Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.

### Microstructural coarsening

Rapid temperature cycling from one extreme to another affects the rate at which the mean particle size in solid or liquid solutions changes.

### Geometry of discrete space

A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.

### Grain shape inference

The distributions of size and shape of a material’s grains can be constructed from a 2D slice of the material and electron diffraction data.

### Serendipity and strategy

In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

### 3d grains from 2d slices

Moment-based methods provide a simple way to describe a population of spherical particles and extract 3d information from 2d measurements.

### Optimal heat exchange networks

Compact heat exchangers can be designed to run at low power if the exchange is concentrated in a crumpled surface fed by a fractal network.

### Eigenvalues of neutral networks

The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.

### Viscosity of polydisperse spheres

A quick and simple way to evaluate the packing fraction of polydisperse spheres, which is a measure of how they crowd around each other.

### Easily repairable networks

When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.

### Structural imperfections

Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.

### Random close packing fractions

Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.

### Towers of strength

The Eiffel tower is now a longstanding example of hierarchical design due to its non-trivial internal structure spanning many length scales.

### Hierarchical structures

The most efficient load-bearing fractals are designed as big structures under gentle loads ... a situation common in aerospace applications.

### Hierarchical space frames

A systematic way to vary the power-law scaling relations between loading parameters and volume of material aids the hierarchical design process.

### Ultralight fractal structures

The transition from solid to hollow beams changes the scaling of stability versus loading analogously to increasing the hierarchical order by one.

### Shear elastic deformation in cells

Analysis of the linear elastic behaviour of plant cell dispersions improves our understanding of how to stabilise and texturise food products.

### Ever-shrinking spheres

Techniques from random sphere packing predict the dimension of the Apollonian gasket, a fractal made up of non-overlapping hyperspheres.