I am a theoretical physicist working on the effects of topology and geometry in condensed matter physics. In particular, I am interested in packing problems, foams and the role played by conformal geometries in these systems.
I hold a lectureship in mathematical modelling at the Institute of Mathematics and Physics (IMAPS) at Aberystwyth University. Currently I am on career break at the Institut fuer Theoretische Physik (LS Klaus Mecke), Friedrich-Alexander Universitaet Erlangen-Nuernberg, Erlangen, Germany
Packing of softly repulsive particles in a spherical box - a generalised Thomson problem. A. Mughal. Submitted to Physical Review E
We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form 1/rγ. We study three regimes in which the charges form an single spherical shell at the edge of the box (γ=1), a series of concentric shells of increasing density (γ=2) and γ=12 for which the charges form shells with a more uniform charge distribution. We conduct numerical simulations for clusters containing up to 5000 charges and compare charge density across the system with continuum limit results. The agreement between numerical (discrete) results and the continuum limit is found to improve with increasing N.
Packing of softly repulsive particles in a spherical box
Screw symmetry in columnar crystals. A. Mughal. Philosophical Magazine (2013).
We have shown that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterised by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all the such packings in the range 1 ≤ D/d ≤ 2.715 .
Screw symmetry in columnar crystals.
Compaction of cereal grain. J. Wychowaniec, I. M. Griffiths, A. Gay, A Mughal, Philosophical Magazine (2013).
We report on simple shaking experiments to measure the compaction of a column of Firth oat grain. Such grains are elongated anisotropic particles with a bimodal polydispersity. In these experiments, the particle configurations start from an initially disordered, low-packing- fraction state and under vertical shaking evolve to a dense state with evidence of nematic-like structure at the surface of the confining tube. This is accompanied by an increase in the packing fraction of the grain.
Compaction of cereal grain.