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ACMD Postdoctoral Opportunities

This document describes National Research Council Postdoctoral Research Associateships tenable within the Applied and Computational Mathematics Division (ACMD) of the NIST Information Technology Laboratory.

 




NIST NRC Research Associateship Program

 

ACMD Research Topics and Advisors 

Gaithersburg, MD

Boulder, CO

  


 

Gaithersburg, MD

 

Mathematical Modeling

 Contact: Geoffrey B. McFadden

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.

Opportunity Number: 50.77.11.B2044

 

Dynamical Systems and Computational Biology

Contact: Fern Hunt

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 studying dynamical systems that arise from the control of computer networks, as well as the emergence of patterned behavior and aggregation in complex networks.

Opportunity Number: 50.77.11.B6285

 

Special Functions

Contact: Daniel W. Lozier

We are conducting a multidisciplinary program of research and development in special functions, focusing on functions that have recognized or potential importance in scientific applications. Scope includes, but is not limited to the functions that are covered in the NIST Digital Library of Mathematical Functions (http://dlmf.nist.gov). Research opportunities exist in (1) mathematical analysis, for example in asymptotics; (2) numerical and symbolic algorithms; (3) error analysis in numerical computations, especially error bounding; (4) numerical and symbolic software; (5) comparative analysis of available software; (6) software testing methodology; and (7) Web services in support of software comparison and testing.

Opportunity Number: 50.77.11.B2053

 

Computational Fluid Dynamics and Mathematical Modeling

Contact: Geoffrey B. McFadden

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.

Opportunity Number: 50.77.11.B2054

 

Parallel Adaptive Finite Elements

Contact: William F. Mitchell

This project focuses on the development and testing of new methods for the fast numerical solution of partial differential equations. We are interested in adaptive grid refinement techniques, hp-adaptive refinement, and reliable a posteriori error estimators for finite elements. We are also developing optimal order multigrid solvers and preconditioners. A primary interest is the effective implementation of these methods on modern high performance computer architectures, such as clusters of multi-core nodes.

Opportunity Number: 50.77.11.B7161

 

Combinatorial and Discrete Algorithms

Contact: Isabel Beichl

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.

Opportunity Number: 50.77.11.B5288

 

Object-Oriented Numerical Software

Contact: Roldan Pozo

We are performing research in the design of object-oriented scientific software in C++, C#, Java, and Python programming languages. Our goal is to produce mathematical software that allows expression of algorithms at a high level of abstraction, resulting in code that is easy to understand, use, and maintain, while obtaining competitive levels of efficiency on high-performance computer architectures. Recent work has focused on the development of software packages for numerical linear algebra, as well as software tools for the analysis of complex systems (network graphs).

Opportunity Number: 50.77.11.B5022

 

Mathematical Modeling of Magnetic Systems

Contact: Michael J. Donahue

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.

Opportunity Number: 50.77.11.B4449

 

Applied Optimization and Simulation

Contact: Anthony J. Kearsley

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.

Opportunity Number: 50.77.11.B4450

 

Finite Element Analysis of Material Microstructure

Contact: Stephen Langer

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.

Opportunity Number: 50.77.11.B4451

 

Real-time Quantitative Visualization

 Contact: Judith E. Terrill

We are working to create visualization systems that serve as precision measurement instruments, supporting interactive probing of "samples" to derive quantitative data to enable scientific discovery. We use virtual samples, built from data obtained from either physical measurement or computational simulation. Our ability to extend measurement science to the virtual world is enabled by advances in the speed and capability of graphics processing units (GPUs). In particular, visualization techniques that employ shaders have the potential to play a central role in measurement and analysis tools within a visualization system because these programs can perform substantial numeric processing within the visualization pipeline where they have direct access to the geometric data describing the objects of study. Additionally, this allows access to the information needed to determine uncertainties, a prerequisite for precision measurement. This research opportunity focuses all aspects of quantitative visualization, i.e., measurement and analysis applied to visualization objects directly in real-time.

Opportunity Number: 50.77.11.B7763

 

Virtual Measurements from Quantum Chemistry

Contact: Raghu N. Kacker

A measurement is the estimated value of a quantity plus a quantitative estimate of its uncertainty. A "virtual measurement" is a measurement produced by computation or simulation. Thus, the goal of this project is to determine the uncertainties associated with predictions from quantum chemistry calculations. Current work focuses on scaling factors, with associated uncertainties, for vibrational frequencies from ab initio and density-functional calculations. For fundamental vibrational frequencies and zero-point energies this has been completed. Scaling factors for anharmonic fundamental frequencies are now being developed. Future work will address predictions of thermochemical quantities such as entropies and heat capacities, which depend on the vibrational partition function. Alternatives to traditional frequency scaling will also be investigated.

Opportunity Number: 50.63.21.B6751

 

Stochastic Modeling, Verification, Validation, and Calibration of Computer Simulations

Contact: Jeffrey T. Fong

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.

Opportunity Number: 50.77.11.B6328

 

Complex Systems and Networks: Performance, Control, and Security 

Contact: V. Marbukh

We are developing novel methodologies and approaches to modeling complex systems consisting of a large number of interacting elements. The models should not only have predictive power, but should also provide guidance for controlling complex systems. Since performance of complex systems is characterized by multiple competing criteria, which include economic efficiency, resilience, and security, the purpose of control is optimization of the corresponding trade-offs. In a situation of complex systems comprised of selfish elements, control should take advantage of market mechanisms, which elicit desirable behavior through incentives. Resilience, robustness, and security should be modeled against malicious agents attempting to cause deterioration in the system performance.

Opportunity Number: 50.77.11.B7430

 

Cloud Computing and Combinatorial Software Testing

Contact: R. Kacker

Investigations of actual faults have shown that software failures can be triggered from certain combinations of the values of up to six variables. We have developed publicly available tools to generate test suites which assure that all t-way combinations for up to six are tested, have few test runs, and accommodate complex constraints inherent in the software under test. We are developing tools to identify faulty combinations from output of combinatorial test suites without assuming statistical models for the faults. Application domains include security, assurance of access control of health records, interoperability of systems, and assurance of modeling and simulation systems. We are investigating development of test infrastructures for cloud computing systems. It could target testing services running in the cloud or testing the cloud infrastructure or both. 

Opportunity Number: 50.77.11.B7496

 

Quantum Algorithms and Complexity

Contact: S. Jordan 

Quantum computers promise to solve certain computational problems faster than is possible using conventional classical algorithms. Although large-scale quantum computers do not yet exist, it is possible to mathematically analyze the computational power that quantum computers will have, if built. One branch of such analysis is the construction of quantum algorithms for specific computational problems. A second branch of such analysis uses the tools of computational complexity theory, which classify computational problems into complexity classes. We are involved in the design and analysis of quantum algorithms and in proving theorems about quantum complexity classes. We are particularly interested in quantum algorithms for simulating physical systems; alternative models of quantum computation, such as the adiabatic model; and quantum algorithms applied to cryptanalysis.

Opportunity Number: 50.77.11.B7891

 

Quantum Information and Cryptography

Contact: Yi-Kai Liu

Quantum mechanical devices can perform certain information processing tasks that are impossible using only classical physics. However, the construction of such devices requires new ideas from computer science, mathematics, and physics. We are interested in a broad range of topics in this area, including quantum devices that implement novel cryptographic functionalities, methods for testing and characterizing experimental quantum information processors, and classical cryptosystems that are secure against quantum adversaries. We are also interested in related areas such as quantum algorithms, complexity theory, and machine learning.

Opportunity Number: 50.77.11.B7913






Boulder, CO

 

Quantum Information Science 

Contact: E. (Manny) Knill

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 at NIST.

Opportunity Number: 50.77.12.B5623

 

Statistics for Quantum Systems 

Contact: S. Glancy or E. (Manny) Knill

Sophisticated, rigorous statistical tools are required to analyze data from experiments that manipulate and measure quantum systems with the goals of quantum computation, communication, and measurement. This project works to develop new methods for data analysis from quantum experiments. Particular applications of interest include quantum state and process tomography, certifying violation of local realism (e.g., in Bell tests), certification/quantification of randomness, and use of quantum resources to improve measurement precision. We work in close collaboration with experimental groups at NIST (trapped ions, superconducting qubits, photons) to assist experiment design and analysis and to inspire new theoretical research.

Opportunity Number: 50.77.12.B7973

 

Uncertainty Quantification and Computational Materials Science

Contact: A. Dienstfrey

We research and develop mathematical and statistical analysis and tools for uncertainty quantification in scientific computing, with particular emphasis on problems in computational material science. Application areas include, but are not limited to structural composites and electronic materials. This work, which is performed in collaboration with the NIST Material Measurement Laboratory, is in response to the multi-agency Materials Genome Initiative (http://www.whitehouse.gov/mgi/), which strives to reduce the time and costs for materials discovery, optimization, and deployment through the promotion of a new research and development paradigm in which computational modeling, simulation, and analysis will decrease the reliance on physical experimentation.

Opportunity Number: 50.77.12.B7897

 

Computational Electromagnetics

Contact: Zydrunas Gimbutas

We are developing high order integral equation methods and numerical tools for computational electromagnetics. This research focuses on the frequency domain electromagnetic field solvers that involve automatic geometry preprocessing/compressing in the presence of geometric singularities and coupling the obtained discretizations to the wideband fast multipole method based accelerators and direct solvers. Applications will include benchmarking, verification, and error analysis of magnetic resonance imaging simulators and electromagnetic scattering codes.

Opportunity Number: 50.77.12.B7912