A covariant representation of the Ball–Chiu vertex

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger–Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern–Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball–Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S   of this decomposition is not a one-loop accident, but persists at higher-loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4$N=4$ SYM theory, in the present approach relates to worldline supersymmetry.     

变工况下旋转机械故障跟踪的相空间曲变方法

为实现在工况变化条件下对旋转机械的故障预测, 提出使用相空间曲变和平滑正交分解理论在变工况条件下跟踪旋转机械的故障演化过程. 首先在对目标系统的观测时间序列相空间重构的基础上, 通过量化相空间曲变构建信号损伤演化的跟踪函数, 为弥补累积模型误差和相空间点局部分布概率差异造成的误差, 将时间序列和相空间进行分割, 并以此构建跟踪矩阵; 再利用平滑正交分解方法将跟踪矩阵中分别由实际损伤劣化和工况变化造成的演化趋势进行分离, 根据平滑正交特征值提取出其中能够反映实际故障演化趋势的平滑正交分量; 最后以变转速情况下轴承外环故障退化的仿真信号为例验证算法的有效性. 计算结果表明: 本文提出的算法能够对旋转机械故障的演化趋势实现有效跟踪, 基本排除转速波动造成的工况变化影响. 关键词： 相空间曲变 平滑正交分解 变工况 故障跟踪     

Modeling microstructure evolution of binary systems subjected to irradiation and mechanical loading

We study a change in mechanical properties of binary systems subjected to irradiation influence described by ballistic flux of atomic mixing having regular and stochastic contributions. By using numerical modeling based on the phase field approach we study dynamics of deformation fields in a previously irradiated system and in the binary system deformed during irradiation. An influence of both deterministic and stochastic components of ballistic flux onto both yield strength and ultimate strength is studied. We have found that degradation of mechanical properties relates to the formation of percolating clusters of shear bands. Considering a hardening coefficient we analyze stages of plastic deformation of both initially irradiated alloy and alloy subjected to sustained irradiation. Stability of binary alloy under mechanical loading in the form of shear strain with a constant rate and cyclic deformation is discussed.     

A study of the activation energy of thermal decomposition of irradiated polymers

The ion irradiation of polymeric solids induces numerous modifications in the polymer properties thus increasing their applicability in various fields. The present work looks into the aspect of thermal modifications induced in the irradiated polymers. The kinetics of thermal decomposition of polymers is investigated by using the thermogravimetric (TG) technique. It has been observed that the degradation of polymers is a multi-step process that involves sequential and competing processes, and obeys the Arrhenius kinetics which allows us to connect the rate constant with the absolute temperature and the activation energy. The activation energy of thermal decomposition has been calculated from the TG curves, and its variation with different irradiation doses has been derived.     

Spectral,X-ray diffraction,surface morphological and thermal studies of gamma-irradiated potassium bis(oxalato)zincate(II)dihydrate

ABSTRACT

Potassium bis(oxalato)zincate(II)dihydrate was prepared and characterized. The sample was irradiated with ⁶⁰Co gamma rays up to 900?kGy. Infrared, Raman and photoluminescence spectra, X-ray diffraction pattern, surface morphology by AFM and SEM and non-isothermal decomposition of the complex were studied before and after irradiation. Spectral studies suggested significant radiation damage. X-ray diffraction studies showed reduction in unit cell volume and average crystallite size. Both unirradiated and irradiated samples of the complex belong to the hexagonal crystal system. Surface morphology of the complex changed upon irradiation. Thermal decomposition was enhanced.     

A fast numerical method for harmonic equation based on natural boundary integral

Based on the coupling of the natural boundary integral method and the finite elements method, we mainly investigate the numerical solution of Neumann problem of harmonic equation in an exterior elliptic. Using our trigonometric wavelets and Galerkin method, there obtained stiffness matrix is symmetrical and circulant, which lead us to a fast numerical method based on fast Fourier transform. Furthermore, we do not need to compute the entries of the stiffness matrix. On the other hand, we prove that the numerical solution possesses exponential convergence rate. Especially, examples state that our method still has good accuracy for small j when the solution u ₀(θ) is almost singular.     

Gauss Decomposition with Prescribed Semisimple Part in Quadratic Groups

Quadratic groups, whose definitions depend on form parameters, contain the orthogonal groups, symplectic groups, classical unitary groups and all the classical groups of Dieudonné [4 Dieudonné , J. ( 1963 ). La Géométrie des Groupes Classiques . Berlin , Heidelberg , New York : Springer . [Google Scholar]] as well as those of Bruhat and Tits [2 Bruhat , F. , Tits , J. ( 1972 ). Groupes réductifs sur un corps local I: Donneés radicielles valuées . Publ. Math. IHES 41 : 5 – 251 . [Google Scholar]]. Gauss decomposition with prescribed semisimple part in these groups is presented. As an application, the analog of a conjecture of Thompson is also studied for these groups.