Measuring complexity through average symmetry

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures

Symmetry of coherent vortices in plane couette flow

A numerical continuation method is carried out in a homotopy space connecting two different flows, the Plane Couette Flow (PCF) and the Laterally Heated Flow in a vertical slot (LHF). This numerical continuation method enables us to obtain an exact steady solution in PCF. The new solution has the shape of hairpin vortices (HVS: hairpin vortex solution), which is observed ubiquitously in turbulent shear flows.

Self-assembly of trehalose molecules on a lysozyme surface: the broken glass hypothesis

To help understand how sugar interactions with proteins stabilise biomolecular structures, we compare the three main hypotheses for the phenomenon with the results of long molecular dynamics simulations on lysozyme in aqueous trehalose solution (0.75 M). We show that the water replacement and water entrapment hypotheses need not be mutually exclusive, because the trehalose molecules assemble in distinctive clusters on the surface of the protein. The flexibility of the protein backbone is reduced under the sugar patches supporting earlier findings that link reduced flexibility of the protein with its higher stability. The results explain the apparent contradiction between different experimental and theoretical results for trehalose effects on proteins.