- complex systems modelling
- linear and nonlinear hydrodynamic stability
- low-dimensional complexity in interfacial fluid mechanics, dissipative solitons and nonlinear waves in free-surface thin-film flows, coherent structures theory for dissipative solitons
- perturbation methods, discrete and essential spectra of differential operators in unbounded domains, bifurcation and dynamical systems theory, centre/invariant manifold projection, stochastic processes, numerical analysis
- micro-/multi-scale fluid mechanics, micro-/meso-scopic dynamics of moving contact lines
- chaotic mixing in micro-drops, chemical reactions in chaotic flows
- transport phenomena in advection/diffusion systems, wave-induced transport in multi-phase flow systems
- hydrodynamic effects induced by chemical wave propagation and chaotic chemical dynamics
- wave propagation in spatially distributed excitable media and nerve signal transmission
- Active-dissipative nonlinear spatially extended media: Complexity, coarse-graining, multiscale analysis and numerical methods.
- Dissipative (low-dimensional) turbulence of soliton gas
- Coherent structures theory for spatially extended media such as the generalized Kuramoto-Sivashinksy
- Mesoscopic hydrodynamics of moving contact lines
- General dynamic density functional theory for classical fluids
- Phase transitions of fluids in nano-confinement
- Pattern formation driven by coupled hydrodynamic and reaction-diffusion instabilities
- "Three-dimensional localized coherent structures of surface turbulence: Model validation with experiments and further computations" with E.A. Demekhin, E.N. Kalaidin and S.Yu. Vlaskin. Article features at PRE Kaleidoscope.
- "Absolute and convective instabilities of a viscous film flowing down a vertical fiber" with C. Duprat, C. Ruyer-Quil and F. Giorgiutti-Dauphine Article features at PRL front cover.
- "Fingering of exothermic reaction-diffusion fronts in Hele-Shaw cells with conducting walls" with J. D' Hernoncourt and A. De Wit
- "Thermocapillary long waves in a liquid film flow. Part 1. Low-dimensional formulation! with C. Ruyer-Quil, B. Scheid, M.G. Velarde and R.Kh. Zeytounian
- Advanced School on "Thin Films of Soft Matter" Udine, Italy, July 18-22, 2005. Co-ordinator with Uwe Thiele. Lecturers: Hsueh-Chia Chang, Jens Eggers, Serafim Kalliadasis, David Quere, Ralf Seeman, Uwe Thiele. My lecture notes: Falling Films Under Complicated Conditions.
- "Dynamics of a Reactive Falling Film" Microgravity Research Center Universite Libre de Bruxelles, Belgium, Sep 5-6, 2005
- "Thin Films in the Presence of Chemical Reactions" Applied Mathematics Seminars for Postgraduate Students, School of Mathematics, University of Birmingham UK, Mar 15, 2006. Lectures slides
- "Recent progress on the moving contact line problem" Programme "Mathematical Modelling and Analysis of Complex Fluids and Active Media in Evolving Domains" Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 2013.
- "Three-dimensional coherent structures of interfacial turbulence" Bristol Centre for Applied Nonlinear Maths, UK, 2007
- ''Three-dimensional wave dynamics in falling liquid films: formation of lattices of interact ing stationary solitary pulses'' Programme ''Pattern Formation in Large Domains '' Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 2005
- ''Self-organization of 3D waves in an active dispersive-dissipative nonlinear medium'' Mechanics Seminar Laboratoire FAST and Laboratoire LIMSI, Universite P. et M. Curie et Paris Sud, France, 2005
Our work is primarily funded by:
- Engineering and Physical Sciences Research Council of the UK (Engineering, Mathematical Sciences and Physics Programmes)
- European Union (FP7-Marie Curie Initial Training Networks and European Research Council)
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