Eliminating the Hadronic Uncertainty

The Standard Model Lagrangian requires the values of the fermion masses, the Higgs mass and three other experimentally well-measured quantities as input in order to become predictive. These are typically taken to be $\alpha$, $G_\mu$ and $M_Z$. Using the first of these, however, introduces a hadronic contribution that leads to a significant error. If a quantity could be found that was measured at high energy with sufficient precision then it could be used to replace $\alpha$ as input. The level of precision required for this to happen is given for a number of precisely-measured observables. The $W$ boson mass must be measured with an error of $\pm13$\,MeV, $\Gamma_Z$ to $0.7$\,MeV and polarization asymmetry, $A_{LR}$, to $\pm0.002$ that would seem to be the most promising candidate. The r\^ole of renormalized parameters in perturbative calculations is reviewed and the value for the electromagnetic coupling constant in the $\overline{\rm MS}$ renormalization scheme that is consistent with all experimental data is obtained to be $\alpha^{-1}_{\overline{\rm MS}}(M^2_Z)=128.17$.Comment: 8 pages LaTeX2

Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times

In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force constructed through an infinite dimensional Gaussian noise process. We study the limit as the particle relaxation time as well as the correlation time of the noise tend to zero and we obtain the limiting equations under appropriate assumptions on the Gaussian noise. We show that the limiting equation depends on the relative magnitude of the two fast time scales of the system. In particular, we prove that in the case where the two relaxation times converge to zero at the same rate there is a drift correction, in addition to the limiting It\^{o} integral, which is not of Stratonovich type. If, on the other hand, the colored noise is smooth on the scale of particle relaxation then the drift correction is the standard Stratonovich correction. If the noise is rough on this scale then there is no drift correction. Strong (i.e. pathwise) techniques are used for the proof of the convergence theorems.Comment: 35 pages, 0 figures, To appear in SIAM J. MM

Apparatus enables automatic microanalysis of body fluids

Apparatus will automatically and quantitatively determine body fluid constituents which are amenable to analysis by fluorometry or colorimetry. The results of the tests are displayed as percentages of full scale deflection on a strip-chart recorder. The apparatus can also be adapted for microanalysis of various other fluids

Studies relating to Polyunsaturated Fatty Acid (PUFA) Supplementation and Fertility in Cattle

End of project reportReproductive inefficiency has a significant impact on the economic performance of both dairy and beef herds, particularly in seasonal calving systems. Nutrition plays a fundamental role in reproduction. Furthermore, there is emerging evidence that supplemental dietary polyunsaturated fatty acids (PUFA) may increase cow fertility independent of their role as energy substrates. A number of studies have reported enhanced reproductive performance in dairy cows following dietary supplementation with sources of n-3 PUFA. However the possible mechanisms involved have not been identified and there is some inconsistency in the published literature on this topic. The objective of the research reported was to conduct a holistic examination of the effects of dietary long-chain n-3 PUFA supplementation on metabolic and reproductive responses in cattle. Such information is essential for the appropriate formulation of diets to enhance cow reproductive performance and in particular embryo survival

MCMC methods for functions modifying old algorithms to make\ud them faster

Many problems arising in applications result in the need\ud to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems

Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States

We study the physics of electron tunneling between multiple quantum dots and the edge of a quantum Hall state. Our results generalize earlier work [G. A. Fiete, W. Bishara, C. Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it was shown that a single quantum dot tunnel coupled to a non-Abelian quantum Hall state can realize a stable multi-channel Kondo fixed point at low-energy. In this work, we investigate the physics of multiple dots and find that a rich set of possible low-energy fixed points arises, including those with non-Fermi liquid properties. Previously unidentified fixed points may also be among the possibilities. We examine both the situation where the dots are spatially separated and where they are in close proximity. We discuss the relation to previous work on two-impurity Kondo models in Fermi liquids and highlight new research directions in multiple quantum impurity problems.Comment: 12 pages, 2 figure

Width and Partial Widths of Unstable Particles in the Light of the Nielsen Identities

Fundamental properties of unstable particles, including mass, width, and partial widths, are examined on the basis of the Nielsen identities (NI) that describe the gauge dependence of Green functions. In particular, we prove that the pole residues and associated definitions of branching ratios and partial widths are gauge independent to all orders. A simpler, previously discussed definition of branching ratios and partial widths is found to be gauge independent through next-to-next-to-leading order. It is then explained how it may be modified in order to extend the gauge independence to all orders. We also show that the physical scattering amplitude is the most general combination of self-energy, vertex, and box contributions that is gauge independent for arbitrary s, discuss the analytical properties of the NI functions, and exhibit explicitly their one-loop expressions in the Z-gamma sector of the Standard Model.Comment: 20 pages (Latex); minor changes included, accepted for publication in Phys. Rev.

High Reynolds Number Test of the Boeing TR77 Airfoil in the Langley 0.3-Meter Transonic Cryogenic Tunnel

A Boeing TR77 airfoil associated with the Advanced Technology Airfoil Test (ATAT) program was tested in the Langley 0.3 m Transonic Cryogenic Tunnel. Limited analysis of the data indicated that increasing Reynolds number for a fixed Mach number resulted in increased normal-force, nose-down pitching moment, and decreased drag coefficient. Increasing Mach number while keeping the Reynolds number constant yielded the expected increase in normal-force slopes, nose-down pitching moment coefficients, and decrease in angle of attack associated with maximum normal-force coefficient. Turbulent boundary layer flow was achieved over the airfoil at low Reynolds numbers for the test Mach number range using aluminum discs

Prospects for Redshifted 21-cm observations of quasar HII regions

The introduction of low-frequency radio arrays over the coming decade is expected to revolutionize the study of the reionization epoch. Observation of the contrast in redshifted 21cm emission between a large HII region and the surrounding neutral IGM will be the simplest and most easily interpreted signature. We find that an instrument like the planned Mileura Widefield Array Low-Frequency Demonstrator (LFD) will be able to obtain good signal to noise on HII regions around the most luminous quasars, and determine some gross geometric properties, e.g. whether the HII region is spherical or conical. A hypothetical follow-up instrument with 10 times the collecting area of the LFD (MWA-5000) will be capable of mapping the detailed geometry of HII regions, while SKA will be capable of detecting very narrow spectral features as well as the sharpness of the HII region boundary. The MWA-5000 will discover serendipitous HII regions in widefield observations. We estimate the number of HII regions which are expected to be generated by quasars. Assuming a late reionization at z~6 we find that there should be several tens of quasar HII regions larger than 4Mpc at z~6-8 per field of view. Identification of HII regions in forthcoming 21cm surveys can guide a search for bright galaxies in the middle of these regions. Most of the discovered galaxies would be the massive hosts of dormant quasars that left behind fossil HII cavities that persisted long after the quasar emission ended, owing to the long recombination time of intergalactic hydrogen. A snap-shot survey of candidate HII regions selected in redshifted 21cm image cubes may prove to be the most efficient method for finding very high redshift quasars and galaxies.Comment: 14 pages, 8 figures. Submitted to Ap