Mathematics research
The Research Centre for Mathematics carries out world-class research in applied mathematics, pure mathematics, and statistics. Within applied mathematics, our research has three major themes: fluid dynamics and acoustics; solid mechanics and nonlinear elasticity; and biomechanics. Much of this research has great relevance to contemporary human affairs, for example the environment and health.
A unifying aspect of our research is the theory of waves and stability in continuous media. This theory is of fundamental importance both in the development of new mathematical methods, and in explaining the world around us. Our research work has unlimited applications in engineering, biology, and medicine.
Our research themes
We carry out research in aeroengine and submarine noise; waves and instabilities in boundary layers on aircraft wings; fingering instabilities in thin film flows; "freak" or "rogue" waves andtsunamis; rationalising the chaos of fluid turbulence and applications of fluid dynamics to geophysics, especially the atmosphere and oceans, and in volcanic lava flows.
Theme lead: Professor C. J. Chapman
Theme members: Professor J. J. Healey, Dr S. Naire, Dr D.Lucas and Professor V. I. Shrira, together with the post-doctoral research fellow Dr S. Annenkov
We carry out research in elastic waves and vibrations in waveguides; stability and pattern formation problems associated with smart materials and structures; structural vibrations induced by fluid flow; the mathematics of thin shells, plates, and rods; ground vibrations produced by high-speed trains; mechanics of multi-layered media; localized dynamic phenomena.
Theme lead: Professor Y. Fu
Theme members: Professor C. J. Chapman, Professor J. D. Kaplunov, Dr D. Prikazchikov, Dr L Prikazchikov, Dr M Nieves.
The main focus is on dynamic homogenization for periodic and functionally graded structures, vibration of carbon nano tubes, nano indentation, and boundary layers within non-local continuum models.
Theme lead: Professor J. Kaplunov
Theme members: Dr D. Prikazchikov, Dr L Prikazchikov, Dr M Nieves.
We carry out research in regenerative medicine and tissue engineering applications, aneurysm rupture in arteries, physiological flow in the lungs and fluid flow dynamics in mechanical thrombectomy devices.
Theme lead: Dr S. Naire
Theme members: Professor Y. Fu
We carry out research in Algebra, Number Theory, and Logic. We study algebraic structures and their applications to problems arising in algebraic geometry, number theory, and combinatorics. Our work in Logic focuses on intuitionism, including implications for mathematical physics.
Theme lead: Dr P. J. Truman
Theme members: Dr D. Bedford, Dr P. Fletcher
We carry out research using statistical methods applied to financial and economic time series.
Theme lead: Dr J. Cheng
Publications
- Fletcher, P (2020) Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey. Journal of Philosophical Logic
- Fu, Y, Kaplunov, J and Prikazchikov, DA (2020) Reduced model for the surface dynamics of a generally anisotropic elastic half-space. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476. 20190590 - 20190590.
- Shrira, V and Almelah, RB (2020) Upper-ocean Ekman current dynamics: a new perspective. Journal of Fluid Mechanics, 887.
- Truman, PJ and Koch, A (2020) Opposite Skew Left Braces and Applications. Journal of Algebra, 546. pp. 218-235.
- Wootton, PT, Kaplunov, J and Prikazchikov, DA (2020) A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane. IMA Journal of Applied Mathematics, 85 (1). 113 - 131.
- Ye, Y, Liu, Y and Fu, Y (2020) Weakly nonlinear analysis of localized bulging of an inflated hyperelastic tube of arbitrary wall thickness. Journal of the Mechanics and Physics of Solids, 135. 103804 - 103804.
Thesis
- Garau, Marta (2020) Dynamic chirality and failure in structured materials with applications. Doctoral thesis, Keele University.
- Chapman, CJ and Powles, CJ (2019) Basic singular fields in the theory of impulsive supersonic leading-edge noise. Wave Motion, 89. pp. 79-92.
- Chapman, CJ and Powles, CJ (2019) Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise. Wave Motion, 2019 (1). 1 - 12 (12).
- Erbaş, B, Kaplunov, J and Palsü, M (2019) A composite hyperbolic equation for plate extension. Mechanics Research Communications, 99. pp. 64-67.
- Garau, M, Nieves, MJ, Carta, G and Brun, M (2019) Transient response of a gyro-elastic structured medium: Unidirectional waveforms and cloaking. International Journal of Engineering Science, 143. 115 - 141.
- Healey, J (2019) Fractal sets of neutral curves for stably-stratified plane Couette flow. Journal of Fluid Mechanics, 872. pp. 697-728.
- Kaplunov, J, Danishevskyy, VV and Colquitt, D (2019) Composite dynamic models for periodically heterogeneous media. Mathematics and Mechanics of Solids, 24 (9). pp. 2663-2693.
- Kaplunov, J, Prikazchikov, D and Sultanova, L (2019) Elastic contact of a stiff thin layer and a half-space. Zeitschrift fur angewandte Mathematik und Physik ZAMP, 70 (22).
- Kaplunov, J, Prikazchikov, DA, Prikazchikova, LA and Sergushova, O (2019) The lowest vibration spectra of multi-component structures with contrast material properties. Journal of Sound and Vibration, 445. 132 -147.
- Lucas, D, Caulfield, CP and Kerswell, RR (2019) Layer formation and relaminarisation in plane Couette flow with spanwise stratification. Journal of Fluid Mechanics, 868. pp. 97-118.
- Mikhasev, G, Avdeichik, E and Prikazchikov, D (2019) Free vibrations of nonlocally elastic rods. Mathematics and Mechanics of Solids, 24 (5). pp. 1279-1293.
- Sultanova, Leyla (2019) High-contrast problems in linear elasticity for a coated half-space. Doctoral thesis, Keele University.
- Truman, PJ and Koch, A (2019) Opposite Skew Left Braces and Applications. Journal of Algebra. (In Press)
- Truman, PJ, Koch, A, Kohl, T and Underwood, R (2019) Isomorphism problems for Hopf-Galois structures on separable field extensions. Journal of Pure and Applied Algebra, 223 (5). pp. 2230-2245.
- Truman, PJ, Koch, A, Kohl, T and Underwood, R (2019) The Structure of Hopf Algebras Acting on Dihedral Extensions. In: Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, 277 . Springer, pp. 201-218.
- Truman, PJ, Kohl, T, Koch, A and Underwood, R (2019) Normality and Short Exact Sequences of Hopf-Galois Structures. Communications in Algebra, 47 (5). pp. 2086-2101.
- Truman, PJ and Taylor, S (2019) The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions. New York Journal of Mathematics, 25. pp. 219-237.
- Wang, S, Guo, Z, Zhou, L, Li, L and Fu, Y (2019) An experimental study of localized bulging in inflated cylindrical tubes guided by newly emerged analytical results. Journal Of The Mechanics And Physics Of Solids, 124. pp. 536-554.
- Andrianov, I, Danishevskyy, VV, Topol, H and Luyt, A (2018) Shear wave propagation in layered composites with degraded matrices at locations of imperfect bonding. Wave Motion, 78. pp. 9-31.
- Annenkov, SY and Shrira, VI (2018) Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations. Journal of Fluid Mechanics, 844. 766 -795.
- Aydin, YE, Erbas, B, Kaplunov, J and Prikazchikova, L (2018) Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate. Mathematics and Mechanics of Solids.
- Carta, G, Nieves, MJ, Jones, IS, Movchan, NV and Movchan, AB (2018) Elastic Chiral Waveguides with Gyro-Hinges. Quarterly Journal of Mechanics and Applied Mathematics, 71 (2). 157 - 185.
- Erbas, B, Kaplunov, J, Nolde, E and Palsu, M (2018) Composite wave models for elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2214).
- Fu, Y, Dorfmann, L and Xie, Y (2018) Localized necking of a dielectric membrane. Extreme Mechanics Letters, 21. pp. 44-48.
- Fu, Y, Xie, YX and Dorfmann, L (2018) A reduced model for electrodes-coated dielectric plates. International Journal of Non-Linear Mechanics, 106. pp. 60-69.
- Garau, M, Carta, G, Nieves, MJ, Jones, IS, Movchan, NV and Movchan, AB (2018) Interfacial waveforms in chiral lattices with gyroscopic spinners. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2215).
- Gou, K, Fok, P-W and Fu, Y (2018) Nonlinear tubular organ modeling and analysis for tracheal angioedema by swelling-morphoelasticity. Journal of Engineering Mathematics, 112. 95 - 117.
- Kaplunov, J, Erbas, B, Nobili, A and Kilic, G (2018) Dispersion of elastic waves in a layer interacting with a Winkler foundation. Journal of the Acoustical Society of America, 144 (5).
- Kaplunov, J, Prikazchikov, D and Sultanova, L (2018) Justification and refinement of Winkler-Fuss hypothesis. Zeitschrift fur angewandte Mathematik und Physik, 69 (3).
- Kolpakov, A, Andrianov, I and Prikazchikov, D (2018) Asymptotic strategy for matching homogenized structures. Conductivity problem. Quarterly Journal of Mechanics and Applied Mathematics, 71 (4). pp. 519-535.
- Nieves, MJ, Carta, G, Jones, IS, Movchan, AB and Movchan, NV (2018) Vibrations and elastic waves in chiral multi-structures. Journal of the Mechanics and Physics of Solids, 121. pp. 387-408.
- Nolde, E, Pichugin, AV and Kaplunov, J (2018) An asymptotic higher-order theory for rectangular beams. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
- Prikazchikov, D and Nobili, A (2018) Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane. European Journal of Mechanics - A/Solids, 70. pp. 86-94.
- Prikazchikov, D, Prikazchikova, LA and Khajiyeva, L (2018) Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space. Mechanics Research Communications, 92. pp. 49-53.
- Rogerson, GA, Andrianov, I and Danishevskyy, VV (2018) Elastic Waves in Periodically Heterogeneous Two-dimensional Media: Locally Periodic and Anti-periodic Modes. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2215).
- Rogerson, GA, Iandrianov, IV and Danishevskyy, VV (2018) Internal Resonances And Modes Interactions In Non-linear Vibrations Of Viscoelastic Heterogeneous Solids. Journal of Sound and Vibration, 433.
- Rogerson, GA, Kolpakov, AG, Andrianov, IV and Rakin, SI (2018) An asymptotic strategy to couple homogenized elastic structures. International Journal of Engineering Science, 131. pp. 26-39.
- Rogerson, GA, Lazarev, NP and Popova, TS (2018) Optimal control of the radius of a rigid circular inclusion in inhomogeneous two-dimensional bodies with cracks. Zeitschrift fur angewandte Mathematik und Physik, 69 (53).
- Russell, E (2018) Making a maths degree work for the workplace. Higher Education Pedagogies, 3 (1). pp. 403-416.
- Sergushova, Olga (2018) Low-frequency vibrations of strongly inhomogeneous multicomponent elastic structures. Doctoral thesis, Keele University.
- Truman, PJ (2018) Commutative Hopf-Galois module structure of tame extensions. Journal of Algebra, 503. pp. 389-408.
- Truman, PJ (2018) Commuting Hopf-Galois structures on a separable extension. Communications in Algebra, 46 (4). pp. 1420-1427.
- Abdulghani, A and Naire, S (2017) An adaptive moving mesh method for thin film flow equations with surface tension. Journal of Computational and Applied Mathematics, 319. pp. 365-384.
- Althobaiti, S, Kaplunov, J and Prikazchikov, D (2017) An edge moving load on an orthotropic plate resting on a Winkler foundation. Procedia Engineering, 199. pp. 2579-2584.
- Andrianov, IV, Topol, H and Danishevskyy, VV (2017) Asymptotic analysis of heat transfer in composite materials with nonlinear thermal properties. International Journal of Heat and Mass Transfer, 111. 736 - 754.
- Chebakov, R, Kaplunov, J and Rogerson, GA (2017) A nonlocal asymptotic theory for thin elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2203).
- Danishevskyy, VV, Andrianov, I, Awrejcewicz, J and Markert, B (2017) Influence of geometric and physical nonlinearities on the internal resonances of a finite continuous rod with a microstructure. Journal of Sound and Vibration, 386. pp. 359-371.
- Ege, N, Erbas, B, Chorozoglou, A, Kaplunov, J and Prikazchikov, DA (2017) On surface wave fields arising in soil-structure interaction problems. Procedia Engineering, 199. 2366 -2371.
- Fletcher, P, Hrbacek, K, Kanovei, V, Katz, MG, Lobry, C and Sanders, S (2017) Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 42 (2). 1 -59.
- Fu, YB, Geng, YN and Cai, ZX (2017) On the near-critical behavior of cavitation in elastic plane membranes. International Journal of Non-Linear Mechanics, 93. pp. 47-52.
- Fu, YB and Wang, J (2017) Effect of double-fibre reinforcement on localized bulging of an inflated cylindrical tube of arbitrary thickness. Journal of Engineering Mathematics, 109 (1). pp. 21-30.
- Geng, YN, Cai, ZX and Fu, YB (2017) On the near-critical behavior of cavitation in elastic plane membranes. International Journal of Non-Linear Mechanics.
- Kaplunov, J and Nobili, A (2017) A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell. Journal of Sound and Vibration, 401. 23 - 35.
- Kaplunov, J and Prikazchikov, D (2017) Asymptotic Theory for Rayleigh and Rayleigh-Type Waves. Advances in Applied Mechanics, 50. pp. 1-106.
- Kaplunov, J, Prikazchikov, DA and Prikazchikova, LA (2017) Dispersion of elastic waves in laminated glass. Procedia Engineering, 199. 1489 -1494.
- Lucas, D and Caulfield, CP (2017) Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence. Journal of Fluid Mechanics, 832.
- Lucas, D, Caulfield, CP and Kerswell, RR (2017) Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities. Journal of Fluid Mechanics, 832. pp. 409-437.
- Mukherjee, NK and Shrira, VI (2017) Intrinsic flame instabilities in combustors: Analytic description of a 1-D resonator model. Combustion and Flame, 185. 188 -209.
- Nieves, MJ (2017) Asymptotic analysis of solutions to transmission problems in solids with many inclusions. SIAM Journal on Applied Mathematics, 77 (4). 1417 - 1443.
- Prikazchikov, D, Kaplunov, J and Prikazchikova, L (2017) Dispersion of elastic waves in a strongly inhomogeneous three-layered plate. International Journal of Solids and Structures, 113/14. pp. 169-179.
- Rogerson, GA and Murphy, JG (2017) Modelling slight compressibility for hyperelastic anisotropic materials. Journal of Elasticity, 131 (2). pp. 171-181.
- Shrira, VI, Quinn, BE and Toledo, Y (2017) Explicit wave action conservation for water waves on vertically sheared flows. Ocean Modelling, 112. pp. 33-47.
- Althobaiti, S and Prikazchikov, D (2016) Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation. Proceedings of National Academy of Sciences of Armenia, 69 (1). pp. 16-24.
- Andrianov, I, Danishevskyy, V, Topol, H and Rogerson, G (2016) Propagation of Floquet - Bloch shear waves in viscoelastic composites: analysis and comparison of interface/interphase models for imperfect bonding. Acta Mechanica, 228 (3). pp. 1177-1196.
- Chapman, CJ and Sorokin, SV (2016) A class of reduced-order models in the theory of waves and stability. Proceedings of the Royal Society A - Mathematical Physical and Engineering Sciences, 472 (2186)
- Chebakov, R, Kaplunov, J and Rogerson, GA (2016) Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects. Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, 472 (2186).
- Chen, Q, Kaleshi, D, Fan, Z and Armour, S (2016) Impact of Smart Metering Data Aggregation on Distribution System State Estimation. IEEE Transactions On Industrial Informatics, 12 (4). 1426 - 1437.
- Cheng, J (2016) Spectral density of Markov switching models: Derivation, simulation studies and application. Model Assisted Statistics and Applications.
- Cheng, J (2016) A Transitional Markov Switching Autoregressive Model. Communications in Statistics - Theory and Methods, 45 (10). pp. 2785-2800.
- Cheng, J, Ruijun, B and Hadri, K (2016) Nonlinearity and Endogeneity in Continuous-Time Regime-Switching Diffusion Models for Market Volatility. Studies in Nonlinear Dynamics and Econometrics.
- Destrade, M, Fu, Y and Nobili, A (2016) Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2193). 20160410 -?.
- Evkin, A, Kolesnikov, M and Prikazchikov, D (2016) Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution. Mathematics and Mechanics of Solids, 22 (6). pp. 1425-1437.
- Fu, Y, Liu, JL and Francisco, GS (2016) Localized bulging in an inflated cylindrical tube of arbitrary thickness - the effect of bending stiffness. Journal of the Mechanics and Physics of Solids, 90. pp. 45-60.
- Geng, YN, Huang, JX and Fu, YB (2016) Shape bifurcation of a pressurized ellipsoidal balloon. International Journal of Engineering Science, 101. pp. 115-125.
- Kaplunov, J, Manevitch, LI and Smirnov, VV (2016) Vibrations of an elastic cylindrical shell near the lowest cut-off frequency. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2189).
- Kaplunov, J and Nobili, A (2016) Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies. Mathematical Methods in the Applied Sciences, 40 (9). pp. 3381-3392.
- Kaplunov, J, Prikazchikov, D and Rogerson, GA (2016) Edge bending wave on a thin elastic plate resting on a Winkler foundation. Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences, 472 (2190).
- Osborne, AD and Pope, NV (2016) Einstein's Lost Legacy: a Critical Review of Contemporary Physics and Cosmology. Amazon/CreateSpace Independent Publishing Platform, ? - ? (260).
- Popova, T and Rogerson, GA (2016) On the problem of a thin rigid inclusion embedded in a Maxwell material. Zeitschrift fur angewandte Mathematik und Physik, 67 (105).
- Rogerson, GA, Andrianov, IV, Danishevskyy, VV and Topol, H (2016) Propagation of Floquet–Bloch shear waves in viscoelastic composites: analysis and comparison of interface/interphase models for imperfect bonding. Acta Mechanica. pp. 1-20.
- Sheremet, A, Gravois, U and Shrira, VI (2016) Observations of meteotsunami on the Louisiana shelf: a lone soliton with a soliton pack. Natural Hazards, 84 (S2). pp. 471-492.
- Truman, PJ (2016) Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions. Communications in Algebra, 44 (3). 1119 - 1130.
- Truman, PJ (2016) Hopf-Galois module structure of tame Cp×Cp extensions. Journal de Theorie des Nombres de Bordeaux, 28 (2). 557 - 582.