scholarly journals Retrieving Storm Electric Fields from Aircraft Field Mill Data. Part II: Applications

2006 ◽  
Vol 23 (10) ◽  
pp. 1303-1322 ◽  
Author(s):  
W. J. Koshak ◽  
D. M. Mach ◽  
H. J. Christian ◽  
M. F. Stewart ◽  
M. G. Bateman
Keyword(s):  
Electric Fields ◽  
Computer Simulations ◽  
Lagrange Multiplier ◽  
Measurement Errors ◽  
Absolute Calibration ◽  
Fair Weather ◽  
Field Function ◽  
Side Constraint ◽  
Side Constraints ◽  
The Mean

Abstract The Lagrange multiplier theory developed in Part I of this study is applied to complete a relative calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the Lagrange multiplier method performs well in computer simulations. For mill measurement errors of 1 V m−1 and a 5 V m−1 error in the mean fair-weather field function, the 3D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair-weather field was also tested using computer simulations. For mill measurement errors of 1 V m−1, the method retrieves the 3D storm field to within an error of about 8% if the fair-weather field estimate is typically within 1 V m−1 of the true fair-weather field. Using this type of side constraint and data from fair-weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. Absolute calibration was completed using the “pitch down method” developed in Part I, and conventional analyses. The resulting calibration matrices were then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably in many respects with results derived from earlier (iterative) techniques of calibration.

scholarly journals Retrieving Storm Electric Fields from Aircraft Field Mill Data. Part I: Theory

2006 ◽  
Vol 23 (10) ◽  
pp. 1289-1302 ◽  
Author(s):  
W. J. Koshak
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
High Voltage ◽  
Lagrange Multipliers ◽  
Optimization Problem ◽  
Absolute Calibration ◽  
Retrieval Process ◽  
Physical Constraints ◽  
Side Constraints ◽  
Derivatives Of

Abstract It is shown that the problem of retrieving storm electric fields from an aircraft instrumented with several electric field mill sensors can be expressed in terms of a standard Lagrange multiplier optimization problem. The method naturally removes aircraft charge from the retrieval process without having to use a high-voltage stinger and linearly combined mill data values. It allows a variety of user-supplied physical constraints (the so-called side constraints in the theory of Lagrange multipliers) and also helps improve absolute calibration. Additionally, this paper introduces an alternate way of performing the absolute calibration of an aircraft that has some benefits over conventional analyses. It is accomplished by using the time derivatives of mill and pitch data for a pitch down maneuver performed at high (>1 km) altitude. In Part II of this study, the above methods are tested and then applied to complete a full calibration of a Citation aircraft.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals On tho proportions of the prevailing winds, the mean temperature, and depth of rain in the climate of London, computed through a cycle of Eighteen Years, or periods of the Moon’s declination

1843 ◽  
Vol 4 ◽  
pp. 300-300
Keyword(s):  
The Moon ◽  
Fair Weather ◽  
North West ◽  
West Wind ◽  
North East ◽  
East Wind ◽  
The North ◽  
The Common ◽  
The Mean ◽  
Solar Influence

In this paper the author investigates the periodical variations of the winds, rain and temperature, corresponding to the conditions of the moon’s declination, in a manner similar to that he has already followed in the case of the barometrical variations, on a period of years extending from 1815 to 1832 inclusive. In each case he gives tables of the average quantities for each week, at the middle of which the moon is in the equator, or else has either attained its maximum north or south declination. He thus finds that a north-east wind is most promoted by the constant solar influence which causes it, when the moon is about the equator, going from north to south; that a south-east wind, in like manner, prevails most when the moon is proceeding to acquire a southern declination ; that winds from the south and west blow more when the moon is in her mean degrees of declination, going either way, than with a full north or south declination ; and that a north-west wind, the common summer and fair weather wind of the climate, affects, in like manner, the mean declination, in either direction, in preference to the north or south, and most when the moon is coming north. He finds the average annual depth of rain, falling in the neighbourhood of London, is 25’17 inches.

scholarly journals The behaviour of electrolytes in mixed solvents. Part I.—The free energies and heat contents of hydrogen chloride in water—Ethyl alcohol solutions

1929 ◽  
Vol 125 (799) ◽  
pp. 694-712 ◽  
Keyword(s):  
Hydrogen Chloride ◽  
Electric Fields ◽  
Mixed Solvents ◽  
Dielectric Constants ◽  
Free Energies ◽  
Dissolved Ions ◽  
Uniform Medium ◽  
The Mean ◽  
Solvent Molecules ◽  
Water Alcohol

Previous studies on the effect of a change of medium on tire properties of dissolved electrolytes have aimed at correlating the behaviour of the electrolyte with the mean physical properties, e. g ., dielectric constants, of the medium. While this approach may be justified in the case of solvents containing molecules of only one kind, it is not sufficient to regard a mixed solvent as a uniform medium affecting the dissolved ions solely through the effect of its dielectric constant on the electric forces between them. For the electric fields of ions exert a differential attraction on molecules possessing different degrees of polarisability and since tire more polarisable molecules must tend to congregate round the ions, the properties of the latter cannot depend solely on tire mean properties of tire medium. Studies on the behaviour of ions in such cases will throw light on the interaction between ions and solvent molecules. The present paper gives tire results of measurements of the free energies and heat contents of hydrogen chloride in water-alcohol solutions, obtained by determining the electromotive forces of cells of the type:— H 2 ( g ) | HCl ( m ), AgCl ( s ) | Ag water-alcohol

MICROFACIES ANALYSIS OF CRETACEOUS SEDIMENTS OF DUKUL FORMATION, YOLA SUB-BASIN, NORTHERN BENUE TROUGH, NIGERIA: PALEO-ENVIRONMENTAL IMPLICATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 310-319
Author(s):  
Babangida M. Sarki Yandoka
Keyword(s):  
Sea Level ◽  
Microfacies Analysis ◽  
Fair Weather ◽  
Environmental Implications ◽  
Benue Trough ◽  
Shallow Marine ◽  
Carbonate Microfacies ◽  
Anoxic Conditions ◽  
The Mean

Carbonate microfacies analysis was conducted on the exposed sediments of Dukul Formation from Yola Sub-basin of the Northern Benue Trough with an objective to reconstruct the paleodepositional environment. The study revealed four (4) major microfacies; oyster wackestone, ostracod oyster wackestone-packestone, bioclastic wackestone and bioclastic packestone microfacies. The microfacies assemblages indicate and affirm that the Dukul Formation sediments were deposited in shallow marine (mid-inner ramp) environment under suboxic to relatively anoxic conditions due to sea-level drop. This is further supported owing to the occurence of corals, brachiopods, bivalves and ostracods immediately below the mean fair-weather wave base (FWWB)

scholarly journals Absolute calibration of the polarisation angle for future CMB B-mode experiments from current and future measurements of the Crab nebula

2020 ◽  
Vol 634 ◽  
pp. A100 ◽  
Author(s):  
J. Aumont ◽  
J. F. Macías-Pérez ◽  
A. Ritacco ◽  
N. Ponthieu ◽  
A. Mangilli
Keyword(s):  
Measurement Errors ◽  
Crab Nebula ◽  
Potential Effect ◽  
Energy Scale ◽  
Absolute Calibration ◽  
Systematic Effect ◽  
Individual Measurement ◽  
Microwave Frequencies ◽  
Mode Spectrum ◽  
The Crab Nebula

A tremendous international effort is currently dedicated to observing the so-called primordial B modes of the cosmic microwave background (CMB) polarisation. If measured, this faint signal, caused by the primordial gravitational wave background, would be evidence of the inflation epoch and quantify its energy scale, providing a rigorous test of fundamental physics far beyond the reach of accelerators. At the unprecedented sensitivity level that the new generation of CMB experiments aims to reach, every uncontrolled instrumental systematic effect will potentially result in an analysis bias that is larger than the much sought-after CMB B-mode signal. The absolute calibration of the polarisation angle is particularly important in this context because any associated error will end up in leakage from the much larger E modes into B modes. The Crab nebula (Tau A), with its bright microwave synchrotron emission, is one of the few objects in the sky that can be used as absolute polarisation calibrators. In this paper we review the currently best constraints on its polarisation angle from 23 to 353 GHz at typical angular scales for CMB observations from WMAP, XPOL, Planck, and NIKA data. These polarisation angle measurements are compatible with a constant angle of −88.26° ±0.27° (assuming that systematic errors are independent between frequencies and that the experiments fully capture the extent of the Crab nebula). We study the uncertainty on this mean angle under different considerations for combinations of the individual measurement errors. For each of the cases, we study the potential effect on the CMB B-mode spectrum and on the recovered r parameter through a likelihood analysis. We find that current constraints on the Crab polarisation angle, assuming it is constant through microwave frequencies, allow us to calibrate experiments with an accuracy enabling the measurement of r ∼ 0.01. On the other hand, even under the most optimistic assumptions, current constraints will lead to an important limitation for the detection of r ∼ 10−3. New realistic measurement of the Crab nebula can change this situation by strengthening the assumption of the consistency across microwave frequencies and reducing the combined error.

scholarly journals Mermin–Wagner fluctuations in 2D amorphous solids

2017 ◽  
Vol 114 (8) ◽  
pp. 1856-1861 ◽  
Author(s):  
Bernd Illing ◽  
Sebastian Fritschi ◽  
Herbert Kaiser ◽  
Christian L. Klix ◽  
Georg Maret ◽  
...  
Keyword(s):  
Computer Simulations ◽  
System Size ◽  
Amorphous Solids ◽  
Two Dimensions ◽  
Density Fluctuations ◽  
Long Wavelength ◽  
Broken Symmetries ◽  
Lindemann Criterion ◽  
The Mean ◽  
2D Crystals

In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016)J Phys Condens Matter28:481001]. It was due to the lack of broken translational symmetry in two dimensions—doubting the existence of 2D crystals—and the first computer simulations foretelling 2D crystals (at least in tiny systems). The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact, but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D in the sense that the mean squared displacement of atoms is not limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals, we disentangle Mermin–Wagner fluctuations from glassy structural relaxations. Furthermore, we demonstrate with computer simulations the logarithmic increase of displacements with system size: Periodicity is not a requirement for Mermin–Wagner fluctuations, which conserve the homogeneity of space on long scales.

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