Localization effects and measure source terms in numerical schemes for balance laws

This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

     

Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Probability Interpretation of the Integral of Fractional Order

We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-isothermal short-range-order kinetics of binary alloys as influenced by solute-vacancy complexes

A model describing the roles of bound and unbound vacancies is proposed in order to predict defect decay and short-range-order kinetics of quenched binary alloys during linear heating experiments. This is an alternative treatment of a previous approach. The model has been applied to the differential scanning calorimetry (DSC) curves of Cu-5 at.% Zn quenched from different temperatures. An expression to calculate the activation energy for migration of solute-vacancy complexes was also developed which make use of DSC trace data. A value of 89.12±0.32 kJ mol^-1 was obtained for the above alloy. The relative contribution of bound and unbound vacancies to partition of effective activation energy corresponding to the ordering process as influenced by quenching temperature was also assessed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Raman properties embeddedof GaSb nanoparticlesin SiO2 films

The Raman shifts of nanocrystalline GaSb excited by an Ar^ ion laser at wavelengths 514.5, 496.5, 488.0, 476.5,and 457.9nm are studied by an SPEX-1403 laser Raman spectrometer respectively, and they are explained by phonon confinement, tensile stress, resonant Raman scattering and quantum size effects. The Stokes and anti-Stokes Raman spectra of GaSb nanocrystals strongly support the Raman feature of GaSb nanocrystals. The calculated optical spectra compare well with experimental data on Raman scattering GaSb nanocrystals.     

Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

Au(111)上烷烃硫醇SAMs表面应力的理论研究

应用已建立的关于金属表面吸附层中表面应力的统计热力学理论 ,计算了Au(111)上烷烃硫醇SAMs的表面应力及其与烷烃硫醇链长、吸附覆盖度的定量关系 .计算结果与实验相符 ,较好地解释了Berger等人的实验结果 ,特别是解决了在表面应力符号性质上理论与实验的矛盾 .在表面吸附层应力的多种物理起源中 ,通过底物的分子间作用力有着决定性的贡献 ,揭示了分子的吸附能间接地起着重要作用 .这与阴离子化学吸附体系Cl-/Au(111)的有关研究结果相同 .     

The study of the influence of uniaxial stress on impurity complexes in silicon

The influence of external uniaxial stress on the different indium-donor complexes in silicon has been studied using the perturbed γ –γ angular correlation (PAC) method. Such effect of an applied stress is detected by means of the probe atoms situated at different complexes in the sample. The current results showed that the responses of the probes in an extrinsic silicon samples are found to be dissimilar for the same value of stress. Such change in the local environments of the probe atoms could be associated with the various strain field created by the implantations of varied size of impurities. The phosphorous implantation in silicon has even lead to the complete absence of observable effect of the applied stress suggesting significant lose of the elasticity of the sample.