Stephen Wiggins

Stephen Ray Wiggins is an American, British and Cherokee applied mathematician best known for his contributions in nonlinear dynamics, chaos theory and nonlinear phenomena, with applications to Lagrangian aspects of fluid transport and mixing and phase space aspects of theoretical chemistry.

Stephen R. Wiggins
Born
Oklahoma City, Oklahoma, US
NationalityAmerican, British, Cherokee
Alma materCornell
Known forFluid dynamics, nonlinear dynamics and chaos in classical mechanics and mechanics applied to atomic systems
Scientific career
FieldsPhysics, Chemistry, Applied Mathematics
InstitutionsUniversity of Bristol
California Institute of Technology
Doctoral advisorPhilip Holmes
Doctoral studentsTasso J. Kaper, Igor Mezić [1]

Early life and education

Wiggins was born in Oklahoma City, Oklahoma in 1959, and has two younger siblings. He is enrolled as a member of the Cherokee Nation.  He received a BSc in physics and mathematics in 1980 from Pittsburg State University in Pittsburg, Kansas. He has an MA in mathematics and a MSc in physics from the University of Wisconsin-Madison, earned in 1983. He attended Cornell University in Ithaca, New York, where he received his PhD in theoretical and applied mechanics in 1985. He also attended the Open University: Milton Keynes, in Great Britain, where he earned a Bachelor of Laws, with honors, in 2005.[2][3]

Academic career and field of study

Wiggins received his PhD from Cornell University, where he was influenced heavily by his PhD advisor Philip Holmes. His dissertation was on "Slowly Varying Oscillators."[4] From 1987 to 2001, he was a professor at Caltech.[5][6] He is actively working on the advancement of computational applied mathematics at the University of Bristol,[7] where he was the head of the Mathematics Department from 2004 until 2008, and was the School Research Director.[8] As of August 2020 Wiggins had 12 PhD students and 60 academic descendants.[4]

Wiggins has contributed in many different areas of applied mathematics, science, and engineering using applied and computational dynamics as the framework for his approach and analysis.[8]

His current focus is on developing the phase space approach to chemical reaction dynamics in the setting of the CHAMPS (Chemistry and Mathematics in Phase Space) project.[3][8]

Honors

Wiggins received the Presidential Young Investigators Award from the National Science Foundation (NSF) in August 1989.[9][8]

He was a Stanislaw M. Ulam Visiting Scholar at the Center for Nonlinear Studies, Los Alamos National Laboratory, from 1989 to 1990.[10]

He received the US Office of Naval Research (ONR) Young Investigator Award in Applied Analysis in 1989.[11]

Selected publications
  • V.J.García-Garrido; M.Katsanikas; M.Agaoglou; S.Wiggins: Tuning the branching ratio in a symmetric potential energy surface with a post-transition state bifurcation using external time dependence, Chemical Physics Letters, 2020-09: DOI: 10.1016/j.cplett.2020.137714 [12]
  • Fang Yang; Yayun Zheng; Jinqiao Duan; Ling Fu; Stephen Wiggins: The tipping times in an Arctic sea ice system under influence of extreme events, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020-06: DOI: 10.1063/5.0006626[13]

Books
  • Global Bifurcations and Chaos -- Analytical Methods. Springer-Verlag Applied Mathematical Science Series. 1988, second printing 1990. ISBN 0387967753
  • Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag textbooks in Applied Mathematics Series, 1990, second printing 1991. Second Edition (expanded) 2003. First edition translated into Japanese. ISBN 0387001778
  • Chaotic Transport in Dynamical Systems. Springer-Verlag Interdisciplinary Applied Mathematical Sciences Series, 1992. ISBN 0387975225
  • Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications. American Mathematical Society, 1993. ISBN 0821892029
  • Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer-Verlag Applied Mathematical Science Series, 1994. ISBN 038794205X
  • Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (with Y. Li). Springer-Verlag Applied Mathematical Science Series, 1997. ISBN 0387949259
  • Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (with R. Samelson). Springer-Verlag Interdisciplinary Applied Mathematical Sciences Series, 2006. Translated into Russian, 2010. ISBN 0387332693
  • Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications Micro to Macro, Fluids to Solids (with R. Sturman and J. M. Ottino). Cambridge University Press, 2006. ISBN 0521868130

Open books
  • Elementary Classical Mechanics. figshare. (2017)[14]
  • Ordinary Differential Equations. figshare. (2017)[15]
  • Solutions to the Exercises in Elementary Classical Mechanics. Figshare. (2018)[16]
  • Lagrangian Descriptors: Discovery and Quantification of Phase Space Structure and Transport[17]
  • Chemical Reactions: A Journey into Phase Space[18]
  • Wiggins, Stephen (2020): Elementary Quantum Mechanics. figshare. Book[19]
  • Wiggins, Stephen (2020): Solutions to the Exercises in Elementary Quantum Mechanics. figshare. Book[20]

References
  1. On the geometrical and statistical properties of dynamical systems : Theory and applications (phd). California Institute of Technology. 1994.
  2. ORCID. "Stephen Wiggins (0000-0002-0780-0911)". orcid.org. Retrieved 2020-09-13.
  3. "Stephen Wiggins". ResearchGate. Retrieved 13 September 2020.
  4. "Stephen Ray Wiggins". Mathgenealogy.org. Retrieved 21 September 2020.
  5. Kovačič, Gregor; Wiggins, Stephen (1992-06-15). "Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation". Physica D: Nonlinear Phenomena. 57 (1): 185–225. doi:10.1016/0167-2789(92)90092-2. ISSN 0167-2789.
  6. Smith, Douglas L. (2002). "Next Exit 0.5 Million Kilometers" (PDF). Engineering & Science. 4: 12. …Steve Wiggins [a Caltech professor from 1987 to2001].
  7. Bristol, University of. "People Profiler navigation". www.bristol.ac.uk. Retrieved 2020-09-21.
  8. "Steve Wiggins". CHAMPS. 2017-05-13. Retrieved 2020-09-21.
  9. "NSF 92-55 Directory of Awards, Engineering Directorate". NSF.gov. 27 May 1992. Retrieved 1 October 2020.
  10. "Center for Nonlinear Studies". cnls.lanl.gov. Retrieved 2020-10-01.
  11. Duan, Jinqiao (29 March 2019). "Big Data and the Dynamical Systems Approach: New Directions and Applications (chemistry, geophysical fluid dynamics) in Applied Mathematics". Retrieved 2020-10-01.
  12. García-Garrido, V. J.; Katsanikas, M.; Agaoglou, M.; Wiggins, S. (2020-09-01). "Tuning the branching ratio in a symmetric potential energy surface with a post-transition state bifurcation using external time dependence". Chemical Physics Letters. 754: 137714. arXiv:2006.05969. doi:10.1016/j.cplett.2020.137714. ISSN 0009-2614. S2CID 219558466.
  13. Yang, Fang; Zheng, Yayun; Duan, Jinqiao; Fu, Ling; Wiggins, Stephen (2020-06-01). "The tipping times in an Arctic sea ice system under influence of extreme events". Chaos: An Interdisciplinary Journal of Nonlinear Science. 30 (6): 063125. arXiv:2003.02407. doi:10.1063/5.0006626. ISSN 1054-1500. PMID 32611094. S2CID 212415032.
  14. Wiggins, Stephen (2017-08-14). "Elementary Classical Mechanics". figshare. doi:10.6084/m9.figshare.5309851.v3.
  15. Wiggins, Stephen (2017-08-15). "Ordinary Differential Equations". figshare. doi:10.6084/m9.figshare.5311612.v1.
  16. Wiggins, Stephen (2018-09-02). "Solutions to the Exercises in Elementary Classical Mechanics". figshare. doi:10.6084/m9.figshare.7038578.v1.
  17. "Authors — Lagrangian Descriptors". champsproject.github.io. Retrieved 2020-10-12.
  18. Agaoglou, Makrina; Aguilar-Sanjuan, Broncio; García-Garrido, Victor Jose; García-Meseguer, Rafael; González-Montoya, Francisco; Katsanikas, Matthaios; Krajňák, Vladimír; Naik, Shibabrat; Wiggins, Stephen (2019). "Chemical Reactions: A Journey into Phase Space". www.chemicalreactions.io. Retrieved 2020-10-12.
  19. Wiggins, Stephen (2020-09-08). "Elementary Quantum Mechanics". figshare. doi:10.6084/m9.figshare.12928595.v1.
  20. Wiggins, Stephen (2020-09-08). "Solutions to the Exercises in Elementary Quantum Mechanics". figshare. doi:10.6084/m9.figshare.12928673.v1.
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