An algebraic index theorem for orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.     

Laser technology application: Deformation and elastic recovery of semi-crystalline polymers

The elastic deformation-recovery and mechanical properties of semi-crystalline polymers (HDPE, LDPE and their blends) were investigated. An optoelectronic technique based on a laser beam was used to analyze the behavior of the samples under radial stress. The laser technology showed that the recovery process develops in two stages. The first one is governed by the elastic component and the second and slower one is controlled by the inelastic component of the material. At low deformation, the overall recovery is attributed to the development of structural micro-domains generated when shearing the amorphous segments of the polymer. The radial Young modulus was also determined and compared to unidirectional measurements. At low deformation both techniques provide very similar values; nevertheless, the radial Young modulus departs significantly from the unidirectional one when increasing the number of cycles of deformation-recovery.     

聚乙烯拉伸过程中晶态变化及形变机理

用红外光谱和X-射线衍射研究了室温拉伸的聚乙烯,结果显示单斜晶存在于室温拉伸的聚乙烯中。对Hendra等关于拉伸过程机理的“微熔融”理论及其所根据实验结果提出异议,而本文的,实验结果支持了Peterlin模型。     

Plastic deformation and performance of engineering polymer materials

The plastic deformation mechanism operating in polymer glasses is analyzed. The whole process consists of two main stages: nucleation of special shear defects, called PSTs (plastic shear transformations), and their disappearance. The important feature of plastic deformation of glasses is the storage of a large amount of internal energy ΔU_def upon straining. Such energy storage is the critical issue for mechanical performance of polymeric material: if the amount of stored energy is high, the appearance of macroscopic failure is very probable while glassy materials collecting a small amount of stored deformation energy are quite ductile. It is proposed that the rate of disappearance of PSTs is a key factor in dissipation of stored deformation energy. A parameter describing the dissipation ability of material upon deformation is introduced.     

PS／LDPE共混体系形变机理的TEM研究

ＰＳ／ＬＤＰＥ共混体系形变机理的ＴＥＭ研究徐世爱，江明（复旦大学高分子科学系、聚合物分子工程实验室，上海，２００４３３）沈静姝（中国科学院北京化学所高分子物理开放实验室）关键词形变机理，银纹，透射电镜，共混物在ＰＳ／ＬＤＰＥ共混体系中加入接枝或嵌段共...     

A theory of flux peaking effect in channeling

The redistribution of the channeled ion flux in the transverse plane has been examined. General formulae describing the flux peaking effect are obtained. Main factors on which the effect depends are investigated. An analysis is made of back-scattering experiments. The study has been made for the axial and planar channeling.     

Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.     

Infinitesimal supersymmetries over Lie groups and their classification for gl(1,1) and sl(1,1)

Infinitesimal supersymmetries over classical Lie groups that are not necessarily induced by a Lie supergroup are described. They yield a notion of supersymmetry that is less rigid than the assumption of a Lie supergroup action but still implies an underlying action of a Lie group. In contrast to Lie supergroups, the arising representation-theoretical Lie supergroups (RTLSG) occur as families associated to Harish–Chandra superpairs. However morphisms of RTLSGs directly correspond to morphisms of Harish–Chandra superpairs. Particular RTLSGs can be derived from the explicit constructions of Lie supergroups given by Kostant and Koszul. The Lie superalgebras $\mathfrak{g}\mathfrak{l}(1,1)$ or $\mathfrak{s}\mathfrak{l}(1,1)$ appearing also in higher dimensional classical Lie superalgebras, provide interesting first examples of RTLSGs. A classification of RTLSGs associated to real and complex $\mathfrak{g}\mathfrak{l}(1,1)$- and $\mathfrak{s}\mathfrak{l}(1,1)$-Harish–Chandra superpairs is given by parameter spaces and complete sets of invariants. The underlying Lie group is assumed to be connected but possibly not simply connected.     

Loading rate and confining pressure effect on dilatancy,acoustic emission,and failure characteristics of fissured rock with two pre-existing flaws

Investigating the dilatancy, acoustic emission and failure characteristics of fissured rock are significant to ensure their geotechnical stability. In this paper, the uniaxial and triaxial compression experiments with AE monitoring under different loading rates were carried out on fissured rock specimens with the same geometrical distribution of two pre-existing flaws. The dilatancy and AE activity of these specimens were discussed, and the effects of the confining pressure and loading rate on the mechanical parameters and failure characteristics were analyzed. The results show that the exponential strength criterion is more suitable than the Mohr–Coulomb strength criterion to characterize the strength characteristics of fissured rock. The crack evolution and failure characteristics of fissured rock specimens are more complicated than those of intact rock specimens. The failure characteristics of the fissured rock follow the tensile shear coalescence model, crack branching occurs with increasing the loading rate, and the multi-section coalescence model is verified with increasing the confining pressure. The phenomena of stress drop and yield platform usually occur after the dilatancy onset, the specimen does not fail instantaneously, and the propagation and coalescence of cracks cause a sharp increase in the AE signals, circumferential strain, and volumetric strain.     

降雨条件下固体废弃物边坡变形及破坏模式试验研究

利用室内模型试验及稳定性分析的手段 ,研究在降雨作用下高速公路通过的城市固体废弃物路堑边坡变形特征及破坏模式 ,分析了边坡各部位在降雨作用下变形量的变化规律 ,得出变形过程的 5个阶段 ,给出了固体废弃物边坡主要以溜坍或滑塌、坡面冲刷及滑坡 3种破坏形式 ,并提出了治理建议