Correlation Functions of a Conformal Field Theory in Three Dimensions

We derive explicit forms of the two--point correlation functions of the $O(N)$ non-linear sigma model at the critical point, in the large $N$ limit, on various three dimensional manifolds of constant curvature. The two--point correlation function, $G(x, y)$, is the only $n$-point correlation function which survives in this limit. We analyze the short distance and long distance behaviour of $G(x, y)$. It is shown that $G(x, y)$ decays exponentially with the Riemannian distance on the spaces $R^2 \times S^1,~S^1 \times S^1 \times R, ~S^2 \times R,~H^2 \times R$. The decay on $R^3$ is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behaviour of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight $\delta=-{1 \over 2}$; we illustrate this using the example of the manifold $S^2 \times R$ whose metric is conformally equivalent to that of $R^3-\{0\}$ up to a reparametrization.Comment: 15 pages, Late

Unsteady transonic aerodynamic and aeroelastic calculations about airfoils and wings

The development and application of transonic small disturbance codes for computing two dimensional flows, using the code ATRAN2, and for computing three dimensional flows, using the code ATRAN3S, are described. Calculated and experimental results are compared for unsteady flows about airfoils and wings, including several of the cases from the AGARD Standard Aeroelastic Configurations. In two dimensions, the results include AGARD priority cases for the NACA 64A006, NACA 64A010, NACA 0012, and MBB-A3 airfoils. In three dimensions, the results include flows about the F-5 wing, a typical wing, and the AGARD rectangular wings. Viscous corrections are included in some calculations, including those for the AGARD rectangular wing. For several cases, the aerodynamic and aeroelastic calculations are compared with experimental results

Role of computational fluid dynamics in unsteady aerodynamics for aeroelasticity

In the last two decades there have been extensive developments in computational unsteady transonic aerodynamics. Such developments are essential since the transonic regime plays an important role in the design of modern aircraft. Therefore, there has been a large effort to develop computational tools with which to accurately perform flutter analysis at transonic speeds. In the area of Computational Fluid Dynamics (CFD), unsteady transonic aerodynamics are characterized by the feature of modeling the motion of shock waves over aerodynamic bodies, such as wings. This modeling requires the solution of nonlinear partial differential equations. Most advanced codes such as XTRAN3S use the transonic small perturbation equation. Currently, XTRAN3S is being used for generic research in unsteady aerodynamics and aeroelasticity of almost full aircraft configurations. Use of Euler/Navier Stokes equations for simple typical sections has just begun. A brief history of the development of CFD for aeroelastic applications is summarized. The development of unsteady transonic aerodynamics and aeroelasticity are also summarized

Computational, unsteady transonic aerodynamics and aeroelasticity about airfoils and wings

Research in the area of computational, unsteady transonic flows about airfoils and wings, including aeroelastic effects is reviewed. In the last decade, there have been extensive developments in computational methods in response to the need for computer codes with which to study fundamental aerodynamic and aeroelastic problems in the critical transonic regime. For example, large commercial aircraft cruise most effectively in the transonic flight regime and computational fluid dynamics (CDF) provides a new tool, which can be used in combination with test facilities to reduce the costs, time, and risks of aircraft development

Transonic unsteady aerodynamic and aeroelastic calculations about airfoils and wings

Research in the area of computational unsteady transonic flows about airfoils and wings, including aeroelastic effects was surveyed. In the last decade, there were extensive developments in computational methods in response to the need for computer codes with which to study fundamental aerodynamic and aeroelastic problems in the critical transonic regime. For example, large commercial aircraft cruise most effectively in the transonic flight regime and computational fluid dynamics (CFD) provides a new tool, which can be used in combination with test facilities to reduce the costs, time, and risks of aircraft development

Studies on vibration of some rib-stiffened cantilever plates

The vibrational mode shapes and frequencies of rib-stiffened skew cantilever plates as determined by holographic interferometry are given. The effects of varying the sweep back angle, rib stiffness and aspect ratio are studied along with the influence of varying the boundary conditions at the root chord on the vibrational behavior of the plates. The study is applicable to investigating the vibrational behavior of stiffened plates often used in the design of guided rockets and missiles

Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers

This paper presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data (MIMD) parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a High Speed Civil Transport type wing-body configuration

ATRAN3S: An unsteady transonic code for clean wings

The development and applications of the unsteady transonic code ATRAN3S for clean wings are discussed. Explanations of the unsteady, transonic small-disturbance aerodynamic equations that are used and their solution procedures are discussed. A detailed user's guide, along with input and output for a sample case, is given

Performance of the Widely-Used CFD Code OVERFLOW on the Pleides Supercomputer

Computational performance studies were made for NASA's widely used Computational Fluid Dynamics code OVERFLOW on the Pleiades Supercomputer. Two test cases were considered: a full launch vehicle with a grid of 286 million points and a full rotorcraft model with a grid of 614 million points. Computations using up to 8000 cores were run on Sandy Bridge and Ivy Bridge nodes. Performance was monitored using times reported in the day files from the Portable Batch System utility. Results for two grid topologies are presented and compared in detail. Observations and suggestions for future work are made