## Applied Analysis

### Inverse Problems in Materials Modelling

Predicting the behaviour of viscoelastic materials under flow or deformation gives rise to many classes of models of integral and differential type. These models contain kernels or discrete parameter sets which have to be inferred indirectly from the results of simple experiments. Estimating material functions from indirect measurements is a rich and exciting source of challenging inverse problems, often with deep mathematical content.

### Homogenisation and the mechanics of composites

The mathematical theory of homogenisation investigates the overall properties of media possessing some sort of ``miscrostructure''. A wealth of observed phenomena in mechanics and other appliead areas is due to complex interactions between various ``elementary'' features, taking place on the range from the atomic to the macroscopic scale. Developing mathematical techniques to study such interactions is our main preoccupation within this research area. It has a strong interplay with other mathematical disciplines, such as the calculus of variations, as well as with industrial applications.

### Main Research Topics

- Wavelet analysis and the continuous relaxation spectrum
- Optimal spring loading
- Relating wave dispersion data to material functions.
- Rigorous analysis of problems in mechanics
- Homogenisation of partial differential equations and integral functionals
- Applications of homogenisation to the mechanics of composite materials
- Scale interaction effects (for example strain-gradient and non-local effects) in the description of the behaviour of heterogeneous media
- Wave propagation in solid mechanics and electromagnetism
- Asymptotic methods in mechanics
- Variational methods in the mechanics of ‘microstructured'’ media
- Theories for the description of dislocations as agents of plastic flow