The inverse problems which are under investigation include ultrasonic scattering, neutron reflectometry and electromagnetic scattering. Wavelets, path integrals, asymptotic and computer modelling are all being used to study these problems. Since there are many wavelet families one question under study by our group is to determine which family is best under which conditions and why. An example of application is the double reconstruction of the voltage time trace measured in an ultrasonic non-destructive evaluation experiment to detect flaws in stainless steel. The other area under investigation with Professor Vignale and students is the statistical mechanics of water, in particular, its dielectric response.
Water is remarkable and has a number of anomalous properties.
It is surprising that this basic constituent of living organisms is so poorly understood. A local field factor was used to take into account the long-range coherent effects of intermolecular interactions. This is combined with the self van Hove correlation function in the Kubo linear response theory using a number-conserving single relaxation time Boltzmann equation to treat the frictional, dissipative effects. This model provides a new generalization of previous theories of molecular liquids which were only valid for small frequency and wave vector.