Exit Trajectories Research Articles

Reverse-time modeling, optimal control and large deviations

A connection between deterministic optimal control and large deviations theory has been known for a number of years, whereby the optimal performance index provides information about exit times of stable systems excited by noise, and the optimal trajectory provides information about exit trajectories asymptotically as the scalar multiplying the noise tends to zero. In this paper, a further connection is made to reverse-time modeling of stationary diffusions and linear, stationary, Gauss-Markov discrete-time systems, in which the drift part of the reverse-time model has the same trajectories as the closed loop system resulting from the solution of the same optimal control problem as used for the previous connection.

Minimal Exit Trajectories with Optimum Correctional Manoeuvres

Minimal exit trajectories with optimum correctional manoeuvers to a rocket between two coplaner, noncoaxial elliptic orbits in an inverse square gravitational field have been investigated. Case of trajectories with no correctional manoeuvres has been analysed. In the end minimal exit trajectories through specified orbital terminals are discussed and problem of ref. (2) is derived as a particular case.

Molecular beam kinetics: Optical model for reactive scattering of alkali atoms and alkyl iodides

Angular distributions of reactively scattered alkali iodides have been measured for reactions of thermal beams of Rb and Cs atoms with beams of alkyl iodides RI, where R=CH3, C2H5, n- and i-C3H7, n-C4H9, and n-C5H11. When shifts expected from kinematic differences are taken into account, the qualitative features are found to confirm the results previously obtained for the analogous K atom reactions. The reaction cross sections increase with the size of the alkali atom, from ∼35 Å2 for K+CH3I to ∼45 Å2 for Rb and ∼75 Å2 for Cs. The fall off in intensity of elastically scattered alkali atoms at wide angles also increases for K→Rb→Cs. The anisotropic angular distribution of products, the magnitude of the reaction cross section, and the fall off of the wide-angle elastic scattering for the K, Rb, and Cs systems are correlated in terms of an extended optical model which simply assumes hard sphere interactions for both the entrance and exit trajectories. The reaction probability derived from the data by use of the optical model is large only for collisions which reach the repulsive wall region but even there it is well below unity for thermal energy collisions.