3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Effect of an annular pupil filter on differential confocal microscopy

Combining differential confocal microscopy and an annular pupil filter, we obtained the normalized axial intensity distribution curve of an optical system. We used the sharp slopes of the axial response curve of the optical system to measure the surface profile of a reflection grating. Experimental results prove that this method can extend the axial dynamic range and improve the transverse resolution of three-dimensional profilometry by sacrificing axial resolution. (C) 2000 Optical Society of America.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

The multi-weight neuron with geometry algorithm and its application

A novel approach for multi-dimension signals processing, that is multi-weight neural network based on high dimensional geometry theory, is proposed. With this theory, the geometry algorithm for building the multi-weight neuron is mentioned. To illustrate the advantage of the novel approach, a Chinese speech emotion recognition experiment has been done. From this experiment, the human emotions are classified into 6 archetypal classes: fear, anger, happiness, sadness, surprise and disgust. And the amplitude, pitch frequency and formant are used as the feature parameters for speech emotion recognition. Compared with traditional GSVM model, the new method has its superiority. It is noted that this method has significant values for researches and applications henceforth.

Mathematical symbols and computing methods in high dimensional biomimetic informatics and their applications

High dimensional biomimetic informatics (HDBI) is a novel theory of informatics developed in recent years. Its primary object of research is points in high dimensional Euclidean space, and its exploratory and resolving procedures are based on simple geometric computations. However, the mathematical descriptions and computing of geometric objects are inconvenient because of the characters of geometry. With the increase of the dimension and the multiformity of geometric objects, these descriptions are more complicated and prolix especially in high dimensional space. In this paper, we give some definitions and mathematical symbols, and discuss some symbolic computing methods in high dimensional space systematically from the viewpoint of HDBI. With these methods, some multi-variables problems in high dimensional space can be solved easily. Three detailed algorithms are presented as examples to show the efficiency of our symbolic computing methods: the algorithm for judging the center of a circle given three points on this circle, the algorithm for judging whether two points are on the same side of a hyperplane, and the algorithm for judging whether a point is in a simplex constructed by points in high dimensional space. Two experiments in blurred image restoration and uneven lighting image correction are presented for all these algorithms to show their good behaviors.

Effects of lattice vibration on the effective mass of quasi-two-dimensional strong-coupling polaron

The effects of lattice vibration on the system in which the electron is weakly coupled with bulk longitudinal optical phonons and strongly coupled with interface optical phonons in an infinite quantum well were studied by using Tokuda' linear-combination operator and a modified LLP variational method. The expressions for the effective mass of the polaron in a quantum well QW as functions of the well's width and temperature were derived. In particular, the law of the change of the vibration frequency of the polaron changing with well' s width and temperature are obtained. Numerical results of the effective mass and the vibration frequency of the polaron for KI/AgCl/Kl QW show that the vibration frequency and the effective mass of the polaron decrease with increasing well's width and temperature, but the contribution of the interaction between the electron and the different branches of phonons to the effective mass and the vibration frequency and the change of their variation with the well's width and temperature are greatly different.

Micro-mould method for self-assembling three-dimensional opal photonic crystals

By vertical sedimentation, silica micro-spheres were grown in different shapes of concave micro-zones which were etched on a (100) p-silicon substrate. The following were found: this method can effectively raise the quality of films by avoiding cracks; the geometry of the micro-zones affects the sediment of the film; regular hexagons and triangles best facilitate the growth of photonic crystals. This method is practical for its ability to fabricate self-assembly photonic crystals in previously designed small areas.

Computational information geometry and its applications

Digitization is the main feature of modern Information Science. Conjoining the digits and the coordinates, the relation between Information Science and high-dimensional space is consanguineous, and the information issues are transformed to the geometry problems in some high-dimensional spaces. From this basic idea, we propose Computational Information Geometry (CIG) to make information analysis and processing. Two kinds of applications of CIG are given, which are blurred image restoration and pattern recognition. Experimental results are satisfying. And in this paper, how to combine with groups of simple operators in some 2D planes to implement the geometrical computations in high-dimensional space is also introduced. Lots of the algorithms have been realized using software.

On the soft wall guiding potentials in realistic quantum waveguides

A transfer matrix method is presented for the study of electron conduction in a quantum waveguide with soft wall lateral confinement. By transforming the two-dimensional Schrodinger equation into a set of second order ordinary differential equations, the total transfer matrix is obtained and the scattering probability amplitudes are calculated. The proposed method is applied to the evaluation of the electron transmission in two types of cavity structure with finite-height square-well confinement. The results obtained by our method, which are found to be in excellent agreement with those from another transfer matrix method, suggest that the infinite square-well potential is a good approximation to finite-height square-well confinement for electrons propagating in the ground transverse mode, but softening of the walls has an obvious effect on the electron transmission and mode-mixing for propagating in the excited transverse mode. (C) 1996 American Institute of Physics.

Observation of N-Shaped Negative Differential Resistance in GaAs-Based Modulation-Doped Field Effect Transistor with InAs Quantum Dots

N-shaped negative differential resistance (NDR) with a high peak-to-valley ratio (PVR) is observed in a GaAs-based modulation-doped field effect transistor (MODFET) with InAs quantum dots (QDs) in the barrier layer (QDFET) compared with a GaAs MODFET. The NDR is explained as the real-space transfer (RST) of high-mobility electrons in a channel into nearby barrier layers with low mobility, and the PVR is enhanced dramatically upon inserting the QD layer. It is also revealed that the QD layer traps holes and acts as a positively charged nano-floating gate after a brief optical illumination, while it acts as a negatively charged nano-floating gate and depletes the adjacent channel when charged by the electrons. The NDR suggests a promising application in memory or high-speed logic devices for the QDFET structure.

Transition from the exhibition to the nonexhibition of negative differential thermal resistance in the two-segment Frenkel-Kontorova model

An extensive study of the one-dimensional two-segment Frenkel-Kontorova FK model reveals a transition from the counterintuitive existence to the ordinary nonexistence of a negative-differential-thermal-resistance NDTR regime, when the system size or the intersegment coupling constant increases to a critical value. A “phase” diagram which depicts the relevant conditions for the exhibition of NDTR was obtained. In the existence of a NDTR regime, the link at the segment interface is weak and therefore the corresponding exhibition of NDTR can be explained in terms of effective phonon-band shifts. In the case where such a regime does not exist, the theory of phonon-band mismatch is not applicable due to sufficiently strong coupling between the FK segments. The findings suggest that the behavior of a thermal transistor will depend critically on the properties of the interface and the system size.

Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky-Moriya interactions

We investigate solitary excitations in a model of a one-dimensional antiferromagnet including a single-ion anisotropy and a Dzyaloshinsky-Moriya antisymmetric exchange interaction term. We employ the Holstein-Primakoff transformation, the coherent state ansatz and the time variational principle. We obtain two partial differential equations of motion by using the method of multiple scales and applying perturbation theory. By so doing, we show that the motion of the coherent amplitude must satisfy the nonlinear Schrodinger equation. We give the single-soliton solution.