Stephen Wiggins

Stephen Wiggins

Applied Mathematics | Nonlinear Dynamics | Chaos Theory

About

Stephen Wiggins is renowned for his pioneering research in applied mathematics, with emphasis on nonlinear dynamics, chaos theory, and geometry and transport in phase space. His work has advanced the understanding of phase space structures, mixing, and transport in dynamical systems, with applications ranging from fluid mechanics to chemical reaction dynamics. Wiggins’s research themes connect mathematical foundations with practical scientific challenges, synergistically influencing fields such as theoretical chemistry and geophysical transport.

Research Themes

Lagrangian Transport

Investigating transport and mixing in geophysical flows (oceanic and atmospheric) using dynamical systems theory, focusing on hyperbolic trajectories and invariant manifolds.

Chemical Reaction Dynamics

Exploring phase space structures in reaction dynamics, including "roaming" mechanisms, transition state theory, and phase space conduits for energy transfer.

Lagrangian Descriptors

Developing and applying the method of Lagrangian descriptors—a trajectory-based scalar field technique—to reveal phase space structures in complex, aperiodically time-dependent systems.

Books

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Selected Publications

  • Roaming: A Phase-Space Perspective

    Annual Review of Physical Chemistry (2017)

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  • The Dynamical Systems Approach to Lagrangian Transport in Oceanic Flows

    Annual Review of Fluid Mechanics (2005)

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  • Painting the Phase Portrait of a Dynamical System with Lagrangian Descriptors

    Notices of the AMS (2022)

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  • Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification – A Tutorial for Beginners

    Notices of the AMS (2025)

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