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Complexity at Mesoscale

Through three examples we illustrate some of the concepts and ingredients required for pattern formation at mesoscopic scales. Two examples build on microscopic models where mesoscopic patterns emerge from homogeneous ground states driven into instability by external forcing. In contrast, the third example builds on a mesoscopic phenomenological Ginzburg-Landau type model of solid-solid structural phase transitions. Here, mesoscopic textures emerge as a result of competing length scales arising from the constraints of elastic compatibility.