## Computational and Applied Mathematics Seminar

## Location and Time

University of Wyoming, Ross Hall 247, Fridays from 4:10-5:00 (unless otherwise stated).

## Seminar Chairs

Professors Craig C. Douglas and Rongsong Liu.

## Support

The CAM seminar series is currently supported through volunteers and the financial contributions by the UW Mathematics Department, MGNet.org, and and an energy grant from ExxonMobil.

## Schedule

For Fall 2018, the speakers are as follows:

Date Speaker From/Note September 21 Xiukun Hu University of Wyoming October 5 Craig C. Douglas University of Wyoming October 26 Yulong Li University of Wyoming November 2 Craig C. Douglas University of Wyoming November 9 Robert A. Lodder University of Kentucky November 30 Chao Lan University of Wyoming * Thursday Colloquium in AG 1030, ** Joint CAM - Analysis seminar

We are constantly looking for speakers for the current academic year! The topics can be original research, a survey of an area, or an interesting paper or papers that would interest the CAM community. If you would like to speak, please contact me by email.

The schedule, titles, and abstracts from Spring 2018 are here.

## Titles and Abstracts

## September 21

## A Data Enabled Model for Coupling Dual Porosity Flow with Free Flow

Mr. Xiukun Hu, Department of Mathematics and Statistcs, University of WyomingWe provide a snapshot of a U.S. National Science Foundation funded project to create a working computational and data science model useful for fractured reservoir simulation. This project carries out systematic research on the development, validation, numerical methods, data assimilation, and mathematical analysis for a dual porosity Navier-Stokes model. In many real world problems and industrial settings, the free flow of a liquid and the confined flow in a dual porosity media are often coupled together and significantly affected by each other. However, the existing Stokes-Darcy types of models cannot accurately describe this type of coupled problem since they only consider single porosity media. Therefore, with the support of external data, we follow the general framework of Stokes-Darcy model and dual-porosity model to develop a new coupled multi-physics multi-scale model and the corresponding numerical methods for accurately describing the coupling of the flow in dual porosity media and the free flow. The resulting coupled dual porosity Navier-Stokes model has higher fidelity than the Darcy, dual-porosity, Navier-Stokes, or Stokes-Darcy equations on their own. Furthermore, the field data provides the possibility to improve and demonstrate the accuracy of the model prediction through data assimilation.

## October 5

## Dynamic Tracking and Identification of Contaminants in Water Bodies Using Mutliscale Models and Sensors

Prof. Craig C. Douglas, Department of Mathematics and Statistcs, University of WyomingWe modify a well known mathematical model of fluid flow in water bodies in order to improve the computational accuracy over time. Our goal is to backtrack observed pollution clouds in order to find the one or more polluters. We use a set of remote sensors and data assimilation on much smaller grid within the large computational mesh. We solve a multiscale interpolation problem on a coarse time scale that provides updates to the predictions from our regular model. Over a sliding window of time, we see far greater accuracy. The technique is similar to solving inverse problems, but less expensive.

## October 26

## Thw Sufficient and Necessary Condition for Smoothness of Solutions of One Dimensional Fractional Diffusion Equations

Mr. Yulong Li, Department of Mathematics and Statistcs, University of WyomingThis talk will deal with one important open question in today’s analysis of fractional differential equa- tions (FDEs): “Under what condition can the smooth data guarantee the smoothness of solution?” The behavior of FDEs has exhibited unusual phenomena compared to integer order PDEs. For example, for integer order elliptic PDEs, it is known that the smoothness of coefficients and the right hand side (plus the smoothness of domain for multidimensional problems) ensures the smoothness of the true solution. However, it is not true for FDEs, which is in sharp contrast to the case of integer order elliptic PDEs. In this talk, one sufficient and necessary condition toward this open question will be established by looking at one dimensional fractional diffusion equation. Furthermore, I will point out some further insights toward the structure of solutions of fractional diffusion equations, which provides instructive information for numerical approximation theory of FDEs.

## November 2

## Connecting Census, Health, and Target Specific Big Datasets

Prof. Craig C. Douglas, Department of Mathematics and Statistcs, University of WyomingThis talk will outline an exploratory, collaborative research performed at the University of Kentucky and the University of Wyoming that works toward the design of a software system designated HENE (Health, Environment and Nutrition Examinations). Using different clustering algorithms to mine data, HENE will utilize the information from Big Databases, e.g., National Health and Nutrition Examination Survey (NHANES), U.S. Census, American Community Survey, and others to identify relationships between health, social, and environmental factors. Software prototyping and testing will be used to build open source tools to manipulate, analyze, and merge databases as they are updated. This planning proposal uses Design Meetings with stakeholders working with Design Scenarios to scope a future project. Objective: Multiple design scenarios and alternatives analysis will be used to develop a robust HENE system for mining databases to answer specific questions and to identify previously unknown associations between items in the databases. Development of HENE will use a spiral development process, which is characterized by repeatedly iterating a set of elemental development processes and managing risk so risk is actively reduced during development. This development process will use teams of experts. The Blue Team will develop appropriate Design Scenarios for testing HENEs while the Red Team will challenge all aspects of the system for each scenario. The dynamically changing Green Team of judges will set constraints on the scenarios, distribute briefing material to the teams, and choose the winner at each iteration. Results will be incorporated into the next round of development. The advantages of iterative development include constant outside stress placed on the system by experts not associated with its development, increasing the likelihood of finding risks of HENE at an early stage, development of alternative approaches to managing risks that are immediately incorporated into the design, and intrinsic stakeholder milestones. The value of HENE lies in the open source, freely available software and in the information gained during the development of the prototypes and validation of the system from using actual scenarios such as hydraulic fracturing ("fracking"). Many health, energy, and sustainability scenarios can be addressed on a national scale using Big Data and HENE. Questions might include: does fracking lead to adverse health outcomes, how does fracking affect area local economies, does frequent moving (e.g., the military and its familes, migrant workers, and long term foreign workers) affect food consumption/health status, do inner city residents who move keep the same diet if they move to the suburbs or farther, or does the ability to speak English affect health in the U.S?

## November 9

## The BEST Approach to the Search for Extraterrestrial Intelligence (SETI)

Prof. Robert A. Lodder, Departments of Pharmacy, Chemistry, and Electrical and Computer Engineering, University of KentuckyThe Bootstrap Error-adjusted Single-sample Technique (BEST) is shown to perform better than the Mahalanobis distance metric in analysis of SETI data from a Project Argus near-infrared telescope. The BEST algorithm is used to identify unusual signals at a desired significance level, and returns a distance in asymmetric nonparametric multidimensional central 68% confidence intervals (equivalent to standard deviations for 1-D data that are normally distributed, or Mahalanobis distance units for normally distributed data of d dimensions). The BEST algorithm is designed for high-speed parallel processing supercomputers, but is also shown to operate efficiently on single processors. Calculation of the Mahalanobis metric requires matrix factorization and is O(d3). In contrast, calculation of the BEST metric does not require matrix factorization and is O(d). Furthermore, the accuracy and precision of the BEST metric are greater than the Mahalanobis metric. Using synthetic multivariate data, the bias and relative standard deviation of the BEST and Mahalanobis metrics are compared as a function of the number of dimensions in hyperspace and the number of training samples in the calibration set. Full near-infared spectra of a stellar system (KIC 8462852, or “Tabby’s star”) are analyzed successfully using the BEST to identify unusual signals.

## November 30

## TBD

Prof. Chao Lan, Department of Computer Science, University of WyomingTBD