Trends Abroad: Australia

published or submitted for publicatio

Mode locking and ultrashort laser pulses by anisotropic molecular liquids

Spectral broadening by the nonlinear dielectric response of anisotropic molecules has been observed and explained by Bloembergen and Lallemand.(1) Any two frequencies, say ω1 and ω2, present in the incident optical beam exert a torque on the molecules at a frequency (ω1-ω2). The resultant oscillation of the average molecular orientation causes a modulation of the dielectric constant at ω1-ω2

Event reconstruction in high resolution Compton telescopes

The development of germanium Compton telescopes for nuclear gamma-ray astrophysics (~0.2-20 MeV) requires new event reconstruction techniques to accurately determine the initial direction and energy of photon events, as well as to consistently reject background events. This paper describes techniques for event reconstruction, accounting for realistic instrument/detector performance and uncertainties. An especially important technique is Compton Kinematic Discrimination, which allows proper interaction ordering and background rejection with high probabilities. The use of these techniques are crucial for the realistic evaluation of the performance and sensitivity of any germanium Compton telescope configuration.Comment: Accepted for publication in A&AS

Spectroscopy of a Globular Cluster in the Local Group dIrr NGC 6822

We present low-resolution Keck spectroscopy for the globular cluster H VIII in the Local Group dIrr galaxy NGC 6822. We find the metallicity of the cluster to be [Fe/H]= -1.58 +/- 0.28 and the age of the cluster to be 3-4 Gyr, slightly older than but consistent with previous age estimates. H VIII seems to be more metal-poor than most intermediate-age globular clusters in the Local Group, and appears most similar to the anomalous Small Magellanic Cloud clusters Lindsay 113 and NGC 339.Comment: 5 pages, including 3 figures. Accepted by MNRAS, uses mn2e.cl

Infinite products involving binary digit sums

Let $(u_n)_{n\ge 0}$ denote the Thue-Morse sequence with values $\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt 2}.\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*} We prove some analytical properties of $f$. We also obtain some new identities similar to the Woods-Robbins product.Comment: Accepted in Proc. AMMCS 2017, updated according to the referees' comment

Early Implementation of Pre-Existing Condition Insurance Plans: Providing an Interim Safety Net for the Uninsurable

Outlines enrollment trends and enrollee traits in a temporary program designed to provide affordable coverage to the uninsured with preexisting conditions, changes to structures and premiums, and estimated out-of-pocket costs by utilization and plan type

Cooperation under incomplete contracting

We examine the notion of the core when cooperation takes place in a setting with time and uncertainty. We do so in a two-period general equilibrium setting with incomplete markets. Market incompleteness implies that players cannot make all possible binding commitments regarding their actions at different date-events. We unify various treatments of dynamic core concepts existing in the literature. This results in definitions of the Classical Core, the Segregated Core, the Two-stage Core, the Strong Sequential Core, and the Weak Sequential Core. Except for the Classical Core, all these concepts can be defined by requiring absence of blocking in period 0 and at any date-event in period 1. The concepts only differ with respect to the notion of blocking in period 0. To evaluate these concepts, we study three market structures in detail: strongly complete markets, incomplete markets in finance economies, and incomplete markets in settings with multiple commodities

Amenability of Groupoids Arising from Partial Semigroup Actions and Topological Higher Rank Graphs

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable set $D\subset G$ such that $c(G^{u})D=Q$ for all $u\in G^{(0)}$. We show that our result is applicable to groupoids arising from partial semigroup actions. We explore these actions in detail and show that these groupoids include those arising from directed graphs, higher rank graphs and even topological higher rank graphs. We believe our methods yield a nice alternative groupoid approach to these important constructions.Comment: Revised as suggested by a very helpful referee. In particular, a gap in the proof of Theorem 5.13 has been repaired resulting in a much improved version (with fewer hypotheses