An Efficient Numerical Method for Calculating the Statistical Distribution of Combined First-Order and Wave-Drift Response

1992 ◽  
Vol 114 (3) ◽  
pp. 195-204 ◽  
Author(s):  
A. Naess ◽  
J. M. Johnsen
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Numerical Method ◽  
Probability Distribution Function ◽  
Numerical Procedure ◽  
Offshore Structures ◽  
Numerical Calculations ◽  
Hydrodynamic Loads ◽  
First Order ◽  
Wave Drift

The paper describes an efficient and accurate numerical procedure for calculating the probability distribution function of combined first-order and slowly varying, second-order hydrodynamic loads and response of compliant offshore structures. No approximations are made except those inherent in the numerical calculations. The method does not require extensive computer capacity; in fact it can be implemented on any standard PC. Several example calculations serve to illustrate the method, and its accuracy is demonstrated by comparison with cases where exact analytical results are available. The accuracy of previously proposed approximations are also discussed.

Remark on the energy determination of high-energy nucleons by means of the absorption calorimeter

1968 ◽  
Vol 46 (10) ◽  
pp. S1107-S1111 ◽  
Author(s):  
A. Somogyi ◽  
G. Válas ◽  
A. Varga
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Analytical Method ◽  
Probability Distribution Function ◽  
High Energy ◽  
Primary Energy ◽  
Numerical Calculations ◽  
Energy Determination ◽  
Ionization Calorimeter

The sources of error in energy determinations carried out by means of an ionization calorimeter are well known as are the values of the relevant corrections. Very little if anything is known, however, of the statistical uncertainties of these corrections. An analytical method has been worked out in order to determine the probability that a certain fraction of the primary energy leaves a calorimeter of a given thickness and thus escapes detection. The method makes due allowance for the fluctuation of the inelasticity coefficient. Numerical calculations have been carried out assuming various forms for the probability distribution function of the inelasticity coefficient, and the results of the calculations are given for various calorimeter thicknesses.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

Audio feature extraction using probability distribution function

2015 ◽  
Author(s):  
Suhaib A. ◽  
Khairunizam Wan ◽  
Azri A. Aziz ◽  
D. Hazry ◽  
Zuradzman M. Razlan ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Audio Feature ◽  
Audio Feature Extraction
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