Applied Mathematics Commons^™

Evaluating The Behaviour Of Centrally Perforated Unreinforced Masonry Walls: Applications Of Numerical Analysis, Machine Learning, And Stochastic Methods, Mohsen Khaleghi, Javid Salimi, Visar Farhangi, Mohammad Javad Moradi, Moses Karakouzian

Civil and Environmental Engineering and Construction Faculty Research

The presence of openings greatly affects the response of unreinforced masonry (URM) walls. This topic greatly attracts the attention of many researchers. Perforated unreinforced masonry (PURM) walls under in-plane loads through the truss discretization method (TDM) along with several machine learning approaches such as Multilayer perceptron (MLP), Group of Method Data Handling (GMDH), and Radial basis function (RBF) are described in this paper. A new method named Multi-pier (MP) that is fast and accurate, is used to determine the behavior of PURM walls. The results of the MP method are expressed as a ratio of lateral load-bearing capacity and initial …

The Pencil Code, A Modular Mpi Code For Partial Differential Equations And Particles: Multipurpose And Multiuser-Maintained, The Pencil Code Collaboration, Chao-Chin Yang

Physics & Astronomy Faculty Research

The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) (A. Brandenburg & Dobler, 2010) to meteorological cloud microphysics (Li et al., 2017) and engineering applications in combustion (Babkovskaia et al., 2011). Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to …

Two New Finite Element Schemes And Their Analysis For Modeling Of Wave Propagation In Graphene, Jichun Li

Mathematical Sciences Faculty Research

© 2020 The Author(s) In this paper, we investigate a system of governing equations for modeling wave propagation in graphene. Compared to our previous work (Yang et al., 2020), here we re-investigate the governing equations by eliminating two auxiliary unknowns from the original model. A totally new stability for the model is established for the first time. Since the finite element scheme proposed in Yang et al. (2020) is only first order in time, here we propose two new schemes with second order convergence in time for the simplified modeling equations. Discrete stabilities inheriting exactly the same form as the …

Computational Study Of The Time Relaxation Model With High Order Deconvolution Operator, Jeffrey Belding, Monika Neda, Fran Pahlevani

Mathematical Sciences Faculty Research

This paper presents a computational investigation for a time relaxation regularization of Navier–Stokes equations known as Time Relaxation Model, TRM, and its corresponding sensitivity equations. The model generates a regularization based on both filtering and deconvolution. We discretize the equations of TRM and the corresponding sensitivity equations using finite element in space and Crank–Nicolson in time. The step problem and the shear layer roll-up benchmark is used to computationally test the performance of TRM across different orders of deconvolution operator as well as the sensitivity of the shear layer computations of the model with respect to the variation of time …

Recent Advances In Computational Mathematics And Applications, Eric Machorro, Jichun Li, Monika Neda, Pengtao Sun, Hongtao Yang

Mathematical Sciences Faculty Research

No abstract provided.

Correlation Coefficients For A Study With Repeated Measures, Guogen Shan, Hua Zhang, Tao Jiang

Environmental & Occupational Health Faculty Publications

Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlation calculation are compared: (1) Pearson correlation; (2) correlation of subject means; (3) partial correlation for subject effect; (4) partial correlation for visit effect; and (5) a mixed model approach. Pearson correlation coefficient is traditionally used in a cross-sectional study. Pearson correlation is close to the correlations computed from mixed-effects models that consider the correlation structure, but Pearson correlation may not be theoretically appropriate in …

Comparison Principle For Stochastic Heat Equation On Rd, Le Chen, Jingyu Huang

Mathematical Sciences Faculty Research

We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on Rd (∂∂t−12Δ)u(t,x)=ρ(u(t,x))M˙(t,x), for measure-valued initial data, where M˙ is a spatially homogeneous Gaussian noise that is white in time and ρ is Lipschitz continuous. ... (See full text for complete abstract)

Inferring The Distribution Of Selective Effects From A Time Inhomogeneous Model, Amei Amei, Shilei Zhour

Mathematical Sciences Faculty Research

We have developed a Poisson random field model for estimating the distribution of selective effects of newly arisen nonsynonymous mutations that could be observed as polymorphism or divergence in samples of two related species under the assumption that the two species populations are not at mutation-selection-drift equilibrium. The model is applied to 91Drosophila genes by comparing levels of polymorphism in an African population of D. melanogaster with divergence to a reference strain of D. simulans. Based on the difference of gene expression level between testes and ovaries, the 91 genes were classified as 33 male-biased, 28 female-biased, and 30 sex-unbiased …

Probabilistic Interpretation Of Solutions Of Linear Ultraparabolic Equations, Michael D. Marcozzi

Mathematical Sciences Faculty Research

We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.

Environmental Effects On Drosophila Brain Development And Learning, Xia Wang, Amei Amei, J. Steven De Belle, Stephen P. Roberts

Mathematical Sciences Faculty Research

Brain development and behavior are sensitive to a variety of environmental influences including social interactions and physicochemical stressors. Sensory input in situ is a mosaic of both enrichment and stress, yet little is known about how multiple environmental factors interact to affect brain anatomical structures, circuits and cognitive function. In this study, we addressed these issues by testing the individual and combined effects of sub-adult thermal stress, larval density and early-adult living spatial enrichment on brain anatomy and olfactory associative learning in adult Drosophila melanogaster. In response to heat stress, the mushroom bodies (MBs) were the most volumetrically impaired among …

Diffusive Logistic Equations With Harvesting And Heterogeneity Under Strong Growth Rate, Saeed Shabani Rokn-E-Vafa, Hossein T. Tehrani

Mathematical Sciences Faculty Research

We consider the equation −Δu=au−b(x)u2−ch(x) in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, b(x) and h(x) are nonnegative functions, and there exists Ω0⊂⊂Ω such that {x:b(x)=0}=Ω¯¯¯0. We investigate the existence of positive solutions of this equation for c large under the strong growth rate assumption a≥λ1(Ω0), where λ1(Ω0) is the first eigenvalue of the −Δ in Ω0 with Dirichlet boundary condition. We show that if h≡0 in Ω∖Ω¯¯¯0, then our equation has a unique positive solution for all c large, provided that a is in a right neighborhood of λ1(Ω0). For this purpose, we prove …

Estimation Of Performance Indices For The Planning Of Sustainable Transportation Systems, Pankaj Maheshwari, Alexander Paz, Pushkin Kachroo

Graduate Publications & Presentations

What is sustainable transportation system?

Fulfill the needs of current generations without compromising the ability of future generations

Utilize resources without compromising their health and productivity Leads to development that improves quality of life

Assimilate economic, ecological, social, and bio-physical components of resource ecosystems

Minimize the use of renewable and non-renewable resources, provide affordability and equity between generations

Dynamic Decision Making And Race Games, Shipra De

Calvert Undergraduate Research Awards

Frequent criticism in dynamic decision making research pertains to the overly complex nature of the decision tasks used in experimentation. To address such concerns we study dynamic decision making with respect to the simple race game Hog, which has a computable optimal decision strategy. In the two-player game of Hog, individuals compete to be the first to reach a designated threshold of points. Players alternate rolling a desired quantity of dice. If the number one appears on any of the dice, the player receives no points for his turn; otherwise, the sum of the numbers appearing on the dice is …

An H-Adaptive Finite-Element Technique For Constructing 3d Wind Fields, Darrell Pepper, Xiuling Wang

Mechanical Engineering Faculty Research

An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions …

Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian

Mechanical Engineering Faculty Research

RedOx-based magnetohydrodynamic MHD[1] flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. …

Application Of Meshless Methods For Thermal Analysis, Darrell Pepper, Bozidar Sarler

Mechanical Engineering Faculty Research

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) — which are simple to implement — for thermal problems. Radial basis functions are the natural generalization of univariate polynomial splines to a multivariate setting that work for arbitrary geometry with high dimensions. RBF functions depend only on the distance from some center point. …

A Fast And Simple Algorithm For Computing M Shortest Paths In Stage Graph, M. Sherwood, Laxmi P. Gewali, Henry Selvaraj, Venkatesan Muthukumar

Electrical & Computer Engineering Faculty Research

We consider the problem of computing m shortest paths between a source node s and a target node t in a stage graph. Polynomial time algorithms known to solve this problem use complicated data structures. This paper proposes a very simple algorithm for computing all m shortest paths in a stage graph efficiently. The proposed algorithm does not use any complicated data structure and can be implemented in a straightforward way by using only array data structure. This problem appears as a sub-problem for planning risk reduced multiple k-legged trajectories for aerial vehicles.

A Fast And Simple Algorithm For Computing M-Shortest Paths In State Graph, M. Sherwood, Laxmi P. Gewali, Henry Selvaraj, Venkatesan Muthukumar

Electrical & Computer Engineering Faculty Research

We consider the problem of computing m shortest paths between a source node s and a target node t in a stage graph. Polynomial time algorithms known to solve this problem use complicated data structures. This paper proposes a very simple algorithm for computing all m shortest paths in a stage graph efficiently. The proposed algorithm does not use any complicated data structure and can be implemented in a straightforward way by using only array data structure. This problem appears as a sub-problem for planning risk reduced multiple k-legged trajectories for aerial vehicles.

Real-Time Travel Time Estimation Using Macroscopic Traffic Flow Models, Pushkin Kachroo, Kaan Ozbay, Antoine G. Hobeika

Electrical & Computer Engineering Faculty Research

This paper presents the estimation of travel time on highways based on macroscopic modelling. The focus is on real-time values as compared to average or static values. The macroscopic models are used for distributed and time/space lumped settings and corresponding travel time estimation functions and algorithms are developed. The implications of these algorithms for the implementation of various incident management and traffic control strategies are also discussed.

Comparison Of Two Distributed Fuzzy Logic Controllers For Flexible-Link Manipulators, Linda Z. Shi, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The paper suggests that fuzzy logic controllers present a computationally efficient and robust alternative to conventional controllers. The paper presents two possible structures for the distributed fuzzy logic controller of a single-link flexible manipulator. A linear quadratic regulator method is used to prove the effectiveness of fuzzy logic controllers.

Design Of Fuzzy Logic Controllers For Optimal Performance, Mohamed Trabia

Mechanical Engineering Faculty Presentations

While fuzzy logic controllers are generally robust, the performance of a system whose behavior is not well understood, or that has a large number of coupled inputs and outputs, may be less than optimal. In this paper, nonlinear programming techniques are used to improve the performance of a fuzzy logic controller for navigating an autonomous vehicle.

Overview Of Fuzzy Logic, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The presentation includes a brief introduction to fuzzy logic and fuzzy logic controllers. These concepts are illustrated by an example of an autonomous vehicle controller.

Alternative Principal Components Regression Procedures For Dendrohydrologic Reconstructions, Hugo G. Hidalgo, Thomas C. Piechota, John A. Dracup

Civil and Environmental Engineering and Construction Faculty Research

Streamflow reconstruction using tree ring information (dendrohydrology) has traditionally used principal components analysis (PCA) and stepwise regression to form a transfer function. However, PCA has several procedural choices that may result in very different reconstructions. This study assesses the different procedures in PCA-based regression and suggests alternative procedures for selection of variables and principal components. Cross-validation statistics are presented as an alternative for independently testing and identifying the optimal model. The objective is to use these statistics as a measure of the model's performance to find a conceptually acceptable model with a low prediction error and the fewest number of …

Validation Of Waimss Incident Duration Estimation Model, Wei Wu, Pushkin Kachroo, Kaan Ozbay

Electrical & Computer Engineering Faculty Research

This paper presents an effort to validate the traffic incident duration estimation model of WAIMSS (wide area incident management support system). Duration estimation model of WAIMSS predicts the incident duration based on an estimation tree which was calibrated using incident data collected in Northern Virginia. Due to the limited sample size, a full scale test of the distribution, mean and variance of incident duration was performed only for the root node of the estimation tree, white only mean tests were executed at all other nodes whenever a data subset was available. Further studies were also conducted on the model error …

Investigating The Use Of Kalman Filtering Approaches For Dynamic Origin-Destination Trip Table Estimation, Pushkin Kachroo, Kaan Ozbay, Arvind Narayanan

Electrical & Computer Engineering Faculty Research

This paper studies the applicability of Kalman filtering approaches for network wide traveler origin-destination estimation from link traffic volumes. The paper evaluates the modeling assumptions of the Kalman filters and examines the implications of such assumptions.

A Mathmatical Model Of Primary Productivity And Limnological Patterns In Lake Mead, Lorne G. Everett

Publications (WR)

The temporal and spatial changes in chemical and biological properties of Lake Mead have been investigated, thereby indicating the sources of water pollution and the time of highest pollution potential. Planktonic organisms have been shown to indicate the presence of water problems. Macro- and micro-nutrient analyses have shown that primary productivity is not inhibited by limiting concentrations. A mathematical model has been developed, tested with one set of independent data, and shown worthy of management utility. Although the model works very well for the Lake Mead area, the physical reality of the Multiple Linear Regression equation should be tested on …