Date of Award

August 2016

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Jennifer M. Schwarz


Active dimers, Anderson localization, Brain folds, Soft Matter

Subject Categories

Physical Sciences and Mathematics


This thesis presents a study of condensed matter systems at different length scales. The first part presents a study of elastic instabilities in biological systems ranging from the cerebral cortex in the brain to the lining of the intestines. Such instabilities lead to a zoo of morphologies ranging from primary folds to villi and crypts to secondary folds and are brought about by growth, mechanical stresses, or a combination of the two. We propose a novel model for the description of primary folds in the cerebral cortex. Motivated by the spatial structure of the cortex, we model its elasticity as a smectic liquid crystal. With this novel description we show that vertical pulling forces via axonal tension from the brain underlying white matter can lead to buckling, which initiates the primary folds. Moreover, we are able to obtain a reasonable estimate of the critical wavelength and strain for buckling. We also model the formation of secondary folds in the cortex to obtain a more comprehensive theory. We continue this study of elastic instabilities due to growth by studying a more general system comprised of two coupled elastic membranes, one of which undergoes growth and one that does not. We employ an active formulation of growth and compare it to the one due to Rodriguez (Rodriguez). We show that different morphologies corresponding to different systems, such as the cerebral cortex and the lining of the intestines, can be obtained from our model by choosing different active stress functional forms to begin to classify the zoo of morphologies observed in seemingly different biological systems. In the second part of this thesis, to work towards a more microscopic view of biological tissues such as the brain tissue, which is composed of neurons, glial cells, and progenitor cells, we model an experiment (Theveneau) studying the dynamic interaction between neural crest cells and placodal cells in which the placodal cells run away from the neural crest cells following contact between the two. Our modeling contributes towards generalizing the rules governing the interplay between different cell types, particularly during collective cell migration. In the final part of this thesis, we move to an even smaller length scale. Our main motivations come from a series of experiments on the localization of light and the application of tight-binding models to the electronic transport properties of DNA sequences. To this end, we study the statistical properties of the conductance distribution and Lyapunov exponents in the Anderson tight-binding model with Levy-type disorder.


Open Access