A three‐dimensional Cartesian cut cell method for incompressible viscous flow with irregular domains

A three‐dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer‐aided design platform (J. Comput. Aided. Des. 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE‐based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscillations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L₁ and L _∞ norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer patterns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd.     

The distance function from the boundary in a Minkowski space

Let the space be endowed with a Minkowski structure (that is, is the gauge function of a compact convex set having the origin as an interior point, and with boundary of class ), and let be the (asymmetric) distance associated to . Given an open domain of class , let be the Minkowski distance of a point from the boundary of . We prove that a suitable extension of to (which plays the rôle of a signed Minkowski distance to ) is of class in a tubular neighborhood of , and that is of class outside the cut locus of (that is, the closure of the set of points of nondifferentiability of in ). In addition, we prove that the cut locus of has Lebesgue measure zero, and that can be decomposed, up to this set of vanishing measure, into geodesics starting from and going into along the normal direction (with respect to the Minkowski distance). We compute explicitly the Jacobian determinant of the change of variables that associates to every point outside the cut locus the pair , where denotes the (unique) projection of on , and we apply these techniques to the analysis of PDEs of Monge-Kantorovich type arising from problems in optimal transportation theory and shape optimization.

     

Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.     

How to Extend the Concept of Convexity Cuts to Derive Deeper Cutting Planes

A new type of cutting plane, termed a decomposition cut, is introduced that can be constructed under the same assumptions as the well-known convexity cut. Therefore it can be applied in algorithms (e.g. cutting plane, branch-and-cut) for various problems of global optimization, such as concave minimization, bilinear programming, reverse-convex programming, and integer programming. In computational tests with cutting plane algorithms for concave minimization, decomposition cuts were shown to be superior to convexity cuts.     

Calculation of compressible flows about complex moving geometries using a three‐dimensional Cartesian cut cell method

A three‐dimensional Cartesian cut cell method is described for modelling compressible flows around complex geometries, which may be either static or in relative motion. A background Cartesian mesh is generated and any solid bodies cut out of it. Accurate representation of the geometry is achieved by employing different types of cut cell. A modified finite volume solver is used to deal with boundaries that are moving with respect to the stationary background mesh. The current flow solver is an unsplit MUSCL–Hancock method of the Godunov type, which is implemented in conjunction with a cell‐merging technique to maintain numerical stability in the presence of arbitrarily small cut cells and to retain strict conservation at moving boundaries. The method is applied to some steady and unsteady compressible flows involving both static and moving bodies in three dimensions. Copyright © 2000 John Wiley & Sons, Ltd.     

噪声对滑动移除近似熵的影响

受外强迫和仪器本身的测量误差等因素的影响, 观测数据中经常包含噪声和扰动等一些虚假的信息. 针对这一问题, 本文研究了各种不同噪声对滑动移除近似熵的影响. 研究结果表明, 滑动移除近似熵的检测结果受尖峰噪声和高斯白噪声的影响较小, 意味着其具有很强的抗噪能力, 这为该方法在实际观测资料中的广泛应用提供了坚实的实验基础.     

基于图谱理论的纹理图像分析

图谱理论作为目前模式识别研究的热门方法之一,广泛应用于聚类与分割,但对其进行图像分析,尤其是复杂的纹理图像分析未见报道。将图谱理论引入到图像分析领域,并结合窗口纹理分析方法构造新的纹理分析算法。首先对图像灰度级进行窗口划分得到不同灰度级下的子图像,然后以各子图像作为图的顶点,子图像间的相似度作为图的边,将原图像解析为一幅带权无向图。利用图谱理论的相关思想对该无向图进行分析,可以从中获得纹理粗糙度等特征,从而完成对原始图像的分析。通过对Brodatz图像库的检索实验证明,该方法优于传统纹理分析算法。     

Ultra-high energy cosmic rays threshold in Randers-Finsler space

Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles to arrive at the earth. It is suggested that the lower bound of particle mass is related with the negative second invariant speed in Randers-Finsler space.     

钻石切工溯源方法的研究

首先加工了一套仿钻石样品,通过送检到可溯源到国家基准的计量检定部门测试,用其测试结果验证比例仪的结果可靠性,达到间接溯源的目的.并对测试结果的不确定度进行详细计算.实验表明该方法简便可行,成本也较低.进而形成了一种用于钻石切工溯源的方法,并制定了标准指导溯源工作.使钻石切工分级真正统一到国家基标准.     

铅在铁路岩石边坡创面人工土壤中的迁移特性研究

山区大规模的铁路建设产生了大量的岩石边坡,前期研究表明边坡创面人工土壤受Pb污染,且有中等程度的富集。土壤类型、植被搭配类型是影响Pb迁移特性的重要因素,而目前却未见人工土壤及植被搭配类型对Pb迁移特性影响的相关报道。该研究以铁路岩石边坡创面人工土壤为对象,利用原子吸收分光光度法、红外光谱法分析了人工土壤对Pb的吸附-解吸特性及机制;运用野外人工模拟降雨实验,进一步考察在暴雨径流作用下,Pb在不同植被搭配类型的边坡人工土壤中的迁移过程。结果表明人工土壤对Pb的吸附量随着溶液平衡浓度的增加而急速增加,等温曲线呈“S”型,Freundlich方程能较好地描述人工土壤对Pb的吸附行为,R2为0.91。二次幂函数方程能较好描述NH₄AC对铅的解吸过程,R2为0.96。人工土壤有高岭石红外光谱特征吸收峰,属于高岭石型图谱。高岭石表面-OH、腐殖质表面-OH和-COOH参与吸附作用,置换出H+。人工土壤易将交通运输产生的Pb固定,但又容易再次释放。不同植被搭配类型边坡Pb流失量表现为草本＞草本+灌木＞草本+灌木+乔木。暴雨径流作用下Pb随沉积物相流失是边坡创面人工土壤Pb流失的主体,边坡土壤的侵蚀是导致Pb迁移扩散的主要原因,因此促进边坡植被的恢复,减小边坡人工土壤的侵蚀作用是防止Pb迁移扩散的关键。