粘性物质中正激波稳定性分析

用线性稳定性理论,分析粘性物质中的正激波稳定性问题.粘性物质中任意强度的一维激波,其稳定性问题可归结为处理复数范围内的特征值问题,该特征值问题由两个一阶常微分方程及一个二阶常微分方程构成.这些常微分方程的系数依赖于流动的基本流场的物理量及其梯度.所获得的特征值问题由一个四阶精度的有限差分离散求解.分析考虑物质粘性的金属铝中的正激波稳定性,可以看出,正激波运动是稳定的,并且激波速度对波前和波后的小扰动量的衰减有相反的作用,而物质粘性有致稳的作用.     

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.     

Grad theory and extended thermodynamics

Grad-type approaches introduce an ansatz involving tensor Hermite functions with coefficients expresed in terms of moments of the ansatz. This formalism in usual form yields terms linear in first-order spatial derivatives in kinetic equations for the moments. Such terms disagree with alternative statistical derivations and phenomenological arguments. This disagreement is removed if different ansatzes are used to calculate entropy and moment equations. These are non-unique, and so Grad theory, while providing theoretical expressions for transport coefficients, does not serve uniquely to determine the structure of phenomenological equations.     

Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.     

Diffusion Lattice Boltzmann Scheme on a Orthorhombic Lattice

We present a diffusion lattice Boltzmann (DLB) scheme which is derived from first principles. As opposed to the traditional lattice BGK schemes the DLB is valid for orthorhombic lattices and it has two eigenvalues of the collision operator. It is shown that the diffusion coefficient depends only on one eigenvalue of the collision operator. Hence, the DLB scheme can be optimized with means of the additional eigenvalue of the collision operator and with different lattice spacing along the principal axes. The properties of the DLB scheme concerning consistency, stability, and accuracy are studied with eigenmode analysis. This analysis shows that the DLB scheme is consistent with diffusion for a wide range of diffusion coefficients, it has unconditional stability, and that it has third-order accuracy. Furthermore, it is shown that accuracy is improved by setting the additional eigenvalue to zero and by densifying the lattice spacing along the direction of the density gradient.     

A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems

This paper investigates optimization of the least eigenvalue of ?Δ with the constraint of one-dimension Hausdorff measure of Dirichlet boundary. We propose the boundary piecewise constant level set (BPCLS) method based on the regularity technique to combine two types of boundary conditions into a single Robin boundary condition. We derive the first variation of the least eigenvalue w.r.t. the BPCLS function and propose a penalty BPCLS algorithm and an augmented Lagrangian BPCLS algorithm. Numerical results are reported for experiments on ellipse and L-shape domains.     

Sparse Density Estimation with Measurement Errors

This paper aims to estimate an unknown density of the data with measurement errors as a linear combination of functions from a dictionary. The main novelty is the proposal and investigation of the corrected sparse density estimator (CSDE). Inspired by the penalization approach, we propose the weighted Elastic-net penalized minimal ℓ2-distance method for sparse coefficients estimation, where the adaptive weights come from sharp concentration inequalities. The first-order conditions holding a high probability obtain the optimal weighted tuning parameters. Under local coherence or minimal eigenvalue assumptions, non-asymptotic oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with a high probability. Some numerical experiments for discrete and continuous distributions confirm the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed in a meteorology dataset. It shows that our method has potency and superiority in detecting multi-mode density shapes compared with other conventional approaches.     

Eigenvalues of structures with uncertain elastic boundary restraints

The eigenvalue problems of structures with random elastic boundary supports are studied in this paper. Using the perturbation method, the differential equations including stochastic distributed parameters and random boundary conditions that govern the eigenproblems are transformed to a series of deterministic differential equations and boundary conditions. Then the differential equations and boundary conditions are discretized utilizing the finite element method (FEM). This process is easy to be implemented since the resulting perturbation equations with different orders own the same FEM meshes. The first-order and second-order sensitivities of eigenvalues are derived through solving the deterministic algebraic equations. Upon determining these sensitivities of eigenvalues, the approximate statistic expressions of random eigenvalues considering uncertain elastic boundary supports are established. At the end, several numerical examples are given to illustrate the application and effectiveness of the present method. Comparison of the present numerical results with those from the Monte-Carlo simulation method verifies the accuracy of the developed method.     

Parametric excitation of two internally resonant oscillators

The response of two-degree-of-freedom systems with quadratic non-linearities to a principal parametric resonance in the presence of two-to-one internal resonances is investigated. The method of multiple scales is used to construct a first-order uniform expansion yielding four first-order non-linear ordinary differential (averaged) equations governing the modulation of the amplitudes and the phases of the two modes. These equations are used to determine steady state responses and their stability. When the higher mode is excited by a principal parametric resonance, the non-trivial steady state value of its amplitude is a constant that is independent of the excitation amplitude, whereas the amplitude of the lower mode, which is indirectly excited through the internal resonance, increases with the amplitude of the excitation. However, in addition to Poincaré-type bifurcations, this response exhibits a Hopf bifurcation leading to amplitude- and phase-modulated motions. When the lower mode is excited by a principal parametric resonance, the averaged equations exhibit both Poincaré and Hopf bifurcations. In some intervals of the parameters, the periodic solutions of the averaged equations, in the latter case, experience period-doubling bifurcations, leading to chaos.     

A NUMERICAL METHOD FOR SCATTERING FROM ACOUSTICALLY SOFT AND HARD THIN BODIES IN TWO DIMENSIONS

This paper presents a numerical method for predicting the acoustic scattering from two-dimensional (2-D) thin bodies. Both the Dirichlet and Neumann problems are considered. Applying the thin-body formulation leads to the boundary integral equations involving weakly singular and hypersingular kernels. Completely regularizing these kinds of singular kernels is thus the main concern of this paper. The basic subtraction-addition technique is adopted. The purpose of incorporating a parametric representation of the boundary surface with the integral equations is two-fold. The first is to facilitate the numerical implementation for arbitrarily shaped bodies. The second one is to facilitate the expansion of the unknown function into a series of Chebyshev polynomials. Some of the resultant integrals are evaluated by using the Gauss-Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral. The numerical implementation basically includes only two parts, one for evaluating the ordinary integrals and the other for solving a system of algebraic equations. Thus, the current method is highly efficient and accurate because these two solution procedures are easy and straightforward. Numerical calculations consist of the acoustic scattering by flat and curved plates. Comparisons with analytical solutions for flat plates are made.     

Relativistic Hydrodynamics of Color-Flavor Locking Phase with Spontaneous Symmetry Breaking

We study the hydrodynamics of color-flavor locking phase of three flavors of light quarks in high density QCD with spontaneous symmetry breaking. The basic hydrodynamic equations are presented based on the Poisson bracket method and the Goldstone phonon and the thermo phonon are compared. The dissipative equations are constructed in the frame of the first-order theory and all the transport coefficients are also defined, which could be looked on as the general case including the Landau's theory and the Eckart's theory.     

Frequency-dependent properties of the hydrogen atom: A generalized eigenvalue equation approach

The time-independent first-order perturbation equations which arise on considering the response of a system to a harmonic time-dependent perturbation are solved by using an expansion in terms of a complete discrete set of solutions of a generalized eigenvalue equation. Explicit formulae are obtained for several frequency-dependent properties of the hydrogen atom.     

An efficient approach toward guided mode extraction in two-dimensional photonic crystals

A rigorous, fast and efficient method is proposed for analytical extraction of guided defect modes in two-dimensional photonic crystals, where each Bloch spatial harmonic is expanded in terms of Hermite-Gauss functions. This expansion, after being substituted in Maxwell’s equations, is analytically projected in the Hilbert space spanned by the Hermite-Gauss basis functions, and then a new set of first order coupled linear ordinary differential equations with non-constant coefficients is obtained. This set of equations is solved by employing successive differential transfer matrices, whereupon defect modes, i.e. the guided modes propagating in the straight line-defect photonic crystal waveguides and coupled resonator optical waveguides, are analytically derived. In this fashion, the governing differential equations are converted into an algebraic and easy to solve matrix eigenvalue problem. Thanks to the analyticity of the proposed approach, the eigenmodes of these structures can be extracted very quickly. The validity of the obtained results is however justified by comparing them to those derived by using the standard finite-difference time-domain method.     

Natural oscillations of multidimensional systems nonlinear in the spectral parameter

A new method of solving the generalized vector self-conjugated Sturm-Liouville boundary value problems with the boundary conditions of the first kind is proposed and developed. The iterative algorithm is based on a constructive procedure of introduction of a small parameter and an efficient correction of the desired eigenvalue. The matrix coefficients of the equations are assumed to be nonlinearly dependent on the spectral parameter. The criterion of proximity is introduced, and it is shown that this method has an accelerated convergence of the second order with respect to a small parameter for a reasonably close initial approximation. Test examples are considered.     

Lattice Boltzmann modeling of microchannel flow in slip flow regime

We present the lattice Boltzmann equation (LBE) with multiple relaxation times (MRT) to simulate pressure-driven gaseous flow in a long microchannel. We obtain analytic solutions of the MRT-LBE with various boundary conditions for the incompressible Poiseuille flow with its walls aligned with a lattice axis. The analytical solutions are used to realize the Dirichlet boundary conditions in the LBE. We use the first-order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel. We validate the LBE results using the compressible Navier–Stokes (NS) equations with a first-order slip velocity, the information-preservation direct simulation Monte Carlo (IP-DSMC) and DSMC methods. As expected, the LBE results agree very well with IP-DSMC and DSMC results in the slip velocity regime, but deviate significantly from IP-DSMC and DSMC results in the transition-flow regime in part due to the inadequacy of the slip velocity model, while still agreeing very well with the slip NS results. Possible extensions of the LBE for transition flows are discussed.     

Fluctuations of Principal Eigenvalues and Random Scales

We investigate the principal Dirichlet eigenvalue of the Laplacian with soft Poissonian obstacles in large boxes of , d≥ 2. With the help of our recent version of the method of enlargement of obstacles [18], we derive quantitative confidence intervals for these eigenvalues. We also provide less quantitative estimates, which however point out the correct size of fluctuations, and indicate a stiffness in their behavior. In the two-dimensional case we derive geometric controls, which relate these eigenvalues to certain empty circular droplets. Our results also have natural applications to the study of the location of minima of certain intermittent random variational problems, motivated by [13, 17]. Received: 13 June 1996 / Accepted: 10 March 1997     

The Cartan-Einstein Unification with Teleparallelism and the Discrepant Measurements of Newton's Constant G

We show that in 1929 Cartan and Einstein almost produced a theory in which the electromagnetic (EM) field constitutes the time-like 2-form part of the torsion of Finslerian teleparallel connections on pseudo-Riemannian metrics. The primitive state of the theory of these connections would not, and did not, permit Cartan and Einstein to realize how their torsion field equations contained the Maxwell system and how the Finslerian torsion contains the EM field. Cartan and Einstein discussed curvature field equations, though failing to focus on the fact that teleparallelism automatically implies gravitational field equations with torsion terms as source, both in first and second order. We further show that the first-order contribution of the EM field to the source of the gravitational field may play havoc with the remeasurement of Newton's gravitational constant, even if the experiment is electrically grounded. These results are also used as support for the thesis that there is an alternative to the present way of dealing with the great theoretical questions of physics. On the practical side, the inconveniences faced in measuring G may be greatly compensated by the possibility of manipulating spacetime with electric fields at the first-order level.     

Spectrum of a Problem of Elasticity Theory in the Union of Several Infinite Layers

The essential spectrum of the Dirichlet problem for the system of Lamé equations in a three-dimensional domain formed by three mutually perpendicular elastic layers occupies the ray [Λ_?,+∞). The lower bound Λ_? > 0 is the least eigenvalue (its existence is established) of the problem of elasticity theory in an infinite two-dimensional cross-shaped waveguide. It is proved that the discrete spectrum of the spatial problem is nonempty. Other configurations of layers and the scalar problem of the junction of quantum waveguides are also considered.     

基于改进的自动散点控制回归算法的遥感影像相对辐射归一化

多时相遥感影像的相对辐射归一化是进行变化检测或拼接不可缺少的步骤。针对现有方法的不足,以自动散点控制回归(Automatic scattergram-controlled regression,ASCR)技术为基础,提出了一种改进的ASCR算法(Im-proved automatic scattergram-controlled regression,IASCR)。它的核心思想是首先利用粗剔除和主成分分析的方法选择占主体信息量的“未变化”像元,然后再利用最小二乘法确定回归方程,对多时相遥感影像进行归一化。以北京地区的多时相TM影像为实验数据对其进行归一化,并与ASCR法、全景简单线性回归法(Simple regression)、暗-亮(Dark setbright set)归一化法、伪不变特征归一化法(Pseudo-invariant feature)的结果进行了比较。实验结果表明,IASCR算法是解决多时相遥感影像辐射归一化问题的有效手段。     

Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains

We consider the Dirichlet eigenvalue problem for the Laplace operator on a variable nonsmooth domain. We extend a result of Lupo and Micheletti concerning the structure of the set of domain perturbations which leave the multiplicity of an eigenvalue unchanged, and we study the set of perturbations which leave a certain eigenvalue unchanged.