Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus

In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(E^2 ln E), where E is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(E^2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature

Molecular-Kinetic Simulations of Escape from the Ex-planet and Exoplanets: Criterion for Transonic Flow

The equations of gas dynamics are extensively used to describe atmospheric loss from solar system bodies and exoplanets even though the boundary conditions at infinity are not uniquely defined. Using molecular-kinetic simulations that correctly treat the transition from the continuum to the rarefied region, we confirm that the energy-limited escape approximation is valid when adiabatic expansion is the dominant cooling process. However, this does not imply that the outflow goes sonic. In fact in the sonic regime, the energy limited approximation can significantly under estimate the escape rate. Rather large escape rates and concomitant adiabatic cooling can produce atmospheres with subsonic flow that are highly extended. Since this affects the heating rate of the upper atmosphere and the interaction with external fields and plasmas, we give a criterion for estimating when the outflow goes transonic in the continuum region. This is applied to early terrestrial atmospheres, exoplanet atmospheres, and the atmosphere of the ex-planet, Pluto, all of which have large escape rates. The paper and its erratum, combined here, are published: ApJL 768, L4 (2013); ApJ, 779, L30 (2013).Comment: 11 pages, 3 figure

Physico-Chemical Principles of Sixteenth Century Metallurgy

Following a review of sixteenth century metallurgical literature and a discussion of Gibbs free energy, this thesis discusses thermodynamic considerations of galena (PbS) reduction by iron from a lead assay of this period. The importance of fluxes in this assay is emphasized. The discussion covers both equilibrium and non-equilibrium conditions at 1100 degrees Celsius. Possible substitutes for iron are also covered. Information from twenty-one small controlled lead assays is correlated with the thermodynamic discussion to determine the purpose of each constituent in the assay

Recent Cases: Bills and Notes — Separate Instruments Read as One and Affecting Status as Holder in Due Course and Negotiability of Promissory Note

Plaintiff finance company followed a policy of refusing to take up negotiable notes from appliance dealers unless the notes were accom­panied by a statement signed by the maker of the note that all mer­chandise had been installed. A dealer forged the signature of defendant maker on the certificate, warranting that all merchandise had been installed. Plaintiff finance company sued the maker on the note. Held: the finance company forfeited its status as a holder in due course by requiring the additional instrument as a condition precedent to acceptance of the note. The court reasoned that since the finance com­pany required the certificate of installation, it was to be held as an original party not only to the certificate but also to the note which accompanied it, and would be subject to all defenses maker could set up on either instrument