Application of the Renormalisation Group to concrete ageing

Cement is the most widely used artificial material on Earth but unfortunately its production alone causes ca. 8% of the global anthropogenic CO2 emission. To attempt to tackle this new forms of concrete are being developed with a lower carbon footprint. The issue with new cement formulations is that experimental data covering decades and even centuries of ageing are simply not available yet. Nanoscale simulations may offer a way around this issue and predict cement ageing. The issue with this is that in material ageing we have processes with a characteristic period at < 10-9 seconds and others with a period ranging from at > 10-3 to 10 seconds. This means that the timescale seperation required to simulate 100 years timescale for cement is 18 orders of magnitude which would take the fastest simulator today millions of years to simulate. Clearly there needs to be a cleverer way to tackle this problem rather than brute force. This is where we can employ the tools of the Renormalisation Group (RG).

Renormalisation Group Theory (RGT) has been used for decades in Particle Theory and Statistical Physics to examine physics on different spatial and temporal scales. We will begin with a formulation of Stochastic Dynamics that resembles 1-D Euclidean Field Theory in order to understand the applications of the RG. In particular we will concern ourselves with the functional Renormalisation Group (fRG) which is a non-perturbative approach built on the Wilsonian Renormalsation Group. We will then generalise to higher dimensional systems and eventually adopt our methods to molecular simlations relevant for a problem such as concrete. This is because the transition of the form of materials, and aging, is due to thermal fluctuations. By applying these concepts from the RG we can study the effects of short time-scale flutuations on longer time-scale dynamics speeding up otherwise impossible simulations. It is hoped we can build on this work to extend the application of RG to stochastic dynamics beyond 1-D to systems with many degrees of freedom and eventually molecular simulations including noise.

With this in mind the aims of the project are the following:
* We will use a particular variant of the RG, namely the fRG to examine physical quantities over long time periods from computational simulations as a proof of concept. This will be achieved by computing a quantity known as the effective potential which takes into account the average
effect of fluctuations with characteristic frequency above a certain value
* We will look at physics playing out on this effective potential which corresponds to physics occuring on longer time scales
* These theoretical results will be verified against molecular simulations as a proof of concept
* We will then use the effective potential of more complicated systems (currently impossible to simulate) to find their long-time behaviour

The project will begin by applying RGT to simple stochastic dynamical systems, describing the motion of particles in a Lenard-Jones potential, or potentials with a barrier, using Langevin dynamics, regarded as a first idealization of creep processes in cement. On the simulations side we will be using the state of-the-art massively parallel HPC simulator LAMMPS, to reproduce the nanostructure of ordinary and new "greener" cement pastes, starting from models that are available at Newcastle University.

To validate the effective potential model as physically relevant, simulations of collective rearrangements in the same model systems will be conducted using current techniques. Examples of these techniques are quasi-static and oscillatory mechanical activation, temperature accelerated dynamics, metadynamics, Autonomous Basin Climbing, and Kinetic ART.