|Welcome to our website. The above slideshow consists of images from recent work in our group, along with some images of my favorite apple orchard. And, yes, the second image in the above slideshow is of me, J. M. Schwarz, sitting in my favorite apple orchard thinking about topological changes in biological systems of all things. In any event, I, along with members of the group, obsess over phase transitions in physical and biological systems with disorder---systems where the individual components do not arrange themselves in a perfect pattern, for example. To be concrete, the cellular cytoskeleton is composed, in part, of actin filaments that are connected by crosslinkers in some random fashion. Or, consider the arrangement of pennies crammed into a penny jar until it is full. Even at the quantum level, impurities in a quantum conductor qualify as a system with disorder.
So while our work involves modelling seemingly rather different systems, it is the disorder that calls for a unified description under the framework called percolation---the theory of everything disordered, so to speak. In less grandiose terms, percolation is the study of connected structures in disordered networks. Such connected structures undergo a phase transition from a non-spanning phase to a spanning phase as their density is increased. Once the connectivity of the system is known, then one can incorporate forces via a network of springs to study the elasticity of the system, and its accompanying phase transition from liquid to solid as the density of connected structures increases beyond the no-spanning/spanning transition. In fact, one can potentially use such an approach to model the elasticity of the actin cytoskeleton to quantitatively understand how a cell changes shape to crawl.
Please tour the rest of this website to become a little more familiar with our work. Do not hesitate to email me, or anyone else in the group, with questions.
|Current Research Projects |
Building correlated percolation models inspired by jamming in granular and glassy systems
Studying the interplay between morphology and rheology in the actin cytoskeleton via rigidity percolation
Looking for discontinuous, disorder-driven localization transitions in quantum systems via quantum percolation
Incorporating effects of microRNAs in models of gene regulation
Jeng's Percolation Applet
New York Complex Matter Workshop