Unsteady two dimensional airloads acting on oscillating thin airfoils in subsonic ventilated wind tunnels

The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump

Application of the Central-Difference with Half-Sweep Gauss-Seidel Method for Solving First Order Linear Fredholm Integro-Differential Equations

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half- Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS method has been shown to rapid compared to the FSGS methods. Some numerical tests were illustrated to show that the HSGS method is superior to the FSGS method

An Improved ADI-DQM Based on Bernstein Polynomial for Solving Two-Dimensional Convection-Diffusion Equations

In this article, we presented an improved formulations based on Bernstein polynomial in calculate the weighting coefficients of DQM and alternating direction implicit-differential quadrature method (ADI-DQM) that is presented by (Al-Saif and Al-Kanani (2012-2013)), for solving convection-diffusion equations with appropriate initial and boundary conditions. Using the exact same proof for stability analysis as in (Al-Saif and Al-Kanani 2012-2013), the new scheme has reasonable stability. The improved ADI-DQM is then tested by numerical examples. Results show that the convergence of the new scheme is faster and the solutions are much more accurate than those obtained in literature. Keywords: Differential quadrature method, Convection-diffusion, Bernstein polynomial, ADI, Accuracy

Application of Random Matrix Theory to Multivariate Statistics

This is an expository account of the edge eigenvalue distributions in random matrix theory and their application in multivariate statistics. The emphasis is on the Painlev\'e representations of these distributions

Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions

We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by resummation prescriptions to "cure" the divergence in large orders of perturbation theory. Generalizations of perturbation theory are necessary which include instanton configurations, characterized by nonanalytic factors exp(-a/g) where a is a constant and g is the coupling. In the case of one-dimensional quantum mechanical potentials with two or more degenerate minima, the energy levels may be represented as an infinite sum of terms each of which involves a certain power of a nonanalytic factor and represents itself an infinite divergent series. We attempt to provide a unified representation of related derivations previously found scattered in the literature. For the considered quantum mechanical problems, we discuss the derivation of the instanton contributions from a semi-classical calculation of the corresponding partition function in the path integral formalism. We also explain the relation with the corresponding WKB expansion of the solutions of the Schroedinger equation, or alternatively of the Fredholm determinant det(H-E) (and some explicit calculations that verify this correspondence). We finally recall how these conjectures naturally emerge from a leading-order summation of multi-instanton contributions to the path integral representation of the partition function. The same strategy could result in new conjectures for problems where our present understanding is more limited.Comment: 66 pages, LaTeX; refs. to part II preprint update