Coarse-grained modelling of biological macromolecules (Polymers and Industrial Mathematics)

Project in collaboration with Dr Sarah Harris (School of Physics & Astronomy)

Current methods for computational simulation of biological macromolecules are generally "particle based", that is they integrate the equations of motion of connected particles (these could represent atoms, or groups of atoms). Further coarse-graining (that is, description of the motion on larger length and timescales) requires a different approach. To do this we are working on building and testing a new continuum algorithm based on elastic and dielectric properties extracted from atomistic simulations. We shall treat macromolecules as continuous heterogeneous media, thus describing macromolecules by tensor fields rather than "particle" positions. Such continuum methods are commonly used in materials modelling, and allow additional physical phenomena such as electrostatic interactions to be handled in a unified framework. We will use finite element (FE) algorithms similar to those we have previously developed for complex viscoelastic media such as polymer melts. FE methods are widely used for solving continuum problems in solid and fluid mechanics and underlie many commercial codes; they are suited for modelling diffusive processes and can handle complex geometries.

Polymers and Industrial Mathematics

Research in the Polymers and Industrial Mathematics group focuses on the mechanics of polymers and other complex fluids, free-surface flows and inverse problems. We are also concerned with the development and implementation of novel numerical and computational solution methods for both ordinary and partial differential equations, from fundamental aspects (the theoretical analysis of numerical methods) to problem-specific aspects (the design, development and practical implementation of novel algorithms). Within the polymer area, we conduct fundamental research into fluids that have a complex microstructure, such as polymer melts and solutions and colloidal dispersions.

Our research combines methods from molecular physics and continuum mechanics to develop multiscale models that link together the microscale motion of individual molecules to the flow behaviour of the bulk material. An important class of industrial flow problems are those involving free surfaces, such as in inkjet printing, film coating and bubble growth in polymeric foams. We also work on a diverse range of inverse problems in heat transfer, porous media, fluid and solid mechanics, acoustics and medicine. This is a strongly interdisciplinary subject and much of our research involves collaborations with independent research groups in science and engineering departments both at Leeds and worldwide, as well as with industry.