It is often impossible to write down exact mathematical expressions to perfectly describe extremely complex natural systems such as the collective behaviour of a colony of ants, gravitational waves generated by orbiting black holes, or the flow of air over an aircraft’s wing. Asymptotic approximation theory can accurately predict how these complicated systems will change and evolve, even when they are far too complicated to solve exactly. Dr Christopher Lustri is an expert in developing new asymptotic approximation methods that capture important behaviour which is hidden from widely-used classical approximation techniques. Using these new methods, he has resolved open mathematical problems arising in practical scientific settings, such as explaining the shape of waves that form behind submerged obstacles, or the energy loss experienced by pulses in laboratory particle chains. He discovered that complex discrete systems contain important ‘tipping points’ that were previously unknown. If subtle changes are made to how the system is set up when the system is near one of these points, its behaviour can change dramatically. Dr Lustri’s methods make it possible to accurately capture how systems behave when they are near these tipping points.
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