Atmospheric Trace Molecule Spectroscopy (ATMOS)

The Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment is a space-borne investigation designed to obtain fundamental information related to the chemistry and physics of the earth's upper atmosphere (20 to 120 km altitude). The instrument, a high resolution (0.01/cm) interferometric spectrometer, measures the atmospheric absorption of solar radiation over the wavelength range from 2 to 16 micrometers, a spectral band which encompasses active transitions of all of the molecular species of current importance in upper atmospheric studies. There are two major aspects to the experiment: (1) the determination of the detailed compositional structure of the stratosphere and mesosphere, and its global, seasonal, and long-term variability; and (2) the study of the partitioning of absorbed solar energy at levels in the atmosphere characterized by dissociation of many of the constituents and by the breakdown of thermodynamic equilibrium. Characteristics of ATMOS are given. This experiment will be part of the atmospheric science research payload flown on the Atmospheric Laboratory for Applications and Science (ATLAS 1) NASA mission planned for late 1990

Formalizing Mathematical Knowledge as a Biform Theory Graph: A Case Study

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory graph is a network of theories connected by meaning-preserving theory morphisms that map the formulas of one theory to the formulas of another theory. Theory graphs are in turn well suited for formalizing mathematical knowledge at the most convenient level of abstraction using the most convenient vocabulary. We are interested in the problem of whether a body of mathematical knowledge can be effectively formalized as a theory graph of biform theories. As a test case, we look at the graph of theories encoding natural number arithmetic. We used two different formalisms to do this, which we describe and compare. The first is realized in ${\rm CTT}_{\rm uqe}$, a version of Church's type theory with quotation and evaluation, and the second is realized in Agda, a dependently typed programming language.Comment: 43 pages; published without appendices in: H. Geuvers et al., eds, Intelligent Computer Mathematics (CICM 2017), Lecture Notes in Computer Science, Vol. 10383, pp. 9-24, Springer, 201

Evaluating LL-functions with few known coefficients

We address the problem of evaluating an $L$-function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that is possible to evaluate the $L$-function more precisely than one would expect from the standard approach. The method, however, requires considerably more computational effort to achieve a given accuracy than would be needed if more Dirichlet coefficients were available.Comment: 14 pages; Added a new section where we evaluate L(1/2 + 100 i, Delta) to 42 decimal places using no Dirichlet series coefficients at al

The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations

We consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts

Radiation/convection coupling in rocket motor and plume analysis

A method for describing radiation/convection coupling to a flow field analysis was developed for rocket motors and plumes. The three commonly used propellant systems (H2/O2, RP-1/O2, and solid propellants) radiate primarily as: molecular emitters, non-scattering small particles (soot), and scattering larger particles (Al2O3), respectively. For the required solution, the divergence of the radiation heat flux was included in the energy equation, and the local, volume averaged intensity was determined by a solution to the radiative transfer equation. A rigorous solution to this problem is intractable, therefore, solution methods which use the ordinary and improved differential approximation were developed. This radiation model was being incorporated into the FDNS code, a Navier-Stokes flowfield solver for multiphase, turbulent combusting flows

Full Wave Form Inversion for Seismic Data

In seismic wave inversion, seismic waves are sent into the ground and then observed at many receiving points with the aim of producing high-resolution images of the geological underground details. The challenge presented by Saudi Aramco is to solve the inverse problem for multiple point sources on the full elastic wave equation, taking into account all frequencies for the best resolution. The state-of-the-art methods use optimisation to find the seismic properties of the rocks, such that when used as the coefficients of the equations of a model, the measurements are reproduced as closely as possible. This process requires regularisation if one is to avoid instability. The approach can produce a realistic image but does not account for uncertainty arising, in general, from the existence of many different patterns of properties that also reproduce the measurements. In the Study Group a formulation of the problem was developed, based upon the principles of Bayesian statistics. First the state-of-the-art optimisation method was shown to be a special case of the Bayesian formulation. This result immediately provides insight into the most appropriate regularisation methods. Then a practical implementation of a sequential sampling algorithm, using forms of the Ensemble Kalman Filter, was devised and explored

Sequential inverse problems Bayesian principles and the\ud logistic map example

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection

On Carbon Burning in Super Asymptotic Giant Branch Stars

We explore the detailed and broad properties of carbon burning in Super Asymptotic Giant Branch (SAGB) stars with 2755 MESA stellar evolution models. The location of first carbon ignition, quenching location of the carbon burning flames and flashes, angular frequency of the carbon core, and carbon core mass are studied as a function of the ZAMS mass, initial rotation rate, and mixing parameters such as convective overshoot, semiconvection, thermohaline and angular momentum transport. In general terms, we find these properties of carbon burning in SAGB models are not a strong function of the initial rotation profile, but are a sensitive function of the overshoot parameter. We quasi-analytically derive an approximate ignition density, $\rho_{ign} \approx 2.1 \times 10^6$ g cm$^{-3}$, to predict the location of first carbon ignition in models that ignite carbon off-center. We also find that overshoot moves the ZAMS mass boundaries where off-center carbon ignition occurs at a nearly uniform rate of $\Delta M_{\rm ZAMS}$/$\Delta f_{\rm{ov}}\approx$ 1.6 $M_{\odot}$. For zero overshoot, $f_{\rm{ov}}$=0.0, our models in the ZAMS mass range $\approx$ 8.9 to 11 $M_{\odot}$ show off-center carbon ignition. For canonical amounts of overshooting, $f_{\rm{ov}}$=0.016, the off-center carbon ignition range shifts to $\approx$ 7.2 to 8.8 $M_{\odot}$. Only systems with $f_{\rm{ov}}$ $\geq 0.01$ and ZAMS mass $\approx$ 7.2-8.0 $M_{\odot}$ show carbon burning is quenched a significant distance from the center. These results suggest a careful assessment of overshoot modeling approximations on claims that carbon burning quenches an appreciable distance from the center of the carbon core.Comment: Accepted ApJ; 23 pages, 21 figures, 5 table