Holonomy and path structures in general relativity and Yang-Mills theory

This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the motion of a test body, and the relation between different such possible motions. Space-time as a Lorentzian manifold is regarded as a secondary construct, and it is shown how to construct it from the primary data. Some technical problems remain. Yang-Mills fields are defined by their holonomy in an analogous construction. I detail the development of this idea in the literature, and give a new version of the construction of a bundle and connection from holonomy data. The field equations of general relativity are discussed briefly in this context.     

Global and local optimization using radial basis function response surface models

The focus of this paper is the optimization of complex multi-parameter systems. We consider systems in which the objective function is not known explicitly, and can only be evaluated through computationally intensive numerical simulation or through costly physical experiments. The objective function may also contain many local extrema which may be of interest. Given objective function values at a scattered set of parameter values, we develop a response surface model that can dramatically reduce the required computation time for parameter optimization runs. The response surface model is developed using radial basis functions, producing a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use of radial basis functions to transform scattered data points, obtained from a complex continuum mechanics simulation of explosive materials, into a response surface model of a function over the given parameter space. Response surface methodology and radial basis functions are discussed in general and are applied to a global optimization problem for an explosive oil well penetrator.     

Poincaré series and holomorphic averaging

Summary We provide an alternate proof of McMullen's theorem on contractive properties of the Poincaré series operator in the special case of the universal covering. This case includes in particular Kra's Theta Conjecture.Oblatum 16-X-1991 & 14-IV-1992First author supported in part by a grant from the National Science Foundation     

AUTOMATED WIND TUNNEL MEASUREMENTS

It is common practice in power transmission to use bundled overhead electrical conductors because the lower rate of corona discharge, compared with single conductors, makes the bundle attractive for high voltages. However, secondary problems may arise from the vibrations induced by the aerodynamic forces which act on the leeward conductors as a result of their immersion in the wake of a windward conductor. Thus, in addition to possible aeolian and galloping oscillations observed for a single conductor, bundle conductors may also be subjected to wake-induced oscillations. ^1,2 Although extensive research has been done on the aeroelastic behavior of single and bundled conductors which are bare, little is known about the galloping or wake oscillation characteristics of given bundle conductors which, depending upon the environmental conditions during the formation of ice, may have five or so representative shaped cross-sections. One important task involves the aerodynamic quasi-static force and moment measurements in a wind tunnel using full scale conductor cross-sections each of which must be rotated through many angles at different spacings. Such measurements are repetitive as well as tediously time consuming and, hence, are beneficially automated. A reliable, accurate and inexpensive automated apparatus is described in this paper which permits the aerodynamic measurements to be performed efficiently and without intervention. Most importantly, it relieves the operator of the usual responsibility for manually controlling the separation and orientation of the sections as well as the need to manually compensate fluctuations in the free stream air speed. For simplicity, the apparatus is detailed in the context of a twin bundle conductor.     

Inhomogeneous Cosmologies, the Copernican Principle and the Cosmic Microwave Background: More on the EGS Theorem

We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmologicalprinciple, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background. We also present some new conformally flat two-fluid solutions of Einstein's field equations.     

Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

In this paper the nonlinear wave equation $$u_u - u_{xx} + v(x)u(x,t) + \varepsilon u^3 (x,t) = 0$$ is studied. It is shown that for a large class of potentials,v(x), one can use KAM methods to construct periodic and quasi-periodic solutions (in time) for this equation.     

A Tensor product generalized ADI method for the method of planes

We consider solving separable, second order, linear elliptic prtial differential equations in three independent variables. If the partial differential opertor separates into two terms, one depending on x and y, and one depending on z, then we use the method of planes to obtain a discrete problem, which we write in tensor product from as We apply a new interative method, the tensor product generalized alternating direction implicit method, to solve the discrete problem. We study a specific implementation that uses Hermite bicubic collocation in the xy direction and symmetric finite differences in the z direction. We demostrate that this method is a fast and accurate way to solve the large linear systems arising from three-dimensional elliptic problems.     

Diels-Alder chemistry on alkene functionalized films

A substrate-independent method has been devised for ring formation at solid surfaces. This entails the aminolysis reaction of allylamine with maleic anhydride pulsed plasma polymer films to yield terminal alkene groups at the surface. Subsequent exposure to 1,3-cyclohexadiene leads to a Diels-Alder type (4 + 2) cycloaddition reaction to give a mixture of endo- and exo-bicyclo[2.2.2]oct-2-ene rings.     

Fluorescence detection and quantitation of recombinant proteins containing oligohistidine tag sequences directly in sodium dodecyl sulfate-polyacrylamide gels

Two fluorophore-nitrilotriacetic acid conjugates, Pro-Q Sapphire 365 and Pro-Q Sapphire 488 oligohistidine gel stains, have been developed for the fluorescence detection of fusion proteins containing oligohistidine tags directly in sodium dodecyl sulfate polyacrylamide gels, without the requirement for electroblotting, reporter enzymes or secondary detection reagents. Pro-Q Sapphire 365 oligohistidine gel stain exhibits bright-blue fluorescence (emission maximum = 450 nm) when illuminated with UV-A or UV-B light from a standard ultraviolet transilluminator. Pro-Q Sapphire 488 oligohistidine gel stain exhibits bright-green fluorescence (emission maximum = 515 nm) when illuminated with visible light from a laser-based gel scanner equipped with a 470 nm second-harmonic generation (SHG) or 488 nm argon-ion laser source. Typically, 25-65 ng of oligohistidine-tagged fusion protein in whole cell lysates is detectable using either stain. After documenting the fluorescence signal from the Pro-Q Sapphire dyes, gels may be post-stained with the red-fluorescent SYPRO Ruby protein gel stain in order to reveal the total protein pattern.