Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

Three-dimensional integrable models and associated tangle invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.     

Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry

Calibration of the relationship between height and phase is of uttermost importance to perform accurate 3D measurements in phase measurement profilometry. This work reports a different approach to this problem by first looking at the analytical expression for this relationship and determining the regime spanned by the fringe analysis method. The conclusions thus ascertained, amply justify confronting the analytical expression with a simple normalization procedure of the experimental data, with a remarkable matching between both results. In light of this, a linear calibration procedure with just one plane is proposed and verified experimentally.     

Furtivity and Masking Problems in Time-Dependent Electromagnetic Obstacle Scattering

In this paper, we consider furtivity and masking problems in time-dependent three-dimensional electromagnetic obstacle scattering. That is, we propose a criterion based on a merit function to minimize or to mask the electromagnetic field scattered by a bounded obstacle when hit by an incoming electromagnetic field and, with respect to this criterion, we drive the optimal strategy. These problems are natural generalizations to the context of electromagnetic scattering of the furtivity problem in time-dependent acoustic obstacle scattering presented in Ref. 1. We propose mathematical models of the furtivity and masking time-dependent three-dimensional electromagnetic scattering problems that consist in optimal control problems for systems of partial differential equations derived from the Maxwell equations. These control problems are approached using the Pontryagin maximum principle. We formulate the first-order optimality conditions for the control problems considered as exterior problems defined outside the obstacle for systems of partial differential equations. Moreover, the first-order optimality conditions derived are solved numerically with a highly parallelizable numerical method based on a perturbative series of the type considered in Refs. 2–3. Finally, we assess and validate the mathematical models and the numerical method proposed analyzing the numerical results obtained with a parallel implementation of the numerical method in several experiments on test problems. Impressive speedup factors are obtained executing the algorithms on a parallel machine when the number of processors used in the computation ranges between 1 and 100. Some virtual reality applications and some animations relative to the numerical experiments can be found in the website http://www.econ.unian.it/recchioni/w10/.     

A 3D-BPP approach for optimising stowage plans and terminal productivity

This paper addresses the problem of determining stowage plans for containers in a ship, that is the so-called master bay plan problem (MBPP).     

Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups

In this paper, the author computes canonical connections and KobayashiNomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.     

Numerical simulation of soft palate movement and airflow in human upper airway by fluid-structure interaction method

In this paper, the authors present airflow field characteristics of human upper airway and soft palate movement attitude during breathing. On the basis of the data taken from the spiral computerized tomography images of a healthy person and a patient with Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS), three-dimensional models of upper airway cavity and soft palate are reconstructed by the method of surface rendering. Numerical simulation is performed for airflow in the upper airway and displacement of soft palate by fluid-structure interaction analysis. The reconstructed three-dimensional models precisely preserve the original configuration of upper airways and soft palate. The results of the pressure and velocity distributions in the airflow field are quantitatively determined, and the displacement of soft palate is presented. Pressure gradients of airway are lower for the healthy person and the airflow distribution is quite uniform in the case of free breathing. However, the OSAHS patient remarkably escalates both the pressure and velocity in the upper airway, and causes higher displacement of the soft palate. The present study is useful in revealing pathogenesis and quantitative mutual relationship between configuration and function of the upper airway as well as in diagnosing diseases related to anatomical structure and function of the upper airway. The project supported by the National Natural Science Foundation of China (10672036, 10472025 and 10421002), the Natural Science Foundation of Liaoning Province (20032109). English text was polished by Yunming Chen.     

山姜素与人血清白蛋白相互作用的荧光光谱法研究

利用荧光光谱法和紫外-可见光谱法研究了山姜素与人血清白蛋白(HSA)之间的相互作用。证实了山姜素对HSA的荧光猝灭为动态猝灭过程,并测定了不同温度下的猝灭常数; 根据Fōrster非辐射能量转移理论,计算出山姜素在蛋白质中的结合位置与色氨酸残基间的距离为4.05 nm; 由求得的热力学参数,推断了山姜素与HSA之间主要靠疏水作用力结合;用三维荧光光谱及同步荧光光谱技术探讨了山姜素对HSA构象的影响。     

基于不同光谱技术的原油样品的荧光分析

应用同步扫描、三维发射以及目前石油荧光仪所采用的二维发射荧光分析技术对胜利油田15个井区25种原油样品在10-4 g·L-1～10 g·L-1浓度范围内进行了光谱采集,对比分析了不同光谱技术所获取的光谱信息与浓度之间的相应关系。结果表明,对于原油这种多组分样品,二维发射光谱难以满足分析要求;三维光谱信息丰富但数据采集与提取困难。同步扫描光谱具有简单快捷、光谱特征丰富明显、干扰小等特点,选择Δλ为40 nm获得的原油同步扫描光谱可反映三维光谱的主要信息。与二维发射光谱和三维光谱相比,同步荧光法在原油样品分析中显现出较大优势和发展空间,可望发展成为石油录井中对岩屑岩芯样品含油量的定量分析的新方法。