Melvin Leok’s Professional Blog

Optimal control problems are formulated and efficient computational procedures are proposed for attitude dynamics of a rigid body with symmetry. The rigid body is assumed to act under a gravitational potential and under a structured control moment that respects the symmetry. The symmetry in the attitude dynamics system yields a conserved quantity, and it causes a fundamental singularity in the optimal control problem. The key feature of this paper is its use of computational procedures that are guaranteed to avoid the numerical ill-conditioning that originates from this symmetry. It also preserves the geometry of the attitude dynamics. The theoretical basis for the computational procedures is summarized, and examples of optimal attitude maneuvers for a 3D pendulum are presented.

arXiv:math.OC/0609482

A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot completely determine the attitude, but an attitude estimation scheme based on this measurement is developed; a feasible set compatible with the measurement is described and it is combined with an attitude dynamics model to obtain an attitude estimate. The attitude is globally represented by a rotation matrix, and the uncertainties are described by ellipsoidal sets. A numerical example for a spacecraft in a circular orbit is presented.

arXiv:math.OC/0609481

My National Science Foundation Applied Mathematics research grant includes funding to hire undergraduate research assistants to work on Computational Geometric Mechanics and its Applications to Geometric Control Theory.

The position is for 8 weeks during the summer, and the stipend is $3,200. Due to funding restrictions, this position is only available to U.S. citizens and permanent residents. Please contact me for more information.

Graduate Research Assistantships are available for students interested in pursuing a Ph.D. under my direction at Purdue. A description of my current research may be found in my research statement and my bibliography. Priority will be given to students who have passed their qualifying examinations.

Please send me an email if you are interested in one of these positions.

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