A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions

Several transiting super-Earths are expected to be discovered in the coming few years. While tools to model the interior structure of transiting planets exist, inferences about the composition are fraught with ambiguities. We present a framework to quantify how much we can robustly infer about super-Earth and Neptune-size exoplanet interiors from radius and mass measurements. We introduce quaternary diagrams to illustrate the range of possible interior compositions for planets with four layers (iron core, silicate mantles, water layers, and H/He envelopes). We apply our model to CoRoT-7b, GJ 436b, and HAT-P-11b. Interpretation of planets with H/He envelopes is limited by the model uncertainty in the interior temperature, while for CoRoT-7b observational uncertainties dominate. We further find that our planet interior model sharpens the observational constraints on CoRoT-7b's mass and radius, assuming the planet does not contain significant amounts of water or gas. We show that the strength of the limits that can be placed on a super-Earth's composition depends on the planet's density; for similar observational uncertainties, high-density super-Mercuries allow the tightest composition constraints. Finally, we describe how techniques from Bayesian statistics can be used to take into account in a formal way the combined contributions of both theoretical and observational uncertainties to ambiguities in a planet's interior composition. On the whole, with only a mass and radius measurement an exact interior composition cannot be inferred for an exoplanet because the problem is highly underconstrained. Detailed quantitative ranges of plausible compositions, however, can be found.Comment: 20 pages, 10 figures, published in Ap

Central Charge and the Andrews-Bailey Construction

From the equivalence of the bosonic and fermionic representations of finitized characters in conformal field theory, one can extract mathematical objects known as Bailey pairs. Recently Berkovich, McCoy and Schilling have constructed a `generalized' character formula depending on two parameters \ra and $\r2$, using the Bailey pairs of the unitary model $M(p-1,p)$. By taking appropriate limits of these parameters, they were able to obtain the characters of model $M(p,p+1)$, $N=1$ model $SM(p,p+2)$, and the unitary $N=2$ model with central charge $c=3(1-{\frac{2}{p}})$. In this letter we computed the effective central charge associated with this `generalized' character formula using a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models.Comment: Latex2e, requires cite.sty package, 13 pages. Additional footnote, citation and reference

Large deployable antenna program. Phase 1: Technology assessment and mission architecture

The program was initiated to investigate the availability of critical large deployable antenna technologies which would enable microwave remote sensing missions from geostationary orbits as required for Mission to Planet Earth. Program goals for the large antenna were: 40-meter diameter, offset-fed paraboloid, and surface precision of 0.1 mm rms. Phase 1 goals were: to review the state-of-the-art for large, precise, wide-scanning radiometers up to 60 GHz; to assess critical technologies necessary for selected concepts; to develop mission architecture for these concepts; and to evaluate generic technologies to support the large deployable reflectors necessary for these missions. Selected results of the study show that deployable reflectors using furlable segments are limited by surface precision goals to 12 meters in diameter, current launch vehicles can place in geostationary only a 20-meter class antenna, and conceptual designs using stiff reflectors are possible with areal densities of 2.4 deg/sq m

Consensus Acceleration in Multiagent Systems with the Chebyshev Semi-Iterative Method

We consider the fundamental problem of reaching consensus in multiagent systems; an operation required in many applications such as, among others, vehicle formation and coordination, shape formation in modular robotics, distributed target tracking, and environmental modeling. To date, the consensus problem (the problem where agents have to agree on their reported values) has been typically solved with iterative decentralized algorithms based on graph Laplacians. However, the convergence of these existing consensus algorithms is often too slow for many important multiagent applications, and thus they are increasingly being combined with acceleration methods. Unfortunately, state-of-the-art acceleration techniques require parameters that can be optimally selected only if complete information about the network topology is available, which is rarely the case in practice. We address this limitation by deriving two novel acceleration methods that can deliver good performance even if little information about the network is available. The first proposed algorithm is based on the Chebyshev semi-iterative method and is optimal in a well defined sense; it maximizes the worst-case convergence speed (in the mean sense) given that only rough bounds on the extremal eigenvalues of the network matrix are available. It can be applied to systems where agents use unreliable communication links, and its computational complexity is similar to those of simple Laplacian-based methods. This algorithm requires synchronization among agents, so we also propose an asynchronous version that approximates the output of the synchronous algorithm. Mathematical analysis and numerical simulations show that the convergence speed of the proposed acceleration methods decrease gracefully in scenarios where the sole use of Laplacian-based methods is known to be impractical

A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure