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

Cargo Logistics Airlift Systems Study (CLASS). Volume 2: Case study approach and results

Models of transportation mode decision making were developed. The user's view of the present and future air cargo systems is discussed. Issues summarized include: (1) organization of the distribution function; (2) mode choice decision making; (3) air freight system; and (4) the future of air freight