|Computational/Applied Math Seminar - SPRING 2015 - Wed 3:35-4:20 Ayres Hall 112|
|Feb 18||Shane Sawyer , JICS, UTK||
A Computational Mathematician's Guide to High Performance Computing
An overview of HPC for computational and applied mathematicians is presented to provide a vantage point for individual researchers wishing to apply HPC techniques to their own problems. Topics of discussion include programming models, computer architecture, modern scientific computing libraries, and tools for performance optimization. Examples demonstrating the basic utilization of modern scientific libraries will be presented in addition to information regarding where individual researchers can find more extensive resources for getting started with the presented tools.
|Feb 25||Tim Krumwiede, Math, UTK||
Crystal Growth Shapes in Bond-Counting Models and Continuum Models
When continuum methods are used to model crystal growth, typically an anisotropic surface energy function is selected. These functions describe surface free energy on a facet depending on its orientation. However, it may be that not all such functions should be admissible when modelling real materials. We examine a simple bond-counting model using Kinetic Monte Carlo method, to determine the relationship between the atoms and bonds of a crystal lattice and its inherent surface free energy. Specifically, we demonstrate that a 12-armed dendrite as modeled in Haxhimali et al. is not a possible growth shape using a bond-counting model on an FCC lattice considering nearest- and next-nearest-neighbor bonds.
|Mar 11||Andreas Malikopoulos , ORNL||
Optimal Control for Complex Systems in Energy and Transportation
Complex systems are encountered in many applications including sustainable transportation, power grids, fusion and other alternative energy strategies, and biological systems. Complex systems consist of diverse entities that interact both in space and time. Referring to something as complex implies that it consists of interdependent, diverse entities that are connected with each other and can adapt to changes, i.e., they can respond to their local and global environment. This talk will address the development of a theoretical framework for the analysis and optimal control of complex systems in transportation, and highlight current research efforts toward making vehicles and transportation systems with the aim of (1) becoming eco-friendly, (2) realizing the optimum efficiency based on consumers’ needs and preferences, and (3) learning how traffic information can positively impact the environment and improve efficiency.
|Mar 25||Kerstin Kuepper , Aachen & ORNL||
Convergence of Filtered Spherical Harmonic Equations for Radiation Transport
We analyze the global convergence properties of the filtered spherical harmonic FPN equations for radiation transport. The well-known spherical harmonic PN equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the global L^2 convergence rate (in space and angle) of the spectral method to the solution of the transport equation depends on the smoothness of the solution (in angle only) and on the order of the filter. The results are confirmed by numerical experiments. Numerical tests have been implemented in MATLAB and are available online.
|Apr 1||Ryan Glasby , JICS-UTK||
A Modular, Extensible, Robust Numerical Solver for the Navier-Stokes Equations
The software tool, entitled Conservative Field Finite Element (COFFE), is a CFD numerical solver that invokes modularity and extensibility from its first principles. A flexible, class-based hierarchy provides the foundation for a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These elements are inherently extensible, maintainable, and robust through the usage of modern software engineering principles. Finally, COFFE includes various approachable interfaces to the underlying functional routines to ensure ease of uptake from a user’s or developer’s perspective.
|April 8||Sanghyun Lee , ICES - UT Austin||
Numerical Simulations of the bouncing jets
The fascinating phenomenon of a leaping shampoo stream, Kaye effect, is a property of non-Newtonian fluid which was first described by Alan Kaye in 1963. It manifest itself, when a thin stream of non-Newtonian fluid is poured into a dish of the fluid. As pouring proceeds, a small stream of liquid occasionally leaps upward from the heap and bounces. In earlier studies, it is known that the reason for bouncing Newtonian jet is the lubricating air layer but for Non-Newtonian jet, the Kaye effect, it has been debated whether non-Newtonian effects are the underlying cause of this phenomenon, making the jet glide on top of a shear-thinning liquid layer, or whether an entrained air layer is responsible. Since there is no mathematical model or numerical simulation studied before for these bouncing jets, as a first approach, we have studied a mathematical model and algorithm to show that the jet slides and bounces on a lubricating air layer and to find the range of parameters to observe the Kaye effects. In this context we propose a modified projection method for Navier-Stokes equation with open boundary, level set method for free boundary and adaptivity.
|Apr 15||Michael Wise , Math, UTK||
Modeling arterial wall drug concentrations following the insertion of a drug-eluting stent |
(paper by McGinty et.al., 2013)
A mathematical model of a drug-eluting stent is presented. The model considers a polymer region, containing the drug initially, and a porous region, consisting of smooth muscle cells embedded in an extracellular matrix. An analytical solution is obtained for the drug concentration both in the target cells and the interstitial region of the tissue in terms of the drug release concentration at the interface between the polymer and the tissue. When the polymer region and the tissue region are considered as a coupled system, under certain assumptions, the drug release concentration satisfies a Volterra integral equation which must be solved numerically in general. The drug concentrations, both in the cellular and extracellular regions, are then determined from the solution of this integral equation and used in deriving the mass of drug in the cells and extracellular space.
|Apr 22||Mustafa Elmas , Math, UTK||
Model of Bacterial Chemotaxis and Its simulation
Bacterial chemotaxis is the movement of motile bacteria in the direction of higher attractant concentrations and away from repellents. In oxytaxis, cells swim towards a region with favorable oxygen concentration, and they consume oxygen. Finding optimal concentration of oxygen is important for cell metabolism and growth. The chemotactic mechanism leads to formation of a band where the density of bacteria is much higher than outside the band. Experimental observation of the aerotactic bacterium Azospirillum brasilense (Azo.b.) is incorporated into a mathematical model consisting of a system of PDEs describing swimming of bacteria and diffusion of oxygen. We make testable predictions about density in the band and its location via numerical simulations.