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Keywords = local thermodynamic equilibrium (LTE)

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15 pages, 6280 KiB  
Article
Abundance Analysis of the Spectroscopic Binary α Equulei
by Anna Romanovskaya and Sergey Zvyagintsev
Galaxies 2025, 13(4), 88; https://doi.org/10.3390/galaxies13040088 - 6 Aug 2025
Abstract
We present the results of a detailed spectroscopic analysis of the double-lined spectroscopic binary system α Equulei. High-resolution spectra obtained with the SOPHIE spectrograph at various orbital phases were used to disentangle the composite spectra into individual components using the spectral line deconvolution [...] Read more.
We present the results of a detailed spectroscopic analysis of the double-lined spectroscopic binary system α Equulei. High-resolution spectra obtained with the SOPHIE spectrograph at various orbital phases were used to disentangle the composite spectra into individual components using the spectral line deconvolution (SLD) iterative technique. The atmospheric parameters of each component were refined with the SME (spectroscopy made easy) package and further validated by following methods: SED (spectral energy distribution), the independence of the abundance of individual Fe iii lines on the reduced equivalent width and ionisation potential, and fitting with the hydrogen line profiles. Our accurate abundance analysis uses a hybrid technique for spectrum synthesis. This is based on classical model atmospheres that are calculated under the assumption of local thermodynamic equilibrium (LTE), together with non-LTE (NLTE) line formation. This is used for 15 out of the 25 species from C to Nd that were investigated. The primary giant component (G7-type) exhibits a typical abundance pattern for normal stars, with elements from He to Fe matching solar values and neutron-capture elements showing overabundances up to 0.5 dex. In contrast, the secondary dwarf component displays characteristics of an early stage Am star. The observed abundance differences imply distinct diffusion processes in their atmospheres. Our results support the scenario in which chemical peculiarities in Am stars develop during the main sequence and may decrease as the stars evolve toward the subgiant branch. Full article
(This article belongs to the Special Issue Stellar Spectroscopy, Molecular Astronomy and Atomic Astronomy)
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25 pages, 4627 KiB  
Article
Laser-Based Characterization and Classification of Functional Alloy Materials (AlCuPbSiSnZn) Using Calibration-Free Laser-Induced Breakdown Spectroscopy and a Laser Ablation Time-of-Flight Mass Spectrometer for Electrotechnical Applications
by Amir Fayyaz, Muhammad Waqas, Kiran Fatima, Kashif Naseem, Haroon Asghar, Rizwan Ahmed, Zeshan Adeel Umar and Muhammad Aslam Baig
Materials 2025, 18(9), 2092; https://doi.org/10.3390/ma18092092 - 2 May 2025
Viewed by 783
Abstract
In this paper, we present the analysis of functional alloy samples containing metals aluminum (Al), copper (Cu), lead (Pb), silicon (Si), tin (Sn), and zinc (Zn) using a Q-switched Nd laser operating at a wavelength of 532 nm with a pulse duration of [...] Read more.
In this paper, we present the analysis of functional alloy samples containing metals aluminum (Al), copper (Cu), lead (Pb), silicon (Si), tin (Sn), and zinc (Zn) using a Q-switched Nd laser operating at a wavelength of 532 nm with a pulse duration of 5 ns. Nine pelletized alloy samples were prepared, each containing varying chemical concentrations (wt.%) of Al, Cu, Pb, Si, Sn, and Zn—elements commonly used in electrotechnical and thermal functional materials. The laser beam is focused on the target surface, and the resulting emission spectrum is captured within the temperature interval of 9.0×103 to 1.1×104 K using a set of compact Avantes spectrometers. Each spectrometer is equipped with a linear charged-coupled device (CCD) array set at a 2 μs gate delay for spectrum recording. The quantitative analysis was performed using calibration-free laser-induced breakdown spectroscopy (CF-LIBS) under the assumptions of optically thin plasma and self-absorption-free conditions, as well as local thermodynamic equilibrium (LTE). The net normalized integrated intensities of the selected emission lines were utilized for the analysis. The intensities were normalized by dividing the net integrated intensity of each line by that of the aluminum emission line (Al II) at 281.62 nm. The results obtained using CF-LIBS were compared with those from the laser ablation time-of-flight mass spectrometer (LA-TOF-MS), showing good agreement between the two techniques. Furthermore, a random forest technique (RFT) was employed using LIBS spectral data for sample classification. The RFT technique achieves the highest accuracy of ~98.89% using out-of-bag (OOB) estimation for grouping, while a 10-fold cross-validation technique, implemented for comparison, yields a mean accuracy of ~99.12%. The integrated use of LIBS, LA-TOF-MS, and machine learning (e.g., RFT) enables fast, preparation-free analysis and classification of functional metallic materials, highlighting the synergy between quantitative techniques and data-driven methods. Full article
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26 pages, 4050 KiB  
Article
Vibrational Excitation of HDO Molecule by Electron Impact
by Mehdi Adrien Ayouz, Alexandre Faure, Ioan F. Schneider, János Zsolt Mezei and Viatcheslav Kokoouline
Atoms 2025, 13(4), 32; https://doi.org/10.3390/atoms13040032 - 8 Apr 2025
Viewed by 401
Abstract
Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for [...] Read more.
Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for various geometries of the target molecule, three-dimensional vibrational states of HDO, and the vibrational frame transformation. The vibrational states of the molecule are evaluated by solving the Schrödinger equation numerically, without relying on the normal-mode approximation, which is known to be inaccurate for water molecules. As a result, couplings and transitions between the vibrational states of HDO are accurately accounted for. From the calculated cross sections, thermally averaged rate coefficients and their analytical fits are provided. Significant differences between the results for HDO and H2O are observed. Additionally, an uncertainty assessment of the obtained data is performed for potential use in modeling non-local thermodynamic equilibrium (non-LTE) spectra of water in various astrophysical environments. Full article
(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)
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15 pages, 15952 KiB  
Article
Synthesis of the Titanium Oxides Using a New Microwave Discharge Method
by Marian Mogildea, George Mogildea, Sorin I. Zgura, Gabriel Chiritoi, Cristian Ionescu, Valentin Craciun, Petronela Prepelita, Natalia Mihailescu, Alexandru Paraschiv, Bogdan Stefan Vasile and Catalin Daniel Constantinescu
Int. J. Mol. Sci. 2025, 26(5), 2173; https://doi.org/10.3390/ijms26052173 - 28 Feb 2025
Viewed by 645
Abstract
This research highlights the different behaviors of titanium (Ti) wires under the action of 500 W and 800 W microwave power levels. Following the interaction between microwaves and a titanium wire placed in the node of the (TM011—transverse magnetic mode) waveguide [...] Read more.
This research highlights the different behaviors of titanium (Ti) wires under the action of 500 W and 800 W microwave power levels. Following the interaction between microwaves and a titanium wire placed in the node of the (TM011—transverse magnetic mode) waveguide in air at atmospheric pressure, plasma was generated. Using optical emission spectroscopy technique it was observed that during plasma generation at 500 W and 800 W microwaves powers, metallic ions, and gas ions were created, and the plasmas fulfilled the local thermodynamic equilibrium (LTE) conditions. The XRD analysis showed that on the surface of the Ti wire exposed to 500 W microwave power a mixture of titanium dioxide (TiO2) and titanium oxide (TiO) grew, while the Ti wire exposed to 800 W microwave power was completely vaporized and a mixture of TiO2 and TiO nanoparticles was synthesized. The SEM analysis showed that the dimensions of the titanium oxide (TiOx) nanoparticles generated by both microwave discharges ranged from 5 nm to 200 nm. The results of EDS analysis showed that the power of microwaves plays an important role in quantitative conversion from Ti wire into a TiOx mixture. The TEM analysis indicates that most of the nanoparticles are either amorphous or nanocrystalline. Using this simple and inexpensive technique one can grow a TiOx layer on the surface of titanium electrodes or can synthetize nanocrystalline TiOx particles. Full article
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13 pages, 2744 KiB  
Article
Experimental Study on the Temporal Evolution Parameters of Laser–Produced Tin Plasma under Different Laser Pulse Energies for LPP–EUV Source
by Yiyi Chen, Chongxiao Zhao, Qikun Pan, Ranran Zhang, Yang Gao, Xiaoxi Li, Jin Guo and Fei Chen
Photonics 2023, 10(12), 1339; https://doi.org/10.3390/photonics10121339 - 4 Dec 2023
Cited by 5 | Viewed by 2028
Abstract
The laser–produced plasma extreme ultraviolet (LPP–EUV) source is the sole light source currently available for commercial EUVL (extreme ultraviolet lithography) machines. The plasma parameters, such as the electron temperature and electron density, affect the conversion efficiency (CE) of extreme ultraviolet radiation and other [...] Read more.
The laser–produced plasma extreme ultraviolet (LPP–EUV) source is the sole light source currently available for commercial EUVL (extreme ultraviolet lithography) machines. The plasma parameters, such as the electron temperature and electron density, affect the conversion efficiency (CE) of extreme ultraviolet radiation and other critical parameters of LPP–EUV source directly. In this paper, the optical emission spectroscopy (OES) was employed to investigate the time–resolved plasma parameters generated by an Nd:YAG laser irradiation on a planar tin target. Assuming that the laser–produced tin plasma satisfies the local thermodynamic equilibrium (LTE) condition, the electron temperature and electron density of the plasma were calculated by the Saha–Boltzmann plot and Stark broadening methods. The experimental results revealed that during the early stage of plasma formation (delay time < 50 ns), there was a significant presence of continuum emission. Subsequently, the intensity of the continuum emission gradually decreased, while line spectra emerged and became predominant at a delay time of 300 ns. In addition, the evolution trend of plasma parameters, with the incident laser pulse energy set at 300 mJ, was characterized by a rapid initial decrease followed by a gradual decline as the delay time increased. Furthermore, with an increase in the incident laser pulse energy from 300 mJ to 750 mJ, the electron temperature and electron density of laser–produced tin plasma exhibiting a monotonically showed increasing trend at the same delay time. Full article
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13 pages, 3325 KiB  
Article
Pathways to the Local Thermodynamic Equilibrium of Complex Autoionizing States
by Frédérick Petitdemange and Frank B. Rosmej
Atoms 2023, 11(11), 146; https://doi.org/10.3390/atoms11110146 - 15 Nov 2023
Viewed by 1818
Abstract
The generally accepted pathway to Local Thermodynamic Equilibrium (LTE) in atomic physics, where collision rates need to be much larger than radiative decay rates, is extended to complex autoionizing states. It is demonstrated that the inclusion of the non-radiative decay (autoionization rate) on [...] Read more.
The generally accepted pathway to Local Thermodynamic Equilibrium (LTE) in atomic physics, where collision rates need to be much larger than radiative decay rates, is extended to complex autoionizing states. It is demonstrated that the inclusion of the non-radiative decay (autoionization rate) on the same footing, like radiative decay, i.e., the LTE criterion ne,crit×CA+Γ (ne,crit is the critical electron density above which LTE holds, C is the collisional rate coefficient, and A is the radiative decay rate) is inappropriate for estimating the related critical density. An analysis invoking simultaneously different atomic ionization stages identifies the LTE criteria as a theoretical limiting case, which provides orders of magnitude too high critical densities for almost all practical applications. We introduced a new criterion, where the critical densities are estimated from the non-autoionizing capture states rather than from the autoionizing states. The new criterion is more appropriate for complex autoionizing manifolds and provides order of magnitude reduced critical densities. Detailed numerical calculations are carried out for Na-like states of aluminum, where autoionization to the Ne-like ground and excited state occurrences are in excellent agreement with the new criterion. In addition, a complex multi-electron atomic-level structure and electron–electron correlation are identified as simplifying features rather than aggravating ones for the concept of thermalization. Full article
(This article belongs to the Special Issue Atomic Physics in Dense Plasmas)
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15 pages, 579 KiB  
Article
NLTE Analysis of High-Resolution H-Band Spectra, V: Neutral Sodium
by Zeming Zhou, Jianrong Shi, Shaolan Bi, Hongliang Yan, Junbo Zhang, Kaike Pan and Xiaodong Xu
Universe 2023, 9(11), 457; https://doi.org/10.3390/universe9110457 - 25 Oct 2023
Cited by 1 | Viewed by 1723
Abstract
In order to derive sodium abundances and investigate the effects of non-local thermodynamic equilibrium (NLTE) on the formation of H-band Na I lines, we update the sodium atomic model by incorporating collision rates with hydrogen from new quantum-mechanical calculations. The differential Na [...] Read more.
In order to derive sodium abundances and investigate the effects of non-local thermodynamic equilibrium (NLTE) on the formation of H-band Na I lines, we update the sodium atomic model by incorporating collision rates with hydrogen from new quantum-mechanical calculations. The differential Na abundances for 13 sample stars are obtained by analyzing high-resolution H-band spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and optical spectra under both local thermodynamic equilibrium (LTE) and NLTE conditions. Consistent abundances from both bands suggest that our updated atomic model is valid for studying the formation of H-band Na I lines. Our calculations show that, in our stellar parameter space, NLTE effects are negative and can result in corrections larger than −0.4 dex on optical lines. The corrections on H-band Na I lines are typically small, within about 0.05 dex, but not negligible if accurate sodium abundance is desired. We note that the [Na/Fe] ratios favor the theoretical galactic chemical model. Full article
(This article belongs to the Section Solar and Stellar Physics)
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21 pages, 5124 KiB  
Article
Multi-Spectroscopic Characterization of MgO/Nylon (6/6) Polymer: Evaluating the Potential of LIBS and Statistical Methods
by Amir Fayyaz, Haroon Asghar, Muhammad Waqas, Asif Kamal, Wedad A. Al-Onazi and Amal M. Al-Mohaimeed
Polymers 2023, 15(15), 3156; https://doi.org/10.3390/polym15153156 - 25 Jul 2023
Cited by 7 | Viewed by 5240
Abstract
The potential of using laser-induced breakdown spectroscopy (LIBS) in combination with various other spectroscopic and statistical methods was assessed for characterizing pure and MgO-doped nylon (6/6) organic polymer samples. The pure samples, obtained through a polycondensation chemical technique, were artificially doped with MgO [...] Read more.
The potential of using laser-induced breakdown spectroscopy (LIBS) in combination with various other spectroscopic and statistical methods was assessed for characterizing pure and MgO-doped nylon (6/6) organic polymer samples. The pure samples, obtained through a polycondensation chemical technique, were artificially doped with MgO prior to analysis for comparative purposes. These artificially doped samples served as crucial reference materials for comparative analysis and reference purposes. The LIBS studies were performed under local thermodynamic equilibrium (LTE) and optically thin plasma conditions. To assess the structural crystallinity of the nylon (6/6) polymer samples, X-ray diffraction (XRD) analysis, and Fourier transform infrared (FTIR) spectroscopy were employed to detect functional groups such as N-H, C-H, and C-N in the adsorbent polyamide nylon sample. Additionally, diffuse reflectance spectroscopy (DRS) analysis was conducted to investigate the effects of doping and temperature on the band gap and material reflectance across different sample temperatures. Chemical compositional analysis was performed using X-ray photoelectron spectroscopy (XPS) with the carbon C1s peak at 248.8 eV serving as a reference for spectrum calibration, along with energy-dispersive X-ray (EDX) analysis, which demonstrated good agreement between the techniques. To validate the different methodologies, the results obtained from CF-LIBS and EDX were compared with those from the standard inductively coupled plasma mass spectrometry (ICP-MS) technique. Finally, for classification analysis, principal component analysis (PCA) was applied to the LIBS spectral data at different sample temperatures (25 °C, 125 °C, 225 °C, and 325 °C). The analyses demonstrated that the combination of LIBS with PCA, along with other methods, presents a robust technique for polymer characterization. Full article
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13 pages, 2923 KiB  
Article
Spectroscopical Characterization of Copper–Iron (Cu-Fe) Alloy Plasma Using LIBS, ICP-AES, and EDX
by Amir Fayyaz, Javed Iqbal, Haroon Asghar, Tahani A. Alrebdi, Ali M. Alshehri, Waqas Ahmed and Nasar Ahmed
Metals 2023, 13(7), 1188; https://doi.org/10.3390/met13071188 - 27 Jun 2023
Cited by 8 | Viewed by 3316
Abstract
In this present work, we demonstrated a spectral characterization of copper–iron (Cu-Fe) alloy using optical emission spectroscopy. The Cu-Fe alloy plasma was generated on the target sample surface by directing the laser pulse of Q-switched Nd: YAG of the second harmonic (2ω) with [...] Read more.
In this present work, we demonstrated a spectral characterization of copper–iron (Cu-Fe) alloy using optical emission spectroscopy. The Cu-Fe alloy plasma was generated on the target sample surface by directing the laser pulse of Q-switched Nd: YAG of the second harmonic (2ω) with a 532 nm optical wavelength. The optical emission spectrum was acquired using five miniature spectrometers that lie within the wavelength range of 200–720 nm. The emission plasma was characterized by validating the local-thermodynamical equilibrium (LTE) as well as optically thin (OT) plasma condition. In addition, the LTE condition was verified using the McWhirter criterion, and the OT condition was validated by comparing theoretically calculated intensity ratios with experimental ones. Plasma parameters, including electron number density as well as plasma temperature, were estimated. In the first stage, the plasma temperature was estimated using the Boltzmann-plot method and the two-line method. The average calculated value of the plasma temperatures were 8014 ± 800 K and 8044 ± 800 K using the Boltzmann-plot and two-line methods, respectively. In the second stage, electron number density was estimated using the Saha–Boltzmann equation and stark-broadening method (SBM). The average number density calculated from the SBM was 2.73×1016 cm3 and from the Saha–Boltzmann equation was 3.9×1016 cm3, showing a good agreement. Finally, the comparative compositional analysis was performed using CF-LIBS, Boltzmann Intercept Method, EDX, and ICP-AES, which showed good agreement with that of the standard composition. Full article
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27 pages, 3766 KiB  
Review
Photoionization and Electron–Ion Recombination in Astrophysical Plasmas
by D. John Hillier
Atoms 2023, 11(3), 54; https://doi.org/10.3390/atoms11030054 - 9 Mar 2023
Cited by 6 | Viewed by 3013
Abstract
Photoionization and its inverse, electron–ion recombination, are key processes that influence many astrophysical plasmas (and gasses), and the diagnostics that we use to analyze the plasmas. In this review we provide a brief overview of the importance of photoionization and recombination in astrophysics. [...] Read more.
Photoionization and its inverse, electron–ion recombination, are key processes that influence many astrophysical plasmas (and gasses), and the diagnostics that we use to analyze the plasmas. In this review we provide a brief overview of the importance of photoionization and recombination in astrophysics. We highlight how the data needed for spectral analyses, and the required accuracy, varies considerably in different astrophysical environments. We then discuss photoionization processes, highlighting resonances in their cross-sections. Next we discuss radiative recombination, and low and high temperature dielectronic recombination. The possible suppression of low temperature dielectronic recombination (LTDR) and high temperature dielectronic recombination (HTDR) due to the radiation field and high densities is discussed. Finally we discuss a few astrophysical examples to highlight photoionization and recombination processes. Full article
(This article belongs to the Special Issue Photoionization of Atoms)
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34 pages, 1875 KiB  
Article
How Flexible Is the Concept of Local Thermodynamic Equilibrium?
by Vijay M. Tangde and Anil A. Bhalekar
Entropy 2023, 25(1), 145; https://doi.org/10.3390/e25010145 - 10 Jan 2023
Cited by 3 | Viewed by 2906
Abstract
It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the [...] Read more.
It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions. Full article
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12 pages, 985 KiB  
Review
Insights into AGB Nucleosynthesis Thanks to Spectroscopic Abundance Measurements in Intrinsic and Extrinsic Stars
by Sophie Van Eck, Shreeya Shetye and Lionel Siess
Universe 2022, 8(4), 220; https://doi.org/10.3390/universe8040220 - 29 Mar 2022
Cited by 4 | Viewed by 2674
Abstract
The foundations of stellar nucleosynthesis have been established more than 70 years ago. Since then, much progress has been made, both on the theoretical side, with stellar evolution and nucleosynthesis models of increasing complexity, using more and more accurate nuclear data, and on [...] Read more.
The foundations of stellar nucleosynthesis have been established more than 70 years ago. Since then, much progress has been made, both on the theoretical side, with stellar evolution and nucleosynthesis models of increasing complexity, using more and more accurate nuclear data, and on the observational side, with the number of analyzed stars growing tremendously. In between, the complex machinery of abundance determination has been refined, taking into account model atmospheres of non-solar chemical composition, three-dimensional, non-LTE (non-local thermodynamic equilibrium) effects, and a growing number of atomic and molecular data. Neutron-capture nucleosynthesis processes, and in particular the s-process, have been scrutinized in various types of evolved stars, among which asymptotic giant branch stars, carbon-enhanced metal-poor stars and post-AGB stars. We review here some of the successes of the comparison between models and abundance measurements of heavy elements in stars, including in binaries, and outline some remaining unexplained features. Full article
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13 pages, 538 KiB  
Article
Inelastic Processes in Strontium-Hydrogen Collisions and Their Impact on Non-LTE Calculations
by Svetlana A. Yakovleva, Andrey K. Belyaev and Lyudmila I. Mashonkina
Atoms 2022, 10(1), 33; https://doi.org/10.3390/atoms10010033 - 17 Mar 2022
Cited by 4 | Viewed by 2441
Abstract
Inelastic processes rate coefficients for low-energy Sr + H, Sr+ + H, Sr+ + H, and Sr2+ + H collisions are calculated using the multichannel quantum model approach. A total of 31 scattering channels of SrH [...] Read more.
Inelastic processes rate coefficients for low-energy Sr + H, Sr+ + H, Sr+ + H, and Sr2+ + H collisions are calculated using the multichannel quantum model approach. A total of 31 scattering channels of SrH+ and 17 scattering channels of SrH are considered. The partial cross sections and the partial rate coefficients are hence calculated for 1202 partial processes in total. Using new quantum data for Sr ii + H i collisions, we updated the model atom of Sr ii and performed the non-local thermodynamic equilibrium (non-LTE) calculations. We provide the non-LTE abundance corrections for the Sr ii resonance lines in two grids of model atmospheres, which are applicable to very metal-poor ([Fe/H] 2) dwarfs and giants. Full article
(This article belongs to the Special Issue Interaction of Electrons with Atoms, Molecules and Surfaces)
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7 pages, 641 KiB  
Article
Revealing the True Nature of Hen 2-428
by Nicole Reindl, Nicolle L. Finch, Veronika Schaffenroth, Martin A. Barstow, Sarah L. Casewell, Stephan Geier, Marcelo M. Miller Bertolami and Stefan Taubenberger
Galaxies 2018, 6(3), 88; https://doi.org/10.3390/galaxies6030088 - 14 Aug 2018
Cited by 6 | Viewed by 4608
Abstract
The nucleus of Hen 2-428 is a short orbital period (4.2 h) spectroscopic binary, whose status as potential supernovae type Ia progenitor has raised some controversy in the literature. We present preliminary results of a thorough analysis of this interesting system, which combines [...] Read more.
The nucleus of Hen 2-428 is a short orbital period (4.2 h) spectroscopic binary, whose status as potential supernovae type Ia progenitor has raised some controversy in the literature. We present preliminary results of a thorough analysis of this interesting system, which combines quantitative non-local thermodynamic (non-LTE) equilibrium spectral modelling, radial velocity analysis, multi-band light curve fitting, and state-of-the art stellar evolutionary calculations. Importantly, we find that the dynamical system mass that is derived by using all available He II lines does not exceed the Chandrasekhar mass limit. Furthermore, the individual masses of the two central stars are too small to lead to an SN Ia in case of a dynamical explosion during the merger process. Full article
(This article belongs to the Special Issue Asymmetric Planetary Nebulae VII)
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14 pages, 660 KiB  
Article
Nonequilibrium Entropy in a Shock
by L.G. Margolin
Entropy 2017, 19(7), 368; https://doi.org/10.3390/e19070368 - 19 Jul 2017
Cited by 20 | Viewed by 5439
Abstract
In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of [...] Read more.
In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy. Full article
(This article belongs to the Special Issue Entropy, Time and Evolution)
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