Applied Math Colloquium - Spring 2018

Colloquium Schedule

Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 a.m. For questions about the seminar schedule, please contact David Shirokoff.

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Date Speaker, Affiliation, and Title Host
February 2 Paulo Arratia, University of Pennsylvania
Life in complex fluids
Many microorganisms (e.g. bacteria, algae, sperm cells) move in fluids or liquids that contain (bio)-polymers and/or solids. Examples include human cervical mucus, intestinal fluid, wet soil, and tissues. These so-called complex fluids often exhibit non-Newtonian rheological behavior due to the non-trivial interaction between the fluid microstructure and the applied stresses. In this talk, I will show how the presence of particles and polymers in the fluid medium can strongly affect the motility (i.e. swimming) behavior of microorganisms such as the bacterium E. coli. For bacteria moving in particle suspensions of different (particle) sizes, we find a regime in which larger (passive) particles can diffuse faster than smaller particles: the particle long-time effective diffusivity exhibits a peak in particle size, which is a deviation from classical thermal diffusion. A minimal model qualitatively explains the existence of the effective diffusivity peak and its dependence on bacterial concentration. These results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics. For swimmers (E. coli and C. reinhardtii) moving in polymeric liquids, we find that fluid elasticity can significantly affect the run-and-tumble mechanism characteristic of E. coli, for example, as well as the swimming speed and kinematics of both pushers and pullers. These results demonstrate the intimate link between swimming kinematics and fluid rheology and that one can control the spreading and motility of microorganisms by tuning fluid properties.
Lou Kondic
February 9 Uwe Beuscher, W. L. Gore & Associates
Investigation of the correlation between gas/liquid porometry and particle filtration using simple network models
In order to better understand the performance of microporous membranes for particle filtration, it is important to determine and measure the appropriate membrane structural properties that influence filtration. One such property is the pore size distribution and a common technique for measuring pore sizes or porous structures is gas/liquid capillary porometry. In this method, the pore size is determined by measuring the capillary pressure distribution of the sample, which is correlated to a pore size distribution using a very simple model structure of parallel capillaries. A numerical study using a simple network model for the porous material, however, has shown that the morphological structure strongly influences the porometry results. Model structures with different morphology and pore size information lead to varying porometry results at similar filtration behavior and vice versa. An attempt is made to correlate numerical porometry and filtration performance as is often done in experimental studies. Finally, the limitations of porometry in predicting filtration behavior are illustrated.
Linda Cummings
February 16 Aleksandar Donev, New York University
Large Scale Brownian Dynamics of Confined Suspensions of Rigid Particles
We introduce new numerical methods for simulating the dynamics of passive and active Brownian colloidal suspensions of particles of arbitrary shape sedimented near a bottom wall. The methods also apply for periodic (bulk) suspensions. Our methods scale linearly in the number of particles, and enable previously unprecedented simulations of tens to hundreds of thousands of particles. We demonstrate the accuracy and efficiency of our methods on a suspension of boomerang-shaped colloids. We also model recent experiments on active dynamics of uniform suspensions of spherical microrollers.
Lou Kondic
February 23 Sue Ann Campbell, University of Waterloo
Mean Field Analysis and the Dynamics of Large Networks of Neurons
We use mean field analysis to study emergent behaviour in networks of all-to-all coupled, pulse-coupled neurons. The individual neurons are represented using a class of two-dimensional integrate and fire model. The mean field model is derived using a population density approach, moment closure assumptions and a quasi-steady state approximation. The resulting model is a system of switching ordinary differential equations, which exhibits a variety of smooth and nonsmooth bifurcations. We show that the results of the mean field analysis are a reasonable prediction of the behaviour seen in numerical simulations of large networks and discuss how the presence of parameter heterogeneity and noise affects the results. This is joint work with Wilten Nicola.
Casey Diekman
March 2 Gene Wayne, Boston University
Roy Goodman
March 9 TBA
March 23 Sanjoy Mahajan, Olin College (secondary affiliation: Massachusetts Institute of Technology)
Street-fighting mathematics for better teaching and thinking
Jonathan Luke (co-hosted by CSLA, Dept. of Physics, and the NJIT Institute for Teaching Excellence)
April 6 Becca Thomases, University of California, Davis
Yuan-Nan Young
April 13 Michael Shelley, New York University / Flatiron Institute
Anand Oza
April 20 Maxim Olshanskii, University of Houston
Shahriar Afkhami
April 27 Yoichiro Mori, University of Minnesota
Yuan-Nan Young

Updated: February 12, 2018