Stephen Wiggins Explained

Stephen R. Wiggins
Birth Place:	Oklahoma City, Oklahoma, US
Nationality:	American, British, Cherokee
Field:	Physics, Chemistry, Applied Mathematics
Work Institution:	University of Bristol California Institute of Technology
Alma Mater:	Pittsburg State University - BSc University of Wisconsin - MA, MSc Cornell University - PhD
Doctoral Advisor:	Philip Holmes
Doctoral Students:	Tasso J. Kaper, Igor Mezić^[1]
Known For:	Fluid dynamics, nonlinear dynamics and chaos in classical mechanics and mechanics applied to atomic systems

Stephen Ray Wiggins (born 1959) is a Cherokee-American applied mathematics researcher and distinguished educator, also of British heritage, best known for his contributions in nonlinear dynamics, chaos theory and nonlinear phenomena. His wide contributions include Lagrangian aspects of fluid dynamics and reaction dynamics in theoretical chemistry.

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 from Pittsburg State University in 1980, an MA in mathematics and an MSc in physics from the University of Wisconsin-Madison in 1983, and a PhD in theoretical and applied mechanics from Cornell University in 1985. He also attended the Open University in Great Britain, where he earned a Bachelor of Laws, with honors, in 2005.^{[2] [3]}

Academic career and field of study

Wiggins 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.

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.

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. Previously he has established quite successful US-UK-Spain research network in building novel foundational connection between applied mathematics and theoretical chemistry.^[9]

Honors

Wiggins received the Presidential Young Investigators Award from the National Science Foundation (NSF) in August 1989.^[10]

He was a Stanislaw M. Ulam Visiting Scholar at the Center for Nonlinear Studies, Los Alamos National Laboratory, from 1989 to 1990.^[11]

He received the US Office of Naval Research (ONR) Young Investigator Award in Applied Analysis in 1989.^[12]

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 ^[13]
• 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^[14]

Books

• Global Bifurcations and Chaos -- Analytical Methods. Springer-Verlag Applied Mathematical Science Series. 1988, second printing 1990.
• 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.
• Chaotic Transport in Dynamical Systems. Springer-Verlag Interdisciplinary Applied Mathematical Sciences Series, 1992.
• Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications. American Mathematical Society, 1993.
• Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer-Verlag Applied Mathematical Science Series, 1994.
• Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (with Y. Li). Springer-Verlag Applied Mathematical Science Series, 1997.
• 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.
• 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.

Open books

• Elementary Classical Mechanics. figshare. (2017)^[15]
• Ordinary Differential Equations. figshare. (2017)^[16]
• Solutions to the Exercises in Elementary Classical Mechanics. Figshare. (2018)^[17]
• Lagrangian Descriptors: Discovery and Quantification of Phase Space Structure and Transport^[18]
• Chemical Reactions: A Journey into Phase Space^[19]
• Wiggins, Stephen (2020): Elementary Quantum Mechanics. figshare. Book^[20]
• Wiggins, Stephen (2020): Solutions to the Exercises in Elementary Quantum Mechanics. figshare. Book^[21]

External links

• CHAMPS Project
• Google Scholar
• ORCID

Notes and References

1. On the geometrical and statistical properties of dynamical systems : Theory and applications. 1994. California Institute of Technology. phd.
2. Web site: ORCID. Stephen Wiggins (0000-0002-0780-0911). 2020-09-13. orcid.org. en.
3. Web site: Stephen Wiggins. 13 September 2020. ResearchGate.
4. Web site: Stephen Ray Wiggins. 21 September 2020. Mathgenealogy.org.
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. en. 57. 1. 185–225. 10.1016/0167-2789(92)90092-2. 0167-2789.
6. Smith. Douglas L.. 2002. Next Exit 0.5 Million Kilometers. Engineering & Science. 4. 12. …Steve Wiggins [a Caltech professor from 1987 to2001]..
7. Web site: Bristol. University of. People Profiler navigation. 2020-09-21. www.bristol.ac.uk. en-GB.
8. Web site: 2017-05-13. Steve Wiggins. 2020-09-21. CHAMPS. en.
9. Uzer. Turgay. Jaffé . C.. Palacián . J.. Yanguas Palacián . P.. Wiggins. Stephen. The geometry of reaction dynamics. Nonlinearity. en. 15. 4. 957.
10. Web site: 27 May 1992. NSF 92-55 Directory of Awards, Engineering Directorate. 1 October 2020. NSF.gov.
11. Web site: Center for Nonlinear Studies. 2020-10-01. cnls.lanl.gov.
12. Web site: Jinqiao Duan. Duan. Jinqiao. 29 March 2019. Big Data and the Dynamical Systems Approach: New Directions and Applications (chemistry, geophysical fluid dynamics) in Applied Mathematics. 2020-10-01.
13. 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. en. 754. 137714. 10.1016/j.cplett.2020.137714. 2006.05969. 219558466. 0009-2614.
14. 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. 10.1063/5.0006626. 32611094. 2003.02407. 212415032. 1054-1500.
15. Wiggins, Stephen. 2017-08-14. Elementary Classical Mechanics. Figshare. en-US. 10.6084/m9.figshare.5309851.v3.
16. Wiggins, Stephen. 2017-08-15. Ordinary Differential Equations. Figshare. en-US. 10.6084/m9.figshare.5311612.v1.
17. Wiggins, Stephen. 2018-09-02. Solutions to the Exercises in Elementary Classical Mechanics. Figshare. en-US. 10.6084/m9.figshare.7038578.v1.
18. Web site: Authors — Lagrangian Descriptors. 2020-10-12. champsproject.github.io.
19. Web site: 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. 2020-10-12. www.chemicalreactions.io. en.
20. Wiggins, Stephen. 2020-09-08. Elementary Quantum Mechanics. Figshare. en-US. 10.6084/m9.figshare.12928595.v1.
21. Wiggins, Stephen. 2020-09-08. Solutions to the Exercises in Elementary Quantum Mechanics. Figshare. en-US. 10.6084/m9.figshare.12928673.v1.