Analytical Fit Research Articles

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: I. Fully vibrationally-resolved electronic excitation of H[formula omitted

We present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of molecular hydrogen suitable for implementation in collisional-radiative models. The adiabatic-nuclei molecular convergent close-coupling method is used to calculate cross sections for excitation of all bound vibrational levels and dissociative excitation of the B1Σu+, C1Πu, EF1Σg+, B′1Σu+, GK1Σg+, I1Πg, J1Δg, D1Πu, H1Σg+, b3Σu+, c3Πu, a3Σg+, e3Σu+, d3Πu, h3Σg+, g3Σg+, i3Πg, and j3Δg electronic states from all vi=0–14 bound vibrational levels of the ground electronic (X1Σg+) state. The data set consists of cross sections from threshold to 500 eV for over 5000 transitions, representing all possible electronic and vibrational transitions between the X1Σg+ state and the n=2–3 singlet and triplet states (where n refers to the united-atoms-limit principle quantum number). The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at http://mccc-db.org.

X-ray measurements of thin liquid films in gas–liquid pipe flow

This paper presents a method for reconstructing the thickness profile of the thin liquid film being present in steady, fully developed gas–liquid annular pipe flow, taking advantage of nonintrusive X-ray measurements. Experiments have been performed with low liquid loading, annular flows, in a near horizontal pipe system (inclination +2.5°), using a high-density gas (SF6) and Exxsol D60 oil. Special care was taken to ensure the flows were fully developed, and statistically steady. The superficial gas velocity was maintained at a constant value of 10 m/s, while the superficial liquid velocity was varied between 0.5 mm/s and 42 mm/s. The X-ray measurements were supplemented by gamma ray densitometer data and isokinetic data. An explicit mathematical method is presented, whereby the shape and thickness of very thin liquid films can be reconstructed if X-ray images of the flow have been obtained from two independent directions: one with a vertical view of the pipe, and another with a horizontal side view. The method can be straightforwardly applied to cases where the film volume dominates the total volume of droplets suspended in the gas phase. This condition is generally satisfied for the experiments presented in this paper, as verified by isokinetic measurements.Mean liquid hold-up values determined by gamma densitometer are in reasonable agreement with the X-ray results. It is found that the mean film thickness at any position on the pipe wall increases with the superficial liquid velocity. While the film thickness is maximal at the pipe bottom in virtually all experimental cases, its profile exhibits multiple local maxima and minima, with the smallest thickness apparently 20°–30° away from at the pipe top. The presented film reconstruction method is highly sensitive; even at extremely low liquid levels, with a superficial liquid velocity less than 0.01% of the mixture velocity, the film and its thickness profile are clearly detected. An analytical fit for the film profile as a function of perimeter angle and superficial liquid velocity is given. The fit captures the main features of the profile as derived from X-ray measurements, for thin films with maximum thickness less than 5% of the pipe diameter.

Pilgrim: A thermal rate constant calculator and a chemical kinetics simulator

Pilgrim is a program written in Python and designed to use direct dynamics in the calculation of thermal rate constants of chemical reactions by the variational transition state theory (VTST), based on electronic structure calculations for the potential energy surface. Pilgrim can also simulate reaction mechanisms using kinetic Monte Carlo (KMC).For reaction processes with many elementary steps, the rate constant of each of these steps can be calculated by means of conventional transition state theory (TST) or by using VTST. In the current version, Pilgrim can evaluate thermal rates using the canonical version of reaction-path VTST, which requires the calculation of the minimum energy path (MEP) associated with each elementary step or transition structure. Multi-dimensional quantum effects can be incorporated through the small-curvature tunneling (SCT) approximation. These methodologies are available both for reactions involving a single structure of the reactants and the transition state and also for reactions involving flexible molecules with multiple conformations of the reactant and/or of the transition state. For systems with many conformers, the program can evaluate each of the elementary reaction rate constants by multipath canonical VTST or multi-structural VTST. Moreover, the reactant can be unimolecular or bimolecular.Torsional anharmonicity can be incorporated through either the MSTor or the Q2DTor programs. Dual-level calculations are also available in Pilgrim: automatic high-level single-point energies can be used to correct the energy of reactants, transition states, products, and MEP points using the interpolated single-point energies (ISPE) algorithm.When the rate constants of all the chemical processes of interest are known, by means of their calculation using Pilgrim or alternatively through analytical fits to the rate constants as functions of temperature, it is possible to simulate a multistep mechanism under specified laboratory conditions using KMC. This algorithm allows performing a kinetic simulation to monitor the evolution of each chemical species with time and obtain the product yields. Program summaryProgram Title: PilgrimCPC Library link to program files:http://dx.doi.org/10.17632/24cj4dwxvg.1Developer’s repository link:https://github.com/cathedralpkg/pilgrim/releases; https://comp.chem.umn.edu/pilgrim; https://conservancy.umn.edu/handle/11299/166578Licensing provisions: MITProgramming language: Python 3Nature of problem: Calculation of thermal rate constants for bimolecular and unimolecular chemical reactions and simulation of reaction mechanismsSolution method: The program uses variational transition state theory to calculate thermal rate constants and kinetic Monte Carlo to simulate reaction mechanisms.Restrictions and unusual features: The program cannot treat reactions without saddle points. Unimolecular reactions are calculated only in the high-pressure limit. Direct dynamics calculations with Pilgrim require an electronic structure package to be supplied by the user; currently, Pilgrim supports the Gaussian [Frisch et al. (2003), Frisch et al. (2016a), Frisch et al. (2016b)] and Orca [Neese (2011)] electronic structure packages. Pilgrim has an especially powerful suite of options for handling torsional anharmonicity and multistructural effects.

Galactic ionizing photon budget during the epoch of reionization in the Cosmic Dawn II simulation

ABSTRACT Cosmic Dawn II yields the first statistically meaningful determination of the relative contribution to reionization by galaxies of different halo mass, from a fully coupled radiation-hydrodynamics simulation of the epoch of reionization large enough (∼100 Mpc) to model global reionization while resolving the formation of all galactic haloes above ${\sim}10^8 \, {\rm M}_{\odot }$. Cell transmission inside haloes is bi-modal – ionized cells are transparent, while neutral cells absorb the photons their stars produce – and the halo escape fraction fesc reflects the balance of star formation rate (SFR) between these modes. The latter is increasingly prevalent at higher halo mass, driving down fesc (we provide analytical fits to our results), whereas halo escape luminosity, proportional to fesc × SFR, increases with mass. Haloes with dark matter masses within $6\times 10^{8} \, {\rm M}_{\odot }\lt M_{\rm halo}\lt 3 \times 10^{10} \, {\rm M}_{\odot }$ produce ∼80 per cent of the escaping photons at z = 7, when the universe is 50 per cent ionized, making them the main drivers of cosmic reionization. Less massive haloes, though more numerous, have low SFRs and contribute less than 10 per cent of the photon budget then, despite their high fesc. High-mass haloes are too few and too opaque, contributing <10 per cent despite their high SFRs. The dominant mass range is lower (higher) at higher (lower) redshift, as mass function and reionization advance together (e.g. at z = 8.5, xH i = 0.9, $M_{\rm halo}\lt 5\times 10^9 \, {\rm M}_{\odot }$ haloes contributed ∼80 per cent). Galaxies with UV magnitudes MAB1600 between −12 and −19 dominated reionization between z = 6 and 8.

Improved Infrared Optical Constants from Pressed Pellets: II. Ellipsometric n and k Values for Ammonium Sulfate with Variability Analysis.

Infrared reflectance analysis is facilitated via the comparison of spectra recorded in situ to a databank of actual or synthetic infrared reflectance spectra. It has recently been shown that reference spectra corresponding to the many different morphological forms of the same chemical can be generated synthetically using the imaginary, k, and real, n, components of the complex refractive index, = n + ik. One method to obtain the n and k vectors is infrared ellipsometry, which measures the changes in amplitude, tan Ψ, and phase, Δ, of polarized light reflected from the sample both as a function of wavenumber and angle of incidence. The method requires specularly reflected light, so best results are usually obtained with polished planar samples of large surface area. Due to the difficulties of obtaining such samples, however, we investigate the possibility of pressing powders of neat materials and obtaining the corresponding optical constants from the pellets. In this paper, variability in the sample pellet and preparation method is investigated, as is variability in the fitting procedure for the derived optical constants. The n/k vectors are derived from the measured ellipsometric parameters, tan ψ and Δ, as they are fit by an oscillator model which yield n() and k() vectors as a function of wavenumber, . Construction of the oscillator model is not automatic and depends on significant input from the analyst as well as the sample's physical characteristics. For pellet pressing, the experimental variability was found to be minimized for size-selected powdered samples as gauged by the minimal variance in ψ and Δ for three different pellets; similarly, the analytical precision for multiple measurements of the same pellet was also quite good, suggesting that a pressed pellet is a viable sample preparation method. Experimental variabilities were comparatively small; the greatest variability came in the analytic fitting procedure with differences in the k-peak values up to 10% for only the sharpest bands arising from four different fits to the same data set. The final ellipsometric n/k data are compared to literature values obtained from crystalline ammonium sulfate ((NH4)2SO4) samples as well as single-angle reflectance measurements that also used pressed pellets. Comparison with the previous literature values shows generally good agreement, although larger k-values are observed for the independent sets of data derived from pressed pellets. These data are suggested as an improved set of optical constants for (NH4)2SO4.

Nucleon effective mass in hot dense matter

Nucleon effective masses are studied in the framework of the Brueckner-Hartree-Fock many-body approach at finite temperature. Self-consistent calculations using the Argonne $V_{18}$ interaction including microscopic three-body forces are reported for varying temperature and proton fraction up to several times the nuclear saturation density. Our calculations are based on the exact treatment of the center-of-mass momentum instead of the average-momentum approximation employed in previous works. We discuss in detail the effects of the temperature together with those of the three-body forces, the density, and the isospin asymmetry. We also provide an analytical fit of the effective mass taking these dependencies into account. The temperature effects on the cooling of neutron stars are briefly discussed based on the results for betastable matter.

Spectral signatures of H-rich material stripped from a non-degenerate companion by a Type Ia supernova

The single-degenerate scenario for Type Ia supernovae should yield metal-rich ejecta that enclose some stripped material from the non-degenerate H-rich companion star. We present a large grid of non-local thermodynamic equilibrium steady-state radiative transfer calculations for such hybrid ejecta and provide analytical fits for the Hα luminosity and equivalent width. Our set of models covers a range of masses for 56Ni and the ejecta, for the stripped material (Mst), and post-explosion epochs from 100 to 300 d. The brightness contrast between stripped material and metal-rich ejecta challenges the detection of H I and He I lines prior to ~100 d. Intrinsic and extrinsic optical depth effects also influence the radiation emanating from the stripped material. This inner denser region is marginally thick in the continuum and optically thick in all Balmer lines. The overlying metal-rich ejecta blanket the inner regions, completely below about 5000 Å, and more sparsely at longer wavelengths. As a consequence, Hβ should not be observed for all values of Mst up to at least 300 days, while Hα should be observed after ~100 d for all Mst ≥ 0.01 M⊙. Observational non-detections capable of limiting the Hα equivalent width to <1 Å set a formal upper limit of Mst < 0.001M⊙. This contrasts with the case of circumstellar-material (CSM) interaction, not subject to external blanketing, which should produce Hα and Hβ lines with a strength dependent primarily on CSM density. We confirm previous analyses that suggest low values of order 0.001 M⊙ for Mst to explain the observations of the two Type Ia supernovae with nebular-phase Hα detection, in conflict with the much greater stripped mass predicted by hydrodynamical simulations for the single-degenerate scenario. A more likely solution is the double-degenerate scenario, together with CSM interaction, or enclosed material from a tertiary star in a triple system or from a giant planet.

Magnetopause Compressibility at Saturn with Internal Drivers

AbstractWe use magnetopause crossings of the Cassini spacecraft to study the response of Saturn's magnetosphere to changes in external and internal drivers. We explain how solar wind pressure can be corrected to account for the local variability in internal plasma particle pressure. The physics‐based method is applied to perform the most robust estimation of magnetopause compressibility at Saturn to date, using 7 years' worth of magnetometer data from the Cassini mission and accounting for variable internal drivers—particle pressure and azimuthal ring current. The concept of magnetopause compressibility is generalized to quantitatively account for its detailed variation with respect to the position of the magnetopause. An analytical fit is provided to map the compressibility index to values of the stand‐off distance. In particular, the procedure shows that the Kronian system appears to behave similarly to that of Jupiter when expanded outwards and more like the Earth's magnetopause when compressed.

Air-Kerma to Personal Dose Equivalent $$\mathbf{H}_{\mathbf{p}}\mathbf{(0.07,\boldsymbol{\alpha})}$$ Conversion Coefficients for Monoenergetic Photons

This study aims to calculate the air Kerma to personal dose equivalent conversion coefficients $${H}_{p}(0.07)$$ for mono-energetic photons from 0.015 to 10 MeV for angles of incidence from 0 $${}^{\circ}$$ to a 75 $${}^{\circ}$$ in steps of 15 $${}^{\circ}$$ using Monte Carlo (MC). In addition to this, we propose a new equation to perform an analytical fit of our Monte Carlo calculated conversion coefficients for photons. $${H}_{p}(0.07)/K_{air}$$ values have been determined by two terms: in term of absorbed dose, according to the definition of this quantity, and also with the term of Kerma approximation. The results obtained are compared to those published in Joint report of ICRU and ICRP, 2017. A good agreement with reference data with a local difference less than $$2\%$$ was observed.

High pressure melt curve of iron from atom-in-jellium calculations

Although usually considered as a technique for predicting electron states in dense plasmas, atom-in-jellium calculations can be used to predict the mean displacement of the ion from its equilibrium position in colder matter, as a function of compression and temperature. The Lindemann criterion of a critical displacement for melting can then be employed to predict the melt locus, normalizing for instance to the observed melt temperature or to more direct simulations such as molecular dynamics (MD). This approach reproduces the high pressure melting behavior of Al as calculated using the Lindemann model and thermal vibrations in the solid. Applied to Fe, we find that it reproduces the limited-range melt locus of a multiphase equation of state (EOS) and the results of ab initio MD simulations, and agrees less well with a Lindemann construction using an older EOS. The resulting melt locus lies significantly above the older melt locus for pressures above 1.5\,TPa, but is closer to recent ab initio MD results and extrapolations of an analytic fit to them. This study confirms the importance of core freezing in massive exoplanets, predicting that a slightly smaller range of exoplanets than previously assessed would be likely to exhibit dynamo generation of magnetic fields by convection in the liquid portion of the core.

A New Fitting Method for Ambipolar Diffusion Length Extraction in Thin Film Structures Using Photoluminescence Measurement with Scanning Excitation

A new simple method is proposed to extract the ambipolar diffusion length for two-dimensional (2D) electronic transport in thin film structures using a scanning photoluminescence microscopy (SPLM) setup. No spatially-resolved photoluminescence detection methods are required. By measuring the excitation-position-dependent PL intensity across the edge of a semiconductor, ambipolar diffusion length can be extracted from the SPLM profile through a simple analytic fitting function. Numerical simulation was first used to verify the fitting method. Then the fitting method was applied to extract the ambipolar diffusion length from the measured SPLM profile of a GaAs thin film structure. Carrier lifetime was obtained in an accompanying time-resolved photoluminescence measurement under the same excitation condition, and thus the ambipolar diffusion coefficient can be determined simultaneously. The new fitting method provides a simple way to evaluate carrier transport properties in 2D electronic transport structures such as thin films or quantum wells.

Air-kerma to Hp(0.07), Hp(3), and Hp(10) conversion coefficients for monoenergetic photons

This work aims for calculating a new set of the personal dose equivalent conversion coefficients Hp(d)/Kair when d = 0.07, 3, and 10 mm, for monoenergetic photons beams ranged from 0.015 to 10 MeV, which have incident on ICRU slab phantom for Hp (0.07) and Hp (10) and cylindrical phantom for Hp (3). The new cylindrical phantom of the ORAMED project was proposed for calculating the eye lens dose equivalent as a cylinder much better approximates the form of a head than a slab. The calculations were carried out with MC and an analytical fit is applied to the data. Our results are found in a good agreement with those previously published, with a local difference less than 1.5%. We have concluded that new analytical fits provide a suitable method for determining conversion coefficients for discrete incident such as MC.

Conversion coefficients from fluence and air kerma to personal dose equivalent for monoenergetic photons using analytical fit and Monte Carlo simulation

Abstract The present study aims to calculate a new database of conversion coefficients from fluence and air Kerma to personal dose equivalent in two terms: absorbed dose and Kerma-approximations. In this work, we propose a new equation to perform an analytical fit of our Monte Carlo (MC) calculated conversion coefficients for photons for different angles. Also, we have calculated the conversion coefficients using the EGSnrc code. The conversion coefficients have been calculated for beams of monoenergetic photons from 0.015 to 10 MeV, incident on phantom ICRU for angles of incidence from 0° to a 75° in steps of 15°. Our computed values agree well when compared with those published for the ICRU 57 in Kerma-approximations with statistical uncertainties in the calculation around 2%. We can conclude from this work that the analytical approach is successful and powerful such as Monte Carlo methods to calculate the operational quantities.

Fingerprint matching of beyond-WIMP dark matter: neural network approach

Improving observation of galactic-scale structure provide important clues to dark matter properties. While weakly interacting massive particles (WIMPs) provide cold dark matter on galactic scales, beyond-WIMP candidates suppress the galactic-scale structure formation. Nevertheless, directly constraining microscopic model parameters from observations involves an interdisciplinary and time-consuming procedure. In practice, some parametrizations of the linear matter power spectrum are introduced. The particle physics community calculates the linear matter power spectrum for a given model parameter set, while the astrophysics community places the constraint on the power spectrum parameters. If maps between the model parameters and the power spectrum parameters and maps between the power spectrum parameters and the likelihood (or observables) are shared among the two communities, they are very useful for both communities, e.g., making a constraint plot of the model parameter space. As suggested in the literature, however, it is necessary to introduce multiple parameters to precisely describe the linear matter power spectrum in a wide range of beyond-WIMP models. It challenges us to express and share the non-linear maps between multiple parameters. In this work, we propose utilizing the neural network technique to this end. The neural network technique is known to automatically express and efficiently share non-linear maps, although it is not as simple as analytic fitting formulas if available. To demonstrate how to work with a concrete example, we consider a simplified model of light feebly interacting massive particles and simple observables for galactic-scale structure. We also reveal the obtained neural networks through the arXiv website.

High-precision four-loop mass and wave function renormalization in QED

The 4-loop QED mass and wave function renormalization constants Z2 and Zm have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants Z2OS and ZmOS which can be obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities.

Direct collapse to supermassive black hole seeds: the critical conditions for suppression of H2 cooling

ABSTRACT Observations of high-redshift quasars imply the presence of supermassive black holes (SMBHs) already at $z$ ∼ 7.5. An appealing and promising pathway to their formation is the direct collapse scenario of a primordial gas in atomic-cooling haloes at $z$ ∼ 10–20, when the $\rm H_{2}$ formation is inhibited by a strong background radiation field, whose intensity exceeds a critical value, Jcrit. To estimate Jcrit, typically, studies have assumed idealized spectra, with a fixed ratio of $\rm H_{2}$ photodissociation rate $k_{\rm H_2}$ to the $\rm H^-$ photodetachment rate $k_{\rm H^-}$. This assumption, however, could be too narrow in scope as the nature of the background radiation field is not known precisely. In this work we argue that the critical condition for suppressing the H2 cooling in the collapsing gas could be described in a more general way by a combination of $k_{\rm H_2}$ and $k_{\rm H^-}$ parameters, without any additional assumptions about the shape of the underlying radiation spectrum. By performing a series of cosmological zoom-in simulations covering a wide range of relevant $k_{\rm H_2}$ and $k_{\rm H^-}$ parameters, we examine the gas flow by following evolution of basic parameters of the accretion flow. We test under what conditions the gas evolution is dominated by $\rm H_{2}$ and/or atomic cooling. We confirm the existence of a critical curve in the $k_{\rm H_2}{\!-\!}k_{\rm H^-}$ plane and provide an analytical fit to it. This curve depends on the conditions in the direct collapse, and reveals domains where the atomic cooling dominates over the molecular cooling. Furthermore, we have considered the effect of $\rm H_{2}$ self-shielding on the critical curve, by adopting three methods for the effective column density approximation in $\rm H_{2}$. We find that the estimate of the characteristic length scale for shielding can be improved by using λJeans25, which is 0.25 times that of the local Jeans length, which is consistent with previous one-zone modelling.

Caloric and isothermal equations of state of solids: empirical modeling with multiply broken power-law densities

Empirical equations of state (EoSs) are developed for solids, applicable over extended temperature and pressure ranges. The EoSs are modeled as multiply broken power laws, in closed form without the use of ascending series expansions; their general analytic structure is explained and specific examples are studied. The caloric EoS is put to test with two carbon allotropes, diamond and graphite, as well as vitreous silica. To this end, least-squares fits of broken power-law densities are performed to heat capacity data covering several logarithmic decades in temperature, the high- and low-temperature regimes and especially the intermediate temperature range where the Debye theory is of limited accuracy. The analytic fits of the heat capacities are then temperature integrated to obtain the entropy and caloric EoS, i.e. the internal energy. Multiply broken power laws are also employed to model the isothermal EoSs of metals (Al, Cu, Mo, Ta, Au, W, Pt) at ambient temperature, over a pressure range up to several hundred GPa. In the case of copper, the empirical pressure range is extended into the TPa interval with data points from DFT calculations. For each metal, the parameters defining the isothermal EoS (i.e. the density–pressure relation) are inferred by nonlinear regression. The analytic pressure dependence of the compression modulus of each metal is obtained as well, over the full data range.

On Weighing the Conflicting Cost Functions for Optimal Energy Management of Electrified Powertrain

Besides fuel economy, gear shifting and engine start-stop frequency in the optimal energy management for hybrid electric vehicles (HEVs) will also influence the overall performance and drivability. However, such drivability concerns will also impact the vehicle’s energy efficiency. To solve this conflicting optimization problem, this paper aims to find the proper weighing of the conflicting costs to achieve a right balance based on sensitivity analysis. The problem is formulated by expanding the conventional cost function with additional penalty items for gear shifting and engine start-stop, and a range extended hybrid delivery truck is modeled as a case study. Dynamic programming (DP) algorithm is applied to guarantee all the comparisons are under the same benchmark, and a split-DP solution is carried out to accelerate the searching process. Analytical fitting and trend analysis methods are used to find the proper penalty factors. Eventually, a comprehensive comparison among optimized, experiential and none penalty factors is shown, indicating that such appropriate weighing can significantly improve drivability with only 0.2% more fuel cost.

Electron impact excitation of highly charged Ge-Like Xe ion

SynopsisA systematic study of electron impact excitation of Ge-like highly charged xenon ions have been carried out in Extreme Ultraviolet (EUV) range within fully relativistic multiconfiguration Dirac-Fock framework. The cross section calculation reported here are performed for dipole allowed transitions for Xe22+ ions from ground state 4s24p2 to 4s24p3 and 4s24p4d excited fine structure levels. The analytic fitting for the cross section data for incident electron energy range within 50 to 1500 eV have been provided for further applications in various plasma diagnostic techniques.

High-precision calculation of the light curve and its interpretation

We present a highly precise calculation of the theoretical light curve and its derivatives for a binary star-planet system in an elliptical orbit. We also describe an analytical fitting by limb-darkening coefficients to reduce the number of parameters for nonlinear fitting. We demonstrate the practical importance of the precision computation of theoretical light curves through the example of the interpretation of the light curve of HD 209458 and the synthetic light curve. We also compare the results obtained using our algorithm to those provided by a lower-precision algorithm to demonstrate the benefits of computing with a higher precision. We discuss the capability of making more accurate conclusions concerning the agreement of the observed light curve with the adopted model.