Our research is of theoretical and computational nature, and focuses on nonequilibrium phenomena in extended systems, and in applications of Statistical Mechanics to problems in Fluid Mechanics, Soft Matter or Biomaterials. We aim at understanding the mechanisms underlying the formation and evolution of spatio temporal patterns in systems driven outside of thermodynamic equilibrium, including the transition to spatio temporal chaos in extended systems. We focus on prototypical systems and related experimental configurations in which to address fundamental issues of nonlinear phenomena, as well as on configurations of that are of interest because of their applications.
The study of of liquid crystal based suspensions is motivated by applications in materials science as well as in biological systems. At a fundamental level, and in contrast with normal suspending fluids, nematic order in a liquid crystalline matrix leads to long range elastic interactions either among colloidal particles or with bounding walls, resulting in a variety of unexpected phenomena. Furthermore, long range order in the matrix is distorted by the suspended particles, resulting in unavoidable topological defects that must move with the particles. On the one hand, the existence of structure in the liquid matrix affords new opportunities for flow control, processing, and suspension stability. At the same time, and for the same reasons, efficient engineering of these systems requires major advances to our current understanding of simple fluid colloids. From proposals for new display technologies and nanofluidic devices to more fundamental questions about the mechanisms of clustering and de-clustering in systems of particles, new experimental findings call for major modeling and analysis efforts. For example, studies of electrophoresis in structured media can facilitate related efforts in biology to model and control nano-fluidic transport as well as contribute towards understanding of motion of cancer cells and their clustering in tumor metastasis.
Block copolymer melts as a complex fluid
Modulated phases are ubiquitous in Nature generally resulting in systems with competing attractive interactions at short distances, and long range repulsion. They are generally characterized by some degree of broken symmetry that is intermediate between fully ordered crystals and completely disordered fluids. We consider general order parameter models that are appropriate for a coarse grained description of modulated phases to address a number of generic non equilibrium features, including slow relaxation accompanying topological defect motion, the breakdown of continuum laws of defect motion, the formation of structural glasses, and their dependence on the symmetry of the phases. We are currently investigating the proper introduction of viscoelastic response in coarse grained models of mesophase evolution, and the consequences on phase rheology and orientation selection under oscillatory shears. (Read more ...).
Topological defect motion in crystalline solids
It is possible to develop a mesoscopic theory of dissipative plastic motion of defects in terms of intrinsic defect coordinates. However, the continuum description that results necessarily ommits any dependence on the underlying latttice, a dependence that is known to be important for defect kinetics. We are extending mesoscopic theories of topological defect motion by introducing a depence of the defect mobility along distinguished slip planes. The extended coarse grained description involves as primitive variables local lattice rotation and Burgers vector densities along distinguished slip systems of the lattice. Symmetry considerations then lead to phenomenological equations for both defect energies and their dissipative motion. This approach includes explicit dependences on the local state of lattice orientation, and allows for differential defect mobilities along distinguished directions. Defect densities and lattice rotation need to determined self consistently, with results already obtained for both square and hexagonal lattices in two spatial dimensions. Within linear response, dissipative equations of motion for the defect densities are derived which contain defect mobilities that depend nonlocally on defect distribution.