Stephen Wiggins

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Global Bifurcations and Chaos: Analytical Methods

Stephen Wiggins, 1988 .

Stephen Wiggins, Stephen Wiggins, 1988 .

An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems

Stephen Wiggins, M. Branicki, 2009 .

Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets

Stephen Wiggins, Kayo Ide, K. Ide, 2002 .

Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets

Stephen Wiggins, Des Small, A. Mancho, 2004 .

Lagrangian Transport through an Ocean Front in the Northwestern Mediterranean Sea

Stephen Wiggins, Des Small, E. Hernández‐García, 2006, physics/0608105.

Foundations of chaotic mixing

Stephen Wiggins, Julio M Ottino, Stephen Wiggins, 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

A Lagrangian description of transport associated with a front–eddy interaction: Application to data from the North-Western Mediterranean Sea

Stephen Wiggins, Ana M. Mancho, Michal Branicki, 2011 .

Time Aperiodic Perturbations of Integrable Hamiltonian Systems

Stephen Wiggins, A. Martínez, A. Martinez, 2000, nlin/0007010.

Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The vortex splitting at upper levels

Stephen Wiggins, C. Mechoso, A. Mancho, 2018, Climate Dynamics.

Phase space structure and dynamics for the Hamiltonian isokinetic thermostat.

Stephen Wiggins, P. Collins, G. S. Ezra, 2010, The Journal of chemical physics.

Wigner's dynamical transition state theory in phase space: classical and quantum

Stephen Wiggins, H. Waalkens, R. Schubert, 2007, 0708.0511.

Escape from planetary neighbourhoods

Stephen Wiggins, Holger Waalkens, A. Burbanks, 2005, Monthly Notices of the Royal Astronomical Society.

Impenetrable barriers in phase-space.

T Uzer, Stephen Wiggins, S Wiggins, 2001, Physical review letters.

Influence of mass and potential energy surface geometry on roaming in Chesnavich's CH4+ model.

Stephen Wiggins, Vladimír Krajňák, 2018, The Journal of chemical physics.

Mixing by cutting and shuffling

Rob Sturman, Julio M. Ottino, Stephen Wiggins, 2010 .

The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids (Cambridge Monographs on Applied and Computational Mathematics)

Rob Sturman, Julio M. Ottino, Stephen Wiggins, 2006 .

Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori

Stephen Wiggins, A. Mancho, 2014 .

Lagrangian and Eulerian analysis of transport and mixing in the three dimensional, time dependent Hill’s spherical vortex

Stephen Wiggins, S. Guth, K. McIlhany, 2015 .

Eulerian indicators for predicting and optimizing mixing quality

Stephen Wiggins, R. Sturman, 2009 .

Background and Documentation of Software for Computing Hamiltonian Normal Forms

A. Burbanks, Stephen Wiggins, H. Waalkens, 2008 .

Normal forms á la moser for aperiodically time-dependent hamiltonians in the vicinity of a hyperbolic equilibrium

Stephen Wiggins, Alessandro Fortunati, 2015, 1503.05134.

Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points

Zeb C. Kramer, Stephen Wiggins, S. Farantos, 2017, Regular and Chaotic Dynamics.

Lagrangian Transport through an Ocean Front in the Northwestern Mediterranean Sea

Stephen Wiggins, Des Small, E. Hernández‐García, 2006, physics/0608105.

Identification of low order manifolds: Validating the algorithm of Maas and Pope.

Stephen Wiggins, Manfred Morari, M. Morari, 1999, Chaos.

Optimizing mixing in lid-driven flow designs through predictions from Eulerian indicators

E. Oran, Stephen Wiggins, D. Mott, 2011 .

Eulerian indicators under continuously varying conditions

Stephen Wiggins, K. McIlhany, 2012 .

Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics.

Stephen Wiggins, Gregory S Ezra, Stephen Wiggins, 2011, The Journal of chemical physics.

Reaction Path Bifurcation in an Electrocyclic Reaction: Ring-Opening of the Cyclopropyl Radical.

Zeb C. Kramer, Stephen Wiggins, G. S. Ezra, 2015, The journal of physical chemistry. A.

Predicting trajectory behaviour via machine-learned invariant manifolds pdf

Stephen Wiggins, Shibabrat Naik, Vladim'ir Krajvn'ak, 2021, Chemical Physics Letters.

The Chesnavich Model for Ion-Molecule Reactions: A Rigid Body Coupled to a Particle

Stephen Wiggins, Gregory S. Ezra, Stephen Wiggins, 2019, Int. J. Bifurc. Chaos.

Preface to the special collection in honor of Gregory S. Ezra

Stephen Wiggins, S. Keshavamurthy, 2015, Theoretical Chemistry Accounts.

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points.

Stephen Wiggins, P. Collins, G. S. Ezra, 2013, The Journal of chemical physics.

DNA microarrays: design principles for maximizing ergodic, chaotic mixing.

Rob Sturman, Stephen Wiggins, Jan-Martin Hertzsch, 2007, Small.

Introduction: mixing in microfluidics

Stephen Wiggins, Julio M Ottino, Stephen Wiggins, 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

Nonstatistical dynamics on the caldera.

Zeb C. Kramer, Stephen Wiggins, P. Collins, 2014, The Journal of chemical physics.

Multiple transition states and roaming in ion-molecule reactions: A phase space perspective

Stephen Wiggins, S. Farantos, P. Collins, 2013, 1309.6432.

Bond breaking in a Morse chain under tension: fragmentation patterns, higher index saddles, and bond healing.

Stephen Wiggins, P. Collins, G. S. Ezra, 2013, The Journal of chemical physics.

A Theoretical Framework for Lagrangian Descriptors

Stephen Wiggins, Carlos Lopesino, Francisco Balibrea-Iniesta, 2017, Int. J. Bifurc. Chaos.

Microcanonical rates, gap times, and phase space dividing surfaces.

Stephen Wiggins, H. Waalkens, G. S. Ezra, 2009, The Journal of chemical physics.

High-Dimensional Hamiltonian Dynamical Systems: Theory and Computational Realization for Theoretical Chemistry

Stephen Wiggins, 2008 .

Efficient procedure to compute the microcanonical volume of initial conditions that lead to escape trajectories from a multidimensional potential well.

Stephen Wiggins, Holger Waalkens, A. Burbanks, 2005, Physical review letters.

Phase space conduits for reaction in multidimensional systems: HCN isomerization in three dimensions.

A. Burbanks, Stephen Wiggins, H. Waalkens, 2004, The Journal of chemical physics.

Roaming: A Phase Space Perspective.

Stephen Wiggins, Frédéric A L Mauguière, Peter Collins, 2017, Annual review of physical chemistry.

Phase Space Analysis of the Nonexistence of Dynamical Matching in a Stretched Caldera Potential Energy Surface

Stephen Wiggins, Matthaios Katsanikas, Stephen Wiggins, 2018, Int. J. Bifurc. Chaos.

Phase Space Structure and Transport in a Caldera Potential Energy Surface

Stephen Wiggins, Matthaios Katsanikas, Stephen Wiggins, 2018, Int. J. Bifurc. Chaos.

Designing Optimal Micromixers

Julio M. Ottino, Stephen Wiggins, Stephen Wiggins, 2004, Science.

Toward Understanding the Roaming Mechanism in H + MgH → Mg + HH Reaction.

Zeb C. Kramer, Stephen Wiggins, Hua Guo, 2016, The journal of physical chemistry. A.

Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.

Stephen Wiggins, Frédéric A L Mauguière, Peter Collins, 2015, The journal of physical chemistry letters.

Bifurcations of normally hyperbolic Invariant Manifolds in analytically Tractable Models and Consequences for reaction Dynamics

Stephen Wiggins, Peter Collins, Gregory S. Ezra, 2013, Int. J. Bifurc. Chaos.

Geometrical models of the phase space structures governing reaction dynamics

Stephen Wiggins, H. Waalkens, 2009, 0906.4914.

ENSO dynamics in current climate models: an investigation using nonlinear dimensionality reduction

Stephen Wiggins, Paul J. Valdes, I. Ross, 2008 .

Phase Space Transport in a Symmetric Caldera Potential with Three Index-1 Saddles and No Minima

Stephen Wiggins, A. Mancho, M. Agaoglou, 2022, Int. J. Bifurc. Chaos.

Lagrangian transport across the upper Arctic waters in the Canada Basin

V. J. García-Garrido, Stephen Wiggins, Laurent Bertino, 2018, Quarterly Journal of the Royal Meteorological Society.

The Application of Lagrangian Descriptors to 3D Vector Fields

V. J. García-Garrido, Stephen Wiggins, C. Mechoso, 2018, Regular and Chaotic Dynamics.

Lagrangian descriptors for two dimensional, area preserving, autonomous and nonautonomous maps

Stephen Wiggins, Carlos Lopesino, Francisco Balibrea-Iniesta, 2015, Commun. Nonlinear Sci. Numer. Simul..

Lagrangian descriptors: A method for revealing phase space structures of general time dependent dynamical systems

Stephen Wiggins, Ana M. Mancho, Jezabel Curbelo, 2011, Commun. Nonlinear Sci. Numer. Simul..

A method for visualization of invariant sets of dynamical systems based on the ergodic partition.

Stephen Wiggins, Igor Mezic, I. Mezić, 1999, Chaos.

Roaming dynamics in ion-molecule reactions: phase space reaction pathways and geometrical interpretation.

Stephen Wiggins, S. Farantos, P. Collins, 2014, The Journal of chemical physics.

Patchiness: A New Diagnostic for Lagrangian Trajectory Analysis in Time-Dependent Fluid Flows

I. Mezić, N. Malhotra, Stephen Wiggins, 1998 .

Synoptic Lagranian maps: Application to surface transport in Monterey Bay

Stephen Wiggins, Kayo Ide, A. D. Kirwan, 2006 .

Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence

Stephen Wiggins, Alessandro Fortunati, 2014, 1405.1268.

Normal form and Nekhoroshev stability for nearly integrable hamiltonian systems with unconditionally slow aperiodic time dependence

Stephen Wiggins, Alessandro Fortunati, 2013, 1311.6290.

Further directions and open problems

Rob Sturman, Julio M. Ottino, Stephen Wiggins, 2006 .

Linked twist map formalism in two and three dimensions applied to mixing in tumbled granular flows

Stephen Wiggins, J. Ottino, R. Sturman, 2008, Journal of Fluid Mechanics.

The flux-flux correlation function for anharmonic barriers.

Stephen Wiggins, H. Waalkens, R. Schubert, 2010, The Journal of chemical physics.

Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations

Stephen Wiggins, Alessandro Fortunati, 2015, Celestial Mechanics and Dynamical Astronomy.

Quantum Theory of Reactive Scattering in Phase Space

Stephen Wiggins, H. Waalkens, R. Schubert, 2010, 1004.5017.

The quantum normal form approach to reactive scattering: The cumulative reaction probability for collinear exchange reactions.

Stephen Wiggins, H. Waalkens, R. Schubert, 2009, The Journal of chemical physics.

Transient invariant and quasi-invariant structures in an example of an aperiodically time dependent uid ow

Stephen Wiggins, Alessandro Fortunati, Stephen Wiggins, 2018 .

The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence

Stephen Wiggins, Alessandro Fortunati, 2016 .

Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium

Stephen Wiggins, Alessandro Fortunati, 2016, 1601.00431.

A Kolmogorov theorem for nearly integrable Poisson systems with asymptotically decaying time-dependent perturbation

Stephen Wiggins, Alessandro Fortunati, 2014, 1409.0430.

Transport enhancement mechanisms in open cavities

Julio M. Ottino, Stephen Wiggins, Guy Metcalfe, 2002, Journal of Fluid Mechanics.

Isomerization dynamics of a buckled nanobeam.

Stephen Wiggins, Gregory S Ezra, Stephen Wiggins, 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

Chaos in the quasiperiodically forced duffing oscillator

Stephen Wiggins, Stephen Wiggins, 1987 .

A computational procedure to detect a new type of high-dimensional chaotic saddle and its application to the 3D Hill's problem

A. Burbanks, Stephen Wiggins, H. Waalkens, 2004, nlin/0403059.

Direct construction of a dividing surface of minimal flux for multi-degree-of-freedom systems that cannot be recrossed

Stephen Wiggins, Holger Waalkens, Stephen Wiggins, 2004 .

Structured pathways in the turbulence organizing recent oil spill events in the Eastern Mediterranean

Stephen Wiggins, A. Mancho, J. Coca, 2022, Scientific Reports.

Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

Stephen Wiggins, Ana M. Mancho, Carlos R. Mechoso, 2017 .

Optimizing mixing in channel flows: kinematic aspects associated with secondary flows in the cross-section

Stephen Wiggins, K. McIlhany, 2011 .

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

Stephen Wiggins, Des Small, A. Mancho, 2006 .

Residence-time distributions for chaotic flows in pipes.

Stephen Wiggins, Igor Mezic, I. Mezić, 1999, Chaos.

Response to “Comment on ‘Identification of low order manifolds: Validating the algorithm of Maas and Pope'” [Chaos 16, 048101 (2006)]

M. Morari, C. Rhodes, Stephen Wiggins, 2006 .

Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics

Stephen Wiggins, Chad Coulliette, Stephen Wiggins, 2000 .

A λ-lemma for normally hyperbolic invariant manifolds

Stephen Wiggins, J. Cresson, 2015 .

A lambda-lemma for normally hyperbolic invariant manifolds

Stephen Wiggins, J. Cresson, 2005, math/0510645.

Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map

Stephen Wiggins, Carlos Lopesino, Francisco Balibrea-Iniesta, 2015, Int. J. Bifurc. Chaos.

Stretching fields and lines in the transport dynamics of the Western Mediterranean

F. d’Ovidio, Stephen Wiggins, J. Isern‐Fontanet, 2007 .

Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets

Stephen Wiggins, Ana M. Mancho, C. Mendoza, 2014 .

Lagrangian study of the final warming in the southern stratosphere during 2002: Part II. 3D structure

Stephen Wiggins, A. Mancho, C. R. Mechoso, 2018, Climate Dynamics.

Detection of Phase Space Structures of the Cat Map with Lagrangian Descriptors

V. J. García-Garrido, Stephen Wiggins, A. Mancho, 2018, Regular and Chaotic Dynamics.

Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

Stephen Wiggins, Atanasiu Stefan Demian, Stephen Wiggins, 2017, Int. J. Bifurc. Chaos.

A dynamical systems perspective for a real-time response to a marine oil spill.

V. J. García-Garrido, V J García-Garrido, A M Mancho, 2016, Marine pollution bulletin.

Response to: "Limitations of the Method of Lagrangian Descriptors" [arXiv:1510.04838]

V. J. García-Garrido, Stephen Wiggins, A. Mancho, 2016, 1602.04243.

Institutions and Pro-Poor Growth: Towards a Framework for Quantitative Analysis.

Stephen Wiggins, M. Calí, D. T. Velde, 2006 .

Roaming: A Phase Space Perspective.

Zeb C. Kramer, Stephen Wiggins, S. Farantos, 2017, Annual review of physical chemistry.

On the integrability and perturbation of three-dimensional fluid flows with symmetry

S. Wiggins, I. Mezić, S. Wiggins, 1994 .

Transport in two-dimensional maps: concepts, examples, and a comparison of the theory of Rom-Kedar and Wiggins with the Markov model of MacKay, Meiss, Ott, and percival

Stephen Wiggins, Vered Rom-Kedar, Stephen Wiggins, 1991 .

Maximal Effective Diffusivity for Time-Periodic Incompressible Fluid Flows

Stephen Wiggins, Igor Mezic, John F. Brady, 1996, SIAM J. Appl. Math..

A Theoretical Framework for Lagrangian Descriptors

V. J. García-Garrido, Stephen Wiggins, A. Mancho, 2017, Int. J. Bifurc. Chaos.

Nonstatistical dynamics on the caldera.

Zeb C. Kramer, Stephen Wiggins, P. Collins, 2014, The Journal of chemical physics.

On Roughness of Exponential Dichotomy

Stephen Wiggins, N. Ju, 2001 .

Phase Space Geometry and Dynamics Associated with the 1:2:2 Resonance

Stephen Wiggins, 1999 .

The quantum normal form approach to reactive scattering: The cumulative reaction probability for collinear exchange reactions.

Stephen Wiggins, H. Waalkens, R. Schubert, 2009, The Journal of chemical physics.

Wigner's dynamical transition state theory in phase space: classical and quantum

Stephen Wiggins, H. Waalkens, R. Schubert, 2007, 0708.0511.

Direct construction of a dividing surface of minimal flux for multi-degree-of-freedom systems that cannot be recrossed

Stephen Wiggins, H. Waalkens, 2004 .

The Time Evolution of the Trajectories After the Selectivity in a Symmetric Potential Energy Surface with a Post-transition-state Bifurcation

Stephen Wiggins, M. Agaoglou, M. Katsanikas, 2021, Regular and Chaotic Dynamics.

A formula to compute the microcanonical volume of reactive initial conditions in transition state theory

A. Burbanks, Stephen Wiggins, H. Waalkens, 2005 .

Sampling Phase Space Dividing Surfaces Constructed from Normally Hyperbolic Invariant Manifolds (NHIMs).

Stephen Wiggins, G. S. Ezra, 2018, The journal of physical chemistry. A.

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone.

Zeb C. Kramer, Stephen Wiggins, S. Farantos, 2010, The Journal of chemical physics.

Periodic-orbit formula for quantum reactions through transition states

Stephen Wiggins, H. Waalkens, R. Schubert, 2010, 1001.3945.

Nonlinear Processes in Geophysics Computation of Hyperbolic Trajectories and Their Stable and Unstable Manifolds for Oceanographic Flows Represented as Data Sets

Stephen Wiggins, Des Small, A. Mancho, 2022 .

A dynamical systems perspective for a real-time response to a marine oil spill.

V. J. García-Garrido, Stephen Wiggins, A. Mancho, 2016, Marine pollution bulletin.

A dynamical systems perspective on the absence of debris associated with the disappearance of flight MH370

V. J. García-Garrido, Stephen Wiggins, A. Mancho, 2015 .

Existence and Computation of Hyperbolic Trajectories of Aperiodically Time Dependent Vector Fields and their Approximations

Stephen Wiggins, Ning Ju, Des Small, 2003, Int. J. Bifurc. Chaos.

A computational procedure to detect a new type of high-dimensional chaotic saddle and its application to the 3D Hill's problem

A. Burbanks, Stephen Wiggins, H. Waalkens, 2004, nlin/0403059.

Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow

Stephen Wiggins, Alessandro Fortunati, 2018, Int. J. Bifurc. Chaos.

Preface: Current perspectives in modelling, monitoring, and predicting geophysical fluid dynamics

Stephen Wiggins, Cristóbal López, Emilio Hernández-García, 2018 .

Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics.

Stephen Wiggins, P. Collins, G. S. Ezra, 2011, The Journal of chemical physics.

Efficient computation of transition state resonances and reaction rates from a quantum normal form.

Stephen Wiggins, H. Waalkens, R. Schubert, 2005, Physical review letters.