Trace formula for a dielectric microdisk with a point scatterer

Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In the present paper we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays, but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.Comment: 39 pages, 18 figures, pdflate

Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Students in Higher Education and their Mental Health

Theme: Nursing students and their mental health needs, focus on practice placement support

Slow light in molecular aggregates nanofilms

We study slow light performance of molecular aggregates arranged in nanofilms by means of coherent population oscillations (CPO). The molecular cooperative behavior inside the aggregate enhances the delay of input signals in the GHz range in comparison with other CPO-based devices. Moreover, the problem of residual absorption present in CPO processes, is removed. We also propose an optical switch between different delays by exploiting the optical bistability of these aggregates.Comment: 4 pages, 4 figure

Atomic Gas in Debris Discs

We have conducted a search for optical circumstellar absorption lines in the spectra of 16 debris disc host stars. None of the stars in our sample showed signs of emission line activity in either H$_{\alpha}$, Ca II or Na I, confirming their more evolved nature. Four stars were found to exhibit narrow absorption features near the cores of the photospheric Ca II and Na I D lines (when Na I D data were available). We analyse the characteristics of these spectral features to determine whether they are of circumstellar or interstellar origins. The strongest evidence for circumstellar gas is seen in the spectrum of HD110058, which is known to host a debris disc observed close to edge-on. This is consistent with a recent ALMA detection of molecular gas in this debris disc, which shows many similarities to the $\beta$ Pictoris system.Comment: Accepted 13/12/2016. Received 2/12/2016; Deposited on 22/11/2016. - 13 Pages, 9 Figures - MNRAS Advance Access published December 15, 201

A Dense Packing of Regular Tetrahedra

We construct a dense packing of regular tetrahedra, with packing density $D > >.7786157$.Comment: full color versio

Effect of Urea and Distillers Inclusion in Dry- Rolled Corn Based Diets on Heifer Performance and Carcass Characteristics

Crossbred heifers (n=96, BW = 810 ± 20) were utilized to evaluate the effects of increasing wet distillers grains plus solubles and urea inclusion in a dry rolled corn based finishing diet on performance and carcass characteristics. Heifers were individually fed using a calan gate system with a 2 × 2 factorial arrangement of treatments. Factors included distillers inclusion at either 10 or 20% of diet DM and urea inclusion at either 0.2 or 1.4% of diet DM. Th ere was no difference for final body weight, average daily gain, and feed conversion on a live or carcass adjusted basis for either urea or distillers inclusion in the diet. Dry matter intake was reduced with increased urea inclusion; however, distillers inclusion did not influence intake. Added distillers and urea in the diet had minimal impact on performance suggesting supplemental urea in a dry rolled corn based finishing diets is of minimal benefit when feeding at least 10% distillers grains