Several basic unsolved questions concerning the spin glass problem, such as the nature of the ordered phase and reentrant behavior, will be investigated. Studies of faster simulation algorithms for these problems will be undertaken. The behavior of neural networks for learning and computation will be analyzed from a statistical mechanics perspective, and algorithms for producing better networks will be investigated. Numerical simulations of alternative models of superconductivity will be undertaken with the goal of understanding the mechanism responsible for the recently discovered high temperature superconductors. Correlation exponents in multifractals will be used to measure the spectrum of dimensions that characterize such systems, and questions concerning the amount of information contained in the scaling dimensions will be investigated. The statistical properties of systems involving ring polymers will be analyzed using a new and efficient algorithm for their generation. The dynamics of DNA molecules will be studied in the context of pulsed field electrophoresis, which is a new technique of great importance in bioengineering. Fundamental questions regarding the role of chaos in quantum mechanics that have been stimulated by recent experiments on hydrogen atoms in strong magnetic fields will be examined. The quantum mechanics of hard spheres, such as a Lorentz gas, will be studied in high dimension, to explore the validity of the Gibbs distribution in closed quantum systems, and to provide an alternative model of energy dissipation involving a finite number of degrees of freedom.
