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Our theoretical 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) as resistor networks, interacting particle models, fiber networks, and even vertex models to which sometimes similar types of analysis can be applied. We aim to answer such questions as:

What is the nature of the rigidity/jamming transition in a packing of frictional granular particles?

What types of disordered spring networks lead to compressional stiffening–a mechanical feature of both biological tissues and cells?

How is the brain (both cerebrum and cerebellum) built so we can more fully understand how it works? For the time being, we are asking how does the brain get its folds?

What role do nuclear cytoskeletal filaments play in chromatin organization?

2018 was a banner year for the Schwarz Group (SG). We submitted three different manuscripts that were collaborations with superb experimentalists. The first manuscript demonstrates that two different somewhat “old” classical elasticity approaches provide a good interpretation for the observed compressional stiffening of both animal and plant tissues—one approach for tissues with extracellular matrix and the other approach for tissues without extracellular matrix. This work was a collaboration with physicists Kasia Pogoda, Paul Janmey, and Katrina Cruz and is soon to appear in Physical Review E. A second manuscript addresses shape change in the developing mouse cerebellum using data at the time of development to determine which type of modeling approach better explains the data—-the more standard purely elastic approach or a new “buckling without bending” model involving a proliferating fluid-like cortex in addition to other elastic components. This work was done in collaboration with biologists Andrew Lawton, Alexandra Joyner, Daniel Turnbull, Daniel Rohrback, Masaaki Omura, Jonathan Mamou and with engineer Teng Zhang and is now published in eLIFE. The third manuscript shows how application of the frictional (3,3) pebble game (developed by physicist Silke Henkes and myself) to a laser-cut lattice under compression can help predict where the fractures occur near the brittle-ductile transition. This third manuscript was done in collaboration with physicists Estelle Berthier, Jonathan Kollmer, and Karen Daniels and is currently under review.

The SG also had two recent Physical Review X articles that were submitted within approximately a month of each other last summer on two somewhat different topics (obviously). Both former post-doc Tyler Engstrom and current graduate student Kuang Liu are to be commended for this achievement.

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, or anyone else in the group, with questions.

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