Theory of the rocket-grenade method of measuring temperature, pressure, density and wind velocity in the upper atmosphere

1966 ◽  
Vol 290 (1420) ◽  
pp. 44-73 ◽  
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Wind Velocity ◽  
Speed Of Sound ◽  
Vertical Component ◽  
Second Order ◽  
Upper Atmosphere ◽  
Lower Atmosphere ◽  
Travel Times ◽  
Sound Waves

A theory is presented for deriving the speed of sound and wind velocity as a function of height in the upper atmosphere from observations on the travel times of sound waves from accurately located grenades, released during rocket flight, to microphones at surveyed positions on the ground. The theory is taken to a second order of approximation, which can be utilized in practice if lower atmosphere (balloon) measurements are available. By means of the gas law and the vertical equation of motion of the atmosphere, formulae are obtained for deriving temperature, pressure and density from the speed-of-sound profile, and these also may be evaluated to a higher accuracy if lower atmosphere measurements are available. An outline is given of the computational procedure followed in the processing of data on the basis of this theory by means of the Pegasus computer. Methods of calculating the correction to travel times due to the finite wave amplitude are discussed and compared, and the effect of neglecting this correction in a particular set of experimental data is examined. Other errors which may affect the determination of pressure are also discussed. Consistency between the theory and experimental data obtained in 13 Skylark rocket flights at Woomera is checked in two ways: by examining least squares residuals associated with the sound arrivals at various microphones; and by treating the vertical component of air motion as unknown and examining its distribution about zero. The reduction in the least squares residuals which occurs when account is taken of second order terms is evaluated on the basis of these sets of experimental data.

Void pattern fluctuation in p-AgBr interactions at 400 GeV/c

2016 ◽  
pp. 4115-4125
Author(s):  
Argha Deb
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Phase Space ◽  
Second Order ◽  
Hadron Phase

The event-by-event fluctuation of hadronic patterns is investigated by finding a measure of the non-hadronic regions, the voids, for the experimental data of p-AgBr interactions at 400 GeV/c considering the anisotropy of phase space. Two moments of the event-to-event fluctuation of voids, <Gq> and Sq have been calculated as defined by R. C. Hwa and Q. H. Zhang to quantify the dependence of the voids on the bin sizes. The results suggest that no quark-hadron phase transition of second order have taken place for p-AgBr interactions at 400 GeV/c. The result have been compared with the result of VENUS generated data.

scholarly journals Testing the Youth Physical Activity Promotion Model during the COVID-19 Pandemic, with Partial Least Squares Second-Order Latent Constructs

2021 ◽  
Vol 18 (12) ◽  
pp. 6398
Author(s):  
Elena Druică ◽  
Rodica Ianole-Călin ◽  
Monica Sakizlian ◽  
Daniela Aducovschi ◽  
Remus Dumitrescu ◽  
...  
Keyword(s):  
Physical Activity ◽  
Least Squares ◽  
Partial Least Squares ◽  
Online Survey ◽  
Physical Activity Promotion ◽  
Second Order ◽  
Latent Constructs ◽  
Activity Promotion ◽  
Youth Physical Activity ◽  
Mediating Mechanisms

We tested the Youth Physical Activity Promotion (YPAP) framework on Romanian students in order to identify actionable determinants to support participation in physical activity. Our sample consisted of 665 responses to an online survey, with participants aged 18–23 (mean = 19 years); 70% were women. We used the partial least squares algorithm to estimate the relationships between students’ behavior and possible predictors during the COVID-19 pandemic. Our results indicate that all the theoretical dimensions of YPAP (predisposing, enabling and reinforcing) have a positive and significant impact on physical activity, with two mediating mechanisms expressed as predisposing factors: able and worth. Unlike previous research, we used second-order latent constructs, unveiling a particular structure for the enabling dimension that only includes sport competence, fitness and skills, but not the environmental factors.

Quantitative Models of Motor Responses Subject to Longitudinal, Lateral, and Preview Constraints

1978 ◽  
Vol 20 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Motor Control ◽  
Linear Models ◽  
Movement Time ◽  
Arm Movements ◽  
Second Order ◽  
Motor Responses ◽  
First Order ◽  
Different Types ◽  
Index Of Difficulty

First- and second-order linear models of mean movement time for serial arm movements aimed at a target and subject to preview constraints and lateral constraints were formulated as extensions of the so-called Fitts's law of motor control. These models were validated on the basis of experimental data from five subjects and found to explain from 80% to 85% of the variation in movement time in the case of the first-order models and from 93% to 95% of such variation for the second-order models. Fitts's index of difficulty (ID) was generally found to contribute more to the movement time than did either the preview ID or the lateral ID defined. Of the different types of errors, target overshoots occurred far more frequently than undershoots.

Global upper-atmospheric heating at Jupiter by the recirculation of auroral energy

2021 ◽  
Author(s):  
James O'Donoghue ◽  
Luke Moore ◽  
Tanapat Bhakyapaibul ◽  
Henrik Melin ◽  
Tom Stallard ◽  
...  
Keyword(s):  
Heat Source ◽  
Acoustic Waves ◽  
Temperature Gradients ◽  
Upper Atmosphere ◽  
Global Temperature ◽  
Lower Atmosphere ◽  
Polar Regions ◽  
High Resolution Data ◽  
Coriolis Forces ◽  
Global Circulation Models

&lt;p&gt;Jupiter's upper atmosphere is significantly hotter than expected based on the amount of solar heating it receives. This temperature discrepency is known as the 'energy crisis' due to it's nearly 50-year duration and the fact it also occurs at Saturn, Uranus and Neptune. At Jupiter, magnetosphere-ionosphere coupling gives rise to intense auroral emissions and enormous energy deposition in the magnetic polar regions, so it was presumed long ago that redistribution of this energy could heat the rest of the planet. However, most global circulation models have difficulty redistributing auroral energy globally due to the strong Coriolis forces and ion drag on this rapidly rotating planet. Consequently, other possible heat sources have continued to be studied, such as heating by gravity and acoustic waves emanating from the lower atmosphere. Each global heating mechanism would imprint a unique signature on global temperature gradients, thus revealing the dominant heat source, but these gradients have not been determined due a lack of planet-wide, high-resolution data. The last global map of Jovian upper-atmospheric temperatures was produced using ground-based data taken in 1993, in which the region between 45&lt;sup&gt;o&lt;/sup&gt; latitude (north &amp; south) and the poles was represented by just 2 pixels. As a result, those maps did not (or could not) show a clear temperature gradient, and furthermore, they even showed regions of hot atmosphere near the equator, supporting the idea of an equatorial heat source, e.g. gravity and/or acoustic wave heating. Therefore observationally and from a modeling perspective, a concensus has not been reached to date. Here we report new infrared spectroscopy of Jupiter's major upper-atmospheric ion H&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;+&lt;/sup&gt;, with a spatial resolution of 2&lt;sup&gt;o&lt;/sup&gt; longitude and latitude extending from pole to equator, capable of tracing the global temperature gradients. We find that temperatures decrease steadily from the auroral polar regions to the equator. Further, during a period of enhanced activity possibly driven by a solar wind compression, a high-temperature planetary-scale structure was observed which may be propagating from the aurora. These observations indicate that Jupiter's upper atmosphere is predominantly heated via the redistribution of auroral energy, and therefore that Coriolis forces and ion drag are observably overcome.&lt;/p&gt;

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

2001 ◽  
Vol 699 ◽  
Author(s):  
D.S. McLachlan ◽  
C. Chiteme ◽  
W.D. Heiss ◽  
Junjie Wu
Keyword(s):  
Experimental Data ◽  
Ac Conductivity ◽  
Volume Fraction ◽  
Power Laws ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Equation ◽  
Scaling Properties ◽  
First Order ◽  
Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

scholarly journals Harnessing of Newly Tailored Poly (Acrylonitrile)-Starch Nanoparticle Graft Copolymer for Copper Ion Removal via Oximation Reaction

2021 ◽  
Author(s):  
khaled Mostafa ◽  
H. Ameen ◽  
A. Ebessy ◽  
A. El-Sanabary
Keyword(s):  
Experimental Data ◽  
Adsorption Capacity ◽  
Graft Copolymer ◽  
Adsorption Kinetics ◽  
Copper Ions ◽  
Copper Ion ◽  
Second Order ◽  
First Order ◽  
Pseudo Second Order ◽  
Pseudo First Order

Abstract Our recently tailored and fully characterized poly (AN)-starch nanoparticle graft copolymer having 60.1 G.Y. % was used as a starting substrate for copper ions removal from waste water effluent after chemical modification with hydroxyl amine via oximation reaction. This was done to change the abundant nitrile groups in the above copolymer into amidoxime one and the resultant poly (amidoxime) resin was used as adsorbent for copper ions. The resin was characterized qualitatively via rapid vanadium ion test and instrumentally by FT-IR spectra and SEM morphological analysis to confirm the presence of amidoxime groups. The adsorption capacity of the resin was done using the batch technique, whereas the residual copper ions content in the filtrate before and after adsorption was measured using atomic adsorption spectrometry. It was found that the maximum adsorption capacity of poly (amidoxime) resin was 115.2 mg/g at pH 7, 400ppm copper ions concentration and 0.25 g adsorbent at room temperature. The adsorption, kinetics and isothermal study of the process is scrutinized using different variables, such as pH, contact time, copper ion concentration and adsorbent dosage. Different kinetics models comprising the pseudo-first-order and pseudo-second-order have been applied to the experimental data to envisage the adsorption kinetics. It was found from kinetic study that pseudo-second-order rate equation was better than pseudo-first-order supporting the formation of chemisorption process. While, in case of isothermal study, the examination of calculated correlation coefficient (R2) values showed that the Langmuir model provide the best fit to experimental data than Freundlich one.

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