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

Two Dimensional Quantum Chromodynamics on a Cylinder

We study two dimensional Quantum Chromodynamics with massive quarks on a cylinder in a light--cone formalism. We eliminate the non--dynamical degrees of freedom and express the theory in terms of the quark and Wilson loop variables. It is possible to perform this reduction without gauge fixing. The fermionic Fock space can be defined independent of the gauge field in this light--cone formalism.Comment: 8 pages, UR-128

Does India attain self sufficiency in Food production

Food production has been one of the major concerns for Indian political climate. Major agricultural changes and policies were initiated to bring more agricultural productivity in India. Union Government also strives to bring more growth in Agricultural sector through five year plan initiations. Yet, result seems to be slower agricultural growth and lack of proper vision & implementation. Major concerns like water availability, improper distribution & water management, pollution, increasing population, rural migration to urban, economic diversion towards other sectors, and increasing rural poverty are in increasing trend. Authors bring statistical evidence for above mentioned concerns and decision makers to consider these issues critically for any policy initiations. Authors stress that unless agricultural productivity increases, average Indian poverty statistics will not reduce. By 2030, India will reach first in world population, might also face severe food crisis. It’s now time for Indian government to rethink on their economic policies to bring life for dieing agricultural sector.Indian agriculture, Food production, Agricultural growth, future of Indian agriculture, Sustainable Agricultural development

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

Novel flow apparatus for investigating shear-enhanced crystallization and structure development in semicrystalline polymers

An instrument to study the effects of shearing on the crystallization process in semicrystalline polymers is described. It can impose transient stresses similar to those encountered in polymer processing and provides in situ monitoring of microstructure development during and after cessation of flow. Box-like wall shear stress profiles (rise and fall times under 50 ms with maximum wall shear stress on the order of 0.1 MPa) can be applied for controlled durations. A unique feature of our device is that it accommodates a wide variety of real-time probes of structure such as visible and infrared polarimetry and light and x-ray scattering measurements. The design also allows us to retrieve the sample for ex situ optical and electron microscopy. Data are acquired with millisecond resolution enabling us to record the extent of shear deformation of the polymer melt during the pressure pulse. Our device works with small sample quantities (as little as 5 g; each experiment takes ~ 500 mg) as opposed to the kilogram quantities required by previous instruments capable of imposing comparable deformations. This orders-of-magnitude reduction in the sample size allows us to study model polymers and new developmental resins, both of which are typically available only in gram-scale quantities. The compact design of the shear cell makes it possible to transport it to synchrotron light sources for in situ x-ray scattering studies of the evolution of the crystalline structure. Thus, our device is a valuable new tool that can be used to evaluate the crystallization characteristics of resins with experimental compositions or molecular architectures when subjected to processing-like flow conditions. We demonstrate some of the features of this device by presenting selected results on isotactic polypropylenes

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