scholarly journals Two-dimensional and three-dimensional probability density functions of underwater noise near the port of Vladivostok

2015 ◽  
Author(s):  
Sergey Gorovoy
Keyword(s):  
Probability Density ◽  
Three Dimensional ◽  
Probability Density Functions ◽  
Density Functions ◽  
Two Dimensional ◽  
Underwater Noise ◽  
Port Of Vladivostok

Maximum Entropy Methods in the Mechanics of Quasi-Static Deformation of Granular Materials

2002 ◽  
Author(s):  
N. P. Kruyt ◽  
L. Rothenburg
Keyword(s):  
Probability Density ◽  
Maximum Entropy ◽  
Granular Materials ◽  
Probability Density Functions ◽  
Contact Forces ◽  
Static Deformation ◽  
Density Functions ◽  
Two Dimensional ◽  
Entropy Methods ◽  
Theoretical Predictions

In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of granular materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of granular materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for granular materials that consist of semirigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.

scholarly journals Joint Delay Doppler Probability Density Functions for Air-to-Air Channels

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Michael Walter ◽  
Dmitriy Shutin ◽  
Uwe-Carsten Fiebig
Keyword(s):  
Probability Density ◽  
Channel Model ◽  
Three Dimensional ◽  
Doppler Frequency ◽  
Probability Density Functions ◽  
Density Functions ◽  
Wide Sense ◽  
Channel Measurements ◽  
Vector Calculus ◽  
Air Channels

Recent channel measurements indicate that the wide sense stationary uncorrelated scattering assumption is not valid for air-to-air channels. Therefore, purely stochastic channel models cannot be used. In order to cope with the nonstationarity a geometric component is included. In this paper we extend a previously presented two-dimensional geometric stochastic model originally developed for vehicle-to-vehicle communication to a three-dimensional air-to-air channel model. Novel joint time-variant delay Doppler probability density functions are presented. The probability density functions are derived by using vector calculus and parametric equations of the delay ellipses. This allows us to obtain closed form mathematical expressions for the probability density functions, which can then be calculated for any delay and Doppler frequency at arbitrary times numerically.

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

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