Stephen Wiggins

Education

Ph.D. Theoretical and Applied Mechanics, Cornell University

M.S. Physics, University of Wisconsin - Madison

M.A. Mathematics, University of Wisconsin - Madison

B.S. Physics and Mathematics, Pittsburg State University

Research Interests

Dynamical systems, transport and mixing, fluid mechanics, theoretical chemistry

Professional Affiliations & Memberships

American Physical Society, American Chemical Society, American Geophysical Union, Association for Computing Machinery, American Mathematical Society, Society for Industrial and Applied Mathematics, AAAS, American Indian Science and Engineering Society (AISES)

Publications

Recent publications

• Phase space barriers and dividing surfaces in the absence of critical points of the potential energy surface. Application to roaming in ozone (with F. A. L. Mauguiere, P. Collins, Z. C. Cramer, B. K. Carpenter, G.S. Ezra, and S. C. Farantos), Journal of Chemical Physics, 2016, 144(5), 054107.
• Toward Understanding the Roaming Mechanism in H + MgH → Mg + HH Reaction (with F. A. L. Mauguiere, P Collins, S. Stamatiadis, A. Li, G. S. Ezra, S. C. Farantos, Z. C.Kramer, B. K. Carpenter, and H. Guo) J. Phys. Chem. A. (2016), 120, 5145-5154, DOI:10.1021/acs.jpca.6b00682.
• Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations (with A. Fortunati), Cel. Mech. Dyn. Astron. (2016). DOI:10.1007/s10569-016-9684-1.
• Normal forms  ́a la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium (with A. Fortunati). Discrete and Continuous Dynamical Systems-S, 2016, 9 (4), 1109-1118.
• Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium (with A. Fortunati), Journal of Mathematical Physics, 2016, 57, 092703.
• A dynamical systems perspective for a real-time response to a marine oil spill (with V. J. Garcia-Garrido, A. Ramos, A. M. Mancho, J. Coca) Marine Pollution Bulletin. 2016, 112, 201-210. Published online at http://dx.doi.org/10.1016/j.marpolbul.2016.08.018.
• The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics. Regular and Chaotic Dynamics, 2016, 21(6), 621638.
• Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems (with F. Balibrea-Iniesta, C. Lopesino, and A. M. Mancho). International Journal of Bifurcation and Chaos, 2016, 26(13), 1630036.
• A theoretical Framework for Lagrangian descriptors (with C. Lopesino, F. Balibrea-Iniesta, V. J. Garcia-Garrido, and A. M. Mancho). International Journal of Bifurcation and Chaos, 2017,27(1), 1730001.
• A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex (with V. J. Garcia-Garrido, J. Curbelo, C. R. Mechoso, A. N. Mancho ). Nonlin. Processes Geophys., 2017, 24, 265-278.
• Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex (with J. Curbelo, V. J. Garcia-Garrido, C. R. Mechoso, A. N. Mancho, C. Niang). Nonlin. Processes Geophys., 2017, 24, 379-392.
• Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics (with B. K. Carpenter, G.S. Ezra, S. C. Farantos, and Z. C. Kramer). J. Phys. Chem. B. DOI: 10.1021/acs.jpcb.7b08707, Publication Date (Web): October 2, 2017.
• Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors (with A. S. Demian), International Journal of Bifurcation and Chaos, 2017, 27 (4), 1750225.
• Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points (with B. K. Carpenter, G.S. Ezra, S. C. Farantos, and Z. C. Kramer), Regular and Chaotic Dynamics, 2018, 23(1), 60-79.
• Lagrangian coherent structure assisted path planning for transoceanic autonomous underwater vehicle missions. ( with A. G. Ramos, V. J. Garcia-Garrido, A. M. Mancho, J. Coca, S. Glenn, O. Schofield, J. Kohut, D. Aragon, J. Kerfoot, T. Haskins, T. Miles, C. Haldeman, N. Strandskov, B. Allsup, C. Jones, and J. Shapiro) Scientific Reports, 2018, 8, 4575.

Books

1. Global Bifurcations and Chaos – Analytical Methods. Springer-Verlag Applied Mathematical Science Series. 1988, second printing 1990.

2. 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.

3. Chaotic Transport in Dynamical Systems. Springer-Verlag Interdisciplinary Applied
Mathematical Sciences Series, 1992.

4. Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and
Applications. American Mathematical Society, 1993.

5. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer-Verlag
Applied Mathematical Science Series, 1994.

6. Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrodinger Equations (with Y. Li). Springer-Verlag Applied Mathematical Science Series, 1997.

7. 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.

8. 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.