Dr Irene M Moroz
CUF Lecturer in Mathematics
Applied Mathematics Fellow, St Hilda's College
CUF Lecturer in Mathematics
Applied Mathematics Fellow, St Hilda's College
My main research interests lie in time series analysis, in the bifurcation theory of nonlinear ordinary and partial differential equations, arising in geophysical fluid mechanics. There are two new exciting possibilities for potential DPhil students in areas of research outlined below.The first is a collaboration with members of the BBC climateprediction.net team, based in Oxford, to perform an uncertainty analysis of forecasting using data from climate models.
The second is to combine a love of Mathematics and Music, extending the work on Voice Morphing to create a performable major musical work.
I am also a member of the Mathematical Geoscience Group (MGG) and the Applied Dynamical Systems and Inverse Problems research group (ADSIP) in the Oxford Centre for Industrial and Applied Mathematics (OCIAM).
Students
Recent and current D. Phil students with completion dates where appropriate are:
- Adam Stephen (POD methods in baroclinic flows): 1997
- Stephen Whitehouse (POD-Galerkin Modelling of the Martian Atmosphere):
1999- Sithi Muniandy (Wavelet-Galerkin modelling of turbulence): 1998
- Isla Gilmour (Nonlinear prediction of baroclinic flows): 1998
- Richard Harrison (Numerical study of the Schrodinger-Newton equations): 2001
- Edgar Perez (Eddy flux parameterisation in models of baroclinic flow and in the oceans) : 2006
- Christina Orphanidou (Voice Morphing):2007
- Max Little (Nonlinear modelling of speech) :2007
- Oscar Martinez-Alvarado (Modelling of the Martian Atmosphere):2007
- Reason Machete (Nonlinear analogue and digital time series analysis):2007
- Xiaodong Luo (Filter analysis in Data Assimilation)
- Judy Simpson (Finite dimensional dynamics in baroclinic chaos)
- Trevor Wood (Mathematical Modelling of Sonar and Radar Contact Tracking)
- Jason Montgomery (Climate modelling)
- Lian Duan (KAUST-sponsored in Oil Field History matching)
We are interested in developing fast numerical algorithms for the dynamic wavelet Galerkin modelling of the two- and (ultimately) the three-dimensional incompressible Navier-Stokes equations for arbitrary boundary conditions, using compactly supported wavelets. Initially we have focussed our efforts upon developing a biorthogonal wavelet Galerkin formulation of the Burgers equation, which is a necessary first stage before attempting to address the two- dimensional Navier-Stokes equations.
We are interested in building on the results of two existing DPhil studies into the use of empirically determined basis functions, calculated from time series of the velocity fields to generate reduced order nonlinear models of baroclinici flows. These include numerical models of the Martian atmosphere with and without topographic features, as well as laboratory models of more complicated baroclinic flows.
Issues of predictability will also be addressed in a project involving the analysis of the effects of parameterisation in climate models currently being used in the climateprediction.net BBC experiment, aimed at improving ensemble predictions of atmospheric processes. Collaboration with colleagues in Atmospheric Physics is envisaged. This projecti will be part of the e-science project on atmospheric prediction.
Hide (1997) has proposed a hierarchy of related self-exciting coupled Faraday-disk dynamos incorporating electric motors as additional electromechanical elements and driven by steady mechanical couples has been proposed. Each system comprises N interacting units which can be arranged in a ring or a lattice. Within each unit are electric motors, driven into motion by the dynamo and connected either in series or in parallel with the coil. Nonlinearity enters solely through the coupling between components. By introducing additional terms into the equations, it is possible to include the effects of biasing from impressed electromotive forces due to thermoelectric or chemical processes, as well as from the presence of ambient magnetic fields. Dissipation is introduced into the models via ohmic heating and mechanical friction in the disk and motors, with the latter playing a crucial role in the generation of chaos (see e.g. Hide et al (1996)).
Ideas from the topological analysis of chaotic systems have been used to classify the attractor of the Hide et al (1996) dynamo as being equivalent to the Lorenz attractor (Moroz, 2007). Furthermore such ideas have been used to determine the templates of other dynamo models.
The voice morphing involves investigating various ways of transforming the time series representing one person's speech into another. Applications include the film and entertainments industries. A new project, in collaboration with a renowned Musical composer, seeks to extend the work listed below to create a major musical work.
Publications
[an error occurred while processing this directive]Tel: 01865-2-70514
E-mail: moroz@maths.ox.ac.ukOctober 2008