Industrial and Applied Math
Date Time 
Location  Speaker  Title – click for abstract  

09/24 4:00pm 
BLOC 117  Manuel Quezada de Luna ERDC 
A monolithic conservative level set method with builtin redistancing
In fluid mechanics the interaction of fluids with distinguishable material
properties (e.g. water and air) is referred as multiphase flow. In this
work we consider twophase incompressible flow and concentrate on the
representation and time evolution of the interface. There is an extensive
list of methods to treat material interfaces. Popular choices include the
volume of fluid and level set techniques. We propose a novel levelset like
methodology for multiphase flow that preserves the initial mass of each
phase. The model combines and reconciles ideas from the volume of fluid and
level set methods by solving a nonlinear conservation law for a
regularized Heaviside of the (distance function) levelset. This guarantees
conservation of the volume enclosed by the zero levelset. The equation is
regularized by a consistent term that assures a nonsingular Jacobian. In
addition, the regularization term penalizes deviations from the distance
function. The result is a nonlinear monolithic model for a phase
conservative levelset where the levelset is given by the distance
function. The continuous model is monolithic (meaning that only one
equation is needed) and has only one parameter that controls the strength
of regularization/penalization in the model. We start the presentation
reviewing the main ingredients of this model: 1) a conservative levelset
method by [Kees et all (2011)], which combines a distanced,
nonconservative levelset method with the volume of fluid method via a
nonlinear correction and 2) elliptic redistancing by [Basting and
Kuzmin(2014)]. Afterwards, we manipulate the conservative levelset method
by [Kees et all (2011)] to motivate our formulation. We present a first
model which we then modify to resolve some difficulties. Finally, we
present a full discretization given by continuous Galerkin Finite Elements
in space and a highorder ImplicitExplicit time integration. We
demonstrate the behavior of this model by solving different benchmark
problems in the literature of levelset methods. T  
10/08 4:00pm 
BLOC 117  Jonathan Tyler Texas A&M 
Mathematical Modeling in the Pharmaceuticals
Mathematical models are used in each step of the drug discovery process to expedite and optimize drug development. Currently, the TransQST (Translational Quantitative Systems Toxicology) consortium is facilitating one such effort to develop open source quantitative systems toxicology (QST) models of four organ systems: GIimmune, heart, kidney, and liver. In this talk, I will give a brief introduction to how math models are used in the drug development process. I will then talk about my summer internship project with Boehringer Ingelheim to make the current TransQST GIimmune model more precise and practical through the addition of key immune species such as cytokines and Th2 cells. Finally, I will present three simulations that address pharmacological issues: (1) Simulation of a Crohn’s patient taking a TNFalpha inhibitor to address the drug's immunosuppressive action, (2) Sensitivity analysis to help guide in vivo and in vitro experiments, and (3) Generation of virtual parameter sets to address drug efficacy across a population.  
10/29 4:00pm 
BLOC 220  Timo de Wolff TU Berlin 
An Experimental Comparison of SONC and SOS Certificates for Unconstrained Optimization
Finding the minimum of a multivariate real polynomial is a wellknown hard problem with various applications. We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials (SONC). As a main result, we carry out the first largescale comparison of SONC, using this algorithm and different geometric programming (GP) solvers, with the classical sums of squares (SOS) approach, using several of the most common semidefinite programming (SDP) solvers. SONC yields bounds competitive to SOS in several cases, but using significantly less time and memory. In particular, SONC/GP can handle much larger problem instances than SOS/SDP. This is joint work with Henning Seidler.  
11/12 4:00pm 
BLOC 220  Sourav Dutta ERDC 
Reduced Order Modeling for Coastal and Hydraulic Applications in the Corps of Engineers
Computational models are becoming increasingly
important for achieving the U.S. Army Corps of Engineer's
mission of delivering vital public and military engineering
services. The multiphysics and multiscale problems we solve
typically require sophisticated, modelspecific numerical
methods that are based on rigorous mathematical models. The
Shallow Water Equations (SWE), for instance, are widely adopted
to study various flow regimes from dam breaks and riverine flows
to atmospheric processes. However, for multiquery, realtime and
slimcomputing scenarios arising in optimal design, risk assessment
or ensemble forecasting problems, that can require thousands of
forward simulations, a fully resolved twodimensional shallow water
model poses a significant computational challenge.
Formal model reduction techniques like the Proper Orthogonal
Decomposition (POD)based methods are a popular choice to alleviate
the computational burden. In this talk, we will review some of the
work focused on the development of reduced order computational tools
for supporting research on both existing and new models for coastal
and hydraulic processes. We will present some efficient model
reduction strategies for such complex nonlinear flows that use a
combination of  1) hyperreduction (Discrete Empirical Interpolation
Method or gappy POD), 2) nonintrusive multivariate radial basis
function (RBFNIROM) interpolation, and 3) POD in a Lagrangian frame
that can effectively capture the lower rank structure of wavelike
solutions even in the presence of large gradients and nonpolynomial
nonlinearities. We will present results involving practical dambreak
scenarios and largescale geophysical flows and discuss the accuracy,
computational performance, and robustness of these methods.
 
11/19 5:00pm 
BLOC 220  Angelica Torres University of Copenhagen 
Stability of steady states and algebraic parameterizations in chemical reaction networks
Criteria such as RouthHurwitz and LiénardChipart are used to
establish whether a steady state of a system of ordinary differential
equations is asymptotically stable, by computing the Jacobian of the system
and studying the sign of the real part of its eigenvalues.
I am interested in determining the stability properties of the steady
states of reaction networks (using massaction kinetics), when the
values of the reaction rate constants are unknown.
To this end, I combine the RouthHurwtiz criterion and the
Lienardchipart criterion, with the use of algebraic parameterizations
of the steady states.
In this talk I will give an overview of this approach, I will present
results obtained for particular networks and, also, conditions under
which bistability of networks can be determined.

The organizer for this seminar is Peter Howard