The following is a public service annoucement: If you are a scientist trying to divy up your time between research, teaching, and service and you are a parent with young children who do not sleep through the night due to health problems and/or you are helping to care for a parent with a terminal illness and/or your one-way commute to school is over an hour, among other things, please, please take time out to rest when your body tells you that you are weary. I did not heed such warnings and ended up taking a nasty spill on a bicycle, in part because of poor judgement. The accident resulted in a ruptured spleen and almost led to me internally hemmorhaging to death because the ruptured spleen was not detected until x number of hours after the spill----"near miss" is what the professionals called it. So much for self-diagnosis. And while I did not heed my own body's warning signs of exhaustion, I hope that others out there in similar situations will and, thereby, reduce their potential of becoming another "near miss" like myself. (On the flip side, this event is driving me to plunge even more deeply into the ocean of physics questions and answers so that my work will have hopefully some meaningful impact on humanity before the "near miss" becomes a "miss".)
And now back to physics!
Our group studies percolation transitions, rigidity transitions, and shape instabilities/transitions in living and nonliving matter. Living matter is another term for biological matter, in vivo or in vitro, while nonliving matter is the more conventional dead stuff that physicists typically study, such as disordered metals, granular materials, and gels. So while our work involves modelling seemingly rather different systems, they are all quantifiable at some level using conductivity networks, interacting particle models, fiber networks, and even vertex models.
Uncorrelated percolation is the study of connected structures in disordered networks or graphs generated by occupying bonds (or sites) randomly and independently from one another. Such connected structures undergo a phase transition from a non-spanning phase to a spanning phase as the number of occupied bonds/sites is increased. The uncorrelated percolation phase transition is a continuous one and in a different universality class from the Ising model phase transition. The Schwarz Group (SG) has built and studied models of correlated percolation where there are constraints on the occupation of bonds/sites---constraints inspired by jamming systems, for example. One can then ask which constraints drive the correlated percolation transition into a different universality class from uncorrelated percolation and which constraints do not to understand how broad (or narrow, depending on how one looks at things) the uncorrelated percolation universality class is. For instance, SG constructed one of the first of two models, dubbed the sandwich model, allowing for a provably discontinuous percolation transition in two-dimensions that exhibits at least one diverging lengthscale, i.e. definitely a different transition from uncorrelated percolation.
One can also incorporate forces into disordered networks or graphs by having each occupied bond represent a spring and then study the elasticity of the network. Interestingly, there exists now a rigidity phase transition from floppy to rigid as the number of springs increases with the emergence of a spanning rigid cluster. The addition of three-body angular springs in particular places allows us to model the mechanics of semiflexible polymer/fiber and biopolymer networks. The SG found that the introduction of angle-constraining crosslinkers to a semiflexible fiber network with freely-rotating crosslinks can cooperatively lower the onset of rigidity to the connectivity percolation threshold---a result speculated for almost 30 years but never before obtained via effective medium theory. The SG is also working on generalizations of the so-called pebble game used to find rigid clusters in frictionless granular packings to now include frictional granular packings.
The SG is also becoming obsessed with understanding the brain as a material to ultimately better understand how it functions. We are studying how the mammalian cerebrum gets its shape in terms of its many intricate folds. We have created a "revised axonal tension model", which is a shape instability driven by axonal tension setting the distance between the folds. Using an alternative framework, we have interpreted the creasing transition in soft, disordered gels (such as the brain) as a Kosterlitz-Thouless transition of ghost shear lag fiber quasiparticles (with a built-in small distance regulator) at an effective critical temperature that then coalesce and, therefore, "cool" to ultimately form actual shear lag fibers via self-contact.
Given the above blurb about our group, please tour the rest of this website to become a little more familiar with our work. Also, do not hesitate to email me at email@example.com , or anyone else in the group, with questions.
|Somewhat 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
Syracuse Soft and Living Matter
New York Complex Matter Workshop