1-6 of 6 results
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Discontinuity-driven mesh adaptation method for hyperbolic conservation laws
PI Mihhail Berezovski
The proposed project is aimed at developing a highly accurate, efficient, and robust one-dimensional adaptive-mesh computational method for simulation of the propagation of discontinuities in solids. The principal part of this research is focused on the development of a new mesh adaptation technique and an accurate discontinuity tracking algorithm that will enhance the accuracy and efficiency of computations. The main idea is to combine the flexibility afforded by a dynamically moving mesh with the increased accuracy and efficiency of a discontinuity tracking algorithm, while preserving the stability of the scheme.
Key features of the proposed method are accuracy and stability, which will be ensured by the ability of the adaptive technique to preserve the modified mesh as close to the original fixed one as possible. To achieve this goal, a special monitor function is introduced along with an accurate grid reallocation technique. The resulting method, while based on the thermodynamically consistent numerical algorithm for wave and front propagation formulated in terms of excess quantities, incorporates special numerical techniques for an accurate and efficient interface tracking, and a dynamic grid reconstruction function. The numerical results using this method will be compared with results of phase-transition front propagation in solids and densification front propagation in metal foam obtained by applying the fixed-mesh method be used to justify the effectiveness and correctness of the proposed framework. This project will contribute significantly towards the development of corresponding methods in higher dimensions including dynamic crack propagation problems. Development of modern high-resolution finite-volume methods for propagation of discontinuities in solids, as well as of supplementary techniques, is essential for a broad class of problems arising in today's science. The broader impact of this project also includes educational purposes. The method used in this project will be incorporated into future projects for computational mathematics major students who will gain an experience in the state-of-the-art computational science.Categories: Faculty-Staff
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Comparison of Grades Based on Learning Mode: How Learning Environment Impacts Grades
PI John Griffith
CO-I Donna Roberts
CO-I Beverly Wood
A comparison of failure rates and grade distribution will be conducted between four learning disciplines utilized by Embry-Riddle Aeronautical University-Worldwide: Eagle Vision Classroom (synchronous classroom to classroom), Eagle Vision Home (synchronous home to home), Online and traditional classroom learning environments. Researchers will examine approximately 20,000 Embry-Riddle end-of-course student grades from the 2015-2016 academic year. The study will determine if significant relationships between failing grades and learning environment (modes) exist between the English, Humanities, Economics and Mathematics disciplines. Due to the continued technological advancements in course delivery, recommendations from previous studies in this area include continued research on the relationship of student performance and learning mode.
Universities are offering a greater number of courses over the Internet in a synchronous mode of instruction, utilizing headsets and webcams along with traditional classroom and online instruction (Foreman & Jenkins, 2005). In light of this continuing shift, this student replicates Dunn's (2013) earlier work, at least in concept, by examining the relationship between learning mode and student performance through analysis of approximately 20,000 student grades.
Embry-Riddle student course grades will be mined from the Campus Solutions database through the ERNIE Dashboard Portal. Data in the form of end of course grades (n=approximately 20,000) for the academic year 2015-2016 will be examined to test the hypotheses. No individual student identification will be obtained, used or reported in this study. Atypical grades including withdraws, incompletes or individual tutorials, will be excluded from the analysis. The researchers plan to use Chi Square tests at the appropriate degrees of freedom (α=.05) to evaluate the data (Gay, Mills, & Airasian, 2006). Four tests will be run for each course discipline (Economics, English, Humanities and Mathematics). The first two tests will evaluate the hypothesis regarding equivalency of failures for all modes of instruction. The first statistical test will compare the number of students who passed versus the number who failed for all modes (EV Home, EV Classroom, On-line and Classroom) of learning. A second statistical test will be conducted comparing just two modes at a time using a 2X2 contingency table to determine if modes and grades are related. Additional tests will be run to evaluate the hypothesis regarding equivalent grade distribution across the learning modes for each discipline. The third test will compare all the modes for each discipline to determine if learning mode and grades are related. The fourth test will allow researchers to compare two modes at a time using a 2X2 contingency table to determine if modes and grades are related.
References
Dunn, L. (2013). A study to compare and contrast student grades and satisfaction levels of traditional classroom and distance learning environments at Embry-Riddle Aeronautical University Worldwide Campus. (Unpublished master's degree Graduate Capstone Project). Embry-Riddle Aeronautical University, Worldwide Campus, Daytona Beach, FL.
Foreman, J., & Jenkins, R. (20015). Full-featured web conferencing systems. Innovate 1 (4) Retrieved from https://courseware.e-education.psu.edu/resources/Article_FullFeaturedWebConferencingSystems.pdf
Gay, L. R., Mills, G. E., & Airasian, P. W. (2006). Educational Research: Competencies for analysis and applications. (8th ed.). Upper Saddle River, New Jersey: Pearson Education, Inc.
Griffith, J. C., Roberts, D. L., & Schultz, M. C. (2014). Relationship between grades and modes of learning. The Journal of American Business Review, Cambridge, 3(1), 81-88.
Categories: Faculty-Staff
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Eco-Dolphin
PI Hong Liu
CO-I Zakaria Daud
CO-I Ci Wen
CO-I Dynamite Obinna
Eco-Dolphin is the name of a fleet of adaptive and cooperative automated underwater vehicles (AUVs) that a team of students at ERAU have been working on since January 2012.
By 2015, the platforms of the AUVs and basic navigation programs were tested. One of the major success is the demonstration of the Yellow Dolphin where four NASA astronauts participated in the NASA Extreme Environmental Mission Operation (NEEMO) during an event in the summer of 2014. Since 2015, the team started developing and testing the autonomous mission control programs based on the MOOS-IvP middleware developed by MIT and Oxford. Two peer reviewed conference proceedings with student coauthors were published. Students gave two to three presentations each year, including
- FURC, Florida Undergraduate Research Conferences 2012, 2013 and 2014
- SIAM SEA conference in FIT Melbourne, FL 2014
- CASE 2014 Creativity in the Arts and Sciences Event
- A3I Conference at Prescott Campus, 2014
- Discovery Day at Daytona Beach Campus, 2014
- Embry-Riddle Undergraduate Math Conference
- SIAM National Annual Conference
Categories: Undergraduate
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Collaborative Research: Wideband Multi-Beam Antenna Arrays: Low-Complexity Algorithms and Analog-CMOS Implementations
PI Sirani Mututhanthrige Perera
PI Arjuna Habarakada Madanayake
PI Soumyajit Mandal
Explosion of millimeter-wave (mm-wave) bandwidth opens up applications in 5G wireless systems spanning communications, localization, imaging, and radar. This project addresses challenges in mathematics, engineering, and science in developing efficient wideband beamformers based on sparse factorizations of the matrix called-delay Vandermonde matrices (DVM). The proposed highly integrated approach is attractive for mobile applications including 5G smart devices, the internet of things, mobile robotics, unmanned aerial vehicles, and other emerging applications focused on mm-waves.
A multi-beam array receiver is deeply difficult to realize in integrated circuit (IC) form due to the underlying complexity of its signal flow graph. Through the proposed work, mathematical methods based on the theories of i) sparse factorization and complexity of the structured complex DVM with the introduction of a super class for the discrete Fourier transform(which is DVM), and ii) approximation transforms are proved to solve this problem.
The resulting matrices are realized with multi-GHz bandwidths using analog ICs. The novel DVM algorithm solves the longstanding "beam squint" problem, i.e., the fact that the beam direction changes with input frequency, making true wideband operation impossible. Moreover, the proposed multi-beamforming networks in analog IC form will be realized efficiently while addressing precision circuit design, digital calibration, built-in self-test, etc. Besides scientific merits, both minority students and female students will be mentored to pursue careers in the STEM disciplines through the proposed project.
This project was funded by the National Science Foundation (the division of Electrical, Communications, and Cyber Systems) with award numbers 1711625 and 1711395.
Categories: Faculty-Staff
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Matrix Analysis and Operator Theory
PI Edward Poon
Matrices and operators are ubiquitous throughout science, engineering, and mathematics; they are the transformations that arise whenever one studies a linear system (or approximates a nonlinear system by a linear one). Examples include rotations and reflections (rigid motions of space), spin operators (quantum mechanics and quantum computing), stress tensors (mechanics), regression and curve fitting (statistics and data analysis), derivatives and linear differential operators (dynamical systems), to name just a few. By studying various properties, relations, and transformations of matrices and operators one may obtain insight into a wide range of phenomena.
One particular class of problems of interest is the study of preservers. For example, if M_n denotes the space of n x n matrices, one might ask for a complete classification of the isometries preserving a fixed norm. More generally, given any (possibly multi-valued) function f of a matrix (such as its determinant, rank, eigenvalues, singular values, numerical range, etc) one can ask for a description of the maps T:M_n -> M_n satisfying f(T(A)) = f(A) for all A in M_n; in this case one says that T preserves f. Usually one imposes some additional structure on T, requiring that it be linear, or simply additive, or multiplicative, and so on. One might also wish to describe those maps T leaving certain special subsets of matrices invariant (such as projections, unitaries, rank one matrices, etc.). A broad range of tools and concepts are used in solving such preserver problems; for example, consideration of the dual norm, coupled with convexity arguments, can be handy in classifying isometries, while majorization may appear in problems involving eigenvalues, singular values, and unitarily invariant norms. Currently, investigation is being conducted on isometries of certain matrix subalgebras, as well as preservers of certain collections of projections.
Categories: Faculty-Staff
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Simulation Based Inquiry Oriented Linear Algebra
CO-I Ashish Amresh
Games that teach introductory concepts in linear algebra such as vectors, span and dependence are created to be used by instructors in an undergraduate class.
A well-established National workforce need and critical challenge is to recruit and train students in Science, Technology, Engineering and Mathematics (STEM) fields. Since mathematics is a fundamental part of all STEM disciplines, success of undergraduate students in mathematics is a crucial ingredient to address this challenge. Linear algebra is a vital transition course for students in the STEM disciplines because of its unifying power within mathematics and its applicability to areas outside of mathematics. Accordingly, effective instruction at this stage in students' development is paramount. The focus of this project will be to improve teaching, learning, and student success in linear algebra by incorporating a blending of technology and several learning theories and applications to lead to new research results and production of curriculum resources. This project will leverage the investigators' previous research and curriculum development in Inquiry-Oriented Linear Algebra (IOLA) and expertise in Technology Based Learning to explore the unification of curriculum design and technology design theories and practices.
The goals of the project are to: (1) create a digital platform that will equip students with a virtual experience of a version of the IOLA curriculum; (2) document the affordances and constraints for learning using a game platform (IOLA-G) in comparison to face-to-face instruction by experienced IOLA instructors; (3) compare different digital gaming formats to determine which are most conducive to inquiry-oriented learning; and (4) use the knowledge gained from (1), (2), and (3) to improve student learning through the developed technology, and, reflexively, to enhance the existing IOLA curriculum and teacher support resources. The project team will investigate students' mathematical activity and learning while the students are engaged with the digital platform and will use this insight to inform further refinement of design. Building on prior research efforts in the learning and teaching of linear algebra and expertise in Game Based Learning (GBL), the team will design IOLA-G to mimic the problem-centered approach of the existing IOLA curriculum and will iteratively refine this platform through teaching experiments with students throughout the project. The project also will explore the extent to which GBL can provide a dynamic approach to addressing the constraints that larger class sizes place on instructors' implementation of inquiry-oriented curricula. In addition to, and as part of the process of, creating the resource technology, the investigators will incorporate a mixed methods approach with a blending of game-based learning design, curriculum design theory, and research from inquiry-based learning to explore the following research questions: What are the mathematical practices that students engage in and the conceptual understandings students develop using IOLA-G compared to when using only the face-to-face IOLA curriculum? What are the affordances and constraints of different game environments in terms of enacting an inquiry-oriented curriculum? The impact of the project will include the positive effects on STEM discipline student learning, knowledge, abilities, and overall success, which will lead to strengthening United States workforce needs in STEM areas.Categories: Faculty-Staff
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