Functional Integral Approach in the Theory of Color Superconductivity

In this series of lectures we present the functional integral method for studying the superconducting pairing of quarks with the formation of the diquarks as well as the quark-antiquark pairing in dense QCD. The dynamical equations for the superconducting order parameters are the nonlinear integral equations for the composite quantum fields describing the quark-quark or quark-antiquark systems. These composite fields are the bi-local fields if the pairing is generated by the gluon exchange while for the instanton induced pairing interactions they are the local ones. The expressions of the free energy densities are derived. The binding of three quarks is also discussed.Comment: 21 pages, 2 figures, Lectures at the VIth Vietnam International School in Theoretical Physics, Vung Tau, 27 December 1999 -- 08 January 200

Monte-Carlo simulation of the durability of glass fibre reinforced composite under environmental stress corrosion

The lifetime distribution of glass fibre subject to permanent environmental stress corrosion is very important for assessing the durability and damage tolerance of composites using glass reinforcement. A mechanical model based on the statistics of flaw spectra during stress corrosion and 3D shear lag model is presented. The proposed approach shows that it is possible to identify the influence of stress corrosion properties on the long term durability of glass fibre reinforced composites (GFRP)

An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings