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.
An experimental study of columnar crystals using monodisperse microbubbles.
A. J. Meagher, F. Garcıa-Moreno, J. Banharta, A. Mughal and S. Hutzler. Colloids and Surfaces A (2015).
We investigate the ordered arrangements of monodisperse microbub- bles confined within narrow cylinders. These foams were imaged using X-ray tomography, allowing the 3D positions of the bubbles of the foam to be accurately determined. The structure of these foams closely re- semble the minimum energy configuration of hard spheres in cylindrical confinement as found in simulations. For larger ratios, λ, of cylinder to bubble diameter two- and three-layered crystals were formed. Each layer of these structures is found to be ordered, with each internal layer resem- bling structures found at lower λ values. The average number of contacts per bubble is seen to increase with λ.
Columnar crystals using monodisperse microbubbles
Theory of cylindrical dense packings of disks. A. Mughal & D. Weaire. Physical Review E (2014)
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. FORMA (2014)
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