The authors describe a new technique for obtaining the phase and electric field from FROG measurements using genetic algorithms. Frequency-Resolved Optical Gating (FROG) has gained prominence as a technique for characterizing ultrashort pulses. FROG consists of a spectrally resolved autocorrelation of the pulse to be measured. Typically a combination of iterative algorithms is used, applying constraints from experimental data, and alternating between the time and frequency domain, in order to retrieve an optical pulse. The authors have developed a new approach to retrieving the intensity and phase from FROG data using a genetic algorithm (GA). A GA is a general parallel search technique that operates on a population of potential solutions simultaneously. Operators in a genetic algorithm, such as crossover, selection, and mutation are based on ideas taken from evolution.

Using Lanczos exact diagonalization, we investigate the effects of the competition between the electro-electron and electron-phonon interactions in the context of the 1-D tight-binding Peierls-Hubbard Hamiltonian, studying various structural, optical, and vibrational properties of strongly correlated systems. We use polyacetylene as our experimental guide, and perform a parameter space search to determine the level at which a unique set of parameters can model this prototypical conducting polymer and, more generally, the applicability of the simple'' 1-D Peierls-Hubbard Hamiltonian to these highly interesting materials. 9 refs., 3 tabs.

Genetic algorithms (GAs), global optimization methods that mimic Darwinian evolution are well suited to the nonlinear inverse problems of geophysics. A standard genetic algorithm selects the best or ''fittest'' models from a ''population'' and then applies operators such as crossover and mutation in order to combine the most successful characteristics of each model and produce fitter models. More sophisticated operators have been developed, but the standard GA usually provides a robust and efficient search. Although the choice of parameter settings such as crossover and mutation rate may depend largely on the type of problem being solved, numerous results show that certain parameter settings produce optimal performance for a wide range of problems and difficulties. In particular, a low (about half of the inverse of the population size) mutation rate is crucial for optimal results, but the choice of crossover method and rate do not seem to affect performance appreciably. Optimal efficiency is usually achieved with smaller (< 50) populations. Lastly, tournament selection appears to be the best choice of selection methods due to its simplicity and its autoscaling properties. However, if a proportional selection method is used such as roulette wheel selection, fitness scaling is a necessity, and a high …