Stephen Wiggins
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View article: Classification of Trajectory Types Exhibiting Dynamical Matching in Caldera-Type Hamiltonian Systems
Classification of Trajectory Types Exhibiting Dynamical Matching in Caldera-Type Hamiltonian Systems Open
In this paper, we study the different types of trajectories that correspond to a particular orbital behavior of caldera-type Hamiltonian systems. This particular orbital behavior is dynamical matching. Dynamical matching is an important ch…
View article: Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners
Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners Open
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 examples, which are understandable to undergraduates, to p…
View article: Roaming in acetaldehyde
Roaming in acetaldehyde Open
We investigate roaming in the photodissociation of acetaldehyde (CH3CHO), providing insights into the contrasting roaming dynamics observed for this molecule compared to formaldehyde. We carry out trajectory studies for full-dimensional ac…
View article: Probabilistic Eddy Identification with Uncertainty Quantification
Probabilistic Eddy Identification with Uncertainty Quantification Open
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 the ocean flow field. However, uncertainty exists in estim…
View article: A Causation-Based Computationally Efficient Strategy for Deploying Lagrangian Drifters to Improve Real-Time State Estimation
A Causation-Based Computationally Efficient Strategy for Deploying Lagrangian Drifters to Improve Real-Time State Estimation Open
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 estimating the flow field prevents using standard determini…
View article: Navigating phase space transport with the origin-fate map
Navigating phase space transport with the origin-fate map Open
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 systems, which exhibit clearly defined start and end states, …
View article: Launching Drifter Observations in the Presence of Uncertainty
Launching Drifter Observations in the Presence of Uncertainty Open
Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Significant uncertainty appears when the flow field is inferred…
View article: Dynamical matching in a three-dimensional Caldera potential-energy surface
Dynamical matching in a three-dimensional Caldera potential-energy surface Open
In a previous paper, we used a recent extension of the periodic-orbit dividing surfaces method to distinguish the reactive and nonreactive parts in a three-dimensional (3D) Caldera potential-energy surface. Furthermore, we detected the phe…
View article: Lagrangian Descriptors with Uncertainty
Lagrangian Descriptors with Uncertainty Open
Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematical framework for computing Lagrangian descriptors when unce…
View article: Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map
Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map Open
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular, …
View article: The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom-III
The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom-III Open
In two previous papers [Katsanikas & Wiggins, 2021a, 2021b], we developed two methods for the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom. We applied the first method (see …
View article: Elementary Classical Mechanics
Elementary Classical Mechanics Open
This book consists of material for a one term course in classical mechanics presented to first year mathematics majors at the University of Bristol. Unlike the undergraduate mathematics curriculum in the United States, the United Kingdom h…
View article: Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map
Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map Open
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular, …
View article: Navigating Phase Space Transport with the Origin-Fate Map
Navigating Phase Space Transport with the Origin-Fate Map Open
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 systems, which exhibit clearly defined start and end states, …
View article: Corrigendum: Very high resolution tools for the monitoring and assessment of environmental hazards in coastal areas
Corrigendum: Very high resolution tools for the monitoring and assessment of environmental hazards in coastal areas Open
In the published article, there was an error regarding the affiliation(s) for Guillermo Garcı́a-Sánchez. As well as having affiliation 1, they should also have: Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politéc…
View article: Barry Carpenter—Pioneering physical organic chemist, teacher, mentor, and friend
Barry Carpenter—Pioneering physical organic chemist, teacher, mentor, and friend Open
This special issue of the Journal of Physical Organic Chemistry is dedicated to an outstanding physical organic chemist, mentor, and friend, Barry Carpenter, on the occasion of his official retirement. Knowing that great minds like his nev…
View article: Barry Carpenter. Pioneering Physical Organic Chemist, Teacher, Mentor and Friend
Barry Carpenter. Pioneering Physical Organic Chemist, Teacher, Mentor and Friend Open
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 occasion of his official retirement.
View article: Quantifying chaos using Lagrangian descriptors
Quantifying chaos using Lagrangian descriptors Open
We present and validate simple and efficient methods to estimate the chaoticity of orbits in low dimensional dynamical systems from computations of Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed for determin…
View article: Seeing Through Turbulence to Track Oil Spills in the Ocean
Seeing Through Turbulence to Track Oil Spills in the Ocean Open
After oil and tar washed up on eastern Mediterranean beaches in 2021, scientists devised a way to trace the pollution back to its sources using satellite imagery and mathematics.
View article: Phase Space Transport in a Symmetric Caldera Potential with Three Index-1 Saddles and No Minima
Phase Space Transport in a Symmetric Caldera Potential with Three Index-1 Saddles and No Minima Open
We apply the method of Lagrangian Descriptors (LDs) to a symmetric Caldera-type potential energy surface which has three index-1 saddles surrounding a relatively flat region that contains no minimum. Using this method we show the phase spa…
View article: Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface
Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface Open
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 range, the minimum and maximum extents of the periodic orb…