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Dispersive hydrodynamics has emerged as a unified mathematical framework for the description of multiscale nonlinear wave phenomena in dispersive media, encompassing both dynamic and stochastic aspects of wave propagation. Recent theoretical and experimental developments have opened up new areas for research, with intriguing open issues in both theory and applications. These include the understanding of fundamental regularisation mechanisms of hydrodynamic singularities via the generation of dispersive shock waves (DSWs) and related phenomena. Physical examples of dispersive hydrodynamic phenomena include undular bores on rivers, in the ocean and atmosphere, nonlinear diffraction patterns in optics and quantum fluids, turbulence in fibre lasers and superfluids.
The mathematical programme weaves together research topics on integrable and nonintegrable dispersive partial differential equations, hyperbolic conservation laws, convex and nonconvex dispersive hydrodynamic systems. Numerous physical applications of dispersive hydrodynamics in geophysics, nonlinear optics, superfluids and magnetic materials will be explored. The programme is designed to encourage interactions amongst mathematicians, physicists, and engineers specialising in the analysis of dispersive systems, experiments and numerical simulations. Special emphasis is given to involving young researchers and to diversity among the participants.
The programme is organized around four overlapping themes:
Left: Solitary wave transmission through a dispersive shock wave in a viscous fluid conduit, Boulder, CO, USA © Mark Hoefer, 2016.
Right: Undular bore on the Severn river near Gloucester, UK © Mark Humpage, 2007.
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INI is a creative collaborative space which is occupied by up to fifty-five mathematical scientists at any one time (and many more when there is a workshop). Some of them may not have met before and others may not realise the relevance of other research to their own work.
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“A world famous place for research in the mathematical sciences with a reputation for efficient management and a warm welcome for visitors”
The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
INI has a vital national role, building on many strengths that already exist in UK universities, aiming to generate a new vitality through stimulating and nurturing research throughout the country.During each scientific programme new collaborations are made and ideas and expertise are exchanged and catalysed through lectures, seminars and informal interaction, which the INI building has been designed specifically to encourage.
For INI’s knowledge exchange arm, please see the Newton Gateway to Mathematics.
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