Nachtrab Diamond Scaffold 2010_EllipsoidsVoronoiHardSpheres.jpgXS 2011_RubiOpticalMicroscopyMichaelThiel.jpg media/2011_RubiSEMMichaelThiel.jpg 2012_MyfCoarseningEvolver.jpg Hard Spheres in Gyroid 2012_3etcFaraday.jpg Auxetic Frontispiece Adv Mat 2011 2011_MinkowskiAdvMaterTOC.jpg 2012_IPPShearedExp.jpg I am grateful to Gerd Beck (Beck Design Nuremberg) for graphical editing of some of the above images, to Michael Thiel (KIT, Karlsruhe) for the SEM images of the butterfly, and to Myfanwy Evans for the foam coarsening image.

"Where there is matter, there is geometry"

Johannes Kepler, 1602

My research revolves around soft condensed matter systems with a complex spatial micro- or nanostructure. I am interested in

  • the spontaneous formation of complex geometries, in particular with negatively curved interfaces, by self-assembly and pattern formation,
  • the quantitative morphological description of spatial structures, in physically relevant terms and applicable to 3D experimental data,
  • the effect that a complex spatial microstructure has on physical and material properties, compared to the bulk situation
  • the occurrence and relevance of complex structures in biology, and their potential for biomimetic designs

I address these questions with methods from theoretical and computational physics, applied maths, as well as differential and integral geometry, often in close collaboration with experimental scientists.

Some current and recent projects

Anisotropy and Local structure characterisation of sphere packs : The local structure of jammed assemblies of hard spheres is often characterised with order metrics that are based on the neighbor bond network. This project explores the geometric shape description ... more

Auxetic deformations of strut frameworks and cellular solids : Auxetic materials are a novel class of structures that fatten when stretched and thin when compressed. This counter-intuitive behaviour is almost always due to an intricate spatial microstructure of the ... more

Shear-flow and diffusive growth of random soap froth : Random Plateau foams exhibit complex ageing behaviour (diffusive coarsening) and rheological flow properties that result from the interplay of area minimisation and topological transitions. We apply modern morphology characterisation tools ... more

Effective mechanical properties of ordered and disordered geometries for bone scaffold engineering : Free-form fabrication or rapid prototyping methods are allowing the fabrication of porous structures with custom-designed microstructures. Structure-property relationships for mechanical properties demonstrate that triply-periodic minimal surfaces and on severed periodic ... more

Morphometry using Minkowski tensors : Morphometry using tensorial Minkowski functionals: Minkowski tensors, or tensorial Minkowski functionals, are a set of morphological measures that provide quantitative morphological information about a complex shape, such as the solid ... more

Chiral biological photonic crystals based on the Gyroid : Certain butterfly wing-scales are structured according to the single Gyroid (or srs) geometry. Because of their chirality, these natural chitin photonic crystals have circularly-polarised reflections, which for the length scale ... more

(this list is not comprehensive, more project items coming soon)