Dynamics of Black Hole Pairs I: Periodic Tables

Although the orbits of comparable mass, spinning black holes seem to defy simple decoding, we find a means to decipher all such orbits. The dynamics is complicated by extreme perihelion precession compounded by spin-induced precession. We are able to quantitatively define and describe the fully three dimensional motion of comparable mass binaries with one black hole spinning and expose an underlying simplicity. To do so, we untangle the dynamics by capturing the motion in the orbital plane. Our results are twofold: (1) We derive highly simplified equations of motion in a non-orthogonal orbital basis, and (2) we define a complete taxonomy for fully three-dimensional orbits. More than just a naming system, the taxonomy provides unambiguous and quantitative descriptions of the orbits, including a determination of the zoom-whirliness of any given orbit. Through a correspondence with the rationals, we are able to show that zoom-whirl behavior is prevalent in comparable mass binaries in the strong-field regime. A first significant conclusion that can be drawn from this analysis is that all generic orbits in the final stages of inspiral under gravitational radiation losses are characterized by precessing clovers with few leaves and that no orbit will behave like the tightly precessing ellipse of Mercury. The gravitational waveform produced by these low-leaf clovers will reflect the natural harmonics of the orbital basis -- harmonics that, importantly, depend only on radius. The significance for gravitational wave astronomy will depend on the number of windings the pair executes in the strong-field regime and could be more conspicuous for intermediate mass pairs than for stellar mass pairs.Comment: 19 pages, lots of figure

Hopf Algebras of Heap Ordered Trees and Permutations

It is known that there is a Hopf algebra structure on the vector space with basis all heap-ordered trees. We give a new bialgebra structure on the space with basis all permutations and show that there is a direct bialgebra isomorphism between the Hopf algebra of heap-ordered trees and the bialgebra of permutations.Comment: 10 pages LaTeX, minor revisio

The use of drug calendars for the diagnosis of cutaneous drug eruptions in the age of electronic medical records

A morbilliform drug eruption is the most common condition leading to a dermatology consultation for a patient in the hospital. Timing is an important diagnostic tool since the onset of a skin rash usually takes place within days-to-weeks of the start of the implicated drug. A comprehensive, thorough, and reliable drug history by the clinician is essential. Therefore, to assist in the task of determining the causative medication of a new skin rash in a hospitalized patient, the creation of a drug calendar is recommended. The development of an electronic version of the drug calendar offers several benefits over the manual version. As the use of electronic medical records continues to become the standard in medicine, the electronic drug calendar will serve as an invaluable tool for the diagnosis of drug hypersensitivity

Phonon Diodes and Transistors from Magneto-acoustics

By sculpting the magnetic field applied to magneto-acoustic materials, phonons can be used for information processing. Using a combination of analytic and numerical techniques, we demonstrate designs for diodes (isolators) and transistors that are independent of their conventional, electronic formulation. We analyze the experimental feasibility of these systems, including the sensitivity of the circuits to likely systematic and random errors.Comment: 5 pages, 4 figure

A simple example of modeling hybrid systems using bialgebras: Preliminary version

The authors describe how to construct a hybrid control system using a specific set of data and conditions specified within the paper. Furthermore, they give examples of how to create continuous systems, discrete systems, and simple hybrid systems. Finally, they touch upon Heisenberg and state space representation

Intermediate Subfactors with No Extra Structure

If $N \subset P,Q \subset M$ are type II_1 factors with $N' \cap M = C id$ and $[M:N]$ finite we show that restrictions on the standard invariants of the elementary inclusions $N \subset P$, $N \subset Q$, $P \subset M$ and $Q \subset M$ imply drastic restrictions on the indices and angles between the subfactors. In particular we show that if these standard invariants are trivial and the conditional expectations onto $P$ and $Q$ do not commute, then $[M:N]$ is 6 or $6 + 4\sqrt 2$. In the former case $N$ is the fixed point algebra for an outer action of $S_3$ on $M$ and the angle is $\pi/3$, and in the latter case the angle is $cos^{-1}(\sqrt 2-1)$ and an example may be found in the GHJ subfactor family. The techniques of proof rely heavily on planar algebras.Comment: 51 pages, 65 figure