Constraining the orbits of sub-stellar companions imaged over short orbital arcs

Imaging a star's companion at multiple epochs over a short orbital arc provides only four of the six coordinates required for a unique orbital solution. Probability distributions of possible solutions are commonly generated by Monte Carlo (MCMC) analysis, but these are biased by priors and may not probe the full parameter space. We suggest alternative methods to characterise possible orbits, which compliment the MCMC technique. Firstly the allowed ranges of orbital elements are prior-independent, and we provide means to calculate these ranges without numerical analyses. Hence several interesting constraints (including whether a companion even can be bound, its minimum possible semi-major axis and its minimum eccentricity) may be quickly computed using our relations as soon as orbital motion is detected. We also suggest an alternative to posterior probability distributions as a means to present possible orbital elements, namely contour plots of elements as functions of line of sight coordinates. These plots are prior-independent, readily show degeneracies between elements and allow readers to extract orbital solutions themselves. This approach is particularly useful when there are other constraints on the geometry, for example if a companion's orbit is assumed to be aligned with a disc. As examples we apply our methods to several imaged sub-stellar companions including Fomalhaut b, and for the latter object we show how different origin hypotheses affect its possible orbital solutions. We also examine visual companions of A- and G-type main sequence stars in the Washington Double Star Catalogue, and show that $\gtrsim50$ per cent must be unbound.Comment: Accepted for publication in MNRA

A Comparison of Semi-Analytic and Smoothed Particle Hydrodynamics Galaxy Formation

We compare the statistical properties of galaxies found in two different models of hierarchical galaxy formation: the semi-analytic model of Cole et al. and the smoothed particle hydrodynamics (SPH) simulations of Pearce et al. Using a `stripped-down' version of the semi-analytic model which mimics the resolution of the SPH simulations and excludes physical processes not included in them, we find that the two models produce an ensemble of galaxies with remarkably similar properties, although there are some differences in the gas cooling rates and in the number of galaxies that populate halos of different mass. The full semi-analytic model, which has effectively no resolution limit and includes a treatment of star formation and supernovae feedback, produces somewhat different (but readily understandable) results. Agreement is particularly good for the present-day global fractions of hot gas, cold dense (i.e. galactic) gas and uncollapsed gas, for which the SPH and stripped-down semi-analytic calculations differ by at most 25%. In the most massive halos, the stripped-down semi-analytic model predicts, on the whole, up to 50% less gas in galaxies than is seen in the SPH simulations. The two techniques apportion this cold gas somewhat differently amongst galaxies in a given halo. This difference can be tracked down to the greater cooling rate in massive halos in the SPH simulation compared to the semi-analytic model. (abridged)Comment: 19 pages, 13 figures, to appear in MNRAS. Significantly extended to explore galaxy progenitor distributions and behaviour of models at high redshift

Expanded microchannel heat exchanger: design, fabrication and preliminary experimental test

This paper first reviews non-traditional heat exchanger geometry, laser welding, practical issues with microchannel heat exchangers, and high effectiveness heat exchangers. Existing microchannel heat exchangers have low material costs, but high manufacturing costs. This paper presents a new expanded microchannel heat exchanger design and accompanying continuous manufacturing technique for potential low-cost production. Polymer heat exchangers have the potential for high effectiveness. The paper discusses one possible joining method - a new type of laser welding named "forward conduction welding," used to fabricate the prototype. The expanded heat exchanger has the potential to have counter-flow, cross-flow, or parallel-flow configurations, be used for all types of fluids, and be made of polymers, metals, or polymer-ceramic precursors. The cost and ineffectiveness reduction may be an order of magnitude or more, saving a large fraction of primary energy. The measured effectiveness of the prototype with 28 micron thick black low density polyethylene walls and counterflow, water-to-water heat transfer in 2 mm channels was 72%, but multiple low-cost stages could realize the potential of higher effectiveness

Optimal traps in graphene

We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us to utilize the Levinson Theorem to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads to us posit the use of `optimal traps' to combat the chiral tunneling found in graphene, which could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find the zero angular momentum states create a dominant peak in scattering cross-section as energy tends towards the Dirac point energy, suggesting a dominant contribution to resistivity.Comment: 11 pages, 5 figure

Fundamental Limits of Classical and Quantum Imaging

Quantum imaging promises increased imaging performance over classical protocols. However, there are a number of aspects of quantum imaging that are not well understood. In particular, it has so far been unknown how to compare classical and quantum imaging procedures. Here, we consider classical and quantum imaging in a single theoretical framework and present general fundamental limits on the resolution and the deposition rate for classical and quantum imaging. The resolution can be estimated from the image itself. We present a utility function that allows us to compare imaging protocols in a wide range of applications.Comment: 4 pages, 3 figures; accepted for Physical Review Letters, with updated title and fixed typo