Current research areas
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 Biophysics or Biomaterials. In the former case, 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 interest because of their applications in soft matter, materials science, and engineering. In the latter case, we are developing a coarse grained description of biomolecules, including reduced models of a protein that can provide high throughput and moderate resolution models of its structure, extending this description to include solvent mediated interactions, and applying them to ongoing protein engineering efforts.
Block copolymers as a structured material
Block copolymers are being extensively investigated as nanoscale templates for
a wide variety of applications that include nanolithography, photonic
components, or high density storage systems. However, given the small
wavelength of the microphases (tens or hundreds of Angstroms), macroscopic
size samples do not completely order through spontaneous self assembly.
Instead, oscillatory shears are commonly introduced in order to accelerate
long range order development over the required distances.
A mesoscopic model of a diblock copolymer is used to study the
formation, stability, and coarsening of lamellar phases, including
their hydrodynamic response to applied external shears. The focus of
our research is on mechanisms controlling long ranged
orientational order, including the motion of grain boundaries or other
topological defects, and the introduction of a mesoscopic theory of
viscoelasticity that can describe the
stability and response of these materials to shears, and account for the
selection of particular orientations depending on the architecture of the
block and the parameters of the shear.
Topological defect motion in modulated phases
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 and the formation of structural glasses, and their
dependence on the symmetry of the phases. We are currently
investigating non potential effects, according to which the evolution
of the system is not simply determined by the minimization of an
appropriate free energy. In particular, we address the consequences of
this assumption on extended defect motion, and the possible transition
to persistent dynamics and spatio temporal chaos.
Protein-protein interactions
Sequencing of the genomes of several species (including humans) opens
the door to a new understanding of biological function, as well as to
the possible elucidation of the genetic mechanisms of many diseases, and
perhaps to their cure through genetic manipulation. This research aims
at improving current computational methods that predict the three
dimensional structure of proteins and of protein-protein interactions
from the knowledge of their amino acid
sequence. Protein function is more closely related to structure than to
sequence, and hence methodologies that can produce large scale
predictions of protein structure are essential in this post-genomic era.
Reduced, lattice based models of proteins, and Monte Carlo simulation
methods are used to analyze the relationship between sequence and
characteristic structural motifs of the folded protein. Statistical
methods are being develop to increase sensitivity in the detection of
functional sites and to calculate the thermodynamics parameters
that describe protein-protein interactions (formation of dimers, trimers,
etc.). The image shows the dimer of GCN4, currently being
studied by replica Monte Carlo.
Faraday waves
Parametrically driven surface waves (also known as Faraday waves)
can be excited on the
free surface of a fluid layer that is periodically vibrated in the direction
normal to the surface at rest if the amplitude of the driving acceleration is
large enough to overcome the dissipative effect of fluid viscosity.
Despite the simplicity of the
configuration, this system displays a large number of features that are
characteristic of strong nonlinearity, and serves as a prototype of many
nonlinear phenomena that are currently under active investigation. Among them we
mention the discovery of stationary quasi-periodic patterns of surface standing
waves (shown in the figure. This pattern is
the analog of a quasi-crystal in solid state physics),
the transition to spatio temporal chaos, super-lattice patterns in systems
vibrated with two frequency components, coexistence of chaotic and regular
regions in extended systems, serving as a laboratory for detailed studies of
turbulence, or its analysis in unconventional systems such as viscoelastic
fluids or granular materials.