Industrial and Applied Math

Date Time 
Location  Speaker 
Title – click for abstract 

02/11 4:00pm 
BLOC 220 
Matthias Maier Texas A&M University 
Finite element methods and adaptive strategies for multiscale problems
A large class of modeling problems in Physics and Engineering is of
multiscale character, meaning that relevant physical processes act on
vastly different length scales. A direct numerical treatment of problems
exhibiting multiscale phenomena usually makes a full resolution of all
scales necessary and leads to high computational costs.
In this talk we give an introduction to the finite element method for
solving partial differential equations and introduced the concept of
(goaloriented) adaptivity. We conclude by highlighting some results for
timeharmonic Maxwell's equations with multiscale character. 

03/04 4:00pm 
BLOC 220 
Tarun Verma Los Alamos National Laboratory 
Variability and Predictability of the Arctic Freshwater System in Community Earth System Model (CESM) Initialized Decadal Predictions
The perennial presence of sea ice and low salinity waters in the Arctic Ocean makes it the largest oceanic reservoir of freshwater. Sea ice (solid freshwater) in the Arctic Ocean regulates the climate by reflecting back most of the incoming solar radiation and insulates the deeper ocean from winddriven stirring. The low salinity waters (liquid freshwater) beneath the sea ice can strengthen ocean stratification, and thus prevent convection. The changes in the freshwater storage of the Arctic Ocean can imply 1) an increase/decrease in freshwater exchange with the adjacent oceans, or 2) a change in surface freshwater sources like precipitation, river runoff, ice sheet melt etc. These can further be linked to largescale changes in oceanic and atmospheric circulation. In recent decades, the Arctic Ocean freshwater system has experienced dramatic changes due to anthropogenic climate change. The sea ice volume has shrunk considerably, while the surface ocean has warmed, and freshened at a rate greater than anywhere else over the globe with implications for future climate change, and economic activity in the Arctic, e.g. shipping routes. In this talk, I will present an overview of historical variations in the Arctic liquid freshwater content using an observationally forced oceansea ice model simulation, followed by an evaluation of a fullycoupled climate model in predicting these changes. These simulations are part of a large ensemble of initialized decadal hindcasts that were performed at National Center for Atmospheric Research (NCAR), and use fullycoupled Community Earth System Model. Some of the relevant challenges in making climate predictions on decadal timescales will also be discussed. 

03/06 Noon 
BLOC 628 
Brian Freno Sandia National Laboratory 


03/25 4:00pm 
BLOC 220 
Carsten Conradi HTW Berlin 
Establishing multistationarity conditions for polynomial ODEs in biology
Polynomial Ordinary Differential Equations are an important tool in many areas of quantitative biology. Due to large measurement uncertainty, few experimental repetitions and a limited number of measurable components, parameter values are accompanied by large confidence intervals. One therefore effectively has to study families of parametrized polynomial ODEs. Multistationarity, that is the existence of at least two positive solutions to the steady state equations has been recognized as an important qualitative property of these ODEs. As a consequence of parameter uncertainty numerical analysis often fails to establish multistationarity. Hence techniques allowing the analytic computation of parameter values where a given system exhibits multistationarity are desirable. In my talk I focus on ODEs that are dissipative and where additionally the steady state variety admits a monomial parameterization. For such systems multistationarity can be decided by studying the sign of the determinant of the Jacobian evaluated at this parameterization. I present examples where this allows to determine semialgebraic descriptions of parameter regions for multistationarity.


04/08 4:00pm 
BLOC 220 
Rachel Neville University of Arizona 
Topological Techniques for the Characterization of Pattern Forming Systems
Examples of complex spatialtemporal patterns are ubiquitous,
but can be difficult to characterize quantitatively. Irregular timevarying
structures, complexity of patterns, and sensitivity to initial conditions,
among other things, can make quantifying and distinguishing patterns
difficult. In recent years, topological data analysis has emerged as a
promising field for characterizing such systems, providing a
lowdimensional summary of the geometric and topological structure of data.
This can be used to quantify of order, for parameters to be learned and
studied, and for the evolution of pattern defects to be studied.
In this talk, I will give a brief introduction to persistent homology and
discuss how persistence can be leveraged to study pattern forming systems.
In particular, I will highlight some of the utility of some of these
techniques in studying the formation of disordered hexagonal arrays of
nanodots and crystalline structures that emerge in ion bombarded surfaces.

The organizer for this seminar is Peter Howard