scholarly journals A general formulation of the quasiclassical trajectory method for reduced-dimensionality reaction dynamics calculations

2018 ◽  
Vol 20 (19) ◽  
pp. 13224-13240 ◽  
Author(s):  
Tibor Nagy ◽  
Anna Vikár ◽  
György Lendvay
Keyword(s):  
Initial Conditions ◽  
Reaction Dynamics ◽  
Black Box ◽  
Reduced Dimensionality ◽  
Trajectory Calculations ◽  
Internal Coordinates ◽  
Trajectory Method

A black-box formalism for generating initial conditions and following trajectories in reduced-dimensionality quasiclassical trajectory calculations using arbitrary internal coordinates.

QUANTUM TRAJECTORY CALCULATIONS FOR BIPOLAR WAVEPACKET DYNAMICS IN ONE DIMENSION: SYNTHETIC SINGLE-WAVEPACKET PROPAGATION

2010 ◽  
Vol 09 (04) ◽  
pp. 711-734 ◽  
Author(s):  
KISAM PARK ◽  
BILL POIRIER
Keyword(s):  
Initial Conditions ◽  
Technical Difficulty ◽  
One Dimension ◽  
Quantum Trajectory ◽  
One Dimensional ◽  
Trajectory Calculations ◽  
Wave Packet Dynamics ◽  
Wavepacket Dynamics ◽  
Trajectory Method ◽  
The Given

In a previous paper [Park K, Poirier B, Parlant G, J Chem Phys129:194112, 2008], a synthetic quantum trajectory method (QTM) was successfully implemented for wave-packet dynamics in a one-dimensional (1D) symmetric Eckart barrier system, utilizing a "double-wavepacket" version of the bipolar decomposition, ψ = ψ+ + ψ- = (ψ1+ + ψ2+) + (ψ1- + ψ2-), to avoid a technical difficulty involving negligible initial ψ- density. In this paper, we develop a new synthetic algorithm which overcomes this difficulty directly, utilizing the original "single-wavepacket" version of the bipolar decomposition, ψ =ψ+ + ψ-, and also show that the initial propagation of ψ- is mainly governed by probability transfer from ψ+, rather than by the given initial conditions for ψ-. The new algorithm makes it possible to apply the synthetic bipolar QTM to asymptotically asymmetric as well as symmetric potential systems. Successful application results for both symmetric and asymmetric Eckart barrier systems in 1D are presented.

Quantum initial conditions in quasi-classical trajectory calculations

1973 ◽  
Vol 19 (1) ◽  
pp. 21-25 ◽  
Author(s):  
Joel M. Bowman ◽  
Aron Kuppermann ◽  
George C. Schatz
Keyword(s):  
Initial Conditions ◽  
Classical Trajectory ◽  
Trajectory Calculations

Oxyhalogen-sulfur chemistry — Kinetics and mechanism of the oxidation of cysteamine by acidic iodate and iodine

2006 ◽  
Vol 84 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Alice Chanakira ◽  
Edward Chikwana ◽  
David H Peyton ◽  
Reuben H Simoyi
Keyword(s):  
Acid Concentration ◽  
Rate Constant ◽  
Oxidation Product ◽  
Initial Conditions ◽  
Reaction Dynamics ◽  
Reaction Scheme ◽  
Kinetics And Mechanism ◽  
Sulfur Chemistry ◽  
Bimolecular Rate Constant ◽  
Acidic Conditions

The oxidation of cysteamine by iodate and aqueous iodine has been studied in neutral to mildly acidic conditions. The reaction is relatively slow and is heavily dependent on acid concentration. The reaction dynamics are complex and display clock behavior, transient iodine production, and even oligooscillatory production of iodine, depending upon initial conditions. The oxidation product was the cysteamine dimer (cystamine), with no further oxidation observed past this product. The stoichiometry of the reaction was deduced to be IO3– + 6H2NCH2CH2SH → I– + 3H2NCH2CH2S-SCH2CH2NH2 + 3H2O in excess cysteamine conditions, whereas in excess iodate the stoichiometry of the reaction is 2IO3– + 10H2NCH2CH2SH → I2 + 5H2NCH2CH2S-SCH2CH2NH2 + 6H2O. The stoichiometry of the oxidation of cysteamine by aqueous iodine was deduced to be I2 + 2H2NCH2CH2SH → 2I– + H2NCH2CH2S-SCH2CH2NH2 + 2H+. The bimolecular rate constant for the oxidation of cysteamine by iodine was experimentally evaluated as 2.7 (mol L–1)–1 s–1. The whole reaction scheme was satisfactorily modeled by a network of 14 elementary reactions.Key words: cysteamine, cystamine, Dushman reaction, oligooscillations.

scholarly journals Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
Matt Landreman ◽  
Wrick Sengupta ◽  
Gabriel G. Plunk
Keyword(s):  
Magnetic Fields ◽  
Fusion Reactor ◽  
Initial Conditions ◽  
Nonlinear Ordinary Differential Equation ◽  
Black Box ◽  
Magnetic Axis ◽  
Direct Construction ◽  
One Dimensional ◽  
Magnetic Spectrum ◽  
Conventional Optimization

Quasisymmetric stellarators are appealing intellectually and as fusion reactor candidates since the guiding-centre particle trajectories and neoclassical transport are isomorphic to those in a tokamak, implying good confinement. Previously, quasisymmetric magnetic fields have been identified by applying black-box optimization algorithms to minimize symmetry-breaking Fourier modes of the field strength $B$. Here, instead, we directly construct magnetic fields in cylindrical coordinates that are quasisymmetric to leading order in the distance from the magnetic axis, without using optimization. The method involves solution of a one-dimensional nonlinear ordinary differential equation, originally derived by Garren & Boozer (Phys. Fluids B, vol. 3, 1991, p. 2805). We demonstrate the usefulness and accuracy of this optimization-free approach by providing the results of this construction as input to the codes VMEC and BOOZ_XFORM, confirming the purity and scaling of the magnetic spectrum. The space of magnetic fields that are quasisymmetric to this order is parameterized by the magnetic axis shape along with three other real numbers, one of which reflects the on-axis toroidal current density, and another one of which is zero for stellarator symmetry. The method here could be used to generate good initial conditions for conventional optimization, and its speed enables exhaustive searches of parameter space.

DIABATIC ELECTRONIC MANIFOLD OF HN2(2A′) AND N + NH REACTION DYNAMICS ON ITS LOWEST ADIABAT

2009 ◽  
Vol 08 (05) ◽  
pp. 849-859 ◽  
Author(s):  
V. C. MOTA ◽  
P. J. S. B. CARIDADE ◽  
A. J. C. VARANDAS
Keyword(s):  
Statistical Error ◽  
Reaction Dynamics ◽  
Chem Phys ◽  
Classical Trajectory ◽  
Title Reaction ◽  
Title System ◽  
Trajectory Method ◽  
Method Yield ◽  
Potential Matrix ◽  
Adiabatic Dynamics

A previously reported approach [J. Chem. Phys.97:867, (1997)] to back transform the diagonal adiabats into a 2 × 2 diabatic potential matrix has been utilized to generate a global multi-sheeted form for the title system. Global adiabatic dynamics calculations carried out on the new form using the quasi-classical trajectory method yield results that lie essentially within the statistical error of similar calculations performed on the best surface reported thus far for the title reaction. This makes it suitable for future adiabatic and nonadiabatic calculations carried out either using classical or quantum methods.

Control Policies for a Large Region of Attraction for Dynamically Balancing Legged Robots: A Sampling-Based Approach

Robotica ◽  
2020 ◽  
Vol 39 (1) ◽  
pp. 107-122
Author(s):  
Pranav A. Bhounsule ◽  
Ali Zamani ◽  
Jeremy Krause ◽  
Steven Farra ◽  
Jason Pusey
Keyword(s):  
Trajectory Optimization ◽  
Exponential Convergence ◽  
Initial Conditions ◽  
Control Policy ◽  
Black Box ◽  
Legged Robots ◽  
Region Of Attraction ◽  
Box Models ◽  
Highly Nonlinear ◽  
Black Box Models

SUMMARYThe popular approach of assuming a control policy and then finding the largest region of attraction (ROA) (e.g., sum-of-squares optimization) may lead to conservative estimates of the ROA, especially for highly nonlinear systems. We present a sampling-based approach that starts by assuming an ROA and then finds the necessary control policy by performing trajectory optimization on sampled initial conditions. Our method works with black-box models, produces a relatively large ROA, and ensures exponential convergence of the initial conditions to the periodic motion. We demonstrate the approach on a model of hopping and include extensive verification and robustness checks.

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