Professor Timothy Moroney

Biography

Professor Moroney's research interests are in the fields of computational mathematics and high performance computing.  Presently, Professor Moroney's areas of focus are: surface reconstruction from scattered data, droplet evaporation and spreading on heterogeneous curved surfaces (such as leaves), time-frequency analysis of signals arising from the wakes of ships, and distributed-order fractional differential equations for describing nonlocal anomalous diffusion. Surface reconstruction.  Using a handheld 3D laser scanner it is possible to generate a point-cloud representation of an entire plant in an hour or so.  Professor Moroney is working on a number of projects that involve the use of such data to better understand droplet impaction, spreading and evaporation on plant leaves, with applications to the agrichemical industry.  Building whole-of-plant virtual models from scanned data requires scattered data interpolation combined with clustering, smoothing, regularisation, partitioning and processing to generate realistic virtual models. Droplet evaporation.  From a realistic virtual leaf, with its undulating surface and heterogenous chemical properties, it is desired to understand how droplets settle on the surface, the interplay between gravitational and surface forces, how contact angles vary with time, the effect of surfactants, and so on, to ultimately increase retention and absorption of agrichemicals.  This requires high-resolution solution of partial differential equations on curved surfaces with spatially-varying chemical properties. Ship wakes.  When a ship moves through the water, it generates a wake: the characteristic V-shaped wave pattern.  This pattern is in some sense characteristic of the vessel.  The relative strength of the transverse and divergent waves, the changing wavelength and frequency, alternating constructive and destructive interference, etc. all carry information about the source of the waves.  The goal is to determine how much information about the ship can be reconstructed from nothing more than a time series surface-height measurements of the wake recorded at sensors fixed in space. Fractional diffusion. In many important practical applications, we are interested in understanding how heat, mass and other quantities diffuse throughout space.  For diffusion in particularly complex media, the laws governing this transport process may involve differential operators that are non-local.  This complicates both the analysis and the numerical solution of these equations.  More complex still are problems where the “index of non-locality” is itself distributed probabilistically.  Our work seeks to better understand these phenomena through both mathematical analysis and computational simulation.