Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Energetics of positron states trapped at vacancies in solids

We report a computational first-principles study of positron trapping at vacancy defects in metals and semiconductors. The main emphasis is on the energetics of the trapping process including the interplay between the positron state and the defect's ionic structure and on the ensuing annihilation characteristics of the trapped state. For vacancies in covalent semiconductors the ion relaxation is a crucial part of the positron trapping process enabling the localization of the positron state. However, positron trapping does not strongly affect the characteristic features of the electronic structure, e.g., the ionization levels change only moderately. Also in the case of metal vacancies the positron-induced ion relaxation has a noticeable effect on the calculated positron lifetime and momentum distribution of annihilating electron-positron pairs.Comment: Submitted to Physical Review B on 17 April 2007. Revised version submitted on 6 July 200

Root and Vigor Response of Big Bluestem to Summer Grazing Strategies

Warm-season grasses e.g., big bluestem (Andropogon gerardii Vitman) are great potential sources of summer forage in eastern Nebraska. Frequent, intensive defoliation can reduce root mass and limit root distribution. Quantifying root structure response to multiple defoliation events in a grazing situation is critical to develop management plans for these types of grasses. This experiment aimed to quantify the cumulative effects of timing and frequency of grazing on root structure and organic reserve estimates in big bluestem pastures

Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Syntbesis and Properries of the Selective Antimuscarinic Agent Cyclohexylphenyl(3-piperidinopropyl)silanol

Die Synthese des selektiven Antimuskarinikums Cyclohexylpheny\{3-piperidinopropyl)sila· nol (1 b) wird beschrieben. 1 b wurde - ausgehend von (3·Chlorpropyl)trimethoxysilan - durch eine vierstufige Reaktionsfolge erhalten und als Hydrochlorid 2b mit einer Gesamtausbeute von etwa 45°/o isoliert. - 1 b ist aufgrund seiner großen pharmakologischen Se· lektivität zu einer Standardsubstanz in der experimentellen Pharmakologie bei der Differenzierung von Muskarinrezeptoren geworden.The synthesis of thc selective antimuscarinic agent cyclohexylphenyl(3-piperidinopropyl)silanol (1 b) is described. Starting with (3-chloropropyl)trimethoxysilane, I b was obtained by four reaction steps and isolated as hydrochloride 2b with a total yield of about 45°/o. - Because of its high pharmacological selectivity 1 b has become a reference drug in experimental pharmacology for the differentiation of muscarinic rcceptors

Tunable Polaronic Conduction in Anatase TiO2

Oxygen vacancies created in anatase TiO2 by UV photons (80–130 eV) provide an effective electron-doping mechanism and induce a hitherto unobserved dispersive metallic state. Angle resolved photoemission reveals that the quasiparticles are large polarons. These results indicate that anatase can be tuned from an insulator to a polaron gas to a weakly correlated metal as a function of doping and clarify the nature of conductivity in this material.open1192sciescopu

A COMPARISON OF SPATIAL PREDICTION METHODS USING INTENSE SPATIALLY-ACQUIRED WATER QUALITY DATA

Water quality information obtained through intensive spatial sampling using automated devices provides opportunities to monitor and forecast the spatial distribution of nutrients and phytoplankton concentrations, and help establish water circulation patterns in estuarine and coastal waters. To be cost effective, efficient sampling designs and estimation methodologies must first be developed. As a starting basis, we applied an original transect sampling design that was used to estimate the spatial distribution of chlorophyll a, salinity, and temperature in the Cienaga Grande de Santa Marta, a coastal lagoon in Colombia. We superimposed the transects over satellite images of the lagoon obtained in the period 1993-2001 to evaluate the efficiency and accuracy of using such transects to estimate the distribution of water quality variables. The satellite images were taken in 1993 (SPOT-3), 1995 (Landsat-6), and 1999 (Landsat-6), and water reflectance values were used as a “proxy” for the water quality variables. Spatial prediction using kriging and thin-plate smoothing splines were used to predict reflectance for a grid network of points taken from the images, and predictions were compared with observed values to compare methods and transect routes. Rapid changes in reflectance in short distances (for example , caused by phytoplankton blooms), complicated the analysis, and neither method proved superior over all transect routes and images, although the kriging predictor remained relatively consistent in performance over the various selected sampling routes