Unimolecular decomposition of methyl chloride. II. Some refinements of the calculations

1967 ◽  
Vol 45 (24) ◽  
pp. 3169-3176 ◽  
Author(s):  
W. Forst ◽  
P. St. Laurent
Keyword(s):  
Angular Momentum ◽  
Rate Constant ◽  
Degrees Of Freedom ◽  
Methyl Chloride ◽  
Computational Procedure ◽  
Intramolecular Energy Transfer ◽  
Collision Theory ◽  
Unimolecular Decomposition ◽  
Rational Argument ◽  
Quantum Version

The quantum version of the statistical collision theory is applied to the unimolecular decomposition of methyl chloride in the second-order region using an improved computational procedure and a more realistic physical model. An attempt is made to determine active degrees of freedom, i.e. degrees of freedom participating in intramolecular energy transfer, by rational argument. These considerations point to at least one overall rotation as active, in addition to all nine vibrations as active. Conservation of angular momentum is explicitly considered in the case of one active rotation and an appropriate correction factor is included in the calculated rate constant, as is a correction for anharmonicity. The theoretical rate constant so computed is within less than a factor of two of the experimental value.

THE UNIMOLECULAR DECOMPOSITION OF METHYL CHLORIDE

1965 ◽  
Vol 43 (11) ◽  
pp. 3052-3056 ◽  
Author(s):  
W. Forst ◽  
P. St. Laurent
Keyword(s):  
Rate Constant ◽  
Level Density ◽  
Methyl Chloride ◽  
Good Deal ◽  
Order Rate Constant ◽  
Unimolecular Decomposition ◽  
Calculated Rate ◽  
Quantum Version ◽  
Experimental Activation Energy ◽  
Made In

The second-order rate constant for the unimolecular decomposition of methyl chloride[Formula: see text]has been calculated on a computer by the quantum version of the Marcus–Rice theory assuming no active rotations and using the experimental activation energy. With a harmonic energy level density count the calculated rate constant is 32 times smaller than the experimental value. When correction for anharmonicity is applied, the agreement is somewhat improved but the calculated rate constant is still some 20 times too small. These results are discussed in the light of the assumptions made in the course of the calculations. It is concluded that the quantum statistical collision theory, to which the Marcus–Rice theory reduces at low pressure, is a good deal more successful than Slater's, which is in error by a factor of 105–106.

scholarly journals The Use of Integrals in Numerical Integrations of theN-Body Problem

1971 ◽  
Vol 10 ◽  
pp. 40-51
Author(s):  
Paul E. Nacozy
Keyword(s):  
Angular Momentum ◽  
Numerical Integration ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Center Of Mass ◽  
Integration Step ◽  
Gravitational System ◽  
Systems Of Differential Equations ◽  
Numerical Integrations ◽  
Original Number

AbstractThe numerical integration of systems of differential equations that possess integrals is often approached by using the integrals to reduce the number of degrees of freedom or by using the integrals as a partial check on the resulting solution, retaining the original number of degrees of freedom.Another use of the integrals is presented here. If the integrals have not been used to reduce the system, the solution of a numerical integration may be constrained to remain on the integral surfaces by a method that applies corrections to the solution at each integration step. The corrections are determined by using linearized forms of the integrals in a least-squares procedure.The results of an application of the method to numerical integrations of a gravitational system of 25-bodies are given. It is shown that by using the method to satisfy exactly the integrals of energy, angular momentum, and center of mass, a solution is obtained that is more accurate while using less time of calculation than if the integrals are not satisfied exactly. The relative accuracy is ascertained by forward and backward integrations of both the corrected and uncorrected solutions and by comparison with more accurate integrations using reduced step-sizes.

Development of a Numerical Method for the Calculation of Power Absorption by Arrays of Similar Arbitrarily Shaped Bodies in a Seaway

1982 ◽  
Vol 26 (01) ◽  
pp. 38-44
Author(s):  
James H. Duncan ◽  
Clinton E. Brown
Keyword(s):  
Wave Energy ◽  
Degrees Of Freedom ◽  
Linear Array ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Hydrodynamic Theory ◽  
Optimal Solutions ◽  
Power Absorption ◽  
Six Degrees Of Freedom ◽  
First Order

A computational procedure is developed using first-order hydrodynamic theory to predict the motions and power absorption from arrays of similar three-dimensional buoys. The buoy shape and the number and placement of the buoys may be arbitrarily selected. The program provides for waves of selected frequency and direction or combinations thereof by simple superposition; thus, the effects on energy absorption of wave energy spectral distributions or short-crestedness can be analyzed. The computer model has been validated by comparison of its results with published analytically derived power optimal solutions for five buoys in a linear array. The program provides the power output of each buoy in the array with the associated motions in six degrees of freedom. The limited number of cases studied has provided the interesting result that identical buoys in an array tend to absorb wave energy at rates close to those of optimized systems for which buoy amplitude and phasing would have to be controlled.

scholarly journals The Limits of Effective Degrees of Freedom in UCA based Orbital Angular Momentum Multiplexed Communications

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Zhipeng Li ◽  
Fengzhong Qu ◽  
Yan Wei ◽  
Guowei Yang ◽  
Wen Xu ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Degrees Of Freedom

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Comparison between Analytical and Vectorial Methods of the Synthesis of Equations of Motion

1983 ◽  
Vol 197 (4) ◽  
pp. 265-274
Author(s):  
Z J Goraj
Keyword(s):  
Angular Momentum ◽  
Analytical Method ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discrete Systems ◽  
Momentum Equation ◽  
Lagrange Equations ◽  
Weak Points ◽  
Complicated Geometry ◽  
Boltzmann Hamel Equations

In this paper the advantages and weak points of the analytical and vectorial methods of the derivation of equations of motion for discrete systems are considered. The analytical method is discussed especially with respect to Boltzmann-Hamel equations, as generalized Lagrange equations. The vectorial method is analysed with respect to the momentum equation and to the generalized angular momentum equation about an arbitrary reference point, moving in an arbitrary manner. It is concluded that, for the systems with complicated geometry of motion and a large number of degrees of freedom, the vectorial method can be more effective than the analytical method. The combination of the analytical and vectorial methods helps to verify the equations of motion and to avoid errors, especially in the case of systems with rather complicated geometry.

scholarly journals Effects of the Coupling between the Orbital Angular Momentum and the Temporal Degrees of Freedom in the Most Intense Ring of Ultrafast Vortices

2020 ◽  
Vol 10 (6) ◽  
pp. 1957 ◽  
Author(s):  
Miguel A. Porras
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Pulse Energy ◽  
Topological Charge ◽  
Degrees Of Freedom ◽  
Maximum Energy ◽  
Laser Source ◽  
Source Spectrum ◽  
Vortex Center ◽  
Peak Intensity

It has recently been shown that the temporal and the orbital angular momentum (OAM) degrees of freedom in ultrafast (few-cycle) vortices are coupled. This coupling manifests itself with different effects in different parts of the vortex, as has been shown for the ring surrounding the vortex where the pulse energy is maximum, and also in the immediate vicinity of the vortex center. However, in many applications, the ring of maximum energy is not of primary interest, but the one where the peak intensity of the pulse is maximum, which is particularly true in nonlinear optics applications such as experiments with ultrafast vortices that excite high harmonics and attosecond pulses that also carry OAM. In this paper, the effects of the OAM-temporal coupling on the ring of maximum pulse peak intensity, which do not always coincide with the ring of maximum pulse energy, are described. We find that there is an upper limit to the magnitude of the topological charge that an ultrafast vortex with a prescribed pulse shape in its most intense ring can carry, and vice versa, a lower limit to the pulse duration in the most intense ring for a given magnitude of the topological charge. These limits imply that, with a given laser source spectrum, the duration of the synthesized ultrafast vortex increases with the magnitude of the topological charge. Explicit analytical expressions are given for the ultrafast vortices that contain these OAM-temporal couplings effects, which may be of interest in various applications, in particular in the study of their propagation and interaction with matter.

Interaction-free generation of orbital angular momentum entanglement

2016 ◽  
Vol 30 (05) ◽  
pp. 1650006
Author(s):  
Yuanyuan Chen ◽  
Dong Jiang ◽  
Xuemei Gu ◽  
Ling Xie ◽  
Lijun Chen
Keyword(s):  
Angular Momentum ◽  
Numerical Analysis ◽  
Orbital Angular Momentum ◽  
Degrees Of Freedom ◽  
Quantum Communication ◽  
Superposition State ◽  
Multiple Degrees Of Freedom ◽  
Free Generation ◽  
Infinite Range ◽  
Interaction Free Measurement

Due to the infinite range of possibly achievable degrees of freedom, orbital angular momentum (OAM) can tremendously increase the capacity of communication system. Here, we propose a scheme to generate OAM entanglement by using interaction-free measurement (IFM). As the superposition state of the quantum absorption object is not changed after IFM, our scheme can be extended to multiparty easily. The numerical analysis results show that the fidelity of generated OAM entanglement can be arbitrarily close to unity. Besides, the implementation issues are also discussed to evaluate the feasibility in experiment. This OAM entanglement with multiple degrees of freedom will play a key role in distributed entanglement computing and efficient quantum communication.

Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers

Science ◽  
2013 ◽  
Vol 340 (6140) ◽  
pp. 1545-1548 ◽  
Author(s):  
Nenad Bozinovic ◽  
Yang Yue ◽  
Yongxiong Ren ◽  
Moshe Tur ◽  
Poul Kristensen ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Optical Fiber ◽  
Orbital Angular Momentum ◽  
Degrees Of Freedom ◽  
Nonlinear Effects ◽  
Data Traffic ◽  
Additional Degree ◽  
Mode Division Multiplexing ◽  
Spatial Modes ◽  
Momentum Mode

Internet data traffic capacity is rapidly reaching limits imposed by optical fiber nonlinear effects. Having almost exhausted available degrees of freedom to orthogonally multiplex data, the possibility is now being explored of using spatial modes of fibers to enhance data capacity. We demonstrate the viability of using the orbital angular momentum (OAM) of light to create orthogonal, spatially distinct streams of data-transmitting channels that are multiplexed in a single fiber. Over 1.1 kilometers of a specially designed optical fiber that minimizes mode coupling, we achieved 400-gigabits-per-second data transmission using four angular momentum modes at a single wavelength, and 1.6 terabits per second using two OAM modes over 10 wavelengths. These demonstrations suggest that OAM could provide an additional degree of freedom for data multiplexing in future fiber networks.

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