Two‐dimensional product probability distributions from trajectory calculations for the H+H2 reaction

1991 ◽  
Vol 94 (9) ◽  
pp. 5980-5984 ◽  
Author(s):  
Donald E. Riederer ◽  
Andrew D. Jorgensen ◽  
Eric A. Gislason
Keyword(s):  
Probability Distributions ◽  
Two Dimensional ◽  
Trajectory Calculations

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (1) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

scholarly journals Improved Particle Trajectory Calculations Through Turbomachinery Affected by Coal Ash Particles

1981 ◽  
Author(s):  
B. Beecher ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Coal Ash ◽  
Two Dimensional ◽  
Flow Properties ◽  
Trajectory Calculations ◽  
Blade Thickness ◽  
Spline Fitting ◽  
Numerical Grid

Trajectories of small coal ash particles encountered in coal-fired gas turbines are calculated with an improved computer analysis currently under development. The analysis uses an improved numerical grid and mathematical spline-fitting techniques to account for three-dimensional gradients in the flow field and blade geometry. The greater accuracy thus achieved in flow field definition improves the trajectory calculations over previous two-dimensional models by allowing the small particles to react to radial variations in the flow properties. A greater accuracy thus achieved in the geometry definition permits particle rebounding in a direction perpendicular to the blade and flow path surfaces rather than in a two-dimensional plane. The improved method also accounts for radial variations in airfoil chord, stagger, and blade thickness when computing particle impact at a blade location.

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (01) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Improved Particle Trajectory Calculations Through Turbomachinery Affected by Coal Ash Particles

1982 ◽  
Vol 104 (1) ◽  
pp. 64-68 ◽  
Author(s):  
B. Beacher ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Coal Ash ◽  
Two Dimensional ◽  
Flow Properties ◽  
Trajectory Calculations ◽  
Blade Thickness ◽  
Spline Fitting ◽  
Numerical Grid

Trajectories of small coal ash particles encountered in coal-fired gas turbines are calculated with an improved computer analysis currently under development. The analysis uses an improved numerical grid and mathematical spline-fitting techniques to account for three-dimensional gradients in the flow field and blade geometry. The greater accuracy thus achieved in flow field definition improves the trajectory calculations over previous two-dimensional models by allowing the small particles to react to radial variations in the flow properties. A greater accuracy thus achieved in the geometry definition permits particle rebounding in a plane perpendicular to the blade and flow path surfaces rather than in a two-dimensional plane. The improved method also accounts for radial variations in airfoil chord, stagger, and blade thickness when computing particle impact at a blade location.

scholarly journals Basins of Convergence in the Circular Sitnikov Four-Body Problem with Nonspherical Primaries

2018 ◽  
Vol 28 (05) ◽  
pp. 1830016 ◽  
Author(s):  
Euaggelos E. Zotos ◽  
Satyendra Kumar Satya ◽  
Rajiv Aggarwal ◽  
Sanam Suraj
Keyword(s):  
Body Problem ◽  
Initial Conditions ◽  
Probability Distributions ◽  
Equilibrium Points ◽  
Two Dimensional ◽  
Optimal Method ◽  
Four Body Problem ◽  
Newton Raphson ◽  
Number Of Iterations

The Newton–Raphson basins of convergence, related to the equilibrium points, in the Sitnikov four-body problem with nonspherical primaries are numerically investigated. We monitor the parametric evolution of the positions of the roots, as a function of the oblateness coefficient. The classical Newton–Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the oblateness coefficient affects the geometry as well as the basin entropy of the convergence regions. The convergence areas are related with the required number of iterations and also with the corresponding probability distributions.

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