arXiv subjects

Adil Mughal

Publications and source records attributed to Adil Mughal.

11 recordsLinked to original sources

arXiv2019

Equilibrium configurations of hard spheres in a cylindrical harmonic potential

A line of hard spheres confined by a transverse harmonic potential, with hard walls at its ends, exhibits a variety of buckled structures as it is compressed longitudinally. Here we show that these may be conveniently observed in a rotating liquid-filled tube (originally introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274 (2017)] to assemble ordered three dimensional structures at higher compressions). The corresponding theoretical model is transparent and easily investigated numerically, as well as by analytic approximations. Hence we explore a wide range of predicted structures occurring via bifurcation, of which the stable ones are also observed in our experiments. Qualitatively similar structures have previously been found in trapped ion systems.

cond-mat.soft↗

arXiv2019

Theory of rotational columnar structures of soft spheres

There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274 (2017)]. They used rapid rotation around a central axis to drive spheres of lower density than the surrounding fluid towards this axis. This resulted in different structures as the number of spheres is varied. Here we present comprehensive analytic energy calculations for such self-assembled structures, based on a generic soft sphere model, from which we obtain a phase diagram. It displays interesting features, including peritectoid points. These analytic calculations are complemented by preliminary numerical simulations for finite sample sizes with soft spheres. A similar analytic approach could be used to study packings of spheres inside cylinders of fixed dimensions, but with a variation in the number of spheres.

cond-mat.soft↗

arXiv2019

Homogeneous and heterogeneous populations of active rods in two-dimensional channels

Active swarms, consisting of individual agents which consume energy to move or produce work, are known to generate a diverse range of collective behaviors. Many examples of active swarms are biological in nature (e.g., fish shoals and bird flocks) and have been modeled extensively by numerical simulations. Such simulations of swarms usually assume that the swarm is homogeneous; that is, every agent has exactly the same dynamical properties. However, many biological swarms are highly heterogeneous, such as multispecies communities of micro-organisms in soil, and individual species may have a wide range of different physical properties. Here we explore heterogeneity by developing a simple model for the dynamics of a swarm of motile heterogeneous rodlike bacteria in the absence of hydrodynamic effects. Using molecular dynamics simulations of active rods confined within a two-dimensional rectangular channel, we first explore the case of homogeneous swarms and show that the key parameter governing both dynamics is ratio of the motility force to the steric force. Next we explore heterogeneous or mixed swarms in which the constituent self-propelled rods have a range of motilities and steric interactions. Our results show that the confining boundaries play a strong role in driving the segregation of mixed populations.

cond-mat.soft↗

arXiv2018

Columnar structures of soft spheres: Metastability and hysteresis

Previously we reported on the stable (i.e. minimal enthalpy) structures of soft monodisperse spheres in a long cylindrical channel. Here, we present further simulations, which significantly extend the original phase diagram up to D/d = 2.714 (ratio of cylinder and sphere diameters), where the nature of densest sphere packing changes. However, macroscopic systems of this kind are not confined to the ideal equilibrium states of this diagram. Consequently, we explore some of the structural transitions to be expected as experimental conditions are varied; these are in general hysteretic. We represent these transitions in a stability diagram for a representative case. Illustrative videos are included in the supplemental material.

cond-mat.soft↗

arXiv2018

Simulation and observation of line-slip structures in columnar structures of soft spheres

We present the computed phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased. A comparable experimental observation is made on a column of bubbles under forced drainage, clearly exhibiting the expected line slip.

cond-mat.soft↗

arXiv2017

Phyllotaxis, disk packing and Fibonacci numbers

We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity and continuity. We show that spiral structures characterised by the widely observed Fibonacci sequence (1,1,2,3,5,8,13...), as well as related structures, occur naturally under such rules. Typical results are presented in a animation.

cond-mat.soft↗

arXiv2016

How bees and foams respond to curved confinement: level set boundary representations in the Surface Evolver

We present a Surface Evolver framework for simulating single bubbles and multicellular foams trapped between curved parallel surfaces. We are able to explore a range of geometries using level set constraints to model the bounding surfaces. Unlike previous work, in which the bounding surfaces are flat (the so called Hele-Shaw geometry), we consider surfaces with non- vanishing Gaussian curvature, specifically the sphere, the torus and the Schwarz Primitive-surface. In the case of multi-cellular foams - our method is to first distribute a set of N points evenly over the surface (using an en- ergy minimisation approach), these seed points are then used to generate a Voronoi partition, that is clipped to the confining space, which in turn forms the basis of a Surface Evolver simulation. In addition we describe our ex- perimental attempt to generate a honeycomb on a negatively curved surface, by trapping bees between two Schwarz Primitive-surfaces. Our aim is to understand how bees adapt the usual hexagonal motif of the honeycomb to cope with a curved surface. To our knowledge this is the first time that an attempt has been made to realise a biological cellular structure of this type.

cond-mat.soft↗

arXiv2013

Theory of cylindrical dense packings of disks

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

cond-mat.soft↗

arXiv2011

Phyllotactic description of hard sphere packing in cylindrical channels

We develop a simple analytical theory that relates dense sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding cylinder, respectively) up to R=1+1/sin(pi/5). Within this range the densest packings are such that all spheres are in contact with the cylindrical boundary. The detailed results elucidate extensive numerical simulations by ourselves and others by identifying the nature of all competing phases.

cond-mat.soft↗

arXiv2009

Effect of dipolar interactions for domain wall dynamics in magnetic thin films

We study the effect of long range dipolar forces on the dynamics and morphology of domain walls in magnetic thin films by numerical simulations of the spin-1 random field Ising model. By studying the size distribution of avalanches of domain wall motion arising as a response to quasistatic external driving, we observe a cross-over from the case dominated by short range interactions to another universality class where the long range dipolar forces become important. This crossover is accompanied with a change of the domain wall morphology from a rough wall to walls with zigzag structure.

cond-mat.mtrl-sci↗

arXiv2009

Modeling domain wall dynamics in thin magnetic strips with disorder

We present a line-based model of transverse domain walls in thin magnetic strips, to study the effect of bulk disorder on the domain wall dynamics within the thermally activated creep regime. The creep velocity is found to exhibit a non-linear dependence on both applied magnetic fields and electric currents, characterized by similar creep exponents for both forms of the external drive. We discuss briefly the significance of the inherently stochastic thermally activated domain wall motion from the point of view of spintronics applications, where it generally is essential to be able to control the domain wall displacement in a deterministic manner.

cond-mat.mtrl-sci↗