A Secular Resonant Origin for the Loneliness of Hot Jupiters

Despite decades of inquiry, the origin of giant planets residing within a few tenths of an astronomical unit from their host stars remains unclear. Traditionally, these objects are thought to have formed further out before subsequently migrating inwards. However, the necessity of migration has been recently called into question with the emergence of in-situ formation models of close-in giant planets. Observational characterization of the transiting sub-sample of close-in giants has revealed that "warm" Jupiters, possessing orbital periods longer than roughly 10 days more often possess close-in, co-transiting planetary companions than shorter period "hot" Jupiters, that are usually lonely. This finding has previously been interpreted as evidence that smooth, early migration or in situ formation gave rise to warm Jupiter-hosting systems, whereas more violent, post-disk migration pathways sculpted hot Jupiter-hosting systems. In this work, we demonstrate that both classes of planet may arise via early migration or in-situ conglomeration, but that the enhanced loneliness of hot Jupiters arises due to a secular resonant interaction with the stellar quadrupole moment. Such an interaction tilts the orbits of exterior, lower mass planets, removing them from transit surveys where the hot Jupiter is detected. Warm Jupiter-hosting systems, in contrast, retain their coplanarity due to the weaker influence of the host star's quadrupolar potential relative to planet-disk interactions. In this way, hot Jupiters and warm Jupiters are placed within a unified theoretical framework that may be readily validated or falsified using data from upcoming missions such as TESS.Comment: 9 pages, 4 figures. Accepted for publication in the Astronomical Journa

On the complexity of barrier resilience for fat regions and bounded ply

In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so that two fixed points can be connected without crossing any region. In this paper, we show that the problem is NP-hard when the collection only contains fat regions with bounded ply ¿ (even when they are axis-aligned rectangles of aspect ratio ). We also show that the problem is fixed-parameter tractable (FPT) for unit disks and for similarly-sized ß-fat regions with bounded ply ¿ and pairwise boundary intersections. We then use our FPT algorithm to construct an -approximation algorithm that runs in time, where .Peer ReviewedPostprint (author's final draft

Geometric Separation and Packing Problems

The first part of this thesis investigates combinatorial and algorithmic aspects of geometric separation problems in the plane. In such a setting one is given a set of points and a set of separators such as lines, line segments or disks. The goal is to select a small subset of those separators such that every path between any two points is intersected by at least one separator. We first look at several problems which arise when one is given a set of points and a set of unit disks embedded in the plane and the goal is to separate the points using a small subset of the given disks. Next, we focus on a separation problem involving only one region: Given a region in the plane, bounded by a piecewise linear closed curve, such as a fence, place few guards inside the fenced region such that wherever an intruder cuts through the fence, the closest guard is at most a distance one away. Restricting the separating objects to be lines, we investigate combinatorial aspects which arise when we use them to pairwise separate a set of points in the plane; hereafter we generalize the notion of separability to arbitrary sets and present several enumeration results. Lastly, we investigate a packing problem with a non-convex shape in ℝ3. We show that ℝ3 can be packed at a density of 0.222 with tori of major radius one and minor radius going to zero. Furthermore, we show that the same torus arrangement yields the asymptotically optimal number of pairwise linked tori

DONA Detector: Further Improvements and Evaluation for Field Applications

The DONA neutron spectrometer concept is based on the measurement of neutron induced activity in a series of small metal disks that have been exposed to a neutron field. The induced activity is measured and the neutron spectrum is calculated using and unfolding technique, based on environmental neutron spectra. The novelty of the approach lies in the concept as such, including usage of carefully selected metal disks arranged in a holder, high performance gamma-ray spectrometry and spectrum unfolding using a library of environmental neutron spectra. This report covers the IRMM exploratory research prolongation project for 2006 and now environmental neutron fields with considerably lower neutron fluence rates are used. The result shows that after further refinement of the detector device and the data evaluation program the detector can very well be used for environmental neutron fluence measurements. Tests were done at PTB, Germany, using their calibrated neutron source and at the MOX fuel fabrication plant Belgonuclearire in Mol, Belgium.JRC.D.4-Isotope measurement

New Structured Matrix Methods for Real and Complex Polynomial Root-finding

We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular numerical approximation of the real roots of a polynomial. Our analysis and experiments show efficiency of the resulting algorithms.Comment: 18 page