Since in coupled-cluster (CC) theory, ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper, we discuss ...the appearance of complex energy values in CC calculations from a mathematical perspective. We analyse the behaviour of the eigenvalues of Hermitian matrices that are perturbed (in a non-Hermitian manner) by a real parameter. Based on these results, we show that for CC calculations with real-valued Hamiltonian matrices the ground-state energy generally takes a real value. Furthermore, we show that in the case of real-valued Hamiltonian matrices complex excitation energies only occur in the context of conical intersections. In such a case, unphysical consequences are encountered such as a wrong dimension of the intersection seam, large numerical deviations from full configuration-interaction (FCI) results close to the conical intersection, and the square-root-like behaviour of the potential surfaces near the conical intersection. In the case of CC calculations with complex-valued Hamiltonian matrix elements, it turns out that complex energy values are to be expected for ground and excited states when no symmetry is present. We confirm the occurrence of complex energies by sample calculations using a six-state model and by CC calculations for the
molecule in a strong magnetic field. We furthermore show that symmetry can prevent the occurrence of complex energy values. Lastly, we demonstrate that in case of complex Hamiltonians the real part of the complex energy value provides a very good approximation to the FCI energy.
Transition wavenumbers contained in line-by-line rovibronic databases can be compromised by errors of various nature. When left undetected, these errors may result in incorrect quantum-state ...energies, potentially compromising a large number of derived spectroscopic data. Spectroscopic networks treat the complete set of line-by-line spectroscopic data as a large graph, and through a least-squares refinement the measured line positions are converted into empirical quantum-state energies. Spectroscopic networks also offer a highly useful framework to develop mathematical tools helping to identify possible errors and conflicts within the dataset. For example, wavenumber errors can be detected by checking for violations of the law of energy conservation. This paper describes a new graph-theory tool, which results in so-called verification labels for the quantum states. Verification labels help to express the vulnerability of a calculated empirical energy value and its uncertainty against possible wavenumber errors, providing complementary information to simple statistical uncertainties.
In the present work, calculated the cross sections of 133CS (A,2N) 135LA reaction By using interpolated and take the cross-sections published in the international literature for the selection of the ...appropriate energies ground level interaction in a computer–based program (MATALAB-17.0), in steps of energies (0.5 MeV). The quasi-experimental equation was derived from tabulated results linking a specific cross-section with energies, accounting for the neutron yield in accordance with the Zeigler neutron interactions formula using the program (SRIM 2013), and accounting for the stopping power which was also drawn and tabulated by measuring the yield at two closely spaced energies E1 and E2, one can determine the average value of the integrand over this energy interval and it turns out that the values are directly proportional until the alpha energy values reach 40 million electron volts. We notice that the change in the values is very slight. The neutron yield values begin to increase until the alpha energy reaches 40 million electron volts, after which the neutron yield becomes almost constant.
Industry 4.0 technologies are reconfiguring energy value chains and changing how we understand efficiency in energy production. Using Scopus, this review identifies research gaps in Industry 4.0 ...technologies in the energy sectors of Germany, China and South Africa, by technology type, effect and impact. Globally, research on the energy sector is skewed toward the Internet of things, Artificial Intelligence, and Big, Real-Time Data. Publications on Machine-Human-Integration and Robotics are limited. China outnumbers Germany in research publications and, South Africa produces the least, leading to the assumption is that such technologies are missing in energy production in South Africa. The literature presents clear content foci: i. using Industry 4.0 technologies to reduce energy intensity through better process-related materials, thereby shrinking the carbon footprint; ii. growing efficiencies through smart energy systems; iii. rethinking energy policy to incentivise research in Industry 4.0 technologies, and iv. managing network securities in within energy systems. Firm-specific, empirical research on South Africa, although valuable, is scarce regarding if, where and how Industry 4.0 technologies affect energy production, increased plant productivity and revenue. The review encourages implementing firm-based, empirical studies, using actual data on Industry 4.0 technologies in energy production in South Africa. Such studies provide improved understanding of a South African energy sector facing a Fourth Industrial Revolution and in crisis, identifying how Industry 4.0 technologies may be leveraged to increase energy productivity and efficiency. Such studies will contribute to evidence-based policy on expanding Industry 4.0 technologies to create an efficient and sustainable South African energy sector.
•Research on energy sector technologies is skewed towards the Internet of things, Artificial Intelligence and Big, Real-Time Data.•Research gaps exist for Robotics and Human-Machine Integration in energy production.•China leads in publication numbers for Industry 4.0 technologies in energy production.•No publications emerged on how Industry 4.0 technologies impact energy production in South Africa.•There are gaps in firm-level data on how Industry 4.0 technologies affect energy production.
Abstract
The pressure signal of oil pulsating flow is a kind of multi-component signal; in order to realise the effective separation of the multi-component pressure signal and extract its vibration ...characteristics, the pressure signal was decomposed by Variational Mode Decomposition (VMD). The slope criterion of the centre frequency is proposed to determine the number of components of VMD decomposition, and the method to judge the main components of the signal by energy value is proposed. The Hilbert envelope demodulation analysis was performed on the main components obtained. The results show that the proposed center frequency slope criterion method is effective in the VMD decomposition of the pressure signal of oil pulsating flow, which is used to decompose the pressure signal into 9 components. Four major components of the pressure signal are obtained by the correlation between each component and the pressure signal, and the energy value calculation of each component. The main component frequency of the pressure signal is one time, 6 times, 11 times and 14 times the frequency of the system spindle rotation; these are the sum of two cosine signals of close frequency and have the characteristic of beat vibration.
Unlocking browse species in semi-arid regions can be a key to improving the livestock productivity. The research was conducted to assess the browse species variation in chemical composition and in ...vitro dry matter degradability as influenced by seasonal (summer and winter) changes. Leaves from ten randomly selected browsable trees from sixteen species (
Vachellia karroo
,
Senegalia nigrescens
,
Vachellia nilotica
,
Balanites maughamii
,
Berchemia discolor, Berchemia zeyheri
,
Bridelia mollis
,
Combretum collinum
,
Combretum imberbe
,
Dalbergia melanoxylon
,
Dichrostachys cinerea
,
Grewia monticola
,
Grewia occidentalis
,
Melia azedarach
,
Ormocarpum kirkii
and
Ziziphus mucronata
) were harvested before defoliation from the site in two seasons (summer and winter) and dried at room temperature and then ground for analysis. Two-way analysis was used to analyse chemical composition and in vitro ruminal dry matter degradability.
Melia azedarach
(343.7 g/kg DM) had the highest (
p
< 0.0001) CP content in summer. In winter,
B. maughamii
(210.3 g/kg DM) had the highest (
p
< 0.05) crude protein content.
Combretum collinum
(2.90 Mcal/kg) had a highest (
p
< 0.0001) metabolizable energy value in summer.
Bridelia mollis, B. maughamii, B. discolor, C. collinum, C. imberbe, O. kirkii, S. nigrescens, V. nilotica, G. occidentalis
and
B. zeyheri
had the same (
p
> 0.0001) dry matter degradability (DMD) 48 values across two seasons. In both seasons, most of these browse species have the potential to supplement low quality natural grasses because they go beyond the minimum requirement of protein and have coherent amounts of fibre concentration. There is a need to assess the bioactive compounds found in these browse species for the amelioration and also to maximize browsing of these species.
The reduction of hematite present in the oxidized Fe-Ti-V ore to magnetite was carried out to use this ore in existing processes. One of the first steps in obtaining vanadium is the magnetic ...separation process, and the oxidized ore exhibits no magnetism. The creation of a reducing atmosphere using air and charcoal at four temperatures (400-700°C) was studied, resulting in an economically viable industrial process. Efficient reduction of hematite to magnetite was achieved at 400°C within 3 h. ICP OES determined the percentage of V 0.40%. After reduction, XRD showed that the entire hematite fraction became magnetite. The experimental data for kinetics were the first-order model, obtaining the apparent activation energy value equal to 15.8 kJ mol-1 and the pre-exponential coefficient equal to 0.49 min-1. Magnetic separation in a low-intensity field, 1500 G, of the reduced ore generated two fractions, the magnetic fraction, which concentrated 90.7% of the V present in the oxidized Fe-Ti-V ore, and the non-magnetic fraction with ilmenite (FeTiOs) and rutile (Ti02). It is important that it does not form vanadium carbide (VC) during the reduction of the ore. Vanadium ore can now be used in the process already applied in industry.
Abstract The microscopic mechanism of size quantization of the conduction band and valence band of semiconductors of cubic and tetrahedral symmetry has been theoretically studied in the Kane ...approximation. It is shown that the matrix Schrödinger equation obtained on the basis of the Kane model cannot be solved analytically for a potential well of an arbitrary profile. Therefore, expressions for the energy spectrum are obtained depending on the two-dimensional wave vector directed along the interface of the heterostructure for various cases that differ in the range of current carrier energy values.
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