Analytical Fit Research Articles

Relativistic calculation of electron impact excitation of tin: cross sections of importance in plasma modeling

The present work includes the calculation of electron impact excitation cross sections for the fine structure resolved transitions in Sn I and Sn II, using the relativistic distorted wave approximation with the aid of Dirac-Fock multiconfigurational wavefunctions. For Sn I, the cross sections are calculated for the excitations from the fine structure resolved energy levels of the manifolds, , , , and including the ground state, to the fine structure resolved levels of , , , , and manifolds for a wide range of projectile electron energy from 0 to 500 eV. Further, the cross sections are also calculated for the excitations of Sn II from the fine structure resolved energy levels of the manifolds, , , , and including the ground state, to the fine structure resolved levels of , , , , and manifolds. All the cross sections for Sn I except for the excitation from the ground state to the fine-structure resolved excited states of , and manifolds and all the cross sections for Sn II are reported for the first time. In order to ensure the consistency of the present calculations, a comparison of the oscillator strengths and transition probabilities is carried out with the available calculations and measurements. The present cross sections are also compared with previous calculations and observed to be in reasonable agreement. The calculated cross sections are of great interest in the modeling and diagnostic of various plasmas such as laser induced plasma, fusion plasma, etc. Further, to ease the use of calculated cross sections, the analytic fitting of the cross sections is also provided.

PO+−He collision: ab initio potential energy surface and inelastic rotational rate coefficients

ABSTRACT Computations involving quantum dynamics are performed to attain cross-sections corresponding to rotational de-excitation and excitation rates of the PO+ species including four rotational lines recently detected in the interstellar molecular clouds. New ab initio potential energy surface (PES) for PO+−He collision is constructed by using CCSD(T) method and basis set extrapolated to complete basis set limit (CBS) considering a rigid rotor approximation. The PES is then trained to create neural network (NN) model to construct an augmented surface with angular coordinates at 1° intervals. The PES has a global minimum located at $\theta =110{}^{\circ }$ and R = 3.1 Å. An analytical fitting is performed on the NN surface to obtain the first 41 radial coefficients needed to solve the equations of the coupled-channel method. The essentially precise close coupling approach is used to compute the rotational (de-)excitation cross-sections till 1400 cm−1 with rotational states converged up to 26. Further, these cross-sections are thermally averaged to get the rate coefficients for various rotational transitions till 200 K. The propensity rule favours the odd transitions (Δj = 1) for the current study. The rate for the transition 5 → 4 is found to be higher than transition 1→ 0 by a factor of 3.1 at T = 20 K that decreases to 2.1 at T = 100 K.

The Integral Momentum Balance Applied to Metering Orifices to Obtain the Pressure Drop and the Flow Rate With High Accuracy

Abstract The established method of calculating the pressure loss and the flow rate of flows through metering orifices requires empirical correction coefficients. In this paper, a completely momentum-based approach is presented to predict the flow rate and the pressure loss. It is shown that the proposed approach is as precise as the established method but without any empirical coefficient. The required physical coefficients solely base on physics. They pinpoint the sources of the inaccuracy that effects the employment of an empirical correction coefficient to correct the established method—and confirm the empirical correction coefficient on a physical foundation. Ultimately, the physical coefficients evade the effort to experimentally calibrate the theory with the experiments. The integral momentum balance is applied to a control volume comprising the orifice reaching up to the respective pressure metering cross section. Depending on the location of the control volume's open boundaries, the pressure loss or the flow rate can be obtained. To substitute the integral with averaged expressions, the introduced physical coefficients are deduced directly from numerical simulations and parametrized by simple analytical fit functions to complete the momentum-based approach. The numerical model and the proposed approach are both verified by the comparison with the results obtained by the standard ISO 5167:2003. The agreement with the classical calculation method as per ISO 5167:2003 is very high and within the specified limits, which shows that no empirical coefficient is necessary for high-accuracy flow metering using the momentum balance.

Improved accuracy and precision of fat-suppressed isotropic 3D T2 mapping MRI of the knee with dictionary fitting and patch-based denoising

PurposeTo develop an isotropic three-dimensional (3D) T2 mapping technique for the quantitative assessment of the composition of knee cartilage with high accuracy and precision.MethodsA T2-prepared water-selective isotropic 3D gradient-echo pulse sequence was used to generate four images at 3 T. These were used for three T2 map reconstructions: standard images with an analytical T2 fit (AnT2Fit); standard images with a dictionary-based T2 fit (DictT2Fit); and patch-based-denoised images with a dictionary-based T2 fit (DenDictT2Fit). The accuracy of the three techniques was first optimized in a phantom study against spin-echo imaging, after which knee cartilage T2 values and coefficients of variation (CoV) were assessed in ten subjects in order to establish accuracy and precision in vivo. Data given as mean ± standard deviation.ResultsAfter optimization in the phantom, whole-knee cartilage T2 values of the healthy volunteers were 26.6 ± 1.6 ms (AnT2Fit), 42.8 ± 1.8 ms (DictT2Fit, p < 0.001 versus AnT2Fit), and 40.4 ± 1.7 ms (DenDictT2Fit, p = 0.009 versus DictT2Fit). The whole-knee T2 CoV reduced from 51.5% ± 5.6% to 30.5 ± 2.4 and finally to 13.1 ± 1.3%, respectively (p < 0.001 between all). The DictT2Fit improved the data reconstruction time: 48.7 ± 11.3 min (AnT2Fit) versus 7.3 ± 0.7 min (DictT2Fit, p < 0.001). Very small focal lesions were observed in maps generated with DenDictT2Fit.ConclusionsImproved accuracy and precision for isotropic 3D T2 mapping of knee cartilage were demonstrated by using patch-based image denoising and dictionary-based reconstruction.Key points• Dictionary T2 fitting improves the accuracy of three-dimensional (3D) knee T2 mapping.• Patch-based denoising results in high precision in 3D knee T2 mapping.• Isotropic 3D knee T2 mapping enables the visualization of small anatomical details.

Black hole superradiance with dark matter accretion

Studies of black hole superradiance often focus on the growth of a cloud in isolation, accompanied by the spin-down of the black hole. In this paper, we consider the additional effect of the accretion of matter and angular momentum from the environment. We show that, in many cases, the black hole evolves by drifting along the superradiance threshold, in which case the evolution of its parameters can be described analytically or semi-analytically. We quantify the conditions under which accretion can serve as a mechanism to increase the cloud-to-black hole mass ratio, beyond the standard maximum of about 10%. This occurs by a process we call over-superradiance, whereby accretion effectively feeds the superradiance cloud, by way of the black hole. We give two explicit examples: accretion from a vortex expected in wave dark matter and accretion from a baryonic disk. In the former case, we estimate the accretion rate by using an analytical fit to the asymptotic behavior of the confluent Heun function. Level transition, whereby one cloud level grows while the other shrinks, can be understood in a similar way.

Mechanism of the Multistep Catalytic Cycle of 6-Hydroxynicotinate 3-Monooxygenase Revealed by Global Kinetic Analysis

The class A flavoenzyme 6-hydroxynicotinate 3-monooxygenase (NicC) catalyzes a rare decarboxylative hydroxylation reaction in the degradation of nicotinate by aerobic bacteria. While the structure and critical residues involved in catalysis have been reported, the mechanism of this multistep enzyme has yet to be determined. A kinetic understanding of the NicC mechanism would enable comparison to other phenolic hydroxylases and illuminate its bioengineering potential for remediation of N-heterocyclic aromatic compounds. Toward these goals, transient state kinetic analyses by stopped-flow spectrophotometry were utilized to follow rapid changes in flavoenzyme absorbance spectra during all three stages of NicC catalysis: (1) 6-HNA binding; (2) NADH binding and FAD reduction; and (3) O2 binding with C4a-adduct formation, substrate hydroxylation, and FAD regeneration. Global kinetic simulations by numeric integration were used to supplement analytical fitting of time-resolved data and establish a kinetic mechanism. Results indicate that 6-HNA binding is a two-step process that substantially increases the affinity of NicC for NADH and enables the formation of a charge-transfer-complex intermediate to enhance the rate of flavin reduction. Singular value decomposition of the time-resolved spectra during the reaction of the substrate-bound, reduced enzyme with dioxygen provides evidence for the involvement of C4a-hydroperoxy-flavin and C4a-hydroxy-flavin intermediates in NicC catalysis. Global analysis of the full kinetic mechanism suggests that steady-state catalytic turnover is partially limited by substrate hydroxylation and C4a-hydroxy-flavin dehydration to regenerate the flavoenzyme. Insights gleaned from the kinetic model and determined microscopic rate constants provide a fundamental basis for understanding NicC's substrate specificity and reactivity.

Spectral pulsations of evolving soliton molecules in an anomalous dispersion fiber laser

We investigate in detail the spectral pulsation of evolving soliton molecules in an anomalous dispersion fiber laser by utilizing the dispersive Fourier transform technique. The spectral pulsations of an evolving soliton molecule with different properties were achieved in our experiments, such as single-period and double-period pulsation. This type pulsation is characterized by the fact that the soliton molecules periodically experience oscillation in spectral profile and peak power due to the periodic vibration evolution of the internal pulses. However, the continuous weak energy exchange between the two solitons inside the soliton molecules results in an almost invariable pulse energy. In addition, analytical fitting models are given to further reveal the spectral pulsation phenomenon of the evolving soliton molecules. These experimental findings can shed some light on the dynamics of soliton molecules in fiber lasers.

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: IV. Vibrationally-resolved ionization of the ground and excited electronic states

We present a comprehensive set of vibrationally-resolved cross sections for electron-impact ionization of molecular hydrogen and its isotopologues (H2, D2, T2, HD, HT, and DT) in both the ground and excited electronic states. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 1000 eV for ionization of the ground and excited vibrational levels of the X1Σg+, B1Σu+, C1Πu, EF1Σg+, a3Σg+, and c3Πu electronic states, representing all states with united-atoms-limit principle quantum number n=1–2. 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 mccc-db.org.

Data-fed, needs-driven: Designing analytical workflows fit for disease surveillance.

Syndromic surveillance has been an important driver for the incorporation of "big data analytics" into animal disease surveillance systems over the past decade. As the range of data sources to which automated data digitalization can be applied continues to grow, we discuss how to move beyond questions around the means to handle volume, variety and velocity, so as to ensure that the information generated is fit for disease surveillance purposes. We make the case that the value of data-driven surveillance depends on a "needs-driven" design approach to data digitalization and information delivery and highlight some of the current challenges and research frontiers in syndromic surveillance.

A predictive model for personalization of nanotechnology-based phototherapy in cancer treatment.

A major challenge in radiation oncology is the prediction and optimization of clinical responses in a personalized manner. Recently, nanotechnology-based cancer treatments are being combined with photodynamic therapy (PDT) and photothermal therapy (PTT). Predictive models based on machine learning techniques can be used to optimize the clinical setup configuration, including such parameters as laser radiation intensity, treatment duration, and nanoparticle features. In this article we demonstrate a methodology that can be used to identify the optimal treatment parameters for PDT and PTT by collecting data from in vitro cytotoxicity assay of PDT/PTT-induced cell death using a single nanocomplex. We construct three machine learning prediction models, employing regression, interpolation, and low- degree analytical function fitting, to predict the laser radiation intensity and duration settings that maximize the treatment efficiency. To examine the accuracy of these prediction models, we construct a dedicated dataset for PDT, PTT, and a combined treatment; this dataset is based on cell death measurements after light radiation treatment and is divided into training and test sets. The preliminary results show that the performance of all three models is sufficient, with death rate errors of 0.09, 0.15, and 0.12 for the regression, interpolation, and analytical function fitting approaches, respectively. Nevertheless, due to its simple form, the analytical function method has an advantage in clinical application and can be used for further analysis of the sensitivity of performance to the treatment parameters. Overall, the results of this study form a baseline for a future personalized prediction model based on machine learning in the domain of combined nanotechnology- and phototherapy-based cancer treatment.

Linac primary barrier transmission: Flattening filter free and field size dependence.

There is widespread consensus in the literature that flattening filter free (FFF) beams have a lower primary barrier transmission than flattened beams. Measurements presented here, however, show that for energy compensated FFF beams, the barrier transmission can be as much as 70% higher than for flattened beams. The ratio of the FFF barrier transmission to the flattened beam barrier transmission increases with increasing barrier thickness. The use of published FFF TVL data for energy compensated FFF beams could lead to an order of magnitude underestimate of the air kerma rate. There are little data in the literature on the field size dependence of the barrier transmission for flattened beams. Barrier transmission depends on the field size at the barrier, not at isocenter Measurements are presented showing the relative dependence of barrier transmission on the field size, measured at the barrier, for 6MV and 10MV beams. An analytical fitting formula is provided for the field size dependence. For field sizes greater than about 150cm in side length, the field size dependence is minimal. For field sizes less than about 100cm, the transmission declines rapidly as the field size decreases.

Quartz defect pair model for exo-electron emission

We present a defect pair model analysis of the physical processes that underlie both thermally stimulated exo-electron emission (TSEE) and optically stimulated exo-electron emission (OSEE) from quartz. We commence our study by examining the sources of electrons within the defect pair model. We then proceed to review the relevant literature on exo-electron emission and note that the electron affinity is the exo-electron parameter best suited for application within our study. Following a brief description of the early literature on quartz TSEE we examine the more recent TSEE and OSEE experimental studies in relation to the underlying electron-generating defect reactions, revealing that in both cases the observed temperature dependencies associated with exo-electron emission can be curve fitted by readily derived parametric expressions. In particular, we find that in each case the electron affinity appears within an appropriate Arrhenius factor. We also find from our analytical curve fitting procedures that TSEE and OSEE are further proportional to the temperature dependencies associated respectively with TL and OSL.

The Li + CaF → Ca + LiF chemical reaction under cold conditions.

The calcium monofluoride (CaF) molecule has emerged as a promising candidate for precision measurements, quantum simulation, and ultracold chemistry experiments. Inelastic and reactive collisions of laser cooled CaF molecules in optical tweezers have recently been reported and collisions of cold Li atoms with CaF are of current experimental interest. In this paper, we report ab initio electronic structure and full-dimensional quantum dynamical calculations of the Li + CaF → LiF + Ca chemical reaction. The electronic structure calculations are performed using the internally contracted multi-reference configuration-interaction method with Davidson correction (MRCI + Q). An analytic fit of the interaction energies is obtained using a many-body expansion method. A coupled-channel quantum reactive scattering approach implemented in hyperspherical coordinates is adopted for the scattering calculations under cold conditions. Results show that the Li + CaF reaction populates several low-lying vibrational levels and many rotational levels of the product LiF molecule and that the reaction is inefficient in the 1-100 mK regime allowing sympathetic cooling of CaF by collisions with cold Li atoms.

Machine Learning-Enhanced Computational Reverse-Engineering Analysis for Scattering Experiments (CREASE) for Analyzing Fibrillar Structures in Polymer Solutions

In this work, we present a machine learning (ML)-enhanced computational reverse-engineering analysis of scattering experiments (CREASE) approach to analyze the small-angle scattering profiles from polymer solutions with assembled semiflexible fibrils with dispersity in fibril diameters (e.g., aqueous solutions of methylcellulose fibrils). This work is an improvement over the original CREASE method [Beltran-Villegas, D. J.; J. Am. Chem. Soc., 2019, 141, 14916−14930], which identifies relevant dimensions of assembled structures in polymer solutions from their small-angle scattering profiles without relying on traditional analytical models. Here, we improve the original CREASE approach by incorporating ML for analyzing assembled semiflexible fibrillar structures with disperse fibril diameters. We first validate our CREASE approach without ML by taking as input the scattering profiles of in silico structures with known dimensions (diameter, Kuhn length) and reproducing as output those known dimensions within error. We then show how the incorporation of ML (specifically an artificial neural network, denoted as NN) within the CREASE approach improves the speed of workflow without sacrificing the accuracy of the determined fibrillar dimensions. Finally, we apply NN-enhanced CREASE to experimental small-angle X-ray scattering profiles from methylcellulose fibrils obtained by Lodge, Bates, and co-workers [Schmidt, P. W.; Macromolecules, 2018, 51, 7767−7775] to determine fibril diameter distribution and compare NN-enhanced CREASE’s output with their fibril diameter distribution fitted using analytical models. The diameter distributions of methylcellulose fibrils from NN-enhanced CREASE are similar to those obtained from analytical model fits, confirming the results by Lodge, Bates, and co-workers that methylcellulose form fibrils with consistent average diameters of ∼15–20 nm regardless of the molecular weight of methylcellulose chains. The successful implementation of NN-enhanced CREASE in handling experimental scattering profiles of complex macromolecular assembled structures with dispersity in dimensions demonstrates its potential for application toward other unconventional fibrillar systems that may not have appropriate analytical models.

What can Gaussian processes really tell us about supernova light curves? Consequences for Type II(b) morphologies and genealogies

ABSTRACT Machine learning has become widely used in astronomy. Gaussian process (GP) regression in particular has been employed a number of times to fit or resample supernova (SN) light curves, however by their nature typical GP models are not suited to fit SN photometric data and they will be prone to overfitting. Recently GP resampling was used in the context of studying the morphologies of Type II and IIb SNe and they were found to be clearly distinct with respect to four parameters: the rise time (trise), the magnitude difference between 40 and 30 d post-explosion (Δm40–30), the earliest maximum (post-peak) of the first derivative (dm1), and minimum of the second derivative (dm2). Here we take a close look at GP regression and its limitations in the context of SN light curves in general, and we also discuss the uncertainties on these specific parameters, finding that dm1 and dm2 cannot give reliable astrophysical information. We do reproduce the clustering in trise–Δm40–30 space, although it is not as clear cut as previously presented. The best strategy to accurately populate the trise–Δm40–30 space will be to use an expanded sample of high-quality light curves [such as those in the Asteroid Terrestrial-impact Last Alert System (ATLAS) transient survey] and analytical fitting methods. Finally, using the bpass fiducial models, we predict that future photometric studies will reveal clear clustering of the Type IIb and II light curve morphologies with a distinct continuum of transitional events.

Outer disc edge: properties of low-frequency aperiodic variability in ultracompact interacting binaries

ABSTRACT Flickering, and more specifically aperiodic broad-band variability, is an important phenomenon used in understanding the geometry and dynamics of accretion flows. Although the inner regions of accretion flows are known to generate variability on relatively fast time-scales, the broad-band variability generated in the outer regions has mostly remained elusive due to its long intrinsic variability time-scales. Ultracompact AM CVn systems are relatively small when compared to other accreting binaries and are well suited to search and characterize low-frequency variability. Here, we present the first low-frequency power spectral analysis of the ultracompact accreting white dwarf system SDSS J1908+3940. The analysis reveals a low-frequency break at ∼6.8 × 10−7 Hz in the time-averaged power spectrum as well as a second higher frequency component with characteristic frequency of ∼1.3 × 10−4 Hz. We associate both components with the viscous time-scales within the disc through empirical fits to the power spectrum as well as analytical fits using the fluctuating accretion disc model. Our results show that the low-frequency break can be associated with the outer disc regions of a geometrically thin accretion flow. The detection of the low-frequency break in SDSS J1908+3940 provides a precedent for further detection of similar features in other ultracompact accreting systems. More importantly, it provides a new observable that can help constrain simulations of accretion flows.

Identification of ORR activity of random graphene-based systems using the general descriptor and predictive model equation

Carbon based electrocatalysts are well known promising candidates for the oxygen reduction reaction (ORR), but the random approach to find the best catalyst using experimental method delayed the screening process and it leads to a huge cost with less proficiency. Using Quantum Mechanics followed by Machine Learning (QM/ML) approach, we can predict the best catalyst faster way and the origin of the cause can be identified for further development of carbon-based catalyst. Using the π electronic descriptor unveiled using density functional theory, we applied the analytical simple fit method and six different machine learning algorithms to develop a highly effective predictive model to estimate ΔGOH. Furthermore, structural relations of ZGNR and AGNR are demonstrated to estimate the Dπ(EF), R-Oπ, and ΔGOH of different widths of ribbon that reduces additional DFT calculations. By applying both SVR predictive model and structural relations, we predicted the ORR performance of 2500 sites of GNRs and listed a few most ideal active carbon sites with lower overpotential (η < 0.5V). To validate our study, we predicted the ORR performance of different sites in 0D, 1D, 2D doped graphene systems using SVR model and confirmed the values with the DFT computed results.

Correlations for the specific heat capacity of [formula omitted] derived from molecular dynamics

UO2 is the primary conventional fuel used in most nuclear reactors with Gd2O3 commonly added as a burnable absorber to produce a more level power distribution in the reactor core at the beginning of operation. It can also be mixed with other actinide oxides to produce mixed oxide (MOx) fuel. In this study, molecular dynamics simulations were used to predict the specific heat capacity of Gd-doped PuO2, UO2 and (U,Pu)O2 MOx accommodating Gd3+ substituted at cation sites via two charge compensation mechanisms - oxygen vacancy formation and the oxidation of U4+ to U5+. The specific heat capacity values for PuO2 and UO2 are in good agreement with other studies showing a distinct peak at high temperatures - above 1800 K. As Gd3+ is added, the peak height reduces for each composition considered. An analytical fit was applied to the data where Gd3+ was fully charge compensated by either oxygen vacancies or U5+. The expression was then validated by predicting the specific heat capacity for three compositions of (UxPu1−x)1−yGdyO2−z containing both oxygen vacancies and U5+, and compared to molecular dynamics data.

Impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves

Black holes located within a dark matter cloud can create overdensity regions known as dark matter spikes. The presence of spikes modifies the gravitational-wave signals from binary systems through changes in the gravitational potential or dynamical friction effects. We assess the importance of including relativistic effects in both the dark matter distribution and the dynamical friction. As a first step we numerically calculate the particle dark matter spike distribution in full general relativity, using both Hernquist and Navarro-Frenk-White profiles in a Schwarzschild background, and we produce analytical fits to the spike profiles for a large range of scale parameters. Then we use a post-Newtonian prescription for the gravitational-wave dephasing to estimate the effect of relativistic corrections to the spike profile and to the dynamical friction. Finally we include the torques generated by dynamical friction in fast-to-generate relativistic models for circular extreme mass-ratio inspirals around a nonspinning black hole. We find that both types of relativistic corrections positively impact the detectability of dark matter effects, leading to higher dephasings and mismatches between gravitational-wave signals with and without dark matter spikes.

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: III. Vibrational excitation via electronic excitation and radiative decay

We present state-resolved cross sections for vibrational excitation via electronic excitation followed by radiative decay (ERD), for electrons scattering on all bound vibrational levels of the ground electronic state (X1Σg+) of molecular hydrogen and its isotopologues (H2, HD, HT, D2, DT and T2). We consider excitation of the singlet n=2–3 states (where n refers to the united-atoms-limit principle quantum number) and account for all possible decay pathways back to the bound vibrational levels of the ground electronic state (X1Σg+) to produce an estimate for the ERD cross sections. A selection of the results are presented in graphical form and a full data set is provided as both numerical values and analytic fit functions in supplementary data files. The uncertainty in the cross sections is estimated to be 11%, except for scattering on the highest bound vibrational level of HD, HT, D2, and DT, where the uncertainty is 21%. The data can be downloaded from the MCCC database at mccc-db.org.