APPLIED MATH/ANALYSIS/Computational SEMINAR

TUESDAY 4:10pm-5:00pm RH 247

Coordinators: Hakima Bessaih/Craig Douglas

 

Spring 2014

Jan 21st 2014: Li Deng, Department of Mathematics (UW)

Title: Numerical Methods Study for GPS Receivers

Abstract:The Global Positioning System (GPS) is used to accurately locate a receiver. Satellite geometry and range measurements introduce errors in positioning algorithms. The goal of this study is to develop new positioning algorithms to improve the accuracy of the estimated position and decrease computation time. Different iterative and direct positioning algorithms have been developed. The iterative algorithm has higher accuracy while the direct algorithm has lower computation time when the two are compared. Due to the inaccuracy of the direct method we use the iterative method to partially solve the original problem and then use the direct method to complete the computation. In this talk, we present both linearized and non-linearized iterative algorithms and both ordinary and generalized least square direct algorithms to solve the trilateration problem. Finally, we compare the accuracy and computational time of the new methods with the traditional Newton-Raphson method.

Feb 11th 2014: Derrick Cerwinsky, Department of Mathematics (UW)

Title: Petascale Computing and the CI-Water Project

Abstract: The Colorado River basin is an important life stream to the American West.  But as the population grows, this resource is becoming overtaxed.  CI-Water is a Utah-Wyoming Cyberinfrastructure water modeling collaboration focused on creating an accurate predictive model of the Colorado River basin watershed.  In my talk I will discuss the challenges and opportunities involved in a hydrological model of this scale.

Feb 18th 2014: Hakima Bessaih, Department of Mathematics (UW)

Title: Splitting up method for the 2d stochastic Navier-Stokes equations.

Abstract: We deal with the convergence of an iterative scheme for the 2d stochastic Navier-Stokes equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given. In particular, we prove that the strong speed of convergence in probabilityis almost 1/2; because of the nonlinearity, this is shown by means of a convergence localized on a set of arbitrary large probability.

Feb 25th 2014: Jeff Clune, Computer Science, (UW)

Title: Automatically designing artificially intelligent robots using computational evolution.

Abstract: Evolution produced all the marvels of the natural world, such as jaguars, hawks, and the human mind. My research harnesses the power of evolution to automatically design artificially intelligent robot bodies and brains. I will discuss how adding certain real-world constraints to such "evolutionary algorithms" and combining them with concepts from developmental biology makes it possible to grow artificial neural networks and morphologies that are more complex and higher performing than via previous methods. Specifically, I will describe how to create neural networks that are structurally organized, in that they exhibit regularity, modularity, and hierarchy, which are three design principles that improve the complexity, performance, and intelligence of both natural animals and engineered designs.  These are important innovations in the ambitious quest to generate artificially intelligent robots that rival their natural counterparts.

Mar 11th 2014: Banu Baydil, University of Maine.

Title:Modeling Passive Transport in Meso-scale Oceanic Turbulence.

Abstract: In this talk, a kinematic time dependent non-Gaussian random field model will be introduced as part of a multi-scale methodology towards modeling transport in meso-scale oceanic turbulence. The model will be calibrated through statistically extracted meso-scale flow field data.    

Mar 25th 2014: Tianzhixi Yin, Department of Statistics (UW)

Title:Analyzing University of Wyoming Students

Abstract: Looking through a plethora of data about the student body at the University of Wyoming over the last few decades coupled with very detailed data since Banner was adopted leads to interesting analysis that offers some surprising results and raises many questions. In this talk, we give some interesting preliminary results and offer some leading questions that should be or can be addressed. This includes detailed and varied analysis related to where the students come from, how they do, and financial aid effects.

Note: This is a Big Data topic being addressed in MA 5490-01 and COSC 5010-05 (joint course) with thanks both to the Registrar and Head of Admissions. This is joint work with other students in the class.

Apr 1st 2014: Alyn Rockwood, Boulder Graphics

Title: Generalized Coon’s Patches with Applications to Design and Visualization

Abstract: We introduce a generalization to the classic (bi-cubically blended) Coons Patch; one that extends the patch to any number of sides.  The resulting N-sided patch continues to interpolate the underlying curves, but the curves may form any topological network -- as opposed to rectilinear networks for Coons.  The consequent surfacing scheme maintains G1 continuity across the boundaries between patches.

Advantages of this technology are illustrated specifically for (1) freeform design and (2) scientific visualization. In (1) we create a curve-based design scheme, which frees the user from topological constraints.  In (2), we create a marching-cubes like algorithm that uses the N-sided patches, instead of planar segments.  The result is a smoother looking, more highly compressed visualization for iso-surface rendering as in the figure in the attached file, which shows a CO2 sequestration iso-surface in water.

Apr 8th 2014: Quanling Deng, Department of Mathematics (UW)

Title: A Postprocessing Technique for the Finite Element Method

Abstract: A naive calculation of fluxes from  the solution produced by a finite element method (FEM)  ​yields non-conservative fluxes. Many applications require that fluxes are locally conservative. We present a postprocessing technique for constructing conservative fluxes from the FEM solution and apply it to some applications.​

Apr 15th 2014: Myron B. Allen, Department of Mathematics (UW)

Title: Deriving Darcy’s Law from Mixture Theory.

Abstract: Darcy’s law governs the velocity of a single fluid flowing in a porous medium.  Originally deduced from experimental data in 1856, the law was extended to a three-dimensional form by the early 20 th century and subsequently to flows with more complicated physics.  While some people describe Darcy’s law as phenomenological, there are many derivations from more fundamental continuum mechanics.  These derivations typically rest on such concepts as volume averaging, ensemble averaging, homogenization, or mixture theory.  Published derivations based on mixture theory tend to be dauntingly technical.  This presentation attempts to present the mixture-theoretic derivation as simply as possible.  Starting with the basic balance laws, we adopt simple constitutive relations, apply thermodynamic constraints, then examine linear extensions from equilibrium that yield Darcy’s law in its most common form.

Apr 17th 2014: Abani Patra, Buffalo.

Title: TBA

Apr 22nd 2014: Open

Apr 29th 2014: Rongsong Liu, Department of Mathematics (UW)

Title: Delayed Action Insecticides and Their Role in Mosquito and Malaria Control

Abstract: There is considerable interest in the management of insecticide resistance in mosquitoes. One possible approach to slowing down the evolution of resistance is to use late-life-acting (LLA) insecticides that selectively kill only the old mosquitoes that transmit malaria, thereby reducing selection pressure favoring resistance. In this talk we consider an age-structured compartmental model for malaria with two mosquito strains that differ in resistance to an insecticide, a compartmental model to describe malaria in the mosquitoes, and thereby incorporating the parasite developmental times for the two strains. The human population is modeled using a susceptible-exposed-infected compartmental model. We consider both conventional insecticides that target all adult mosquitoes and LLA insecticides that target only old mosquitoes.

According to a linearised theory, the potency of the insecticide affects mainly the speed of evolution of resistance. Mutations that confer resistance can also affect other parameters such as mean adult life span and parasite developmental time. For both conventional and LLA insecticides the stability of the malaria-free equilibrium, with only the resistant mosquito strain present, depends mainly on these other parameters. This suggests that the main long term role of an insecticide could be to induce genetic changes that have a desirable effect on a vital parameter such as adult life span. However, when this equilibrium is unstable, numerical simulations suggest that a potent LLA insecticide can slow down the spread of malaria in humans, but that the timing of its action is very important.

<