Mathematical modelling and theoretical analysis, in combination with numerical methods, make it possible to investigate and simulate generic problems in the natural and life sciences, and in the financial world. This covers the entire chain of large-scale geophysical problems, right down to microscale or nanoscale processes, with applications in engineering, e.g. optical devices for ICT, flows (and multiphase flows), mechanical systems, biochemical sensors, biology and medicine. Almost all of these problems are characterized by enormous differences in the relevant scales of length or time. Efficient techniques for modelling and simulating multi-scale problems are therefore essential to further progress in these fields.
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