Dr Mark Jones
Faculties, departments and locations
- Faculty of Engineering, Computing and the Environment
- Department of Computer Science
- School of Computer Science and Mathematics
- Penrhyn Road
Senior lecturer
- Email:
- [email protected]
About
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.
Qualifications
- BSc
- PhD
Domains
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.
Publications
On two types of stability of solutions to a pair of damped coupled nonlinear evolution equations
Jones, Mark, 2024, Advances in Pure Mathematics (14), 5, pp 354-366
Double degeneracy in the immiscible Wilton ripple phenomenon : a three perturbation parameter problem in bifurcation theory
Jones, M.C.W., 2021, International Journal of Bifurcation and Chaos (31), 13, pp 2150190
Conservation laws for a non-linear system describing the propagation of "triadic" waves
Jones, Mark and Hunter, Gordon, 2019, Proceedings of the Institute of Acoustics (41), 1, pp 137-145
Resonant interfacial capillary-gravity waves in the presence of damping effects
Jones, M.C.W., 2018, European Journal of Mechanics - B/Fluids (68), pp 20-29
A singularity in resonant interfacial fluid flow leading to role reversal in the space time continuum of the evolution equations
Jones, Mark, 2017, Wave Motion (75), pp 77-87
Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary-gravity waves
Jones, M.C.W., 2016, Applied Mathematical Modelling (40), 3, pp 2134-2142
Group equivariant singularity theory in the bifurcation of interfacial Wilton ripples
Jones, Mark, 2015, International Journal of Bifurcation and Chaos (25), 11, pp e1550147
The bifurcation of interfacial capillary-gravity waves under O(2) symmetry
Jones, M., 2011, Communications on Pure and Applied Analysis (10), 4, pp 1183-1204
On 1:2 resonant waves which arise between two stratified fluids of finite vertical extent in the presence of mean flow effects
Jones, M.C.W., 2010, European Journal of Mechanics B/Fluids (29), 5, pp 395-402
Internal waves caused by the interaction of three harmonics under no restoring forces
Jones, M.C.W., 2007, Applied Mathematics Letters (20), 7, pp 723-728
On the evolution and stability of interfacial ripples on and off the critical frequency
Jones, Mark, 2001, Geophysical and Astrophysical Fluid Dynamics (93), 3/4, pp 143-172
On nonlinearly detuned third harmonic ripples between two stratified fluids
Jones, Mark, 2001, Quarterly of Applied Mathematics (59), 2, pp 241-268
A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua
Jones, Mark, 2000, Zeitschrift fuer Angewandte Mathematik und Physik (51), 5, pp 651-673
A nonlinear multiple scales approach to modelling almost third harmonic interfaces
Jones, M., 1999, Zeitschrift für Angewandte Mathematik und Physik (50), 1, pp 47-63
Nonlinear nearly Wilton ripples between two uniform stream flows
Jones, M., 1999, The Quarterly Journal of Mechanics and Applied Mathematics (52), 2, pp 237-252
A new system of equations which predicts the evolution of a wave packet due to a fluid-fluid interaction under a narrow bandwidth assumption
Jones, M., 1997, Fluid Dynamics Research (21), 6, pp 455-475
Group invariances, unfoldings and the bifurcation of capillary-gravity waves
Jones, M., 1997, International Journal of Bifurcation and Chaos (ijbc) (7), 6, pp 1243-1266
Nonlinear ripples of Kelvin-Helmholtz type which arise from an interfacial mode interaction
Jones, M.C.W., 1997, Journal of Fluid Mechanics (341), pp 295-315
Group invariances and second and third harmonic resonant capillary-gravity waves
Jones, M., 1996, (32), 10, pp 59-90
Evolution equations and stability results for finite-depth Wilton ripples
Jones, Mark, 1996, International Journal of Non-Linear Mechanics (31), 1, pp 41-58
On the stability of a wavetrain caused by interacting wave modes
Jones, M., 1995, Rocky Mountain Journal of Mathematics (25), 1, pp 299-313
Evolution equations which model the ripples arising from an adjacent mode interaction
Jones, M.C.W., 1995, Dynamics and Stability of Systems (10), pp 163-178
Further results on the stability of symmetric and asymmetric resonant capillary-gravity waves
Jones, M.C.W., 1994, Japan Journal of Industrial and Applied Mathematics (11), 3, pp 465-483
On the stability of finite-depth capillary-gravity waves by means of the fourth order evolution equation
Jones, M., 1994, Canadian Applied Mathematics Quarterly (2), 3, pp 325-348
On coupled differential equations which model the evolution of interacting capillary-gravity wave modes and related questions of stability
Jones, M.C.W., 1993, IMA Journal of Applied Mathematics (50), 1, pp 13-28
Nonlinear stability of resonant capillary-gravity waves
Jones, M., 1992, Wave Motion (15), 3, pp 267-283
On the stability of a third harmonic resonant wavetrain
Jones, M. C. W., 1992, Stability and Applied Analysis of Continuous Media (2), pp 323-338
A non-uniqueness theorem in the theory of Voronoi sets
Jones, M., 1991, International Journal of Mathematics and Mathematical Sciences (14), 4, pp 817-820
A public key cryptosystem as hard as a factorisation
Jones, M. Christopher W., 1990, Irish Mathematical Society Bulletin (24), pp 59-66
Mathematics for an undergraduate course in artificial intelligence : aspirational perspectives and initial lessons learned
Hunter, Gordon, Bosy, Michal, Jones, Mark and Wyman, Christopher(2024). In: CETL-MSOR 2024, 29-30 Aug 2024 :Limerick, Ireland