Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.     

Perpendicular Dissections of Space

For each pair (Q _i ,Q _j ) of reference points and each real number r there is a unique hyperplane h \perp Q _i Q _j such that d(P,Q _i ) ² - d(P,Q _j ) ² = r for points P in h . Take n reference points in d -space and for each pair (Q _i ,Q _j ) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real, additive gain graph (this is a graph with an additive real number associated invertibly to each edge) whose set of balanced flats has the same structure as the intersection semilattice. We examine the requirements for genericity, which are related to behavior at infinity but remain mysterious; also, variations in the construction rules for perpendiculars. We investigate several particular arrangements with a view to finding the exact numbers of faces of each dimension. The prototype, the arrangement of all perpendicular bisectors, was studied by Good and Tideman, motivated by a geometric voting theory. Most of our particular examples are suggested by extensions of that theory in which voters exercise finer discrimination. Throughout, we propose many research problems. Received July 20, 2000, and in revised form September 29, 2001, and October 12, 2001. Online publication March 4, 2002.     

Triples of arrangements and local systems

For a triple of complex hyperplane arrangements, there is a well-known long exact sequence relating the cohomology of the complements. We observe that this result extends to certain local coefficient systems, and use this extension to study the characteristic varieties of arrangements. We show that the first characteristic variety may contain components that are translated by characters of any order, thereby answering a question of A. Suciu.

     

Characterization of rankings generated by linear discriminant analysis

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.     

On active redundancy allocation for coherent systems—from the viewpoint of minimal cut decomposition

This paper deals with coherent systems with one active redundancy. For systems with the subclass of minimal cuts associated with one component covering that of another, assigning the redundancy to the former component is proved to bring forth a more reliable redundant system. As for symmetric systems with lower tail permutation decreasing component lifetimes, allocating the redundancy to the less reliable component results in a longer system lifetime. Several numerical examples are also presented to illustrate the new findings.     

Real Hypersurfaces Having Many Pseudo-hyperplanes

Abstract

Let nand dbe natural integers satisfying n ≥ 3 and d ≥ 10. Let Xbe an irreducible real hypersurface Xin ? ⁿ of degree dhaving many pseudo-hyperplanes. Suppose that Xis not a projective cone. We show that the arrangement ? of all d ? 2 pseudo-hyperplanes of Xis trivial, i.e., there is a real projective linear subspace Lof ? ⁿ (?) of dimension n ? 2 such that L ? Hfor all H ∈ ?. As a consequence, the normalization of Xis fibered over ?¹in quadrics. Both statements are in sharp contrast with the case n = 2; the first statement also shows that there is no Brusotti-type result for hypersurfaces in ? ⁿ , for n ≥ 3.     

基态H_2~－（X~2_U~＋）的ACQM计算

基态Ｈ_２~－（Ｘ~2_U~＋）的ＡＣＱＭ计算俞华根（中国科学院，成都有机所，６１００６５）关键词：排列通道量子力学，通道波函数，１９７７年，Ｌｅｖｉｎ和Ｋｒｇｅｒ￣［１］首次将排列通道量子力学（ＡＣＱＭ）方法用于计算和Ｈ＿２基态势能曲线后，经改进的ＡＣ?..     

Chemical metrology in New Zealand

Recent developments in international trade will have a significant impact on New Zealand’s measurement infrastructure, especially for chemical metrology. This article describes the background to these developments and outlines the activities of the Measurement Standards Laboratory, New Zealand’s National Metrology Institute, in response to these developments.     

Heterosynthons in molecular complexes of azopyridine and 1,2-bis(4-pyridyl)ethylene with dicarboxylic acids

A series of co-crystals of azaaromatic molecule with the present of dicarboxylic acid, [SA·BPE], [FA·AZP], [AA·BPE], [AA·AZP], [SEA·AZP] and [OA·AZP] (BPE=1,2-bis(4-pyridyl)ethylene, AZP=azopyridine, SA=succinic acid, FA=fumaric acid, AA=adipic acid, SEA=sebacic acid, OA=oxalic acid), have been synthesized for the regularity investigation of their supramolecular alignments driven by hydrogen bonding. It is significant for the design and synthesis of supramolecular co-crystals with multiple components. For linear molecules with recognition sites on both ends, the stacking regularity of the molecules in the co-crystals is proposed that the interlaced arrangement (motif III) is preferred when the size of the azaaromatic molecule is comparable with that of dicarboxylic acid and the inclined arrangement (motif II) is adopted when the length of azaaromatic molecule is much different from those of dicarboxylic acids.