Professor Stephen R Wiggins

Search results

• 2014

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

  Fortunati, A. & Wiggins, S., 2014, In: Regular and Chaotic Dynamics. 19, 3, p. 363-373 11 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Stability Result 100%
  • Hamiltonian Systems 100%
  • Smallness 100%
  7 Citations (Scopus)

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

  Fortunati, A. & Wiggins, S., 2014, In: Regular and Chaotic Dynamics. 19, 5, p. 586-600 15 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Torus 38%
  12 Citations (Scopus)

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

  Mauguiere, F. A. L., Collins, P., Ezra, G. S., Farantos, S. C. & Wiggins, S., 7 Apr 2014, In: Journal of Chemical Physics. 140, 13, 17 p., 134112.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Geometrical Interpretation 100%
  • Phase Space 100%
  • Surface (Surface Science) 100%
  • Methane 100%
  • Transition State 75%
  35 Citations (Scopus)

• Roaming dynamics in ketene isomerization

  Mauguiere, F. A. L., Collins, P., Ezra, G. S., Farantos, S. C. & Wiggins, S., 10 Jun 2014, In: Theoretical Chemistry Accounts. 133, 7, 13 p., 1507.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Ketene 100%
  • Isomerization 100%
  • Phase Space 100%
  • Surface (Surface Science) 100%
  • Orbit 66%
  17 Citations (Scopus)
• 2013

  BIFURCATIONS OF NORMALLY HYPERBOLIC INVARIANT MANIFOLDS IN ANALYTICALLY TRACTABLE MODELS AND CONSEQUENCES FOR REACTION DYNAMICS

  Mauguiere, F. A. L., Collins, P., Ezra, G. S. & Wiggins, S., Dec 2013, In: International Journal of Bifurcation and Chaos. 23, 12, 20 p., 1330043.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Invariant Manifold 100%
  • Hyperbolicity 100%
  • Time Distribution 50%
  • Degree of Freedom 25%
  17 Citations (Scopus)

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

  Mauguière, F. A. L., Collins, P. R. C., Ezra, G. S. & Wiggins, S. R., 2013, In: Journal of Chemical Physics. 138, 13

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Initial Condition 100%
  • Phase Space 100%
  • Saddle Point 100%
  • Tension 100%
  • Probability Theory 50%
  18 Citations (Scopus)

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

  Collins, P., Carpenter, B. K., Ezra, G. S. & Wiggins, S., 21 Oct 2013, In: Journal of Chemical Physics. 139, 15, p. 154108

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Ridge 100%
  • Inflection Point 100%
  • Surface Energy 100%
  • Minor Variation 33%
  • Potential Energy Model 33%
  53 Citations (Scopus)
• 2012

  Isomerization dynamics of a buckled nanobeam

  Collins, P., Ezra, G. S. & Wiggins, S., 29 Nov 2012, In: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics. 86, 5, 16 p., 056218.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Energy Engineering 100%
  • Potential Energy 100%
  • Phase Space 100%
  • Surface Energy 100%
  • Isomerization 100%
  17 Citations (Scopus)
• 2011

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

  Branicki, M., Mancho, A. M. & Wiggins, S. R., 1 Feb 2011, In: Physica D: Nonlinear Phenomena. 240, 3, p. 282-304 23 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Hyperbolic Trajectory 100%
  • Ocean Models 100%
  • Mediterranean Sea 100%
  • Dynamical System 100%
  • Numerical Model 50%
  25 Citations (Scopus)

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

  Collins, P., Ezra, G. S. & Wiggins, S., 28 Jun 2011, In: Journal of Chemical Physics. 134, 24, 19 p., 244105.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Phase Space 100%
  • Parametrization 100%
  • Initial Condition 100%
  • Explicit Formula 100%
  • Mathematical Method 100%
  37 Citations (Scopus)
• 2010

  A periodic orbit formula for quantum reactions through transition states

  Schubert, R., Waalkens, H., Goussev, A. & Wiggins, S., 22 Jan 2010, In: Physical Review A.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Transition State 100%
  • Transition State Theory 100%
  • Orbit 100%
  • Phase Space 50%
  1 Citation (Scopus)

• Phase space structure and dynamics for the Hamiltonian isokinetic thermostat

  Collins, P., Ezra, G. S. & Wiggins, S., 7 Jul 2010, In: Journal of Chemical Physics. 133, 1, 18 p., 014105.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Phase Space 100%
  • Surface (Surface Science) 100%
  • Lifetime Distribution 80%
  • Reactant 60%
  • Density 50%
  10 Citations (Scopus)

• Quantum Theory of Reactive Scattering in Phase Space

  Goussev, A., Schubert, R., Waalkens, H. & Wiggins, S., 28 Apr 2010, Unstable States in the Continuous Spectra, Part I: Analysis, Concepts, Methods, and Results. Elsevier Inc., p. 269-332 (Advances in Quantum Chemistry; vol. 60).

  Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

  • Phase Space 100%
  • Reactive Scattering 100%
  • Quantum Theory 100%
  • Space Structure 100%
  • System Theory 100%
  14 Citations (Scopus)

• The Flux-Flux Correlation Function for Anharmonic Barriers

  Goussev, A., Schubert, R., Waalkens, H. & Wiggins, S., 28 Dec 2010, In: Journal of Chemical Physics. 133, 24

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • One Dimensional 100%
  • Fourth Order 100%
  • Harmonics 100%
  4 Citations (Scopus)
• 2009

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

  Branicki, M. & Wiggins, S., 1 Aug 2009, In: Physica D: Nonlinear Phenomena. 238, 16, p. 1625 - 1657 33 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Invariant Manifold 100%
  • Dimensional Dynamical System 100%
  • Lagrangian 50%
  • Codimension 33%
  • Manifold 33%
  41 Citations (Scopus)

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

  Ezra, G., Waalkens, H. & Wiggins, S., Apr 2009, In: Journal of Chemical Physics. 130, 16, 15 p., 164118.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Phase Space 100%
  • Reactant 50%
  • Isomerization 37%
  • Time Distribution 25%
  • Transition State 25%
  64 Citations (Scopus)

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

  Goussev, A., Schubert, R., Waalkens, H. & Wiggins, S., Oct 2009, In: Journal of Chemical Physics. 131, 14, 8 p., 144103.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Reactive Scattering 100%
  • Transition State Theory 50%
  • Quantum Transition 50%
  • Hydrogen 50%
  8 Citations (Scopus)
• 2008

  Lagrangian transport through an ocean front in the North-Western Mediterranean Sea

  Mancho, A., Hernandez-Garcia, E., Small, D., Wiggins, S. & Fernandez, V., Jun 2008, In: Journal of Physical Oceanography. 38, issue 6, p. 1222 - 1237 16 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Freshwater 100%
  • Velocity Distribution 100%
  • Hyperbolic Trajectory 100%
  • Mediterranean Sea 100%
  • Dynamical System 100%
  57 Citations (Scopus)

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

  Sturman, R., Meier, S., Ottino, J. & Wiggins, S., May 2008, In: Journal of Fluid Mechanics. 602, p. 129 - 174 46 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Three-Dimension 100%
  • Two Dimensions 100%
  • Granular Flow 100%
  • Dimensional Case 100%
  • Two Dimensional 100%
  36 Citations (Scopus)

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

  Waalkens, H., Schubert, R. & Wiggins, S., Jan 2008, In: Nonlinearity. 21, 1, 118 p., R1.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Phase Space 100%
  • Transition State 100%
  • Space Structure 100%
  • Degree of Freedom 100%
  • Autocorrelation 100%
  174 Citations (Scopus)
• 2007

  DNA microarrays: Design principles for maximising ergodic, chaotic mixing

  Hertzsch, J., Sturman, R. & Wiggins, S., Feb 2007, In: Small. 3 (2), p. 202 - 218 17 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Microarrays 100%
  • Design Criterion 100%
  • Mixers (Machinery) 33%
  • Source-Sink Pair 33%
  • Pulsed Source 33%
  41 Citations (Scopus)
• 2006

  A comparison of methods for interpolating chaotic flows from discrete velocity data

  Mancho, A., Small, D. & Wiggins, S., May 2006, In: Computers and Fluids. 35 (4), p. 416 - 428

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Polynomial 100%
  • Discrete Collection 100%
  • Data Point 100%
  • Velocity Distribution 100%
  32 Citations (Scopus)

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

  Mancho, A., Small, D. & Wiggins, S., Dec 2006, In: Physics Reports. 437 (3-4), p. 55 - 124

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Velocity Field 100%
  • Finite Time 100%
  • Oceanic Flow 100%
  • Dynamical System 100%
  • Dynamical System Theory 75%

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

  Schubert, R., Waalkens, H. & Wiggins, S., Jun 2006, In: Physical Review Letters. 96 (21), p. 1 - 4 4 p., Art No 218302.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Degree of Freedom 100%
  • Freedom System 100%
  • Phase Space 100%
  32 Citations (Scopus)

• Lobe dynamics in a kinematic model of a meandering jet. I. Geometry and statistics of transport and lobe dynamics with accelerated convergence

  Raynal, F. & Wiggins, S., 1 Nov 2006, In: Physica D: Nonlinear Phenomena. 223 (1), p. 7 - 25

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Statistics 100%
  • Exact Result 100%
  • Time Average 100%
  • Geometric Structure 100%
  • Truncation 100%
  12 Citations (Scopus)

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

  Rhodes, C., Morari, M. & Wiggins, S., 2006, In: Chaos. 16 (4)

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Timescale 100%
  • Manifold 100%
  • Counterexample 100%
  • Slow Manifold 100%
  • Chaos 100%

• Synoptic Lagranian maps: Application to surface transport in Monterey Bay

  Lipphardt, B., Small, D., Kirwan, A., Wiggins, S., Ide, K., Grosch, C. & Paduan, J., Mar 2006, In: Journal of Marine Research. 64 (2), p. 221 - 247

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Open Ocean 100%
  • Tidal Current 50%
  • Surface Water 50%
  • Timescale 50%
  • Radar Measurement 50%
• 2005

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

  Waalkens, H., Burbanks, A. & Wiggins, S., Nov 2005, In: Journal of Physics A: Mathematical and General. 38 (45), p. L759 - L768

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Initial Condition 100%
  • Phase Space 100%
  • Energy Engineering 33%
  • Computational Efficiency 33%
  31 Citations (Scopus)

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

  Waalkens, H., Burbanks, A. & Wiggins, S., Aug 2005, In: Physical Review Letters. 95 (8) 084301, p. 1 - 4 4 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Initial Condition 100%
  • Phase Space 100%
  • Potential Well 100%
  • Minimizes 33%
  • Spectral Theorem 33%
  49 Citations (Scopus)

• Escape from planetary neighbourhoods

  Waalkens, H., Burbanks, A. & Wiggins, S., Aug 2005, In: Monthly Notices of the Royal Astronomical Society. 361 (3), p. 763 - 775 13 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Star Cluster 100%
  • Extrasolar Gas Giants 100%
  • Space Structure 100%
  • Transport Theory 100%
  • Kuiper Belt 100%
  37 Citations (Scopus)

• The dynamical systems approach to Lagrangian transport in oceanic flows

  Wiggins, S., Jan 2005, In: Annual Review of Fluid Mechanics. 37, p. 295 - 328 34 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Velocity Field 100%
  • Dynamical System Approach 100%
  • Oceanic Flow 100%
  • Dynamical System 100%
  • Lagrangian 100%
  214 Citations (Scopus)
• 2004

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

  Waalkens, H., Burbanks, A. & Wiggins, S., Jun 2004, In: Journal of Physics A: Mathematical and General. 37 (24), p. L257 - L265

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Invariant Manifold 100%
  • Hamiltonian Systems 50%
  • Point of Equilibrium 50%
  • Phase Space 50%
  • Degree of Freedom 50%
  57 Citations (Scopus)

• Applied physics - Designing optimal micromixers

  Ottino, J. & Wiggins, S., 23 Jul 2004, American Association for the Advancement of Science.

  Research output: Other contribution

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

  Mancho, A., Small, D. & Wiggins, S., Feb 2004, In: Nonlinear Processes in Geophysics. 11 (1), p. 17 - 33 17 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Unstable Manifold 100%
  • Stable Manifold 100%
  • Rectangular Domain 50%
  • Finite Time 50%
  • Velocity Distribution 50%
  59 Citations (Scopus)

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

  Waalkens, H. & Wiggins, S., 3 Sept 2004, In: Journal of Physics A: Mathematical and General. 37 (35), p. L435 - L445 11 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Surface (Surface Science) 100%
  103 Citations (Scopus)

• Foundations of chaotic mixing

  Wiggins, S. & Ottino, J., 15 May 2004, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 362 (1818), p. 937 - 970

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Two Dimensional 100%
  • Two Dimensional Flow 100%
  • Duct 66%
  • Dimensional Flow 66%
  • Dynamical System 50%
  324 Citations (Scopus)

• Introduction: mixing in microfluids

  Ottino, J. & Wiggins, S., 15 May 2004, Royal Soc London.

  Research output: Other contribution

  • microbalances 100%

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

  Waalkens, H., Burbanks, A. & Wiggins, S., 1 Oct 2004, In: Journal of Chemical Physics. 121 (13), p. 6207 - 6225 19 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Three-Dimension 100%
  • Multidimensional Systems 100%
  • Phase Space 100%
  • Surface (Surface Science) 100%
  • Degree of Freedom 33%
  102 Citations (Scopus)
• 2003

  Chaos-assisted capture of irregular moons

  Astakhov, S., Burbanks, A., Wiggins, S. & Farrelly, D., May 2003, In: Nature. 423 (6937), p. 264 - 267 4 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Extrasolar Gas Giants 100%
  • Circular Orbit 100%
  • Monte Carlo Method 100%
  94 Citations (Scopus)

• Computation of Stable and Unstable Manifolds of hyperbolic Trajectories in Two-dimensional, Aperiodically Time-Dependent Vector Fields

  Mancho, A. M., Small, D., Wiggins, S. & Ide, K., Aug 2003, In: Physica D: Nonlinear Phenomena. 182 (3-4), p. 188 - 222 35 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Unstable Manifold 100%
  • Stable Manifold 100%
  • Time Dependent Vector Field 100%
  • Manifold 33%
  • Duffings Equation 33%
  84 Citations (Scopus)

• Existence and computation of hyperbolic trajectories of aperiodically time dependent vector fields and their approximations

  Ju, N., Small, D. & Wiggins, S., Jun 2003, In: International Journal of Bifurcation and Chaos. 13(6), p. 1449 - 1457

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Time Dependent Vector Field 100%
  • Vector Field 50%
  • time interval τ 50%
  • Timescale 50%
  • Sufficient Condition 50%
  33 Citations (Scopus)

• Time-frequency analysis of chaotic systems

  Chandre, C., Wiggins, S. & Uzer, T., Jul 2003, In: Physica D: Nonlinear Phenomena. 181 (3-4), p. 171 - 196 26 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Phase Space 100%
  • Space Structure 100%
  • Time Frequency Analysis 100%
  • Chaotic Systems 100%
  • Hamiltonian Systems 50%
  135 Citations (Scopus)
• 2002

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

  Ide, K., Small, D. & Wiggins, S., May 2002, In: Nonlinear Processes in Geophysics. 9 (3-4), p. 237 - 263

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Computational Approach 100%
  • Velocity Distribution 100%
  • Lagrangian 66%
  • time interval τ 50%
  • Systems Theory 50%
  102 Citations (Scopus)

• The geometry of reaction dynamics

  Uzer, T., Jaffé, C., Palacián, J., Yanguas, P. & Wiggins, S., Jul 2002, In: Nonlinearity. 15 (4), p. 957 - 992 36 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Energy Surface 100%
  • Phase Flow 100%
  • Phase Space 100%
  • Transition State 100%
  • Reaction Dynamics 100%
  259 Citations (Scopus)

• Transport enhancement mechanisms in open cavities

  Horner, M., Metcalfe, G., Wiggins, S. & Ottino, J., 10 Feb 2002, In: Journal of Fluid Mechanics. 452, p. 199 - 229

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Transients 100%
  • Forcing Frequency 100%
  • Streamlines 100%
  • Open Cavity 100%
  • Velocity Distribution 100%
  55 Citations (Scopus)
• 2001

  Impenetrable barriers in phase-space

  Wiggins, S., Wiesenfeld, L., Jaffe, C. & Uzer, T., Jun 2001, In: Physical Review Letters. 86 (24), p. 5478 - 5481 4 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Phase Space 100%
  • System Theory 100%
  • Dynamical System 33%
  • Transition State 33%
  • Transition State Theory 33%
  205 Citations (Scopus)
• 2000

  Erratum to Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems

  Rudnev, M. & Wiggins, S., 2000, In: Physica D: Nonlinear Phenomena. 145(3-4), p. 349 - 354

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

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

  Coulliette, C. & Wiggins, S., 2000, In: Nonlinear Processes in Geophysics. 7, p. 59 - 85

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  43 Citations (Scopus)

• On a homoclinic splitting problem

  Rudnev, M. & Wiggins, S. R., 2000, In: Regular and Chaotic Dynamics. 5, 2, p. 227-242 16 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Submanifold 100%
  • Lagrangian 100%
  • Vector Field 50%
  • Unstable Manifold 50%
  • Scalar Function 50%
  9 Citations (Scopus)
• 1999

  On a partially hyperbolic KAM theorem

  Rudnev, M. & Wiggins, S. R., 1999, In: Regular and Chaotic Dynamics. 4, 4, p. 39--58

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  3 Citations (Scopus)