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Anti-diffusive (`negative viscosity') phenomena are the remarkable processes by which up-gradient transport leads to mesoscopic structure formation in many physical and biological systems, including those that are chaotic or turbulent. The formation of layers or staircases – i.e., regular patterns in which steep-gradient layers (transport barriers) are situated between zones of stronger mixing – is a typical outcome of anti-diffusion. This state of inhomogeneous mixing resembles closely that of spontaneous phase separation, familiar from statistical mechanics, and so is contrary to the naively expected limiting case of homogenisation. Layered systems exhibit very different transport properties to those of familiar weakly inhomogeneous systems. Understanding the physics of anti-diffusion and layering is therefore crucial to developing an accurate description of transport in multi-phase and active fluids, metallurgy, magnetically-confined plasmas, oceanographic and atmospheric flows – which determine climate – and stellar interiors. In addition to the physical applications, important fundamental questions remain unanswered concerning an underlying common mathematical foundation for the different physical phenomena. Furthermore, since, mathematically, the anti-diffusion problem in its starkest form is ill-posed, there is considerable interest in how the problem can be regularised, and in the dynamics resulting from different approaches. On the computational side, the efficient and accurate representation of states with two or more highly disparate scales represents a significant challenge. The programme will be extremely broad and interdisciplinary, bringing together researchers in fluid dynamics – particularly geophysical and astrophysical – in plasma physics and in active matter, as well as experts on the mathematical analysis and computational aspects of anti-diffusive phenomena.
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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.
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