Higher Order Perturbation Analysis of Stochastic Thermal Systems With Correlated Uncertain Properties

2000 ◽  
Vol 123 (2) ◽  
pp. 390-398 ◽  
Author(s):  
A. F. Emery
Keyword(s):  
Standard Deviation ◽  
Boundary Conditions ◽  
Perturbation Analysis ◽  
Perturbation Methods ◽  
Higher Order ◽  
Order Perturbation ◽  
Thermal Systems ◽  
The Mean ◽  
Almost All ◽  
Correlated Parameters

How the behavior of thermal systems depends on uncertainties in properties and boundary conditions is an important aspect of simulation. This dependence is usually judged by the statistics of the response, i.e., the mean response and its standard deviation which are often determined by perturbation methods, ranging from 1st to 3rd order. The aim of this paper is to be a tutorial for those interested in estimating uncertainties by summarizing the author’s experience in using higher order perturbation analysis for thermal problems, detailing the underlying assumptions, and presenting several examples. Problems involving correlated parameters, which occur in almost all thermal experiments, are also treated. It is shown that the scale of correlation has a strong effect upon the statistics of the response and that such correlation should not be ignored. It is recommended that the 1st order estimates of the standard deviation and 2nd order estimates of the mean response be used when characterizing thermal systems with random variables, regardless of the degree of correlation.

scholarly journals Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation

1996 ◽  
Vol 54 (3) ◽  
pp. 2976-2981 ◽  
Author(s):  
R. A. Kraenkel ◽  
M. A. Manna ◽  
V. Merle ◽  
J. C. Montero ◽  
J. G. Pereira
Keyword(s):  
Perturbation Analysis ◽  
Higher Order ◽  
Order Perturbation ◽  
Multiple Time ◽  
Long Wavelength

A second- and higher-order perturbation analysis of two-body trajectories

AIAA Journal ◽  
1971 ◽  
Vol 9 (4) ◽  
pp. 589-593 ◽  
Author(s):  
T. T. SOONG ◽  
N. A. PAUL
Keyword(s):  
Perturbation Analysis ◽  
Higher Order ◽  
Order Perturbation

Higher Order Perturbation Solutions for Electrochemical Machining

1976 ◽  
Vol 4 (2) ◽  
pp. 90-96 ◽  
Author(s):  
Henning Rasmussen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Electrochemical Machining ◽  
Higher Order ◽  
Order Perturbation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Initial Distance ◽  
Perturbation Solutions

The calculation of higher order perturbation solutions is discussed for electrochemical machining and is illustrated for a particular two-dimensional problem, which consists of a plane cathode and an anode whose initial distance from the cathode varies spatially in a sinusoidal manner. Terms up to fourth order are obtained as the solutions to six ordinary coupled differential equations which are solved numerically. Also shown is how the effects of changes in the boundary conditions due to overpotential can be included.

scholarly journals Carbon Cycle Uncertainty in REgional Carbon Cycle Assessment and Processes (RECCAP)

2012 ◽  
Vol 9 (8) ◽  
pp. 2889-2904 ◽  
Author(s):  
I. G. Enting ◽  
P. J. Rayner ◽  
P. Ciais
Keyword(s):  
Standard Deviation ◽  
Carbon Cycle ◽  
Probability Distributions ◽  
Location Parameter ◽  
Carbon Budgets ◽  
Space And Time ◽  
Full Form ◽  
The Mean ◽  
Almost All ◽  
The Impact

Abstract. Characterisation of estimates of regional carbon budgets and processes is inherently a statistical task. In full form this means that almost all quantities used or produced are realizations or instances of probability distributions. We usually compress the description of these distributions by using some kind of location parameter (e.g. the mean) and some measure of spread or uncertainty (e.g. the standard deviation). Characterising and calculating these uncertainties, and their structure in space and time, is as important as the location parameter, but uncertainties are both hard to calculate and hard to interpret. In this paper we describe the various classes of uncertainty that arise in a process like RECCAP and describe how they interact in formal estimation procedures. We also point out the impact these uncertainties will have on the various RECCAP synthesis activities.

scholarly journals RECCAP uncertainty

2012 ◽  
Vol 9 (2) ◽  
pp. 1829-1868 ◽  
Author(s):  
I. G. Enting ◽  
P. J. Rayner ◽  
P. Ciais
Keyword(s):  
Standard Deviation ◽  
Probability Distributions ◽  
Location Parameter ◽  
Carbon Budgets ◽  
Space And Time ◽  
Estimation Procedures ◽  
Full Form ◽  
The Mean ◽  
Almost All ◽  
The Impact

Abstract. Characterisation of regional carbon budgets and processes (the overall task addressed in this series of articles) is inherently a statistical task. In full form this means that almost all quantities used or produced are realizations or instances of probability distributions. We usually compress the description of these distributions by using some kind of location parameter (e.g. the mean) and some measure of spread or uncertainty (e.g. the standard deviation). Characterising and calculating these uncertainties, and their structure in space and time, is as important as the location parameter but uncertainties are both harder to calculate and harder to interpret. In this paper we describe the various classes of uncertainty that arise in a process like RECCAP and describe how they interact in formal estimation procedures. We also point out the impact these uncertainties will have on the various RECCAP synthesis activities.

scholarly journals Metallicity-Dependent Transformations for Red Giants with Synthetic Colours of UBV and ugr

2013 ◽  
Vol 30 ◽  
Author(s):  
S. Karaali ◽  
E. Yaz Gökçe
Keyword(s):  
Standard Deviation ◽  
Synthetic Data ◽  
Red Giants ◽  
The Mean ◽  
Almost All

AbstractWe present metallicity-dependent transformation equations between UBV and SDSS ugr colours for red giants with synthetic data. The ranges of the colours used for the transformations are 0.400 ≤ (B − V)0 ≤ 1.460, −0.085 ≤ (U − B)0 ≤ 1.868, 0.291 ≤ (g − r)0 ≤ 1.326, and 1.030 ≤ (u − g)0 ≤ 3.316 mag, and cover almost all the observational colours of red giants. We applied the transformation equations to six clusters with different metallicities and compared the resulting (u − g)0 colours with those estimated by the calibration of the fiducial sequences of the clusters. The mean and standard deviation of the residuals for all clusters are <Δ(u − g)0> = −0.01 and σ(u − g)0 = 0.07 mag, respectively. We showed that interstellar reddening plays an important role on the derived colours. The transformations can be applied to clusters as well as to field stars. They can be used to extend the colour range of the red giants in the clusters which are restricted due to the saturation of the SDSS data.

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