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MCSD Postdoctoral OpportunitiesThis document describes National Research Council Postdoctoral Research Associateships tenable within the Mathematical and Computational Sciences Division of the NIST Information Technology Laboratory.
Application Deadline: February 1 or August 1
Working closely with scientists in other NIST laboratories, we formulate large-scale but computationally feasible models, develop efficient computer programs, and validate our simulations by comparison with experimental results. This position requires knowledge of analytical and numerical methods and application areas. It is suitable for candidates whose interest is more in mathematical modeling than in the specific application. Candidates with backgrounds in applied mathematics, engineering, physics, and materials science are encouraged to suggest a specific project. 50.89.11.B2044
This work focuses on improving the environment for mathematical software research, development, and use. We are particularly interested in measurement techniques and tools which enable the testing and evaluation of mathematical software components for performance, reliability, reusability, and maintainability. Relevant areas of interest include special functions; partial differential equations; large, sparse linear systems; parallel algorithms; object-oriented software design; automated distribution mechanisms; and expert advisory systems. Recent examples of this work include the Matrix Market, a source of test data for evaluating large sparse matrix algorithms; and the Guide to Available Mathematical Software, a virtual mathematical software repository. Both are operated as publicly available network services. 50.89.11.B5020
This work centers around the NIST Digital Library of Mathematical Functions (DLMF), a new Web-based compendium on the special functions of applied mathematics, which is being modeled after the NBS Handbook of Mathematical Functions (U.S. Government Printing Office, 1964). The DLMF will provide significant new formulae, graphs, and tables in the form of a highly interactive Web-based information resource. A variety of challenges related to the on-line presentation and exploitation of mathematical reference data - both symbolic and numeric - are raised by this work. Among these are (1) dynamic, "intelligent" visualizations which enable insights into mathematical functions and their applications; (2) semantic-based representation, transformation, search, and retrieval of complex mathematical formulae; (3) development of dynamic mathematical content; (4) human-computer interfaces for mathematical reference data; and (5) client/server architectures for automated table generation and testing of user-supplied special function software. 50.89.11.B5021
We are collaborating with the NIST Physics and Electronics and Electrical Engineering Laboratories to developm technologies that enable computation to be done using quantum states of matter. We are interested in practical questions of mathematical physics arising in particular technologies being developed in the Physics Laboratory, such as trapped atoms and ions, as well as questions related to the theory of computation on devices of this type. Topics of interest include quantum computer architecture, quantum circuit design, quantum error control, quantum communications, quantum cryptography, quantum-based authentication, quantum algorithms, quantum languages, and quantum information theory. 50.89.11.B4824
Problems in applied mechanics of interest to NIST scientists are studied using methods of applied mathematics, especially a combination of asymptotic perturbation techniques and computation. Current research focuses on applications of ideas from nonlinear dynamics to physical problems arising in the study of manufacturing operations. Two particularly challenging and interesting classes of problems of this type involve the mathematical modeling of material deformation and of tool chatter during high-speed machining processes. 50.89.11.B2047
This work centers around reliable, computationally fast image restoration methods, with applications to medical and industrial imaging. Methods for estimating the system point spread function from the given degraded image are of interest, as are image enhancement procedures based on "shock filters". Geometric techniques for edge detection and segmentation for situations where the system point spread function is unobtainable, are of particular interest. 50.89.11.B2048
Our research projects are concerned with the application of stochastic processes in nonlinear dynamical systems and computational biology. Data from complex physical and biological systems present challenges to conventional modeling and statistical techniques. The goal is to apply recent theoretical advances in probability and dynamical systems to areas relevant to NIST's mission. We are currently concerned with probabilistic methods of detecting the onset of anomalous states or behavior in complex systems. Recent research has demonstrated the feasibility of real-time anomaly detection in physical systems that display nonlinear dynamics. Our research seeks to build on these advances by developing real-time methods for determining when such procedures would work. Our research in computational biology involves developing methods of pattern recognition and matching to be applied to current problems in bioinformatics. 50.89.11.B4448
This research opportunity focuses on improving numerical and symbolic computing support for the classical special functions of mathematical physics in parallel and other advanced computational settings through the development of algorithms and mathematical software. Emphasis in algorithm development is placed on functions of one or more complex variables. For example, a recurrence relation or differential equation can sometimes be solved in parallel to form a stable and effective algorithm in the complex domain. This approach has been applied successfully to Airy, Bessel, and other functions. The emphasis in software development is placed on the construction of robust and highly reliable packages and test procedures. An essential component is the use of the Internet to provide an interactive capability in the dissemination of mathematical reference data for special functions. The further development of these topics will require skills in real and complex analysis, numerical analysis, classical special functions, approximation theory, and parallel computing. 50.89.11.B2053
Numerical and analytical methods are used to study problems that involve convection or diffusion in physics and chemistry. Of particular interest is the formulation and implementation of methods that are suitable for large-scale computations. Analysis of model problems is also pursued when appropriate. One application is the description of convection occurring during the solidification of binary alloys. Interesting features of this problem include the existence of significantly different time scales associated with diffusion of temperature and concentration, and the behavior of the interface between the liquid and solid phases of the material. 50.89.11.B2054
We combine prababilistic methods with combinatorics to solve problems in the physical sciences, which can be formulated as combinatorial counting questions on graphs. We have devised novel formulations of statistical techniques such as importance sampling and Monte Carlo time that can be applied to these graph problems. We plan to extend these techniques to other fundamental problems related to measurement science and optimization of communications. 50.89.11.B5288
We are performing research in the design of object-oriented numerical software libraries. Our goal is to produce mathematical software which allows expression of algorithms at a high level of abstraction, is easy to use and maintain, and obtains optimal levels of efficiency on high performance and parallel architectures. Recent work has focused on the development of library suites for numerical linear algebra in C++ and Java for use in a variety of scientific and engineering applications. 50.89.11.B5022
We work with scientists in other NIST laboratories to develop computer simulation and analysis of magnetic systems. Model verification is achieved by comparison against experiment and by development of standard problems. This work includes development of public domain software for reference and research. Research focuses on micromagnetic modeling. 50.89.11.B4449
Applied Optimization and simulation form an area of engineering that sits between mathematics and computer science. They include computational tools used to solve important problems in engineering, economics, and all branches of science. Current concerns include the development and analysis of algorithms for the solution of problems of estimation, simulation and control of complex systems, and their implementations on computers. We are particularly interested in nonlinear optimization problems, which involve computationally intensive function evaluations. Such problems are ubiquitous; they arise in simulations with finite elements, in making statistical estimates, or simply in dealing with functions that are very difficult to handle. The comparability among the various techniques for numerical approximation through optimization algorithms is very important. What makes one formulation for the solution of a problem more desirable than another? This work requires the study and understanding of the delicate balance between the choices of mathematical approximation, computer architecture, data structures, and other factors - a balance crucial to the solution of many application-driven problems. 50.89.11.B4450
We are developing object-oriented computational tools for the analysis of material microstructure. The goal is to predict the macroscopic behavior of a material from knowledge of its microscopic geometry. Starting from a digitized micrograph, the program identifies features in the image, assigns material properties to them, generates a finite element mesh, and performs virtual measurements to determine the effect of the microstructure on the macroscopic properties of the system. More information is available at http://www.ctcms.nist.gov/oof/. Opportunities exist in image analysis, materials science, physics, and computer science. 50.89.11.B4451
With the continuing increase in speed and capability of commodity graphics processors, immersive visualization offers increasing opportunities to express scientifically meaningful results. Data at NIST spans a wide range from nano to cement to models that exhibit complex dynamics. This research will build on our open source software that runs on a linux desktop as well as immersively. Opportunities exist for 1) investigating the use of immersive visualization as a scientific instrument for exploration and representation of data, 2) developing ways to merge analysis with visualization and provide quantitative feedback into the visualization, 3) exploring and expressing uncertainties, 4) harnessing the growing capability of graphics processors to provide insight, 5) advancing the use of abstraction to express meaning in data, 6) developing user interaction methods, including direct manipulation techniques. 50.89.11.B6663
NIST scientists are currently automating experiments resulting in increasing amounts of generated data in multidimensional spaces. The data come primarily from combinatorial experiments in materials science. This type of data consists of image data with additional measurements at each pixel. Other experiments result in spectra-like measurements taken over spatial domains. These datasets require techniques that can sift through large amounts of data for items of potential interest, as well as for discovery. We are collaborating with these scientists on ways to mine this data for scientific insight. Opportunities exist for the application of datamining techniques such as classification, rule finding, and automated model building to these datasets, as well as for the development of new techniques. 50.89.11.B4825
The output of a computer model for the physical or chemical property of a material is frequently referred to as a virtual measurement to distinguish it from a physical measurement. Physical measurements are unable to keep pace with the faster and increasing needs of industry for properties of new materials. Interest in virtual measurements is also growing in applications involving toxic substances. Any measurement, whether physical or virtual, is incomplete without a statement of its associated uncertainty. This research program focuses on developing methodlogies for quantifying uncertainty associated with virtual measurements. This uncertainty arises almost entirely from systematic effects (biases) as opposed to statistical uncertainties. Therefore, new methodolgies for systematic effects need to be developed. Current interest is in quantum chemistry models and transition state theory. This research program has both methodological and computational components. 50.89.11.B5622
Simulations of high-consequence engineering, physical, chemical, and biological systems depend on complex mathematical models. Such models may include large number of variables, parameters with uncertainties, incomplete physical principles, and imperfect methods of numerical solution. To ensure the public that decisions made on the basis of such models are well founded, rigorous techniques for verification and validation of computer simulations must be developed. Techniques under investigation include stochastic modeling, metrology-based error analysis, standard reference benchmarks and protocols, design of physical and numerical experiments, and uncertainty analysis. We are also interested in applications to specific engineering, physical, chemical, and biological systems of technological importance; and basic research in continuum physics, irreversible non-equilibrium thermodynamics, nonlinear viscoplasticity theory, fatigue, fracture, and damage mechanics; fire-structure dynamics; nanoscale contact mechanics; cochlear mechanics of human inner ear; and stability of stochastic elastic, viscoelastic, and viscoplastic systems. 50.89.11.B6328
As the size and computational power of parallel and distributed computing systems increase, it is important to continually investigate the appropriateness of the algorithms we use for our scientific applications. Although we always strive to design and build scalable parallel applications, we must re-think these deigns when the available computational resources increase in power by even as small as a single order of magnitude with respect to the number of processors, main memory size, network speed, or other relevant parameters. This research opportunity focuses on (1) investigating and developing new parallel algorithms, especially for scientific applications, for the next generation of computing platforms; (2) characterizing the programming models presented by new parallel and distributed computing platforms; (3) investigating the design and performance of parallel programming languages and libraries; and (4) investigating the role of web services, fourth generation languages such as Matlab and Mathematica, computational grids, and other developing technologies in providing novel high-performance computing environments. 50.89.11.B6377
Problems arising in modeling communication systems, including antennas, microwave guides, and opto-electronic devices, are attacked with tools from scientific computation, numerical analysis, and applied mathematics. Particular emphasis is placed on high-order convergent and reduced computational complexity techniques for numerical solution of integral equations and partial differential equations, including quadrature methods, fast multipole methods, and wavelet methods. Recently we have also explored coding issues arising in communication protocols, using analytical methods to understand issues of noise resilience and communication security. 50.89.12.B3967
Quantum information science covers the theoretical and experimental areas involving the use of quantum mechanics in communication and computation. We are particularly interested in benchmarking proposed physical system's performance on quantum information processing tasks, scalably realizing logical qubits, and developing algorithms that take advantage of quantum resources. The research is inspired by and will contribute to the technologies being developed in the NIST Physics Laboratory. 50.89.12.B5623 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
