scholarly journals THERMODYNAMIC q-DISTRIBUTIONS THAT AREN’T

1994 ◽  
Vol 09 (01) ◽  
pp. 1-9 ◽  
Author(s):  
STAMATIS VOKOS ◽  
COSMAS ZACHOS
Keyword(s):  
Energy Distribution ◽  
Critical Frequency ◽  
Black Body ◽  
Distribution Functions ◽  
Maximum Temperature ◽  
Cavity Size ◽  
Free Distribution ◽  
Planck Distribution ◽  
The Subject ◽  
Body Energy

Bosonic q-oscillators commute with themselves and so their free distribution is Planckian. In a cavity, their emission and absorption rates may grow or shrink – and even diverge – but they nevertheless balance to yield the Planck distribution via Einstein’s equilibrium method, (a careless application of which might produce spurious q-dependent distribution functions). This drives home the point that the black-body energy distribution is not a handle for distinguishing q-excitations from plain oscillators. A maximum cavity size is suggested by the inverse critical frequency of such emission/absorption rates at a given temperature, or a maximum temperature at a given frequency. To remedy fragmentation of opinion on the subject, we provide some discussion, context, and references.

scholarly journals Influence of Microlensing on Spectral Anomalies of the Lensed Objects

2011 ◽  
Vol 20 (3) ◽  
Author(s):  
S. Simić ◽  
L. Č. Popović ◽  
P. Jovanović
Keyword(s):  
Energy Distribution ◽  
Spectral Energy Distribution ◽  
Angular Size ◽  
Black Body ◽  
Spectral Energy

AbstractHere we consider the influence of microlensing on the spectrum of a lensed object with the angular size 5 μas accepting that the composite emission of this object originates from three different regions arranged around its center. We assume that the lensed object has three concentric regions with a black-body emission; the temperatures of these regions are 10 000 K, 7500 K and 5000 K. We investigate how the integral spectral energy distribution (SED) of such stratified source changes due to microlensing by a group of solarmass stars. We find that the SED and flux ratios in the photometric B, V and R passbands show considerable changes during a microlens event. This indicates that the flux anomaly observed in some lensed quasars may be caused by microlensing of a stratified object.

Beyond the heuristic approach to Kolmogorov-Smirnov theorems

1982 ◽  
Vol 19 (A) ◽  
pp. 359-365 ◽  
Author(s):  
David Pollard
Keyword(s):  
Weak Convergence ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Heuristic Approach ◽  
Convergence Theory ◽  
Simple Method ◽  
Starting Point ◽  
Kolmogorov Smirnov ◽  
The Subject

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.

Electron Energy Distribution Functions of Hydrogen: The Effect of Superelastic Vibrational Collisions and of the Dissociation Process

1979 ◽  
Vol 34 (5) ◽  
pp. 585-593 ◽  
Author(s):  
M. Capitelli ◽  
M. Dilonardo
Keyword(s):  
Boltzmann Equation ◽  
Energy Distribution ◽  
Electron Energy ◽  
Distribution Functions ◽  
Electron Energy Distribution ◽  
Hydrogen Atoms ◽  
Dissociation Process ◽  
Excitation Rate ◽  
The Boltzmann Equation ◽  
Energy Distribution Functions

Abstract Electron energy distribution functions (EDF) of molecular H2 have been calculated by numerically solving the Boltzmann equation including all the inelastic processes with the addition of superelastic vibrational collisions and of the hydrogen atoms coming from the dissociation process. The population densities of the vibrational levels have been obtained both by assuming a Boltz-mann population at a vibrational temperature different from the translational one and by solving a system of vibrational master equations coupled to the Boltzmann equation. The results, which have been compared with those corresponding to a vibrationally cold molecular gas, show that the inclusion of superelastic collisions and of the parent atoms affects the EDF tails without strongly modifying the EDF bulk. As a consequence the quantities affected by the EDF bulk, such as average and characteristic energies, drift velocity, 0-1 vibrational excitation rate are not too much affected by the inclusion of superelastic vibrational collisions and of parent atoms, while a strong influence is observed on the dissociation and ionization rate coefficients which depend on the EDF tail. Calculated dissociation rates, obtained by EDF's which take into account both the presence of vibrationally excited molecules and hydrogen atoms, are in satisfactory agreement with experimental results.

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