Origin and evolution of planetary atmospheres

Spacecraft and groundbased observations of the atmospheres of solar system objects have provided a definition of their present characteristics and have yielded clues about their past history. Table 1 presents a summary of our current knowledge of the atmospheric properties of all the planets, except Pluto, and several satellites. The masses of these atmospheres range from the very miniscule values for the Moon, Mercury, and Io, to the more substantial values for the Earth, Venus, Mars, and Titan, to the very large values for the giant planets, where the atmosphere constitutes a significant fraction of the total planetary mass. The compositions of these atmospheres encompass ones dominated by rare gases (the Moon and Mercury), ones containing highly oxidized compounds of carbon, nitrogen, and sulfur (the outer three terrestrial planets and Io), and ones with highly reduced gases (Titan and the giant planets). What factors account for this enormous diversity in properties

Gluing and wormholes for the Einstein constraint equations

We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions can be made either when the initial manifold is compact or asymptotically Euclidean or asymptotically hyperbolic, with suitable corresponding conditions on the extrinsic curvature. In the compact setting a mild nondegeneracy condition is required. In the final section of the paper, we list a number ways this construction may be used to produce new types of vacuum spacetimes.Comment: 42 pages, 4 figures, minor typos corrected, 1 reference added. To appear in Comm. Math. Phys. v3 (v2 had old Latex source file

Saltation thresholds and entrainment of fine particles at Earth and Martian pressures

An open circuit wind tunnel designed to operate in a large vacuum chamber was built at NASA-Ames to investigate saltation threshold, flux, deflation rates, and other aeolian phenomena on the planet Mars. The vacuum chamber will operate at pressures as low as 4 mbar, and the tunnel operates at windspeeds as high as 150 m/sec. Either air or CO2 can be used as a working fluid. It was found that, to a first order approximation, the same dynamic pressure was required at Martian pressure to entrain or saltate particles as was required on Earth, although wind and particle speed are considerably higher at Martian pressure. A 2nd wind tunnel, designed to operate aboard the NASA KC-135 0-g aircraft to obtain information on the effect of gravity on saltation threshold and the interparticle force at 0-g, is also described and test data presented. Some of the experiments are summarized and various aspects of low pressure aeolian entrainment for particles 12 to 100 micron in diameter are discussed, some of them unique to low pressure testing and some common in Earth pressure particle transport testing. The facility, the modes of operation, and the materials used are described

Giant planets: Clues on current and past organic chemistry in the outer solar system

The giant planets of the outer solar system - Jupiter, Saturn, Uranus, and Neptune - were formed in the same flattened disk of gas and dust, the solar nebula, as the terrestrial planets were. Yet, the giant planets differ in some very fundamental ways from the terrestrial planets. Despite enormous differences, the giant planets are relevant to exobiology in general and the origin of life on the Earth in particular. The giant planets are described as they are today. Their basic properties and the chemistry occurring in their atmospheres is discussed. Theories of their origin are explored and aspects of these theories that may have relevance to exobiology and the origin of life on Earth are stressed

Stratospheric dynamics

A global circulation model is being used to study the dynamical behavior of stratospheric planetary waves (waves having horizontal wavelengths of tens of thousands of kilometers) forced by growing cyclonic disturbances of intermediate scale, typically with wavelengths of a few thousand kilometers, which occur in the troposphere. Planetary scale waves are the dominant waves in the stratosphere, and are important for understanding the distribution of atmospheric trace constituents. Planetary wave forcing by intermediate scale tropospheric cyclonic disturbances is important for producing eastward travelling planetary waves of the sort which are prominent in the Southern Hemisphere during winter. The same global circulation model is also being used to simulate and understand the rate of dispersion and possible stratospheric climatic feedbacks of the El Chichon volcanic aerosol cloud. By comparing the results of the model calculation with an established data set now in existence for the volcanic cloud spatial and temporal distribution, stratospheric transport processes will be better understood, and the extent to which the cloud modified stratospheric wind and temperature fields can be assessed

Some Lambda Calculus and Type Theory Formalized

"This paper is about our hobby." That is the first sentence of [MP93], the first report on our formal development of lambda calculus and type theory, written in autumn 1992. We have continued to pursue this hobby on and off ever since, and have developed a substantial body of formal knowledge, including Church-Rosser and standardizationtheorems for beta reduction, and the basic theory ofPure Type Systems (PTS) leading to the strengthening theorem and type checking algorithms for PTS. Some of this work is reported in [MP93, vBJMP94, Pol94b, Pol95]. In the present paper we survey this work, including some new proofs, and point out what we feel has been learned about the general issues of formalizing mathematics. On the technical side, we describe an abstract, and simplified, proof of standardization for beta reduction, not previously published, that doesnot mention redex positions or residuals. On the general issues, we emphasize the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts. The LEGO Proof Development System [LP92] was used to check the work in an implementation of the Extended Calculus of Constructions(ECC) with inductive types [Luo94]. LEGO is a refinement styleproof checker, publicly available by ftp and WWW, with a User's Manual [LP92] and a large collection of examples. Section 1.3 contains information on accessing the formal development described in this paper. Other interesting examples formalized in LEGO include program specification and data refinement [Luo91], strong normalization of System F [Alt93], synthetic domain theory [Reu95, Reu96], and operational semantics for imperative programs [Sch97]