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.

Staff

Publications

2024

Richardson, S. H., Mackenzie, J., Thekkethil, N., Feng, L., Lee, J., Berry, C., Hill, N., Luo, X., Gao, H. (2024) Cardiac perfusion coupled with a structured coronary network tree. Computer Methods in Applied Mechanics and Engineering, 428, (doi: 10.1016/j.cma.2024.117083)

Asghari, H., Miller, L., Penta, R., Merodio, J. (2024) On an isotropic porous solid cylinder: the analytical solution and sensitivity analysis of the pressure. Applied Mathematics and Mechanics,

Hunter, E., Teed, R. J. (2024) Multiple jets in a rotating annulus model with an imposed azimuthal magnetic field. Geophysical and Astrophysical Fluid Dynamics,

Xia, Y., Ahmed, Z., Karimullah, A., Mottram, N., Heidari, H., Ghannam, R. (2024) Thermal controlled cholesteric liquid crystal wavelength filter lens for photosensitive epilepsy treatment. Cell Reports Physical Science,

Dorfmann, L., Ogden, R. W. (2024) Hard-magnetic soft magnetoelastic materials: energy considerations. International Journal of Solids and Structures, 294, (doi: 10.1016/j.ijsolstr.2024.112789)

Kory, J., Stewart, P.S., Hill, N.A., Luo, X., Pandolfi, A. (2024) A discrete-to-continuum model for the human cornea with application to keratoconus. Royal Society Open Science,

Zhuan, X., Guan, D., Theobald, P., Luo, X. (2024) A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865241242998)

Dalton, D., Husmeier, D., Gao, H. (2024) Physics and Lie Symmetry Informed Gaussian Processes.

Köry, J., Hill, N.A., Luo, X.Y., Stewart, P.S. (2024) Discrete-to-continuum models of pre-stressed cytoskeletal filament networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480, (doi: 10.1098/rspa.2023.0611)

Miller, L., Penta, R. (2024) Effective double-poroelasticity derived via homogenisation of two non-interacting solid phases percolated by a viscous fluid. European Journal of Mechanics - A/Solids, 105, (doi: 10.1016/j.euromechsol.2023.105219)

Spelman, T. A., Onah, I. S., MacTaggart, D., Stewart, P. S. (2024) Elastic jump propagation across a blood vessel junction. Royal Society Open Science,

Du, Y., Luo, X., Hill, N. A. (2024) Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865241238985)

Thekkethil, N., Köry, J., Guo, M., Stewart, P. S., Hill, N. A., Luo, X. (2024) Modelling the rheology of living cell cytoplasm: Poroviscoelasticity and fluid-to-solid transition. Biomechanics and Modeling in Mechanobiology,

Girelli, A., Giantesio, G., Musesti, A., Penta, R. (2024) Multiscale homogenisation for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymph node. Royal Society Open Science,

Cousins, J. R.L., Bhadwal, A. S., Mottram, N. J., Brown, C. V., Wilson, S. K. (2024) Flow manipulation of a nematic liquid crystal in a Hele-Shaw cell with an electrically-controlled viscous obstruction. Journal of Fluid Mechanics,

Yang, Y., Husmeier, D., Gao, H., Berry, C., Carrick, D., Radjenovic, A. (2024) Automatic detection of myocardial ischaemia using generalisable spatio-temporal hierarchical Bayesian modelling of DCE-MRI. Computerized Medical Imaging and Graphics, 113, (doi: 10.1016/j.compmedimag.2024.102333)

Wang, Z., Wang, C., Zhao, F., Ren, F., Luo, X., Tang, H. (2024) Fluid-structure interaction in phaco-emulsification based cataract surgery. International Journal of Mechanical Sciences, 267, (doi: 10.1016/j.ijmecsci.2024.109022)

Yan, Z., Kowal, K. N. (2024) A controllable sliding law for thin-film flows over slippery fluid-saturated substrates: theory and experiments. Journal of Fluid Mechanics, 982, (doi: 10.1017/jfm.2024.127)

Guan, D., Tian, L., Li, W., Gao, H. (2024) Using LDDMM and a kinematic cardiac growth model to quantify growth and remodelling in rat hearts under PAH. Computers in Biology and Medicine, 171, (doi: 10.1016/j.compbiomed.2024.108218)

Al Mudarra, M. M., Ramírez-Torres, A. (2024) Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865241230269)

Feng, L., Gao, H., Luo, X. (2024) Whole-heart modelling with valves in a fluid–structure interaction framework. Computer Methods in Applied Mechanics and Engineering, 420, (doi: 10.1016/j.cma.2023.116724)

Miller, L., Penta, R. (2024) Homogenization of a coupled electrical and mechanical bidomain model for the myocardium. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865231207600)

Haider, M. A., Pearce, K. J., Chesler, N. C., Hill, N. A., Olufsen, M. S. (2024) Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries. International Journal for Numerical Methods in Biomedical Engineering, (doi: 10.1002/cnm.3798)

2023

Zhou, J., Husmeier, D., Gao, H., Yin, C., Qiu, C., Jing, X., Qi, Y., Liu, W. (2023) Bayesian inversion of frequency-domain airborne EM data with spatial correlation prior information. IEEE Transactions on Geoscience and Remote Sensing, 62, (doi: 10.1109/TGRS.2023.3344946)

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, 75, (doi: 10.1007/s00033-023-02141-3)

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, 417, (doi: 10.1016/j.cma.2023.116351)

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)

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)

Ge, Y., Husmeier, D., Lazarus, A., Rabbani, A., Gao, H. (2023) Bayesian inference of cardiac models emulated with a time series Gaussian process. International Aset Inc.

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)

Guan, D., Wang, Y., Luo, X., Danton, M., Gao, H. (2023) A Modelling Study of Pulmonary Regurgitation in a Personalized Human Heart. (doi: 10.1007/978-3-031-35302-4_60)

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)

2022

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/j.jcp.2022.111542)

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)

2021

Candelaresi, S., Hornig, G., MacTaggart, D., Simitev, R. D. (2021) On self and mutual winding helicity. Communications in Nonlinear Science and Numerical Simulation, 103, (doi: 10.1016/j.cnsns.2021.106015)

Kowal, K. N. (2021) Viscous banding instabilities: non-porous viscous fingering. Journal of Fluid Mechanics, 926, (doi: 10.1017/jfm.2021.660)

Morrow, A. et al. (2021) Rationale and design of the Medical Research Council Precision medicine with Zibotentan in microvascular angina (PRIZE) trial MRI sub-study. (doi: 10.1136/heartjnl-2021-BSCMR.3)

Teed, R. J., Latter, H. N. (2021) Axisymmetric simulations of the convective overstability in protoplanetary discs. Monthly Notices of the Royal Astronomical Society, 507, pp. 5523-5541. (doi: 10.1093/mnras/stab2311)

Miller, L., Penta, R. (2021) Double poroelasticity derived from the microstructure. Acta Mechanica, 232, pp. 3801-3823. (doi: 10.1007/s00707-021-03030-4)

Wang, D.Y., Luo, X.Y., Stewart, P.S. (2021) Energetics of collapsible channel flow with a nonlinear fluid-beam model. Journal of Fluid Mechanics, 926, (doi: 10.1017/jfm.2021.642)

Melnikov, A., Ogden, R. W., Dorfmann, L., Merodio, J. (2021) Bifurcation analysis of elastic residually-stressed circular cylindrical tubes. International Journal of Solids and Structures, 226-27, (doi: 10.1016/j.ijsolstr.2021.111062)

Ramírez-Torres, A., Di Stefano, S., Grillo, A. (2021) Influence of non-local diffusion in avascular tumour growth. Mathematics and Mechanics of Solids, 26, pp. 1264-1293. (doi: 10.1177/1081286520975086)

Romaszko, L., Borowska, A., Lazarus, A., Dalton, D., Berry, C., Luo, X., Husmeier, D., Gao, H. (2021) Neural network-based left ventricle geometry prediction from CMR images with application in biomechanics. Artificial Intelligence In Medicine, 119, (doi: 10.1016/j.artmed.2021.102140)

Guan, D., Luo, X., Gao, H. (2021) Constitutive modelling of soft biological tissue from ex vivo to in vivo: myocardium as an example. Springer

Feng, L., Gao, H., Qi, N., Danton, M., Hill, N. A., Luo, X. (2021) Fluid-structure interaction in a fully coupled three-dimensional mitral-atrium-pulmonary model. Biomechanics and Modeling in Mechanobiology, 20, pp. 1267-1295. (doi: 10.1007/s10237-021-01444-6)

Huang, R., Ogden, R., Penta, R. (2021) Mathematical modelling of residual-stress based volumetric growth in soft matter. Journal of Elasticity, 145, pp. 223-241. (doi: 10.1007/s10659-021-09834-8)

Dalton, D., Lazarus, A., Rabbani, A., Gao, H., Husmeier, D. (2021) Graph Neural Network Emulation of Cardiac Mechanics. (doi: 10.11159/icsta21.127)

Miller, L., Penta, R. (2021) Homogenized balance equations for nonlinear poroelastic composites. Applied Sciences, 11, (doi: 10.3390/app11146611)

Wang, D., Luo, X., Stewart, P. S. (2021) Multiple steady and oscillatory solutions in a collapsible channel flow. International Journal of Applied Mechanics, 13, (doi: 10.1142/S1758825121500587)

Cai, L., Zhang, R., Li, Y., Zhu, G., Ma, X., Wang, Y., Luo, X., Gao, H. (2021) The comparison of different constitutive laws and fiber architectures for the aortic valve on fluid-structure interaction simulation. Frontiers in Physiology, 12, (doi: 10.3389/fphys.2021.682893)

Quinn, J., MacTaggart, D., Simitev, R. D. (2021) Kelvin-Helmholtz instability and collapse of a twisted magnetic nullpoint with anisotropic viscosity. Astronomy and Astrophysics, 650, (doi: 10.1051/0004-6361/202140460)

Thomson, S. J., Durey, M., Rosales, R. R. (2021) Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice. Physical Review E, 103, (doi: 10.1103/PhysRevE.103.062215)

Cruz-González, O.L., Ramírez-Torres, A., Rodríguez-Ramos, R., Otero, J.A., Penta, R., Lebon, F. (2021) Effective behavior of long and short fiber-reinforced viscoelastic composites. Applications in Engineering Science, 6, (doi: 10.1016/j.apples.2021.100037)

Guan, D., Zhuan, X., Holmes, W., Luo, X., Gao, H. (2021) Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systole. Journal of Engineering Mathematics, 128, (doi: 10.1007/s10665-021-10102-w)

da Costa, F. P., Grinfeld, M., Mottram, N. J., Pinto, J. T., Xayxanadasy, K. (2021) Steady state solutions in a model of a cholesteric liquid crystal sample. Afrika Matematika, 32, pp. 645-672. (doi: 10.1007/s13370-020-00851-9)

Aziz, M. H.N., Simitev, R. D. (2021) Code for Estimation of Parameters for an Archetypal Model of Cardiomyocyte Membrane Potentials. (doi: 10.5281/zenodo.4568662)

Heath Richardson, S. I., Gao, H., Cox, J., Janiczek, R., Griffith, B. E., Berry, C., Luo, X. (2021) A poroelastic immersed finite element framework for modeling cardiac perfusion and fluid-structure interaction. International Journal for Numerical Methods in Biomedical Engineering, 37, (doi: 10.1002/cnm.3446)

Dorfmann, L., Ogden, R. W. (2021) The effect of residual stress on the stability of a circular cylindrical tube. Journal of Engineering Mathematics, 127, (doi: 10.1007/s10665-021-10097-4)

Wang, Y., Cai, L., Feng, X., Luo, X., Gao, H. (2021) A ghost structure finite difference method for a fractional FitzHugh-Nagumo monodomain model on moving irregular domain. Journal of Computational Physics, 428, (doi: 10.1016/j.jcp.2020.110081)

Mortensen, P., Gao, H., Smith, G., Simitev, R. D. (2021) Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling. Mathematical Medicine and Biology, 38, pp. 106-131. (doi: 10.1093/imammb/dqaa014)

Durey, M., Bush, J. W.M. (2021) Classical pilot-wave dynamics: the free particle. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31, (doi: 10.1063/5.0039975)

Li, W., Gao, H., Mangion, K., Berry, C., Luo, X. (2021) Apparent growth tensor of left ventricular post myocardial infarction – in human first natural history study. Computers in Biology and Medicine, 129, (doi: 10.1016/j.compbiomed.2020.104168)

Su, Y., Ogden, R. W., Destrade, M. (2021) Bending control and stability of functionally graded dielectric elastomers. Extreme Mechanics Letters, 43, (doi: 10.1016/j.eml.2020.101162)

Simitev, R. D., Busse, F. H. (2021) Onset of inertial magnetoconvection in rotating fluid spheres. Fluids, 6, (doi: 10.3390/fluids6010041)

Mather, J. F., Simitev, R. D. (2021) Regimes of thermo-compositional convection and related dynamos in rotating spherical shells. Geophysical and Astrophysical Fluid Dynamics, 115, pp. 61-84. (doi: 10.1080/03091929.2020.1762875)

Cai, L., Ren, L., Wang, Y., Xie, W., Zhi, G., Gao, H. (2021) Surrogate models based on machine learning methods for parameter estimation of left ventricular myocardium. Royal Society Open Science, 8, (doi: 10.1098/rsos.201121)

Cruz-González, O. L., Ramírez-Torres, A., Rodríguez-Ramos, R., Penta, R., Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Sabina, F. J., Lebon, F. (2021) A hierarchical asymptotic homogenization approach for viscoelastic composites. Mechanics of Advanced Materials and Structures, 28, pp. 2190-2201. (doi: 10.1080/15376494.2020.1722872)

Mortensen, P., Gao, H., Smith, G., Simitev, R. D. (2021) Addendum: Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling. Mathematical Medicine and Biology, 38, pp. 292-298. (doi: 10.1093/imammb/dqab005)

Penta, R., Ramirez Torres, A., Merodio, J., Rodríguez-Ramos, R. (2021) Effective governing equations for heterogenous porous media subject to inhomogeneous body forces. Mathematics in Engineering, 3, pp. 1-17. (doi: 10.3934/mine.2021033)

Da Silva Costa, A., Mortensen, P., Hortigon-Vinagre, M. P., van der Heyden, M. A. G., Burton, F. L., Gao, H., Simitev, R. D., Smith, G. L. (2021) Electrophysiology of hiPSC-cardiomyocytes co-cultured with HEK cells expressing the inward rectifier channel. International Journal of Molecular Sciences, 22, (doi: 10.3390/ijms22126621)

2020

Silva, L., Gupta, P., Mactaggart, D., Simitev, R. (2020) Effects of shell thickness on cross-helicity generation in convection-driven spherical dynamos. Fluids, 5, (doi: 10.3390/fluids5040245)

Paun, L. M., Colebank, M. J., Olufsen, M. S., Hill, N. A., Husmeier, D. (2020) Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation. Journal of the Royal Society: Interface, 17, (doi: 10.1098/rsif.2020.0886)

Hashlamoun, K., Abusara, Z., Ramirez Torres, A., Grillo, A., Herzog, W., Federico, S. (2020) Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy. Biomechanics and Modeling in Mechanobiology, 19, pp. 2397-2412. (doi: 10.1007/s10237-020-01346-z)

Lockington, D., Wang, Z., Qi, N., Malyugin, B., Cai, L., Wang, C., Tang, H., Ramaesh, K., Luo, X. (2020) Modelling floppy iris syndrome and the impact of pupil size and ring devices on iris displacement. Eye, 34, pp. 2227-2234. (doi: 10.1038/s41433-020-0782-7)

Cruz-González, O.L., Rodríguez-Ramos, R., Otero, J.A., Ramirez Torres, A., Penta, R., Lebon, F. (2020) On the effective behavior of viscoelastic composites in three dimensions. International Journal of Engineering Science, 157, (doi: 10.1016/j.ijengsci.2020.103377)

Ogden, R.W. (2020) Peter Chadwick. 23 March 1931—12 August 2018. Biographical Memoirs of Fellows of the Royal Society, 69, pp. 109-131. (doi: 10.1098/rsbm.2020.0012)

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

Miller, L., Penta, R. (2020) Effective balance equations for poroelastic composites. Continuum Mechanics and Thermodynamics, 32, pp. 1533-1557. (doi: 10.1007/s00161-020-00864-6)

Chen, S., Ratna Sari, C., Gao, H., Lei, Y., Segers, P., De Beule, M. (2020) Mechanical and morphometric study of mitral valve chordae tendineae and related papillary muscle. Journal of the Mechanical Behavior of Biomedical Materials, 111, (doi: 10.1016/j.jmbbm.2020.104011)

Morrow, A. J. et al. (2020) Rationale and design of the Medical Research Council precision medicine with Zibotentan in microvascular angina (PRIZE) trial. American Heart Journal, 229, pp. 70-80. (doi: 10.1016/j.ahj.2020.07.007)

Durey, M. (2020) Bifurcations and chaos in a Lorenz-like pilot-wave system. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30, (doi: 10.1063/5.0020775)

Durey, M. (2020) The Who Wants to be a Millionaire dilemma. Mathematics Magazine, 93, pp. 374-377. (doi: 10.1080/0025570X.2020.1826848)

El Hamdaoui, M., Merodio, J., Ogden, R.W. (2020) Two-phase piecewise homogeneous plane deformations of a fibre-reinforced neo-Hookean material with application to fibre kinking and splitting. Journal of the Mechanics and Physics of Solids, 143, (doi: 10.1016/j.jmps.2020.104091)

Di Stefano, S., Miller, L., Grillo, A., Penta, R. (2020) Effective balance equations for electrostrictive composites. Zeitschrift für Angewandte Mathematik und Physik, 71, (doi: 10.1007/s00033-020-01365-x)

Kowal, K. N., Worster, M. G. (2020) The formation of grounding zone wedges: theory and experiments. Journal of Fluid Mechanics, 898, (doi: 10.1017/jfm.2020.393)

Dehghani, H., Noll, I., Penta, R., Menzel, A., Merodio, J. (2020) The role of microscale solid matrix compressibility on the mechanical behaviour of poroelastic materials. European Journal of Mechanics - A/Solids, 83, (doi: 10.1016/j.euromechsol.2020.103996)

Durey, M., Bush, J. W.M. (2020) Hydrodynamic quantum field theory: the onset of particle motion and the form of the pilot wave. Frontiers in Physics, 8, (doi: 10.3389/fphy.2020.00300)

Liu, R., Xu, S., Luo, X., Liu, Z. (2020) Theoretical and Numerical Analysis of mechanical behaviors of a metamaterial-based shape memory polymer stent. Polymers, 12, (doi: 10.3390/polym12081784)

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

Zhuan, X., Luo, X. (2020) Residual stress estimates from multi-cut opening angles of the left ventricle. Cardiovascular Engineering and Technology, 11, pp. 381-393. (doi: 10.1007/s13239-020-00467-x)

Thomson, S. J., Durey, M., Rosales, R. R. (2020) Collective vibrations of a hydrodynamic active lattice. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476, (doi: 10.1098/rspa.2020.0155)

Durey, M., Turton, S. E., Bush, J. W. M. (2020) Speed oscillations in classical pilot-wave dynamics. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476, (doi: 10.1098/rspa.2019.0884)

Conroy Broderick, H., Righi, M., Destrade, M., Ogden, R. W. (2020) Stability analysis of charge-controlled soft dielectric plates. International Journal of Engineering Science, 151, (doi: 10.1016/j.ijengsci.2020.103280)

Durey, M., Milewski, P. A., Wang, Z. (2020) Faraday pilot-wave dynamics in a circular corral. Journal of Fluid Mechanics, 891, (doi: 10.1017/jfm.2020.140)

Melnikov, A., Dorfmann, L., Ogden, R. W. (2020) Bifurcation of finitely deformed thick-walled electroelastic spherical shells subject to a radial electric field. International Journal of Non-Linear Mechanics, 121, (doi: 10.1016/j.ijnonlinmec.2020.103429)

Li, W., Lazarus, A., Gao, H., Martinez De Azcona Naharro, A., Fontana, M., Hawkins, P., Biswas, S., Janiczek, R., Cox, J., Berry, C., Husmeier, D., Luo, X. (2020) Analysis of cardiac amyloidosis progression using model-based markers. Frontiers in Physiology, 11, (doi: 10.3389/fphys.2020.00324)

Holzapfel, G., Ogden, R. (2020) A damage model for collagen fibres with an application to collagenous soft tissues. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476, (doi: 10.1098/rspa.2019.0821)

Quinn, J., MacTaggart, D., Simitev, R. (2020) The effect of anisotropic viscosity on the nonlinear MHD kink instability. Communications in Nonlinear Science and Numerical Simulation, 83, (doi: 10.1016/j.cnsns.2019.105131)

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

Holzapfel, G. A., Ogden, R. W. (2020) An arterial constitutive model accounting for collagen content and cross-linking. Journal of the Mechanics and Physics of Solids, 136, (doi: 10.1016/j.jmps.2019.103682)

Guan, D., Yao, J., Luo, X., Gao, H. (2020) Effect of myofibre architecture on ventricular pump function by using a neonatal porcine heart model: from DT-MRI to rule-based methods. Royal Society Open Science, 7, (doi: 10.1098/rsos.191655)

Griffiths, I.M., Mitevski, I., Vujkovac, I., Illingworth, M.R., Stewart, P.S. (2020) The role of tortuosity in filtration efficiency: a general network model for filtration. Journal of Membrane Science, 598, (doi: 10.1016/j.memsci.2019.117664)

Spelman, T.A., Stewart, P.S. (2020) Shock wave propagation along the central retinal blood vessels. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476, (doi: 10.1098/rspa.2019.0269)

Merodio, J., Ogden, R. (2020) Basic equations of continuum mechanics. Springer

(2020) Constitutive Modelling of Solid Continua. (doi: 10.1007/978-3-030-31547-4)

Wang, Y., Lan, H., Yin, T., Zhang, X., Huang, J., Fu, H., Huang, J., McGinty, S., Gao, H., Wang, G., Wang, Z. (2020) Covalent immobilization of biomolecules on stent materials through mussel adhesive protein coating to form biofunctional films. Materials Science and Engineering C: Materials for Biological Applications, 106, (doi: 10.1016/j.msec.2019.110187)

Merodio, J., Ogden, R. (2020) Finite deformation elasticity theory. Springer

Dorfmann, L., Ogden, R. (2020) Nonlinear constitutive modeling of electroelastic solids. Springer

Dorfmann, L., Ogden, R. W. (2020) Waves and vibrations in a finitely deformed electroelastic circular cylindrical tube. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476, (doi: 10.1098/rspa.2019.0701)

Bravo-Castillero, J., Ramírez-Torres, A., Sabina, F. J., García-Reimbert, C., Guinovart-Díaz, R., Rodríguez-Ramos, R. (2020) Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites. Waves in Random and Complex Media, 30, pp. 593-613. (doi: 10.1080/17455030.2018.1546063)

Bourne, D.P., Kok, P.J.J., Roper, S.M., Spanjer, W.D.T. (2020) Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes. Philosophical Magazine, 100, pp. 2677-2707. (doi: 10.1080/14786435.2020.1790053)

2019

Yañez-Olmos, D., Bravo-Castillero, J., Ramírez-Torres, A., Rodríguez-Ramos, R., Sabina, F. J. (2019) Effective coefficients of isotropic complex dielectric composites in a hexagonal array. Technische Mechanik, 39, pp. 220-228. (doi: 10.24352/UB.OVGU-2019-020)

Grillo, A., Di Stefano, S., Ramírez‐Torres, A., Loverre, M. (2019) A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity. GAMM Mitteilungen, 42, (doi: 10.1002/gamm.201900015)

Feng, L., Gao, H., Griffith, B. E., Niderer, S. A., Luo, X. (2019) Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve. International Journal for Numerical Methods in Biomedical Engineering, 35, (doi: 10.1002/cnm.3254)

Ramírez-Torres, A., Penta, R., Rodríguez-Ramos, R., Grillo, A. (2019) Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach. Mathematics and Mechanics of Solids, 24, pp. 3554-3574. (doi: 10.1177/1081286519847687)

Sherifova, S., Sommer, G., Viertler, C., Regitnig, P., Caranasos, T., Smith, M. A., Griffith, B. E., Ogden, R. W., Holzapfel, G. A. (2019) Failure properties and microstructure of healthy and aneurysmatic human thoracic aortas subjected to uniaxial extension with a focus on the media. Acta Biomaterialia, 99, pp. 443-456. (doi: 10.1016/j.actbio.2019.08.038)

Davies, V., Noè, U., Lazarus, A., Gao, H., Macdonald, B., Berry, C., Luo, X., Husmeier, D. (2019) Fast parameter inference in a biomechanical model of the left ventricle by using statistical emulation. Journal of the Royal Statistical Society: Series C (Applied Statistics), 68, pp. 1555-1576. (doi: 10.1111/rssc.12374)

Marchena-Menéndez, J., Ramírez-Torres, A., Penta, R., Rodríguez-Ramos, R., Merodio, J. (2019) Macroscopic thermal profile of heterogeneous cancerous breasts. A three-dimensional multiscale analysis. International Journal of Engineering Science, 144, (doi: 10.1016/j.ijengsci.2019.103135)

Liu, R., McGinty, S., Cui, F., Luo, X., Liu, Z. (2019) Modelling and simulation of the expansion of a shape memory polymer stent. Engineering Computations, 36, pp. 2726-2746. (doi: 10.1108/EC-10-2018-0462)

Cai, L., Wang, Y., Gao, H., Ma, X.S., Zhu, G.Y., Zhang, R.H., Shen, X.Q., Luo, X. (2019) Some effects of different constitutive laws on simulating mitral valve dynamics with FSI. Scientific Reports, 9, (doi: 10.1038/s41598-019-49161-6)

Cruz-González, O.L., Guinovart-Sanjuán, D., Rodríguez-Ramos, R., Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Penta, R., Otero, J. A., Dumont, S., Lebon, F., Sabina, F.J. (2019) An approach for modeling non-ageing linear viscoelastic composites with general periodicity. Composite Structures, 223, (doi: 10.1016/j.compstruct.2019.110927)

Ramírez-Torres, A., Penta, R., Rodríguez-Ramos, R., Grillo, A., Preziosi, L., Merodio, J., Guinovart-Díaz, R., Bravo-Castillero, J. (2019) Homogenized out-of-plane shear response three-scale fiber-reinforced composites. Computing and Visualization in Science, 20, pp. 85-93. (doi: 10.1007/s00791-018-0301-6)

Kowal, K. N., Davis, S. H., Voorhees, P. W. (2019) Surface deformations in dynamic thermocapillary convection under partial slip. Physical Review E, 100, (doi: 10.1103/PhysRevE.100.022802)

Guan, D., Ahmad, F., Theobald, P., Soe, S., Luo, X., Gao, H. (2019) On the AIC based model reduction for the general Holzapfel-Ogden myocardial constitutive law. Biomechanics and Modeling in Mechanobiology, 18, pp. 1213-1232. (doi: 10.1007/s10237-019-01140-6)

Romaszko, L., Borowska, A., Lazarus, A., Gao, H., Luo, X., Husmeier, D. (2019) Direct Learning Left Ventricular Meshes from CMR Images. (doi: 10.11159/icsta19.25)

Paun, L. M., Colebank, M., Qureshi, M. U., Olufsen, M., Hill, N., Husmeier, D. (2019) MCMC with Delayed Acceptance using a Surrogate Model with an Application to Cardiovascular Fluid Dynamics. (doi: 10.11159/icsta19.28)

Romaszko, L., Lazarus, A., Gao, H., Borowska, A., Luo, X., Husmeier, D. (2019) Massive Dimensionality Reduction for the Left Ventricular Mesh. (doi: 10.11159/icsta19.24)

Yang, Y., Gao, H., Berry, C., Radjenovic, A., Husmeier, D. (2019) Quantification of Myocardial Perfusion Lesions Using Spatially Variant Finite Mixture Modelling of DCE-MRI. (doi: 10.11159/icsta19.26)

Husmeier, D., Lazarus, A., Noè, U., Davies, V., Borowska, A., Macdonald, B., Gao, H., Berry, C., Luo, X. (2019) Statistical Emulation of Cardiac Mechanics: an Important Step Towards a Clinical Decision Support System. (doi: 10.11159/icsta19.29)

Hori, K., Teed, R. J., Jones, C.A. (2019) Anelastic torsional oscillations in Jupiter's metallic hydrogen region. Earth and Planetary Science Letters, 519, pp. 50-60. (doi: 10.1016/j.epsl.2019.04.042)

Cai, L., Guo, M., Li, Y., Ying, W., Gao, H., Luo, X. (2019) Nonstandard finite difference method for nonlinear Riesz space fractional reaction-diffusion equation. International Journal of Numerical Analysis and Modeling, 16, pp. 925-938.

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

Wang, Y., Cai, L., Luo, X., Ying, W., Gao, H. (2019) Simulation of action potential propagation based on the ghost structure method. Scientific Reports, 9, (doi: 10.1038/s41598-019-47321-2)

Noè, U., Lazarus, A., Gao, H., Davies, V., Macdonald, B., Mangion, K., Berry, C., Luo, X., Husmeier, D. (2019) Gaussian process emulation to accelerate parameter estimation in a mechanical model of the left ventricle: a critical step towards clinical end-user relevance. Journal of the Royal Society: Interface, 16, (doi: 10.1098/rsif.2019.0114)

Kowal, K. N., Worster, M. G. (2019) Stability of lubricated viscous gravity currents. Part 1. Internal and frontal analyses and stabilisation by horizontal shear. Journal of Fluid Mechanics, 871, pp. 970-1006. (doi: 10.1017/jfm.2019.321)

Duanmu, Z., Chen, W., Gao, H., Yang, X., Luo, X., Wang, T., Hill, N. A. (2019) A one-dimensional hemodynamic model of the coronary arterial tree. Frontiers in Physiology, 10, (doi: 10.3389/fphys.2019.00853)

Stewart, P. S., Foss, A. J.E. (2019) Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation. ANZIAM Journal, 61, pp. 320-348. (doi: 10.1017/S1446181119000117)

Kowal, K. N., Worster, M. G. (2019) Stability of lubricated viscous gravity currents. Part 2. Global analysis and stabilisation by buoyancy forces. Journal of Fluid Mechanics, 871, pp. 1007-1027. (doi: 10.1017/jfm.2019.322)

Guan, D., Yao, J., Luo, X., Gao, H. (2019) Effects of Myofibre Architecture on Biventricular Biomechanics: a Simulation Study.

Lesniewska, M., Henrich, O., Mottram, N. (2019) Microfluidic Flow of Colloid-Liquid Crystal Composite Materials.

Holzapfel, G., Ogden, R., Sherifova, S. (2019) On fibre dispersion modelling of soft biological tissues: a review. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 475, (doi: 10.1098/rspa.2018.0736)

Melnik, A. V., Luo, X., Ogden, R. W. (2019) A para-universal relation for orthotropic materials. Mechanics Research Communications, 97, pp. 46-51. (doi: 10.1016/j.mechrescom.2019.04.006)

Li, B., Roper, S. M., Wang, L., Luo, X., Hill, N.A. (2019) An incremental deformation model of arterial dissection. Journal of Mathematical Biology, 78, pp. 1277-1298. (doi: 10.1007/s00285-018-1309-8)

Dorfmann, L., Ogden, R. W. (2019) Electroelastic plate instabilities based on the Stroh method in terms of the energy function Ω*(F, DL) Mechanics Research Communications, 96, pp. 67-74. (doi: 10.1016/j.mechrescom.2019.03.002)

Dehghani, H., Penta, R., Merodio, J. (2019) The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues. Materials Research Express, 6, (doi: 10.1088/2053-1591/aaf5b9)

Kowal, K. N., Davis, S. H. (2019) Strong shear-flow modulation of instabilities in rapid directional solidification. Acta Materialia, 164, pp. 464-472. (doi: 10.1016/j.actamat.2018.10.054)

Umar Qureshi, M., Colebank, M. J., Paun, L. M., Ellwein, L., Chesler, N., Haider, M. A., Hill, N. A., Husmeier, D., Olufsen, M. S. (2019) Hemodynamic assessment of pulmonary hypertension in mice: a model based analysis of the disease mechanism. Biomechanics and Modeling in Mechanobiology, 18, pp. 219-243. (doi: 10.1007/s10237-018-1078-8)

Zhuan, X., Luo, X., Gao, H., Ogden, R. W. (2019) Coupled agent-based and hyperelastic modelling of the left ventricle post-myocardial infarction. International Journal for Numerical Methods in Biomedical Engineering, 35, (doi: 10.1002/cnm.3155)

Teed, R.J., Jones, C.A., Tobias, S.M. (2019) Torsional waves driven by convection and jets in Earth’s liquid core. Geophysical Journal International, 216, pp. 123-129. (doi: 10.1093/gji/ggy416)

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

Rodríguez-Ramos, R., Ramírez-Torres, A., Bravo-Castillero, J., Guinovart-Díaz, R., Guinovart-Sanjuán, D., Cruz-González, O. L., Sabina, F. J., Merodio, J., Penta, R. (2019) Multiscale homogenization for linear mechanics. Springer

Penta, R., Miller, L., Grillo, A., Ramírez-Torres, A., Mascheroni, P., Rodríguez-Ramos, R. (2019) Porosity and diffusion in biological tissues. Recent advances and further perspectives. Springer

Silva, L. A.C., Mather, J. F., Simitev, R. D. (2019) The onset of thermo-compositional convection in rotating spherical shells. Geophysical and Astrophysical Fluid Dynamics, 113, pp. 377-404. (doi: 10.1080/03091929.2019.1640875)

2018

Cousins, J. R.L., Wilson, S. K., Mottram, N. J., Wilkies, D., Weegels, L., Lin, K. (2018) A Model for the Formation of Mura During the One-Drop-Filling Process.

Melnik, A. V., Luo, X., Ogden, R. W. (2018) A generalised structure tensor model for the mixed invariant I8. International Journal of Non-Linear Mechanics, 107, pp. 137-148. (doi: 10.1016/j.ijnonlinmec.2018.08.018)

Feng, L., Qi, N., Gao, H., Sun, W., Vazquez, M., Griffith, B.E., Luo, X.Y. (2018) On the chordae structure and dynamic behaviour of the mitral valve. IMA Journal of Applied Mathematics, 83, pp. 1066-1091. (doi: 10.1093/imamat/hxy035)

Singh, B., Ogden, R. W. (2018) Reflection of plane waves from the boundary of an incompressible finitely deformed electroactive half-space. Zeitschrift für Angewandte Mathematik und Physik, 69, (doi: 10.1007/s00033-018-1044-4)

Kowal, K. N., Davis, S. H., Voorhees, P. W. (2018) Thermocapillary instabilities in a horizontal liquid layer under partial basal slip. Journal of Fluid Mechanics, 855, pp. 839-859. (doi: 10.1017/jfm.2018.684)

Ramírez-Torres, A., Di Stefano, S., Grillo, A., Rodríguez-Ramos, R., Merodio, J., Penta, R. (2018) An asymptotic homogenization approach to the microstructural evolution of heterogeneous media. International Journal of Non-Linear Mechanics, 106, pp. 245-257. (doi: 10.1016/j.ijnonlinmec.2018.06.012)

Di Stefano, S., Ramírez-Torres, A., Penta, R., Grillo, A. (2018) Self-influenced growth through evolving material inhomogeneities. International Journal of Non-Linear Mechanics, 106, pp. 174-187. (doi: 10.1016/j.ijnonlinmec.2018.08.003)

Dorfmann, L., Ogden, R. W. (2018) The effect of deformation dependent permittivity on the elastic response of a finitely deformed dielectric tube. Mechanics Research Communications, 93, pp. 47-57. (doi: 10.1016/j.mechrescom.2017.09.002)

Holzapfel, G. A., Ogden, R. W. (2018) Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components. American Journal of Physiology: Heart and Circulatory Physiology, 315, pp. H540-H549. (doi: 10.1152/ajpheart.00117.2018)

Durey, M., Milewski, P. A., Bush, J. W. M. (2018) Dynamics, emergent statistics, and the mean-pilot-wave potential of walking droplets. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, (doi: 10.1063/1.5030639)

Li, K., Ogden, R. W., Holzapfel, G. A. (2018) An exponential constitutive model excluding fibers under compression: application to extension-inflation of a residually stressed carotid artery. Mathematics and Mechanics of Solids, 23, pp. 1206-1224. (doi: 10.1177/1081286517712077)

Păun, L. M., Qureshi, M. U., Colebank, M., Hill, N. A., Olufsen, M. S., Haider, M. A., Husmeier, D. (2018) MCMC methods for inference in a mathematical model of pulmonary circulation. Statistica Neerlandica, 72, pp. 306-338. (doi: 10.1111/stan.12132)

Zhang, S., Luo, X., Cai, Z. (2018) Three-dimensional flows in a hyperelastic vessel under external pressure. Biomechanics and Modeling in Mechanobiology, 17, pp. 1187-1207. (doi: 10.1007/s10237-018-1022-y)

Silva, L. A.C., Simitev, R. D. (2018) Pseudo-spectral Code for Numerical Simulation of Nonlinear Thermo-compositional Convection and Dynamos in Rotating Spherical Shells. (doi: 10.5281/zenodo.1311203)

Silva, L. A.C., Simitev, R. D. (2018) Spectral Code for Linear Analysis of the Onset of Thermo-compositional Convection in Rotating Spherical Fluid Shells. (doi: 10.5281/zenodo.1307245)

Durey, M., Milewski, P. A. (2018) Faraday wave–droplet dynamics: discrete-time analysis. Journal of Fluid Mechanics, 821, pp. 296-329. (doi: 10.1017/jfm.2017.235)

Melnikov, A., Ogden, R. W. (2018) Bifurcation of finitely deformed thick-walled electroelastic cylindrical tubes subject to a radial electric field. Zeitschrift für Angewandte Mathematik und Physik, 69, (doi: 10.1007/s00033-018-0954-5)

Qi, N., Lockington, D., Wang, H., Hill, N. A., Ramaesh, K., Luo, X. (2018) Modelling floppy iris syndrome and the impact of phenylephrine on iris buckling. International Journal of Applied Mechanics, 10, (doi: 10.1142/S1758825118500485)

Simitev, R. D., Busse, F. H. (2018) Flows and dynamos in a model of stellar radiative zones. Journal of Plasma Physics, 84, (doi: 10.1017/S0022377818000612)

Mangion, K., Gao, H., Husmeier, D., Luo, X., Berry, C. (2018) Advances in computational modelling for personalised medicine after myocardial infarction. Heart, 104, pp. 550-557. (doi: 10.1136/heartjnl-2017-311449)

El Hamdaoui, M., Merodio, J., Ogden, R. W. (2018) Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube. Journal of Engineering Mathematics, 109, pp. 31-45. (doi: 10.1007/s10665-017-9904-z)

Wang, L., Hill, N. A., Roper, S. M., Luo, X. (2018) Modelling peeling- and pressure-driven propagation of arterial dissection. Journal of Engineering Mathematics, 109, pp. 227-238. (doi: 10.1007/s10665-017-9948-0)

Dorfmann, L., Ogden, R. W. (2018) Instabilities of soft dielectrics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377, (doi: 10.1098/rsta.2018.0077)

Hori, K., Teed, R.J., Jones, C.A. (2018) The dynamics of magnetic Rossby waves in spherical dynamo simulations: a signature of strong-field dynamos? Physics of the Earth and Planetary Interiors, 276, pp. 68-85. (doi: 10.1016/j.pepi.2017.07.008)

Richardson, S.I. H., Baggaley, A.W., Hill, N.A. (2018) Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows. Physical Review Fluids, 3, (doi: 10.1103/PhysRevFluids.3.023102)

Valdés-Ravelo, F., Ramírez-Torres, A., Rodríguez-Ramos, R., Bravo-Castillero, J., Guinovart-Díaz, R., Merodio, J., Penta, R., Conci, A., Sabina, F. J., García-Reimbert, C. (2018) Mathematical modeling of the interplay between stress and anisotropic growth of avascular tumors. Journal of Mechanics in Medicine and Biology, 18, (doi: 10.1142/s0219519418500069)

Li, K., Ogden, R. W., Holzapfel, G. A. (2018) Modeling of fibrous biological tissues with a general invariant that excludes compressed fibers. Journal of the Mechanics and Physics of Solids, 110, pp. 38-53. (doi: 10.1016/j.jmps.2017.09.005)

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

Duanmu, Z., Yin, M., Fan, X., Yang, X., Luo, X. (2018) A patient-specific lumped-parameter model of coronary circulation. Scientific Reports, 8, (doi: 10.1038/s41598-018-19164-w)

(2018) Multiscale Soft Tissue Mechanics and Mechanobiology: State-of-the-art Modeling.

Li, K., Ogden, R. W., Holzapfel, G. A. (2018) A discrete fibre dispersion method for excluding fibres under compression in the modeling of fibrous tissues. Journal of the Royal Society: Interface, 15, (doi: 10.1098/rsif.2017.0766)

Penta, R., Ramírez-Torres, A., Merodio, J., Rodríguez-Ramos, R. (2018) Effective balance equations for elastic composites subject to inhomogeneous potentials. Continuum Mechanics and Thermodynamics, 30, pp. 145-163. (doi: 10.1007/s00161-017-0590-x)

Ramírez-Torres, A., Penta, R., Rodríguez-Ramos, R., Merodio, J., Sabina, F. J., Bravo-Castillero, J., Guinovart-Díaz, R., Preziosi, L., Grillo, A. (2018) Three scales asymptotic homogenization and its application to layered hierarchical hard tissues. International Journal of Solids and Structures, 130-31, pp. 190-198. (doi: 10.1016/j.ijsolstr.2017.09.035)

Penta, R., Gerisch, A. (2018) An introduction to asymptotic homogenization. Springer

Mortensen, P., Bin Noor Aziz, M. H., Gao, H., Simitev, R. D. (2018) Modelling and Simulations of Electrical Propagation in Transmural Slabs of Scarred Left Ventricular Tissue.

(2018) Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications. 122, (doi: 10.1007/978-3-319-73371-5)

2017

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)

2016

Mangion, K., Gao, H., Mccomb, C., Carrick, D., Clerfond, G., Zhong, X., Luo, X., Haig, C., Berry, C. (2016) A novel method for estimating myocardial strain: assessment of deformation tracking against reference magnetic resonance methods in healthy volunteers. Scientific Reports, 6, (doi: 10.1038/srep38774)

Goodman, M. E., Luo, X., Hill, N. (2016) A mathematical model on the feedback between wall shear stress and intimal hyperplasia. International Journal of Applied Mechanics, 8, (doi: 10.1142/S1758825116400111)

Melnikov, A., Ogden, R. W. (2016) Finite deformations of an electroelastic circular cylindrical tube. Zeitschrift für Angewandte Mathematik und Physik, 67, (doi: 10.1007/s00033-016-0733-0)

Li, W., Luo, X. Y. (2016) An invariant-based damage model for human and animal skins. Annals of Biomedical Engineering, 44, pp. 3109-3122. (doi: 10.1007/s10439-016-1603-9)

Corson, L.T., Mottram, N.J., Duffy, B.R., Wilson, S.K., Tsakonas, C., 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, (doi: 10.1103/PhysRevE.94.043112)

Mottram, N.J., Newton, C.J.P. (2016) Liquid crystal theory and modeling. Springer

Hao, Y., Cai, Z., Roper, S., Luo, X. (2016) An Arnoldi-frontal approach for the stability analysis of flows in a collapsible channel. International Journal of Applied Mechanics, 8, (doi: 10.1142/S1758825116500733)

Corson, L.T., Tsakonas, C., Duffy, B.R., Mottram, N.J., Brown, C.V., Wilson, S.K. (2016) Electro-Manipulation of Droplets for Microfluidic Applications. (doi: 10.1007/978-3-319-23413-7)

Stewart, P. S., Waters, S. L., El Sayed, T., Vella, D., Goriely, A. (2016) Wrinkling, creasing, and folding in fiber-reinforced soft tissues. Extreme Mechanics Letters, 8, pp. 22-29. (doi: 10.1016/j.eml.2015.10.005)

Chen, W.W., Gao, H., Luo, X.Y., Hill, N.A. (2016) Study of cardiovascular function using a coupled left ventricle and systemic circulation model. Journal of Biomechanics, 49, pp. 2445-2454. (doi: 10.1016/j.jbiomech.2016.03.009)

Griffiths, I. M., Kumar, A., Stewart, P.S. (2016) Designing asymmetric multilayered membrane filters with improved performance. Journal of Membrane Science, 511, pp. 108-118. (doi: 10.1016/j.memsci.2016.02.028)

Ahamed, T., Dorfmann, L., Ogden, R.W. (2016) Modeling of residually stressed material with application to AAA. Journal of the Mechanical Behavior of Biomedical Materials, 61, pp. 221-234. (doi: 10.1016/j.jmbbm.2016.01.012)

Nam, N.T., Merodio, J., Ogden, R.W., Vinh, P.C. (2016) The effect of initial stress on the propagation of surface waves in a layered half-space. International Journal of Solids and Structures, 88-89, pp. 88-100. (doi: 10.1016/j.ijsolstr.2016.03.019)

Penta, R., Raum, K., Grimal, Q., Schrof, S., Gerisch, A. (2016) Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues. Bioinspiration and Biomimetics, 11, (doi: 10.1088/1748-3190/11/3/035004)

Teed, R., Proctor, M. R.E. (2016) Destruction of large-scale magnetic field in non-linear simulations of the shear dynamo. Monthly Notices of the Royal Astronomical Society, 458, pp. 2885-2889. (doi: 10.1093/mnras/stw490)

Li, K., Ogden, R. W., Holzapfel, G. A. (2016) Computational method for excluding fibers under compression in modeling soft fibrous solids. European Journal of Mechanics - A/Solids, 57, pp. 178-193. (doi: 10.1016/j.euromechsol.2015.11.003)

Matsui, H. et al. (2016) Performance benchmarks for a next generation numerical dynamo model. Geochemistry, Geophysics, Geosystems, 17, pp. 1586-1607. (doi: 10.1002/2015GC006159)

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

Kowal, K. N., Pegler, S. S., Worster, M. G. (2016) Dynamics of laterally confined marine ice sheets. Journal of Fluid Mechanics, 790, (doi: 10.1017/jfm.2016.37)

Merodio, J., Ogden, R. W. (2016) Extension, inflation and torsion of a residually-stressed circular cylindrical tube. Continuum Mechanics and Thermodynamics, 28, pp. 157-174. (doi: 10.1007/s00161-015-0411-z)

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

Ritos, K., Borg, M. K., Mottram, N. J., 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, (doi: 10.1098/rsta.2015.0025)

Mangion, K., Gao, H., Radjenovic, A., Luo, X., Haig, C., Berry, C. (2016) Pixel-tracking derived strain using the GlasgowHeart Method. Journal of Cardiovascular Magnetic Resonance, 18, (doi: 10.1186/1532-429X-18-S1-P9)

Teed, R. (2016) Excitation of Torsional Waves in the Earth's Core.

2015

Land, S. et al. (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.

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. 

Seminars

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.