Stephen Tate

PhD Mathematics, University of Warwick, UK (advisor: Daniel Ueltschi); MMath Mathematics, Christ's College Cambridge, UK; BA Mathematics, Christ's College Cambridge, UK


I was a Research Associate in the Complex Multiscale Systems group at Imperial College London. Prior to starting this appointment, I undertook a three month London Mathematics Society Postdoctoral Mobility Grant to work with Dr Dimitrios Tsagkarogiannis at the University of Sussex and a six month postdoc at the Ruhr Universität Bochum with Jun.Prof. Dr. Sabine Jansen, funded by SFB TR12 - Symmetries and Universality in Mesoscopic Systems. I completed my PhD at the University of Warwick under the supervision of Dr Daniel Ueltschi. This was on the Combinatorics of the Cluster and Virial Expansions. I also have an MMath and BA from Christ's College Cambridge.

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My current research is on Dynamic Density Functional Theory through an EPSRC funded project entitled, 'Statistical mechanics of soft matter: Derivation, analysis and implementation of dynamic density functional theories', which is a collaborative project with Dr Ben Goddard and Prof Greg Pavliotis, and with principal investigator Prof Serafim Kalliadasis.

Some key aspects of this project include: looking at more realistic pair correlation functions in a Dynamic Density Functional Theory and performing computer simulations based upon these; exploring the non-commutativity of limits taken towards obtaining a density functional theory; and developing density functional theories that are either time dependent or involve states away from equilibrium.

The key subject of my other research projects is cluster and virial expansions. In my PhD project, I focussed on understanding combinatorial aspects of the expansions with the aim of finding cancellations to provide more effective bounds on the coefficients. The cluster and virial coefficients are expressed in terms of weighted sums over connected, respectively two-connected graphs. The weights can often have combinatorial interpretations and alternate in sign. Understanding how to make more refined approximations of the weighted sums leads to a better udnerstanding of the equation of state in statistical mechanics.

In projects in collaboration with Jun. Prof. Dr. Sabine Jansen of Ruhr Universität Bochum and Dr Dimitrios Tsagkarogiannis of the University of Sussex, the idea of cluster expansions is applied to canonical ensemble calculations for multispecies models connected to a model of clusters to describe a process of solid formation in a classical gas model.

A further ongoing research project involves using partition schemes that were developed for weighted connected graphs towards weighted two-connected graphs for the virial coefficients. This is in collaboration with Mr Sanjay Ramawadh at Utrecht Universiteit. Developing such a partition scheme for two-connected grpahs allows us to find improved bounds for the virial coefficients and find alternative ways to derive the coefficients in more general models. This project will continue to develop how the partition scheme can provide both estimates and accurate computationsof the virial coefficients for particular models.

I also have wider mathematical interests in further applications of Statistical Mechanics and also more fundamental aspects of the subject. I am also particularly interested in combinatorics and the connections within Statistical Mechanics and Mathematical Physics.