Staff and structure of the Laboratory

The Laboratory for Advanced Computation is located in the School of Mathematics at the University of Bristol. The Director is Professor Stephen Wiggins.

Staff Details

• Professor Stephen Wiggins
• Dr. Des Small
• Dr. Jan-Martin Hertzsch

Alumni

• Dr. Ana Maria Mancho

Professor Stephen Wiggins

Professor Wiggins has broad ranging interests in dynamical systems theory, from pure, to applied to computational. His particular style of research involves finding developing areas of applications where new mathematical and computational methodologies are needed to make progress.

For example, a current topic of interest is the application of the methods of nonlinear dynamics to the study of transport phenomena in fluids. In the past five years there have been significant advances in dynamical systems theory to the point where the framework can now be utilized in the context of "real" problems. However, this approach leads to a new idea of a ``dynamical system'' in this context. Rather than being defined by a set of equations, our dynamical systems are defined by ``data sets'', which can only be known for a finite amount of time. This brings up some fundamentally new mathematical problems that must be addressed.

An important objective is to develop the theoretical framework for a geometrical theory of dynamical systems that are defined for a finite time interval. At the same time, we will develop computational algorithms and implement them in software so that we may pursue ``real world'' applications of these tools such as for velocity fields in coastal zones derived from high frequency radar arrays and other velocity fields derived from large scale computation and remote sensing. As oceanography enters a "data rich" era with the availability of barely manageable amounts of data from satellites and radar arrays the framework of dynamical systems theory is now poised to lead to numerous breakthroughs in the analysis and interpretation of this data.

Another area of interest is the application of the methods of nonlinear dynamics to the study of problems arising in theoretical chemistry. The mathematical approach and techniques of dynamical systems theory are ideally suited for many of the questions of interest in molecular dynamics since they are often global and geometrical in nature. For example, questions related to intramolecular and intermolecular energy transfer are formulated as phase space transport problems whose answers depend on the geometry and dynamics associated with invariant manifolds in phase space. A central goal is to develop mathematical and computational techniques that apply to high dimensional systems, as well as understand higher dimensional dynamical phenomena in general.

Dr. Des Small

Dr. Small is working as a Scientific Programmer with Professor Wiggins and Dr. Mancho, on the dynamical systems approach to transport in geophysical flows. Dr. Small previously worked for Dyson.

Dr. Jan-Martin Hertzsch

Research interests: granular matter including planetary rings, pattern formation in vibrated granulates, collisions between granular particles, influence of fluid flow on sediment patterns; high-velocity impacts. Studied physics in Merseburg and Leipzig, obtained the doctoral degree in theoretical physics 1997 from Universität Potsdam, was a doctoral student at Max-Planck-Group "Nonlinear Dynamics" Potsdam, worked as a visiting scientist at Observatoire de Nice for 9 months, was a scientific assistant at Max-Planck-Institut für Aeronomie, a research asistant at Brunel University and a temporary staff scientist at Museum für Naturkunde Berlin. For more details visit his website.

Dr. Ana Maria Mancho

Dr. A. M. Mancho is working as a Research Assistant with Professor S. Wiggins and Dr. D. Small in applying dynamical systems theory to geophysical mixing processes.

Her research interests are fluid dynamics, formation of spatio-temporal structures far from thermodynamic equilibrium, nonlinear dynamics of complex systems, bifurcation theory and symmetries, and application of nonlinear concepts to Earth and Planetary Sciences.

How to Contact Us

Contact information is provided for general enquiries, questions regarding the hardware facilities and the applications procedure for computing resources
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