Index of content:
Volume 131, Issue 4, 28 July 2009
We report a detailed numerical investigation of the relative abundance of periodic and chaotic oscillations in phase diagrams for the Belousov–Zhabotinsky (BZ) reaction as described by a nonpolynomial, autonomous, three-variable model suggested by Györgyi and Field [Nature (London)355, 808 (1992)]. The model contains 14 parameters that may be tuned to produce rich dynamical scenarios. By computing the Lyapunov spectra, we find the structuring of periodic and chaotic phases of the BZ reaction to display unusual global patterns, very distinct from those recently found for gas and semiconductor lasers, for electric circuits, and for a few other familiar nonlinear oscillators. The unusual patterns found for the BZ reaction are surprisingly robust and independent of the parameter explored.
131(2009); http://dx.doi.org/10.1063/1.3187240View Description Hide Description
Ab initio methods for the electronic structure of molecules have reached a satisfactory accuracy for calculations of static properties but remain too expensive for quantum dynamics calculations. We propose an efficient semiclassical method for evaluating the accuracy of a lower level quantum dynamics, as compared to a higher level quantum dynamics, without having to perform any quantum dynamics. The method is based on the dephasing representation of quantum fidelity and its feasibility is demonstrated on the photodissociationdynamics of . Our accuracy test can be easily implemented in existing molecular dynamics codes, thus offering wide applicability.