Publications (94)
Predicting trajectory behaviour via machine-learned invariant manifolds
VladimÃr KrajÅák, Shibabrat Naik, Stephen Wiggins
In this paper, we use support vector machines (SVM) to develop a machine learning framework to discover phase space structures that distinguish between distinct reaction pathways.…
The role of depth and flatness of a potential energy surface in chemical reaction dynamics
Wenyang Lyu, Shibabrat Naik, Stephen Wiggins
In this study, we analyze how changes in the geometry of a potential energy surface in terms of depth and flatness can affect the reaction dynamics. We formulate depth and flatness…
Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points
Barry K. Carpenter, Gregory S. Ezra, Stavros C. Farantos +2
In this paper we analyze a two degree of freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells sur…
Symplectic Constraints in Classical Reaction Dynamics: From Gromov's Camel to Reaction Rates
Stephen Wiggins
We investigate whether ideas from symplectic topology, in particular Gromov's non-squeezing theorem and symplectic capacity, can provide useful geometric insight into classical rea…
Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points
Peter Collins, Barry K. Carpenter, Gregory S. Ezra +1
We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection point. We compute fractiona…
Symplectic Constraints in Quantum Reaction Dynamics: Squeezed-State Suppression and Candidate Width Scales
Stephen Wiggins
Classical reaction dynamics suggests transport through an index-1 saddle is organized not just by flux, but by local symplectic width scales of bounded proxy neighborhoods near the…
Lobe Dynamics, Phase-Space Transport, and Non-Adiabatic Leakage Thresholds in the Nonautonomous Kerr-Cat Qubit
Stephen Wiggins
The Kerr-nonlinear parametric oscillator (KPO) provides a foundational semiclassical model for cat-state quantum hardware. Standard analyses of the KPO typically rely on autonomous…
Finite-time Lagrangian transport analysis: Stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents
Michal Branicki, Stephen Wiggins
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time int…
Finding NHIM: Identifying High Dimensional Phase Space Structures in Reaction Dynamics using Lagrangian Descriptors
Shibabrat Naik, VÃctor J. GarcÃa-Garrido, Stephen Wiggins
Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative…
Bifurcation of dividing surfaces constructed from a pitchfork bifurcation of periodic orbits in a symmetric potential energy surface with a post-transition-state bifurcation
Matthaios Katsanikas, Makrina Agaoglou, Stephen Wiggins
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. T…
An entropic bottleneck, dynamical gating, and outward redistribution of roaming in a designed Chesnavich-type model
Stephen Wiggins
Roaming reactions are organized not by potential-energy saddles but by transition states that are unstable invariant objects in phase space, periodic orbits in the two degrees of f…
The Role of Variability in Transport for Large-Scale Flow Dynamics
Kayo Ide, Stephen Wiggins
We develop a framework to study the role of variability in transport across a streamline of a reference flow. Two complementary schemes are presented: a graphical approach for indi…
Probabilistic Eddy Identification with Uncertainty Quantification
Jeffrey Covington, Nan Chen, Stephen Wiggins +1
Mesoscale eddies are critical in ocean circulation and the global climate system. Standard eddy identification methods are usually based on deterministic optimal point estimates of…
Index k saddles and dividing surfaces in phase space, with applications to isomerization dynamics
Peter Collins, Gregory S. Ezra, Stephen Wiggins
In this paper we continue our studies of the phase space geometry and dynamics associated with index k saddles (k > 1) of the potential energy surface. Using normal form theory, we…
Using Lagrangian descriptors to uncover invariant structures in Chesnavich's Isokinetic Model with application to roaming
Vladimir Krajnak, Gregory S. Ezra, Stephen Wiggins
Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invarian…
Dynamics of capture in the restricted three-body problem
S. A. Astakhov, Andrew D. Burbanks, Stephen Wiggins +1
We propose a new dynamical model for capture of irregular moons which identifies chaos as the essential feature responsible for initial temporary gravitational trapping within a pl…
Geometric Diagnostics of Scrambling-Related Sensitivity in a Bohmian Preparation Space
Stephen Wiggins
The Out-of-Time-Order Correlator (OTOC) is a standard algebraic diagnostic of quantum information scrambling, but it offers limited direct geometric intuition. In this note, we pro…
The Chaotic Saddle in the Lozi map, autonomous and non-autonomous versions
Carlos Lopesino, Francisco Balibrea-Iniesta, Stephen Wiggins +1
In this paper we prove the existence of a chaotic saddle for a piecewise linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area pre…
Influence of mass and potential energy surface geometry on roaming in Chesnavich's CH model
Vladimir Krajnak, Stephen Wiggins
Chesnavich's model Hamiltonian for the reaction CH CH is known to exhibit a range of interesting dynamical phenomena including roaming. The model system con…
A Kolmogorov theorem for nearly-integrable Poisson systems with asymptotically decaying time-dependent perturbation
Alessandro Fortunati, Stephen Wiggins
The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly-integrable Poisson systems associated to a real analytic Hamiltonian with ap…
Preparation-Space Diagnostics and Logical Information Loss in a Driven Kerr-Cat Qubit
Stephen Wiggins
A Kerr-cat qubit encodes a logical bit in the two wells of a parametrically driven nonlinear oscillator, and a logic gate is a transient change of the drive. In the phase plane the…
A Bernoulli linked-twist map in the plane
James Springham, Stephen Wiggins
We prove that a Lebesgue measure-preserving linked-twist map defined in the plane is metrically isomorphic to a Bernoulli shift (and thus strongly mixing). This is the first such r…
The Influence of a Parameter that Controls the Asymmetry of a Potential Energy Surface with an Entrance Channel and Two Potential Wells
Makrina Agaoglou, Matthaios Katsanikas, Stephen Wiggins
In this paper we study an asymmetric valley-ridge inflection point (VRI) potential, whose energy surface (PES) features two sequential index-1 saddles (the upper and the lower), wi…
Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems
Ana M. Mancho, Stephen Wiggins, Jezabel Curbelo +1
In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as…
Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
Holger Waalkens, Stephen Wiggins
Hamiltonian dynamical systems possessing equilibria of stability type display \emph{reaction-type dynamics} for energies close t…
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
Holger Waalkens, Roman Schubert, Stephen Wiggins
A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is…
Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics
VladimÃr KrajÅák, Stephen Wiggins
We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct…
A Phase Space Signature of Quantum Roaming in Chesnavich's Model
Stephen Wiggins
Roaming reactions occur when a molecule enters a near-dissociation region, avoids immediate separation, and later forms products by a pathway not controlled by the conventional tig…
A Periodic Orbit Trace Formula for Quantum Scrambling: The Role of the Normally Hyperbolic Invariant Manifold
Stephen Wiggins
Out-of-Time-Order Correlators (OTOCs) quantify quantum information scrambling, but their connection to localized phase-space structures, such as chemical transition states, require…
Barry Carpenter. Pioneering Physical Organic Chemist, Teacher, Mentor and Friend
Stephanie R. Hare, Allan R. Pinhas, Julia Rehbein +2
This is the preface to a special issue of the Journal of Physical Organic Chemistry dedicated to an outstanding physical organic chemist, mentor and friend, Barry Carpenter on the…
Transport and roaming on the Double van der Waals Potential Energy Surface
Francisco Gonzalez Montoya, VÃctor J. GarcÃa-Garrido, Broncio Aguilar-Sanjuan +1
This paper explores the phase space structures characterising transport for a double-well van der Waals potential surface. Trajectories are classified as inter-well, intra-well, an…
Nonstatistical dynamics on the caldera
Peter Collins, Zeb C. Kramer, Barry K. Carpenter +2
We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles ass…
The Flux-Flux Correlation Function for Anharmonic Barriers
Arseni Goussev, Roman Schubert, Holger Waalkens +1
The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classi…
Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations
Alessandro Fortunati, Stephen Wiggins
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly…
Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence
Alessandro Fortunati, Stephen Wiggins
The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a toru…
Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface
Matthaios Katsanikas, Makrina Agaoglou, Stephen Wiggins
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of two period-doubling bifurcations in a 2D caldera-type potential. We study the structure, the…
Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone
Frédéric A. L. Mauguière, Peter Collins, Zeb C. Kramer +4
We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic in…
Transport Induced by Mean-Eddy Interaction: I. Theory, and Relation to Lagrangian Lobe Dynamics
Kayo Ide, Stephen Wiggins
In this paper we develop a method for the estimation of {\bf T}ransport {\bf I}nduced by the {\bf M}ean-{\bf E}ddy interaction (TIME) in two-dimensional unsteady flows. The method…
Born-Oppenheimer, Born-Huang, and exact factorization: quantum geometry and error in analytically transparent benchmark models
Stephen Wiggins
The phrase "potential energy surface" refers to several distinct objects. The Born-Oppenheimer construction gives a clamped-nucleus electronic eigenvalue, the single-surface Born-H…
Data-Driven Model Identification Using Time Delayed Nonlinear Maps for Systems with Multiple Attractors
Athanasios P. lliopoulos, Evelyn Lunasin, John G. Michopoulos +2
This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach…
Lagrangian transport through an ocean front in the North-Western Mediterranean Sea
Ana M. Mancho, Emilio Hernandez-Garcia, Des Small +2
We analyze with the tools of lobe dynamics the velocity field from a numerical simulation of the surface circulation in the Northwestern Mediterranean Sea. We identify relevant hyp…
Roaming in acetaldehyde
VladimÃr KrajÅák, Stephen Wiggins
We investigate roaming in the photodissociation of acetaldehyde (CHCHO), providing insight into the contrasting roaming dynamics observed for this molecule compared to formalde…
Phase space geometry and reaction dynamics near index two saddles
Gregory S. Ezra, Stephen Wiggins
We study the phase space geometry associated with index 2 saddles of a potential energy surface and its influence on reaction dynamics for degree-of-freedom (DoF) Hamiltonian s…
Phase Space Analysis of the Non-Existence of Dynamical Matching in a Stretched Caldera Potential Energy Surface
Matthaios Katsanikas, Stephen Wiggins
In this paper we continue our studies of the two dimensional caldera potential energy surface in a parametrized family that allows for a study of the effect of symmetry on the phas…
Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The Vortex Splitting at Upper Levels
Jezabel Curbelo, Carlos R. Mechoso, Ana M. Mancho +1
The present two-part paper provides a Lagrangian perspective of the final southern warming in 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting…
A periodic orbit formula for quantum reactions through transition states
Roman Schubert, Holger Waalkens, Arseni Goussev +1
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized…
The Quantum Normal Form Approach to Reactive Scattering: The Cumulative Reaction Probability for Collinear Exchange Reactions
Arseni Goussev, Roman Schubert, Holger Waalkens +1
The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for he…
Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems
VladimÃr KrajÅák, VÃctor J. GarcÃa-Garrido, Stephen Wiggins
We develop the geometrical, analytical, and computational framework for reactive island theory for three degrees-of-freedom time-independent Hamiltonian systems. In this setting, t…
Lagrangian Descriptors for Two Dimensional, Area Preserving, Autonomous and Nonautonomous Maps
Carlos Lopesino, Francisco Balibrea-Iniesta, Stephen Wiggins +1
In this paper we generalize the method of Lagrangian descriptors to two dimensional, area preserving, autonomous and nonautonomous discrete time dynamical systems. We consider four…
A Causation-Based Computationally Efficient Strategy for Deploying Lagrangian Drifters to Improve Real-Time State Estimation
Erik Bollt, Nan Chen, Stephen Wiggins
Deploying Lagrangian drifters that facilitate the state estimation of the underlying flow field within a future time interval is practically important. However, the uncertainty in…
The tipping times in an Arctic sea ice system under influence of extreme events
Fang Yang, Yayun Zheng, Jinqiao Duan +2
In light of the rapid recent retreat of Arctic sea ice, the extreme weather events triggering the variability in Arctic ice cover has drawn increasing attention. A non-Gaussian $α…
Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium
Alessandro Fortunati, Stephen Wiggins
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations…
Roaming at Constant Kinetic Energy: Chesnavich's Model and the Hamiltonian Isokinetic Thermostat
VladimÃr KrajÅák, Gregory S. Ezra, Stephen Wiggins
We consider the roaming mechanism for chemical reactions under the nonholonomic constraint of constant kinetic energy. Our study is carried out in the context of the Hamiltonian is…
Multiple Transition States and Roaming in Ion-Molecule Reactions: a Phase Space Perspective
Frederic A. L. Mauguiere, Peter Collins, Gregory S. Ezra +2
We provide a dynamical interpretation of the recently identified `roaming' mechanism for molecular dissociation reactions in terms of geometrical structures in phase space. These a…
Isomerization dynamics of a buckled nanobeam
Peter Collins, Gregory S. Ezra, Stephen Wiggins
We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consid…
Finding NHIM in 2 and 3 degrees-of-freedom with Hénon-Heiles type potential
Shibabrat Naik, Stephen Wiggins
We present the capability of Lagrangian descriptors for revealing the high dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 sad…
Roaming dynamics in Ketene isomerization
Frédéric A. L. Mauguière, Peter Collins, Gregory S. Ezra +2
A reduced two dimensional model is used to study Ketene isomerization reaction. In light of recent results by Ulusoy \textit{et al.} [J.\ Phys.\ Chem.\ A {\bf 117}, 7553 (2013)], t…
Phase Space Bottlenecks in an Adiabatic Marcus Hamiltonian: Cusp Geometry, NHIMs, and Mixed Valence Electron Transfer
Stephen Wiggins
Marcus--Hush theory explains electron transfer in terms of reorganization energies, driving forces, electronic couplings, and reduced free-energy or energy-gap descriptions. These…
High Dimensional Cluster Analysis Using Path Lengths
Kevin McIlhany, Stephen Wiggins
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension (). The data set is first reduced to a smaller set of par…
Hamiltonian pitchfork bifurcation in transition across index-1 saddles
Wenyang Lyu, Shibabrat Naik, Stephen Wiggins
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in…
The time evolution of the trajectories after the selectivity in a symmetric potential energy surface with a post-transition-state bifurcation
Douglas Haigh, Matthaios Katsanikas, Makrina Agaoglou +1
Selectivity is an important phenomenon in chemical reaction dynamics. This can be quantified by the branching ratio of the trajectories that visit one or the other wells to the tot…
A Theoretical Framework for Lagrangian Descriptors
Carlos Lopesino, Francisco Balibrea-Iniesta, VÃctor J. GarcÃa-Garrido +2
This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds…
Transport Induced by Mean-Eddy Interaction: II. Analysis of Transport Processes
Kayo Ide, Stephen Wiggins
We present a framework for the analysis of transport processes resulting from the mean-eddy interaction in a flow. The framework is based on the {\bf T}ransport {\bf I}nduced by th…
Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium
Alessandro Fortunati, Stephen Wiggins
The classical theorem of Moser, on the existence of a normal form in the neighbourhood of a hyperbolic equilibrium, is extended to a class of real-analytic Hamiltonians with aperio…
Bridging Classical Sensitivity and Quantum Scrambling: A Tutorial on Out-of-Time-Ordered Correlators
Stephen Wiggins
In classical dynamical systems, chaotic behavior is often associated with exponential sensitivity to initial conditions together with global phase-space structure. Translating this…
A bridge between invariant dynamical structures and uncertainty quantification
Guillermo GarcÃa-Sánchez, Ana M. Mancho, Stephen Wiggins
We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase…
Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence
Alessandro Fortunati, Stephen Wiggins
The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians. Th…
New links between invariant dynamical structures and uncertainty quantification
Guillermo Garcia-Sanchez, Ana Maria Mancho, Makrina Agaoglou +1
This paper proposes a new uncertainty measure, appropriate for quantifying the performance of transport models in assessing the origin or source of a given observation. It is found…
The Nature of Reactive and Non-reactive Trajectories for a Three Dimensional Caldera Potential Energy Surface
Matthaios Katsanikas, Stephen Wiggins
We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of the…
Microcanonical rates, gap times, and phase space dividing surfaces
Gregory S. Ezra, Holger Waalkens, Stephen Wiggins
The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for m…
Tilting and Squeezing: Phase space geometry of Hamiltonian saddle-node bifurcation and its influence on chemical reaction dynamics
VÃctor J. GarcÃa-Garrido, Shibabrat Naik, Stephen Wiggins
In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goa…
Quantum dynamics of a one degree-of-freedom Hamiltonian saddle-node bifurcation
Wenyang Lyu, Shibabrat Naik, Stephen Wiggins
In this paper, we study the quantum dynamics of a one degree-of-freedom (DOF) Hamiltonian that is a normal form for a saddle node bifurcation of equilibrium points in phase space.…
A lambda-lemma for normally hyperbolic invariant manifolds
Jacky Cresson, Stephen Wiggins
Let be a smooth manifold and be a , diffeomorphism. Let be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue…
Phase space structure and escape time dynamics in a Van der Waals model for exothermic reactions
Francisco Gonzalez Montoya, Stephen Wiggins
We study the phase space structures that control the transport in a classical Hamiltonian model for a chemical reaction. This model has been proposed to study the yield of products…
Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautomous Henon Map
Francisco Balibrea-Iniesta, Carlos Lopesino, Stephen Wiggins +1
In this paper we analyze chaotic dynamics for two dimensional nonautonomous maps through the use of a nonautonomous version of the Conley-Moser conditions given previously. With th…
Quantum Theory of Reactive Scattering in Phase Space
Arseni Goussev, Roman Schubert, Holger Waalkens +1
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective o…
Navigating Phase Space Transport with the Origin-Fate Map
Malcolm Hillebrand, Matthaios Katsanikas, Stephen Wiggins +1
We introduce and demonstrate the usage of the origin-fate map (OFM) as a tool for the detailed investigation of phase space transport in reactant-product type systems. For these sy…
Elementary exposition of realizing phase space structures relevant to chemical reaction dynamics
Wenyang Lyu, Shibabrat Naik, Stephen Wiggins
In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical rea…
Phase Space Structure and Transport in a Caldera Potential Energy Surface
Matthaios Katsanikas, Stephen Wiggins
We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow…
The efficient computation of transition state resonances and reaction rates from a quantum normal form
Roman Schubert, Holger Waalkens, Stephen Wiggins
A quantum version of a recent formulation of transition state theory in {\em phase space} is presented. The theory developed provides an algorithm to compute quantum reaction rates…
Lagrangian Descriptors with Uncertainty
Nan Chen, Evelyn Lunasin, Stephen Wiggins
Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematic…
A Mathematical Framework for Quantifying Nonlinear Uncertainty Propagation in Eddy Identification Criteria
Charlotte Moser, Nan Chen, Stephen Wiggins
Ocean eddies are swirling mesoscale features that play a fundamental role in oceanic transport and mixing. Eddy identification relies on diagnostic criteria that are inherently non…
Lagrangian study of the final warming in the southern stratosphere during 2002: Part II. 3D structure
Jezabel Curbelo, Carlos R. Mechoso, Ana M. Mancho +1
This two-part paper aims to provide a Lagrangian perspective of the final southern warming in spring of 2002, during which the stratospheric polar vortex (SPV) experienced a unique…
Impenetrable Barriers in Phase Space for Deterministic Thermostats
Gregory S. Ezra, Stephen Wiggins
We investigate the relation between the phase space structure of Hamiltonian and non-Hamiltonian deterministic thermostats. We show that phase space structures governing reaction d…
Exploring Isomerization Dynamics on a Potential Energy Surface with an Index-2 Saddle using Lagrangian Descriptors
VÃctor J. GarcÃa-Garrido, Makrina Agaoglou, Stephen Wiggins
In this paper we explore the phase space structures governing isomerization dynamics on a potential energy surface with four wells and an index-2 saddle. For this model, we analyze…
Revealing Roaming on the Double Morse Potential Energy Surface with Lagrangian Descriptors
Francisco Gonzalez Montoya, Stephen Wiggins
In this paper, we analyse the phase space structure of the roaming dynamics in a two degree of freedom potential energy surface consisting of two identical planar Morse potentials…
Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems
Francisco Balibrea-Iniesta, Carlos Lopesino, Stephen Wiggins +1
In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent th…
A Three-Degree-of-Freedom Chesnavich Model for Roaming: Derivation, Phase-Space Geometry, NHIM-Anchored Dividing Surfaces, and Roaming Transport
Stephen Wiggins
Roaming reactions, in which a dissociating fragment moves through a flat region of the potential surface rather than down the minimum-energy path, lie outside the assumptions of co…
Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners
Nan Chen, Stephen Wiggins, Marios Andreou
This paper provides a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more in this area. It exploits many very simple…
Phase space structure and dynamics for the Hamiltonian isokinetic thermostat
Peter Collins, Gregory S. Ezra, Stephen Wiggins
We investigate the phase space structure and dynamics of a Hamiltonian isokinetic thermostat, for which ergodic thermostat trajectories at fixed (zero) energy generate a canonical…
Structured pathways in the turbulence organizing recent oil spill events in the Eastern Mediterranean
Guillermo Garcia-Sanchez, Ana M. Mancho, Antonio G. Ramos +2
The chaotic nature of ocean motion is a major challenge that hinders the discovery of spatio-temporal current routes that govern the transport of material. Certain material, such a…
Phase space barriers and dividing surfaces in the absence of critical points of the potential energy
Gregory S. Ezra, Stephen Wiggins
We consider the existence of invariant manifolds in phase space governing reaction dynamics in situations where there are no saddle points on the potential energy surface in the re…
Launching Drifter Observations in the Presence of Uncertainty
Nan Chen, Evelyn Lunasin, Stephen Wiggins
Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Sign…
Support vector machines for learning reactive islands
Shibabrat Naik, VladimÃr KrajÅák, Stephen Wiggins
We develop a machine learning framework that can be applied to data sets derived from the trajectories of Hamilton's equations. The goal is to learn the phase space structures that…