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cirque.bib
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@article{Soley2018,
author = {Soley, Micheline B. and Heller, Eric J.},
doi = {10.1103/PhysRevA.98.052702},
file = {:Users/bas/Downloads/soley2018.pdf:pdf},
issn = {2469-9926},
journal = {Physical Review A},
month = {nov},
number = {5},
pages = {052702},
publisher = {American Physical Society},
title = {{Classical approach to collision complexes in ultracold chemical reactions}},
url = {https://link.aps.org/doi/10.1103/PhysRevA.98.052702},
volume = {98},
year = {2018}
}
@article{Henon1982,
abstract = {This note describes a method for finding simply and accurately the intersections of a numerically integrated trajectory with a surface of section.},
author = {Henon, M.},
doi = {10.1016/0167-2789(82)90034-3},
file = {:Users/bas/Downloads/henon1982.pdf:pdf},
issn = {0167-2789},
journal = {Physica D: Nonlinear Phenomena},
month = {sep},
number = {2-3},
pages = {412--414},
publisher = {North-Holland},
title = {{On the numerical computation of Poincar{\'{e}} maps}},
url = {https://www.sciencedirect.com/science/article/abs/pii/0167278982900343},
volume = {5},
year = {1982}
}
@article{Kraka2010,
abstract = {Computational approaches to understanding chemical reaction mechanisms generally begin by establishing the relative energies of the starting materials, transition state, and products, that is, the ...},
author = {Kraka, Elfi and Cremer, Dieter},
doi = {10.1021/ar900013p},
file = {:Users/bas/Downloads/kraka2010.pdf:pdf},
issn = {0001-4842},
journal = {Accounts of Chemical Research},
month = {may},
number = {5},
pages = {591--601},
publisher = {American Chemical Society},
title = {{Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States}},
url = {https://pubs.acs.org/doi/10.1021/ar900013p},
volume = {43},
year = {2010}
}
@article{Carpenter2018,
abstract = {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 surrounded by an unbounded flat region containing no critical points. In addition, the model has an index one saddle between the potential wells. We study the dynamical mechanisms underlying transport between the two potential wells, with emphasis on the role of the flat region surrounding the wells. The model allows us to probe many of the features of the “roaming mechanism” whose reaction dynamics are of current interest in the chemistry community.},
author = {Carpenter, Barry K. and Ezra, Gregory S. and Farantos, Stavros C. and Kramer, Zeb C. and Wiggins, Stephen},
doi = {10.1134/S1560354718010069},
file = {:Users/bas/Downloads/Dynamics{\_}on{\_}the{\_}Double{\_}Morse{\_}Potential{\_}A{\_}Paradigm{\_}.pdf:pdf},
issn = {1560-3547},
journal = {Regular and Chaotic Dynamics},
keywords = {Dynamical Systems and Ergodic Theory},
month = {jan},
number = {1},
pages = {60--79},
publisher = {Springer},
title = {{Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points}},
url = {http://link.springer.com/10.1134/S1560354718010069},
volume = {23},
year = {2018}
}
@article{GonzalezMontoya2020,
author = {{Gonzalez Montoya}, Francisco and Wiggins, Stephen},
doi = {10.1088/1751-8121/ab8b75},
file = {:Users/bas/Library/Application Support/Mendeley Desktop/Downloaded/Gonzalez Montoya, Wiggins - 2020 - Revealing roaming on the double morse potential energy surface with lagrangian descriptors.pdf:pdf},
issn = {1751-8113},
journal = {Journal of Physics A: Mathematical and Theoretical},
month = {apr},
publisher = {IOP Publishing},
title = {{Revealing roaming on the double morse potential energy surface with lagrangian descriptors}},
url = {https://iopscience.iop.org/article/10.1088/1751-8121/ab8b75},
year = {2020}
}
@article{netz2004dynamic,
title={Dynamic anomalies of fluids with isotropic doubled-ranged potential},
author={Netz, Paulo A and Raymundi, Jos{\'e} Fernando and Camera, Adriana Simane and Barbosa, Marcia C},
journal={Physica A: Statistical Mechanics and its Applications},
volume={342},
number={1-2},
pages={48--53},
year={2004},
publisher={Elsevier}
}
@misc{montoya2020phase,
title={The phase space structure and the escape time dynamics in a Van der Waals model for exothermic reactions},
author={Francisco Gonzalez Montoya and Stephen Wiggins},
year={2020},
eprint={2006.15611},
archivePrefix={arXiv},
primaryClass={nlin.CD}
}
@article{Carpenter2017,
author = {Carpenter, Barry K. and Ezra, Gregory S. and Farantos, Stavros C. and Kramer, Zeb C. and Wiggins, Stephen},
title = {Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics},
journal = {The Journal of Physical Chemistry B},
volume = {122},
number = {13},
pages = {3230-3241},
year = {2018},
doi = {10.1021/acs.jpcb.7b08707},
note ={PMID: 28968092},
URL = {
https://doi.org/10.1021/acs.jpcb.7b08707
},
eprint = {
https://doi.org/10.1021/acs.jpcb.7b08707
}
}
@article{Demian2017,
author = {Demian, Atanasiu Stefan and Wiggins, Stephen},
title = {Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors},
journal = {International Journal of Bifurcation and Chaos},
volume = {27},
number = {14},
pages = {1750225},
year = {2017},
doi = {10.1142/S021812741750225X},
URL = {
https://doi.org/10.1142/S021812741750225X
},
eprint = {
https://doi.org/10.1142/S021812741750225X
}
,
abstract = { The purpose of this paper is to apply Lagrangian Descriptors, a concept used to describe phase space structure, to autonomous Hamiltonian systems with two degrees of freedom in order to detect periodic solutions. We propose a method for Hamiltonian systems with saddle-center equilibrium and apply this approach to the classical Hénon–Heiles system. The method was successful in locating the unstable Lyapunov orbits in phase space. }
}
@article{Gonzalez2020,
title = "Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom",
journal = "Communications in Nonlinear Science and Numerical Simulation",
volume = "90",
pages = "105282",
year = "2020",
issn = "1007-5704",
doi = "https://doi.org/10.1016/j.cnsns.2020.105282",
url = "http://www.sciencedirect.com/science/article/pii/S1007570420301143",
author = "Francisco {Gonzalez Montoya} and Florentino Borondo and Christof Jung",
keywords = "Chaotic scattering, Caustics, Hamiltonian systems, Transport, Invariant manifolds",
abstract = "We study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degree of freedom (3-dof) model is studied by first considering the non-vibrating 2-dof model for different values of the energy. The set of singularities of the scattering functions shows the structure of the tangle between the stable and unstable manifolds of the fixed point at an infinite distance to the Cu surface in the Poincaré map. These invariant manifolds of the 2-dof system and their tangle can be used as a starting point for the construction of the stable and unstable manifolds and their tangle for the 3-dof coupled model. When the surface vibrates, the system has an extra closed degree of freedom and it is possible to represent the 3-dof tangle as deformation of a stack of 2-dof tangles, where the stack parameter is the energy of the 2-dof system. Also for the 3-dof system, the resulting invariant manifolds have the correct dimension to divide the constant total energy manifold. By this construction, it is possible to understand the chaotic scattering phenomena for the 3-dof system from a geometric point of view. We explain the connection between the set of singularities of the scattering function, the Jacobian determinant of the scattering function, the relevant invariant manifolds in the scattering problem, and the cross-section, as well as their behavior when the coupling due to the surface vibration is switched on. In particular, we present in detail the relation between the changes as a function of the energy in the structure of the caustics in the cross-section and the changes in the zero level set of the Jacobian determinant of the scattering function."
}