Theoretical energies for the n = 1 and 2 states of the helium isoelectronic sequence up to Z = 100

1988 ◽  
Vol 66 (7) ◽  
pp. 586-611 ◽  
Author(s):  
G. W. Drake
Keyword(s):  
Experimental Data ◽  
High Precision ◽  
Quantum Electrodynamic ◽  
Lamb Shift ◽  
Isoelectronic Sequence ◽  
Shift Measurement ◽  
Wide Range ◽  
Variational Calculations ◽  
The Unified Method ◽  
Unified Method

The unified method described previously for combining high-precision nonrelativistic variational calculations with relativistic and quantum electrodynamic corrections is applied to the 1s2 1S0, 1s2s 1S0, 1s2s 3S1, 1s2p 1P1, and 1s2p 3P0,1,2 staters of helium-like ions. Detailed tabulations are presented for all ions in the range 2 ≤ Z ≤ 100 and are compared with a wide range of experimental data up to 34Kr+. The results for 90U+ significantly alter the recent Lamb shift measurement of Munger and Gould from 70.4 ± 8.3 to 71.0 ± 8.3 eV, in comparison with a revised theoretical value of 74.3 ± 0.4 eV. The improved agreement is due to the inclusion of higher order two-electron corrections in the present work.

RELATIVISTIC ENERGY, OSCILLATOR STRENGTHS AND TRANSITION RATES OF THE 1s2 2 ln l 1S(m)(n =2–6, m1–5) STATES FOR Be-LIKE SYSTEM

2005 ◽  
Vol 16 (06) ◽  
pp. 951-968 ◽  
Author(s):  
MENG ZHANG ◽  
BING-CONG GOU
Keyword(s):  
Experimental Data ◽  
Energy Levels ◽  
Oscillator Strengths ◽  
Relativistic Energy ◽  
Transition Rates ◽  
Isoelectronic Sequence ◽  
Polarization Effects ◽  
First Order ◽  
Variational Calculations ◽  
First Order Perturbation

Variational calculations are carried out with a multiconfiguration-interaction wave function to obtain the relativistic energies of the 1s2 2 ln l 1 S (m)(n =2–6, m1–5) states for the beryllium isoelectronic sequence (Z =4–10). Relativistic corrections and the mass polarization effects are evaluated with the first-order perturbation theory. The identifications of the energy levels for 1s2 2 ln l 1 S (m)(n =2–6, m1–5) states in the Be-like ions are reported. The oscillator strengths, transition rates and wavelengths are also calculated. The calculated results are compared with other theoretical and experimental data in the literature.

Lamb-shift measurement in hydrogen by the anisotropy method

1998 ◽  
Vol 76 (2) ◽  
pp. 95-103 ◽  
Author(s):  
A van Wijngaarden ◽  
F Holuj ◽  
G W Drake
Keyword(s):  
High Precision ◽  
Precision Measurement ◽  
Lamb Shift ◽  
High Precision Measurement ◽  
Shift Measurement

A high-precision measurement of the Lamb shift in hydrogen by theanisotropy method is presented. The result of 1057.852(15) MHz isconsistent with theory and other measurements, thereby confirming thatthe anisotropy method and its interpretation are valid at the 15 partsper million level of accuracy. For the case of He+, a discrepancyof 70(12) parts per million between theory (including two-loop bindingcorrections) and experiment remains to be resolved.PACS Nos. 3130J, 3220D

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

scholarly journals Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 968-980
Author(s):  
Xueping Du ◽  
Zhijie Chen ◽  
Qi Meng ◽  
Yang Song
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Exchanger ◽  
Correlation Equation ◽  
Tube Heat Exchanger ◽  
Flow Friction ◽  
Air Inlet ◽  
Comparison Results ◽  
Wide Range ◽  
Oval Tube

Abstract A high accuracy of experimental correlations on the heat transfer and flow friction is always expected to calculate the unknown cases according to the limited experimental data from a heat exchanger experiment. However, certain errors will occur during the data processing by the traditional methods to obtain the experimental correlations for the heat transfer and friction. A dimensionless experimental correlation equation including angles is proposed to make the correlation have a wide range of applicability. Then, the artificial neural networks (ANNs) are used to predict the heat transfer and flow friction performances of a finned oval-tube heat exchanger under four different air inlet angles with limited experimental data. The comparison results of ANN prediction with experimental correlations show that the errors from the ANN prediction are smaller than those from the classical correlations. The data of the four air inlet angles fitted separately have higher precisions than those fitted together. It is demonstrated that the ANN approach is more useful than experimental correlations to predict the heat transfer and flow resistance characteristics for unknown cases of heat exchangers. The results can provide theoretical support for the application of the ANN used in the finned oval-tube heat exchanger performance prediction.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

scholarly journals Optical whispering-gallery mode barcodes for high-precision and wide-range temperature measurements

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Jie Liao ◽  
Lan Yang
Keyword(s):  
High Precision ◽  
Dynamic Range ◽  
Single Mode ◽  
Whispering Gallery Mode ◽  
Temperature Measurements ◽  
Laser Source ◽  
Multiple Modes ◽  
Whispering Gallery ◽  
Wide Range ◽  
Thermal Sensing

AbstractTemperature is one of the most fundamental physical properties to characterize various physical, chemical, and biological processes. Even a slight change in temperature could have an impact on the status or dynamics of a system. Thus, there is a great need for high-precision and large-dynamic-range temperature measurements. Conventional temperature sensors encounter difficulties in high-precision thermal sensing on the submicron scale. Recently, optical whispering-gallery mode (WGM) sensors have shown promise for many sensing applications, such as thermal sensing, magnetic detection, and biosensing. However, despite their superior sensitivity, the conventional sensing method for WGM resonators relies on tracking the changes in a single mode, which limits the dynamic range constrained by the laser source that has to be fine-tuned in a timely manner to follow the selected mode during the measurement. Moreover, we cannot derive the actual temperature from the spectrum directly but rather derive a relative temperature change. Here, we demonstrate an optical WGM barcode technique involving simultaneous monitoring of the patterns of multiple modes that can provide a direct temperature readout from the spectrum. The measurement relies on the patterns of multiple modes in the WGM spectrum instead of the changes of a particular mode. It can provide us with more information than the single-mode spectrum, such as the precise measurement of actual temperatures. Leveraging the high sensitivity of WGMs and eliminating the need to monitor particular modes, this work lays the foundation for developing a high-performance temperature sensor with not only superior sensitivity but also a broad dynamic range.

The Petrogenetic Model, an Extension of Bowen's Petrogenetic Grid

1962 ◽  
Vol 99 (6) ◽  
pp. 558-569 ◽  
Author(s):  
Peter J. Wyllie
Keyword(s):  
Experimental Data ◽  
Constant Pressure ◽  
Three Dimensional ◽  
Pore Fluid ◽  
Fluid Composition ◽  
Solid Reaction ◽  
Petrogenetic Model ◽  
Wide Range ◽  
Opposite Face ◽  
Reaction Surfaces

AbstractBowen's petrogenetic grid is a PT projection containing univariant curves for decarbonation, dehydration, and solid-solid reactions, with vapour pressure (Pf) equal to total pressure (Ps). Analysis of experimental data in the system MgO–CO2–H2O leads to an expansion of this grid. Three of the important variables in metamorphism when Pf = Ps are P, T, and variation of the pore fluid composition between H2O and CO2. These can be illustrated in a three-dimensional petrogenetic model; one face is a PT plane for reactions occurring with pure H2O, and the opposite face is a similar plane for reactions with pure CO2; these are separated by an axis for pore fluid composition varying between H2O and CO2. Superposition of the PT faces of the model provides the petrogenetic grid. The reactions within the model are represented by divariant surfaces, which may meet along univariant lines. For dissociation reactions, the surfaces curve towards lower temperatures as the proportion of non-reacting volatile increases, and solid-solid reaction surfaces are parallel to the vapour composition axis and perpendicular to the PT axes. The relative temperatures of reactions and the lines of intersections of the surfaces can be illustrated in isobaric sections. Isobaric sections are used to illustrate reactions proceeding at constant pressure with (1) pore fluid composition remaining constant during the reaction, with temperature increasing (2) pore fluid composition changing during the reaction, with temperature increasing, and (3) pore fluid changing composition at constant temperature. The petrogenetic model provides a convenient framework for a wide range of experimental data.

Effects of Multiple Impacts and Size Distribution of Particles on Erosion Predictions Using CFD

2007 ◽  
Author(s):  
Yongli Zhang ◽  
Brenton S. McLaury ◽  
Siamack A. Shirzai
Keyword(s):  
Experimental Data ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Target Material ◽  
Average Particle ◽  
Multiple Impacts ◽  
Cfd Simulations ◽  
Erosion Damage ◽  
Wide Range

Erosion equations are usually obtained from experiments by impacting solid particles entrained in a gas or liquid on a target material. The erosion equations are utilized in CFD (Computational Fluid Dynamics) models to predict erosion damage caused by solid particle impingements. Many erosion equations are provided in terms of an erosion ratio. By definition, the erosion ratio is the mass loss of target material divided by the mass of impacting particles. The mass of impacting particles is the summation of (particle mass × number of impacts) of each particle. In erosion experiments conducted to determine erosion equations, some particles may impact the target wall many times and some other particles may not impact the target at all. Therefore, the experimental data may not reflect the actual erosion ratio because the mass of the sand that is used to run the experiments is assumed to be the mass of the impacting particles. CFD and particle trajectory simulations are applied in the present work to study effects of multiple impacts on developing erosion ratio equations. The erosion equation as well as the CFD-based erosion modeling procedure is validated against a variety of experimental data. The results show that the effect of multiple impacts is negligible in air cases. In water cases, however, this effect needs to be accounted for especially for small particles. This makes it impractical to develop erosion ratio equations from experimental data obtained for tests with sand in water or dense gases. Many factors affecting erosion damage are accounted for in various erosion equations. In addition to some well-studied parameters such as particle impacting speed and impacting angle, particle size also plays a significant role in the erosion process. An average particle size is usually used in analyzing experimental data or estimating erosion damage cases of practical interest. In petroleum production applications, however, the size of sand particles that are entrained in produced fluids can vary over a fairly broad range. CFD simulations are also performed to study the effect of particle size distribution. In CFD simulations, particle sizes are normally distributed with the mean equaling the average size of interest and the standard deviation varying over a wide range. Based on CFD simulations, an equation is developed and can be applied to account for the effect of the particle size distribution on erosion prediction for gases and liquids.

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