limit of this range is a kind of compromise between the need to make the stress field at the disc’s center independent of the boundary conditions while keeping at the same time the contact angle large enough to reduce the stress concentration and the risk for premature fracture initiation far from the disc’s center.For jaws with radius of curvature exceeded by that suggested by ISRM,the stress field at the disc’s center is significantly influenced.Especially for jaws with radius approaching that of the disc,the stress field at the disc’s center is dramatically distorted rendering Hondros’ formula inapplicable and the test results erroneous.

AN INTERFACE INCLUSION BETWEEN TWO DISSIMILAR PIEZOELECTRIC MATERIALS

The generalized two-dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh theory. The problem was reduced to a Hilbert problem, and then closed-form expressions were obtained, respectively, far the complex potentials in piezoelectric media, the electric field inside the inclusion and the tip fields near the inclusion. it is shown that in the media, all field variables near the inclusion-tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity. In addition, it is found that the electric field inside the inclusion is singular and oscillatory too, when approaching the inclusion-tips from inside the inclusion.

INTERACTION OF A SCREW DISLOCATION IN THE INTERPHASE LAYER WITH THE INCLUSION AND MATRIX

The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with . An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwatz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution . By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.

PLANE STRAIN PROBLEM OF PIEZOELECTRIC SOLID WITH ELLIPTIC INCLUSION

By using the complex variables function theory, a plane strain electro-elastic analysis was performed on a transversely isotropic piezoelectric material containing an elliptic elastic inclusion, which is subjected to a uniform stress field and a uniform electric displacement loads at infinity. Based on the present finite element results and some related theoretical solutions, an acceptable conjecture was found that the stress field is constant inside the elastic inclusion. The stress field solutions in the piezoelectric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric boundary conditions.

Positron scattering and ionization of neon atoms—theoretical investigations

Although positron scattering with inert gas atoms has been studied in theory as well as in experiment, there are discrepancies. The present work reports all the major total cross sections of e＋-neon scattering at incident energies above ionization threshold, originating from a complex potential formalism. Elastic and cumulative inelastic scatterings are treated in the complex spherical e＋-atom potential. Our total inelastic cross section includes positronium formation together with ionization and excitation channels in Ne. Because of the Ps formation channel it is difficult to separate out ionization cross sections from the total inelastic cross sections. An approximate method similar to electron-atom scattering has been applied to bifurcate ionization and cumulative excitation cross sections at energies from threshold to 2000 eV. Comparisons of present results with available data are made. An important outcome of this work is the relative contribution of different scattering processes, which we have shown by a bar-chart at the ionization peak.

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

Electron inelastic mean free paths in solids:A theoretical approach

In the present paper, the inelastic mean free path （IMFP） of incident electrons is calculated as a function of energy for silicon （Si）, oxides of silicon （SiO2）, SiO, and A1203 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.

BASIC SOLUTION FOR THE THREE-PHASE COMPOSITE CONSTITUTIVE MODEL IN ANTIPLANE PIEZOELECTRICITY

A basic solution in series form for the three-phase composite cylindrical model in antiplane piezoelectricity subjected to the action of a singularity in the intermediate matrix region is presented. The solution is obtained through the complex potential approach in conjunction with the techniques of analytical continuation, singularity analysis, Laurent series expansion in an annular region and Cauchy integral formulae, etc. Based on the complex potentials obtained, explicit expressions for the distribution of stress and electric displacement in the three regions are also derived.

Effects of organic acids on the leaching process of ion-adsorption type rare earth ore

To examine the activation of organic acids on the leaching process of ion-adsorption type rare earth ore（IRE-ore）, the leaching behavior of rare earth（RE） and zeta potential of IRE-ore were investigated in the absence and presence of carboxylic acids. The results show that all the tested organic acids（acetic acid,malonic acid, citric acid, tartaric acid, succinic acid, and malic acid） can promote RE extraction. At relatively high concentrations of organic acids, the activation efficiency of organic acids on RE extraction is generally consistent with their complexation ability; whereas at their low concentrations, the change of zeta potential on the IRE-ore surface with organic acid concentration and p H has a close association with RE extraction, which indicates that organic acids can impact the surface electrical property of IREore via their adsorption/desorption, and thereby increase/decrease the affinity of RE ions to IRE-ore.Therefore the influence of organic acids on the IRE-ore surface electrical property also plays an important role in RE extraction in addition to their complexation with RE ions.