Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Three-dimensional finite element analysis of composites with coated spherical inclusions

A three-dimensional finite element analysis has been used to determine the internal stresses in a three-phase composite. The stresses have been determined for a variety of interphase properties, the thicknesses of the interphase and the volume fractions of particles. Young's modulus has been calculated from a knowledge of these stresses and the applied deformation. The calculations show that stress distributions in the matrix and the mechanical properties are sensitive to the interphase property in the three-phase composites. The interfacial stresses in the three-dimensional analysis are in agreement with results obtained by an axisymmetric analysis. The predicted bulk modulus in three-dimensional analysis agrees well with the theoretical solution obtained by Qui and Weng, but it presents a great divergence from that in axisymmetric analyses. An investigation indicates that this divergence may be caused by the difference in the unit cell structure between two models. A comparison of the numerically predicted bulk and shear modulus for two-phase composites with the theoretical results indicates that the three-dimensional analysis gives quite satisfactory results.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

High Order Multi-Moment Constrained Finite Volume Method. Part I: Basic Formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously. (C) 2007 Optical Society of America

Electron tunneling through a planar single barrier in HgTe quantum wells with inverted band structures

We present a theoretical study on the electron tunneling through a single barrier created in a two-dimensional electron gas (2DEG) and quantum spin Hall (QSH) bar in a HgTe/CdTe quantum well with inverted band structures. For the 2DEG, the transmission shows the Fabry-Perot resonances for the interband tunneling process and is blocked when the incident energy lies in the bulk gap of the barrier region. For the QSH bar, the transmission gap is reduced to the edge gap caused by the finite size effect. Instead, transmission dips appear due to the interference between the edge states and the bound states originated from the bulk states. Such a Fano-like resonance leads to a sharp dip in the transmission which can be observed experimentally.

Quantum phase transitions in the S=1/2 distorted diamond chain

By means of the second derivative of the ground-state and first-excited energy, the quantum phase transitions (QPTs) for the distorted diamond chain (DDC) with ferromagnetic and antiferromagnetic frustrated interactions and the trimerized case are investigated, respectively. Our results show the plentiful quantum phases owing to the spin interaction competitions in the model. Meanwhile, by using the transfer-matrix renormalization-group technique, we study the two-site thermal entanglement of the DDC model in the thermodynamic limit for a further understanding of the QPTs.

Quantum efficiency of GaAs/AlGaAs thin films with two-dimensional photonic crystals

The optical properties of GaAs/AlGaAs thin films with photonic crystals were investigated by measuring their photoluminescence spectra. The spectral intensities, lifetimes, and quantum efficiencies decreased greatly compared with those in blank material without photonic crystals. The quantum efficiencies in the material were also calculated from spectral intensities and lifetimes and the quantum efficiencies calculated from those two methods agreed with each other to some extent.

Classical two-site fidelity and quantum phase transitions in the Ising model and the extended Hubbard model

In this Letter, the classical two-site-ground-state fidelity (CTGF) is exploited to identify quantum phase transitions (QPTs) for the transverse field Ising model (TFIM) and the one-dimensional extended Hubbard model (EHM). Our results show that the CTGF exhibits an abrupt change around the regions of criticality and can be used to identify QPTs in spin and fermionic systems. The method is especially convenient when it is connected with the density-matrix renormalization group (DMRG) algorithm. (C) 2008 Elsevier B.V. All rights reserved.

Spin states in semiconductor quantum dot with a single magnetic ion

We investigate theoretically CdTe quantum dots containing a single Mn2+ impurity, including the sp-d exchange interaction between carriers and the magnetic ion and the short-range exchange interaction between electron and hole. We find anticrossing behaviors in the energy spectrum of the electron-hole (e-h) pair that arise from the interplay between exchange interactions and the magnetic field. In addition to the s-d exchange interaction, we find that other mechanisms inducing the anticrossings become important in the strong heavy hole-light hole (hh-lh) mixing regime. The transition strengths between the states with spin projection of Mn2+ ion S-z not equal -5/2 (S-z = -5/2) decrease (increase) with increasing magnetic fields due to the alignment of the Mn2+ spin. The spin splitting of the e-h pair states depends sensitively on the external magnetic and electric field, which reveals useful information about the spin orientation and position of the magnetic ion. Meanwhile, the manipulation of the position of the magnetic ion offers us a way to control the spin splitting of the carriers. (C) 2008 Elsevier B.V. All rights reserved.

Coherence loss and recovery of an electron spin coupled inhomogeneously to a one-dimensional interacting spin bath: An adaptive time-dependent density-matrix renormalization group study

Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, are studied using the adaptive time-dependent density-matrix renormalization group method. It is found that the interplay of the coupling inhomogeneity and the transverse intrabath interactions results in two qualitatively different coherence evolutions, namely, a coherence-preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by an electron-spin flip at time tau exhibit stable recoherence pulse sequence for the periodic evolution and a single peak at root 2 tau for the decoherence evolution, respectively. With the diagonal intrabath interaction included, the specific feature of the periodic regime is kept, while the root 2 tau-type echo effect in the decoherence regime is significantly affected. To render the experimental verifications possible, the Hahn echo envelope as a function of tau is calculated, which eliminates the inhomogeneous broadening effect and serves for the identification of the different status of the dynamic coherence evolution, periodic versus decoherence.

Mn-including InAs quantum dots fabricated by Mn implantation

Mn-including InAs quantum dots (QDs) were fabricated by Mn-ion implantation and subsequent annealing. The optical, compositional, and structural properties of the treated samples were analyzed by photoluminescence (PL) and microscopy. Energy dispersive X-ray (EDX) results indicate that Mn ions diffused from the bulk GaAs into the InAs QDs during annealing, and the diffusion appears to be driven by the strain in the InAs QDs. The temperature dependence of the PL of Mn-including InAs QD samples exhibits QDs PL characteristics. At the same time, the heavy Mn-including InAs QD samples have ferromagnetic properties and high T-c. (c) 2008 Elsevier B.V. All rights reserved.

A fully three-dimensional atomistic quantum mechanical study on random dopant-induced effects in 25-nm MOSFETs

A fully 3-D atomistic quantum mechanical simulation is presented to study the random dopant-induced effects in nanometer metal-oxide-semiconductor field-effect transistors. The empirical pseudopotential is used to represent the single particle Hamiltonian, and the linear combination of bulk band method is used to solve the million atom Schrodinger equation. The gate threshold fluctuation and lowering due to the discrete dopant configurations are studied. It is found that quantum mechanical effects increase the threshold fluctuation while decreasing the threshold lowering. The increase of threshold fluctuation is in agreement with the researchers' early study based on an approximated density gradient approach. However, the decrease in threshold lowering is in contrast with the density gradient calculations.

Confined LO-phonon-assisted magnetotunneling in a parabolic quantum well with double barriers

The confined longitudinal-optical phonon-assisted tunneling through a parabolic quantum well with double barriers in a magnetic field perpendicular to the interfaces is studied theoretically based on a dielectric continuum model. The numerical results show that the applied magnetic field sharpens and heightens the phonon-assisted tunneling peaks in agreement with experimental observation. Furthermore, the phonon-assisted magnetotunneling peaks shift towards the higher biases as the magnetic field increases. In contrast to the results for a rectangular quantum well, the ratio of peak to valley of the phonon-assisted tunneling is larger for the wider well case. It also indicates that the phonon-assisted tunneling current peaks can be easily observed for a wider parabolic quantum well. (C) 2008 Published by Elsevier B.V.