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.

Basic equations for ferroelectrics

A set of new formula of energy functions for ferroelectrics was proposed, and then the new basic equations were derived in this paper. The finite element formulation based on the new basic equations was improved to avoid the equivalent nodal load produced by remnant polarization. With regard to the fundamentals of mathematics and physics, the new energy functions and basic equations are reasonable for the material element of ferroelectrics in finite element analysis.

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 block SPP algorithm for multidimensional tridiagonal equations with optimal message vector length

A parallel strategy for solving multidimensional tridiagonal equations is investigated in this paper. We present in detail an improved version of single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication cost. We show the resulting block SPP can achieve good speedup for a wide range of message vector length (MVL), especially when the number of grid points in the divided direction is large. Instead of only using the largest possible MVL, we adopt numerical tests and modeling analysis to determine an optimal MVL so that significant improvement in speedup can be obtained.

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

Simultaneous three-photon absorption induced ultraviolet upconversion in Pr3+:Y2SiO5 crystal by femtosecond laser irradiation

Near-infrared to ultraviolet upconversion luminescence was observed in the Pr3+ :Y2SiO5 crystal with 120 fs, 800 mn infrared laser irradiation. The observed emissions at around 270 nm and 305 nm could be assigned to 5d -> 4f transitions of Pr3+ ions. The relationship between the upconversion luminescence intensity and the pump power of the femtosecond laser reveals that the UV emission belongs to simultaneous three-photon absorption induced upconversion luminescence. (c) 2007 Elsevier B.V. All rights reserved.

Characteristics of recording and thermal fixing in lithium niobate

We present a theoretical model in which the band-transport equations and the coupled-wave equations are considered to study the two thermal-fixing methods (simultaneous fixing and postfixing) in Fe:LiNbO3. We found that, in simultaneous fixing, the existing ionic-grating affects the writing of the electronic grating by reduction of the coupling gain, and the grating envelope of the fixed-index grating is quite uniform inside the photorefractive crystal in comparison with the method of postfixing. The resulting diffraction efficiency of the fixed-volume grating is dependent mainly on the initial intensity modulation of the two writing beams. A set of experiments is also presented. (C) 1998 Optical Society of America.

Vectorial solution of Kukhtarev equations for doubly doped crystals and optimal choice of recording directions in nonvolatile holographic storage

Vectorial Kukhtarev equations modified for the nonvolatile holographic recording in doubly doped crystals are analyzed, in which the bulk photovoltaic effect and the external electrical field are both considered. On the basis of small modulation approximation, both the analytic solution to the space-charge field with time in the recording phase and in the readout phase are deduced. The analytic solutions can be easily simplified to adapt the one-center model, and they have the same analytic expressions given those when the grating vector is along the optical axis. Based on the vectorial analyses of the band transport model an optimal recording direction is given to maximize the refractive index change in doubly doped LiNbO3:Fe: Mn crystals. (c) 2007 Optical Society of America.

Simultaneous phase-shifting ellipsometry based on grating beamsplitter

Simultaneous phase-shifting ellipsometry based on a grating beamsplitter is presented. In the corresponding setup, an orthogonal grating and analyzer array are used. The latter is composed of four separate analyzers arranged in a 2x2 grid, the polarization axes of which are set to 0, 45, 90, and 135 deg. A mask allows only four diffracted beams of the fist order, having the same optical intensities, to pass. Each beam is incident on one of the analyzers of the array. The intensities of the four beams are simultaneously detected by a quadrant detector. The ellipsometric parameters are obtained using the four intensity signals. The feasibility of simultaneous phase shifting ellipsometry is thus demonstrated. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

Simultaneous three-photon-excited violet upconversion luminescence of Ce3+: Lu2Si2O7 single crystals by femtosecond laser irradiation

We found that Ce3+:Lu2Si2O7 single crystals could be excited at 800 nm by using a femtosecond Ti:sapphire laser. The emission spectra of Ce3+:Lu2Si2O7 crystals were the same for one-photon excitation at 267 nm as for excitation at 800 nm. The emission intensity of Ce3+: Lu2Si2O7 crystals was found to depend on the cube of the laser power at 800 nm, consistent with simultaneous absorption of three 800 nm photons. The measured value of the three-photon absorption cross section is sigma'(3) = 2.44 x 10(-77) cm(6) s(2). (c) 2006 Optical Society of America.