Non-circular features in Saturn's D ring: D68

D68 is a narrow ringlet located only 67,627 km (1.12 planetary radii) from Saturn's spin axis. Images of this ringlet obtained by the Cassini spacecraft reveal that this ringlet exhibits persistent longitudinal brightness variations and a substantial eccentricity (ae=25+/-1 km). By comparing observations made at different times, we confirm that the brightness variations revolve around the planet at approximately the local orbital rate (1751.6 degrees/day), and that the ringlet's pericenter precesses at 38.243+/-0.008 degrees/day, consistent with the expected apsidal precession rate at this location due to Saturn's higher-order gravitational harmonics. Surprisingly, we also find that the ringlet's semi-major axis appears to be decreasing with time at a rate of 2.4+/-0.4 km/year between 2005 and 2013. A closer look at these measurements, along with a consideration of earlier Voyager observations of this same ringlet, suggests that the mean radius of D68 moves back and forth, perhaps with a period of around 15 Earth years or about half a Saturn year. These observations could place important constraints on both the ringlet's local dynamical environment and the planet's gravitational field.Comment: 39 Pages, 11 Figures accepted for publication in Icarus Text slightly modified to match corrections to proof

Corrugations and eccentric spirals in Saturn's D ring: New insights into what happened at Saturn in 1983

Previous investigations of Saturn's outer D ring (73,200-74,000 km from Saturn's center) identified periodic brightness variations whose radial wavenumber increased linearly over time. This pattern was attributed to a vertical corrugation, and its temporal variability implied that some event --possibly an impact with interplanetary debris-- caused the ring to become tilted out the planet's equatorial plane in 1983. This work examines these patterns in greater detail using a more extensive set of Cassini images in order to obtain additional insights into the 1983 event. These additional data reveal that the D ring is not only corrugated, but also contains a time-variable periodic modulation in its optical depth that probably represents organized eccentric motions of the D-ring's particles. This second pattern suggests that whatever event tilted the rings also disturbed the radial or azimuthal velocities of the ring particles. Furthermore, the relative amplitudes of the two patterns indicate that the vertical motions induced by the 1983 event were 2.3+/-0.5 times larger than the corresponding in-plane motions. If these structures were indeed produced by an impact, material would need to strike the ring at a steep angle (more than 60 degrees from the ring plane) to produce such motions. Meanwhile, the corrugation wavelengths in the D ring are about 0.7% shorter than one would predict based on extrapolations from similar structures in the nearby C ring. This could indicate that the D-ring was tilted/disturbed about 60 days before the C ring. Such a timing difference could be explained if the material that struck the ring was derived from debris released when some object broke up near Saturn some months earlier. This debris would need to have a substantial initial velocity dispersion and have its orbital properties perturbed by solar tides prior to its collision with the rings.Comment: 53 Pages, 11 Figures, Accepted for publication in Icarus, Includes small corrections found in the proof stag

A Survey for Outer Satellites of Mars: Limits to Completeness

We surveyed the Hill sphere of Mars for irregular satellites. Our search covered nearly the entire Hill Sphere, but scattered light from Mars excluded the inner few arcminutes where the satellites Phobos and Deimos reside. No new satellites were found to an apparent limiting red magnitude of 23.5, which corresponds to radii of about 0.09 km using an albedo of 0.07.Comment: 5 figures (1 color), 2 Tables, to appear in AJ Nov. 200

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law

A direct nuclear magnetic resonance method to investigate lysine acetylation of intrinsically disordered proteins

Intrinsically disordered proteins are frequent targets for functional regulation through post-translational modification due to their high accessibility to modifying enzymes and the strong influence of changes in primary structure on their chemical properties. While lysine Nε-acetylation was first observed as a common modification of histone tails, proteomic data suggest that lysine acetylation is ubiquitous among both nuclear and cytosolic proteins. However, compared with our biophysical understanding of the other common post-translational modifications, mechanistic studies to document how lysine Nε-acetyl marks are placed, utilized to transduce signals, and eliminated when signals need to be turned off, have not kept pace with proteomic discoveries. Herein we report a nuclear magnetic resonance method to monitor Nε-lysine acetylation through enzymatic installation of a13C-acetyl probe on a protein substrate, followed by detection through 13C direct-detect spectroscopy. We demonstrate the ease and utility of this method using histone H3 tail acetylation as a model. The clearest advantage to this method is that it requires no exogenous tags that would otherwise add steric bulk, change the chemical properties of the modified lysine, or generally interfere with downstream biochemical processes. The non-perturbing nature of this tagging method is beneficial for application in any system where changes to local structure and chemical properties beyond those imparted by lysine modification are unacceptable, including intrinsically disordered proteins, bromodomain containing protein complexes, and lysine deacetylase enzyme assays

Dosimetric Comparison of VMAT, IMRT and Proton Therapy for Post- Prostatectomy Radiation Therapy for Prostate Cancer

Purpose/Objectives: Radiation therapy (RT) for the treatment of prostate cancer after radical prostatectomy (RP) is widely accepted. With technological advances, radiation treatment technique and dosimetry may vary. The purpose of this study is to quantify dosimetric difference of proton therapy versus VMAT and IMRT focusing on bladder and rectal dose sparing and target coverage. American Society for Therapeutic Radiation Oncology (ASTRO) 52nd Annual Meeting October 31 - November 4, San Diego, C