Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd

Quantum master-equation approach to quantum transport through mesoscopic systems

For quantum transport through mesoscopic systems, a quantum master-equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cumulant expansion of the tunneling Hamiltonian; then follows the conditional average over the electrode reservoir states. As a consequence, in the usual weak-tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nanoelectronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master equation with the well-known time-dependent density functional theory. The key ingredients of this paper include (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e., the device); and (iii) the construction of Kohn-Sham master equations for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOMs) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along with the propagation of the Kohn-Sham master equation and the EOMs of the auxiliary functions.

Pressure Drop of Bubbly Two-Phase Flow in a Square Channel at Reduced Gravity

A new set of experimental pressure drop data, collected aboard the Russian IL-76MDK, is reported for bubbly airwater two-phase flow in a square channel with a cross-sectional area of 12x 12mm(2). The present data are compared to several frequently used empirical models, e.g. homogeneous model, Lockhart-Martinelli-Chisholm correlation and Friedel's model. It is shown that the predictions of the models mentioned above are generally not satisfied. A new homogeneous model is developed based on the analysis of the characteristics of bubbly two-phase flow at reduced gravity. It is tested with the present data and other data collected by other researchers in circular pipes. Some questions related to the present model are also discussed. (C) 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Monte-Carlo simulation of surface crack growth rate for offshore structural steel E36-Z35

The Monte- Carlo method is used to simulate the surface fatigue crack growth rate for offshore structural steel E36-Z35, and to determine the distributions and relevance of the parameters in the Paris equation. By this method, the time and cost of fatigue crack propagation testing can be reduced. The application of the method is demonstrated by use of four sets of fatigue crack propagation data for offshore structural steel E36-Z35. A comparison of the test data with the theoretical prediction for surface crack growth rate shows the application of the simulation method to the fatigue crack propagation tests is successful.

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

A lattice Boltzmann equation for waves

We propose a lattice Boltzmann model for the wave equation. Using a lattice Boltzmann equation and the Chapman-Enskog expansion, we get 1D and 2D wave equations with truncation error of order two. The numerical tests show the method can be used to simulate the wave motions.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.