Continuum mechanics

The Continuum Mechanics group brings together researchers who consider both the underlying mathematical theories that accurately describe the mechanics of fluid and solid materials, and the application of these theories to real-world problems.




Mascheroni, P., Penta, R., Merodio, J. (2023) The impact of vascular volume fraction and compressibility of the interstitial matrix on vascularised poroelastic tissues Biomechanics and Modeling in Mechanobiology, 22, pp. 1901-1917. (doi: 10.1007/s10237-023-01742-1)

Guan, J. H., Magoon, C. W., Durey, M., Camassa, R., Saenz, P. J. (2023) Traveling Faraday waves Physical Review Fluids, 8, (doi: 10.1103/PhysRevFluids.8.110501)

Ramírez-Torres, A., Penta, R., Grillo, A. (2023) Effective properties of fractional viscoelastic composites via two-scale asymptotic homogenization Mathematical Methods in the Applied Sciences, 46, pp. 16500-16520. (doi: 10.1002/mma.9457)

Gupta, P., MacTaggart, D., Simitev, R. D. (2023) Differential rotation in convecting spherical shells with non-uniform viscosity and entropy diffusivity Fluids, 8, (doi: 10.3390/fluids8110288)

Liu, N., Durey, M., Bush, J. W. M. (2023) Pilot-wave dynamics in a rotating frame: the onset of orbital instability Journal of Fluid Mechanics, 973, (doi: 10.1017/jfm.2023.742)

Fülöp, Z. B., Ramírez-Torres, A., Penta, R. (2023) Multiscale modelling of fluid transport in vascular tumours subjected to electrophoresis anticancer therapies Zeitschrift für Angewandte Mathematik und Physik,

Miller, L., Penta, R. (2023) Homogenization of a coupled electrical and mechanical bidomain model for the myocardium Mathematics and Mechanics of Solids,

Han, H., Guo, B., Gao, P., Yang, F., Sun, C., Hill, N. A., Liu, H. (2023) Finite‐element simulation of in‐plane tear propagation in the dissected aorta: implications for the propagation mechanism International Journal for Numerical Methods in Biomedical Engineering, 39, (doi: 10.1002/cnm.3743)

Dalton, D., Husmeier, D., Gao, H. (2023) Physics-informed graph neural network emulation of soft-tissue mechanics computer methods in applied mechanics and engineering Computer Methods in Applied Mechanics and Engineering,

Guan, D., Zhuan, X., Luo, X., Gao, H. (2023) An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling Acta Biomaterialia, 166, pp. 375-399. (doi: 10.1016/j.actbio.2023.05.022)

Girelli, A., Giantesio, G., Musesti, A., Penta, R. (2023) Effective governing equations for dual porosity Darcy-Brinkman systems subjected to inhomogeneous body forces and their application to the lymph node Proceedings of the Royal Society Series A: Mathematical, Physical and Engineering Sciences, 479, (doi: 10.1098/rspa.2023.0137)

Xia, Y., Yuan, M., Dobrea, A., Li, C., Heidari, H., Mottram, N., Ghannam, R. (2023) Reconfigurable wearable antenna for 5G applications using nematic liquid crystals Nano Select, 4, pp. 513-524. (doi: 10.1002/nano.202200209)

Durey, M., Milewski, P. A. (2023) Resonant triad interactions of gravity waves in cylindrical basins Journal of Fluid Mechanics, 966, (doi: 10.1017/jfm.2023.441)

Miller, L., Ramirez-Torres, A., Rodríguez-Ramos, R., Penta, R. (2023) Effective governing equations for viscoelastic composites Materials, 16, (doi: 10.3390/ma16144944)

Teed, R. J., Dormy, E. (2023) Solenoidal force balances in numerical dynamos Journal of Fluid Mechanics, 964, (doi: 10.1017/jfm.2023.332)

Roque-Piedra, A., Rodríguez-Ramos, R., Penta, R., Ramírez-Torres, A. (2023) Effective properties of homogenised nonlinear viscoelastic composites Materials, 16, (doi: 10.3390/ma16113974)

Rabbani, A., Gao, H., Lazarus, A., Dalton, D., Ge, Y., Mangion, K., Berry, C., Husmeier, D. (2023) Image-based estimation of the left ventricular cavity volume using deep learning and Gaussian process with cardio-mechanical applications Computerized Medical Imaging and Graphics, 106, (doi: 10.1016/j.compmedimag.2023.102203)

Miller, L., Penta, R. (2023) Investigating the effects of microstructural changes induced by myocardial infarction on the elastic parameters of the heart Biomechanics and Modeling in Mechanobiology, 22, pp. 1019-1033. (doi: 10.1007/s10237-023-01698-2)

Watson, S. J. (2023) Navier-Stokes-Fourier system with phase transitions Meccanica, 58, pp. 1163-1172. (doi: 10.1007/s11012-022-01620-7)

Simitev, R. D., Al dawoud, A., Aziz, M. H.N., Myles, R., Smith, G. L. (2023) Phenomenological analysis of simple ion channel block in large populations of uncoupled cardiomyocytes Mathematical Medicine and Biology, 40, pp. 175-198. (doi: 10.1093/imammb/dqad001)

Cai, L., Zhao, T., Wang, Y., Luo, X., Gao, H. (2023) Fluid–structure interaction simulation of pathological mitral valve dynamics in a coupled mitral valve-left ventricle model Intelligent Medicine, 3, pp. 104-114. (doi: 10.1016/j.imed.2022.06.005)

Al Sariri, T., Simitev, R. D., Penta, R. (2023) Optimal heat transport induced by magnetic nanoparticle delivery in vascularised tumours Journal of Theoretical Biology, 561, (doi: 10.1016/j.jtbi.2022.111372)

Zhang, C., Gao, H., Hu, X. (2023) A multi-order smoothed particle hydrodynamics method for cardiac electromechanics with the Purkinje network Computer Methods in Applied Mechanics and Engineering, 407, (doi: 10.1016/j.cma.2023.115885)

Miller, L., Penta, R. (2023) Micromechanical analysis of the effective stiffness of poroelastic composites European Journal of Mechanics - A/Solids, 98, (doi: 10.1016/j.euromechsol.2022.104875)

Cousins, J. R.L., Bhadwal, A. S., Corson, L. T., Duffy, B. R., Sage, I. C., Brown, C. V., Mottram, N. J., Wilson, S. K. (2023) Weak-anchoring effects in a thin pinned ridge of nematic liquid crystal Physical Review E, 107, (doi: 10.1103/PhysRevE.107.034702)

Thekkethil, N., Rossi, S., Gao, H., Richardson, S. I. H., Griffith, B. E., Luo, X. (2023) A stabilized linear finite element method for anisotropic poroelastodynamics with application to cardiac perfusion Computer Methods in Applied Mechanics and Engineering, 405, (doi: 10.1016/j.cma.2022.115877)

Wang, D., Luo, X., Liu, Z., Stewart, P. S. (2023) Flow-induced surface instabilities in a flexible-walled channel with a heavy wall Journal of Fluid Mechanics, 956, (doi: 10.1017/jfm.2022.1086)

Du, Y., Stewart, P., Hill, N. A., Yin, H., Penta, R., Köry, J., Luo, X., Ogden, R. (2023) Nonlinear indentation of second-order hyperelastic materials Journal of the Mechanics and Physics of Solids, 171, (doi: 10.1016/j.jmps.2022.105139)

Stewart, P. S., Hilgenfeldt, S. (2023) Gas-liquid foam dynamics: from structural elements to continuum descriptions Annual Reviews of Fluid Mechanics, 55, pp. 323-350. (doi: 10.1146/annurev-fluid-032822-125417)

Bourne, D.P., Pearce, M., Roper, S.M. (2023) Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport Mechanics Research Communications, 127, (doi: 10.1016/j.mechrescom.2022.104023)

Miller, L., Di Stefano, S., Grillo, A., Penta, R. (2023) Homogenised governing equations for pre-stressed poroelastic composites Continuum Mechanics and Thermodynamics, 35, pp. 2275-2300. (doi: 10.1007/s00161-023-01247-3)


Al Sariri, T., Penta, R. (2022) Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours Mathematical Medicine and Biology, 39, pp. 332-367. (doi: 10.1093/imammb/dqac009)

Egan, C.P., Bourne, D.P., Cotter, C.J., Cullen, M.J.P., Pelloni, B., Roper, S.M., Wilkinson, M. (2022) A new implementation of the geometric method for solving the Eady slice equations Journal of Computational Physics, 469, (doi: 10.1016/

Gupta, P., Simitev, R.D., MacTaggart, D. (2022) A study of global magnetic helicity in self-consistent spherical dynamos Geophysical and Astrophysical Fluid Dynamics, 116, pp. 521-536. (doi: 10.1080/03091929.2022.2137878)

Yang, Y., Gao, H., Berry, C., Carrick, D., Radjenovic, A., Husmeier, D. (2022) Classification of myocardial blood flow based on dynamic contrast-enhanced magnetic resonance imaging using hierarchical Bayesian models Journal of the Royal Statistical Society: Series C (Applied Statistics), 71, pp. 1085-1115. (doi: 10.1111/rssc.12568)

Lachaud, Q., Aziz, M. H. N., Burton, F. L., Macquaide, N., Myles, R. C., Simitev, R. D., Smith, G. L. (2022) Electrophysiological heterogeneity in large populations of rabbit ventricular cardiomyocytes Cardiovascular Research, 118, pp. 3112-3125. (doi: 10.1093/cvr/cvab375)

Dalton, D., Gao, H., Husmeier, D. (2022) Emulation of cardiac mechanics using Graph Neural Networks Computer Methods in Applied Mechanics and Engineering, 401, (doi: 10.1016/j.cma.2022.115645)

Giusteri, G. G., Penta, R. (2022) Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials Mechanics Research Communications, 126, (doi: 10.1016/j.mechrescom.2022.104001)

Barry, R. G., Hill, N. A., Stewart, P. S. (2022) Continuum soft tissue models from upscaling of arrays of hyperelastic cells Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478, (doi: 10.1098/rspa.2022.0065)

Aziz, M. H.N., Simitev, R. D. (2022) Estimation of parameters for an archetypal model of cardiomyocyte membrane potentials International Journal of Bioautomation, 26, pp. 255-272. (doi: 10.7546/ijba.2022.26.3.000832)

Lesniewska, M., Mottram, N., Henrich, O. (2022) Controllable particle migration in liquid crystal flows Soft Matter, 18, pp. 6942-6953. (doi: 10.1039/D2SM00707J)

Cruz-González, O.L., Ramírez-Torres, A., Rodríguez-Ramos, R., Penta, R., Lebon, F. (2022) Hierarchical heterogeneous one-dimensional problem in linear viscoelastic media European Journal of Mechanics - A/Solids, 95, (doi: 10.1016/j.euromechsol.2022.104617)

Lazarus, A., Gao, H., Luo, X., Husmeier, D. (2022) Improving cardio-mechanic inference by combining in vivo strain data with ex vivo volume–pressure data Journal of the Royal Statistical Society: Series C (Applied Statistics), 71, pp. 906-931. (doi: 10.1111/rssc.12560)

Husmeier, D., Dalton, D., Lazarus, A., Gao, H. (2022) Forward and Inverse Uncertainty Quantification in Cardiac Mechanics (doi: 10.11159/icsta22.161)

Yang, Y., Gao, H., Berry, C., Radjenovic, A., Husmeier, D. (2022) Myocardial Perfusion Classification Using A Markov Random Field Constrained Gaussian Mixture Model (doi: 10.11159/icsta22.146)

Brown, C. V., Bhadwal, A. S., Edwards, A. M. J., Sage, I. C., Saxena, A., Mottram, N. J. (2022) Frequency-controlled dielectrophoresis-driven wetting of nematic liquid crystals Journal of Physics D: Applied Physics, 55, (doi: 10.1088/1361-6463/ac6466)

Simitev, R. D., MacTaggart, D., Teed, R., Candelaresi, S. (2022) Introduction Geophysical and Astrophysical Fluid Dynamics, 116, pp. 235-236. (doi: 10.1080/03091929.2022.2107377)

Guan, D., Luo, X., Gao, H. (2022) Effect of Myofibre Dispersion on Ventricular Pump Function

Guan, D., Tian, L., Gao, H. (2022) Growth and Remodelling of Right Ventricle Under Pulmonary Arterial Hypertension

Leung, L. T., Kowal, K. N. (2022) Lubricated viscous gravity currents of power-law fluids. Part 1. Self-similar flow regimes Journal of Fluid Mechanics, 940, (doi: 10.1017/jfm.2022.214)

Leung, L. T., Kowal, K. N. (2022) Lubricated viscous gravity currents of power-law fluids. Part 2. Stability analysis Journal of Fluid Mechanics, 940, (doi: 10.1017/jfm.2022.263)

Guan, D., Gao, H., Cai, L., Luo, X. (2022) A new active contraction model for the myocardium using a modified Hill model Computers in Biology and Medicine, 145, (doi: 10.1016/j.compbiomed.2022.105417)

Quinn, J. J., Simitev, R. D. (2022) Flute and kink instabilities in a dynamically twisted flux tube with anisotropic plasma viscosity Monthly Notices of the Royal Astronomical Society, 512, pp. 4982-4992. (doi: 10.1093/mnras/stac704)

Lazarus, A., Dalton, D., Husmeier, D., Gao, H. (2022) Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics Biomechanics and Modeling in Mechanobiology, 21, pp. 953-982. (doi: 10.1007/s10237-022-01571-8)

Borowska, A., Gao, H., Lazarus, A., Husmeier, D. (2022) Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle International Journal for Numerical Methods in Biomedical Engineering, 38, (doi: 10.1002/cnm.3593)

Qi, N., Lockington, D., Wang, L., Ramaesh, K., Luo, X. (2022) Estimations of critical clear corneal incisions required for lens insertion in cataract surgery: a mathematical aspect Frontiers in Physiology, 13, (doi: 10.3389/fphys.2022.834214)

Griffiths, I. M., Stewart, P. S. (2022) A hybrid discrete–continuum framework for modelling filtration Journal of Membrane Science, 647, (doi: 10.1016/j.memsci.2022.120258)

Zhuan, X., Luo, X.Y. (2022) Volumetric growth of soft tissues evaluated in the current configuration Biomechanics and Modeling in Mechanobiology, 21, pp. 569-588. (doi: 10.1007/s10237-021-01549-y)

Cousins, J. R.L., Duffy, B. R., Wilson, S. K., Mottram, N. J. (2022) Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478, (doi: 10.1098/rspa.2021.0849)

Škarabot, M., Mottram, N. J., Kaur, S., Imrie, C. T., Forsyth, E., Storey, J. M. D., Mazur, R., Piecek, W., Komitov, L. (2022) Flexoelectric polarization in a nematic liquid crystal enhanced by dopants with different molecular shape polarities ACS Omega, 7, pp. 9785-9795. (doi: 10.1021/acsomega.2c00023)

Herrada, M.A., Blanco-Trejo, S., Eggers, J., Stewart, P.S. (2022) Global stability analysis of flexible channel flow with a hyperelastic wall Journal of Fluid Mechanics, 934, (doi: 10.1017/jfm.2021.1131)

Ren, J., Sun, H., Zhao, H., Gao, H., Maclellan, C., Zhao, S., Luo, X. (2022) Effective extraction of ventricles and myocardium objects from cardiac magnetic resonance images with a multi-task learning U-Net Pattern Recognition Letters, 155, pp. 165-170. (doi: 10.1016/j.patrec.2021.10.025)

Huethorst, E., Mortensen, P., Simitev, R. D., Gao, H., Pohjolainen, L., Talman, V., Ruskoaho, H., Burton, F. L., Gadegaard, N., Smith, G. L. (2022) Conventional rigid 2D substrates cause complex contractile signals in monolayers of human induced pluripotent stem cell derived cardiomyocytes Journal of Physiology, 600, pp. 483-507. (doi: 10.1113/JP282228)

Ramírez-Torres, A., Penta, R., Grillo, A. (2022) Two-scale, non-local diffusion in homogenised heterogeneous media Archive of Applied Mechanics, 92, pp. 559-595. (doi: 10.1007/s00419-020-01880-3)

Wang, Z., Wang, C., Zhao, F., Qi, N., Lockington, D., Ramaesh, K., Stewart, P. S., Luo, X., Tang, H. (2022) Simulation of fluid-structure interaction during the phaco-emulsification stage of cataract surgery International Journal of Mechanical Sciences, 214, (doi: 10.1016/j.ijmecsci.2021.106931)

Guan, D., Mei, Y., Xu, L., Cai, L., Luo, X., Gao, H. (2022) Effects of dispersed fibres in myocardial mechanics, Part I: passive response Mathematical Biosciences and Engineering, 19, pp. 3972-3993. (doi: 10.3934/mbe.2022183)

Guan, D., Wang, Y., Xu, L., Cai, L., Luo, X., Gao, H. (2022) Effects of dispersed fibres in myocardial mechanics, Part II: active response Mathematical Biosciences and Engineering, 19, pp. 4101-4119. (doi: 10.3934/mbe.2022189)

Cai, L., Hao, Y., Ma, P., Zhu, G., Luo, X., Gao, H. (2022) Fluid-structure interaction simulation of calcified aortic valve stenosis Mathematical Biosciences and Engineering, 19, pp. 13172-13192. (doi: 10.3934/mbe.2022616)


Teed, R., Hori, K., Tobias, S., Jones, C. A. (2017) Observation and Excitation of Magnetohydrodynamic Waves in Numerical Models of Earth's Core

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

Sevostianov, I., Trofimov, A., Merodio, J., Penta, R., Rodriguez-Ramos, R. (2017) Connection between electrical conductivity and diffusion coefficient of a conductive porous material filled with electrolyte International Journal of Engineering Science, 121, pp. 108-117. (doi: 10.1016/j.ijengsci.2017.08.013)

Stewart, P. S., Hilgenfeldt, S. (2017) Cracks and fingers: dynamics of ductile fracture in an aqueous foam Colloids and Surfaces A: Physicochemical and Engineering Aspects, 534, pp. 58-70. (doi: 10.1016/j.colsurfa.2017.03.057)

Griffith, B. E., Luo, X. (2017) Hybrid finite difference/finite element immersed boundary method International Journal for Numerical Methods in Biomedical Engineering, 33, (doi: 10.1002/cnm.2888)

Kowal, K. N., Davis, S. H., Voorhees, P. W. (2017) Instabilities in rapid directional solidification under weak flow Physical Review E, 96, (doi: 10.1103/PhysRevE.96.062802)

Holzapfel, G. A., Ogden, R. W. (2017) On fiber dispersion models: exclusion of compressed fibers and spurious model comparisons Journal of Elasticity, 129, pp. 49-68. (doi: 10.1007/s10659-016-9605-2)

Holzapfel, G. A., Ogden, R. W. (2017) Comparison of two model frameworks for fiber dispersion in the elasticity of soft biological tissues European Journal of Mechanics - A/Solids, 66, pp. 193-200. (doi: 10.1016/j.euromechsol.2017.07.005)

Penta, R., Merodio, J. (2017) Homogenized modeling for vascularized poroelastic materials Meccanica, 52, pp. 3321-3343. (doi: 10.1007/s11012-017-0625-1)

Gao, H., Mangion, K., Carrick, D., Husmeier, D., Luo, X., Berry, C. (2017) Estimating prognosis in patients with acute myocardial infarction using personalized computational heart models Scientific Reports, 7, (doi: 10.1038/s41598-017-13635-2)

Gao, H., Qi, N., Feng, L., Ma, X., Danton, M., Berry, C., Luo, X. (2017) Modelling mitral valvular dynamics–current trend and future directions International Journal for Numerical Methods in Biomedical Engineering, 33, (doi: 10.1002/cnm.2858)

MacTaggart, D., Stewart, P. (2017) Optimal energy growth in current sheets Solar Physics, 292, (doi: 10.1007/s11207-017-1177-1)

Kowal, K. N., Altieri, A. L., Davis, S. H. (2017) Strongly nonlinear theory of rapid solidification near absolute stability Physical Review E, 96, (doi: 10.1103/PhysRevE.96.042801)

Ramírez-Torres, A., Rodríguez-Ramos, R., Merodio, J., Penta, R., Bravo-Castillero, J., Guinovart-Díaz, R., Sabina, F. J., García-Reimbert, C., Sevostianov, I., Conci, A. (2017) The influence of anisotropic growth and geometry on the stress of solid tumors International Journal of Engineering Science, 119, pp. 40-49. (doi: 10.1016/j.ijengsci.2017.06.011)

Mascheroni, P., Penta, R. (2017) The role of the microvascular network structure on diffusion and consumption of anticancer drugs International Journal for Numerical Methods in Biomedical Engineering, 33, (doi: 10.1002/cnm.2857)

Paun, L., Haider, M., Hill, N., Olufsen, M., Qureshi, M., Papamarkou, T., Husmeier, D. (2017) Parameter Inference in the Pulmonary Blood Circulation

Gao, H., Feng, L., Qi, N., Berry, C., Griffith, B. E., Luo, X. (2017) A coupled mitral valve - left ventricle model with fluid-structure interaction Medical Engineering and Physics, 47, pp. 128-136. (doi: 10.1016/j.medengphy.2017.06.042)

Stewart, P. S. (2017) Instabilities in flexible channel flow with large external pressure Journal of Fluid Mechanics, 825, pp. 922-960. (doi: 10.1017/jfm.2017.404)

Ramírez-Torres, A., Rodríguez-Ramos, R., Sabina, F. J., García-Reimbert, C., Penta, R., Merodio, J., Guinovart-Díaz, R., Bravo-Castillero, J., Conci, A., Preziosi, L. (2017) The role of malignant tissue on the thermal distribution of cancerous breast Journal of Theoretical Biology, 426, pp. 152-161. (doi: 10.1016/j.jtbi.2017.05.031)

Dorfmann, L., Ogden, R. W. (2017) Nonlinear electroelasticity: material properties, continuum theory and applications Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 473, (doi: 10.1098/rspa.2017.0311)

Paun, L. M., Qureshi, M. U., Colebank, M., Haider, M. A., Olufsen, M. S., Hill, N. A., Husmeier, D. (2017) Parameter Inference in the Pulmonary Circulation of Mice

Gao, H., Aderhold, A., Mangion, K., Luo, X., Husmeier, D., Berry, C. (2017) Changes and classification in myocardial contractile function in the left ventricle following acute myocardial infarction Journal of the Royal Society: Interface, 14, (doi: 10.1098/rsif.2017.0203)

Watson, S. J. (2017) Lorentzian symmetry predicts universality beyond scaling laws Europhysics Letters, 118, (doi: 10.1209/0295-5075/118/56001)

Teed, R. J., Proctor, M. R. E. (2017) Quasi-cyclic behaviour in non-linear simulations of the shear dynamo Monthly Notices of the Royal Astronomical Society, 467, pp. 4858-4864. (doi: 10.1093/mnras/stx421)

Van Hirtum, A., Wu, B., Gao, H., Luo, X.Y. (2017) Constricted channel flow with different cross-section shapes European Journal of Mechanics - B/Fluids, 63, pp. 1-8. (doi: 10.1016/j.euromechflu.2016.12.009)

Shumaylova, V., Teed, R. J., Proctor, M. R.E. (2017) Large-to small-scale dynamo in domains of large aspect ratio: kinematic regime Monthly Notices of the Royal Astronomical Society, 466, pp. 3513-3518. (doi: 10.1093/mnras/stw3379)

Cai, L., Wang, Y., Gao, H., Li, Y., Luo, X. (2017) A mathematical model for active contraction in healthy and failing myocytes and left ventricles PLoS ONE, 12, (doi: 10.1371/journal.pone.0174834)

Ramírez-Torres, A., Rodríguez-Ramos, R., Conci, F.J., García-Reimbert, C., Preziosi, L., Merodio, J., Lebon, F. (2017) A semi-analytical heterogeneous model for thermal analysis of cancerous breasts Springer

Li, W., Bird, N. C., Luo, X. (2017) A pointwise method for identifying biomechanical heterogeneity of the human gallbladder Frontiers in Physiology, 8, (doi: 10.3389/fphys.2017.00176)

Wang, L., Roper, S. M., Hill, N. A., Luo, X. (2017) Propagation of dissection in a residually-stressed artery model Biomechanics and Modeling in Mechanobiology, 16, pp. 139-149. (doi: 10.1007/s10237-016-0806-1)

Cai, L., Xu, W., Luo, X. (2017) A double-distribution-function lattice Boltzmann method for bed-load sediment transport International Journal of Applied Mechanics, 9, (doi: 10.1142/S1758825117500132)

Penta, R., Gerisch, A. (2017) The asymptotic homogenization elasticity tensor properties for composites with material discontinuities Continuum Mechanics and Thermodynamics, 29, pp. 187-206. (doi: 10.1007/s00161-016-0526-x)

Simitev, R. D., Busse, F. H. (2017) Baroclinically-driven flows and dynamo action in rotating spherical fluid shells Geophysical and Astrophysical Fluid Dynamics, 111, pp. 369-379. (doi: 10.1080/03091929.2017.1361945)

(2017) Biomechanics: Trends in Modeling and Simulation Springer

Teed, R. (2017) Identifying MHD Waves in Numerical Models of the Geodynamo

McGinty, S., Hyndman, L., Mottram, N., McKee, S., Webb, S. (2017) In-silico Characterisation of the Kirkstall QV900 In-Vitro System for Advanced Cell Culture

Noè, U., Chen, W. W., Filippone, M., Hill, N., Husmeier, D. (2017) Inference in a Partial Differential Equations Model of Pulmonary Arterial and Venous Blood Circulation using Statistical Emulation (doi: 10.1007/978-3-319-67834-4_15)

Teed, R. (2017) Nonlinear Properties of the Shear Dynamo Model

Ogden, R. W. (2017) Nonlinear continuum mechanics and modelling the elasticity of soft biological tissues with a focus on artery walls Springer International Publishing

Interian, R., Rodríguez-Ramos, R., Valdés-Ravelo, F., Ramírez-Torres, A., Ribeiro, C. C., Conci, A. (2017) Tumor growth modelling by cellular automata Mathematics and Mechanics of Complex Systems, 5, pp. 239-259. (doi: 10.2140/memocs.2017.5.239)


Land, S., Gurev, V., Arens, S., Augustin, C. M., Baron, L., Blake, R., Bradley, C., Castro, S., Crozier, A., Favino, M., Fastl, T. E., Fritz, T., Gao, H., Gizzi, A., Griffith, B. E., Hurtado, D. E., Krause, R., Luo, X., Nash, M. P., Pezzuto, S., Plank, G., Rossi, S., Ruprecht, D., Seemann, G., Smith, N. P., Sundnes, J., Rice, J. J., Trayanova, N., Wang, D., Wang, Z., Niederer, S. A. (2015) Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 471, (doi: 10.1098/rspa.2015.0641)

Qureshi, M. U., Hill, N. A. (2015) A computational study of pressure wave reflections in the pulmonary arteries Journal of Mathematical Biology, 71, pp. 1525-1549. (doi: 10.1007/s00285-015-0867-2)

Qi, N., Gao, H., Ogden, R. W., Hill, N. A., Holzapfel, G. A., Han, H., Luo, X. (2015) Investigation of the optimal collagen fibre orientation in human iliac arteries Journal of the Mechanical Behavior of Biomedical Materials, 52, pp. 108-119. (doi: 10.1016/j.jmbbm.2015.06.011)

Stewart, P. S., Davis, S. H., Hilgenfeldt, S. (2015) Microstructural effects in aqueous foam fracture Journal of Fluid Mechanics, 785, pp. 425-461. (doi: 10.1017/jfm.2015.636)

Gao, H., Li, W.G., Cai, L., Berry, C., Luo, X.Y. (2015) Parameter estimation in a Holzapfel–Ogden law for healthy myocardium Journal of Engineering Mathematics, 95, pp. 231-248. (doi: 10.1007/s10665-014-9740-3)

Ramírez-Torres, A., Rodríguez-Ramos, R., Merodio, J., Bravo-Castillero, J., Guinovart-Díaz, R., Alfonso, J.C.L. (2015) Mathematical modeling of anisotropic avascular tumor growth Mechanics Research Communications, 69, pp. 8-14. (doi: 10.1016/j.mechrescom.2015.06.002)

Bezekci, B., Idris, I., Simitev, R.D., Biktashev, V.N. (2015) Semianalytical approach to criteria for ignition of excitation waves Physical Review E, 92, (doi: 10.1103/PhysRevE.92.042917)

Hori, K., Jones, C.A., Teed, R.J. (2015) Slow magnetic Rossby waves in the Earth's core Geophysical Research Letters, 42, pp. 6622-6629. (doi: 10.1002/2015GL064733)

Stewart, P. S., Feng, J., Kimpton, L. S., Griffiths, I. M., Stone, H. A. (2015) Stability of a bi-layer free film: simultaneous or individual rupture events? Journal of Fluid Mechanics, 777, pp. 27-49. (doi: 10.1017/jfm.2015.346)

El Hamdaoui, M., Merodio, J., Ogden, R. W. (2015) Loss of ellipticity in the combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube International Journal of Solids and Structures, 63, pp. 99-108. (doi: 10.1016/j.ijsolstr.2015.02.043)

Teed, R. J., Jones, C. A., Tobias, S. M. (2015) The transition to Earth-like torsional oscillations in magnetoconvection simulations Earth and Planetary Science Letters, 419, pp. 22-31. (doi: 10.1016/j.epsl.2015.02.045)

Ghorai, S., Singh, R., Hill, N.A. (2015) Wavelength selection in gyrotactic bioconvection Bulletin of Mathematical Biology, 77, pp. 1166-1184. (doi: 10.1007/s11538-015-0081-9)

Holzapfel, G. A., Niestrawska, J. A., Ogden, R. W., Reinisch, A. J., Schriefl, A. J. (2015) Modelling non-symmetric collagen fibre dispersion in arterial walls Journal of the Royal Society: Interface, 12, (doi: 10.1098/rsif.2015.0188)

Ramírez-Torres, A., Rodríguez-Ramos, R., Merodio, J., Bravo-Castillero, J., Guinovart-Díaz, R., Alfonso, J.C.L. (2015) Action of body forces in tumor growth International Journal of Engineering Science, 89, pp. 18-34. (doi: 10.1016/j.ijengsci.2014.11.009)

Penta, R., Gerisch, A. (2015) Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study Computing and Visualization in Science, 17, pp. 185-201. (doi: 10.1007/s00791-015-0257-8)

MacTaggart, D., Guglielmino, S.L., Haynes, A.L., Simitev, R., Zuccarello, F. (2015) The magnetic structure of surges in small-scale emerging flux regions Astronomy and Astrophysics, 576, (doi: 10.1051/0004-6361/201424646)

Kowal, K. N., Worster, M. G. (2015) Lubricated viscous gravity currents Journal of Fluid Mechanics, 766, pp. 626-655. (doi: 10.1017/jfm.2015.30)

Watson, S. J. (2015) Emergent parabolic scaling of nano-faceting crystal growth Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 471, pp. 20140560. (doi: 10.1098/rspa.2014.0560)

Cai, L., Gao, H., Luo, X., Nie, Y. (2015) Multi-scale modelling of the human left ventricle Scientia Sinica Physica, Mechanica and Astronomica, 45, (doi: 10.1360/SSPMA2013-00100)

Hermans, T., Bishop, K., Stewart, P., Davis, S., Grzybowski, B. (2015) Vortex flows impart chirality-specific lift forces Nature Communications, 6, (doi: 10.1038/ncomms6640)

Penta, R., Ambrosi, D. (2015) The role of the microvascular tortuosity in tumor transport phenomena Journal of Theoretical Biology, 364, pp. 80-97. (doi: 10.1016/j.jtbi.2014.08.007)

Ogden, R., Saccomandi, G., Wineman, A. (2015) Foreword to the special issue Mechanics of Rubber: In memory of Alan Gent International Journal of Non-Linear Mechanics, 68, pp. 1-8. (doi: 10.1016/j.ijnonlinmec.2014.08.004)

Penta, R., Ambrosi, D., Quarteroni, A. (2015) Multiscale homogenization for fluid and drug transport in vascularized malignant tissues Mathematical Models and Methods in Applied Sciences, 25, pp. 79-108. (doi: 10.1142/S0218202515500037)

Holzapfel, G. A., Ogden, R. W. (2015) On the tension–compression switch in soft fibrous solids European Journal of Mechanics - A/Solids, 49, pp. 561-569. (doi: 10.1016/j.euromechsol.2014.09.005)

Hermans, T. M., Stewart, P. S., Grzybowski, B. A. (2015) A pH-oscillator stretched in space but frozen in time Journal of Physical Chemistry Letters, 6, pp. 760-766. (doi: 10.1021/jz502711c)

Bourne, D.P., Roper, S.M. (2015) Centroidal power diagrams, Lloyd's algorithm and applications to optimal location problems SIAM: Journal on Numerical Analysis, 53, pp. 2545-2569. (doi: 10.1137/141000993)

Simitev, R. D., Kosovichev, A. G., Busse, F. H. (2015) Dynamo effects near transition from solar to anti-solar differential rotation Astrophysical Journal, 810, (doi: 10.1088/0004-637X/810/1/80)

Gao, H., Qi, N., Ma, X., Griffith, B. E., Berry, C., Luo, X. (2015) Fluid-structure interaction model of human mitral valve within left ventricle Springer International Publishing

Gao, H., Berry, C., Luo, X. (2015) Image-derived human left ventricular modelling with fluid-structure interaction Springer International Publishing

Argungu, M., Bayram, S., Brook, B., Chakrabarti, B., Clayton, R. H., Daly, D. M., Dyson, R. J., Holloway, C., Manhas, V., Naire, S., Shearer, T., Simitev, R. D. (2015) Modelling Afferent Nerve Responses to Bladder Filling

Luo, X.Y. (2015) Modelling flows in collapsible tubes Eolss Publishers

Wang, L., Roper, S. M., Luo, X.Y., Hill, N.A. (2015) Modelling of tear propagation and arrest in fibre-reinforced soft tissue subject to internal pressure Journal of Engineering Mathematics, 95, pp. 249-265. (doi: 10.1007/s10665-014-9757-7)

(2015) Nonlinear Mechanics of Soft Fibrous Materials Springer-Verlag Wien

Ogden, R. W. (2015) Nonlinear elasticity with application to soft fibre-reinforced materials Springer-Verlag Wien

Agraval, U., Qi, N., Stewart, P., Luo, X., Williams, G., Rotchford, A., Ramaesh, K. (2015) Optimum size of iridotomy in uveitis Clinical and Experimental Ophthalmology, 43, pp. 692-696. (doi: 10.1111/ceo.12528)

Stewart, P. S., Jensen, O. E. (2015) Patterns of recruitment and injury in a heterogeneous airway network model Journal of the Royal Society: Interface, 12, (doi: 10.1098/rsif.2015.0523)

Busse, F.H., Simitev, R.D. (2015) Planetary dynamos Elsevier B.V.

Penta, R., Ambrosi, D. (2015) The role of microvascular tortuosity in tumor transport phenomena and future perspective for drug delivery PAMM: Proceedings in Applied Mathematics and Mechanics, 15, pp. 101-102. (doi: 10.1002/pamm.201510041)

Penta, R., Mascheroni, P. (2015) The role of the angiogenic network structure on diffusion and consumption of anticancer drugs

Teed, R., Jones, C., Tobias, S. (2015) Torsional Waves Operating in Geodynamo and Magnetoconvection Simulations


Saxena, P., Ogden, R.W. (2012) On Love-type waves in a finitely deformed magnetoelastic layered half-space Zeitschrift für Angewandte Mathematik und Physik, 63, pp. 1177-1200. (doi: 10.1007/s00033-012-0204-1)

Gao, H., Carrick, D., Kadir, K., McComb, C., Foster, J., Soraghan, J., Luo, X., Berry, C. (2012) Semi-automatic OEDEMA quantification from direct T2 map cardiac MRI Heart, 98, pp. A7-A7. (doi: 10.1136/heartjnl-2012-302951.022)

Kadir, K., Gao, H., Payne, A., Soraghan, J., Berry, C. (2012) LV wall segmentation using the variational level set method (LSM) with additional shape constraint for oedema quantification Physics in Medicine and Biology, 57, pp. 6007-6023. (doi: 10.1088/0031-9155/57/19/6007)

Li, W.G., Luo, X.Y., Hill, N.A., Ogden, R.W., Smythe, A., Majeed, A.W., Bird, N. (2012) A quasi-nonlinear analysis of the anisotropic behaviour of human gallbladder wall Journal of Biomechanical Engineering, 134, pp. 101009. (doi: 10.1115/1.4007633)

Al-Atabi, M., Ooi, R.C., Luo, X.Y., Chin, S.B., Bird, N.C. (2012) Computational analysis of the flow of bile in human cystic duct Medical Engineering and Physics, 34, pp. 1177-1183. (doi: 10.1016/j.medengphy.2011.12.006)

Jensen, O.E., Hill, N.A. (2012) Preface to special issue dedicated to Professor T.J. Pedley on his 70th birthday Journal of Fluid Mechanics, 705, pp. 1-1. (doi: 10.1017/jfm.2012.252)

Olufsen, M.S., Hill, N.A., Vaughan, G.D.A., Sainsbury, C., Johnson, M. (2012) Rarefaction and blood pressure in systemic and pulmonary arteries Journal of Fluid Mechanics, 705, pp. 280-305. (doi: 10.1017/jfm.2012.220)

Teed, R. J., Jones, C. A., Hollerbach, R. (2012) On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus Physics of Fluids, 24, (doi: 10.1063/1.4711398)

Simitev, R.D., Busse, F.H. (2012) How far can minimal models explain the solar cycle? Astrophysical Journal, 749, (doi: 10.1088/0004-637X/749/1/9)

Lockington, D., Luo, X.Y., Wang, H., Hill, N.A., Ramaesh, K. (2012) Mathematical and computer simulation modelling of intracameral forces causing pupil block due to air bubble use in Descemet's Stripping Endothelial Keratoplasty: the mechanics of iris buckling Clinical and Experimental Ophthalmology, 40, pp. 182-186. (doi: 10.1111/j.1442-9071.2011.02653.x)

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

Steigmann, D.J., Ogden, R.W. (2012) A note on residual stress, lattice orientation and dislocation density in crystalline solids Journal of Elasticity, 109, pp. 275-283. (doi: 10.1007/s10659-012-9378-1)

Simitev, R.D., Busse, F.H. (2012) Bistable attractors in a model of convection-driven spherical dynamos Physica Scripta, 86, pp. 018409. (doi: 10.1088/0031-8949/86/01/018409)

Stewart, P. S., Davis, S. H. (2012) Dynamics and stability of metallic foams: Network modeling Journal of Rheology, 56, pp. 543. (doi: 10.1122/1.3695029)

Luo, X.Y., Griffith, B.E., Ma, X.S., Yin, M., Wang, T.J., Liang, C.L., Watton, P.N., Bernacca, G.M. (2012) Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve Biomechanics and Modeling in Mechanobiology, 11, pp. 815-827. (doi: 10.1007/s10237-011-0354-7)

da Costa, F.P., Grinfeld, M., Langer, M., Mottram, N.J., 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)

Abiza, Z., Destrade, M., Ogden, R. (2012) Large acoustoelastic effect Wave Motion, 49, pp. 364-374. (doi: 10.1016/j.wavemoti.2011.12.002)

Mottram, N.J., Newton, C.J.P. (2012) Liquid crystal theory and modelling Springer

Norris, S.A., Watson, S.J. (2012) Mean-field theory for coarsening faceted surfaces Physical Review E, 85, pp. 021608. (doi: 10.1103/PhysRevE.85.021608)

Teed, R., Jones, C., Tobias, S. (2012) Rapidly Rotating Plane Layer Convection with Zonal Flow

Teed, R., Jones, C., Tobias, S. (2012) Searching for Torsional Oscillations in Earth-like Dynamo Simulations

Norris, S.A., Watson, S.J. (2012) Simulating the kinematics of completely faceted surfaces Journal of Computational Physics, 231, pp. 4560-4577. (doi: 10.1016/

Simitev, R.D., Busse, F.H. (2012) Solar cycle properties described by simple convection-driven dynamos Physica Scripta, 86, pp. 018407. (doi: 10.1088/0031-8949/86/01/018407)

Liu, H.F., Luo, X.Y., Cai, Z.X. (2012) Stability and energy budget of pressure-driven collapsible channel flows Journal of Fluid Mechanics, 705, pp. 348-370. (doi: 10.1017/jfm.2011.254)

Simitev, R.D., MacTaggart, D. (2012) The mathematics of fluid dynamos Commutator, 3, pp. 36-41.


Gao, D.Y., Ogden, R.W. (2008) Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation Quarterly Journal of Mechanics and Applied Mathematics, 61, pp. 497-522. (doi: 10.1093/qjmam/hbn014)

Li, W.G., Luo, X.Y., Chin, S.B., Hill, N.A., Johnson, A.G., Bird, N.C. (2008) Non-Newtonian bile flow in elastic cystic duct: one- and three-dimensional modeling Annals of Biomedical Engineering, 36, pp. 1893-1908. (doi: 10.1007/s10439-008-9563-3)

Gao, H., Long, Q. (2008) Effects of varied lipid core volume and fibrous cap thickness on stress distribution in carotid arterial plaques Journal of Biomechanics, 41, pp. 3053-3059. (doi: 10.1016/j.jbiomech.2008.07.011)

Busse, F.H., Simitev, R.D. (2008) Toroidal flux oscillations as possible causes of geomagnetic excursions and reversals Physics of the Earth and Planetary Interiors, 168, pp. 237-243. (doi: 10.1016/j.pepi.2008.06.007)

Zhu, Y., Luo, X.Y., Ogden, R.W. (2008) Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure International Journal of Solids and Structures, 45, pp. 3410-3429. (doi: 10.1016/j.ijsolstr.2008.02.005)

Trabi, C. L., Brown, C. V., Smith, A. A. T., 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, (doi: 10.1063/1.2938722)

Gao, D.Y., Ogden, R.W. (2008) Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem Zeitschrift für Angewandte Mathematik und Physik, 59, pp. 498-517. (doi: 10.1007/s00033-007-7047-1)

Plaut, E., Lebranchu, Y., Simitev, R., Busse, F.H. (2008) Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell Journal of Fluid Mechanics, 602, pp. 303-326. (doi: 10.1017/S0022112008000840)

Quintans Carou, J., Wilson, S. K., Mottram, N. J., 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)

Luo, X.Y., Cai, Z.X., Li, W.G., Pedley, T.J. (2008) The cascade structure of linear instability in collapsible channel flows Journal of Fluid Mechanics, 600, pp. 45-76. (doi: 10.1017/S0022112008000293)

Li, W.G., Luo, X.Y., Hill, N.A., Smythe, A., Chin, S.B., Johnson, A.G., Bird, N.C. (2008) Correlation of mechanical factors and gallbladder pain Computational and Mathematical Methods in Medicine, 9, pp. 27-45. (doi: 10.1080/17486700701780266)

Biktashev, V.N., Suckley, R., Elkin, Y.E., Simitev, R.D. (2008) Asymptotic analysis and analytical solutions of a model of cardiac excitation Bulletin of Mathematical Biology, 70, pp. 517-554. (doi: 10.1007/s11538-007-9267-0)

Al-Atabi, M., Chin, S.B., Luo, X.Y., Beck, S. (2008) Investigation of the flow in a compliant idealised human cystic duct Journal of Biomechanical Science and Engineering, 3, pp. 411-418. (doi: 10.1299/jbse.3.411)

Watton, P.N., Luo, X.Y., Yin, M., Bernacca, G.M., Wheatley, D.J. (2008) Effect of ventricle motion on the dynamic behaviour of chorded mitral valves Journal of Fluids and Structures, 24, pp. 58-74. (doi: 10.1016/j.jfluidstructs.2007.06.004)

Norris, S.A., Davis, S.H., Watson, S.J., Voorhees, P.W. (2008) Faceted interfaces in directional solidification Journal of Crystal Growth, 310, pp. 414-427. (doi: 10.1016/j.jcrysgro.2007.10.048)

Ottenio, M., Destrade, M., Ogden, R.W. (2008) Incremental magnetoelastic deformations, with application to surface instability Journal of Elasticity, 90, pp. 19-42. (doi: 10.1007/s10659-007-9120-6)

Roper, S.M., Davis, S.H., Voorhees, P.W. (2008) An analysis of convection in a mushy layer with a deformable permeable interface Journal of Fluid Mechanics, 596, pp. 333-352. (doi: 10.1017/S0022112007009469)

Simitev, R., Biktashev, V.N. (2008) Analytically solvable asymptotic model of atrial excitability Birkhäuser

Kassianidis, F., Ogden, R.W., Merodio, J., Pence, T.J. (2008) Azimuthal shear of a transversely isotropic elastic solid Mathematics and Mechanics of Solids, 13, pp. 690-724. (doi: 10.1177/1081286507079830)

Trabi, C. L., Smith, A. A. T., Mottram, N. J., Brown, C. V. (2008) Flexoelectric polarisation effects in nematic liquid crystal phase gratings (doi: 10.1117/12.794912)

Bustamante, R., Dorfmann, A., Ogden, R.W. (2008) On boundary conditions in nonlinear magneto- and electroelasticity Taylor & Francis

Bustamante, R., Dorfmann, A., Ogden, R.W. (2008) On variational formulations in nonlinear magnetoelastostatics Mathematics and Mechanics of Solids, 13, pp. 725-745. (doi: 10.1177/1081286507079832)

Brush, L.B., Roper, S.M. (2008) The thinning of lamellae in surfactant-free foams with non-Newtonian liquid phase Journal of Fluid Mechanics, 616, pp. 235-262. (doi: 10.1017/S0022112008003790)


Mottram, N., Davidson, A. (2007) Mutistable reflective liquid crystal device

Norris, S.A., Watson, S.J. (2007) Geometric simulation and surface statistics of coarsening faceted surfaces Acta Materialia, 55, pp. 6444-6452. (doi: 10.1016/j.actamat.2007.08.014)

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

Zhang, J., Watson, S.J., Wong, H. (2007) Fluid flow and heat transfer in a dual-wet micro heat pipe Journal of Fluid Mechanics, 589, pp. 1-31. (doi: 10.1017/S0022112007007823)

Roper, S.M., Davis, S.H., Norris, S.A., Golovin, A.A., Vorhees, P.W., Weiss, M. (2007) Steady growth of nanowires via the vapor-liquid-solid method Journal of Applied Physics, 102, pp. 034304. (doi: 10.1063/1.2761836)

Palto, S. P., Mottram, N. J., 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, (doi: 10.1103/PhysRevE.75.061707)

Luo, X., Calderhead, B., Liu, H., Li, W. (2007) On the initial configurations of collapsible channel flow Computers and Structures, 85, pp. 977-987. (doi: 10.1016/j.compstruc.2006.11.010)

Ghorai, S., Hill, N.A. (2007) Gyrotactic bioconvection in three dimensions Physics of Fluids, 19, pp. 054107. (doi: 10.1063/1.2731793)

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

Roper, S.M., Davis, S.H., Voorhees, P.W. (2007) Convection in a mushy zone forced by sidewall heat losses Metallurgical and Materials Transactions A, 38, pp. 1069-1079. (doi: 10.1007/s11661-007-9119-4)

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

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

Luo, X., Li, W., Bird, N., Chin, S. B., Hill, N.A., Johnson, A. G. (2007) On the mechanical behavior of the human biliary system World Journal of Gastroenterology, 13, pp. 1384-1392. (doi: 10.3748/wjg.v13.i9.1384)

Dorfmann, A., Ogden, R.W., Wineman, A.S. (2007) A three-dimensional non-linear constitutive law for magnetorheological fluids, with applications International Journal of Non-Linear Mechanics, 42, pp. 381-390. (doi: 10.1016/j.ijnonlinmec.2007.03.002)

Ogden, R.W., Saccomandi, G., Sgura, I. (2007) Computational aspects of Worm-Like-Chain interpolation formulas Computers and Mathematics with Applications, 53, pp. 276-286. (doi: 10.1016/j.camwa.2006.02.024)

Bustamante, R., Dorfmann, A., Ogden, R.W. (2007) A nonlinear magnetoelastic tube under extension and inflation in an axial magnetic field: numerical solution Journal of Engineering Mathematics, 59, pp. 139-153. (doi: 10.1007/s10665-006-9088-4)

Ottenio, M., Destrade, M., Ogden, R.W. (2007) Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid International Journal of Non-Linear Mechanics, 42, pp. 310-320. (doi: 10.1016/j.ijnonlinmec.2006.10.001)

Roper, S.M., Lister, J.R. (2007) Buoyancy-driven crack propagation: the limit of large fracture toughness Journal of Fluid Mechanics, 580, pp. 359-380. (doi: 10.1017/S0022112007005472)

Getling, A.V., Simitev, R., Busse, F.H. (2007) Can cellular convection in a rotating spherical shell maintain both global and local magnetic fields? International Journal of Geomagnetism and Aeronomy, 7, pp. GI1004. (doi: 10.1029/2005GI000138)

Watton, P.N., Luo, X.Y., Wang, X., Bernacca, G.M., Molloy, P., Wheatley, D.J. (2007) Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method Journal of Biomechanics, 40, pp. 613-626. (doi: 10.1016/j.jbiomech.2006.01.025)

Busse, F.H., Dormy, E., Simitev, R., Soward, A.M. (2007) Dynamics of rotating fluids CRC Press

Al-Atabi, M., Chin, S.B., Beck, S., Luo, X.Y. (2007) Flow in idealised compliant human cystic duct models Springer

Ogden, R.W. (2007) Incremental statics and dynamics of pre-stressed elastic materials Springer

Ogden, R.W., Saccomandi, G. (2007) Introducing mesoscopic information into constitutive equations for arterial walls Biomechanics and Modeling in Mechanobiology, 6, pp. 333-344. (doi: 10.1007/s10237-006-0064-8)

Vaughan, G.A., Connell, J., Johnson, M.K., Olufsen, M.S., Hill, N.A., Sainsbury, C.A.R. (2007) Investigating the relationship between microvascular rarefaction and systemic hypertension: a mathematical and computational model of the circulation Journal of Human Hypertension, 21, pp. 840-840.

Holzapfel, G.A., Sommer, G., Auer, M., Regitnig, P., Ogden, R.W. (2007) Layer-specific 3D residual deformations of human aortas with non-atherosclerotic intimal thickening Annals of Biomedical Engineering, 35, pp. 530-545. (doi: 10.1007/s10439-006-9252-z)

Kassianidid, F., Ogden, R. (2007) On large bending deformations of transversely isotropic rectangular elastic blocks Note di Matematica, 27, pp. 131-154. (doi: 10.1285/i15900932v27n2p131)

Luo, X.Y., Li, W.G., Bird, N., Chin, S.B., Hill, N.A., Johnson, A.G. (2007) On the mechanical behaviour of the human biliary system World Journal of Gastroenterology, 13, pp. 1384-1392.

Li, W.G., Luo, X.Y., Johnson, A.G., Hill, N.A., Bird, N., Chin, S.B. (2007) One-dimensional models for the human biliary system Journal of Biomechanical Engineering, 129, pp. 164-173. (doi: 10.1115/1.2472379)

Busse, F.H., Simitev, R. (2007) Planetary dynamos Elsevier

Liu, Z.S., Luo, X.Y., Lee, H.P., Lu, C. (2007) Snoring source identification and snoring noise prediction Journal of Biomechanics, 40, pp. 861-870. (doi: 10.1016/j.jbiomech.2006.03.022)

Steigmann, D. J., Ogden, R. W. (2007) Surface waves supported by thin-film/substrate interactions IMA Journal of Applied Mathematics, 72, pp. 730-747. (doi: 10.1093/imamat/hxm018)

Lebranchu, Y., Plaut, E., Simitev, R., Busse, F. (2007) Étude théorique d'ondes De Rossby thermiques non linéaires en géométrie sphérique: influence du mode de chauffage Comptes Rendus Rencontre du Non Linéaire, 2007, pp. 95-100.


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

Bird, N.C., Ooi, R.C., Luo, X.Y., Chin, S.B., Johnson, A.G. (2006) Investigation of the functional three-dimensional anatomy of the human cystic duct: A single helix? Clinical Anatomy, 19, pp. 528-534. (doi: 10.1002/ca.20219)

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

Al-Atabi, M., Chin, S.B., Luo, X.Y. (2006) Visualization experiment of flow structures inside two-dimensional human biliary system models Journal of Mechanics in Medicine and Biology (JMMB), 6, pp. 249-260. (doi: 10.1142/S0219519406001911)

Busse, F.H., Simitev, R. (2006) Dynamos of giant planets Proceedings of the International Astronomical Union, 2, pp. 467-474. (doi: 10.1017/S1743921307000920)

Getling, A.V., Simitev, R., Busse, F.H. (2006) Generation of coupled global and local magnetic fields by a cellular MHD dynamo Proceedings of the International Astronomical Union, 2, pp. 482-487. (doi: 10.1017/S1743921307000944)

Busse, F.H., Simitev, R. (2006) Parameter dependences of convection-driven dynamos in rotating spherical fluid shells Geophysical and Astrophysical Fluid Dynamics, 100, pp. 341-361. (doi: 10.1080/03091920600784873)

Al-Atabi, M., Al-Zuhair, S., Chin, S.B., Luo, X.Y. (2006) Pressure drop in laminar and turbulent flows in circular pipe with baffles − an experimental and analytical study International Journal of Fluid Mechanics Research, 33, pp. 303-319. (doi: 10.1615/InterJFluidMechRes.v33.i4.10)

Mottram, N., Ramage, A., Kelly, G., Davidson, A. (2006) Bistable liquid crystal device

Biktasheva, I.V., Simitev, R., Suckley, R., Biktashev, V.N. (2006) Asymptotic properties of mathematical models of excitability Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 364, pp. 1283-1298. (doi: 10.1098/rsta.2006.1770)

Watson, S.J., Norris, S.A. (2006) Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation Physical Review Letters, 96, pp. 176103. (doi: 10.1103/PhysRevLett.96.176103)

Simitev, R., Biktashev, V.N. (2006) Conditions for propagation and block of excitation in an asymptotic model of atrial tissue Biophysical Journal, 90, pp. 2258-2269. (doi: 10.1529/biophysj.105.072637)

Sgura, I., Saccomandi, G., Ogden, R.W. (2006) On worm-like chain models within the three-dimensional continuum mechanics framework Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 462, pp. 749-768. (doi: 10.1098/rspa.2005.1592)

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

Watton, P.N., Luo, X.Y., Yin, M., Bernacca, G.M., Molloy, P., Wheatley, D.J. (2006) Effects of Ventricle Motion on Chorded Mitral Prostheses (doi: 10.1115/PVP2006-ICPVT-11-93877)

Guillou, A., Ogden, R.W. (2006) Growth in soft biological tissue and residual stress development Springer-Verlag

Gasser, T.C., Ogden, R.W., Holzapfel, G.A. (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations Journal of the Royal Society: Interface, 3, pp. 15-35. (doi: 10.1098/rsif.2005.0073)

(2006) Mechanics of Biological Tissue

Dorfmann, A., Ogden, R.W. (2006) Nonlinear electroelastic deformations Journal of Elasticity, 82, pp. 99-127. (doi: 10.1007/s10659-005-9028-y)

Bustamante, R., Ogden, R.W. (2006) On nonlinear universal relations in nonlinear elasticity Zeitschrift für Angewandte Mathematik und Physik, 57, pp. 708-721. (doi: 10.1007/s00033-006-0068-3)

Merodio, J., Ogden, R.W. (2006) On the equivalence of strong ellipticity in the material and spatial settings of finite elasticity Zeitschrift für Angewandte Mathematik und Physik, 57, pp. 1096-1101. (doi: 10.1007/s00033-006-0078-1)

Domanski, W., Ogden, R.W. (2006) On the null condition for nonlinearly elastic solids Archives of Mechanics, 58, pp. 339-361.

Merodio, J., Ogden, R.W. (2006) The influence of the invariant I8I8 on the stress–deformation and ellipticity characteristics of doubly fiber-reinforced non-linearly elastic solids International Journal of Non-Linear Mechanics, 41, pp. 556-563. (doi: 10.1016/j.ijnonlinmec.2006.02.001)

Bustamante, R., Ogden, R.W. (2006) Universal relations for nonlinear electroelastic solids Acta Mechanica, 182, pp. 125-140. (doi: 10.1007/s00707-005-0290-7)

Bustamante, R., Dorfmann, A., Ogden, R.W. (2006) Universal relations in isotropic nonlinear magnetoelasticity Quarterly Journal of Mechanics and Applied Mathematics, 59, pp. 435-450. (doi: 10.1093/qjmam/hbl010)

Idris, I., Simitev, R., Biktashev, V.N. (2006) Using novel simplified models of excitation for analytic description of initiation propagation and blockage of excitation waves Computers in Cardiology, 33, pp. 213-216.


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

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

Simitev, R. (2003) Inertial wave convection in rotating spherical fluid shells Defense Technical Information Center

Watson, S.J., Lewicka, M. (2003) Temporal asymptotics for the p’th power Newtonian fluid in one space dimension Zeitschrift für Angewandte Mathematik und Physik, 54, pp. 633-651. (doi: 10.1007/s00033-003-1149-1)

Watson, S.J., Otto, F., Rubinstein, B.Y., Davis, S.H. (2003) Coarsening dynamics of the convective Cahn-Hilliard equation Physica D: Nonlinear Phenomena, 178, pp. 127-148. (doi: 10.1016/S0167-2789(03)00048-4)

Kirkinis, E., Ogden, R.W. (2003) On helical shear of a compressible elastic circular cylindrical tube Quarterly Journal of Mechanics and Applied Mathematics, 56, pp. 105-122. (doi: 10.1093/qjmam/56.1.105)

Cai, Z.X., Luo, X.Y. (2003) A fluid-beam model for flow in collapsible channels Journal of Fluids and Structures, 17, pp. 125-146. (doi: 10.1016/S0889-9746(02)00112-3)

Merodio, J., Ogden, R.W. (2003) A note on strong ellipticity for transversely isotropic linearly elastic solids Quarterly Journal of Mechanics and Applied Mathematics, 56, pp. 589-591. (doi: 10.1093/qjmam/56.4.589)

Dorfmann, A., Ogden, R.W. (2003) A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubber International Journal of Solids and Structures, 40, pp. 2699-2714. (doi: 10.1016/S0020-7683(03)00089-1)

(2003) Biomechanics of Soft Tissue in Cardiovascular Systems 441,

McKay, G., MacKenzie, K.R., Mottram, N.J. (2003) Competing polarization effects in a homeotropically aligned smectic liquid crystal (doi: 10.1080/00150190490509854)

Busse, F.H., Grote, E., Simitev, R. (2003) Convection in rotating spherical shells and its dynamo action Taylor & Francis

Luo, X.Y., Li, W.G., Li, J. (2003) Geometrical stress reducing factors in the anisotropic porcine heart valves Journal of Biomechanical Engineering, 125, pp. 735-744. (doi: 10.1115/1.1614821)

Merodio, J., Ogden, R.W. (2003) Instabilities and loss of ellipticity in fiber-reinforced compressible non-linearly elastic solids under plane deformation International Journal of Solids and Structures, 40, pp. 4707-4727. (doi: 10.1016/S0020-7683(03)00309-3)

Dorfmann, A., Ogden, R.W. (2003) Magnetoelastic modelling of elastomers European Journal of Mechanics - A/Solids, 22, pp. 497-507. (doi: 10.1016/S0997-7538(03)00067-6)

Ogden, R.W. (2003) Nonlinear Elasticity with Application to Material Modelling Polish Academy of Sciences

Ogden, R.W. (2003) Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue Springer-Verlag

Simitev, R., Busse, F.H. (2003) Parameter dependences of convection driven spherical dynamos Springer

Simitev, R., Busse, F.H. (2003) Patterns of convection in rotating spherical shells New Journal of Physics, 5, pp. 97. (doi: 10.1088/1367-2630/5/1/397)


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

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

Roberts, A., Hill, N.A., Hicks, R. (2000) Simple mechanisms organise orientation of escape swimming in embryos and hatchling tadpoles of Xenopus laevis Journal of Experimental Biology, 203, pp. 1869-1885.

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

Watson, S. (2000) Unique global solvability for initial-boundary value problems in one-dimensional nonlinear thermoviscoelasticity Archive for Rational Mechanics and Analysis, 153, pp. 1-37. (doi: 10.1007/s002050050007)

Ghorai, S., Hill, N.A. (2000) Wavelengths of gyrotactic plumes in bioconvection Bulletin of Mathematical Biology, 62, pp. 429-450. (doi: 10.1006/bulm.1999.0160)

Hill, N.A., Plumpton, L.A. (2000) Control strategies for the polarotactic orientation of the microorganism Euglena gracilis Journal of Theoretical Biology, 203, pp. 357-365. (doi: 10.1006/jtbi.2000.1090)

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

Ghorai, S., Hill, N.A. (2000) Periodic arrays of gyrotactic plumes in bioconvection Physics of Fluids, 12, pp. 5-22. (doi: 10.1063/1.870249)

Holzapfel, G.A., Gasser, T.C., Ogden, R.W. (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models Journal of Elasticity, 61, pp. 1-48. (doi: 10.1023/A:1010835316564)

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

Mottram, N. J., 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, pp. 323-333. (doi: 10.1080/10587250008023282)

Luo, X., Pedley, T.J. (2000) Multiple solutions and flow limitation in collapsible channel flows Journal of Fluid Mechanics, 420, pp. 301-324.

Elston, S. J., Mottram, N. (2000) Order parameter variation in smectic liquid crystals Wiley

Mottram, N.J., Sluckin, T.J., Elston, S.J., 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)

Postgraduate research students

Refine By

Continuum Mechanics - Example Research Projects

Information about postgraduate research opportunities and how to apply can be found on the Postgraduate Research Study page. Below is a selection of projects that could be undertaken with our group.

Continuous production of solid metal foams (PhD)

Supervisors: Peter Stewart
Relevant research groups: Continuum Mechanics

Porous metallic solids, or solid metal foams, are exceedingly useful in many engineering applications, as they can be manufactured to be strong yet exceedingly lightweight. However, industrial processing methods for producing such foams are problematic and unreliable, and it is not currently possible to control the porosity distribution of the final product a priori.

This project will consider a new method of solid foam production, where bubbles of gas are introduced continuously into a molten metal flowing through a heat exchanger; foaming and solidification then occur almost simulatanously, allowing the foam structure to be controlled pointwise. The aim of this project is to construct a simple mathematical model for a gas bubble moving in a liquid filled channel ahead of a solidification front, to predict optimal conditions whereby the gas bubble is drawn toward the phase boundary, hence forming a porous solid.

This project will require some background in fluid mechanics and a combination of analytical and numerical techniques for solving partial differential equations.

Radial foam fracture (PhD)

Supervisors: Peter Stewart
Relevant research groups: Continuum Mechanics

Gas-liquid foams are a useful analgoue of crystalline atomic solids. 2D foam fracture has been used to study the mechanisms of fracture in metals. A two-dimenisonal network model (formed from a large system of differential equations) has recently been produced to study foam fracture in a rectangular channel which is pressurised along one edge. This model has helped to explain the origin of the velocity gap (a range of inadmissable steady fracture velocities), observed both in foam fracture experiments and in atomistic simulations of brittle fracture. This project will apply this network modelling approach to study radial foam fracture in a Hele-Shaw cell, to mimick recent experiments. This system has strong similarity to radial Saffmann-Taylor fingering, where fingering has been observed when a less viscous fluid displaces a more viscous fluid in a confined geometry. This project will involve studying systems of ordinary and partial differential equations using both numerical and analytical methods.

Numerical simulations of planetary and stellar dynamos (PhD)

Supervisors: Radostin Simitev
Relevant research groups: Geophysical & Astrophysical Fluid DynamicsContinuum Mechanics

Using Fluid Dynamics and Magnetohydrodynamics to model the magnetic fields of the Earth, planets, the Sun and stars. Involves high-performance computing.

Mathematical models of vasculogenesis (PhD)

Supervisors: Peter Stewart
Relevant research groups: Mathematical BiologyContinuum Mechanics

Vasculogenesis is the process of forming new blood vessels from endothelial cells, which occurs during embryonic development. Viable blood vessels facilitate tissue perfusion, allowing the tissue to grow beyond the diffusion-limited size. However, in the absence of vasculogenesis, efforts to engineer functional tissues (eg for implantation) are restricted to this diffusion-limited size. This project will investigate mathematical models for vasculogenesis and explore mechanisms to stimulate blood vessel formation for in vitro tissues. The project will involve collaboration with Department of Biological Engineering at MIT, as part of the SofTMechMP project.

A coupled cardiovascular-respiration model for mechanical ventilation (PhD)

Supervisors: Peter Stewart, Nicholas A Hill
Relevant research groups: Mathematical BiologyContinuum Mechanics

Mechanical ventilation is a clinical treatment used to draw air into the lungs to facilitate breathing, used in treatment of premature babies with respiratory distress syndrome and in the treatment of severe Covid pneumonia. The aim is to oxygenate the blood while simultaneously removing unwanted by-products. However, over-inflation of the lungs can reduce the blood supply to the gas exchange surfaces, leading to a ventilation-perfusion mis-match. This PhD project will give you the opportunity to develop a mathematical model to describe the coupling between blood flow in the pulmonary circulation and air flow in the lungs (during both inspiration and expiration). You will devise a coupled computational framework, capable of testing patient-specific ventilation protocols. This is an ideal project for a postgraduate student with an interest in applying mathematical modelling and image analysis to predictive healthcare. The project will give you the opportunity to join a cross-disciplinary Research Hub that aims to push the boundaries of quantitative medicine and improve clinical decision making using innovative mathematical and statistical modelling.

Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD) (PhD)

Supervisors: Radostin Simitev, David MacTaggart, Robert Teed
Relevant research groups: Geophysical & Astrophysical Fluid DynamicsContinuum Mechanics

Solar magnetic fields are produced by a dynamo process in the Solar convection zone by turbulent motions acting against Ohmic dissipation. Solar magnetic activity affects nearEarth space environment and can harm modern technology and endanger human health. Further, Solar magnetism poses fundamental physical and mathematical problems, e.g. about the nature of plasma turbulence and the topology of magnetic field generation. Current models of the global Solar dynamo fall in two classes (a) mean-field dynamos (b) convection-driven dynamos. The mean-field models are only phenomenological as they replace turbulent interactions by ad-hoc source and quenching terms. On the other hand, spherical convection-driven dynamo models are derived from basic principles with minimal assumptions and potentially offer true predictive power; these can also be extended to other stars and giant planets. However, at present, convection driven dynamo models operate in a wrong dynamical regime and have limited success in reproducing a number of important 1 observations including (a) the sunspot cycle period, polarity reversals and the sunspot butterfly diagram, (b) the poleward migration of diffuse surface magnetic fields, (c) the polar field strength and phase relationships between poloidal/toroidal components. The aims of this project are to (a) develop a three-dimensional convection-driven Solar dynamo model constrained by assimilation of helioseismic data, and (b) start to use the model to estimate turbulent properties that determine the internal dynamics and activity cycles of the Sun.

Modelling the force balance in planetary dynamos (PhD)

Supervisors: Robert TeedRadostin Simitev
Relevant research groups: Geophysical & Astrophysical Fluid DynamicsContinuum Mechanics

Current simulations of magnetic field (the 'dynamo process') generation in planets are run, not under the conditions of planetary cores and atmospheres, but in a regime idealised for computations. To forecast changes in planetary magnetic fields such as reversals and dynamo collapse, it is vital to understand the actual fluid dynamics of these regions. The aim of this project is to produce simulations of planetary cores and atmospheres with realistic force balances and, in doing so, understand how such force balances arise and affect the dynamics of the flow. The importance of different forces (e.g. Coriolis, Lorentz, viscous forces) determine the dynamics, the dynamo regime, and hence the morphology and strength of the magnetic field that is produced. This project would involve working with existing numerical code to perform the simulations and developing new techniques to determine the heirarchy of forces at play.

Identifying waves in dynamo models (PhD)

Supervisors: Robert Teed
Relevant research groups: Geophysical & Astrophysical Fluid DynamicsContinuum Mechanics 

This project would involve using existing (and developing new) techniques to isolate and study magnetohydrodynamic (MHD) waves in numerical calculations. Various classes of waves exist and may play a role in the dynamo process (which generates planetary magnetic fields) and/or help us better understand changes in the magnetic field.

Magnetic helicity as the key to dynamo bistability (PhD)

Supervisors: David MacTaggart, Radostin Simitev
Relevant research groups: Geophysical & Astrophysical Fluid DynamicsContinuum Mechanics

The planets in the solar system exhibit very different types of large-scale magnetic field.The Earth has a strongly dipolar field, whereas the fields of other solar system planets, such as Uranus and Neptune, are far more irregular. Although the different physical compositions of the planets of the solar system will influence the behaviour of the large-scale magnetic fields that they generate, the morphology of planetary magnetic fields can depend on properties of dynamos common to all planets. Here, we refer to an important and recent discovery from dynamo simulations. Remarkably, two very different types of chaotic dipolar dynamo solutions have been found to exist over identical values of the basic parameters of a generic model of convection-driven dynamos in rotating spherical shells. The two solutions mentioned above can be characterised as ‘mean dynamos’, MD, where a strong poloidal field dominates and ‘fluctuating dynamos’, FD, where the poloidal component is weaker and the large-scale field can be described as multipolar. Although these two states have been shown to be bistable (co-exist) for a wide range of identical parameters, it is not clear how a particular state, MD or FD, is chosen and how/when one state can change to the other. Some of the bifurcations of such states has been investigated, but a deep understanding of the dynamics that cause the bifurcations remains to be developed. Since the magnetic topology of MD and FD states are fundamentally different, an important part of this project will be to probe the nature of MD and FD states by studying magnetic helicity, a magnetohydrodynamic invariant that combines information on the topology of the magnetic field with the magnetic flux. The role of magnetic helicity and other helicities (e.g. cross helicity) is currently not well understood in relation to MD and FD states, but these quantities are conjectured to be very important in the development of MD and FD states.  

Bistability is also related to a very important phenomenon in dynamos - global field reversal. A strongly dipolar (MD) field can change to a transitional multipolar (FD) state before a reversal and then settle into another dipolar equilibrium (of opposite polarity) again after the reversal.This project aims to develop a coherent picture of how bistability operates in spherical dynamos. Since bistability is a fundamental property of dynamos, a characterisation of how bistable solutions form and develop is key for any deep understanding of planetary dynamos and, in particular, could be crucial for understanding magnetic field reversals.

Stellar atmospheres and their magnetic helicity fluxes (PhD)

Supervisors: Radostin Simitev, David MacTaggart, Robert Teed
Relevant research groups: Geophysical & Astrophysical Fluid DynamicsContinuum Mechanics

Our Sun and many other stars have a strong large-scale magnetic field with a characteristic time variation. We know that this field is being generated via a dynamo mechanism driven by the turbulent convective motions inside the stars. The magnetic helicity, a quantifier of the field’s topology, is and essential ingredient in this process. In turbulent environments it is responsible for the inverse cascade that leads to the large-scale field, while the build up of its small-scale component can quench the dynamo.
In this project, the student will study the effects of magnetic helicity fluxes that happen below the stellar surface (photosphere), within the stellar atmosphere (chromosphere and corona) and between these two layers. This will be done using two-dimensional mean field simulations that allow parameter studies for different physical parameters. A fully three-dimensional model of a convective stellar wedge will then be used to provide a more detailed picture of the helicity fluxes and their effect on the dynamo. Using recent advancements that allow us to extract surface helicity fluxes from solar observations, the student will make use of observations to verify the simulation results. Other recent observational results on the stellar magnetic helicity will be used to benchmark the findings.

Efficient asymptotic-numerical methods for cardiac electrophysiology (PhD)

Supervisors: Radostin Simitev
Relevant research groups: Mathematical BiologyContinuum Mechanics

The mechanical activity of the heart is controlled by electrical impulses propagating regularly within the cardiac tissue during one's entire lifespan. A large number of very detailed ionic current models of cardiac electrical excitability are available.These realistic models are rather difficult for numerical simulations. This is due not only to their functional complexity but primarily to the significant stiffness of the equations.The goal of the proposed project is to develop fast and efficient numerical methods for solution of the equations of cardiac electrical excitation with the help and in the light of newly-developed methods for asymptotic analysis of the structure of cardiac equations (Simitev & Biktashev (2006) Biophys J; Biktashev et al. (2008), Bull Math Biol; Simitev & Biktashev (2011) Bull Math Biol)

The student will gain considerable experience with the theory of ordinary and partial differential equations, dynamical systems and bifurcation theory, asymptotic and perturbation methods,numerical methods. The applicant will also gain experience in computerprogramming, scientific computing and some statistical methods for comparison with experimental data.

Electrophysiological modelling of hearts with diseases (PhD)

Supervisors: Radostin Simitev
Relevant research groups: Mathematical BiologyContinuum Mechanics

The exact mechanisms by which heart failure occurs are poorly understood. On a more optimistic note, a revolution is underway in healthcare and medicine - numerical simulations are increasingly being used to help diagnose and treat heart disease and devise patient-specific therapies. This approach depends on three key enablers acting in accord. First, mathematical models describing the biophysical changes of biological tissue in disease must be formulated for any predictive computation to be possible at all. Second, statistical techniques for uncertainty quantification and parameter inference must be developed to link these models to patient-specific clinical measurements. Third, efficient numerical algorithms and codes need to be designed to ensure that the models can be simulated in real time so they can be used in the clinic for prediction and prevention. The goals of this project include designing more efficient algorithms for numerical simulation of the electrical behaviour of hearts with diseases on cell, tissue and on whole-organ levels. The most accurate tools we have, at present, are so called monolithic models where the differential equations describing constituent processes are assembled in a single large system and simultaneously solved. While accurate, the monolithic approaches are expensive as a huge disparity in spatial and temporal scales between relatively slow mechanical and much faster electrical processes exists and must be resolved. However, not all electrical behaviour is fast so the project will exploit advances in cardiac asymptotics to develop a reduced kinematic description of propagating electrical signals. These reduced models will be fully coupled to the original partial-differential equations for spatio-temporal evolution of the slow nonlinear dynamic fields. This will allow significantly larger spatial and time steps to be used in monolithic numerical schemes and pave the way for clinical applications, particularly coronary perfusion post infarction. The models thus developed will be applied to specific problems of interest, including (1) coupling among myocyte-fibroblast-collagen scar; (2) shape analysis of scar tissue and their effects on electric signal propagation; (3) personalized 3D heart models using human data. The project will require and will develop knowledge of mathematical modelling, asymptotic and numerical methods for PDEs and software development and some basic knowledge of physiology. Upon completion you will be a mature researcher with broad interdisciplinary education. You will not only be prepared for an independent scientific career but will be much sought after by both academia and industry for the rare combination of mathematical and numerical skills.

Fast-slow asymptotic analysis of cardiac excitation models (PhD)

Supervisors: Radostin Simitev
Relevant research groups: Mathematical BiologyContinuum Mechanics

Mathematical models of cardiac electrical excitation describe processess ocurring on a wide range of time and length scales. 


Regular seminars relevant to the group are held as part of the Applied Mathematics seminar series. You can find a full list of the seminars within the school on the main seminars page, where you can subscribe to their respective calendars.

We focus on both the underlying mathematical theories that accurately describe a wide range of materials, and the application of these theories to real-world systems. Our research spans a vast array of lengthscales: models of dense swarms of swimming bacteria; the development of an accurate model of both the fluid and elastic behaviour of the heart; the flow of vast glaciers; the fluid dynamics of the sun.

Many group members are also involved in SofTMech - a large and established Centre of Mathematics for Healthcare, which has had support from the EPSRC since 2016. SofTMech consists of multiple academic, clinical and industrial partners and combines extensive expertise in mathematical, statistical and computational modelling of cardiac and cancer physiology and disease.