Automation of The Guiding Center Expansion

We report on the use of the recently-developed Mathematica package \emph{VEST} (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the transformation order-by-order. This procedure has several novel features. (1) It is designed to allow the user to easily explore the guiding center transformation's numerous non-unique forms or representations. (2) The procedure proceeds entirely in cartesian position and velocity coordinates, thereby producing manifestly gyrogauge invariant results; the commonly-used perpendicular unit vector fields $e_1,e_2$ are never even introduced. (3) It is easy to apply in the derivation of higher-order contributions to the guiding center transformation without fear of human error. Our code therefore stands as a useful tool for exploring subtle issues related to the physics of toroidal momentum conservation in tokamaks.Comment: 34 page

Effect of unsaturated zone soil moisture content on vapor phase pollutant propagation in controlled laboratory experiments

Experiments were conducted to assess and model the effects of unsaturated zone soil moisture content on vapor-phase pollutant propagation in a controlled setting. A two-dimensional sandtank was utilized for controlled vapor-phase experiments, with pollutant vapors of octane and diesel fuel introduced through a finely slotted source tube. Soil moisture content was varied from 0% to 10% by weight for octane experiments, and from 0% to 5% by weight for diesel fuel. The effects of introduced soil moisture on the transport of each pollutant vapor were observed via soil-gas sampling from access ports. Soil-gas samples were analyzed with FID gas chromatography to determine a gross hydrocarbon concentration for discrete time intervals and distances from the vapor source; Analytical modeling methods based on Fickian diffusion, developed by Kreamer (1982), were used to estimate two primary diffusion parameters D{dollar}\sb{\rm e}{dollar}, the effective diffusion coefficient, and A*, the sorption corrected porosity. Estimations were carried out using a FORTRAN program with a non-linear subroutine. The estimated parameters were used to model concentration curves for each moisture content. The modeling indicated adverse effects on vapor propagation near 2% moisture content for octane and 2% moisture content for diesel fuel; A trend observed for the octane vapor modeling illustrates the relationship of D{dollar}\rm\sb{e},\ D\sb{k},{dollar} and A* to the tortuosity factor. Tortuosity was observed to decrease as moisture content increased up to 5% by mass. As moisture content increase beyond 5% gravimetrically, tortuosity began to increase as the porosity became occluded by water molecules

Examining Atmospheric Dust Deposition and its Effects on Alpine Lakes in the Uinta Mountains, Utah

The composition and effects of atmospheric dust on remote alpine lakes were investigated using geological and paleolimnolgical techniques. Short cores (\u3c 50 cm long) were retrieved from five lakes on the eastern side of the Uinta Mountains, Utah. Sediment core chronologies are based on 210 Pb and 14C dates. Dust and lake sediment core samples were analyzed for their particle size distribution, mineralogy, and chemistry. Dust was fine grained (\u3c 10 μm) and was enriched (i.e., 50X greater concentrations) in 31 major, minor and trace elements relative to local bedrock material. In lake sediments, changes in the concentrations of key dust elements were recorded beginning in ~ AD 1900. Elements that increased in all five lakes included metals (Bi, Pb, Sb, Sn) and the nutrient P. The metals Cu and Cd also increased in four lakes. These changes are coincident with European settlement, the onset of mining, and the intensification of agriculture. The findings of this thesis show that atmospheric deposition in the Uinta Mountains is unique in composition relative to the last several hundred years. Percentage organics also increased during this period indicating increased productivity. Cladocera community composition recorded changes potentially caused by variations in atmospheric deposition of Ca in this region, although results were inconclusive

General formulas for adiabatic invariants in nearly-periodic Hamiltonian systems

While it is well-known that every nearly-periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely-defined scalar. A less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally-applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.Comment: 32 pages, submitted to JPP special issue on Hamiltonian systems in plasma physic

Supersonic plasma turbulence in the laboratory

The properties of supersonic, compressible plasma turbulence determine the behavior of many terrestrial and astrophysical systems. In the interstellar medium and molecular clouds, compressible turbulence plays a vital role in star formation and the evolution of our galaxy. Observations of the density and velocity power spectra in the Orion B and Perseus molecular clouds show large deviations from those predicted for incompressible turbulence. Hydrodynamic simulations attribute this to the high Mach number in the interstellar medium (ISM), although the exact details of this dependence are not well understood. Here we investigate experimentally the statistical behavior of boundary-free supersonic turbulence created by the collision of two laser-driven high-velocity turbulent plasma jets. The Mach number dependence of the slopes of the density and velocity power spectra agree with astrophysical observations, and supports the notion that the turbulence transitions from being Kolmogorov-like at low Mach number to being more Burgers-like at higher Mach numbers

S. A. J. Clark to his Father (23 May 1863)

Regarding a Memphis newspaper report naming killed and wounded; also mentions Jackson, MS, and Vicksburg, MShttps://egrove.olemiss.edu/ciwar_corresp/1546/thumbnail.jp