Goddard, Benjamin

Ocone, Raffaella

Hurst, Timothy

Engineering and Physical Sciences Research Council (EPSRC)

2020-10-05T09:10:02Z

2020-10-05T09:10:02Z

2020-07-28

There are many challenges in modelling granular media, in particular due to hard particle interactions such as collisions. Modelling and simulating at a microscopic level produces very accurate results, but simulations are generally restricted to relatively small systems of particles. It is also difficult to construct a simple continuum model which accurately describes all the properties of granular media. In this thesis, we consider a number of the problems associated with modelling granular media. We first look at the microscopic dynamics of individual particles and how to derive physically appropriate interactions between them, and discuss Event-Driven Particle Dynamics (EDPD) as an accurate and efficient way to model a system of hard, spherical particles. We then present a novel derivation of the weak form of the Liouville equation which can model systems where particles interact instantaneously (e.g. via inelastic collisions). From here we construct the BBGKY hierarchy and use moment closure methods to construct a new, accurate continuum model for granular media, based on Dynamical Density Functional Theory (DDFT). We then use EDPD to construct approximations for the radial correlation function which accounts for friction, packing fraction and inelasticity. This is then included in the DDFT in simulated examples.

https://hdl.handle.net/1842/37335

http://dx.doi.org/10.7488/era/621

en

The University of Edinburgh

T. D. Hurst, B. D. Goddard, and M. Wilkinson, A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions, 2019. arXiv: 1910 . 06656 [cond-mat.stat-mech].

B. D. Goddard, T. D. Hurst, and R. Ocone, Modelling inelastic granular media using dynamical density functional theory, 2020. arXiv: 2003.07327 [cond-mat.stat-mech].

B. D. Goddard and T. Hurst, Multiple superadiabatic transitions and Landau-Zener formulas, 2018. arXiv: 1804.04660 [physics.chem-ph].

V. Betz, B. D. Goddard, and T. D. Hurst, “Nonadiabatic transitions in multiple dimensions,” SIAM Journal on Scientific Computing, vol. 41, no. 5, B1011–B1033, 2019

O. M. Crook, T. Hurst, C.-B. Schönlieb, M. Thorpe, and K. C. Zygalakis, PDE-Inspired algorithms for semi-supervised learning on point clouds, 2019. arXiv: 1909.10221 [math.NA]

granular media

mathematical modelling

hard particles as a fluid

microscopic simulations

Event-Driven Particle Dynamics

Dynamical Density Functional Theory

Granular media at multiple scales: mathematical analysis, modelling and computation

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy