Many physical systems contain a large number of particles which may have complicated interactions. The use of statistical methods to describe such apparently intractable problems has been one of the greatest triumphs of theoretical physics. While classical statistical mechanics has explained both the foundations and the intricate consequences of thermodynamics, in recent years the emphasis has shifted towards applying probabilistic approaches to almost any type of complex phenomenon, extending from physics and chemistry into biology, social sciences and economics.
The Open University organises an annual Open Statistical Physics meeting, usually held in late March.
The understanding of rainfall is still far from complete. Michael Wilkinson has recently analysed a test-tube model for rainfall, in which partially miscible liquids show periodic cycles of precipitation. A theory based upon Ostwald ripening gives an excellent agreement with the experimental data.
The standard model of planet formation builds planets from dust particles in a circumstellar accretion disc. Using estimates of relative velocities of particles in turbulent flows, Michael Wilkinson argued that the collisions are too energetic to allow dust grains to aggregate. An alternative hypothesis for planet formation, termed 'concurrent collapse', was proposed where planets form by gravitational collapse at the same time as their star.
This model explains way many extra-solar planets have highly eccentric orbits. It also stimulated a critical evaluation of existing models for gravitational collapse, resulting in a new model, termed the 'shock-fragmentation' model.
Condensed matter physics describes physical systems composed of very large numbers of atoms or molecules, which interact strongly with each other and are bound by relatively short-range forces. This subject area encompasses a huge a range of physical phenomena, including that of crystalline solids, amorphous solids and liquids.
Within the Applied Mathematics department, most research in this area concentrates on a quantum mechanical description of the electronic properties of solid matter. Such properties include transport phenomena, magnetic properties of matter, and the exploitation of electronic spin in material devices. Describing and understanding these properties is currently of great importance, because of their potential for use in novel electronic devices.
Michael Wilkinson has long-standing interests in transport phenomena. Recent highlights include an explanation for the anomalous exponents of photoconductive response of semiconductors, based upon the rate of electron-hole recombination being limited by hot-electron effects. The theory explains the predominance of observations of the anomalous exponent taking values close to 3/4 or 2/3.
Other recent developments include the definition and identification of 'semi-linear response', and a new model for hopping conduction processes based upon an analogy to repeatedly breaking a stick at its weakest point.