skip to content

Arrested phase separation in a scalar active fluidAbout the Group

Professor Mike Cates, appointed in 2015 as the Lucasian Professor of Mathematics, is head of the Soft Matter Research Group in DAMTP. The other staff members are Dr Ronojoy Adhikari (Lecturer) and Dr Rob Jack (Interdisciplinary Lecturer, joint with Chemistry Department). At any time the group has one or two self-funded research fellows, three or four grant-funded postdocs, and a variable number of PhD students.

Soft Matter includes colloids, polymers, emulsions, foams, surfactant solutions, powders, liquid crystals, and similar materials. Domestic examples are paint, engine oil, mayonnaise, shaving cream, shampoo, and talc; high-tech counterparts are found in laptop displays, sensors, and drug delivery systems. Many biological systems involve "active" soft matter which, like life itself, is sustained by a continuous supply of energy.

Using both analytic and computational methods, the group addresses fundamental problems, such as how the basic principles of statistical mechanics are modified by activity, and more applied ones, such as how to predict the remarkable flow properties of very dense suspensions which suddenly transform from liquid to solid and back again depending on the applied stress level.

The mathematical methods used within the group include statistical field theory; exact and approximate solution of stochastic differential equations and PDEs; particle-based simulation; and numerical simulation of continuum field equations. Often as much time is spent figuring out what the proper equations of motion are, as is spent solving them: the field offers great scope for scientific as well as mathematical creativity. We have strong collaborations with researchers in Paris, Edinburgh, and around the world. 

We welcome PhD applications in all areas described above. An idea of the type of work currently in progress can be seen from the selected publications listed here.

Here are some areas in which PhD projects may be available:

1.  Flow of dense suspensions: from birth and death of particle contacts to macroscopic flow behaviour. (Prof Cates)

2. Field theories for absorbing-state models. In an absorbing state, the system gets into a region of phase space from which there is no escape. For example, in a process where particles can split or disappear, if a fluctuation takes the particle number to zero, it remains there forever. Continuum field theories of such processes are widespread, and somehow capture the same physics via a fluctuating density field, but the actual path to the absorbing state is not clear. (Prof Cates, Dr Jack)

3.. Brownian dynamics simulations of semi-flexible active polymers: from individual motion to collective dynamics on manifolds. (Dr Adhikari)

4. Geometric discretisation of field theories with broken time-reversal invariance on evolving manifolds, with applications to active matter. (Dr Adhikari)

5. Rare events: many soft-matter systems show metastable behaviour, where they can get trapped for long periods in non-typical states. Large deviation theories can be used to analyse the properties of such events, and to control their probabilities. Directions include the development of new mathematical methods, and the analysis of rare events in quantum-mechanical systems. (Dr Jack)

6. Glassy systems: there is a long-running debate as to whether the dynamics of highly-viscous liquids are controlled by some kind of thermodynamic phase transition. Recent work hints that if there is such a link, the universal properties of the phase transition might be related to an Ising model in a random field. Testing this idea will require a combination of numerical work with new theoretical ideas. (Dr Jack)

For more details please contact those named in the first instance. We hope to recruit 1-3 students in total. DAMTP has a small number of EPSRC-funded studentships with nationality restrictions; these are awarded competitively within the Department. Other students will need to apply for studentships offered by the Cambridge Trust and similar organizations. Deadlines for these schemes are in early January.