scholarly journals Roaming dynamics in ion-molecule reactions: Phase space reaction pathways and geometrical interpretation

2014 ◽  
Vol 140 (13) ◽  
pp. 134112 ◽  
Author(s):  
Frédéric A. L. Mauguière ◽  
Peter Collins ◽  
Gregory S. Ezra ◽  
Stavros C. Farantos ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Geometrical Interpretation ◽  
Reaction Pathways ◽  
Ion Molecule Reactions

scholarly journals Identifying reaction pathways in phase space via asymptotic trajectories

2020 ◽  
Vol 22 (18) ◽  
pp. 10087-10105
Author(s):  
Yutaka Nagahata ◽  
F. Borondo ◽  
R. M. Benito ◽  
Rigoberto Hernandez
Keyword(s):  
Phase Space ◽  
Reaction Pathway ◽  
Reaction Pathways

The asymptotic trajectories indicate the edge of the reaction pathway.

Ion/molecule reactions of arsenic and phosphorus cluster ions: ionization potentials and novel reaction pathways

1991 ◽  
Vol 95 (1) ◽  
pp. 98-104 ◽  
Author(s):  
Jeffrey A. Zimmerman ◽  
Stephan B. H. Bach ◽  
Clifford H. Watson ◽  
John R. Eyler
Keyword(s):  
Ionization Potentials ◽  
Reaction Pathways ◽  
Cluster Ions ◽  
Ion Molecule Reactions

scholarly journals Models of Hot Cores with Complex Molecules

2011 ◽  
Vol 7 (S280) ◽  
pp. 79-87
Author(s):  
Susanna L. Widicus Weaver ◽  
Robin T. Garrod ◽  
Jacob C. Laas ◽  
Eric Herbst
Keyword(s):  
Gas Phase ◽  
Reaction Pathways ◽  
High Mass ◽  
Phase Reaction ◽  
Complex Molecules ◽  
Warm Up ◽  
Ion Molecule Reactions ◽  
Relative Abundances ◽  
Surface Ice ◽  
Grain Surface

AbstractRecent models of hot cores have incorporated previously-uninvestigated chemical pathways that lead to the formation of complex organic molecules (COMs; i.e. species containing six or more atoms). In addition to the gas-phase ion-molecule reactions long thought to dominate the organic chemistry in these regions, these models now include photodissociation-driven grain surface reaction pathways that can also lead to COMs. Here, simple grain surface ice species photodissociate to form small radicals such as OH, CH3, CH2OH, CH3O, HCO, and NH2. These species become mobile at temperatures above 30 K during the warm-up phase of star formation. Radical-radical addition reactions on grain surfaces can then form an array of COMs that are ejected into the gas phase at higher temperatures. Photodissociation experiments on pure and mixed ices also show that these complex molecules can indeed form from simple species. The molecules predicted to form from this type of chemistry reasonably match the organic inventory observed in high mass hot cores such as Sgr B2(N) and Orion-KL. However, the relative abundances of the observed molecules differ from the predicted values, and also differ between sources. Given this disparity, it remains unclear whether grain surface chemistry governed by photodissociation is the dominant mechanism for the formation of COMs, or whether other unexplored gas-phase reaction pathways could also contribute significantly to their formation. The influence that the physical conditions of the source have on the chemical inventory also remains unclear. Here we overview the chemical pathways for COM formation in hot cores. We also present new modeling results that begin to narrow down the possible routes for production of COMs based on the observed relative abundances of methyl formate (HCOOCH3) and its C2H4O2 structural isomers.

scholarly journals Multiple transition states and roaming in ion–molecule reactions: A phase space perspective

2014 ◽  
Vol 592 ◽  
pp. 282-287 ◽  
Author(s):  
Frédéric A.L. Mauguière ◽  
Peter Collins ◽  
Gregory S. Ezra ◽  
Stavros C. Farantos ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Transition States ◽  
Ion Molecule Reactions

scholarly journals Gravitational Dynamics—A Novel Shift in the Hamiltonian Paradigm

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 13
Author(s):  
Abhay Ashtekar ◽  
Madhavan Varadarajan
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Geometrical Interpretation ◽  
Lie Derivative ◽  
Hamiltonian Constraint ◽  
Yang Mills ◽  
Dirac Quantization ◽  
Perturbative Regime ◽  
Point Of Departure ◽  
Double Copy

It is well known that Einstein’s equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that time evolution of the gravitational field can be re-expressed as (a gauge covariant generalization of) the Lie derivative along a novel shift vector field in spatial directions. Thus, the canonical transformation generated by the Hamiltonian constraint acquires a geometrical interpretation on the Yang-Mills phase space, similar to that generated by the diffeomorphism constraint. In classical general relativity this geometrical interpretation significantly simplifies calculations and also illuminates the relation between dynamics in the ‘integrable’ (anti)self-dual sector and in the full theory. For quantum gravity, it provides a point of departure to complete the Dirac quantization program for general relativity in a more satisfactory fashion. This gauge theory perspective may also be helpful in extending the ‘double copy’ ideas relating the Einstein and Yang-Mills dynamics to a non-perturbative regime. Finally, the notion of generalized, gauge covariant Lie derivative may also be of interest to the mathematical physics community as it hints at some potentially rich structures that have not been explored.

scholarly journals REDUCED PHASE SPACE QUANTIZATION OF SPHERICALLY SYMMETRIC EINSTEIN-MAXWELL THEORY INCLUDING A COSMOLOGICAL CONSTANT

1994 ◽  
Vol 03 (01) ◽  
pp. 293-298 ◽  
Author(s):  
T. Thiemann
Keyword(s):  
Phase Space ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Electric Charge ◽  
Present Model ◽  
Geometrical Interpretation ◽  
Spherically Symmetric ◽  
Maxwell Theory ◽  
Canonical Variables ◽  
Symmetric Quantum

We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We also compare the reduced phase space quantization to the algebraic quantization. Altogether, we observe that the present model serves as an interesting testing ground for full (3+1) gravity. We use the new canonical variables introduced by Ashtekar which simplifies the analysis tremendously.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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