Industrial Mathematics Group

The BOS and DOS (Bath-Oxford-Strathclyde and Durham-Oxford-Strathclyde) Networks

Objectives

The DOS, and its predecessor BOS, network unites researchers with an interest in anisotropy or directionality in materials, be they solids or liquids. The network brings together for the first time leading research groups in continuum mechanics from Durham, Oxford and Strathclyde.

Anisotropy means the "existence of special or distinguished directions" and "reduced symmetry" since all directions are not physically equivalent. This, in turn, implies directional physical, optical, mechanical and rheological properties that pave the way for new applications. Nematic liquid crystals are classical examples of anisotropic complex fluids for which the constituent asymmetric molecules have translational freedom but tend to align along certain preferred directions, leading to long-range orientational order.

Apala Majumdar leads the Strathclyde side, and specializes in the mathematics and modelling of nematic liquid crystals, in particular spatio-temporal pattern formation for nematics in confined geometries and how their orientational anisotropy may be tailored by material properties, geometrical properties and temperature using techniques from the calculus of variations, algebraic topology, dynamical systems approaches and numerical studies. Her work is largely motivated by questions in the display industry or new experiments on nano-confined systems.

Ian Griffiths leads the Oxford side, and has recently started to specialize in anisotropic solids, for example, porous media with non-periodic pores and spatially dependent permeabilities. This can be mathematically studied using new techniques in homogenization theory, with new applications in filtration and environmental problems. A recently studied example concerns a porosity-graded filter, whose porosity varies with depth, such as fibrous filters and ceramic filters. Each of these materials offers the possibility of improved performance either by filtering out particles more uniformly in the depth or by reducing the pressure required to drive fluid through the filter, and there is ample scope for new mathematical insights from asymptotics, analysis and up-scaling methods.

Nigel Mottram co-led the Strathclyde side until his recent move to the University of Glasgow. He specializes in the mathematics and applications of nematic liquid crystals, with a more recent interest in bio-inspired active liquid crystals. Active liquid crystals are inherently non-equilibrium systems, constantly producing and dissipating energy with striking and unique mechanical and rheological responses, such as low Reynolds number turbulence, rapid density fluctuations and exotic singularities. Active liquid crystals are ubiquitous in biology, common examples being the cell cytoskeleton and the human DNA and a lot remains to be understood about the active terms in the phenomenological theories for active systems and the new resulting anisotropies.

Halim Kusumaatmaja leads the Durham side, and is interested in a wide range of soft matter and biological problems which often show anisotropic behaviour. Examples of current interest include phase behaviour on non-uniform curved surfaces, spreading dynamics on structured surfaces, and reconfigurable elastic structures. His work is largely motivated by a strong interest to understand and mimic nature for engineering and industrial applications. He uses a combination of analytical and numerical techniques. The latter include Monte Carlo, Molecular Dynamics, lattice Boltzmann and energy landscape exploration techniques.

Meeting 8: Durham hosted

30 June - 1 July 2022

Speakers:

• Apala Majumdar (University of Strathclyde), "Solution Landscapes of Thin Nematic Systems"
• Andrew Krause (Durham University), "Pattern Formation in Stratified and Heterogeneous Domains"
• Sourav Patranabish (IIT Delhi), "Cybotactic clusters of bent-core nematic liquid crystals - theory and experiments"
• Halim Kusumaatmaja (Durham University), "Colloidal Assemblies on Curved Surfaces: From Spheres to Tori and Cones"
• Jack Paget (Loughborough University), "A complex tensor model for smectic layering"
• Ijuptil Joseph (University of Glasgow), "Instabilities in a Planar-Aligned Active Liquid Crystal"
• Jesús Enrique Macĺas Durán (UNAM Mexico), "Multiparticle collision dynamics simulations of active nematic liquid crystals"
• Tyler Shendruk (University of Edinburgh), "Coarse-grained, particle-based models for active nematic fluids"
• Stephen Morris (University of Oxford), "3D Laser Sculpturing in Liquid Crystal Devices"
• Devesh Mistry (University of Leeds), "How hierarchies of anisotropy in liquid crystal elastomers influence mechanics"
• Joe Pollard (Durham University), "The Topological Classification of Disclination Lines in Cholesteric Liquid Crystals"

Meeting 7: Durham hosted (remote)

13 September 2021

Speakers:

• Philip Hands (Edinburgh). Liquid crystal lasers: Low-cost, compact and tuneable light sources.
• Debasish Das (Strathclyde). Active chiral particles driven by electric and magnetic fields
• Gaetano Napoli (Salento). Cooling a spherical nematic shell
• Adam Townsend (Durham). Microorganisms swimming through structured networks: from the point of view of the microorganism
• Joseph Cousins (Glasgow). on-uniqueness of equilibrium states for a static ridge of nematic liquid crystals
• Aurore Loisy (Aix-Marseille). Self-propulsion of a drop of active nematic

Meeting 6: Oxford hosted (remote)

18 September 2020

Speakers:

• David MacTaggart (University of Glasgow). Anisotropy in magnetohydrodynamics - effects on nonlinear instabilities
• Hilary Ockendon (University of Oxford). Recycling carbon fibres.
• Sam Avis (Durham University). Reconfigurability of 3D buckled mesostructures.
• Jingmin Xia (University of Oxford). A double Landau-de Gennes mathematical model of smectic A liquid crystals.
• Linda Cummings (New Jersey Institute of Technology). Dewetting and dielectrowetting in thin films of nematic liquid crystal.

Meeting 5: Durham hosted (remote)

8 July 2020

Speakers:

• Priya Subramanian (Mathematical Institute, University of Oxford) – Title TBD
• Margarita Staykova (Physics, University of Durham) – Tearing of lipid and polymeric membranes upon stretch
• Chris Prior (Mathematical Sciences, University of Durham) – Modes of internal buckling of bundle system
• Joseph Cousins (Mathematics and Statistics, University of Strathclyde) – A static ridge of nematic liquid crystal
• Anders Aufderhorst-Roberts (Physics, University of Leeds) – Title: TBD

Meeting 4: Strathclyde hosted (remote)

12 May 2020

Speakers:

• Francesco Giglio (School of Mathematics and Statistics, University of Glasgow) – Exact equations of state for nematics
• Mark Miller (Department of Chemistry, Durham University) – Continuum percolation of nanorod mixtures in quadrupole fields
• Joshua Walton (Department of Mathematics and Statistics, University of Strathclyde) – Active Fluid Flows in Two-Dimensional Geometries
• Elsen TJHung (Department of Physics, Durham University) – Splay-bend phases in 2d liquid crystals: long-range order and beam-splitter
• Alison Ramage (Department of Mathematics and Statistics, University of Strathclyde) – A Moving Mesh Finite Element Methods for Modelling Defects in Liquid Crystals

Meeting 3: Strathclyde

24 September 2019

Speakers:

• Apala Majumdar (Bath, Mathematics/Strathclyde, Mathematics and Statistics) – Pattern Formation in Confined Nematic Systems
• Josh Walton (Strathclyde, Mathematics and Statistics) – Pressure-driven states in channel flow of active nematic liquid crystals
• Oliver Whitehead (Oxford, Mathematics) – Active and passive driving in liquid crystal devices
• Oliver Henrich (Strathclyde, Physics) – Microfluidic flow of colloid-liquid crystal composite materials
• Joseph Cousins (Strathclyde, Mathematics and Statistics) –Nematic liquid crystal flow during the manufacture of liquid crystal devices
• Carl Brown (Nottingham Trent, Physics) – Competition of flow and electric field alignment in nematics

Meeting 2: Oxford

22 May 2019

Speakers:

Patrick Farrell (Mathematics, Oxford) – Computing disconnected bifurcation diagrams of partial differential equations
Lidong Fang (Natural Sciences, Shanghai Jiao Tong University) – Bifurcation diagrams in the Landau de Gennes theory on rectangles
Josh Walton (Mathematics and Statistics, Strathclyde) – Ericksen–Leslie and Q-Tensor models of spontaneous flow transitions in active nematic liquid crystals
Marcin Mucha-Kruczynski (Physics, Bath) – Van der Waals heterostructures
Magdalena Lesniewska (Physics, Strathclyde) – Microfluidic flow of colloid–liquid-crystal composite materials
Andreas Muench – Thin-film models for an active gel (Mathematics, Oxford)

Meeting 1: Bath

10 April 2019

Speakers:

• Konark Bisht – Morphologies of nano-included liquid crystals in 2d square wells
• Ian Griffiths – Anisotropic media in industrial applications
• Joseph Harris – The well order reconstruction solution for three-dimensional wells
• Nigel Mottram – Rheology of active and inactive liquid crystals
• Galina Printsypar – Multiscale modelling of filtration processes under different operational conditions
  

Selected publications

[1] Flow and nematic director profiles in a microfluidic channel: the interplay of nematic material constants and backflow
S. Mondal, I.M. Griffiths, F. Charlet & A. Majumdar
2018
MDPI Fluids (in press)

[2] Nematohydrodynamics for Colloidal Self-Assembly and Transport Phenomena
S. Mondal, A. Majumdar & I.M. Griffiths
2018
J. Coll. Interf. Sci. (in press)

[3] Solution landscapes in nematic microfluidics
M. Crespo, A. Majumdar, A. Manuel Ramos & I.M. Griffiths.
2017
Physica D, 351-352, 1-13.