Dr Eric Hester
Research interests:
Eric’s research develops accurate models and efficient simulations for multiphase systems in continuum mechanics. Applications span from optimising manufacture times in small-scale industrial microfluidics, through to assessing planetary-scale influence of ice-ocean interactions in global climate modelling. This research combines several techniques: developing software to automate asymptotic analysis of singularly perturbed partial differential equations, implementation of high performance numerical codes in the flexible and efficient Dedalus computational framework, as well as performing laboratory experiments of phase change phenomena. A unifying theme is how a sensible choice of “coordinates” (e.g. the elegant differential geometry of the signed-distance function for moving boundary layers, or the comprehensive algebra of Jacobi polynomials for sparse methods in numerical differential equations) can achieve rapid convergence, and thereby enable more efficient and explanatory models. The ultimate goal is to distill these methods into simple and generalisable predictions that help domain experts understand and optimise complex physical phenomena.
LINKS:
Eric Hester on the University of Bath research portal
Professor Stephen K. Wilson FIMA
I have made contributions to the mathematical modelling and analysis of a wide range of problems in fluid mechanics, including thin-film flows, evaporating droplets, rivulets and dry-patches, dielectrophoresis, microfluidics, liquid crystals, non-Newtonian fluids (including viscoplastic fluids, thixotropic fluids and nanofluids), anti-surfactants and self-rewetting fluids, fluid-structure interaction problems, biomechanics, nucleate boiling, confined bubbles, thermocapillary (Marangoni) and thermoviscosity effects, spin coating, magnetohydrodynamics, and fluid impact problems. The common theme running through all of my work is the use of a range of mathematical (namely asymptotic, analytical and numerical) methods to bring new insights into a wide range of “real world” problems ranging from boiling and evaporation through industrial coating processes to biological systems such as the human knee.
Stephen Wilson on the University of Bath Research Portal
Dr Michael Murray
I am a Lecturer in the Department of Mathematical Sciences and am interested in the theoretical foundations and technological development of modern machine learning systems: in particular, reconciling modern phenomena with conventional machine learning wisdom as well as using theory to drive algorithmic innovation.
Michael Murray on the University of Bath Research Portal
Dr Federico Cornalba
Federico’s research sits at the intersection between stochastic analysis, numerical analysis, and PDE theory. Primarily, he is interested in describing large-scale interacting particle systems (these are ubiquitous in a whole range of applications in physics, social/opinion dynamics, and more) by using equivalent continuous models (often in the form of stochastic equations). These continuous models are, in general, more tractable than the particle models they stem from, especially when it comes to computational costs and specific interpretability features. He deploys methods from stochastic analysis, numerical analysis, and PDE theory to study relevant aspects of these continuous models. He is also interested in Machine Learning tools: so far, he has researched Deep Reinforcement Learning methods for asset-trading applications.
Federico Cornalba on the University of Bath Research Portal
Dr Avi Mayorcas
Avi Mayorcas on the University of Bath Research Portal
Dr Christoforos Panagiotis
I am interested in mathematical models arising from statistical physics both in the classical setting of the hypercubic lattice and more generally on groups. This specifically includes percolation, the Ising model, the Potts model, the Blume-Capel model, self-avoiding walk, and Abelian sandpile percolation.
Dr Matthew Schrecker
Much of my research to date has focused on the compressible Euler equations. The Euler equations have a rich mathematical structure underpinning one of the most basic physical processes in the universe: the flow of gases. Over the past 250 years, the equations have inspired developments in mathematical analysis, functional and harmonic analysis, dynamical systems and geometric analysis. The Euler equations are also relevant in understanding phenomena in the physical world ranging from the flow out of an exhaust pipe to the motion of galaxies and collapse of stars. In all of these physical processes, the formation of shock waves is a ubiquitous phenomenon (as seen physically, for example, in a sonic boom coming from a Concorde aircraft) that causes a drastic loss of regularity in solutions of the system. The presence of shocks has led to the need to study weak solutions of the Euler equations, as classical (differentiable) solutions will generically blow up in finite time, and so my research has focused on both of these aspects: the existence of weak solutions and the properties and behaviour of smooth solutions on approach to singularity formation.
More recently, I have also been working on the problem of the gravitational collapse of stars, a different type of singularity formation in which the physical variables of the system (particularly the density of a star) blow up in finite time as matter falls in towards the centre of the star. Such a phenomenon is also modelled with the Euler equations, but now with a gravitational field as well.
Research Interests:
Matthew Schrecker on the University of Bath Research Portal
Dr Haiyan Zheng
Haiyan is interested in the design and analysis of clinical trials, particularly in the field of precision medicine. Her research is directed towards added efficiency of trials. This includes (1) leveraging historical data, (2) permitting mid-course adaptations, (3) simultaneous evaluation of multiple treatments, multiple subgroups, or both, under one overarching protocol, (4) enrichment strategies, etc.
Haiyan’s work has wider applications going beyond clinical trials. For instance, a few Bayesian methods developed to deal with a prior-data conflict can be applied broadly to augment studies or experiments suffering from data sparsity with external information.
Haiyan Zheng on University of Bath Research Portal
