Characterization of thermoconvective instabilities in spatially extended systems

Abstract

Many systems in nature are spactially extended, this means that any structure or pattern that emerges inside them is characterized by finite spatial scales much smaller than the system size. The time evolution or dynamics of these systems may also sustain finite temporal scales or frequencies. Some systems exhibit spatiotemporal modulated patterns or lattice patterns which fit a wave description in terms of an amplitude and a phase that involves the wave number and frequency. Lattice patterns surround our daily lives: ripples over the sand, waves over the oceans, morphogenesis of flowers and shells, crystal growth of snow flakes. In order to understand the genesis of patterns physicists stand close to the onset of the instability which gives rise to a new stable pattern. Depending on the microscopic physics, most patterns break some symmetries of the system at the onset of an instability, as Curie observed long time ago. These are called symmetry breaking instabilities.