Research students

Present and former research students

Present research students

Former research students

Some potential topics for PhD projects

Mechanical properties of aperiodic framework structures

With additive manufacturing (3D printing) becoming more and more accessible, it is possible to print aperiodic structures based on tilings with non-crystallographic symmetries, which are expected to have more isotropic mechanical behaviour than lattice-based structures, and thus may be of interest for applications in a a variety of areas. The project is concerned with the development and verification of modelling the mechanical properties of such structures. This is closely related to the EPSRC-funded research on Novel superior materials based on aperiodic tilings.

Matrix cocycles and spectral properties of inflation systems

The diffraction measure for inflation-based structures is very rich; it can contain pure point, singular continuous and absolutely continuous components. The presence or absence of these components can be studied via a matrix cocycle. This may provide a link to the spectral properties of corresponding Schrödinger operators, which seem to behave in a quite different way, but can also be deduced from matrix product properties. This project is linked to EPSRC-funded research on Lyapunov Exponents and Spectral Properties of Aperiodic Structures.

Mathematical diffraction of aperiodic structures

Mathematical diffraction is a method to assess the degree of order in a structure, and is closely related to the diffraction used in crystallography to study periodic and aperiodic crystals. The classification of the diffraction from aperiodic structures is thus one approach to classify these structures. The research will focus on aperiodic structures obtained by inflation, for which there are still many open questions, in particualr with regard to continuous components in the diffraction spectrum.

Spectral properties of aperiodic Schrödinger operators

Aperiodically ordered quantum systems are of interest in the theoretical description of quasicrystals, a particular kind of ordered solid lacking the periodic structure of ordinary crystals. Such systems exhibit rather unusual spectral properties, including singular continuous spectra and multifractal eigenfunctions. The work aims at unravelling the connection between spectral properties on the one hand and quantum diffusion on the other hand, employing a combination of analytical and numerical techniques.

Stastistical mechanics of aperiodically ordered and disordered systems

The properties of a system at, or close to, a second-order phase transition are assumed to be universal. Roughly, this means that they do not depend on any particular details of the system. However, aperiodic order or disorder, either in the coupling constants or in the underlying discrete structure, may influence the critical behaviour. The work comprises the investigation of the effects of aperiodic order and disorder in classical and quantum spin models, particularly the Ising model.

Any student who is interested to join me on one of the above topics, or would like to know more about my research interests, is cordially invited to contact me!

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Uwe Grimm
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