Speed of travelling fronts: Two-dimensional and ballistic dispersal probability 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.

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Probabilistic aspects of the SU(2)-harmonic oscillator

Journal of Applied Probability ◽

10.1017/s0021900200015461 ◽

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.

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Two-Dimensional Discrete Probability Distributions

SIAM Review ◽

10.1137/1016090 ◽

1974 ◽

Vol 16 (4) ◽

pp. 546-546

Author(s):

P. Beckmann

Keyword(s):

Probability Distributions ◽

Two Dimensional ◽

Discrete Probability ◽

Discrete Probability Distributions

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

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418300161 ◽

2018 ◽

Vol 28 (05) ◽

pp. 1830016 ◽

Cited By ~ 6

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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Comparing Evaporative Sources of Terrestrial Precipitation and Their Extremes in MERRA Using Relative Entropy

Journal of Hydrometeorology ◽

10.1175/jhm-d-13-053.1 ◽

2014 ◽

Vol 15 (1) ◽

pp. 102-116 ◽

Cited By ~ 32

Author(s):

Paul A. Dirmeyer ◽

Jiangfeng Wei ◽

Michael G. Bosilovich ◽

David M. Mocko

Keyword(s):

Relative Entropy ◽

Moisture Transport ◽

Probability Distributions ◽

Back Trajectory ◽

Two Dimensional ◽

Monthly Data ◽

Atmospheric Rivers ◽

Time Period ◽

Key Factor ◽

Modern Era

Abstract A quasi-isentropic, back-trajectory scheme is applied to output from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and a land-only replay with corrected precipitation to estimate surface evaporative sources of moisture supplying precipitation over every ice-free land location for the period 1979–2005. The evaporative source patterns for any location and time period are effectively two-dimensional probability distributions. As such, the evaporative sources for extreme situations like droughts or wet intervals can be compared to the corresponding climatological distributions using the method of relative entropy. Significant differences are found to be common and widespread for droughts, but not wet periods, when monthly data are examined. At pentad temporal resolution, which is more able to isolate floods and situations of atmospheric rivers, values of relative entropy over North America are typically 50%–400% larger than at monthly time scales. Significant differences suggest that moisture transport may be a key factor in precipitation extremes. Where evaporative sources do not change significantly, it implies other local causes may underlie the extreme events.

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