Atomic-phase interference devices based on ring-shaped Bose-Einstein condensates: Two ring case

We theoretically investigate the ground-state properties and quantum dynamics of a pair of adjacent ring-shaped Bose-Einstein condensates that are coupled via tunneling. This device, which is the analogue of a symmetric superconducting quantum interference device, is the simplest version of what we term an Atomic-Phase Interference Device (APHID). The two-ring APHID is shown to be sensitive to rotation.Comment: 8 page

New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split

I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. [This is also known as variation with natural boundary conditions.] Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose corresponding velocities are, respectively, the abovementioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations, which shall be provided in a second paper.Comment: 11 page

Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme

I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle models (RPM's). If there is also commutation with Lin - the Kuchar observables condition - the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchar observables is explicitly resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kuchar observables are formally known, giving the relational triangle as an example. As a second route, I apply an indirect method that generalizes both group-averaging and Barbour's best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 sharp-edged window function. I leave the elsewise-improved softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide comments on Halliwell's approach and how well it fares as regards the various facets of the Problem of Time and as an implementation of QM propositions.Comment: An improved version of the text, and with various further references. 25 pages, 4 figure

The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis

Methods are presented to define and compute source multipoles of dynamical horizons in numerical relativity codes, extending previous work from the isolated and dynamical horizon formalisms in a manner that allows for the consideration of horizons that are not axisymmetric. These methods are then applied to a binary black hole merger simulation, providing evidence that the final remnant is a Kerr black hole, both through the (spatially) gauge-invariant recovery of the geometry of the apparent horizon, and through a detailed extraction of quasinormal ringing modes directly from the strong-field region.Comment: 12 pages, 13 figures. Published version. Some references have been added and reordered, and the figures cleaned up

The Link between General Relativity and Shape Dynamics

We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity and Shape Dynamics, a theory with fixed foliation but spatial conformal invariance. This streamlines the rather complicated construction of this equivalence performed previously. We use this streamlined argument to extend the result to General Relativity with asymptotically flat boundary conditions. The improved understanding of linking theories naturally leads to the Lagrangian formulation of Shape Dynamics, which allows us to partially relate the degrees of freedom.Comment: 19 pages, LaTeX, no figure

Flight evaluation of two-segment approaches using area navigation guidance equipment

A two-segment noise abatement approach procedure for use on DC-8-61 aircraft in air carrier service was developed and evaluated. The approach profile and procedures were developed in a flight simulator. Full guidance is provided throughout the approach by a Collins Radio Company three-dimensional area navigation (RNAV) system which was modified to provide the two-segment approach capabilities. Modifications to the basic RNAV software included safety protection logic considered necessary for an operationally acceptable two-segment system. With an aircraft out of revenue service, the system was refined and extensively flight tested, and the profile and procedures were evaluated by representatives of the airlines, airframe manufacturers, the Air Line Pilots Association, and the Federal Aviation Adminstration. The system was determined to be safe and operationally acceptable. It was then placed into scheduled airline service for an evaluation during which 180 approaches were flown by 48 airline pilots. The approach was determined to be compatible with the airline operational environment, although operation of the RNAV system in the existing terminal area air traffic control environment was difficult

Pilot Human Factors in Stall/Spin Accidents of Supersonic Fighter Aircraft

A study has been made of pilot human factors related to stall/spin accidents of supersonic fighter aircraft. The military specifications for flight at high angles of attack are examined. Several pilot human factors problems related to stall/spin are discussed. These problems include (1) unsatisfactory nonvisual warning cues; (2) the inability of the pilot to quickly determine if the aircraft is spinning out of control, or to recognize the type of spin; (3) the inability of the pilot to decide on and implement the correct spin recovery technique; (4) the inability of the pilot to move, caused by high angular rotation; and (5) the tendency of pilots to wait too long in deciding to abandon the irrecoverable aircraft. Psycho-physiological phenomena influencing pilot's behavior in stall/spin situations include (1) channelization of sensory inputs, (2) limitations in precisely controlling several muscular inputs, (3) inaccurate judgment of elapsed time, and (4) disorientation of vestibulo-ocular inputs. Results are given of pilot responses to all these problems in the F14A, F16/AB, and F/A-18A aircraft. The use of departure spin resistance and automatic spin prevention systems incorporated on recent supersonic fighters are discussed. These systems should help to improve the stall/spin accident record with some compromise in maneuverability