Melvin Leok’s Professional Blog

I have received a National Science Foundation Faculty Early Career Development (CAREER) Award in support of my work on “Computational Geometric Mechanics: Foundations, Computation, and Applications.” This is being funded by the Applied Mathematics Program of the Division of Mathematical Sciences.

NSF DMS-0747659
CAREER: Computational Geometric Mechanics: Foundations, Computation, and Applications
Melvin Leok, Purdue University

Abstract:

Symmetry, and the study of invariant and equivariant objects, is a deep and unifying principle underlying a variety of mathematical fields. In particular, geometric mechanics is characterized by the application of symmetry and differential geometric techniques to Lagrangian and Hamiltonian mechanics, and geometric integration is concerned with the construction of numerical methods with geometric invariant and equivariant properties. Computational geometric mechanics blends these fields, and uses a self-consistent discretization of geometry and mechanics to systematically construct geometric structure-preserving numerical schemes. The proposed research will combine theoretical and computational tools arising from Dirac mechanics and geometry, noncommutative harmonic analysis, and uncertainty quantification to dramatically extend the applicability of computational geometric mechanics and geometric control to engineering problems that evolve intrinsically on nonlinear spaces, such as Lie groups and homogeneous spaces. This will provide insights into the canonical discretization of Dirac constraints, nonholonomic constraints, and interconnected systems. In addition, the study of uncertainty in the context of geometric control will improve the robustness and reliability of the resulting numerical and computational tools.

This research will improve our ability to control interconnected systems of autonomous vehicles in a robust and efficient fashion, by explicitly taking into account the uncertainty inherent in our knowledge of the surrounding environment. Our results will be applicable to the control of distributed sensor networks, consisting of an interconnected set of satellites, unmanned aerial vehicles and underwater vehicles. Such sensor networks are an exciting new development in the field of remote sensing that has the potential to dramatically increase the efficiency, coverage, and reliability of the information we obtain about our oceans, environment, and climate. More broadly, most complex engineering systems can be expressed as an interconnected system of more elementary components, and our mathematical framework will allow us to more readily understand complex systems in terms of the behavior of its component parts and the manner in which they are interconnected.

Synopsis of CAREER Program
The Faculty Early Career Development (CAREER) Program is a Foundation-wide activity that offers the National Science Foundation’s most prestigious awards in support of the early career-development activities of those teacher-scholars who most effectively integrate research and education within the context of the mission of their organization. Such activities should build a firm foundation for a lifetime of integrated contributions to research and education.

SIAM is administering a travel grant program funded by the NSF for individuals affiliated with US institutions to attend the ICIAM conference in Zurich.

SIAM ICIAM website

Objectives
The objectives of the Young Investigator Program (YIP) are to attract to naval research outstanding new faculty members at institutions of higher education, to support their research, and to encourage their teaching and research careers. ONR anticipates making about 24 new awards in Fiscal Year 2007 to academic researchers who have received Ph.D. or equivalent degrees on or after 1 November 2001.

Awards
Awards of up to $100,000 per year for three years, with the possibility of additional support for capital equipment or collaborative research with a Navy laboratory, are made, based on research proposals and supporting materials. Special attention will be given to proposals in naval priority research areas, listed in the announcement. In addition, it is anticipated that two of these applicants receiving an ONR Young Investigator award will also be selected to receive a Presidential Early Career Award for Scientists and Engineers.

Eligibility
This program is open to U.S. citizens, nationals, and permanent residents holding tenure track or permanent faculty positions at U.S. institutions of higher education who have received graduate degrees (Ph.D. or equivalent) on or after the date published in the full announcement.

Grant website

PRF Summer Faculty Grant: Summer salary support of $7000 for two summer months of research.

PRF Research Grants: One year awards for 0.5 FTE PRF Research Assistantships.

PRF International Travel Grants: Up to $1000 for travel to present a paper, or serve in an official capacity in recognized international meetings.

These awards are intended to enhance the careers of the very best young faculty members in specified fields of science. Currently a total of 116 fellowships are awarded annually in seven fields: chemistry, computational and evolutionary molecular biology, computer science, economics, mathematics, neuroscience, and physics.

Fellowship website

Packard Fellowships for Science and Engineering
2006 Guidelines
Program Overview

The success of the Hewlett-Packard Company has been built on technology, derived in large measure from research and development in university laboratories. Because the endowment of the David and Lucile Packard Foundation would not have been possible without the success of HP and the research performed by university-educated engineers and scientists employed by this company, the Foundation has a long-standing interest in strengthening both university-based research and graduate education.

In 1988, the Foundation established the Packard Fellowships for Science and Engineering to allow the nation’s most promising young professors to pursue their science and engineering research with few funding restrictions and limited paperwork requirements. Every year, the Foundation invites the presidents of 50 universities to nominate two young professors each from their institutions. Nominations are carefully reviewed by an Advisory Panel of distinguished scientists and engineers. Recipients will receive individual grants of $625,000 distributed over 5 years. Of the $125,000 paid each year, $12,500 is available to the university as compensation for administrative costs.

What We Fund

Candidates must be faculty members who are eligible to serve as principal investigators engaged in research in the natural and physical sciences or engineering and must be within the first three years of their faculty careers. Disciplines that will be considered include physics, chemistry, mathematics, biology, astronomy, computer science, earth science, ocean science, and all branches of engineering. Candidates engaged in research in the social sciences will not be considered.

The intent of the Fellowship Program is to provide support for unusually creative researchers early in their careers; faculty members who are well established and well funded are less likely to receive the award. It is further the intent of the Foundation to emphasize support for innovative individual research that involves the Fellows, their students, and junior colleagues, rather than extensions or components of large-scale, ongoing research programs.

What We Do Not Fund

Recognizing that certain areas of contemporary science and engineering already have access to relatively generous funding (for example, clinical research, research associated with the design and construction of large national facilities such as accelerators and space stations, and applied research of direct relevance to national security), the Packard Fellowships are directed to other, less generously supported fields.

Nomination Procedure

Nominations are requested in January of each year from the presidents of 50 universities selected by the Advisory Panel. Two nominations may be made by the president of each institution. Candidates must be faculty members in the first three years of their faculty careers, that is, whose initial faculty appointments began no earlier than May 31, 2003, and no later than May 31, 2006.

Fellowship website

The AMS Centennial Research Fellowship Program makes awards annually to outstanding mathematicians to help further their careers in research. From 1997-2001, the fellowship program was aimed at recent PhDs. Recently, the AMS Council approved changes in the rules for the fellowships. The eligibility rules are as follows.

The primary selection criterion for the Centennial Fellowship is the excellence of the candidate’s research. Preference will be given to candidates who have not had extensive fellowship support in the past. Recipients may not hold the Centennial Fellowship concurrently with another research fellowship such as a Sloan or NSF Postdoctoral fellowship. Under normal circumstances, the fellowship cannot be deferred. A recipient of the fellowship shall have held his or her doctoral degree for at least three years and not more than twelve years at the inception of the award (that is, received between September 1, 1995 and September 1, 2004). Applications will be accepted from those currently holding a tenured, tenure track, post-doctoral, or comparable
(at the discretion of the selection committee) position at an institution in North America.

The stipend for fellowships awarded for 2007-2008 is expected to be US$66,000, with an additional expense allowance of about US$3,500. Acceptance of the fellowship cannot be postponed.

The number of fellowships to be awarded is small and depends on the amount of money contributed to the program. The Society supplements contributions as needed. One fellowship will be awarded for the 2007-2008 academic year. A list of previous fellowship winners can be found at http://www.ams.org/prizes-awards.

Applications should include a cogent plan indicating how the fellowship will be used. The plan should include travel to at least one other institution and should demonstrate that the fellowship will be used for more than reduction of teaching at the candidate’s home institution. The selection committee will consider the plan in addition to the quality of the candidate’s research, and will try to award the fellowship to those for whom the award would make a real difference in the development of their research careers. Work in all areas of mathematics, including interdisciplinary work, is eligible.

The deadline for receipt of applications is December 1, 2006.
Awards will be announced in February 2007 or earlier if possible.

Application forms can be printed from html or pdf files.

Reference forms can also be printed from html or pdf versions.

If you would like application and reference forms sent to you by US mail, contact the

Membership and Programs Department
American Mathematical Society
201 Charles Street
Providence, RI 02904-2294
prof-serv@ams.org
401-455-4107

Completed application and reference forms should be sent to the AMS at the address given above.

CAREER: The Faculty Early Career Development (CAREER) Program is a Foundation-wide activity that offers the National Science Foundation’s most prestigious awards in support of the early career-development activities of those teacher-scholars who most effectively integrate research and education within the context of the mission of their organization. Such activities should build a firm foundation for a lifetime of integrated contributions to research and education. NSF encourages submission of CAREER proposals from junior faculty members at all CAREER-eligible organizations and especially encourages women, members of underrepresented minority groups, and persons with disabilities to apply.

NSF CAREER Program

Writing an NSF Career Award proposal

So you want to win a CAREER award

CAREER Resources at TAMU

Science Career Development: Grants and Grant Writing Index

Funding opportunities for new and young faculty

Description of NSF DMS

Dear Colleague:

The Computational Mathematics Program of the Division of Mathematical
Sciences (DMS) at the National Science Foundation has a long history of
supporting basic research on numerical methods and algorithm design in
large-scale computation for problems in science and engineering. This
letter is to inform the mathematics community that the program has a
focused topic area in Fiscal Year 2007 that addresses long-time behavior
(LTB) of numerical methods in large scale scientific computing. This
area of emphasis should not discourage the community from submitting
proposals in the usual wide variety of computation-related fields, but
should be viewed as a special topic of interest.

The number of degrees of freedom, in particular the number of time
steps, for solving partial differential equations grows as computational
resources grow. Errors or numerical artifacts that may be insignificant
when the number of time steps to solution is relatively small can
dominate a calculation as this number reaches the tens or hundreds of
thousands. Such non-physical artifacts can come in a variety of forms,
from the accumulation of numerical truncation error, round-off error,
uncertainty in physical parameter values, model uncertainty, etc.
Theoretical error estimates containing constants that grow exponentially
with time are not adequate to address these effects. Further, as
computational platforms grow in size with increasing numbers of CPUs,
the advent of commodity multi-core processors, and the increasing
heterogeneity of computing environments, increasing care must be paid to
designing algorithms that are conducive to such architectures. The
trend in computational hardware is to have tens or hundreds of thousands
of processors with limited memory associated with each processor and
nodes that contain clusters of processors. It is critical that proposed
numerical approaches take into account various latencies and load
balancing issues that will certainly be encountered on such
architectures. Such large calculations produce very large data sets.
Algorithms for the efficient analysis and visualization of very large
data sets on such modern architectures in order to uncover hidden
correlations and structures are also of interest. Above all, the
physical correctness of the calculation is the most important issue.
Arriving at a physically relevant answer requires careful attention to
the above issues as well as others.

The Division of Mathematical Sciences of the Directorate for
Mathematical and Physical Sciences of the National Science Foundation
recognizes the needs and opportunities posed by this recent surge in
interest in long-time and large-scale computing. Unsolicited research
proposals to DMS addressing cross-cutting topics in one or more aspects
of large-scale scientific computing are considered a focused topic area
by the Computational Mathematics Program. We invite novel and creative
numerical approaches that address solving real physical problems in such
environments.

Proposals addressing this focused topic area should include the label
“LTB:” at the beginning of the proposal title. Such proposals should be
submitted to the Computational Mathematics Program before January 15,
2007; see the NSF web site,
http://www.nsf.gov/div/index.jsp?div=DMS.
Prior to submitting a proposal, investigators are strongly encouraged to
contact the Computational Mathematics Program.

Primary Contacts:
Dr. Leland Jameson, 703-292-4883, ljameson@nsf.gov
Dr. Thomas Russell, 703-292-4863, trussell@nsf.gov
Dr. Junping Wang, 703-292-4488, jwang@nsf.gov

Sincerely,
Peter March
Division Director
Division of Mathematical Sciences

The text of this letter is also found at
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf07002