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Diffusion Limited Aggregation Link to some images of clusters being analysed.

Powders Images from Warwick powder experiments.
There is a real (albeit somewhat over-hyped) opportunity here to sort an outstanding state of matter. Whilst models are coming into surplus, the challenge remains to sort out fundamental principals and make contact with/impact on the established Engineering discipline of soil mechanics. We are making progress on how the statics depend on the microscopic powder geometry; a harder challenge is to close the theory by relating that geometry to material history. (RB)

Colloid Rheology New computer simulation techniques developed to cope with hydrodynamically coupled particles have opened up the rich field of how concentrated colloids flow. The sensitivity of shear thickening to near contact interactions is a new discovery which has prompted new theoretical ideas as well as having practical consequences. A more complete theory of flow induced structure is now a priority as the phase diagram emerges from simulation. (RB)

Fracture The serious theoretical work in this subject has been mainly in two dimensions, and addressing the onset of fracture. The challenge today is to understand propagating cracks and their three dimensional evolution - where we are near to completing the stability analysis. We are also trying to remedy the fact that Theoretical Physics still says almost nothing about the crack tip. (RB)

Protein Folding Computer Simulation (around the world) is beginning to solve the forwards folding problem with realistic potentials. This opens up a corresponding new dimension in protein engineering: how can we design real protein sequences to fold in a given way? Direct attack on this problem has spin-off in optimisation more generally. We are investigating how efficiently to optimise a design whose performance can only be sampled statistically. (RB)

Fractal Structure The days of hunting Fractal Dimensions are over, and the challenge is to find richer quantitative science in this field of beautiful images. I am exploring the information encoded in the three point correlation function, with the claim that it quantifies the linearised renormalisation group. (RB)

Soft Condensed Matter Physics can provide a framework on which to build a profound understanding of complex biological and chemical systems. Our goal is to understand universal behaviour shared by all similar systems. Techniques drawn from statistical and continuum mechanics are being employed to tackle problems involving both tethered and stacked fluid membranes as well as surface and interfacial phenomena in polymer systems. (MST,RAR)

Non-Linear Phenomena Chaotic behaviour and turbulence are characteristic of systems with non- linear equations of motion, which recent developments, particularly in mathematics, are making increasingly accessible. There is work on the precursor instabilities to full turbulence in convective systems and plasmas. There are also links with the large non-linear systems group in the mathematics department. (GR)

Periodicity and Dynamics in Non-linear Systems We have already shown that a Hamiltonian functional with suitably scaled parameters can successfully reproduce phenomena such as Wigner Crystallisation in two dimensional Jellium. An open challenge is to generalise such approaches to include Entropy, and hence predict behaviour at non-zero temperatures - with a wide range of applications including phase transitions and cross-over effects. We are also interested in generalising the Wigner Crystal work to include magnetic fields. In simpler classical reaction-diffusion systems we are taking a dynamical approach, and finding solitonic and other propagating modes. (JMD)

Interacting Electron Systems The interaction between electrons is behind virtually all electronic properties which are not properly understood. The basic problem is that the electrons cannot always be treated as if they moved in the average potential of the other electrons. The group is developing the theory of interacting electrons in high temperature superconductors, looking particularly at the couplings between spin and charge excitations, crystal field effects and the magnetic ordering. (ND'A, RAR)

Quantum Chaos Statistical properties of quantum systems which are chaotic in classical limit have been studied for a long time. Experimentally, it is now possible to construct small phase coherent samples with very simple, yet chaotic, classical dynamics (see picture). We use advanced field theoretical methods to study energy levels and wavefunctions in such systems. (BM, RAR)

Electronic Structure Theory This work is based on density functional theory and relies upon high performance computing for its application to problems such as metallic magnetism and alloy physics. A strength of the work is that it is `first-principled' so that many aspects can be tested in quantitative detail by a range of experimental measurements. The group collaborates with several others both nationally and internationally, and participates actively in the large European electronic structure networks. Together with groups at Bristol, CCLRC and Imperial College a new aim is to make ab initio studies of properties of materials where strong electron correlation effects are profound, such as metal-insulator transitions, high Tc and 'exotic' superconductivity and rare-earth material properties. Here are further details of the research in this area. (JBS)

Disordered Electronic Systems Traditionally, research in solid state physics has concentrated on the properties and applications of crystalline solids. Nevertheless true crystals represent a clear minority of real materials. Mostly, solids will have distortions of the crystalline structure due to, e.g., dislocations, vacancies, the presence of impurity atoms, and isotope defects.

Furthermore, at low T, an even more significant difference between the behavior of crystals on one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from conducting behavior with resistance R>0 to insulating behavior with as R->infinity. This phenomenon is called the disorder-driven metal-insulator transition (MIT) and it is a quantum mechanical effect which is characteristic to non-crystalline materials. In our research, we want to elucidate properties of disordered systems by studying, e.g., the influence of different types of disorder, of magnetic fields, of many-particle interactions on the MIT, etc. This is being achieved by the investigation of simple models of non-interacting but disordered and also interacting systems, such as the Anderson model, spinless fermions and the Hubbard model. We also make extensive use of high-performance computational methods such as energy-level statistics, transfer-matrix methods and finite-size-scaling approaches. (RAR)