Department of Mathematics
PEOPLE: Faculty

Florence J. Lin

Lecturer

Contact Information
E-mail: fjlin@usc.edu
Phone: (213) 740-0559
Office: KAP 266B

LINKS
Personal Website
 

Biographical Sketch

Prior to joining USC, Dr. Lin was a Bunting Fellow in applied mathematics at the Radcliffe Institute for Advanced Study at Harvard University and was awarded a National Science Foundation research planning grant in mathematics at the University of California at Berkeley. Dr. Lin held a faculty post in the Department of Chemistry and Biochemistry at the University of California at Los Angeles, and earlier held research posts at the Harvard-Smithsonian Center for Astrophysics and at Brookhaven National Laboratory.

Dr. Lin develops novel interdisciplinary research results merging geometric mechanics, molecular dynamics, and classical and quantum mechanics to obtain results supported by both experimental and computational observations in molecular dynamics. This research has been presented nationally and internationally to audiences including mathematicians, chemists, and physicists. Prof. Lin developed a course in wavelets for advanced undergraduate and graduate students, has taught numerical analysis, and has received teaching kudos with annual enrollments of 400 students providing annual revenues in excess of $1.6 million in 2005-06, 2006-07, and 2007-08.

Education

  • A.M. Physics, Harvard University
  • Ph.D. Chemical Physics, Harvard University
  • A.B. Mathematics and Chemistry, University of California, Berkeley
  • M.A. Mathematics, University of California, Berkeley
  • M.B.A. (Investments/Finance), University of Southern California

Description of Research

Summary Statement of Research Interests
Dr. Lin's research interests merge applied mathematics, physical chemistry, and chemical physics. In applied mathematics, Lin's work focuses on Hamiltonian dynamical systems, geometric mechanics, and numerical analysis. In physical chemistry and chemical physics, Lin's work focuses on classical and quantum molecular dynamics and computational molecular dynamics.

In current work, Lin combines ideas from classical mechanics (in physics), geometric mechanics (in mathematics), and classical molecular dynamics (in chemistry) to provide new insights for the molecular N-body problem, a classic problem in math and physics with applications in chemistry. By analogy with planets interacting through gravitational forces, Lin describes the dynamics of atoms interacting through intermolecular forces. Though relationships between overall rotation and internal motion within a rotating molecule are often ignored, Lin instead formulates the net overall rotation due to internal motion by using the principle of conservation of the total angular momentum (Discrete and Continuous Dynamical Systems, Supplement, vol. 2007, pp. 655 - 666 (2007)). Lin's formula for the net overall rotation due to internal motions (like the righting motion of a falling cat) explains why the net overall rotation will be large in particular situations. Both experimental and computational observations support this formula, including findings on rotations in proteins. The separation of overall rotation and internal motion in the N-body problem dates back to the work of Whittaker (in mathematics), Eckart (in physics) and Jellinek and Li (in chemistry); it is related to the theory of reduction in geometric mechanics (in mathematics). Lin's work has been presented nationally and internationally (in Canada, France, and Portugal) to audiences including mathematicians, chemists, and physicists.

Research Keywords
Hamiltonian dynamical systems, geometric mechanics, numerical analysis, classical and quantum molecular dynamics, computational molecular dynamics

Affiliations with Research Centers, Labs, and Other Institutions

  • Claremont Center for the Mathematical Sciences, faculty participant, Claremont Colleges Math-in-Industry Workshop, July 27-31, 2009,http://ccms.claremont.edu/mini

Conferences and Other Presentations

Conference Presentations
  • "Dynamics of the three-body problem in chemistry", World Congress of Nonlinear Analysts 2008, Talk/Oral Presentation, , Orlando, FL, International Federation of Nonlinear Analysts, Invited, 07/03/2008  
  • "Discrete mechanics and optimal control of molecular dynamics", International Conference on Difference Equations and Applications 2007, Talk/Oral Presentation, , Lisbon, Portugal, International Society of Difference Equations, Invited, 07/24/2007  
  • "Applications of geometric phases in classical mechanics: Molecular dynamics", 2006 Society of Industrial and Application Mathematics Annual Meeting, Talk/Oral Presentation, , Boston, MA, Society for Industrial and Applied Mathematics, Invited, 07/11/2006  
  • "Geometric mechanics and classical molecular dynamics", Program for Women in Mathematics, Talk/Oral Presentation, , Princeton, NJ, Institute for Advanced Study, Invited, 05/18/2002  
  • "Applications of symplectic mechanics in molecular dynamics", Program for Women in Mathematics, Talk/Oral Presentation, , Princeton, NJ, Institute for Advanced Study, Invited, 05/16/2002  
  • "Geometric mechanics, symmetry, and van der Waals complexes", William A. Klemperer Retiral Symposium, Talk/Oral Presentation, , Cambridge, MA, Harvard University, Invited, 05/11/2002  

Publications

Journal Article
  • Lin, F. J. (2008). Dynamics of the N-body problem: I. Molecular rotation due to internal motions.
  • Lin, F. J. (1997). Symplectic reduction, geometric phase, and three-body molecular dynamics. Physics Letters A/Elsevier. Vol. 234, pp. 291 - 300.
  • Lin, F. J., Marsden, J. E. (1992). Symplectic reduction and topology for applications in classical molecular dynamics. Journal of Mathematical Physics/American Institute of Physics. Vol. 33, pp. 1281 - 1294.
  • Lin, F. J., Muckerman, J. T. (1991). Solution of the time-dependent Schrodinger equation employing a basis of explicit discrete coordinate eigenfunctions: spherical and azimuthal symmetry, adiabaticity, and multiphoton excitation of a rotating Morse oscillator. Computer Physics Communications/Elsevier. Vol. 63, pp. 538 - 568.
  • Lin, F. J., Chance, K. V., Traub, W. A. (1987). Atomic oxygen in the lower thermosphere. Journal of Geophysical Research-Atmospheres/American Geophysical Union. Vol. 92, pp. 4325 - 4335.
  • Leopold, K. R., Fraser, G. T., Lin, F. J., Nelson, Jr., D. D., Klemperer, W. (1984). Microwave and radiofrequency Stark spectrum of ArHCN: A highly nonrigid molecule. Journal of Chemical Physics/American Institute of Physics. Vol. 81, pp. 4922 - 4931.
Proceedings
  • Lin, F. J. (2007). Hamiltonian dynamics of atom-diatomic molecule complexes and collisions. pp. 655 - 666. Discrete and Continuous Dynamical Systems, Supplement/American Institute of Mathematical Sciences.
  • Lin, F. J. (2003). Geometric mechanics for applications in diatomic and triatomic molecular dynamics. pp. 403-408. Philadelphia. Physical and Mathematical Aspects of Symmetries, Proceedings of the Twenty-Fourth International Colloquium on Group Theoretical Methods in Physics held in Paris, France, 15-20 July, 2002/Institute of Physics.

Advisement

Other Advisement or Time Devoted to Students
  • Co-founding faculty advisor, USC Student Chapter of the Society for Industrial and Applied Mathematics, 2004-2006  

New Courses Developed

  • MATH 499, Mathematics, Introduction to Fourier analysis and wavelets, Spring 2003   

Honors and Awards

  • USC or School/Dept Award for Teaching, Certificate of Appreciation, USC Chapter of Alpha Lambda Delta national honor society, 2006  
  • USC Women in Science and Engineering Award, Major Support for Continuing Faculty, 2003  
  • Bunting Institute Fellow, Radcliffe Institute for Advanced Study, Harvard University, 1993-1994   

Service to the University

Administrative Appointments
  • Assistant Director, Mathematics Computing Laboratories, Department of Mathematics, USC, 1999-2004  
Committees
  • Member, Non-tenure-track Faculty Policy Committee, Academic Senate, USC, 2008-2009   

Service to the Profession

Conferences Organized
  • Minisymposium organizer, Society for Industrial and Applied Mathematics Annual Meeting, Boston, MA, Applications of the geometric phase in classical mechanics, 2006  
Professional Memberships
  • Association for Women in Mathematics, 1993-  
  • American Mathematical Society, 1988-  
  • Society for Industrial and Applied Mathematics, 1983-  
  • American Physical Society, 1980-  
Other Service to the Profession
  • Session chair, N-Body Dynamics, Society for Industrial and Applied Mathematics (SIAM) Conference on Applications of Dynamical Systems, May 17-21, 2009, Snowbird, Utah, 05/17/2009  
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