Fearless: Josh Griffiths

Continually a strong voice for the underrepresented on campus, working with other students and faculty to take initiative in changing campus policy and culture toward the LGBTQ community, and serving as a leader in multiple groups and organizations on campus, Josh Griffiths ’14 fearlessly advocates for members of our campus community, making Gettysburg a more open and welcoming space. [excerpt

Augmentations and Rulings of Legendrian Knots

A connection between holomorphic and generating family invariants of Legendrian knots is established; namely, that the existence of a ruling (or decomposition) of a Legendrian knot is equivalent to the existence of an augmentation of its contact homology. This result was obtained independently and using different methods by Fuchs and Ishkhanov. Close examination of the proof yields an algorithm for constructing a ruling given an augmentation. Finally, a condition for the existence of an augmentation in terms of the rotation number is obtained.Comment: 21 pages, 16 figure

A Self-Critical Phenomenology of Criticism

Noel Carroll, a central figure in analytic (Anglo-American) philosophy of art, and spouse of renowned dance scholar Sally Banes (who co-authored several of these essays), offers us something remarkable in his new book—namely, a collection of thirty years of his theoretical essays and dance reviews. Carroll wrote some of the pieces while he was a graduate student at the University of Illinois, Chicago, and there have been some dramatic changes since then in both the art world and Carroll’s philosophical views. Thus, he modestly characterizes the book as “an archeological artifact” of a “somewhat confessional” variety (p. 267). Inspired by Carroll, I too will adopt an archeological stance, with a promise that the reader’s patience will be repaid with something surprising at the end of the dig

Bratt\u27s By the Vision of Another World: Worship in American History (Book Review)

A Review of By the Vision of Another World: Worship in American History, edited by James D. Bratt. Grand Rapids, MI: Eerdmans, 2012. 213 pp. $25.00. ISBN 978-080286710

It takes a village to raise a tide: nonlinear multiple-mode coupling and mode identification in KOI-54

We explore the tidal excitation of stellar modes in binary systems using Kepler observations of the remarkable eccentric binary KOI-54 (HD 187091; KIC 8112039), which displays strong ellipsoidal variation as well as a variety of linear and nonlinear pulsations. We report the amplitude and phase of over 120 harmonic and anharmonic pulsations in the system. We use pulsation phases to determine that the two largest-amplitude pulsations, the 90th and 91st harmonics, most likely correspond to axisymmetric m=0 modes in both stars, and thus cannot be responsible for resonance locks as had been recently proposed. We find evidence that the amplitude of at least one of these two pulsations is decreasing with a characteristic timescale of ~100 yr. We also use the pulsations' phases to confirm the onset of the traveling wave regime for harmonic pulsations with frequencies <~50 Omega_orbit, in agreement with theoretical expectations. We present evidence that many pulsations that are not harmonics of the orbital frequency correspond to modes undergoing simultaneous nonlinear coupling to multiple linearly driven parent modes. Since coupling among multiple modes can lower the threshold for nonlinear interactions, nonlinear phenomena may be easier to observe in highly eccentric systems, where broader arrays of driving frequencies are available. This may help to explain why the observed amplitudes of the linear pulsations are much smaller than the theoretical threshold for decay via three-mode coupling.Comment: Accepted for publication in MNRAS. Only minor corrections. 16 Pages; 8 Figures; 3 Table

Optimal state discrimination and unstructured search in nonlinear quantum mechanics

Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.Comment: 14 pages, 4 figures; published version, with minor corrections and an improved discussion of the validity of the Gross-Pitaevskii approximatio