These characteristics of turbulent flows may be induced by their coherent structures. Traditional models of turbulence diffusion, such as stochastic differential equations with Brownian motion input and Markov random fields, are not capable of capturing these coherent structures. This project will develop some new classes of models and tools to represent and analyse the long-range dependence, infinite variance and coherent structures of turbulent random fields. These include stochastic differential equations driven by modified fractional Brownian fields and higher-order wavelet spectra. Application to financial modelling and two-dimensional turbulence will be undertaken.
Ion channels are fundamentally important in the regulation of cellular physiology.
The project will develop probabilistic, statistical and computational methods for the study of these systems, emphasising interactive and spatial aspects about which little is presently known. Some of these methods will also be applied to multiprocessors comprising processors and buffers with application to system reliability. Multivariate failure times arise in a wide variety of practical situations, such as when repeated episodes of the same event occur on an individual, when times to different events are recorded on the same individual, or when single events occur for each case, but where cases may be associated by environmental, genetic or other factors. This project aims to develop a suite of methods to achieve this. It is proposed to develop methods for estimating the regression function without assuming that its form is known.