Guidance and control strategies for aerospace vehicles

A simplified method of matched asymptotic expansions was developed where the common part in composite solution is generated as a polynomial in stretched variable instead of actually evaluating the same from the outer solution. This methodology was applied to the solution of the exact equations for three dimensional atmospheric entry problems. Compared to previous works, the present simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods. The optimal control problem arising in the noncoplanar orbital transfer employing aeroassist was also addressed

PushPush and Push-1 are NP-hard in 2D

We prove that two pushing-blocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a question we raised in [DDO00] for a variant we call Push-1. Both puzzles consist of unit square blocks on an integer lattice; all blocks are movable. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover when a block is pushed it slides the maximal extent of its free range. In the Push-1 version, the agent can only push one block one square at a time, the minimal extent---one square. Both NP-hardness proofs are by reduction from SAT, and rely on a common construction.Comment: 10 pages, 11 figures. Corrects an error in the conference version: Proc. of the 12th Canadian Conference on Computational Geometry, August 2000, pp. 211-21

Collective electromagnetic relaxation in crystals of molecular magnets

We study the magnetization reversal and electromagnetic radiation due to collective Landau-Zener relaxation in a crystal of molecular magnets. Analytical and numerical solutions for the time dependence of the relaxation process are obtained. The power of the radiation and the total emitted energy are computed as functions of the crystal parameters and the field sweep rate.Comment: 7 pages, 9 figure

PushPush is NP-hard in 2D

We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game *PushPush*, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 2D by reduction from SAT.Comment: 18 pages, 13 figures, 1 table. Improves cs.CG/991101

Minimizing the Potential for Groundwater Contamination from Agricultural Point Sources

An activated charcoal filtration unit was designed to remove pesticides from leftover pesticide solutions and rinsates generated under farm-like conditions. The system, fabricated for less than $1400 using readily available components, effectively removed the pesticides atrazine, benomyl, carbaryl, fluometuron, metolachlor, and trifluralin from wastewater generated on the University of Arkansas Agronomy Farm located in Fayetteville, AR. A total of 2253 L of wastewater were treated using the system. Of these 1768 L were generated from washing out the spray tank (rinsates) while 485 L stemmed from leftover pesticide solutions that were mixed, but not applied. Typical initial pesticide concentrations in the wastewater were on the order of 500 to 1000 parts per million (ppm). The final pesticide concentrations remaining after charcoal filtration were generally less than 10 ppm. Approximately 1514 L of wastewater was treated with 23 kg of charcoal before the charcoal was replaced. This resulted in an estimated pesticide loading rate on the charcoal of 0.05 to 0.10 kg pesticide active ingredient per kg activated charcoal. Incubation of alachlor-treated charcoal with a mixed culture of microorganisms resulted in approximately a 30% loss of alachlor after 21 d. These results suggest that on-site degradation of spent charcoal may be a feasible alternative to incineration, however more research is needed to fully determine its potential. A reduced adsorption of methylene blue dye with increasing amounts of trifluralin sorbed to charcoal occurred. Activated charcoal treated with 222 mg/g trifluralin sorbed only 19% of the amount sorbed by the control with no trifluralin present. These results suggest that methylene blue or other dyes might be used to indicate the remaining adsorptive capacity of a charcoal used for removing pesticides from wastewater

Examples, Counterexamples, and Enumeration Results for Foldings and Unfoldings between Polygons and Polytopes

We investigate how to make the surface of a convex polyhedron (a polytope) by folding up a polygon and gluing its perimeter shut, and the reverse process of cutting open a polytope and unfolding it to a polygon. We explore basic enumeration questions in both directions: Given a polygon, how many foldings are there? Given a polytope, how many unfoldings are there to simple polygons? Throughout we give special attention to convex polygons, and to regular polygons. We show that every convex polygon folds to an infinite number of distinct polytopes, but that their number of combinatorially distinct gluings is polynomial. There are, however, simple polygons with an exponential number of distinct gluings. In the reverse direction, we show that there are polytopes with an exponential number of distinct cuttings that lead to simple unfoldings. We establish necessary conditions for a polytope to have convex unfoldings, implying, for example, that among the Platonic solids, only the tetrahedron has a convex unfolding. We provide an inventory of the polytopes that may unfold to regular polygons, showing that, for n>6, there is essentially only one class of such polytopes.Comment: 54 pages, 33 figure

Enumerating Foldings and Unfoldings between Polygons and Polytopes

We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous questions for unfolding polytopes to polygons. Our answers are, roughly: exponentially many, or nondenumerably infinite.Comment: 12 pages; 10 figures; 10 references. Revision of version in Proceedings of the Japan Conference on Discrete and Computational Geometry, Tokyo, Nov. 2000, pp. 9-12. See also cs.CG/000701

SPATIAL ANALYSIS OF FEEDER CATTLE HEDGING RISK

Optimal hedge ratios are estimated for various weights of feeder cattle in four cash markets based on CME data from 1992 to 1999. Three-month uniform hedges are simulated for every weight, contract, and cash market combination. Hedging effectiveness is compared empirically across locations to identify spatial differences in hedging risk.feeder cattle, hedging risk, hedge ratios, Livestock Production/Industries, Risk and Uncertainty,

In situ imaging of vortices in Bose-Einstein condensates

Laboratory observations of vortex dynamics in Bose-Einstein condensates (BECs) are essential for determination of many aspects of superfluid dynamics in these systems. We present a novel application of dark-field imaging that enables \texttt{\it in situ} detection of two-dimensional vortex distributions in single-component BECs, a step towards real-time measurements of complex two-dimensional vortex dynamics within a single BEC. By rotating a $^{87}$Rb BEC in a magnetic trap, we generate a triangular lattice of vortex cores in the BEC, with core diameters on the order of 400 nm and cores separated by approximately 9 $\mu$m. We have experimentally confirmed that the positions of the vortex cores can be determined without the need for ballistic expansion of the BEC.Comment: 5 pages, 4 figure