Sarah Lukens

University of Pittsburgh
Department of Mathematics
Tulane Center for Computational Science
709 Thackeray Hall
(412)624-7365

email me

I am a post doctoral researcher at the University of Pittsburgh in the Department of Mathematics working in the area of mathematical biology, with focus on host-level modeling of influenza A virus infection and data driven modeling of inflammation and sepsis

I completed my PhD. at Tulane University in the subject of computational fluid dynamics with applications in mathematical biology with Dr. Lisa Fauci.

Research Interests

Mathematical biology
Parameter estimation and stochastic methods
Numerical methods and scientific computing
Biological fluid flow applications

Research

Influenza A Virus: Mathematical models of a host-level response to influenza A virus (IAV) infection are a valuable tool for estimating biological rates describing viral kinetics and immune response and summarizing experimental data. However, even in the most simplistic model, data is limited and overparametrization makes estimation of parameters difficult. An ensemble approach may account for patient and strain variability, and uncertainty in data used to calibrate the models. I am interested in using statistical methods to generate collections of models and corresponding parameters that fit experimental data, and use these parameters to characterize models of influenza infection.
More information

Ciliary LCS

I am interested in applying dynamical systems theory to study flow fields from biological applications arising from fluid-structure interactions, which incorporate an elastic boundary immersed in fluid. I have studied an integrative ciliary model of the airway surface of the respiratory tract, using Lagrangian coherent structures (LCS) to look for mixing and qualitative features of transport in the ASL. I am also studying peristaltic pumping in closed end channels to look for mixing in both Newtonian and viscoelastic fluids.

Curriculum Vitae

Publications

B.J. Smith, S. Lukens, E. Yamaguchi, D.P. Gaver III, "Lagrangian transport properties of pulmonary interfacial flows" . J. Fluid Mech., 705, 2012.
S. Lukens, X. Yang, L. Fauci, "Using Lagrangian coherent structures to analyze fluid mixing by cilia" . Chaos, 20:1, 5 January 2010.

Lagrangian coherent structures in the media

The New York Times (Sept. 2009) "Finding the structures in various settings has also given researchers a fresh perspective on what remains a great scientific puzzle: the dynamics of flow."

The Economist (Nov. 2009) "Research is revealing a hidden structure within liquids and gases that guides the movement of everything from pollution to aeroplanes."

Courses (Teaching):

University of Pittsburgh:

Fall 2011: Math 280 (Introduction to Matrices & Linear Algebra)

Link to Pitt CourseWeb:
Pitt CourseWeb

Tulane University:

Fall 2009: Math 114 (Statistics for Business)
Homework Assignments for 114

Summer 2009: Math 122 (Calculus II)

Spring 2008: Math 116 (Long Calculus II)

Fall 2007: Math 115 (Long Calculus I)

Link to My Tulane blackboard:
Tulane Blackboard

Fun Stuff

How to Compute the Eigenvalues to Everyone's Favorite Tridiagonal Matrix

Numerical ODE's: Consistency and Convergence for Single Step Methods

Tether Points for Dummies Having trouble computing forces in your immersed boundary simulation?

Sita likes math!

Even Funner Stuff

I FOUND A BUG IN MATHEMATICA 6!!!
...but they fixed it in Mathematica 8.0! Math people are funny.

Let it Snow! Some pictures as proof it really did snow in New Orleans December 2008

Some computational art that I've generated from simulations and results

Fun Math powerpoint presentation: Funshine Bear loves sines and cosines

The MATH game!!!!!

If I were a Springer-Verlag Graduate Text in Mathematics, I would be J.L. Doob's Measure Theory.

I am different from other books on measure theory in that I accept probability theory as an essential part of measure theory. This means that many examples are taken from probability; that probabilistic concepts such as independence, Markov processes, and conditional expectations are integrated into me rather than being relegated to an appendix; that more attention is paid to the role of algebras than is customary; and that the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.

Which Springer GTM would you be? The Springer GTM Test

Links

Tulane Waterpolo In the scant time when I'm not studying math, I play water polo with Tulane

Some proof that if you use a calculator too much, you'll turn into one!!