7,025 research outputs found
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 -hypergeometric series.
Of those, mock theta functions have been particularly intriguing, and by work
of Zwegers, we now know how these curious -series fit into the theory of
automorphic forms. The analytic theory of partial theta functions however,
which have -expansions resembling modular theta functions, is not well
understood. Here we consider families of -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
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