Quantum Gauge Equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and spatial axial gauges to what we call ``common form,'' in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages, REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author

Analysis and design of a flat central finned-tube radiator

Computer program based on fixed conductance parameter yields minimum weight design. Second program employs variable conductance parameter and variable ratio of fin length to tube outside radius, and is used for radiator designs with geometric limitations. Major outputs of the two programs are given

Parametric study of B-58 acceleration response to turbulence and comparisons with flight data, August 1967 - August 1968

Parametric study of B-58 acceleration response to turbulence and comparisons with flight dat

Performance and materials aspects of Ge:Be photoconductors

Ge:Be photoconductors were developed for low photon background applications in the 30 to 50 MM wavelength region. These detectors provide higher responsivity and lower noise equivalent power (NEP) than the Ge:Ga detectors currently operating in this wavelength range. Beryllium doped single crystals were grown by the Czochralski method from a carbon susceptor under a vacuum of approx. one million torr. An optimum detective quantum efficiency of 46% at a background flux of 1.5 x 10 to the 8th power photons/second (7 x 10 to the 13th power W) was reported. Ge:Be detector performance is strongly influenced by the absolute concentrations and the concentration ratio of residual shallow donors and shallow acceptors

King: MELVILLE WESTON FULLER, CHIEF JUSTICE OF THE UNITED STATES 1888-1910.

A Review of MELVILLE WESTON FULLER, CHIEF JUSTICE OF THE UNITED STATES 1888-1910. By Willard L. King

Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.Comment: 5 pages, 5 figure

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples