Leslie Greengard - US grants

Dr. Tamar Schlick is supported by a grant from the Theoretical and Computational Chemistry Program in the Chemistry Division, the Databases, Software Development and Computational Biology Program in the Division of Instrumentation and Resources, and the New Technologies Program in the Division of Advanced Scientific Computing to develop new computer algorithms for performing molecular mechanics and molecular dynamics calculations. These new algorithms will be used to predict nucleic acid and protein structures with the aid of supercomputers. In this research Schlick and coworkers will continue to address some of the fundamental computational and theoretical problems in the field of molecular modeling by: 1) devising more efficient nonlinear minimization techniques for complex large scale problems; 2) using larger time steps in molecular dynamics simulations; 3) including quantum-mechanical effects in molecular dynamics simulations; and 4) reducing the computation time for the pairwise nonbonded interactions. The algorithms which are developed will be used to study sequence-dependent folding pathways of closed circular DNA duplexes. The ultimate goal of this research is to explore the detailed folding pathways and important transitions in nucleic acids and proteins.

One goal is to incorporate the Fast Multipole Method (FMM) into the molecular dynamics simulation package being developed by Charles Peskin and Tamar Schlick at the Courant Institute. In such particle simulations, the greatest computational burden has classically been that of evaluating the self-consistent electrostatic field induced by all of the partially charged individual atoms. This is precisely the problem addressed by the FMM. The hope is that certain inaccuracies in molecular dynamics calculations can be eliminated, yielding more physically reasonable results. The second major area of research is potential theory for the heat equation. Earlier work, in collaboration with John Strain, has yielded a scheme for the rapid evaluation of heat potentials. It is planned to devote substantial research time over the next few years to the examination of extensions of this scheme as well as its ramifications. The combination of potential theory and integral equations may provide a fundamental change in the way heat equations are solved, since spatially complex and time- dependent domains are handled without additional difficulty. It also appears likely that the method will extend in a natural way to variable coefficient and nonlinear parabolic partial differential equations. The third area of research is phase separation in material science. A new integral equation-based scheme has been constructed for the Laplace equation in multiply connected domains. It is planned to incorporate this method into a model of "Ostwald ripening," which follows the dynamic motion of the interface between two phases. This requires the solution of Laplace's equation at each step.

9404376 Kohn Coherent phase transformations lead to mixtures of different phases or phase variants with characteristic fine scale structures. The modelling of these microstructures is crucial for understanding macroscopic phenomena such as shape-memory behavior and hysteresis, as well as microscopic phenomena such as the morphology of twinning. In some situations the observed fine scale structures and macroscopic effects can be explained on the basis of elastic energy minimization. Mathematically, the essence of the matter is the minimization of nonconvex elastic energies with "multi-well structure. This project brings to bear a variety of tools, many of them relatively new, including relaxation of variational problems, the translation method, Young measure limits, H-measures, and singular perturbations. Energy minimizing microstructures can be viewed as composite materials with extremal effective behavior, so methods from homogenization and the analysis of composite materials are also relevant. The goals of this project include developing new mathematical tools, and also applying these tools to specific problems from materials science. One objective is to understand why some shape-memory alloys maintain their shape-memory behavior in polycrystalline form while others do not. Another is to explain experimental observations concerning twinning and hysteresis in single crystals of CuAlNi.

This is a proposal to modernize the computer network and the display terminals used by researchers of the Courant Institute in order to support research using high-performance computers and to support high-performance visualization methods in computer and information science and engineering research.

DMS Award Abstract
Award #: 0101439
PI: Kohn, Robert
Institution: New York University
Program: Applied Mathematics
Program Manager: Catherine Mavriplis

Title: Focused Research Group: Analysis and Simulation of Magnetic Devices

Nanoscale magnetic devices are of critical technological importance. This project will advance our understanding of their properties through a coordinated program of modeling, analysis, simulation and experiment. Topics to be addressed include (a) development of improved numerical methods for the simulation of magnetic materials and devices; (b) exploration of the micromagnetic "energy landscape" and the role of noise in thermally activated switching; and (c) investigation of specific nanoscale effects such as configurational anisotropy and geometrically constrained walls. Mathematics has much to contribute and much to gain. The study of appropriate limits leads to challenging problems of analysis whose solution will shed light on the essential physics. The analysis of noise and switching leads to the study of the energy landscape and to physically relevant examples of stochastic partial differential equations. Modeling coordinated with laboratory experiments will refine our understanding of the relevant phenomena. This Focused Research Group activity will draw expertise from a multidisciplinary group of mathematicians, physicists and computational scientists. The project includes a collaboration with IBM and training of postdoctoral scientists and graduate students.

Magnetic storage devices lie at the foundation of modern computing. Their modeling, simulation, analysis and design raise fundamental questions of physics and mathematics, many still unanswered. As device size decreases, the relevant science changes: defects, spatial disorder and thermal fluctuations become crucial in the nanoscale regime. Mathematics has much to contribute and much to gain. The study of appropriate limits leads to challenging problems of analysis whose solution will shed light on the essential physics. The analysis of noise and switching will be studied in a three-pronged approach: by mathematical analysis, numerical modeling and experimental investigation. Modeling coordinated with laboratory experiments will refine our understanding of the relevant phenomena. This Focused Research Group activity will draw expertise from a multidisciplinary group of mathematicians, physicists and computational scientists. The project includes a collaboration with IBM and training of postdoctoral scientists and graduate students.


Date: June 26, 2001

Many achievements in the biological and biomedical sciences are fueled by advances in technology and computational science. To address the complex challenges in the biological sciences in the 21st century, there is a growing need for professionals who can translate scientific problems in biology into mathematics and computations; for such productive work, familiarity with modern scientific computing approaches as well as key biological challenges is essential.

Intellectual Merit: This IGERT award is for a multidisciplinary Computational Biology (COB) doctoral program at NYU and MSSM targeting students interested in pursuing research in biology/biomedicine who require a transition from/to the mathematical/computer/physical sciences to best meet scientific challenges and career goals. This experimental, bidirectional program will offer integrative training that exploits NYU's strengths in applied mathematics, computer science, biology, and biochemistry, and Sinai's leadership in biomedicine. The major COB research themes - macromolecular modeling, computational genomics, and physiological modeling - will train students to investigate biological systems spanning wide temporal and spatial scales, from atoms and macromolecules, to cells and organs, to organisms. Modeling biological systems across such scales is essential for a modern systems biology approach aimed at understanding physiological processes and diseases and applying this knowledge to biomedicine.

To integrate training in biological and computational areas and provide trainees broad scientific perspectives and work experiences, the COB PhD program includes: (1) Dual faculty mentorship for thesis research; (2) Interdisciplinary training through flexible and background-tailored tracks in scientific computing and computational biology (courses in computer science, applied mathematics, biology, and biomedicine), trainee-led seminars, and ethics/research conduct courses, while ensuring competitive time to degree (5 years); (3) Summer internships in industry, academia, government (Agilent, IBM, Celera, Merck, Novasite and 3D Pharmaceuticals, supercomputing centers), or international laboratories; (4) Learning environments and activities that promote interdisciplinary interactions and broader collaborations within and outside NYU/MSSM, including: trainee-led COB seminars, annual COB retreat, and common COB lab/lounge; and (5) Mentoring and career development activities to ensure student retention, especially women and underrepresented groups, through student advisory committees, trainee-led support group, and partnerships with Burroughs Wellcome Fund and NYC's IGERT programs at CUNY and Columbia. The COB doctoral program will be evaluated and evolved continuously by its executive and internal/external advisors in close collaboration with the pedagogical experts of NYU's Center for Teaching Excellence (CTE).

Broader Impacts: COB will train math/computer science students to successfully model biological systems and, in turn, provide biology students the grounding in computational techniques so they can tailor the model and algorithms to specific biological problems. To help bridge disciplinary gaps, we will design background-tailored short (non-credit) courses before Year 1 and promote peer learning by pairing students from complementary backgrounds. We expect that COB's activities will enable trainees to act as catalysts for novel interdisciplinary collaborations and to acquire expertise in cutting-edge research areas; these experiences will prepare them uniquely for research and education careers in academia, industry, and government. In addition, COB's program of integrating scientific grounding, experience in team-oriented multidisciplinary projects, mentoring, and career broadening activities will serve as a new model of graduate training at NYU/MSSM and beyond, promote the development of curricula for computational biology, and provide the opportunity to develop the COB doctoral degree at NYU based on the new model. Recognizing the urgent need for diversity in the sciences, we will make concerted efforts in conjunction with participating departments and with successful new minority initiatives at NYU to recruit and retain the brightest students, especially women and other underrepresented groups.

IGERT is an NSF-wide program intended to meet the challenges of educating U.S. Ph.D. scientists and engineers with the interdisciplinary background, deep knowledge in a chosen discipline, and the technical, professional, and personal skills needed for the career demands of the future. The program is intended to catalyze a cultural change in graduate education by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. In this sixth year of the program, awards are being made to institutions for programs that collectively span the areas of science and engineering supported by NSF.

For at least two decades, high-level reports on the health of mathematical sciences research in the United States have recommended creation of a more direct path between this research and its users. The most obvious means for improving this connection is software, which is ubiquitous in science, engineering, business, medicine, as well as everyday life. Mathematics embodied in software can quickly bring new knowledge, insights, and methods to bear in contexts ranging from detecting tumors to finding the best travel route to deciding how to invest. The role of software as standard-bearer for the mathematical sciences is especially important for industry, where mathematical discoveries tend to be applied only if they have been transformed into software.
Successful production of high-quality, timely mathematical software brings an array of complex intellectual challenges requiring training not only in mathematics, but also in software development and the needs of application areas. Accordingly, the goal of this Research Training Group is to produce mathematical scientists with a deep, hands-on understanding of mathematical algorithms and their instantiation in software; in addition, we intend to make the crucial elements of the training program broadly available.
The faculty involved with this activity, from the Courant Institute of Mathematical Sciences at New York University, and the Applied Physics and Applied Mathematics Department at Columbia University, represent a variety of experiences in applied and computational mathematics, numerical algorithms and software, and real-world applications. Our belief is that the combined expertise of these researchers will provide a rich source of common insights that currently exist in relative isolation.
The Research Training Group will provide, for undergraduates, Ph.D. students, and postdoctoral researchers:
(1) training that explores in depth the relationships among mathematical modeling, algorithm design, software choices, and the hardware environment;
(2) understanding of how algorithm and software design may be affected, even driven, by the nature of problems and the contexts in which they need to be solved;
(3) hands-on experience of designing software that succeeds when it can and fails gracefully when it cannot.
At all levels, participants will experience individual and team involvement with mathematical software development. The undergraduate part of the program will include an enhanced curriculum and summer research experiences directly connecting the mathematical sciences with real-world applications. Ph.D. student training will include joint mentoring by faculty with expertise in applied and computational mathematics and scientific software, an enhanced curriculum that builds on the strengths of the two universities, and internships in government and industrial research laboratories. Postdocs will join longer-term projects with emphasis on applications, and will also be involved in undergraduate and graduate student training.
Our hope is that the experiences of this Research Training Group will be helpful in developing other programs with similar goals.

Fast Multipole Methods (FMMs) are widely used in many branches of science and technology, but there is a need for general-purpose, well-documented open source implementations of optimized versions of the method, suitable for use in the geosciences and other fields. One of the pressing needs for using FMMs is in conducting large-scale mathematical modeling of the occurrence of many earthquakes over a long period of time. Such simulations would produce a synthetic catalog of earthquakes, whose statistical properties, in both space and time, may be similar to the actual distribution of earthquakes that occur in nature. Such simulations are analogous to the global circulation models used by meteorologists and climate scientists to simulate weather and climate. In both cases, the objective is to use basic physical laws to simulate the behavior of a large and complex natural system. We have only recently gained enough knowledge about the complex non-linear geosystem that generates earthquakes that it is possible to conduct realistic earthquake simulations and test them against observed earthquake behavior. It is now possible that the simulations can be sufficiently realistic in detail and large enough in scale that they can be useful in understanding the physics of earthquakes as well as the probabilities of earthquake occurrence, understandings that have important societal benefits. This project will develop FMM algorithms and implement them for use with earthquake simulator codes. These improved codes will also be used to conduct much-improved earthquake simulations. The software we create will be useful for a variety of other applications in science and engineering beyond the one we focus on; we will provide our documented libraries with example problems on an open website and will publicize this to the scientific community.

This project will develop, test, and apply new generations of efficient computer programs that can generate hitherto impossible long artificial histories of earthquakes. These histories will enable scientists to understand patterns of occurrence that can be used for estimating the hazard that earthquakes pose to human life and property. For example, the California Earthquake Authority, which sets earthquake insurance rates with billions of dollars of implications for California and the world, presently bases its estimates of the probability of earthquake occurrence on methodology that many experts feel is inadequate. The ability to create computer models that generate many long sequences of earthquakes is regarded by experts as the next important step in improving our understanding of when and where earthquakes may occur in many earthquake prone regions of the USA and abroad. In many ways this approach is similar to the computer-based forecasts of weather and climate that are presently much more advanced than are forecasts of earthquake occurrence. The project involves a new and tight collaboration between mathematicians and earthquake scientists who previously have been developing state-of-the-art approaches in their fields independently. The computer programs that are produced will enhance the ability or society to make fast and efficient computer models with benefits in a range of scientific and engineering applications in addition to their usefulness in understanding earthquakes. The programs will be documented, publicized, and made freely available on a web site.