Differential Astrometry of Sub-arcsecond Scale Binaries at the Palomar Testbed Interferometer

We have used the Palomar Testbed Interferometer to perform very high precision differential astrometry on the 0.25 arcsecond separation binary star HD 171779. In 70 minutes of observation we achieve a measurement uncertainty of approximately 9 micro-arcseconds in one axis, consistent with theoretical expectations. Night-to-night repeatability over four nights is at the level of 16 micro-arcseconds. This method of very-narrow-angle astrometry may be extremely useful for searching for planets with masses as small as 0.5 Jupiter Masses around a previously neglected class of stars -- so-called ``speckle binaries.'' It will also provide measurements of stellar parameters such as masses and distances, useful for constraining stellar models at the 10^-3 level.Comment: 19 pages including 6 figures. Submitted to ApJ. Typos corrected, several parts reworded for clarificatio

Charge assignments in multiple-U(1) gauge theories

We discuss the choice of gauge field basis in multiple-U(1) gauge theories. We find that there is a preferred basis, specified by the charge orthogonality condition, in which the U(1) gauge fields do not mix under one-loop renormalization group running.Comment: 7 pages, LaTe

Calibration of Computational Models with Categorical Parameters and Correlated Outputs via Bayesian Smoothing Spline ANOVA

It has become commonplace to use complex computer models to predict outcomes in regions where data does not exist. Typically these models need to be calibrated and validated using some experimental data, which often consists of multiple correlated outcomes. In addition, some of the model parameters may be categorical in nature, such as a pointer variable to alternate models (or submodels) for some of the physics of the system. Here we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a Bayesian Smoothing Spline (BSS) ANOVA framework. The BSS-ANOVA framework has several advantages over the traditional Gaussian Process, including ease of handling categorical inputs and correlated outputs, and improved computational efficiency. Finally this framework is then applied to the problem that motivated its design; a calibration of a computational fluid dynamics model of a bubbling fluidized which is used as an absorber in a CO2 capture system

Ultracold, radiative charge transfer in hybrid Yb ion - Rb atom traps

Ultracold hybrid ion-atom traps offer the possibility of microscopic manipulation of quantum coherences in the gas using the ion as a probe. However, inelastic processes, particularly charge transfer can be a significant process of ion loss and has been measured experimentally for the Yb$^{+}$ ion immersed in a Rb vapour. We use first-principles quantum chemistry codes to obtain the potential energy curves and dipole moments for the lowest-lying energy states of this complex. Calculations for the radiative decay processes cross sections and rate coefficients are presented for the total decay processes. Comparing the semi-classical Langevin approximation with the quantum approach, we find it provides a very good estimate of the background at higher energies. The results demonstrate that radiative decay mechanisms are important over the energy and temperature region considered. In fact, the Langevin process of ion-atom collisions dominates cold ion-atom collisions. For spin dependent processes \cite{kohl13} the anisotropic magnetic dipole-dipole interaction and the second-order spin-orbit coupling can play important roles, inducing couplingbetween the spin and the orbital motion. They measured the spin-relaxing collision rate to be approximately 5 orders of magnitude higher than the charge-exchange collision rate \cite{kohl13}. Regarding the measured radiative charge transfer collision rate, we find that our calculation is in very good agreement with experiment and with previous calculations. Nonetheless, we find no broad resonances features that might underly a strong isotope effect. In conclusion, we find, in agreement with previous theory that the isotope anomaly observed in experiment remains an open question.Comment: 7 figures, 1 table accepted for publication in J. Phys. B: At. Mol. Opt. Phys. arXiv admin note: text overlap with arXiv:1107.114

Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.Comment: 96 page

Dynamical symmetry of isobaric analog 0+ states in medium mass nuclei

An algebraic sp(4) shell model is introduced to achieve a deeper understanding and interpretation of the properties of pairing-governed 0+ states in medium mass atomic nuclei. The theory, which embodies the simplicity of a dynamical symmetry approach to nuclear structure, is shown to reproduce the excitation spectra and fine structure effects driven by proton-neutron interactions and isovector pairing correlations across a broad range of nuclei.Comment: 7 pages, 5 figure

Composite Scalars at LEP: Constraining Technicolor Theories

LEPI and LEPII data can be used to constrain technicolor models with light, neutral pseudo-Nambu-Goldstone bosons, Pa. We use published limits on branching ratios and cross sections for final states with photons, large missing energy, jet pairs, and b bbar pairs to constrain the anomalous Pa Z0 Z0, Pa Z0 photon, and Pa photon photon couplings. From these results, we derive bounds on the size of the technicolor gauge group and the number of technifermion doublets in models such as Low-scale Technicolor.Comment: 27 pages (including title page), 15 figures, 6 tables. version 2: In addressing PRD referee comments, we have significantly expanded our manuscript, to include detailed discussion of limits from LEP II data, as well as expanding the number or specific models to which we apply our results. As a result, we have changed the title from "Z0 decays to composite scalars: constraining technicolor theories