Applied Mathematics Commons^™

Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh

Faculty Publications

The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds …

P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

Western Research Forum

Global Exponential Stabilization on SO(3)

Computational Algorithms For Improved Representation Of The Model Error Covariance In Weak-Constraint 4d-Var, Jeremy A. Shaw

Dissertations and Theses

Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error covariance matrix, the w4D-Var formulation requires information on the model error statistics and …

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

P-31 Sufficient Conditions For The Existence Of Positive Solutions To An Elliptic Model, Timothy Robertson

Honors Scholars & Undergraduate Research Poster Symposium Programs

We study the existence of solutions to a general elliptic model. Specifically, we give conditions for the existence and non-existence of steady-state solutions to a general, nonlinear population model of two cooperating species.

Differences In Hemodynamics And Rupture Rate Of Aneurysms At The Bifurcation Of The Basilar And Internal Carotid Arteries, Ravi Doddasomayajula, Bong Jae Chung, Farid Hamzei-Sichani, Christopher M. Putman, Juan Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Cerebral aneurysms in the posterior circulation are known to have a higher rupture risk than those in the anterior circulation. We sought to test the hypothesis that differences in hemodynamics can explain the difference in rupture rates.

MATERIALS AND METHODS: A total of 117 aneurysms, 63 at the tip of the basilar artery (27 ruptured, 36 unruptured, rupture rate = 43%) and 54 at the bifurcation of the internal carotid artery (11 ruptured, 43 unruptured, rupture rate = 20%) were analyzed with image-based computational fluid dynamics. Several hemodynamic variables were compared among aneurysms at each location and …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Libraries' Newsletters

No abstract provided.

Utilizing Social Network Analysis To Study Communities Of Women In Conflict Zones, James R. Gatewood, Candice R. Price

Journal of Humanistic Mathematics

This article proposes to study the plight of women in conflict zones through the lens of social network analysis. We endorse the novel idea of building a social network within troubled regions to assist in understanding the structure of women's communities and identifying key individuals and groups that will help rebuild and empower the lives of women. Our main argument is that we can better understand the complexity of a society with quantitative measures using a network analysis approach. Given the foundation of this paper, one can develop a model that will represent the connections between women in these communities. …

Application Of An Rbf Blending Interpolation Method To Problems With Shocks, Michael Harris, Eduardo Divo, Alain J. Kassab

Publications

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high …

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Extracting Geography From Datasets In Social Sciences, Yuke Li, Tianhao Wu, Nicholas Marshall, Stefan Steinerberger

Yale Day of Data

No abstract provided.

Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

The Kabod

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.

Numerical Simulation Of Acoustic Emission During Crack Growth In 3-Point Bending Test, Mihhail Berezovski, Arkadi Berezovski

Publications

Numerical simulation of acoustic emission by crack propagation in 3-point bending tests is performed to investigate how the interaction of elastic waves generates a detectable signal. It is shown that the use of a kinetic relation for the crack tip velocity combined with a simple crack growth criterion provides the formation of waveforms similar to those observed in experiments.

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …

Solitary Wave Solution Of Flat Surface Internal Geophysical Waves With Vorticity, Alan Compelli

Conference papers

A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is con-sidered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then considered and extended to produce a KdV approximation. Finally, a solitary wave solution is obtained.

Weihrauch Reducibility And Finite-Dimensional Subspaces, Sean Sovine

Theses, Dissertations and Capstones

In this thesis we study several principles involving subspaces and decompositions of vector spaces, matroids, and graphs from the perspective of Weihrauch reducibility. We study the problem of decomposing a countable vector space or countable matroid into 1-dimensional subspaces. We also study the problem of producing a finite-dimensional or 1-dimensional subspace of a countable vector space, and related problems for producing finite-dimensional subspaces of a countable matroid. This extends work in the reverse mathematics setting by Downey, Hirschfeldt, Kach, Lempp, Mileti, and Montalb´an (2007) and recent work of Hirst and Mummert (2017). Finally, we study the problem of producing a …

2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs

Graduate School

Graduate Handbook on the MAEM Program at Otterbein University.

A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal

Mathematics and Applied Mathematics Publications

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between …

High Performance Techniques Applied In Partial Differential Equations Library, Shilei Lin

All College Thesis Program, 2016-2019

This thesis explores various Trilinos packages to determine a method for updating the deal.ii library, which specializes in solving partial differential equations by finite element methods. It begins with introducing related concepts and general goals, followed by exploring computational and mathematical methods which are analytical solutions of one-dimensional Boussinesq equations and developing newer prototypes for solvers in deal.ii based on Trilinos packages. After demonstrating the methods, it indicates the reducing solving time in newer prototypes. Based on results from the prototype, similar methods are applied to update the deal.ii library. In the end, a testing program is exploited to demonstrate …