Monte Carlo Approach to Generating the Probability-Distribution Function of a Classical Harmonic Oscillator

1996 ◽  
Vol 73 (8) ◽  
pp. 724
Author(s):  
Robert A. Craig ◽  
Stephen W. Bigger
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Probability Distribution ◽  
Harmonic Oscillator ◽  
Probability Distribution Function ◽  
Monte Carlo Approach

scholarly journals Convergence of estimated optimal inventory levels in models with probabilistic demands

2003 ◽  
Vol 13 (2) ◽  
pp. 217-227
Author(s):  
Carlos Bouza
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Search Algorithms ◽  
Inventory Level ◽  
Density Functions ◽  
Monte Carlo Experiments ◽  
Unknown Probability ◽  
Optimal Inventory Level

The behavior of estimations of the optimal inventory level is analyzed. Two models are studied. The demands follow unknown probability distribution function. The included density functions are estimated and a plug-in rule is suggested for computing estimates of the optimal levels. Two search algorithms are proposed and compared using Monte Carlo experiments. .

scholarly journals Modified guidance laws to escape microbursts with turbulence

2002 ◽  
Vol 8 (1) ◽  
pp. 43-67 ◽  
Author(s):  
Atilla Dogan ◽  
Pierre T. Kabamba
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Probability Distribution ◽  
Monte Carlo Simulations ◽  
Probability Distribution Function ◽  
Random Variable ◽  
Guidance Strategies ◽  
Low Altitude ◽  
Guidance Laws

This paper introduces Modified Altitude- and Dive-Guidance laws for escaping a microburst with turbulence. The goal is to develop a procedure to estimate the highest altitude at which an aircraft can fly through a microburst without running into stall. First, a new metric is constructed that quantifies the aircraft upward force capability in a microburst encounter. In the absence of turbulence, the metric is shown to be a decreasing function of altitude. This suggests that descending to a low altitude may improve safety in the sense that the aircraft will have more upward force capability to maintain its altitude. In the presence of stochastic turbulence, the metric is treated as a random variable and its probability distribution function is analytically approximated as a function of altitude. This approximation allows us to determine the highest safe altitude at which the aircraft may descend, hence avoiding to descend too low. This highest safe altitude is used as the commanded altitude in Modified Altitude- and Dive-Guidance. Monte Carlo simulations show that these Modified Altitude- and Dive-Guidance strategies can decrease the probability of minimum altitude being lower than a given value without significantly increasing the probability of crash.

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.

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