applied math

Applied Math Seminar

Thursday 10:00-11:00AM, Weber 117

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Reivew of Past Applied Math Seminar Schedules [2008-2009] [2007-2008] [2006-2007]

Fall 2009

Sept 3   Sept 10   Sept 15   Sept 24   Oct 1   Oct 8   Oct 15   Oct 19   Oct 29   Nov 5   Nov 10   Nov 12   Nov 17   Nov 19  
Nov 26   Dec 4  
 
 
September 3   Back to top

Larry Belfiore

Department of Chemical & Biological Engineering, Colorado State University

Title Stress-sensitive nutrient consumption via steady and non-reversing dynamic shear in continuous-flow tubular and rotational bioreactors

Abstract  Stress-sensitive biological response is simulated in a modified parallel-disk viscometer that implements steady and unidirectional dynamic shear under physiological conditions. Anchorage-dependent mammalian cells adhere to a protein coating on the surface of the rotating plate, receiving nutrients and oxygen from an aqueous medium that flows radially and tangentially, accompanied by transverse diffusion in the z-direction toward the active surface. This process is modeled as radial convection and axial diffusion with angular symmetry in cylindrical coordinates. The reaction/diffusion boundary condition on the surface of the rotating plate includes position-dependent stress-sensitive nutrient consumption via the zr- and z-theta-elements of the velocity gradient tensor at the cell/aqueous-medium interface. Linear transport laws in chemically reactive systems that obey Curie's theorem predict the existence of cross-phenomena between scalar reaction rates and the magnitude of the second-rank velocity gradient tensor, selecting only those elements of the velocity gradient tensor that are experienced by anchorage-dependent cells bound to protein-active sites. Stress sensitivity via the formalism of irreversible thermodynamics introduces a zeroth-order contribution to heterogeneous reaction rates that must be quenched via Heaviside step functions when nutrients, oxygen, chemically anchored cells, or vacant active protein sites are not present on the surface of the rotating plate. Computer simulations of nutrient consumption profiles via simple nth-order kinetics (i.e., n=1,2) suggest that rotational bioreactor designs should consider stress-sensitivity when the shear-rate-based Damkhler number (i.e., ratio of the stress-dependent zeroth-order rate of nutrient consumption relative to the rate of nutrient diffusion toward active cells adhered to the rotating plate) is greater than 25% of the stress-free Damkhler number. Rotational bioreactors for tissue regeneration are analyzed with simple first-order, simple second-order, and complex stress-free kinetics, where the latter includes a fourth-order rate expression that considers adsorption/desorption equilibria via the Fowler-Guggenheim modification of the Langmuir isotherm for receptor-mediated cell-protein binding, accompanied by the formation of receptor complexes. Dimensionless parameters are identified to obtain equivalent stress-free nutrient consumption in the exit streams of 2-dimensional creeping-flow rotational bioreactors and 1-dimensional laminar-flow tubular bioreactors. Modulated rotation of the active plate at physiological frequencies mimics pulsatile cardiovascular flow and demonstrates that these rotational bioreactors must operate above the critical stress-sensitive Damkhler number, identified under steady shear conditions, before dynamic shear has a distinguishable effect on bioreactor performance.  
 
 
September 10   Back to top

Bengt Fornberg

Department of Applied Mathematics, University of Colorado

Title  Radial Basis Functions for Solving Partial Differential Equations

Abstract  For the task of solving PDEs, finite difference (FD) methods are particularly easy to implement. Finite element (FE) methods are more flexible geometrically, but tend to be difficult to make very accurate. Pseudospectral (PS) methods can be seen as a limit of FD methods if one keeps on increasing their order of accuracy. They are extremely effective in many situations, but this strength comes at the price of very severe geometric restrictions. A more standard introduction to PS methods (rather than via FD methods of increasing orders of accuracy) is in terms of expansions in orthogonal functions (such as Fourier, Chebyshev, etc.).
   Radial basis functions (RBFs) were first proposed around 1970 as a tool for interpolating scattered data. Since then, both our knowledge about them and their range of applications have grown tremendously. In the context of solving PDEs, we can see the RBF approach as a major generalization of PS methods, abandoning the orthogonality of the basis functions and in return obtaining much improved simplicity and flexibility. Spectral accuracy becomes now easily available also when using completely unstructured meshes, permitting local node refinements in critical areas. A very counterintuitive parameter range (making all the RBFs very flat) turns out to be of special interest.
   As was shown recently by Dr. Natasha Flyer and collaborators, RBF discretization competes very favorably against all previous approaches for solving many convection-dominated PDEs on a sphere or in spherical shells - geometries that are ubiquitous in weather, climate, and geophysical modeling.  
 
 
September 15, Tuesday, 3:00-4:00PM, Weber 223   Back to top

Jao van de Lagemaat

Chemical and Biosciences Center, National Renewable Energy Laboratory

Title  Plasmon-enhanced organic, excitonic Photovoltaics

Abstract A novel way to increase solar-energy conversion is through surface plasmons. Surface plasmons can be described as collective surface oscillations of conducting electrons in metal nanostructures. They are known to enhance optical processes in their vicinity such as Raman scattering and optical absorption. The use of absorption enhancement potentially allows for the development of solar cells that circumvent the necessary tradeoff between optical thickness and carrier transport. However, because strong recombination can occur at metal surfaces in contact with the active layer of a solar cell, attempts have not been very successful to date. In this paper, we describe the successful use of surface-plasmon enhancement in organic, excitonic solar cells. We have recently succeeded in circumventing the recombination issues by employing buffer layers between the plasmonically active material and the active layer of the solar cell. Results of model cell systems employing both metal nanoparticles and random nanohole arrays, as well as electromagnetic calculations will be shown. Lastly, we also employed a hybrid approach, where plasmonic effects potentially enable third-generation solar-energy conversion. The latter promises a quantum leap in energy conversion efficiency by hybridizing excitonic states to surface plasmons.  
 
 
September 24   Back to top

Matthew Beard

National Renewable Energy Laboratory

Title  Multiple Exciton Generation, charge Carrier dyanmics, and solar energy conversion in electroically coupled films of PbSe Nanocrystals

Abstract  Multiple exciton generation (MEG) is a process that occurs in semiconductor nanocrystals where one highly energetic photon produces multiple charge carriers and can significantly enhance solar energy conversion efficiencies. Recently we have developed a simple, ITO/PbSe-NC/metal photovoltaic cell via a Schottky junction at the back electrode that produces a large short-circuit photocurrent (> 20 mA cm2) and solar conversion efficiencies of ~>2%. The PbSe NCs films are chemically treated using 1,2-ethandithiol (EDT) to produce highly photoconductive films that yield EQEs of 65% across the visible and up to 25% in the infrared region of the solar spectrum, with IQEs approaching 90%. A layer-by-layer technique is used to deposit the films and produces smooth, high quality, reproducible films. We have measured the n and k of our layer-by-layer PbSe nanocrystal films and constructed an optical model in order to understand the optical generation rate in our devices. We discuss limitations of our device structure in observing MEG photocurrents and report progress towards overcoming those limitations. These encouraging results provide incentive to study and understand the carrier dynamics in these films.

Using ultrafast transient absorption spectroscopy we studied MEG in two series of chemically-treated PbSe nanocrystal (NC) films. We find that the average number of excitons produced per absorbed photon varies between 1.0 and 2.4 (± 0.2) at a photon energy of ~4Eg for films consisting of 3.7 nm NCs, and between 1.1 and 1.6 (± 0.1) at hv~5Eg for films consisting of 7.4 nm NCs. The variations in MEG depend upon the size of the NCs and the chemical treatment used to electronically couple the NCs in each film. The single and multi-exciton lifetimes also change with the chemical treatment: biexciton lifetimes increase with stronger inter-NC electronic coupling and exciton delocalization, while single exciton lifetimes decrease after most treatments relative to the same NCs in solution. These results imply that a better understanding of the effects of surface chemistry on film doping, NC carrier dynamics, and inter-NC interactions is necessary to build solar energy conversion devices that can harvest the multiple carriers produced by MEG. Our results show that the MEG efficiency is very sensitive to the condition of the NC surface as well as to NC size, and suggest that the wide range of MEG efficiencies reported in the recent literature may be a result of uncontrolled differences in NC surface chemistry.  
 
 
October 1   Back to top

Suhuai Wei

Theoretical Material Science Group, National Renewable Energy Laboratory

Title  First-principles design of functional materials for energy applications

Abstract  Materials design using first-principles techniques is one the ultimate goals in computational materials science. Due to the recent advancement in first-principles electronic structure theory and computing power, it is now possible to perform knowledge-based computational design of materials with unique optical, electrical, or magnetic properties that are tuned to specific energy related applications. This vital tool, therefore, has the great potential to accelerate scientific discovery. In this talk, selective recent works from my group will be discussed to illustrate how computational methods can be used to design functional materials. These include (i) Absorber materials through cation mutation for solar cells, (ii) n-type, p-type or bipolarly dopable transparent conducting oxides (TCO) for optoelectronic devices. (iii) Defect complexes that has shallow donor or acceptor levels. (iv) Filled tetrahedron nitride compounds for solid state lighting applications. (v) Low band gap oxides for photoelectrochemical hydrogen production through water splitting.  
 
 
October 8   Back to top  
 
 
October 15   Back to top

Josh Thompson

Department of Mathematics, Colorado State University

 
 
 
October 19, Monday, 4:00-5:00PM   Back to top

James Keener

Department of Mathematics, University of Utah
Title  How cells make measurements

Abstract  A fundamental problem of cell biology is to understand how cells make measurements and then make behavioral decisions in response to these measurements. The full answer to this question is not known but there are some underlying principles that are coming to light. The short answer is that the rate of molecular diffusion contains quantifiable information that can be transduced by biochemical feedback to give control over physical structures.
   In this talk, this principle will be illustrated by two specific examples of how rates of molecular diffusion contain information that is used to make a measurement and a behavioral decision.
   Example 1: Bacterial populations of P. aeruginosa are known to make a decision to secrete polymer gel on the basis of the size of the colony in whch they live. This process is called quorum sensing and only recently has the mechanism for this been sorted out. It is now known that P. aeruginosa produces a chemical whose rate of diffusion out of the cell provides information about the size of the colony which when coupled with positive feedback gives rise to a hysteretic biochemical switch.
   Example 2: Salmonella employ a mechanism that combines molecular diffusion with a negative feedback chemical network to "know" how long its flagella are. As a result, if a flagellum is cut off, it will be regrown at the same rate at which it grew initially.  
 
 
October 29   Back to top
 
 
 
November 5   Back to top

Math day, no seminar

 
 
 
November 10, Tuesday, 3:00-4:00PM, Weber 117   Back to top

Jingmei Qiu

Department of Mathematics, Colorado School of Mines

Title  High order semi-Lagrangian finite difference methods for advection in incompressible flow

Abstract  We propose a novel semi-Lagrangian finite difference formulation for approximating conservative form of advection equations with general variable coefficients. Compared with the traditional semi-Lagrangian finite difference schemes, which are designed by approximating the advective form of equation via direct characteristics tracing, the scheme we proposed approximates the conservative form of equation. This essential difference makes the proposed scheme conservative by nature, and extendable to equations with variable coefficients. The proposed semi-Lagrangian finite difference framework is coupled with high order essentially non-oscillatory (ENO) or weighted ENO (WENO) reconstructions to achieve high order accuracy in smooth parts of the solution and capture sharp interfaces without introducing oscillations. The scheme is extended to high dimensional problem by Strang splitting.
   The performance of the proposed schemes is demonstrated by linear advection, several challenging examples of rigid body rotation and swirling deformation in multi-dimensions. As the information is propagating along characteristics, the semi-Lagrangian scheme does not have CFL time step restriction, allowing for a cheaper and more flexible numerical realization than the regular finite difference scheme for some problems.  
 
 
November 12   Back to top

Weishi Liu

Department of Mathematics, University of Kansas

Title  Poisson-Nernst-Planck systems for ion channel problems

Abstract  The Poisson-Nernst-Planck (PNP) system serves as a basic model for electro-diffusion processes. In this talk, we will consider the dynamics of the PNP system taken as a model for ion flows through membrane channels. A general dynamical system framework will be set up for the PNP systems and special properties for this specific problem will be discussed. Recent results on the multiplicity and spatial behavior of steady-states will be reported.  
 
 
November 17, Tuesday, 3:00-4:00PM, Weber 117   Back to top

Gustavo Cruz Pacheco

Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México
(Applied Mathematics and Systems Research Institute, National Autonomous University of Mexico)
Title  Dispersion, nonlinearity and modulation theory in two dimensions

Abstract  In this talk we will use Whitham modulation theory to study the interaction between dispersion and nonlinearity in the plane. We are particularly interested in the form in which the dispersion interact with coherent structures of the type of solitary waves. We will do some applications to electromigration and nonlinear optics.  
 
 
November 19   Back to top

Aime Fournier

Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research
Title  Two applications of spatial wavelets to atmospheric modeling: Identification of flow coherent structures, and representation of background covariance

Abstract  The Navier-Stokes equations and similar systems are still being explored at the frontier of high-performance, high-resolution simulation. These systems exhibit activity coupled across all scales, including ``incoherent'' turbulence that can contain ``coherent structures''. After a brief review of past wavelet applications in atmospheric and related sciences, we will present preliminary results of new wavelet applications to two strongly multiscale systems. First, we use a coherent vortex extraction method based on that of Farge et al. (ongoing since 1999) to identify and study coherent structures in the largest rotating-turbulence simulation ever performed, a size of $1536^3$ pseudospectral computation of the 3D rotating Navier-Stokes eqs. at Reynolds number $\approx$ 5600, Rossby number $\approx$ 0.06 (Mininni & Pouquet 2009). Second, we describe and illustrate various recent wavelet approaches aimed at modeling 100-terabyte size covariance matrices with about 10 megabytes of parameters, for operational data assimilation i.e., optimal use of observations for (re-)initializing the Weather Research and Forecasting and other numerical weather-prediction systems.  
 
 
November 26   Back to top

Fall recess, no seminar

 
 
 
December 4   Back to top

Pilhwa Lee

University of Connecticut Health Center