LIMIT-CYCLE STABILITY REVERSAL NEAR A HOPF BIFURCATION WITH AEROELASTIC APPLICATIONS

The objective of this paper is to present an analytical/numerical analysis of the phenomenon of limit-cycle stability reversal (from unstable to stable, and vice versa). A singular perturbation technique, the method of the normal form (in the asymptotic- expansion version), is utilized. The number of equations is then reduced to a “minimal set”, for which the results are in good agreement with those from the original equations. This minimal set is determined by the amplitude of the λ̂-points (a concept closely related to the small divisors in the KAM theory). This set is larger than that corresponding to the zero real-part eigenvalues (center-manifold theorem). The method is applied to a specific problem: an aeroelastic section with cubic free-play non-linearities where the parameter μ is the flight speed. Numerical studies have been performed to show the dependence of the Hopf bifurcation characteristics upon the structural and geometric properties of the wing section. Plots depicting amplitudes and frequency versus flight speed are presented.     

Magnetic field effects on the hydrogen abstraction reaction of triplet 4-methoxybenzophenone with thiophenol as studied by a picosecond laser flash photolysis technique

The hydrogen abstraction reaction of triplet 4-methoxybenzophenone with thiophenol at 265 K has been studied with a newly developed picosecond laser flash photolysis apparatus under magnetic fields of 0–1.7 T. The decay rate constant of the radical pair generated was found to increase from 3.42 × 10⁹ s^?1 to 4.15 × 10⁹ s^?1 with increasing the magnetic field from 0 to 1.7 T. The observed magnetic field effects can be explained by the Δg mechanism. Using the simple kinetics model with the Δg mechanism, the rate constant of the escape process from the pair (k _esc) and two rate constants for the T-S spin conversion process (k _T-S) at 0 and 1.7 T were found to be 1.97 × 10⁹ s^?1, 1.45 × 10⁹ s^?1, and 2.12 × 10⁹ s^?1, respectively. From the magnetic field dependence on k _T-S, the difference in the g values of the 4-methoxybenzophenone ketyl and phenylthiyl radicals was estimated to be 0.0087.