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Name of scholarship/program

Brownian motion, diffusion and fractals in disordered media

Important description
Some of the most important processes in nature and engineering take place in highly inhomogeneous and spatially complex environments. For example, the interior of biological cells is a dense labyrinth of structures ranging in size from nanometres to micrometres. Molecules diffusing through this dense soup must find each other efficiently so that the biochemical and biophysical processes on which all life depends can proceed, such as protein synthesis and DNA replication. Kinetic theory is the part of physics whose job it is to derive expressions for quantities such as collision probabilities and reaction rates, which can be used to predict the speed and efficiency of these processes. In complex media such as that inside a cell, however, assumptions made in classical kinetic theory are not valid, and phenomena such as anomalous diffusion dominate the dynamics of these processes. Although some recent advances have been made in this area, the kinetic theory of complex media is largely unknown, and this area still has many important open questions. This is an area at the cutting edge of statistical physics, with enormous importance for many applications in diverse fields.

This project aims to develop a systematic kinetic theory for complex media, with an eye for applications in molecular biology, where these phenomena are expected to play a crucial role. This project will aim to derive analytical expressions for the crucial quantities characterising the kinetics, such as the collision rate and reaction rates. Numerical simulations will also be used to test the theoretical predictions. We will focus on diffusion-limited processes (this is the case of most biological processes), and how they are affected by the geometrical properties of disordered media. This research fits into the broad field of non-equilibrium statistical physics, which is one of the major open frontiers in 21-st century physics.

The successful applicant will have a first or upper second class degree (or equivalent) in Physics, Applied Mathematics/Physical Chemistry. Knowledge of Statistical Physics and/or stochastic processes would be advantageous.

Eligibility and other criteria
If you have the correct qualifications and access to your own funding, either from your home country or your own finances, your application to work with this supervisor will be considered.

Application deadline
*Applications accepted all year round

Additional information, and important URL
Applications can be accepted from students worldwide. Applicants should note that there is no funding attached to this project therefore the successful candidate will entirely responsible for the payment of tuition fees, living expenses and other such costs associated with living and studying in Aberdeen.

The project will be awarded to the first suitable applicant. The start date will be agreed between the successful applicant and their supervisors.

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