Grants and Awards
In FY 2005 the WPI Department of Mathematical Sciences crossed the threshold of over $1 million in research funding.
Below is a list of newly awarded and continuing grants in 2008-2009.
Yakovlev, V.
Comprehensive Electromagnetic-Thermal-Mechanical Model for Microwave Sintering of Particulate Materials
EADS Foundation
2009
Vadim Yakovlev was awarded a grant by the EADS Foundation (EADS is best known for being the parent company of Airbus), for the project "Comprehensive Electromagnetic-Thermal-Mechanical Model for Microwave Sintering of Particulate Materials".
WPI's portion ($65,500 Euros) is a part of the total of 159,900 Euros (currently, nearly $240,000) awarded by the Foundation to the team of three research groups (including the Materials Science and Engineering Laboratory of the Grenoble Institute of Technology, France and the Microwave for Materials Processing Group of EMPA - the Swiss Federal Laboratories for Materials Science and Technology). The program is dedicated to the development of an innovative technique for modeling of microwave sintering of realistic particulate (including nano-structured) materials. The project aims to build up a comprehensive macroscopic numerical model embracing three most essential components of high temperature microwave sintering of dielectric and metallic powders.
Mitrea, I.
Support of Sonia Kovalevsky High School Mathematics Day
Association For Women In Mathematics
2009
Sonia Kovalevsky High School Mathematics Day is aimed at 9th and 10th grade women students from the Worcester area. The event will consist of a mix of plenary lectures that introduce participants to the lives and mathematical accomplishments of remarkable women mathematicians and parallel sessions on different topics in mathematics of interest to high school students. It is expected that the program will bring together 60 women high school students, 15 high school teachers, and women undergraduate and graduate students in mathematics at WPI.
Walker, H.
Anderson Acceleration for Fixed-Point Iteration
National Science Foundation
2009 - 2011
This research will focus on acceleration methods for fixed-point iteration that are based on a method introduced by D. G. Anderson in 1965. This method has been used widely and with considerable success within the computational physics, chemistry, and materials communities as a means of accelerating the self-consistent field iteration used in electronic structure computations. However, it has been untried or underexploited in many other important applications in which it seems likely to be equally successful. Moreover, it has received relatively little attention from mathematicians and numerical analysts, despite there being many significant unanswered mathematical questions. The goals of this research are to analyze the convergence of the method, to explore its effectiveness across a broad range of important applications, and ultimately to develop extensions with improved global convergence and stability properties.
Fehribach, J., Co-PI: Vernescu, B.
Collaborative Research: Special Meetings: The MPI Workshop
National Science Foundation
2008 - 2011
This proposal is a collaborative effort amongst researchers at Rensselaer Polytechnic Institute, the University of Delaware, and Worcester Polytechnic Institute to expand and strengthen the Mathematical Problems in Industry (MPI) Workshop, an annual meeting run each June in cooperation with the Graduate Student Mathematical Modeling (GSMM) Camp. The MPI Workshop is a five-day meeting which attracts leading applied mathematicians, scientists and engineers from industry, universities and national laboratories. The focus of the Workshop is a set of problems brought by contributing participants from industry. These problems span a wide range of application areas, often in fluid and solid mechanics but also in mathematical biology, data analysis, and mathematical finance, among others. Work on the problems is done in vertically integrated teams consisting of the representatives from industry, senior and junior faculty, postdocs and graduate students. The main objective of the Workshop is to provide links between mathematicians at universities and scientists and engineers from industry for the mutual benefit of both sides.
Fehribach, J.
Vector Spaces and Kirchhoff Graphs
National Science Foundation
2007 - 2009
This project concerns chemical, electrochemical, and biochemical reaction networks, reaction routes (reaction pathways) through these networks, and the depiction of these networks using Kirchhoff graphs. This work will build on a vector space approach to reaction routes to establish that one or more Kirchhoff graphs exist for any given reaction network and to develop a method for constructing these graphs. Neither of these results is obvious for arbitrary reaction networks.
Gobert, J., Co-PIs: Kim, R., Heffernan, N., Ruiz, C.
ASSISTments Meets Inquiry
National Science Foundation
2007 - 2009
The Worcester Polytechnic Institute (WPI) five-year proposal addresses middle school students need to learn science more deeply through the improvement of inquiry science assessment. An outgrowth of the WPI-developed ASSISTments Systems for Math, and REC-funded Modeling Across the Curriculum, the proposal's main goal is to develop a rigorous, technology-based system for middle school standards-aligned assessment of inquiry skills (i.e., interpreting data, formulating hypotheses and predictions, conducting experiments, collecting data, mathematizing, and communicating and defending hypotheses) in six physical science content areas (i.e., Properties of Matter; Elements, Compounds, and Mixtures; Motion of Objects; Forms of Energy; and Heat Energy). Assessments will be aligned with the Massachusetts Curricular Framework and the National Science Education Standards.
Larsen, C.
Damage and Fracture Evolution
National Science Foundation
2008 - 2011
The investigator develops and studies models for the evolution of elastic damage (i.e., regions of weakened elastic properties) and fracture. Difficulties come from, among other things, the irreversibility of these phenomena, and the fact that existing models are essentially variational (static). The general strategy is to first develop quasi-static models that are consistent with these variational principles, and prove existence and approximation results. Next, the goal is to extend these results to the fully dynamic setting. The first step has been essentially completed for damage and brittle fracture, and the investigator works on developing corresponding methods for cohesive fracture. Dynamic models and their analysis are major open problems for all these phenomena, and are the main focus of this project.
Sunar, B., Co-PI: Martin, W.
Exploring Physical Functions for Lightweight and Robust Cryptography
National Science Foundation
2008 - 2010
Low cost devices, e.g. RFIDs, smartcards, sensor nodes, etc., are becoming crucial for building the next generation pervasive and ubiquitous heterogeneous networks. Given the massive volume, the per-unit manufacturing cost will play a key role in the adoption of these technologies. These devices are constrained in their available computational power and footprint. Yet, their cryptographic units, which tend to be among the most demanding components in the device architecture, need to be hardened against physical tampering. The project is exploiting hardware anomalies for cryptographic ends. Even as chip manufacturing progresses and becomes more precise, one can always expect slight variations along the production line which can be used to distinguish one physical device from any other manufactured on the same production line. The team is developing models, processes and hardware primitives which contribute to the goal of exploiting these individual fingerprints so that they can be used to efficiently identify devices and enable secure, tamper-resilient communication. This initiative is providing low-cost, tamper-resilient cryptography from physical functions, and thereby plays an enabling role in the adoption of a wide array of products and applications to the benefit of the national economy and national security. The results of this project include new physically unclonable function (PUF) constructions with a particular emphasis on constructions which naturally permit reduction to computationally difficult problems, PUF-enabled cryptographic building blocks (such as secure and efficient storage, tamper-resilient state machines, etc.) and PUF-enabled cryptographic primitives (e.g. authentication schemes, block ciphers, pseudo-random generators).
Mosco, U., Co-PI: Vernescu, B.
Transmission Problems and Large Surfaces
National Science Foundation
2008 - 2011
The investigator and his colleagues study mathematical problems with large surfaces and small volumes that arise in physics (e.g., highly fragmented electrical conductors, high voltage electric discharges, electrolytic deposition, diffusion-limited aggregation), chemistry (catalytic converters, surface chemistry), biology (cell membranes, vascular systems), engineering (hydraulic fracturing in oil wells, thin ramified fibers, elastic thin bodies, towers and bridges in open space). In all these problems a lower-dimensional physical body -- the "surface" -- intrudes and interacts with a full dimensional surrounding body -- the "volume." The volume is small, the surface is large, possibly fractal and with infinite area. In this project, the mathematics of fractal structures in space is focused on two fundamental issues: 1) second order transmission conditions for second order operators; 2) singular homogenization with fractal terms. New tools of analysis are developed, like Hoelder metrics and measure-valued Lagrangeans. Finite element numerical approximations provide the quantitative and flexible setting required by prospective applications such as those mentioned above.
Tang, D., Co-PIs: Petruccelli, J., Walker, H.,
Multi-Physics Modeling and Meshless Methods for Atherosclerotic Plaque Progression
National Science Foundation
2006 - 2009
Cardiovascular disease (CVD) is the leading cause of death in the developed world and is expected to become the leading cause of death worldwide by 2020. In the US alone, 36% of 45 year olds and 80% of those 75 and older have CVD (American Heart Association Statistics 2005). Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Many victims of the disease who are apparently healthy die suddenly without prior symptoms. Non-invasive screening and diagnostic methods are urgently needed to identify the victims early and avoid those tragic events. The objective of this project is to combine computational modeling, magnetic resonance imaging (MRI) and pathological analysis to simulate plaque progression and quantify critical blood flow and plaque stress/strain conditions under which plaque rupture is likely to occur. MRI and pathological analysis will be used to quantify human carotid plaque morphology and progression and to assess plaque vulnerability. For the first time, multi-year MRI patient-tracking data will be obtained to quantify human atherosclerotic plaque progression. MRI-based three-dimensional (3D) computational models with multi-component plaque structure and fluid-structure interactions (FSI) will be developed and solved by numerical methods based on the meshless local Petrov-Galerkin (MLPG) method to obtain critical flow and plaque stress/strain conditions, to identify suitable plaque rupture risk indicators for more accurate plaque assessment, and to simulate plaque progression for early prediction and diagnosis of related cardiovascular diseases.
Tang, D., Co-PIs: Sotak, C., Hoffman, A., Woodard, PK.
MRI-Based Computational Modeling for Carotid Plaque Rupture and Stroke
Department of Health and Human Services
2004 - 2009
The objectives of this project are to integrate computational modeling, Magnetic Resonance Imaging (MRI) technology, ultrasound/Doppler technology (US), mechanical testing, and pathological analysis to perform quantitative mechanical analysis to atherosclerotic carotid plaques, to quantify critical blood flow and plaque stress/strain conditions under which plaque rupture is likely to occur, and to seek the potential that quantitative mechanical analysis can be integrated into state-of-the-art imaging technologies for better screening and diagnostic applications.
Tang, D.
Image-Based Computational Mechanical Analysis and Indexing for Cardiovascular Diseases From Invention to Commercialization
The Kalenian Award
2008 - 2009
Volkov, D.
Reconstruction of faults from surface displacements
National Science Foundation
2007 - 2010
The goals of the proposed research are (1) to measure surface displacements and use the measured surface displacements as data for the inverse problem of locating faults and portraying their geometry, and (2) to develop criteria for deciding whether a fault system is in its nucleation phase, which would suggest that an earthquake is imminent. First, the mathematical framework for a stability analysis of displacement fields near equilibrium will be developed, and the Green's tensor for the half-space fault eigenvalue problem will be derived. Next, using rigorous mathematical analysis, questions of convergence will be addressed as the depth of the medium increases, and convergence rates will be verified by high-order numerical schemes for hypersingular boundary integral equations. Finally, closed form recovery formulas hinging on the dominant term of the depth asymptotics will be derived and combined with a fast minimization method. The PI will infer robust algorithms for solving the fault inverse problem. Reconstruction methods will be tested first on synthetic data and then used on data coming from field measurements of surface dislocations.
Weekes, S.
REU Site: Research Experience for Undergraduates in Industrial Mathematics and Statistics
National Science Foundation
2007 - 2009
The Research Experience for Undergraduates in Industrial Mathematics and Statistics at WPI provides a unique educational experience for students of mathematics by introducing them to research in an industrial environment. The students work in teams on problems provided by local business and industry. They work closely with a company representative to define the problem and develop solutions of immediate value to the company. They work closely with a faculty advisor to maintain a clear focus on the mathematics and statistics at the core of the project.
The site is supported by the Department of Defense in partnership with the NSF REU program.
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Last modified: November 12, 2009 10:18:21