R Mike L Evans Department of Applied Mathematics 
Statistical Mechanics 
My research interests are in theoretical physics, specifically nonequilibrium statistical mechanics, soft matter physics and the development of new methods of analysis. Nonequilibrium statistical mechanics is a very broad topic, with applications ranging from the flow of molten plastics to Darwinian evolution. 
Soft matter includes colloids, emulsions, liquid crystals, amphiphiles and polymeric fluids. It's ubiquitous, constituting virtually all foods, biological materials, and pretty much anything squidgy. Such materials have useful properties that are exploited in industrial applications including plastics, displays, adhesives, coatings, cosmetics and countless others. But my interest is not motivated so much by their useful applications as by the elegant physics that governs their behaviour. 

In soft matter, we find an exotic menagerie of complex structures that can be understood in terms of their interesting symmetries and statistical properties. For instance, in this idealized simulation of amphiphiles (molecules with a waterloving end and a greaseloving end, like in washingup liquid), the interplay between random thermal motion and the stickiness of the greasy ends of the molecules (here coloured black) leads to the spontaneous formation of wormlike structures called micelles, or striped structures called "lamellae" that form at higher chemical potential. These structures ultimately result from the statistics and sysmmetries of the molecules' random motion.
When soft matter flows, it exhibits much more interesting behaviour than simple fluids, including flowalignment, shearbanding, jamming, and even (in the case of several polymer melts) expelling itself completely from the measurement apparatus. 
Polydispersity  
Equilibrium properties of such materials become difficult to calculate if the constituent particles are not all identical, but vary in size, shape, charge etc. I have developed methods for simplifying the mathematics associated with such 'polydisperse' substances, so that their 'phase behaviour' (e.g. when they crystallize / boil / dissolve) can be understood. My current research focuses on polydisperse systems that are out of equilibrium, to model the dynamics of mixing and demixing. 
Microrheology
 
Rheology is usually conducted by applying largescale shear to the fluid under investigation, by moving parallel plates. In microrheology, tiny sample volumes can be studied by analysing the motion of microscopic testbeads suspended in the fluid. This motion may be either Brownian, or driven by an applied magnetic field. In ongoing work, in collaboration with Dr M Tassieri, we calculate ways to extract, from the correlated motions of many probeparticles, accurate measurements of the macroscopic viscoelastic shear moduli, which are unaffected by the finitesize boundary effects that usually plague such measurements. For details, click here. 
Evolution
 
I investigate models of evolution, both numerically and analytically, specifically to answer the longposed question of how altruism can ever arise by Darwinian evolution. This is a topic of current interest in biology, philosophy and games theory, and has recently become a hot topic in statistical mechanics. The standard methods of statistical mechanics are well suited to making progress in this area, where some oversimplified mathematical models have previously failed. 
Driven Steady States  
Currently, I am interested in the steady states that exist when complex fluids are subjected to a uniform shear flow, e.g. by two parallel plates that are moved relative to each other. Such steady states cannot be described by classical statistical thermodynamics, because they are not at equilibrium, but are "driven" by the work input at the boundaries. Some fluids "shearthicken", i.e. become more viscous when they are sheared, while others shearthin. Nematic liquid crystals (such as in LCDs) are composed of rodlike molecules that tend to allign with the direction of the flow. Some materials even separate into nonuniform bands when subjected to shear. 
In the equilibrium case (without flux), theorists know how to construct informative simplified models of thermodynamic systems; they must respect the "principle of detailed balance" which ensures that the model system will operate in an unbiased manner that conforms to the known laws of statistical mechanics. For nonequilibrium systems such as complex fluids in shear flow, on the other hand, theorists have so far been guided only by intuition when constructing models, in the absence of any well developed nonequilibrium statistical mechanics. 
But an exact theorem exists, relating to the statistics of motion in flowing systems. It governs the steady state motion of any sheared fluid that is stochastic (subject to thermal noise from its environment), ergodic (sufficiently mobile to thoroughly explore its space of available states) and microscopically reversible (contains normal particles with no sense of direction; this does not apply, for instance, to traffic flow). 
The new theorem embodies a set of rules that put constraints on the
modelling of nonequilibrium systems, ensuring selfconsistency and no
unwarranted bias. The resulting mathematical structure bears beautiful
similarities to that of equilibrium statistical mechanics, and has as much
potential for diverse and important applications. I believe that this
development will shift the paradigm for theoretical modelling of
nonequilibrium systems, removing the arbitrariness from the subject, and
providing a foundation of rigorous statistical arguments. Potentially, the
formalism should be able to explain much of the phase behaviour of fluids
under flow.

This development has been timely, as there is rapidly increasing interest in exact nonequilibrium statistical mechanics, following a number of other recent exact theorems: "Fluctuation Theorems" have been discovered, quantifying the probability of momentary violations of the second law of thermodynamics, and "Nonequilibrium Work Theorems" have provided some exact criteria for the work done by nonequilibrium changes to the constraints on a thermodynamic system (with implications e.g. for experiments on forced unfolding of proteins). Also, the LeeYang theory of phase transitions has been generalised to a large class of nonequilibrium models. ( Richard Blythe is one of the authors of that work.) The subject area of nonequilibrium steady states now has huge potential for important discoveries. 
My aim is now to explore the implications of the new theorems, by constructing simplified models, as well as making calculations for real systems (such as polymers under flow) that can be tested experimentally. 
Numerical comparison of a constrained path ensemble and a driven quasisteady state
Milos Knezevic and R M L Evans,
Phys. Rev. E 89, 012132 (2014)
.
Open access preprint:
arXiv:1310.4384 [condmat.statmech]
Statistical mechanics far from equilibrium: Prediction and test for a sheared system
R M L Evans, R A Simha, A Baule and P D Olmsted,
Phys. Rev. E 81, 051109 (2010).
The effects of polydispersity and metastability on crystal growth kinetics
J J Williamson and R M L Evans,
Soft Matter, Advance Article (2013).
Open access preprint at
arxiv.org/abs/1208.3804
Direct conversion of rheological compliance measurements into storage and loss moduli
R M L Evans, Manlio Tassieri, Dietmar Auhl, and Thomas A. Waigh,
Phys. Rev. E 80, 012501 (2009).
Invariant quantities in shear flow
A Baule and R M L Evans,
Phys. Rev. Lett. 101, 240601 (2008).
Dynamics of Semiflexible Polymer Solutions in the Highly Entangled
Regime
Manlio Tassieri, R. M. L. Evans, Lucian BarbuTudoran, G. Nasir
Khaname, John Trinick, and Tom A. Waigh,
Phys. Rev. Lett. 101, 198301 (2008).
Rules for
transition rates in nonequilibrium steady states ,
R M L Evans,
Phys. Rev. Lett. 92, 150601 (2004).
Universal law of fractionation for slightly
polydisperse systems
R M L Evans, D J Fairhurst and W C K Poon,
Phys. Rev. Lett. 81, 13261329 (1998).
Colloidpolymer mixtures at triple coexistence: Kinetic maps from
freeenergy landscapes,
W C K Poon, F Renth, R M L Evans, D J Fairhurst, M E Cates and P N Pusey,
Phys. Rev. Lett. 83, 12391242 (1999).
Correlation length by measuring empty space in simulated
aggregates,
R M L Evans and M D Haw,
Europhys. Lett. 60(3), 404410 (2002).
Role of metastable states in phase ordering
dynamics,
R M L Evans, W C K Poon and M E Cates,
Europhys. Lett. 38, 595600 (1997).
Detailed balance
has a counterpart in nonequilibrium steady states,
R M L Evans,
J. Phys. A: Math. Gen. 38, 293313 (2005).
For a full list of publications, click here.