Approximating Nonlinear Forces with Phase-Space Decoupling

Beam tracking software for accelerators typically falls into two categories: fast envelope simulations limited to linear beam optics, and slower multiparticle simulations that can model nonlinear effects. To find a middle ground between these approaches, we introduce virtual coordinates in position and momentum which have a cross-dependency (i.e. p=f(x) where x is an initial position and p* is a virtual projection of momentum onto the position axis). This technique approximates multiparticle simulations with a significant reduction in calculation cost

Harnessing Health Care Markets for the Public Interest: Insights for U.S. Health Reform From the German and Dutch Multipayer Systems

Outlines how the German and Dutch systems offer universal coverage via competing insurance plans and promote effective and efficient care. Highlights insurance exchanges, multipayer policies and group purchasing, information systems, and public reporting

Fingerprints of giant planets in the photospheres of Herbig stars

Around 2% of all A stars have photospheres depleted in refractory elements. This is hypothesized to arise from a preferential accretion of gas rather than dust, but the specific processes and the origin of the material -- circum- or interstellar -- are not known. The same depletion is seen in 30% of young, disk-hosting Herbig Ae/Be stars. We investigate whether the chemical peculiarity originates in a circumstellar disk. Using a sample of systems for which both the stellar abundances and the protoplanetary disk structure are known, we find that stars hosting warm, flaring group I disks typically have Fe, Mg and Si depletions of 0.5 dex compared to the solar-like abundances of stars hosting cold, flat group II disks. The volatile, C and O, abundances in both sets are identical. Group I disks are generally transitional, having radial cavities depleted in millimetre-sized dust grains, while those of group II are usually not. Thus we propose that the depletion of heavy elements emerges as Jupiter-like planets block the accretion of part of the dust, while gas continues to flow towards the central star. We calculate gas to dust ratios for the accreted material and find values consistent with models of disk clearing by planets. Our results suggest that giant planets of ~0.1 to 10 M_Jup are hiding in at least 30% of Herbig Ae/Be disks.Comment: 5 pages, 3 figures, accepted for publication in A&A Letter

Partial theta functions and mock modular forms as q-hypergeometric series

Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of automorphic forms. The analytic theory of partial theta functions however, which have $q$-expansions resembling modular theta functions, is not well understood. Here we consider families of $q$-hypergeometric series which converge in two disjoint domains. In one domain, we show that these series are often equal to one another, and define mock theta functions, including the classical mock theta functions of Ramanujan, as well as certain combinatorial generating functions, as special cases. In the other domain, we prove that these series are typically not equal to one another, but instead are related by partial theta functions.Comment: 13 page

The probability that the number of points on the Jacobian of a genus 2 curve is prime

In 2000, Galbraith and McKee heuristically derived a formula that estimates the probability that a randomly chosen elliptic curve over a fixed finite prime field has a prime number of rational points. We show how their heuristics can be generalized to Jacobians of curves of higher genus. We then elaborate this in genus 2 and study various related issues, such as the probability of cyclicity and the probability of primality of the number of points on the curve itself. Finally, we discuss the asymptotic behavior as the genus tends to infinity.Comment: Minor edits, 37 pages. To appear in Proceedings of the London Mathematical Societ