A Boussinesq fluid inside a stably thermally stratified square container whose walls are inclined ${45}^{\circ }$ with respect to gravity, two opposite kept at constant temperatures and the other insulated is nearly isothermal in regions above below horizontal diagonal. The flow concentrated wall boundary layers shear layer centred about equilibrium maintained by balance between dissipation lay...

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynami...

We describe the formation of spatial structures generated by diffusive instabilities in bistable systems. The coupling between the different spatial modes emanating from the two homogeneous steady states can then give rise to self-parametric instabilities favoring the occurrence of resonant rhombic or quasiperiodic structures such as superlattices or quasicrystalline patterns.