The walls and components of nuclear reactors are exposed to irradiation throughout their lifetime. Radiation damage causes vacancies and interstitial atoms in the crystal lattice. These impurities diffuse and may annihilate, "healing" the damage, or accumulate, creating voids in the material and depositing interstitial atoms on the surface. In either case, diffusion of defects through a material accelerates processes driving the steel material toward chemical equilibrium. In a fusion reactor, every atom will suffer many such displacements, and so materials are sought which can successfully heal themselves in the face of this onslaught. We will tackle the problem at the atomic level, by characterising the relevant defects at teh atomistic level. There are three hierarchical approaches, each possible topics for PhD study:
The project forms part of a six-nation project (NuFuSe) applying exascale computing to problems in nuclear fusion. They may be held within the Condensed Matter DTC.
Liquid crystals are a fascinating example of soft materials. Like liquids, they flow and may be poured from one vessel to another. Like solids, they possess long range orientational order. Common examples are nematic liquid crystals (in which molecules align along a preferred axis) and cholesterics (in which this ordering axis acquires a spatial twist). Both are used in optical displays. Edinburgh physicists have developed lattice Boltzmann algorithms for large-scale numerical simulations of the hydrodynamics of liquid crystals, and used this to study permeation flows and the exotic 'blue phase' [1]. We have also studied binary mixtures of simple fluids, and colloids (including magnetic colloids) in single and binary solvents; this has led to the prediction by simulation of a completely new material [2] which was then found experimentally by our collaborators [3]. In progressing this leading edge work to the next stage, you will exploit our existing codes as well as develop new ones, aiming to investigate a new class of soft materials in which colloids (possibly magnetic) are dispersed in liquid crystals, and/or binary fluid mixtures are formed in which one of the two fluids is liquid crystalline. Such materials should allow new levels of control over properties and unusual responses to fields and flow. There is so far only a small experimental literature on these composite systems [4] and virtually no simulation work. The field is open for new discoveries: our in-house experimental collaborators [3,4] await our findings with interest!
[1] Ordering Dynamics of Blue Phases entails Kinetic Stabilization of Amorphous Networks. O. Henrich, K. Stratford, D. Marenduzzo and M. E. Cates, Proc. Nat. Acad. Sci. USA, 107, 13212 (2010)
[2] Colloidal Jamming at Interfaces: A Route to Fluid-Bicontinuous Gels. K Straftord, R Adhikari, I Pagonabarraga, J-C Desplat and M E Cates, Science 309, 2198-2201 (2005); E Kim et al, Langmuir 24, 6549-6556 (2008)
[3] Bicontinuous Emulsions Stabilized by Colloidal Particles, E M Herzig, K A White, A B Schofield, W C K Poon and P S Clegg, Nature Materials 6, 966-971 (2007)
[4] Network Formation in Colloid-Liquid Crystal Mixtures, J Cleaver and W C K Poon, J. Phys. Condensed Matter 16, S1901-1909 (2004)
"Rare events" happen very infrequently, but have dramatic consequences – for example, earthquakes, stock market crashes or the spontaneous nucleation of an ice crystal. Special techniques are needed to study rare events using computer simulations, since in normal simulations there is not enough time in the simulation run to observe the event. One of these methods is the forward flux sampling (or FFS) method, which was developed by Dr. Allen and coworkers in 2006. This method can speed up simulations of rare events by many orders of magnitude. Basically, FFS involves pushing the system from an initial state to a final state.
Although FFS works well for some rare event processes in soft matter and biological physics (such as genetic switch flipping and some crystal nucleation processes), there are many important problems for which it works less well (such as protein folding and glass formation). This project will involve developing new rare event simulation methods which do work for these problems, and applying them to exciting and challenging physical systems. The problems chosen will depend on the student, but might include simulating cage hopping in glasses or the dynamics of biological membranes.
This project will use atomistic computer simulations to investigate the structure and dynamics of a three-components liquid mixtures: water, alcohol and hydrocarbons. The production of alcohols to act as fuel additives to petroleum offers the potential for both enhancing the octane-rating of the fuel, whilst at the same time being produced from renewable sources. But there are real problems; not just with the production of the alcohols from biomass, but also because hydrocarbons and alcohols don't mix particularly well. And the presence of even a small amount of water makes matters much worse, causing the two phases to separate.
Despite being a relatively simple 3-component mixture, a detailed understanding of the structure and dynamics at the molecular level of the alcohol-hydrocarbon-water system is still missing, and recent studies of alcohol-water mixtures have shown that these systems can be anything but simple [1]. This project will attempt to elucidate the nature of this system at an atomistic level and also identify how this may influence the liquid-phase separations on a macroscopic level. It will used a variety of different computational codes (both classical and quantum mechanical) on machines as diverse as a simple desktop to IBMs Blue Gene system, managed by EPCC.
[1] S. Dixit, J. Crain, W.C.K. Poon, J.L. Finney and A.K. Soper, Nature 416 (2002)
The development of statistical mechanics throughout the nineteenth and twentieth century has allowed a deep understanding of systems in thermal equilibrium. However, particularly in the biophysical arena, most real-world systems are not in equilibrium. Thus the focus of statistical mechanics in the twenty-first century is firmly on systems out of equilibrium. For example, one is still very much in the dark about the nature of non-equilibrium steady states which can support currents and are not described by the usual Boltzmann distribution.
To make progress we study simple mathematical models which may admit exact solution. Major successes have been the identification of models with simple steady state structures such as factorised steady states and steady states of matrix product form. The project is to extend these exact analytical solutions through the calculation of non-equilibrium correlation functions, for example, and to identify new exactly solvable cases.
A major question concerning non-equilibrium systems is how their properties differ from systems in thermal equilibrium and in particular what is the nature of non-equilibrium phase transitions. A major achievement of our work in Edinburgh has been the realisation that phase transitions and, in particular, spontaneous symmetry breaking may occur in one-dimensional (1d) systems as opposed to equilibrium systems where phase transitions cannot occur in 1d. Such systems are realised, for example, by traffic and granular flow. A related non-equilibrium phase transition is `real-space condensation' the characteristic feature of which is that above a critical density of the microscopic constituents a finite fraction of constituents `condense' onto one site of the corresponding lattice model. The project is to extend our understanding of and to discover new non-equilibrium phase transitions through numerical and analytical studies.
Almost invariably biophysical systems are out-of-equilibrium, therefore the techniques of modern statistical physics are required for their description. Some examples are the dynamics of molecular motors moving along microtubules; the dynamics of genetic switches (see also project of Dr R. J. Allen); and the dynamics of evolving populations. The project involves creating statistical mechanics models for particular systems and developing methods of studying the models both numerically and by analytical solution.
Statistical mechanics is set up to handle the complexity that emerges in physical systems that comprise many interacting particles and that are governed by some known (classical or quantum mechanical) equations of motion. Many other systems exist where interactions between many entities lead to emergent regularities, but where we don't have the luxury of knowing the underlying equations of motion. Social systems provide pertinent examples. Why do some new ideas or technologies (such as low-energy light bulbs) become widely adopted among a community when others fail? What governs the pace at which a language change takes place?
To answer questions like this, we need to understand the dynamics of imitation and learning in human populations. In collaboration with linguists and psychologists, we have devised stochastic models for cultural learning and change that have been applied to field and experimental studies. Nevertheless, many gaps in our understanding of how cultural change takes place remain. Your work in developing our current mathematical theories and/or computational models of social learning, cultural change and related processes will be instrumental in plugging these gaps.
Statistical physics provides a set of theoretical tools for handling thermal fluctuations in physical systems. Similar methods can be used to study fluctuations in complex interacting systems more generally. In particular, the randomness of birth and death events leads to fluctuations in biological populations with important and interesting consequences. For example, initially identical populations will become less similar over time. These fluctuations also have important effects on interspecies competition: species can "win" through chance alone, even though on average it reproduces at the same rate as (or even slower than) its competitor. Other interesting effects of randomness have recently been discovered including oscillations in population sizes.
In this project we will study the consequences of randomness in evolutionary dynamical systems. As an example, a very simple theory, called "neutral theory", assumes that populations are unstructured and that there are no systematic differences between species, yet it has been found to make good predictions in some cases. Given that most systems are not "neutral", it remains unclear why neutral theory does so well. We may investigate this by studying more complex models and seeing how they map onto neutral theory. We may also investigate the very important question of how initially identical populations diverge in time, motivated by experiments on microbial ecosystems. This project will involve a mixture of analytical theory and computer simulations.
Ecosystems, in which different populations grow and interact, are complex dynamical systems where the techniques of statistical and computational physics can greatly improve our understanding. Physicists have already made important contributions in this area, by developing simple model systems, most famously for predator-prey (Lotka-Volterra dynamics). However many questions remain, including: “what factors can promote cooperative rather than competitive interactions between species?”, “what generates and maintains the diversity of species that we observe in nature?” and “how sensitive are the dynamics of ecosystems to small perturbations?”.
In this project, we will develop and analyse simple ecosystem models, in order to address these questions. The project will involve computer simulations but could also have the potential for analytical theory. The balance between simulations and theory can be adjusted depending on the preference of the student. A particularly exciting aspect of the project is that it has the potential for close interactions with experimental work on real microbial ecosystems which is going on in the Schools of Physics and Biology in Edinburgh.
