Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Influence of temperature on pea aphid Acyrthosiphon pisum (Hemiptera: Aphididae) resistance to natural enemy attack

The ability to resist or avoid natural enemy attack is a critically important insect life history trait, yet little is understood of how these traits may be affected by temperature. This study investigated how different genotypes of the pea aphid Acyrthosiphon pisum Harris, a pest of leguminous crops, varied in resistance to three different natural enemies (a fungal pathogen, two species of parasitoid wasp and a coccinellid beetle), and whether expression of resistance was influenced by temperature. Substantial clonal variation in resistance to the three natural enemies was found. Temperature influenced the number of aphids succumbing to the fungal pathogen Erynia neoaphidis Remaudiere & Hermebert, with resistance increasing at higher temperatures (18 vs. 28degreesC). A temperature difference of 5degreesC (18 vs. 23degreesC) did not affect the ability of A. pisum to resist attack by the parasitoids Aphidius ervi Haliday and A. eadyi Stary Gonzalez & Hall. Escape behaviour from foraging coccinellid beetles (Hippodamia convergens Guerin-Meneville) was not directly influenced by aphid clone or temperature (16 vs. 21degreesC). However, there were significant interactions between clone and temperature (while most clones did not respond to temperature, one was less likely to escape at 16degreesC), and between aphid clone and ladybird presence (some clones showed greater changes in escape behaviour in response to the presence of foraging coccinellids than others). Therefore, while larger temperature differences may alter interactions between Acyrthosiphon pisum and an entomopathogen, there is little evidence to suggest that smaller changes in temperature will alter pea aphid-natural enemy interactions.

Gas-phase rate coefficients for the reactions of O(3P), S(3P), Se(3P), and Te(3P) with alkenes: application of perturbation frontier molecular orbital theory, correlations, and structure-activity relations (SARs)

The kinetics of the reactions of the atoms O(P-3), S(P-3), Se(P-3), and Te((3)p) with a series of alkenes are examined for correlations relating the logarithms of the rate coefficients to the energies of the highest occupied molecular orbitals (HOMOs) of the alkenes. These correlations may be employed to predict rate coefficients from the calculated HOMO energy of any other alkene of interest. The rate coefficients obtained from the correlations were used to formulate structure-activity relations (SARs) for reactions of O((3)p), S(P-3), Se (P-3), and Te((3)p) with alkenes. A comparison of the values predicted by both the correlations and the SARs with experimental data where they exist allowed us to assess the reliability of our method. We demonstrate the applicability of perturbation frontier molecular orbital theory to gas-phase reactions of these atoms with alkenes. The correlations are apparently not applicable to reactions of C(P-3), Si(P-3), N(S-4), and Al(P-2) atoms with alkenes, a conclusion that could be explained in terms of a different mechanism for reaction of these atoms.