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.
Theory of cylindrical dense packings of disks. A. Mughal & D. Weaire. Submitted to Physical Review E
We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation of the density for line-slip structures, close to the symmetric ones. We show that rhombic structures, which are of a lower density, are always unstable i.e. can be increased in density by small perturbations
Theory of cylindrical dense packing of disks
Packing of softly repulsive particles in a spherical box - a generalised Thomson problem. A. Mughal. Submitted to FORMA
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.