List of works - Stephen Wiggins

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

scientific article

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

scientific article published in March 1999

Applied physics. Designing optimal micromixers.

scientific article published in July 2004

Bernoulli linked-twist maps in the plane

article published in 2010

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

scientific article published in April 2013

Chaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators

Chaos in the quasiperiodically forced duffing oscillator

Chaotic Transport in Dynamical Systems

Chaotic advection in a Rayleigh-Bénard flow

scientific article published on 01 January 1991

Chaotic dynamics of a whirling pendulum

article

Coherent structures and chaotic advection in three dimensions

DNA microarrays: design principles for maximizing ergodic, chaotic mixing

scientific article published in February 2007

Detecting reactive islands in a system-bath model of isomerization

scientific article published on 01 June 2020

Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

Dynamics associated with a quasiperiodically forced Morse oscillator: Application to molecular dissociation

scientific article published on 01 April 1992

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

scientific article published on 2 June 2006

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

scientific article published on 18 August 2005

Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics.

scientific article published on 2 October 2017

Eulerian indicators for predicting and optimizing mixing quality

Finite-Time Lagrangian Transport Analysis: Stable and Unstable Manifolds of Hyperbolic Trajectories and Finite-Time Lyapunov Exponents

Global Bifurcations and Chaos

Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications

article

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

scientific article published in March 1999

Impenetrable barriers in phase-space.

scientific article published in June 2001

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

scientific article published on June 28, 2011

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

article

Introduction: mixing in microfluidics.

scientific article published in May 2004

Invariant manifold templates for chaotic advection

Isomerization dynamics of a buckled nanobeam

scientific article published on 29 November 2012

Lagrangian coherent structure assisted path planning for transoceanic autonomous underwater vehicle missions.

scientific article published on 15 March 2018

Microcanonical rates, gap times, and phase space dividing surfaces

scientific article published on 01 April 2009

Nonergodicity, accelerator modes, and asymptotic quadratic-in-time diffusion in a class of volume-preserving maps

scientific article published on 01 September 1995

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

scientific article published in October 2013

Nonstatistical dynamics on the caldera. ⬇️

scientific article published in July 2014

Normally Hyperbolic Invariant Manifolds in Dynamical Systems

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

article

Phase Space Reaction Dynamics Associated with an Index-2 Saddle Point for Time-Dependent Hamiltonian Systems

scientific article published in 2022

Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.

scientific article published on 5 October 2015

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

scientific article published in February 2016

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

scientific article published in October 2004

Phase space structure and dynamics for the Hamiltonian isokinetic thermostat.

scientific article published in July 2010

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

scientific article published on 15 June 2015

Reactive islands for three degrees-of-freedom Hamiltonian systems

scientific article published in 2021

Residence-time distributions for chaotic flows in pipes.

scientific article published in March 1999

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

scientific article

Roaming: A Phase Space Perspective.

scientific article

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

scientific article published on 12 October 2018

Slowly varying oscillators

Statistical relaxation under nonturbulent chaotic flows: Non-Gaussian high-stretch tails of finite-time Lyapunov exponent distributions

scientific article published on 01 January 1993

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

The flux-flux correlation function for anharmonic barriers.

scientific article published in December 2010

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

scientific article published in October 2009

The tipping times in an Arctic sea ice system under influence of extreme events

scientific article published on 01 June 2020

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

scientific article

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

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

Vladimir Igorevich Arnold

scholarly article published in 2010

List of works by Stephen Wiggins

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

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

Applied physics. Designing optimal micromixers.

Bernoulli linked-twist maps in the plane

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

Chaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators

Chaos in the quasiperiodically forced duffing oscillator

Chaotic Transport in Dynamical Systems

Chaotic advection in a Rayleigh-Bénard flow

Chaotic dynamics of a whirling pendulum

Coherent structures and chaotic advection in three dimensions

DNA microarrays: design principles for maximizing ergodic, chaotic mixing

Detecting reactive islands in a system-bath model of isomerization

Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

Dynamics associated with a quasiperiodically forced Morse oscillator: Application to molecular dissociation

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

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

Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics.

Eulerian indicators for predicting and optimizing mixing quality

Finite-Time Lagrangian Transport Analysis: Stable and Unstable Manifolds of Hyperbolic Trajectories and Finite-Time Lyapunov Exponents

Global Bifurcations and Chaos

Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications

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

Impenetrable barriers in phase-space.

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

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

Introduction: mixing in microfluidics.

Invariant manifold templates for chaotic advection

Isomerization dynamics of a buckled nanobeam

Lagrangian coherent structure assisted path planning for transoceanic autonomous underwater vehicle missions.

Microcanonical rates, gap times, and phase space dividing surfaces

Nonergodicity, accelerator modes, and asymptotic quadratic-in-time diffusion in a class of volume-preserving maps

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

Nonstatistical dynamics on the caldera. ⬇️

Normally Hyperbolic Invariant Manifolds in Dynamical Systems

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

Phase Space Reaction Dynamics Associated with an Index-2 Saddle Point for Time-Dependent Hamiltonian Systems

Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.

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

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

Phase space structure and dynamics for the Hamiltonian isokinetic thermostat.

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

Reactive islands for three degrees-of-freedom Hamiltonian systems

Residence-time distributions for chaotic flows in pipes.

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

Roaming: A Phase Space Perspective.

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

Slowly varying oscillators

Statistical relaxation under nonturbulent chaotic flows: Non-Gaussian high-stretch tails of finite-time Lyapunov exponent distributions

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

The flux-flux correlation function for anharmonic barriers.

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

The tipping times in an Arctic sea ice system under influence of extreme events

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

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

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

Vladimir Igorevich Arnold

Whiskered tori and chaos in resonant Hamiltonian normal forms