Mathematical theories underpinning different classes of phenomena possess a universal character, with the same mathematical equations appearing to govern phenomena of different nature. The Mathematics of Complex and Nonlinear Phenomena can therefore be seen as the seed for cross-fertilisation between different research areas and disciplines.
Complexity and nonlinearity are often concomitant features of real-world phenomena that are commonly associated to the notion of disorder and chaos.
Unexpectedly, disordered structures and chaotic behaviours observed from fluid dynamics, classical and quantum physics to biological systems, economic and social sciences can be related, under suitable conditions, to the emergence of beautiful ordered and stable structures, as well as coherent, cooperative or cyclic behaviours.
The formation of tsunamis and rogue waves, laser pulses, turbulence of accretion disks around black holes, phase transitions from ordered to disordered states of matter are just some examples where disorder/chaos and order/coherence arise as two sides of the same coin.
Most amazingly, mathematical theories underpinning such different classes of phenomena turn out to possess a universal character so that the same mathematical equations appear to govern phenomena of (seemingly) different nature. Hence, the Mathematics of Complex and Nonlinear Phenomena (MCNP) can be seen naturally as the seed for cross-fertilisation between different research areas and disciplines.
Northumbria's MCNP Research Group conducts interdisciplinary research aiming at impacting on challenges posed by a fast-changing world. It is engaged in ground-breaking research in the hottest areas of modern Mathematics, Physics, Biology and other sciences, including multiple international collaborations with other leading experts.
MCNP research activity focuses mainly on the advancement of mathematical methods for the extensive study of nonlinear partial differential equations and dynamical systems. This ranges from their classification to the development of analytical and numerical techniques to calculate or extract qualitative and quantitative information on their solutions, e.g. asymptotic methods, multiscale analysis, nonlinear stability analysis, bifurcation theory and methods of integrable systems.
The findings of the MCNP research group are concerned with the study of mechanisms for the formation and propagation of nonlinear classical and quantum waves, coherent and localised structures, dynamic emergence of instabilities and singularities under different regimes of dispersion and dissipation, diffraction, interference, delays, phase transitions, classical and quantum chaos, geometric structures associated to differential equations and Riemann surfaces.
Applications that are currently under investigation include the solutions of models for ferromagnetic nanostructures, topological insulators, climate components, magnetohydrodynamics, biological phenomena as cyclic rhythms in glucose regulation, liquid crystals and complex networks.
The MCNP research group has successfully received funding from EPSRC, Leverhulme Trust, London Mathematical Society.
|Staff||Research fellows||Research students|
|Prof Gennady El||Dr Costanza Benassi||Adam Bridgewater|
|Dr Arseni Goussev||Dr Thibault Congy||Marta dell'Atti|
|Dr Benoit Huard||David Graham|
|Dr Oleg Kirillov||Joris Labarbe|
|Dr Yiping Ma||Giacomo Roberti|
|Dr Antonio Moro||Marzia Romano|
|Dr Matteo Sommacal||Oleg Senkevich|
|Dr Costanza Benassi|
|Dr Thibault Congy|
Personal page: https://tcongy.github.io/
|Prof Gennady El|
Funding: EPSRC (2017-2010, Grant No. EP/R00515X/1); Dstl (2017-2020, Contract No DSTLX-1000116851); LMS Research in Pairs Grants (2014, 2015, 2017, 2018), the Royal Society International Exchanges Scheme (2014-2016).
Full details in the Dispersive Hydrodynamics page.
|Dr Arseni Goussev|
Personal page: https://sites.google.com/site/aogscifi
|Dr Benoit Huard|
|Dr Yiping Ma|
|Dr Antonio Moro|
Nonlinear Conservation laws and applications
For more details click here.
|Dr Matteo Sommacal|
Adam Bridgewater (October 2015-December 2018). Principal supervisor B. Huard.
Mathematical description of oscillatory regimes in the glucose-insulin regulation
Marta dell'Atti. Principal supervisor A. Moro.
David Graham. Principal supervisor A. Moro.
Joris Labarbe (October 2018- ). Principal supervisor O. Kirillov.
Giacomo Roberti (October 2018- ). Principal supervisor G. El.
Analysis and control of large-amplitude fluctuations of incoherent optical field in fibre lasers: integrable turbulence framework
Marzia Romano (to be submitted, December 2018-March 2019). Principal supervisor M. Sommacal.
The 3-wave resonant interaction model: spectra and instabilities of plane waves
Oleg Senkevich. Principal supervisor A. Moro.
David Snee. Principal supervisor Y. Ma.
Nonlinear edge waves in mechanical topological insulators
Maximilien Barbier (February 2017). Principal supervisor A. Goussev.
Dynamics of matter wave packets in the presence of time-dependent absorption
Francesco Giglio (February 2018). Principal supervisor A. Moro.
Wave dynamics and catastrophes in thermodynamic phase diagrams
Emrah Haspolat (February 2018). Principal supervisor B. Huard.
Mathematical modelling of Arabidopsis flowering time gene regulatory network
The group runs the weekly Mathematics and Mathematical Physics series of research seminars and colloquia. Full details can be found at the seminars page.
Kraych, Adrien, Suret, Pierre, El, Gennady and Randoux, Stephane (2019) Nonlinear evolution of the locally induced modulational instability in fiber optics. Physical Review Letters, 122. pp. 054101. ISSN 0031-9007
Haspolat, Emrah, Huard, Benoit and Angelova, Maia (2019) Deterministic and stochastic models of Arabidopsis Thaliana flowering. Bulletin of Mathematical Biology, 81 (1). pp. 277-311. ISSN 0092-82402018
Congy, Thibault, El, Gennady, Hoefer, Mark and Shearer, Michael (2018) Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Studies in Applied Mathematics. ISSN 0022-2526 (In Press)
Demontis, Francesco, Lombardo, Sara, Sommacal, Matteo, van der Mee, Cornelis and Vargiu, F. (2018) Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation. Communications in Nonlinear Science and Numerical Simulation, 64. pp. 35-65. ISSN 1007-5704
De Matteis, Giovanni, Giglio, Francesco and Moro, Antonio (2018) Exact equations of state for nematics. Annals of Physics, 396. pp. 386-396. ISSN 0003-4916
Randoux, Stéphane, Suret, Pierre, Chabchoub, Amin, Kibler, Bertrand and El, Gennady (2018) Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments. Physical Review E, 98 (2). 022219. ISSN 2470-0045
Degasperis, Antonio, Lombardo, Sara and Sommacal, Matteo (2018) Integrability and linear stability of nonlinear waves. Journal of Nonlinear Science, 28 (4). pp. 1251-1291. ISSN 0938-8974
Goussev, Arseni, Reck, Phillipp, Moser, Florian, Moro, Antonio, Gorini, Cosimo and Richter, Klaus (2018) Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking. Physical Review A (PRA), 98. 013620. ISSN 2469-9926
Demontis, Francesco, Ortenzi, Giovanni and Sommacal, Matteo (2018) Heisenberg ferromagnetism as an evolution of a spherical indicatrix: localized solutions and elliptic dispersionless reduction. Electronic Journal of Differential Equations, 2018 (106). pp. 1-34. ISSN 1072-6691
Maiden, Michelle D., Anderson, Dalton V., Franco, Nevil A., El, Gennady and Hoefer, Mark A. (2018) Solitonic Dispersive Hydrodynamics: Theory and Observation. Physical Review Letters, 120 (14). ISSN 0031-9007
Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2018) The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. II. IST and closed-form soliton solutions. Ricerche di Matematica. ISSN 0035-5038 (In Press)
Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2018) The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory. Ricerche di Matematica. ISSN 0035-5038 (In Press)
Sprenger, Patrick, Hoefer, Mark and El, Gennady (2018) Hydrodynamic optical soliton tunneling. Physical Review E, 97 (3). ISSN 2470-0045
Reck, Phillipp, Gorini, Cosimo, Goussev, Arseni, Krueckl, Viktor, Fink, Mathias and Richter, Klaus (2018) Towards a quantum time mirror for nonrelativistic wave packets. New Journal of Physics, 20. 033013. ISSN 1367-2630
El, Gennady, Nguyen, Lu Trong Nguyen and Smyth, Noel (2018) Dispersive shock waves in systems with nonlocal dispersion of Benjamin–Ono type. Nonlinearity, 31 (4). pp. 1392-1416. ISSN 0951-7715
El, Gennady, Hoefer, Mark A. and Shearer, Michael (2018) Stationary Expansion Shocks for a Regularized Boussinesq System. Studies in Applied Mathematics, 140 (1). pp. 27-47. ISSN 0022-25262017
Suret, Pierre, El, Gennady, Onorato, Miguel and Randoux, Stéphane (2017) Rogue waves in integrable turbulence: semi-classical theory and fast measurements. In: Nonlinear Guided Wave Optics: A testbed for extreme waves. IOP Publishing, 12-1-12-32. ISBN 978-0-7503-1460-2
Gaididei, Yuri, Goussev, Arseni, Kravchuk, Volodymyr, Pylypovskyi, Oleksandr, Robbins, Jonathan, Sheka, Denis, Slastikov, Valeriy and Vasylkevych, Sergiy (2017) Magnetization in narrow ribbons: curvature effects. Journal of Physics A: Mathematical and Theoretical, 50. p. 385401. ISSN 1751-8113
Hoefer, Mark, El, Gennady and Kamchatnov, Anatoly (2017) Oblique Spatial Dispersive Shock Waves in Nonlinear Schrödinger Flows. SIAM Journal on Applied Mathematics, 77 (4). pp. 1352-1374. ISSN 0036-1399
Tikan, Alexey, Billet, Cyril, El, Gennady, Tovbis, Alexander, Bertola, Marco, Sylvestre, Thibaut, Gustave, Francois, Randoux, Stephane, Genty, Goëry, Suret, Pierre and Dudley, John M. (2017) Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation. Physical Review Letters, 119 (3). 033901. ISSN 0031-9007
Goussev, Arseni (2017) Rotating Gaussian wave packets in weak external potentials. Physical Review A (PRA), 96. 013617. ISSN 1050-2947
Randoux, Stéphane, Gustave, François, Suret, Pierre and El, Gennady (2017) Optical Random Riemann Waves in Integrable Turbulence. Physical Review Letters, 118 (23). ISSN 0031-9007
Reck, Phillipp, Gorini, Cosimo, Goussev, Arseni, Krueckl, Viktor, Fink, Mathias and Richter, Klaus (2017) Dirac quantum time mirror. Physical Review B, 95 (16). p. 165421. ISSN 2469-9950
Huard, Benoit, Bridgewater, Adam and Angelova, Maia (2017) Mathematical investigation of diabetically impaired ultradian oscillations in the glucose-insulin regulation. Journal of Theoretical Biology, 418. pp. 66-76. ISSN 0022-5193
El, Gennady, Hoefer, Mark and Shearer, Michael (2017) Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws. SIAM Review, 59 (1). pp. 3-61. ISSN 0036-1445
Chesnokov, A. A., El, Gennady, Gavrilyuk, S. L. and Pavlov, M. V. (2017) Stability Of Shear Shallow Water Flows with Free Surface. SIAM Journal on Applied Mathematics, 77 (3). pp. 1068-1087. ISSN 0036-13992016
El, Gennady and Hoefer, Mark (2016) Dispersive shock waves and modulation theory. Physica D: Nonlinear Phenomena, 333. pp. 11-65. ISSN 0167-2789
Giglio, Francesco, Landolfi, Giulio and Moro, Antonio (2016) Integrable extended van der Waals model. Physica D: Nonlinear Phenomena, 333. pp. 293-300. ISSN 0167-2789
Tovbis, Alexander and El, Gennady (2016) Semiclassical limit of the focusing NLS: Whitham equations and the Riemann–Hilbert Problem approach. Physica D: Nonlinear Phenomena, 333. pp. 171-184. ISSN 0167-2789
Bertola, Marco, El, Gennady and Tovbis, Alexander (2016) Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2194). p. 20160340. ISSN 1364-5021
Onorato, Miguel, Proment, Davide, El, Gennady, Randoux, Stephane and Suret, Pierre (2016) On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type. Physics Letters A, 380 (39). pp. 3173-3177. ISSN 0375-9601
El, Gennady, Khamis, Eduardo and Tovbis, Alex (2016) Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves. Nonlinearity, 29 (9). pp. 2798-2836. ISSN 0951-7715
Randoux, Stéphane, Suret, Pierre and El, Gennady (2016) Inverse scattering transform analysis of rogue waves using local periodization procedure. Scientific Reports, 6 (1). p. 29238. ISSN 2045-2322
Goussev, Arseni, Jalabert, Rodolfo, Pastawski, Horacio and Wisniacki, Diego (2016) Loschmidt echo and time reversal in complex systems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374 (2069). p. 20150383. ISSN 1364-503X
El, Gennady, Hoefer, Mark and Shearer, Michael (2016) Expansion shock waves in regularized shallow-water theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2189). p. 20160141. ISSN 1364-5021
Goussev, Arseni, Robbins, Jonathan, Slastikov, Valeriy and Tretiakov, Oleg (2016) Dzyaloshinskii-Moriya domain walls in magnetic nanotubes. Physical Review B (PRB), 93 (5). 054418. ISSN 1098-01212015
Barbier, Maximilien, Beau, Mathieu and Goussev, Arseni (2015) Comparison between two models of absorption of matter waves by a thin time-dependent barrier. Physical Review A (PRA), 92 (053630). ISSN 1050-2947
Huard, Benoit, Easton, Jonathan and Angelova, Maia (2015) Investigation of stability in a two-delay model of the ultradian oscillations in glucose-insulin regulation. Communications in Nonlinear Science and Numerical Simulation, 26 (1-3). pp. 211-222. ISSN 1007-5704
Barra, Adriano and Moro, Antonio (2015) Exact solution of the van der Waals model in the critical region. Annals of Physics, 359. pp. 290-299. ISSN 0003-4916
Arsie, Alessandro, Lorenzoni, Paolo and Moro, Antonio (2015) Integrable viscous conservation laws. Nonlinearity, 28 (6). pp. 1859-1895. ISSN 0951-7715
Dubrovin, Boris, Grava, Tamara, Klein, Christian and Moro, Antonio (2015) On critical behaviour in systems of Hamiltonian partial differential equations. Journal of Nonlinear Science, 25 (3). pp. 631-707. ISSN 0938-8974
Goussev, Arseni (2015) Manipulating quantum wave packets via time-dependent absorption. Physical Review A (PRA), 91 (4). 043638. ISSN 1050-29472014
Barra, Adriano, Guerra, Francesco, Di Lorenzo, Andrea and Moro, Antonio (2014) On quantum and relativistic mechanical analogues in mean field spin models. Proceedings of the Royal Society A, 470 (2172). ISSN 1471-2946
Arsie, Alessandro, Lorenzoni, Paolo and Moro, Antonio (2014) On integrable conservation laws. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (201401). ISSN 1471-2946
Moro, Antonio (2014) Shock dynamics of phase diagrams. Annals of Physics, 343. pp. 49-60. ISSN 0003-4916
Goussev, Arseni, Robbins, Jonathan and Slastikov, Valeriy (2014) Domain wall motion in thin ferromagnetic nanotubes: Analytic results. Europhysics Letters, 105 (6). p. 67006. ISSN 0295-5075
Dubertrand, Remy and Goussev, Arseni (2014) Origin of the exponential decay of the Loschmidt echo in integrable systems. Physical Review E, 89. 022915. ISSN 1539-3755
Moro, Antonio and Trillo, Stefano (2014) Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation. Physical Review E (PRE), 89 (2). ISSN 1550-2376
de Nittis, Giuseppe, Lorenzoni, Paolo and Moro, Antonio (2014) Integrable multi-phase thermodynamic systems and Tsallis' composition rule. Journal of Physics: Conference Series, 482 (1). 012009. ISSN 1742-6588
3rd IMA Conference on Nonlinearity and Coherent Structures, 10-12 July 2019 (Supported by the IMA).
Integrable Systems in Newcastle , 5-6 April 2019 (Supported by the LMS).
Mathematics of Biological Rhythms, 3-5 December 2018 (Supported by the Academy of Medical Sciences).
- London Mathematical Society Northern Regional Meeting, 23-25 May 2018 (Supported by the LMS).