Rheology of non-Brownian amorphous materials:
There is growing evidence that flows of dense particle assemblies (granular matter, emulsions and suspensions) display critical behavior at the jamming transition, where the flow stops. As the packing fraction of particles increases, particle motion becomes more collective and a diverging effective viscosity is observed. A set of experiments have shown that two constitutive relations control the rheology, whose scaling properties are determined by the distance to the threshold. No accepted microscopic description exists. Developing predictive theories leading to new technological applications of these materials is of fundamental importance, since they represent the second-most manipulated materials in industry. Controlling the rheology can help avoid the problem of clogging in multiphase flows, enhance concrete mixing or fight vaso-occlusive crisis among others.
Elasticity of disordered media:
Gels of semi-flexible polymers, network glasses made of low valence elements and softly compressed ellipses are examples of floppy materials. These systems exhibit collective motions with almost no restoring force. The elasticity of floppy systems play an important role in many complex systems, from the understanding of dense suspensions under flow to the stiffening property of biological tissues. Obtaining a microscopic theory will be very helpful in designing new materials and bio-materials with controlled and tunable elastic properties.
Wave turbulence
Turbulent-like behavior seem to be ubiquitous in nature. Different continuous media subjected to an external source of energy show similar transport properties, but little is known about the general microscopic mechanisms which control the out of equilibrium statistics. In addition, the complexity varies significantly among different systems. Hydrodynamic turbulence is the paradigm of unsolved problems in classical physics and probably represents the hardest case. Somewhat simpler are systems of weakly non-linear dispersive waves,whose long-time statistical properties can be described by the theory of weak turbulence. In practice, however, the range of validity of this theory has shown to be very narrow and new approaches need to be developed. In many cases, the narrow range of validity of the theory is due to the appearance of coherent structures, which breakdown the weak turbulence scenario. These fully non linear structures (solitons, pulses, condensates, etc..) interact with the random wave background, producing a rich and complex dynamics. Understanding such statistical properties has important applications, from predictions of wave amplitudes and rogue wave formation in oceanography, to the possible suppression of shock wave formation by turbulent mixing, and the generation of supercontinua sources in optics.
(a) Wave turbulence in elastic plates. (b) Wave condensation of optical waves, Fleischer group.