Leverhulme Lectures on Mathematical Problems in Materials Science
L3, Andrew Wiles Building, Oxford 4.00pm, Friday 11 November 2016
Richard D James (University of Minnesota)
Materials and methods for the direct conversion of heat to electricity
There are enormous reservoirs of energy stored on earth at small temperature difference, including natural sources such as the temperature difference between ocean (~0 C) and ambient (-40 to -20 C) in the arctic, focused sources such as solar-thermal arrays, and man-made sources like the waste heat from power plants, air conditioners, computers and hand-held electronic devices. The conversion of this heat to useable forms of energy challenges basic thermodynamic concepts. Any such conversion device is necessarily of low efficiency, but is efficiency relevant when one is not paying for the heat? Some heat engines are highly efficient, but their ability to absorb significant amounts of heat is limited. We present a new family of methods for the direct conversion of heat to electricity using phase transformations in multiferroic materials. The lecture will focus on the basic theory of energy conversion by phase transformation and mathematical questions that arise from the analysis of these methods.
This lecture is part of a Solid Mechanics meeting with this talk starting at 5.00pm, full details
L4, Mathematical Institute, Andrew Wiles Building, Oxford 4.00pm, Monday 14 November 2016
Twisted X-Rays, Orbital Angular Momentum and the Determination of Atomic Structure
We find exact solutions of Maxwell's equations that are the precise analog of plane waves, but in the case that the translation group is replaced by the Abelian helical group. These waves display constructive/destructive interference with helical atomic structures, in the same way that plane waves interact with crystals. We show how the resulting far-field pattern can be used for structure determination. We test the method by doing theoretical structure determination on the Pf1 virus from the Protein Data Bank. The underlying mathematical idea is that the structure is the orbit of a group, and this group is a subgroup of the invariance group of the differential equations.
Joint work with Dominik Juestel and Gero Friesecke. (Acta Crystallographica A72 and SIAM J. Appl Math).
L6, Mathematical Institute, Andrew Wiles Building, Oxford 11.00am Tuesday 15 November 2016
Theory-based discovery of highly reversible phase-transforming materials
We summarize recent theoretical and experimental work on the discovery of highly reversible transforming alloys.
These are poised to play a major role in diverse areas of technology, and give rise to fascinating mathematical questions.
Registration is open until Tuesday 8 November. To register for one/all of the lectures