Professor Nigel Mottram

Professor (Mathematics)

ORCID iD https://orcid.org/0000-0002-7265-0059

Research interests

Research Interests

My research interests are in the mathematical modelling of real-world systems, generally focussing on those that include the dynamics of non-Newtonian fluids. I am particularly interested in anisotropic fluids such as liquid crystals, where viscoelasticity is an important consideration, as is their behaviour under electric fields.

Current projects also include investigations of active fluids, such as bacterium or micro-organism organisation within fluid flows, and biological flow systems, and more generally in the areas of medical and biological systems.

In a wider context I am a member of the British Liquid Crystal Society, the Edinburgh Mathematical Society, and a Fellow of the Institute for Mathematics and its Applications, as well as an active participant in the European Consortium for Mathematics in Industry and the UK Fluids Network.

I am interested in mathematics applied to real-world problems in a general sense and I welcome enquiries from anyone interested to understand more about mathematical modelling.

I currently have PhD projects available and prospective applicants should email me at nigel.mottram@glasgow.ac.uk.

Typical project areas include the following:

Anisotropy in the natural environment: swimming/self-organised organisms, tissue growth, mixing
Order parameter changes in nematic liquid crystals: defects, field induced changes, Q tensor theory
Theories of biaxial nematic liquid crytals
Surface effects: induced order, bistabilty in anisotropic fluids
Disclination line motion: annihilation, formation, effects of electric field and surface interactions
Thin films: flow in thin films of anisotropic fluids, painting and spin-coating
Use of fractional calculus to represent memory in dynamical systems
Physiologically-based Pharmacokinetics and dynamics
Blood flow: non-newtonian models of blood flow in microfluidic devices
Oxygen transfer: novel medical device modelling for artificial livers

A video about liquid crystals I created with the Universities of Strathclyde, Nottingham Trent and Wiretrace, images by Dr Stephen Cowling (York)

Research Groups

Publications

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Number of items: 61.

2020

Cousins, J.R.L., Wilson, S.K., Mottram, N. , Wilkes, D. and Weegels, L. (2020) Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring. Physical Review E, 102, 062703. (doi: 10.1103/PhysRevE.102.062703)

Walton, J., McKay, G., Grinfeld, M. and Mottram, N. J. (2020) Pressure-driven changes to spontaneous flow in active nematic liquid crystals. European Physical Journal E, 43(8), 51. (doi: 10.1140/epje/i2020-11973-8) (PMID:32743686)

Bhadwal, A.S., Mottram, N.J. , Saxena, A., Sage, I.C. and Brown, C.V. (2020) Electrically controlled topological micro cargo transportation. Soft Matter, 16(12), pp. 2961-2970. (doi: 10.1039/C9SM01956A) (PMID:32119011)

2019

Cousins, J.R.L., Wilson, S.K., Mottram, N.J. , Wilkes, D. and Weegels, L. (2019) Squeezing a drop of nematic liquid crystal with strong elasticity effects. Physics of Fluids, 31(8), 083107. (doi: 10.1063/1.5110878)

Lesniewska, M., Henrich, O. and Mottram, N. (2019) Microfluidic Flow of Colloid-Liquid Crystal Composite Materials. 5th International Soft Matter Conference (ISMC2019), Edinburgh, UK, 03-07 Jun 2019.

Alqahtani, Z.M., El-Shahed, M. and Mottram, N.J. (2019) Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations. Letters in Biomathematics, 6(1), pp. 32-49. (doi: 10.1080/23737867.2019.1656115)

2018

Cousins, J. R.L., Wilson, S. K., Mottram, N. J. , Wilkies, D., Weegels, L. and Lin, K. (2018) A Model for the Formation of Mura During the One-Drop-Filling Process. 25th International Display Workshop 2018, Nagoya, Japan, 12-14 Dec 2018.

Walton, J., Mottram, N.J. and McKay, G. (2018) Nematic liquid crystal director structures in rectangular regions. Physical Review E, 97(2), 022702. (doi: 10.1103/PhysRevE.97.022702)

2017

Da Costa, F. P., Grinfeld, M., Mottram, N. J. and Pinto, J. T. (2017) A mathematical study of a bistable nematic liquid crystal device. Mathematical Models and Methods in Applied Sciences, 17(12), pp. 2009-2034. (doi: 10.1142/S0218202507002546)

McGinty, S. , Hyndman, L., Mottram, N. , McKee, S. and Webb, S. (2017) In-silico Characterisation of the Kirkstall QV900 In-Vitro System for Advanced Cell Culture. In: 5 th International Conference on Computational and Mathematical Biomedical Engineering (CMBE2017), Pittsburgh, PA, USA, 10-12 April 2017, pp. 1174-1177. ISBN 9780956291448

2016

Corson, L.T., Mottram, N.J. , Duffy, B.R., Wilson, S.K., Tsakonas, C. and Brown, C.V. (2016) Dynamic response of a thin sessile drop of conductive liquid to an abruptly applied or removed electric field. Physical Review E, 94(4), 043112. (doi: 10.1103/PhysRevE.94.043112)

Corson, L.T., Tsakonas, C., Duffy, B.R., Mottram, N.J. , Brown, C.V. and Wilson, S.K. (2016) Electro-Manipulation of Droplets for Microfluidic Applications. In: ECMI 2014, Taormina, Italy, 9-13 Jun 2014, pp. 1073-1080. ISBN 9783319234120 (doi:10.1007/978-3-319-23413-7)

McKee, S., Dougall, E. A. and Mottram, N. J. (2016) Analytic solutions of a simple advection-diffusion model of an oxygen transfer device. Journal of Mathematics in Industry, 6, 3. (doi: 10.1186/s13362-016-0019-3)

Mottram, N.J. , McKay, G., Brown, C.V., Russell, C.T., Sage, I.C. and Tsakonas, C. (2016) Flow-induced delayed Freedericksz transition. Physical Review E, 93(3), 030701(R). (doi: 10.1103/PhysRevE.93.030701)

Ritos, K., Borg, M. K., Mottram, N. J. and Reese, J. M. (2016) Electric fields can control the transport of water in carbon nanotubes. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2060), 20150025. (doi: 10.1098/rsta.2015.0025) (PMID:26712640) (PMCID:PMC4696074)

2014

Corson, L.T., Tsakonas, C., Duffy, B.R., Mottram, N.J. , Sage, I.C., Brown, C.V. and Wilson, S.K. (2014) Deformation of a nearly hemispherical conducting drop due to an electric field: theory and experiment. Physics of Fluids, 26(12), 122106. (doi: 10.1063/1.4903223)

2013

Mottram, N.J. , Pinto, J.T. and McKay, G. (2013) Decoupling of the Ericksen-Leslie equations. Liquid Crystals, 40(6), pp. 787-798. (doi: 10.1080/02678292.2013.783134)

2012

Davidson, A.J. and Mottram, N. (2012) Conformal mapping techniques for the modelling of liquid crystal devices. European Journal of Applied Mathematics, 23(1), pp. 99-119. (doi: 10.1017/S0956792510000380)

da Costa, F.P., Grinfeld, M., Langer, M., Mottram, N.J. and Pinto, J.T. (2012) Kickback in nematic liquid crystals. Quarterly of Applied Mathematics, 70, pp. 99-110. (doi: 10.1090/S0033-569X-2011-01265-5)

2011

Grinfeld, M., Langer, M. and Mottram, N. J. (2011) Nematic viscosity estimation using director kickback dynamics. Liquid Crystals, 38(8), pp. 981-987. (doi: 10.1080/02678292.2011.588969)

Brown, C. V., McHale, G. and Mottram, N. J. (2011) Analysis of a static undulation on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces. Journal of Applied Physics, 110(2), 024107. (doi: 10.1063/1.3606435)

Majumdar, A. and Mottram, N. (2011) Liquid crystal theory and modelling: Discussion meeting. Liquid Crystals Today, 20(1), pp. 20-21. (doi: 10.1080/1358314x.2010.527662)

2010

Evans, C. R., Davidson, A. J., Brown, C. V. and Mottram, N. J. (2010) Static alignment states in a bistable azimuthal nematic device with blazed grating sidewalls. Journal of Physics D: Applied Physics, 43(49), 495105. (doi: 10.1088/0022-3727/43/49/495105)

Davidson, A. J., Brown, C. V., Mottram, N. J. , Ladak, S. and Evans, C. R. (2010) Defect trajectories and domain-wall loop dynamics during two-frequency switching in a bistable azimuthal nematic device. Physical Review E, 81(5), 051712. (doi: 10.1103/PhysRevE.81.051712) (PMID:20866252)

2009

Ladak, S., Davidson, A., Brown, C. V. and Mottram, N. J. (2009) Sidewall control of static azimuthal bistable nematic alignment states. Journal of Physics D: Applied Physics, 42(8), 085114. (doi: 10.1088/0022-3727/42/8/085114)

Da Costa, F. P., Grinfeld, M., Mottram, N. J. and Pinto, J. T. (2009) Uniqueness in the Freedericksz transition with weak anchoring. Journal of Differential Equations, 246(7), pp. 2590-2600. (doi: 10.1016/j.jde.2009.01.033)

2008

Trabi, C. L., Brown, C. V., Smith, A. A. T. and Mottram, N. J. (2008) Interferometric method for determining the sum of the flexoelectric coefficients (e1+e3) in an ionic nematic material. Applied Physics Letters, 92, 223509. (doi: 10.1063/1.2938722)

Quintans Carou, J., Wilson, S. K., Mottram, N. J. and Duffy, B. R. (2008) Asymptotic and numerical analysis of a simple model for blade coating. Journal of Engineering Mathematics, 63, pp. 155-176. (doi: 10.1007/s10665-008-9226-2)

Trabi, C. L., Smith, A. A. T., Mottram, N. J. and Brown, C. V. (2008) Flexoelectric polarisation effects in nematic liquid crystal phase gratings. In: Conference on Liquid Crystals XII, San Diego, CA, USA, 11-12 August 2008, (doi:10.1117/12.794912)

2007

Diaz, A., McKay, G. and Mottram, N. J. (2007) Effect of decoupled azimuthal and zenithal anchoring on smectic-C chevron structures. Physical Review E, 76(4), 041705. (doi: 10.1103/physreve.76.041705)

Palto, S. P., Mottram, N. J. and Osipov, M. A. (2007) Flexoelectric instability and a spontaneous chiral-symmetry breaking in a nematic liquid crystal cell with asymmetric boundary conditions. Physical Review E, 75(6), 061707. (doi: 10.1103/PhysRevE.75.061707)

Quintans Carou, J., Mottram, N. J. , Wilson, S. K. and Duffy, B. R. (2007) A mathematical model for blade coating of a nematic liquid crystal. Liquid Crystals, 34(5), pp. 621-631. (doi: 10.1080/13682820701261801)

Smith, A. A. T., Brown, C. V. and Mottram, N. J. (2007) Theoretical analysis of the magnetic Fréedericksz transition in the presence of flexoelectricity and ionic contamination. Physical Review E, 75(4), 041704. (doi: 10.1103/PhysRevE.75.041704)

Tsakonas, C., Davidson, A. J., Brown, C. V. and Mottram, N. J. (2007) Multistable alignment states in nematic liquid crystal filled wells. Applied Physics Letters, 90(11), 111913. (doi: 10.1063/1.2713140)

2006

Mottram, N. J. , Care, C. M. and Cleaver, D. J. (2006) Control of the nematic-isotropic phase transition by an electric field. Physical Review E, 74(4), 041703. (doi: 10.1103/PhysRevE.74.041703)

Mottram, N. J. and Brown, C. V. (2006) Pulsed addressing of a dual-frequency nematic liquid crystal. Physical Review E, 74(3), 031703. (doi: 10.1103/PhysRevE.74.031703)

Quintans Carou, J., Duffy, B. R., Mottram, N. J. and Wilson, S. K. (2006) Shear-driven and pressure-driven flow of a nematic liquid crystal in a slowly varying channel. Physics of Fluids, 18(2), 027105. (doi: 10.1063/1.2145750)

2005

Diaz, A., Mottram, N. J. and McKay, G. (2005) Theoretical model of the transition between C1 and C2 chevron structures in smectic liquid crystals. European Physical Journal E, 18, pp. 231-237. (doi: 10.1140/epje/i2005-10041-7)

Miroshnychenko, D., Hill, N.A. , Mottram, N.J. and Lydon, J.E. (2005) Evolution from A 2 defect to 1/2 defects in a cylindrical geometry. Molecular Crystals and Liquid Crystals, 437(1), pp. 1495-1511. (doi: 10.1080/15421400590955334)

Diaz, A., Mottram, N. J. and McKay, G. (2005) Effects of weak anchoring on C1 and C2 chevron structures. Molecular Crystals and Liquid Crystals, 438(1), 17[1581]-25[1589]. (doi: 10.1080/15421400590957080)

Kelly, G., Mottram, N. J. and Ramage, A. (2005) Electric field effects on nematic wetting layers. Molecular Crystals and Liquid Crystals, 438(1), 271[1835]-282[1846]. (doi: 10.1080/15421400590955541)

Miroshnychenko, D., Hill, N.A., Mottram, N.J. and Lydon, J.E. (2005) Liquid Crystal Pre-patterning in Mitosis. In: 2005 Summer Bioengineering Conference, Vail, CO., US, 22 -26 Jun 2005, ISBN 9780974249216

Quintans Carou, J., Duffy, B. R., Mottram, N. J. and Wilson, S. K. (2005) Steady flow of a nematic liquid crystal in a slowly varying channel. Molecular Crystals and Liquid Crystals, 438(1), 237[1801]-249[1839]. (doi: 10.1080/15421400590955569)

2004

Woods, P. D., Stewart, I. W. and Mottram, N. J. (2004) Flow effect in director relaxation of bookshelf aligned smectic C liquid crystals. Molecular Crystals and Liquid Crystals, 413(1), pp. 271-278. (doi: 10.1080/15421400490437088)

2003

Brown, C. V. and Mottram, N. J. (2003) Influence of flexoelectricity above the nematic Fréedericksz transition. Physical Review E, 68(3), 031702. (doi: 10.1103/PhysRevE.68.031702) (PMID:14524783)

Webster, R. E., Mottram, N. J. and Cleaver, D. J. (2003) Molecular simulation of chevrons in confined smectic liquid crystals. Physical Review E, 68(2), 021706. (doi: 10.1103/PhysRevE.68.021706) (PMID:14524992)

McKay, G., MacKenzie, K.R. and Mottram, N.J. (2003) Competing polarization effects in a homeotropically aligned smectic liquid crystal. In: 9th International Conference on Ferroelectric Liquid Crystals, FLC 2003, Dublin, Ireland, 24-29 Aug 2003, (doi:10.1080/00150190490509854)

2002

Davidson, A. J. and Mottram, N. J. (2002) Flexoelectric switching in a bistable nematic device. Physical Review E, 65(5), 051710. (doi: 10.1103/PhysRevE.65.051710) (PMID:12059580)

Mottram, N.J. and Hogan, S.J. (2002) Magnetic field-induced changes in molecular order in nematic liquid crystals. Continuum Mechanics and Thermodynamics, 14, pp. 281-295. (doi: 10.1007/s00161-002-0097-x)

2001

Beccherelli, R., Judge, L. A., Mottram, N. J. and Elston, S. J. (2001) Surface evanescent field characterisation of antiferroelectric liquid crystals. Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 358(1), pp. 263-274. (doi: 10.1080/10587250108028286)

Beldon, S.M., Mottram, N.J. and Elston, S.J. (2001) A chevron model of the electroclinic effect across the Sa*-SC* phase transition in a SSFLC. Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 365, pp. 729-738. (doi: 10.1080/10587250108025352)

Mottram, N. J. and Elston, S. J. (2001) The influence of polar surface anchoring on switching in antiferroelectric liquid crystals. Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 364(1), pp. 361-371. (doi: 10.1080/10587250108025005)

2000

Mottram, N. J. and Elston, S. J. (2000) Theoretical investigation into the effects of polar anchoring in antiferroelectric liquid crystal cells. Physical Review E, 62(5), pp. 6787-6794. (doi: 10.1103/PhysRevE.62.6787) (PMID:11102031)

Mottram, N. J. , Sluckin, T. J., Elston, S. J. and Towler, M. J. (2000) Shear-induced melting of smectic-A liquid crystals. Physical Review E, 62(4), pp. 5064-5080. (doi: 10.1103/PhysRevE.62.5064) (PMID:11089055)

Mottram, N. J. and Elston, S. J. (2000) Thresholdless and hysteretic switching in aflc cells with polar anchoring. Ferroelectrics, 246(1), pp. 51-59. (doi: 10.1080/00150190008230052)

Beccherelli, R., Mottram, N.J. and Elston, S.J. (2000) Homogeneous and heterogeneous switching in antiferroelectric liquid crystals. European Physical Journal: Applied Physics, 9(3), pp. 247-252. (doi: 10.1051/epjap:2000111)

Elston, S. J. and Mottram, N. (2000) Order parameter variation in smectic liquid crystals. In: Jadish, K.V. (ed.) Advances in Liquid Crystals. A special volume, volume 113. Series: Advances in chemical physics. Wiley. ISBN 9780471180838

Mottram, N.J. and Sluckin, T.J. (2000) Defect-induced melting in nematic liquid crystals. Liquid Crystals, 27(10), pp. 1301-1304. (doi: 10.1080/026782900423340)

Mottram, N.J. , Sluckin, T.J., Elston, S.J. and Towler, M.J. (2000) Periodic layer slipping in a sheared smectic a cell. Molecular Crystals and Liquid Crystals, 347, pp. 179-188. (doi: 10.1080/10587250008024839)

Mottram, N. J. and Elston, S. J. (2000) Formation and stability of smectic C chevrons. Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 351(1), pp. 323-333. (doi: 10.1080/10587250008023282)

1999

Mottram, N. J. and Elston, S. J. (1999) Order parameter theory for switching in antiferroelectric liquid crystals. Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 330(1), pp. 557-564. (doi: 10.1080/10587259908025634)

This list was generated on Wed Jan 20 12:43:55 2021 GMT.

Jump to: Articles | Book Sections | Conference or Workshop Item | Conference Proceedings

Number of items: 61.

Articles

Walton, J., Mottram, N.J. and McKay, G. (2018) Nematic liquid crystal director structures in rectangular regions. Physical Review E, 97(2), 022702. (doi: 10.1103/PhysRevE.97.022702)

Mottram, N.J. , Pinto, J.T. and McKay, G. (2013) Decoupling of the Ericksen-Leslie equations. Liquid Crystals, 40(6), pp. 787-798. (doi: 10.1080/02678292.2013.783134)

Grinfeld, M., Langer, M. and Mottram, N. J. (2011) Nematic viscosity estimation using director kickback dynamics. Liquid Crystals, 38(8), pp. 981-987. (doi: 10.1080/02678292.2011.588969)

Majumdar, A. and Mottram, N. (2011) Liquid crystal theory and modelling: Discussion meeting. Liquid Crystals Today, 20(1), pp. 20-21. (doi: 10.1080/1358314x.2010.527662)

Mottram, N. J. , Care, C. M. and Cleaver, D. J. (2006) Control of the nematic-isotropic phase transition by an electric field. Physical Review E, 74(4), 041703. (doi: 10.1103/PhysRevE.74.041703)

Mottram, N. J. and Brown, C. V. (2006) Pulsed addressing of a dual-frequency nematic liquid crystal. Physical Review E, 74(3), 031703. (doi: 10.1103/PhysRevE.74.031703)

Brown, C. V. and Mottram, N. J. (2003) Influence of flexoelectricity above the nematic Fréedericksz transition. Physical Review E, 68(3), 031702. (doi: 10.1103/PhysRevE.68.031702) (PMID:14524783)

Davidson, A. J. and Mottram, N. J. (2002) Flexoelectric switching in a bistable nematic device. Physical Review E, 65(5), 051710. (doi: 10.1103/PhysRevE.65.051710) (PMID:12059580)

Mottram, N. J. and Elston, S. J. (2000) Thresholdless and hysteretic switching in aflc cells with polar anchoring. Ferroelectrics, 246(1), pp. 51-59. (doi: 10.1080/00150190008230052)

Mottram, N.J. and Sluckin, T.J. (2000) Defect-induced melting in nematic liquid crystals. Liquid Crystals, 27(10), pp. 1301-1304. (doi: 10.1080/026782900423340)

Book Sections

Conference or Workshop Item

Lesniewska, M., Henrich, O. and Mottram, N. (2019) Microfluidic Flow of Colloid-Liquid Crystal Composite Materials. 5th International Soft Matter Conference (ISMC2019), Edinburgh, UK, 03-07 Jun 2019.

Conference Proceedings

This list was generated on Wed Jan 20 12:43:55 2021 GMT.

Grants

2020-2023 - EPSRC grant EP/T012501/1: Control of free-surface flow morphologies in anisotropic liquids

with Profs Stephen Wilson (Strathclyde) and Carl Brown (Nottingham Trent)

Project Partners: e-Vision Smart Optics; FlexEnable Limited; Merck KGaA; OpSec Security Ltd

2020-2021 - EPSRC IAA grant: Optimising fringing fields effects in LCOS devices

Project Partners: Envisics Ltd

Teaching

I teach, or have taught, various courses - at undergraduate, masters and postgraduate level, and to mathematicians, phsyicists, engineers, chemists and environmental scientists.

Over the last few years I have become increasingly interested in the effects of online teaching methods in mathematics, including the use of lecture capture. I have developed online resources that can enhance standard lecture classes, but I have also created a number of completely online maths modules, designed for distance learning and to assist in widening participation, particularly through the Graduate Apprenticeship programme.

2020-21 Teaching

SMSTC Continuum Mechanics
2D Mathematical Methods & Modelling

Photo of Prof. Nigel Mottram

School of Mathematics and Statistics, Glasgow, G12 8QQ

School of Mathematics & Statistics

Professor Nigel Mottram

Research interests

Research Interests

Research Groups

Publications

2020

2019

2018

2017

2016

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

Articles

Book Sections

Conference or Workshop Item

Conference Proceedings

Grants

Teaching