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The University of Southampton
Mathematical Sciences

Research project: Computational Physics

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We model a variety of physical systems: superfluids in geometry that range in size from Bose Einstein condensates of cold atoms to neutron stars; combustion in flames and supernova explosions; relativistic shockwaves in astrophysical plasmas; collisions of black holes. Our research tackles both the mathematical foundations required for stable and accurate calculations, and the implementation of advanced finite difference and finite volume simulations on machines from desktops to massively parallel HPC resources.

Bose-Einstein condensates

Bose-Einstein condensates

If we cool an atomic gas in very high vacuum to ultralow temperatures (a millionth of a Kelvin), the quantum mechanical properties of the gas as a whole become very important and spectacular things happen. For example, the gas can become superfluid, which flows with no resistance. This superfluid is to atoms what laser light is to photons - a very special state of matter. We can simulate its motion on a computer using quantum hydrodynamics and we can observe for example vortices forming a triangular array when the gas is stirred (a normal fluid would only form a single vortex like that in a cup of tea or a tornado in the atmosphere). Or we can see interference phenomena between clouds of atoms - something that we usually associate with light.  

Fluid modelling

Fluid modelling

The dynamics of fluids can be extremely complex: to convince yourself of this you just need to look at the eddies and whirls of a rapidly flowing stream. Modelling fluid requires large computational resources and powerful algorithms to keep track of the multiple time and length scales involved in fluid flow from the large eddies of a wave to the microscale where energy is dissipated by viscosity. Numerical simulation of fluid flow requires us to keep track of these multiple scales in three dimensions, while at the same time including the chemical (flames) or nuclear (supernovae explosions) reactions that put the fluid in motion.

Astrophysical simulations

Astrophysical simulations

Astrophysical observations of black holes and neutron stars can tell us about the extremes of physics, where hot, dense, magnetic plasmas meet strong gravitational fields. To get a quantitative match to our models we need numerical simulations of Einstein’s equations of General Relativity, coupled to relativistic hydrodynamics. Our work focuses on increasing the physics that can be practically simulated, to improve the qualitative accuracy of the simulations. This includes simulations of extreme mass ratio black holes, relativistic elastic matter for the neutron star crust and relativistic superfluids.

Computational studies of light and matter

Computational studies of light and matter

We perform large-scale computational studies on light-mediated interactions in atomic and other resonant emitter systems in order to analyse their cooperative properties. In atomic superfluid systems, we study ultracold atomic gases and Bose-Einstein condensation, for instance, topological defects and textures in complex ordered phases. The computational studies also include quantum optical systems and quantum technologies as a part of the UK National Quantum Programme.

Related research groups

Applied Mathematics and Theoretical Physics
Computational Applied Mathematics
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