Order Reconstruction of Nematic Liquid Crystals in Microfluidic Channels
Lidia Mrad
Molecules of a nematic liquid crystal tend to align along preferred directions, producing partially-ordered material. This results in peculiar physical properties that render them useful in a range of applications, including their widespread use in optical displays. When confined to thin planar cells or channels, the fluid flow extends the applications of nematics further to optofluidic devices and guided micro-cargo transport. Our goal is to examine the intrinsic coupling between the fluid motion and the orientation of nematic molecules within a reduced Beris-Edwards framework. We consider steady unidirectional flows and obtain a system of nonlinear and coupled differential equations. Our results analyze and simulate flows that produce order reconstruction solutions, where samples have distinct sub-domains separated by domain walls with each sub-domain possessing different directions. This is joint work with J. Dalby and A. Majumdar.
The Influence of the Endothelial Surface Layer on the Motion of Red Blood Cells

Ying Zhang

The endothelial lining of blood vessels presents a large surface area for exchanging materials between blood and tissues. The endothelial surface layer (ESL) plays a critical role in regulating vascular permeability, hindering leukocyte adhesion as well as inhibiting coagulation during inflammation. Once the ESL is pathologically altered, the changes in its topography are believed to cause vascular hyperpermeability and induce thrombus formation during sepsis. The occurrence of these biological phenomena requires Red Blood Cells (RBCs) stay within close proximity to the ESL, initiating RBC-layer interaction. To investigate the influence of various physical properties of the ESL on the motion of RBCs, we construct two models to represent the ESL combined with the immersed boundary method. In particular, we focus on analyzing how lift force and drag force change over time when a RBC is placed close to the ESL as the width, bumpiness, permeability, and sparsity of the ESL vary. Our preliminary results suggest that increase in the ESL thickness has a dominant effect in slowing down the motion of RBCs, whereas increase in the permeability of the ESL leads to a more apparent decrease in the lift force and thus hindering the migration of RBCs from the layer.

Panagiota Birmpa

Mathematical and Computational Approaches to Social Justice

Chad Topaz

Civil rights leader, educator, and investigative journalist Ida B. Wells said that “the way to right wrongs is to shine the light of truth upon them.” This talk will demonstrate how mathematical and computational approaches can shine a light on social injustices and help build solutions to remedy them. I will present quantitative social justice projects on topics ranging from diversity in art museums to equity in criminal sentencing to affirmative action, health care access, and other fields. The tools engaged include crowdsourcing, clustering, hypothesis testing, causal analysis, Markov chains, data visualization, and more. I hope that this talk leaves you informed about the breadth of social justice applications that one can tackle using quantitative tools in careful collaboration with other scholars and activists.


Quantization of Benjamin-Ono periodic traveling waves

Alexander Moll

The Benjamin-Ono equation is a model for a variety of classical fluid interfaces in two spatial dimensions.  In addition, the “quantization” of this model is conjectured to describe such interfaces at scales in which quantum effects must be taken into account.  In this talk, we review the essentials of the mathematical procedure of quantization (from a probabilistic point of view and without any path integrals) and present recent results on the quantization of Benjamin-Ono periodic traveling waves.

Moyi Tian