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I was educated at University College London where I graduated with a Bachelor of Science in Mathematics. I then moved to the University of Bath where I wrote my doctoral thesis entitled 'The Bifurcation and Secondary Bifurcation of Capillary-Gravity waves in the presence of symmetry' under the supervision of Professor JF Toland FRS. I then moved to the Queens University of Belfast and subsequently joined Kingston in 2000.
My research is mostly concerned with the mathematical study of water waves. My early research work was quite pure mathematical in nature, consisting of a study of the waves which may bifurcate from the line of trivial solutions when the solution space of the underlying linearized model equation is two dimensional. I have returned to aspect of this problem throughout my career, generalising it to interfacial waves.
The other strand of my research involves a study of the stability of these waves. I have employed the method of multiple scales to show how they may be modelled by a pair of coupled nonlinear partial differential equations for the wave amplitudes. These equations can then be used to determine the stability properties of the waves.
Jones, Mark and Hunter, Gordon (2019) Conservation laws for a non-linear system describing the propagation of "triadic" waves. Proceedings of the Institute of Acoustics, 41(1), pp. 137-145. ISSN (print) 1478-6095
Jones, MCW (2018) Double degeneracy in the immiscible Wilton ripple phenomenon : a three perturbation parameter problem in bifurcation theory. International Journal of Bifurcation and Chaos, ISSN (print) 0218-1274 (In Press)
Jones, M.C.W. (2018) Resonant interfacial capillary-gravity waves in the presence of damping effects. European Journal of Mechanics - B/Fluids, 68, pp. 20-29. ISSN (print) 0997-7546
Jones, Mark (2017) A singularity in resonant interfacial fluid flow leading to role reversal in the space time continuum of the evolution equations. Wave Motion, 75, pp. 77-87. ISSN (print) 0165-2125
Jones, M.C.W. (2016) Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary-gravity waves. Applied Mathematical Modelling, 40(3), pp. 2134-2142. ISSN (print) 0307-904X
Jones, Mark (2015) Group equivariant singularity theory in the bifurcation of interfacial Wilton ripples. International Journal of Bifurcation and Chaos, 25(11), e1550147. ISSN (print) 0218-1274
Jones, M. (2011) The bifurcation of interfacial capillary-gravity waves under O(2) symmetry. Communications on Pure and Applied Analysis, 10(4), pp. 1183-1204.
Jones, M.C.W. (2010) On 1:2 resonant waves which arise between two stratified fluids of finite vertical extent in the presence of mean flow effects. European Journal of Mechanics B/Fluids, 29(5), pp. 395-402. ISSN (print) 0997-7546
Jones, M.C.W. (2007) Internal waves caused by the interaction of three harmonics under no restoring forces. Applied Mathematics Letters, 20(7), pp. 723-728. ISSN (print) 0893-9659
Jones, Mark (2001) On the evolution and stability of interfacial ripples on and off the critical frequency. Geophysical and Astrophysical Fluid Dynamics, 93(3/4), pp. 143-172. ISSN (print) 0309-1929
Jones, Mark (2001) On nonlinearly detuned third harmonic ripples between two stratified fluids. Quarterly of Applied Mathematics, 59(2), pp. 241-268. ISSN (print) 0033-569X
Jones, Mark (2000) A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua. Zeitschrift fuer Angewandte Mathematik und Physik, 51(5), pp. 651-673. ISSN (print) 0044-2275
Jones, M. (1999) A nonlinear multiple scales approach to modelling almost third harmonic interfaces. Zeitschrift für Angewandte Mathematik und Physik, 50(1), pp. 47-63. ISSN (print) 0044-2275
Jones, M. (1999) Nonlinear nearly Wilton ripples between two uniform stream flows. The Quarterly Journal of Mechanics and Applied Mathematics, 52(2), pp. 237-252. ISSN (print) 1464-3855
Jones, M. (1997) A new system of equations which predicts the evolution of a wave packet due to a fluid-fluid interaction under a narrow bandwidth assumption. Fluid Dynamics Research, 21(6), pp. 455-475. ISSN (print) 0169-5983
Jones, M. (1997) Group invariances, unfoldings and the bifurcation of capillary-gravity waves. International Journal of Bifurcation and Chaos (ijbc), 7(6), pp. 1243-1266. ISSN (print) 0218-1274
Jones, M.C.W. (1997) Nonlinear ripples of Kelvin-Helmholtz type which arise from an interfacial mode interaction. Journal of Fluid Mechanics, 341, pp. 295-315. ISSN (print) 0022-1120
Jones, M. (1996) Group invariances and second and third harmonic resonant capillary-gravity waves. Computers & Mathematics with Applications, 32(10), pp. 59-90. ISSN (print) 0898-1221
Jones, Mark (1996) Evolution equations and stability results for finite-depth Wilton ripples. International Journal of Non-Linear Mechanics, 31(1), pp. 41-58. ISSN (print) 0020-7462
Jones, M. (1995) On the stability of a wavetrain caused by interacting wave modes. Rocky Mountain Journal of Mathematics, 25(1), pp. 299-313. ISSN (print) 0035-7596
Jones, M.C.W. (1995) Evolution equations which model the ripples arising from an adjacent mode interaction. Dynamics and Stability of Systems, 10, pp. 163-178. ISSN (print) 1468-9367
Jones, M.C.W. (1994) Further results on the stability of symmetric and asymmetric resonant capillary-gravity waves. Japan Journal of Industrial and Applied Mathematics, 11(3), pp. 465-483. ISSN (print) 0916-7005
Jones, M. (1994) On the stability of finite-depth capillary-gravity waves by means of the fourth order evolution equation. Canadian Applied Mathematics Quarterly, 2(3), pp. 325-348. ISSN (print) 1073-1849
Jones, M.C.W. (1993) On coupled differential equations which model the evolution of interacting capillary-gravity wave modes and related questions of stability. IMA Journal of Applied Mathematics, 50(1), pp. 13-28. ISSN (print) 0272-4960
Jones, M. (1992) Nonlinear stability of resonant capillary-gravity waves. Wave Motion, 15(3), pp. 267-283. ISSN (print) 0165-2125
Jones, M. C. W. (1992) On the stability of a third harmonic resonant wavetrain. Stability and Applied Analysis of Continuous Media, 2, pp. 323-338. ISSN (print) 1120-4222
Jones, M. (1991) A non-uniqueness theorem in the theory of Voronoi sets. International Journal of Mathematics and Mathematical Sciences, 14(4), pp. 817-820. ISSN (print) 0161-1712
Jones, M. Christopher W. (1990) A public key cryptosystem as hard as a factorisation. Irish Mathematical Society Bulletin, 24, pp. 59-66. ISSN (print) 0790-1690