Non-Lorentzian Shape of the Depolarized Rayleigh Line and the Correlation Function of the Tensor Polarization

1973 ◽  
Vol 28 (9) ◽  
pp. 1385-1388
Author(s):  
S. Hess ◽  
H. Vestner
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Rayleigh Line ◽  
Tensor Polarization ◽  
Pressure Broadening ◽  
Exponential Functions ◽  
Linear Molecules ◽  
Lorentzian Shape

The correlation function of the tensor polarization relevant for the depolarized Rayleigh line of a gas of rotating linear molecules is calculated for the pressure broadening regime. Point of depar­ture is the Waldmann-Snider equation for the distribution function of the gas. Due to the collisional coupling between the tensor polarization and other moments of the distribution function the cor­relation function turns out to be a sum of exponential functions. Consequently the depolarized Rayleigh line has a non-Lorentzian shape.

The pressure broadening of the depolarized Rayleigh line in pure gases of linear molecules

Physica ◽  
1974 ◽  
Vol 75 (3) ◽  
pp. 515-547 ◽  
Author(s):  
R.A.J. Keijser ◽  
K.D. Van Den Hout ◽  
M. De Groot ◽  
H.F.P. Knaap
Keyword(s):  
Rayleigh Line ◽  
Pressure Broadening ◽  
Linear Molecules

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

2012 ◽  
Vol 26 (23) ◽  
pp. 1250151 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Probability Distribution Function ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Exponential Functions ◽  
Multiple Characteristic ◽  
Sum Of Products

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

ON THE TWO-POINT CORRELATION FUNCTION FOR DISPERSIONS OF NONOVERLAPPING SPHERES

1998 ◽  
Vol 08 (02) ◽  
pp. 359-377 ◽  
Author(s):  
KONSTANTIN Z. MARKOV ◽  
JOHN R. WILLIS
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Characteristic Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Integral Formula ◽  
Probability Densities ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Point Level

Random dispersions of spheres are useful and appropriate models for a wide class of particulate random materials. They can be described in two equivalent and alternative ways — either by the multipoint moments of the characteristic function of the region, occupied by the spheres, or by the probability densities of the spheres' centers. On the "two-point" level, a simple and convenient integral formula is derived which interconnects the radial distribution function of the spheres with the two-point correlation of the said characteristic function. As one of the possible applications of the formula, the behavior of the correlation function near the origin is studied in more detail and related to the behavior of the radial distribution function at the "touching" separation of the spheres.

The pressure broadening of the depolarized rayleigh line in N2-noble-gas mixtures

Physica ◽  
1974 ◽  
Vol 76 (3) ◽  
pp. 577-584 ◽  
Author(s):  
R.A.J. Keijser ◽  
K.D. Van Den Hout ◽  
H.F.P. Knaap
Keyword(s):  
Noble Gas ◽  
Gas Mixtures ◽  
Rayleigh Line ◽  
Pressure Broadening

Notizen: Kinetic Theory for the Broadening of the Depolarized Rayleigh Line

1969 ◽  
Vol 24 (11) ◽  
pp. 1852-1853
Author(s):  
Siegfried Hess
Keyword(s):  
Kinetic Theory ◽  
Theory Approach ◽  
Rayleigh Line ◽  
Linear Molecules ◽  
Rayleigh Light

Abstract Collisional and diffusional broadening of the depolarized Rayleigh light scattered by a gas of linear molecules are studied by a kinetic theory approach based on the Waldmann-Snider equation.

scholarly journals SPATIAL STATISTICS FOR SIMULATED PACKINGS OF SPHERES

2011 ◽  
Vol 20 (3) ◽  
pp. 203 ◽  
Author(s):  
Alexander Bezrukov ◽  
Dietrich Stoyan ◽  
Monika Bargieł
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Spatial Statistics ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Simulation Methods ◽  
Coordination Numbers ◽  
Contact Distribution ◽  
Contact Distribution Function ◽  
Random Packings

This paper reports on spatial-statistical analyses for simulated random packings of spheres with random diameters. The simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm. The sphere diameters are taken as constant or following a bimodal or lognormal distribution. Standard characteristics of spatial statistics are used to describe these packings statistically, namely volume fraction, pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretic union of all spheres. Furthermore, the coordination numbers are analysed.

scholarly journals Spatial patterns of primary seed dispersal and adult tree distributions: Genipa americana dispersed by Cebus capucinus – CORRIGENDUM

2015 ◽  
Vol 32 (1) ◽  
pp. 88-88
Author(s):  
Kim Valenta ◽  
Mariah E. Hopkins ◽  
Melanie Meeking ◽  
Colin A. Chapman ◽  
Linda M. Fedigan
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Nearest Neighbour ◽  
Study Region ◽  
Adult Tree ◽  
The Mean ◽  
K Function ◽  
Typical Point

Within the second paragraph of page 494 incorrect language was used to characterize the summary characteristics used. Sentences 3–11 of this paragraph should have read:Second, we calculated three univariate summary characteristics: the nearest neighbour distribution function D(r), the pair-correlation function g(r) and the K-function K(r). The use of multiple summary characteristics holds increased power to characterize variation in spatial patterns (Wiegand et al. 2013). The univariate nearest neighbour distribution function D(r) can be interpreted as the probability that the typical adult tree has its nearest neighbouring adult tree within radius r (or alternatively, the probability that the typical defecation has its nearest neighbouring defecation within radius r). The univariate pair-correlation function g(r) is a non-cumulative normalized neighbourhood density function that gives the expected number of points within rings of radius r and width w centred on a typical point, divided by the mean density of points λ in the study region (Wiegand et al. 2009). We applied g(r) to trees and defecation point patterns separately, using a ring width of 10 m. The K-function K(r) provides a cumulative counterpart to the non-cumulative pair-correlation function g(r) by analysing dispersion and aggregation up to distance r rather than at distance r (Weigand & Moloney 2004). The K-function can be defined as the number of expected points (i.e. either trees or defecations) within circles of radius r extending from a typical point, divided by the mean density of points λ within the study region. Here, we apply the square root transformation L(r) to the K-function to remove scale dependence and stabilize the variance: $L( r ) = \scriptstyle\sqrt {\frac{{K( r )}}{\pi }} - r$ (Besag 1977, Wiegand & Moloney 2014).

Restitution conditions of the parent cubic texture from the inherited hexagonal texture in the β–α phase transformation

1999 ◽  
Vol 32 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Michel Humbert ◽  
Nathalie Gey
Keyword(s):  
Phase Transformation ◽  
Distribution Function ◽  
Correlation Function ◽  
Room Temperature ◽  
Hexagonal Phase ◽  
Parent Phase ◽  
Orientation Distribution ◽  
Variant Selection ◽  
Qualitative Information ◽  
Α Phase

Different factors calculated from theCcoefficients of the inherited orientation distribution function (ODF) allow us to check the importance of the variant selection. When no variant selection or a slight variant selection occurs by the cubic-to-hexagonal phase transformation, it is possible to calculate the ODF of the cubic parent phase present at high temperature from the ODF of the inherited hexagonal phase at room temperature. When a stronger variant selection occurs, qualitative information about the parent ODF can be obtained by using a specific correlation function, which we have named R(g).

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