New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations.Comment: 42 page

Symmetries of the Einstein Equations

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.Comment: 15 pages, FTG-114-USU, Plain Te

Magnetic instability of a two-dimensional Anderson non-Fermi liquid

We show that in the Anderson model for a two-dimensional non-Fermi liquid a magnetic instability can lead to the itinerant electron ferromagnetism. The critical temperature and the susceptibility of the paramagnetic phase have been analytically calculated. The usual Fermi behaviour is re-obtained taking the anomalous exponent to be zero.Comment: 3 pages, Revte

Chaotic Dynamics of Stellar Spin in Binaries and the Production of Misaligned Hot Jupiters

Many exoplanetary systems containing hot Jupiters are observed to have highly misaligned orbital axes relative to the stellar spin axes. Kozai-Lidov oscillations of orbital eccentricity/inclination induced by a binary companion, in conjunction with tidal dissipation, is a major channel for the production of hot Jupiters. We demonstrate that gravitational interaction between the planet and its oblate host star can lead to chaotic evolution of the stellar spin axis during Kozai cycles. As parameters such as the planet mass and stellar rotation period vary, periodic islands can appear in an ocean of chaos, in a manner reminiscent of other dynamical systems. In the presence of tidal dissipation, the complex spin evolution can leave an imprint on the final spin-orbit misalignment angles.Comment: 26 pages, 13 figures. Includes supplementary materials. To be published in the September 12, 2014 edition of Science Magazine. For additional information, please visit http://astro.cornell.edu/~dong/sciencepaper.htm

The Education of Real Estate Salespeople and the Value of the Firm

In order to protect the public, most states require salespeople and brokers to meet specific licensing requirements, typically in the form of classroom instruction and/or successful completion of an examination. Frequently, however, many real estate brokers require their sales staff to undertake education that exceeds these minimum requirements. In this study, we derive a theoretical model that shows how optimally-timed, firm provided education that exceeds legal minimums can increase staff productivity, reduce litigation risks and perhaps raise and/or maximize the expected value of the firm.

Impact of online professional development in the work environment

Online distance education programs are populated by adult learners who try to continue or complete their education without having to leave their jobs or places of residence. Their work environment becomes not just their working place, but also the labs where they apply new knowledge. The general expectation is that after graduation they will make an impact in their work environment through their job and through interacting with peers and supervisors. This study explored the influence that K-12 teachers had in their work environment as they pursued and graduated from an online Masters program in Education. The study showed the impact that the participants have and how they become agents of change in their immediate workplace.publishedpeer reviewe

Tuning in on Cepheids: Radial velocity amplitude modulations. A source of systematic uncertainty for Baade-Wesselink distances

[Abridged] I report the discovery of modulations in radial velocity (RV) curves of four Galactic classical Cepheids and investigate their impact as a systematic uncertainty for Baade-Wesselink distances. Highly precise Doppler measurements were obtained using the Coralie high-resolution spectrograph since 2011. Particular care was taken to sample all phase points in order to very accurately trace the RV curve during multiple epochs and to search for differences in linear radius variations derived from observations obtained at different epochs. Different timescales are sampled, ranging from cycle-to-cycle to months and years. The unprecedented combination of excellent phase coverage obtained during multiple epochs and high precision enabled the discovery of significant modulation in the RV curves of the short-period s-Cepheids QZ Normae and V335 Puppis, as well as the long-period fundamental mode Cepheids l Carinae and RS Puppis. The modulations manifest as shape and amplitude variations that vary smoothly on timescales of years for short-period Cepheids and from one pulsation cycle to the next in the long-period Cepheids. The order of magnitude of the effect ranges from several hundred m/s to a few km/s. The resulting difference among linear radius variations derived using data from different epochs can lead to systematic errors of up to 15% for Baade-Wesselink-type distances, if the employed angular and linear radius variations are not determined contemporaneously. The different natures of the Cepheids exhibiting modulation in their RV curves suggests that this phenomenon is common. The observational baseline is not yet sufficient to conclude whether these modulations are periodic. To ensure the accuracy of Baade-Wesselink distances, angular and linear radius variations should always be determined contemporaneously.Comment: 7 pages, 5 figures, 1 table. Accepted for publication in A&A letter