Theoretical comparison of maser materials for a 32-GHz maser amplifier

The computational results of a comparison of maser materials for a 32 GHz maser amplifier are presented. The search for a better maser material is prompted by the relatively large amount of pump power required to sustain a population inversion in ruby at frequencies on the order of 30 GHz and above. The general requirements of a maser material and the specific problems with ruby are outlined. The spin Hamiltonian is used to calculate energy levels and transition probabilities for ruby and twelve other materials. A table is compiled of several attractive operating points for each of the materials analyzed. All the materials analyzed possess operating points that could be superior to ruby. To complete the evaluation of the materials, measurements of inversion ratio and pump power requirements must be made in the future

Carbon Dioxide in Exoplanetary Atmospheres: Rarely Dominant Compared to Carbon Monoxide and Water in Hot, Hydrogen-dominated Atmospheres

We present a comprehensive study of the abundance of carbon dioxide in exoplanetary atmospheres in hot, hydrogen-dominated atmospheres. We construct novel analytical models of systems in chemical equilibrium that include carbon monoxide, carbon dioxide, water, methane and acetylene and relate the equilibrium constants of the chemical reactions to temperature and pressure via the tabulated Gibbs free energies. We prove that such chemical systems may be described by a quintic equation for the mixing ratio of methane. By examining the abundances of these molecules across a broad range of temperatures (spanning equilibrium temperatures from 600 to 2500 K), pressures (via temperature-pressure profiles that explore albedo and opacity variations) and carbon-to-oxygen ratios, we conclude that carbon dioxide is subdominant compared to carbon monoxide and water. Atmospheric mixing does not alter this conclusion if carbon dioxide is subdominant everywhere in the atmosphere. Carbon dioxide and carbon monoxide may attain comparable abundances if the metallicity is greatly enhanced, but this property is negated by temperatures above 1000 K. For hydrogen-dominated atmospheres, our generic result has the implication that retrieval studies may wish to set the subdominance of carbon dioxide as a prior of the calculation and not let its abundance completely roam free as a fitting parameter, because it directly affects the inferred value of the carbon-to-oxygen ratio and may produce unphysical conclusions. We discuss the relevance of these implications for the hot Jupiter WASP-12b and suggest that some of the previous results are chemically impossible. The relative abundance of carbon dioxide to acetylene is potentially a sensitive diagnostic of the carbon-to-oxygen ratio.Comment: Accepted by ApJ. 12 pages, 8 figures, 2 table

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van't Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients) and procedures associated with the Gibbs free energy (minimisation, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.Comment: Accepted by ApJ. 9 pages, 4 figure

Discrete analogue computing with rotor-routers

Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently check that a computation has been carried out correctly in less time than the computation itself required, provided one has a certificate that can itself be computed by the rotor-router network. Rotor-router networks can be viewed as both discrete analogues of continuous linear systems and deterministic analogues of stochastic processes.Comment: To appear in Chaos Special Focus Issue on Intrinsic and Designed Computatio

Mars Dust Storms: Interannual Variability and Chaos

The hypothesis is that the global climate system, consisting of atmospheric dust interacting with the circulation, produces its own interannual variability when forced at the annual frequency. The model has two time-dependent variables representing the amount of atmospheric dust in the northern and southern hemispheres, respectively. Absorption of sunlight by the dust drives a cross-equatorial Hadley cell that brings more dust into the heated hemisphere. The circulation decays when the dust storm covers the globe. Interannual variability manifests itself either as a periodic solution in which the period is a multiple of the Martian year, or as an aperiodic (chaotic) solution that never repeats. Both kinds of solution are found in the model, lending support to the idea that interannual variability is an intrinsic property of the global climate system. The next step is to develop a hierarchy of dust-circulation models capable of being integrated for many years