Research
I have the ultimate scientific goal of deeply understanding the statistical physics of disordered systems. From my early projects on spin glasses to my recent work on the jamming transition, I have routinely employed methods from statistical mechanics and field theory as well as state-of-the-art computational tools and numerical simulations to explain the role played by disorder into diverse physical phenomena. My current interests fall primarily into the topic of Soft Matter, which has sparkled my interest since graduate school. I have made early contributions on the development of genuine statistical mechanical models of liquid crystals; simulations of the smectic phase and a unifying theory for its spacetime microstructure; the first bona-fide effective-medium theory of jamming. I also have contributions in miscellaneous fields, from superconductivity and spin glasses to plasticity and more. As a FAPESP Young Investigator, I am currently researching geometric and topological aspects of considerable relevance to two general topics in the area of soft matter: Smectic Liquid Crystals and Disordered Elastic Systems.
Geometry, topology and soft matter
Geometry, disorder and topology have a central role in condensed matter. Their interplay and synergy lead to some of the most intriguing phenomena in soft-matter physics. I have studied crystalline lattices whose disordered topology is crafted to model the elastic properties of jamming (a ubiquitous transition describing many systems from molecular glasses and granular media to dislocation tangles and biological tissues). I have also used the mathematics of martensites (iron, shape-memory alloys) to study focal conic domains — the most iconic defect of smectic liquid crystals displaying Lorentz invariance and neat arrangements of ellipses and hyperbolas. Much of the current frontier in soft-matter science involves a deep understanding of the interplay between geometry, disorder and topology.
Superconductivity under extreme conditions
Computational materials research is steadily moving from pure characterization towards discovery and design of optimal materials. We are using it to design, characterize and optimize superconductors for use under extreme conditions of high fields or frequencies. We tailor superconductors so that vortices nucleate at fields much higher than the lower critical field, and so that they dissipate less power at high frequencies. We model the effects of impurities into thin surface layers of superconductors to increase their quality at high surface fields. Superconducting radio-frequency (SRF) cavities for particle accelerators are important for technological applications and serve as testbeds and experimental validation for our theoretical predictions of superconducting materials under extreme conditions.
Miscellaneous
Early in graduate school, I have worked in the field of spin glasses, with interest to both disordered antiferromagnets [read more] and mixtures of hydrogen-bonded crystals [read more]. I have also developed one of the few analytically-tractable models for a gas of Janus particles, where directional interactions are suitably incorporated in a Bethe lattice [read more]. With several students and collaborators of the Sethna group, I have helped in the development of an information-geometric based effective hamiltonian of spin glasses, applications of normal form theory to study corrections to scaling and universality families in the context of the renormalization group [read more], and algorithms that use dimension-reduction and sloppy models to optimize particle accelerators [read more]. More recently, I have collaborated with the Wang group at Cornell to develop a computational apparatus to simulate the mechanical response of DNA and nucleosome arrays and give insights into the mechanisms behind their exciting experimental results.