Spectral Points Research Articles

A discrete integral transform for rapid spectral synthesis

Accurate synthetic spectra that rely on large Line-By-Line (LBL)-databases are used in a wide range of applications such as high temperature combustion, atmospheric re-entry, planetary surveillance and laboratory plasmas. Conventionally synthetic spectra are calculated by computing a lineshape for every spectral line in the database and adding those together, which may take multiple hours for large databases. In this paper we propose a new approach for spectral synthesis based on an integral transform: the synthetic spectrum is calculated as the integral over the product of a Voigt profile and a newly proposed three-dimensional “lineshape distribution function”, which is a function of spectral position and Gaussian- & Lorentzian width coordinates. A fast discrete version of this transform based on the Fast Fourier Transform (FFT) is proposed, which improves performance compared to the conventional approach by several orders of magnitude while maintaining accuracy. Strategies that minimize the discretization error are discussed. A Python implementation of the method is compared against state-of-the-art spectral code RADIS, and is since adopted as RADIS's default synthesis method. The synthesis of a benchmark CO2 spectrum consisting of 1.8 M spectral lines and 200k spectral points took only 3.1 s using the proposed method (1011 lines × spectral points/s), a factor ∼300 improvement over the state-of-the-art, with the relative improvement generally increasing for higher number of lines and/or number of spectral points. An experimental GPU-implementation of the method was also benchmarked, which demonstrated another 2~3 orders performance increase, achieving up to 5 ⋅ 1014 lines × spectral points/s.

The relationship between the Raman spectral form and the location of the corresponding sample within the overall thin-film carbon genome

We investigate whether the thin-film carbon Raman spectral form is determined by the location of the corresponding sample within the framework of a ternary phase characterization of thin-film carbon. We do this through a critical examination of a collection of experimentally acquired Raman spectra corresponding to an ensemble of thin-film carbon samples, whose sp2 and sp3 bonding contents and hydrogen content are known. Both qualitative and quantitative analyzes are pursued. For our qualitative analysis, we compare the gross features of the various Raman spectra considered in this analysis. For our quantitative analysis, the Raman spectral intensity at key spectral reference points are evaluated. Within the scope of its limitations, our analysis does confirm that there is indeed a relationship between the form of the Raman spectrum and the location of the corresponding sample within the thin-film carbon genome, as defined by the ternary phase diagram.

Adaptive photonic RF spectral shaper.

The radio frequency spectral shaper is an essential component in emerging multi-service mobile communications, multiband satellite and radar systems, and future 5G/6G radio frequency systems for equalizing spectral unevenness, removing out-of-band noise and interference, and manipulating multi-band signal simultaneously. While it is easy to achieve simple spectral functions using either conventional microwave photonic filters or the optical spectrum to microwave spectra mapping techniques, it is challenging to enable complex spectral shaping functions over tens of GHz bandwidth as well as to achieve point-by-point shaping capability to fulfill the needs in dynamic wireless communications. In this paper, we proposed and demonstrated a novel spectral shaping system, which utilizes a two-section algorithm to automatically decompose the target RF response into a series of Gaussian functions and to reconstruct the desired RF response by microwave photonic techniques. The devised spectral shaping system is capable of manipulating the spectral function in various bands (S, C, and X) simultaneously with step resolution of as fine as tens of MHz. The resolution limitation in optical spectral processing is mitigated using the discrete convolution technique. Over 10 dynamic and independently adjustable spectral control points are experimentally achieved based on the proposed spectral shaper.

Geometrically nonlinear Euler–Bernoulli and Timoshenko micropolar beam theories

Two ways of incorporating moderate rotations of planes normal to the axis of a straight beam into the Euler–Bernoulli and the Timoshenko micropolar beam theories are presented. In the first case, the von Karman nonlinear strains are used to incorporate the moderate rotations of normal planes into the beam theories. In the second case, appropriate approximations are made on the nonlinear Cosserat deformation gradient to reflect the condition of moderate rotations of the normal planes. The governing nonlinear differential equations and corresponding natural boundary conditions in both cases are derived using the principle of virtual displacements. A weak-form Galerkin displacement finite element formulation is presented for the developed nonlinear beam theories. The phenomenon of locking usually encountered in beam displacement finite elements is eliminated using higher-order finite elements with nodes located at spectral points. Finally, numerical examples are presented to illustrate the effect of coupling number and bending characteristic length scale on deflections and microrotations when a micropolar beam is modeled with the developed nonlinear beam theories.

SNR G39.2−0.3, an hadronic cosmic rays accelerator

ABSTRACT Recent results obtained with gamma-ray satellites have established supernova remnants as accelerators of GeV hadronic cosmic rays. In such processes, CRs accelerated in SNR shocks interact with particles from gas clouds in their surrounding. In particular, the rich medium in which core-collapse SNRs explode provides a large target density to boost hadronic gamma-rays. SNR G39.2–0.3 is one of the brightest SNR in infrared wavelengths, and its broad multiwavelength coverage allows a detailed modelling of its radiation from radio to high energies. We reanalysed the Fermi-LAT data on this region and compare it with new radio observations from the MWISP survey. The modelling of the spectral energy distribution from radio to GeV energies favours a hadronic origin of the gamma-ray emission and constrains the SNR magnetic field to be at least ∼100 µG. Despite the large magnetic field, the present acceleration of protons seems to be limited to ∼10 GeV, which points to a drastic slow down of the shock velocity due to the dense wall traced by the CO observations, surrounding the remnant. Further investigation of the gamma-ray spectral shape points to a dynamically old remnant subjected to severe escape of CRs and a decrease of acceleration efficiency. The low-energy peak of the gamma-ray spectrum also suggests that that the composition of accelerated particles might be enriched by heavy nuclei which is certainly expected for a core-collapse SNR. Alternatively, the contribution of the compressed pre-existing Galactic cosmic rays is discussed, which is, however, found to not likely be the dominant process for gamma-ray production.

Experimental Analysis of Small-Scale Rotors with Serrated Trailing Edge for Quiet Drone Propulsion

Drones are a growing business in Europe, delivering services in all environments, including urban areas: delivery of goods and e–commerce, precision agriculture, mapping, infrastructure inspections. In order to allow the integration of this platform in urban areas and to obtain public acceptance, it is necessary to significantly reduce the noise produced by the propellers. Currently, the level of noise generated by propellers is too relevant in terms of annoying effects induced on living beings. In particular, low altitude flights have been found to disturb citizens and frighten animals. With the aim to tackle such an issue, this paper describes an experimental parametric analysis of a passive noise control technique to reduce the signature generated by small–scale propeller employed for mini unmanned aerial propulsion.The noise control strategy here proposed is based on a serration pattern realized at the trailing edge (TE) of the blade. Despite the same approach has already been successfully employed to mitigate noise generated by wind turbines and fixed wing aircraft, few studies have been devoted to investigate the effects of a serration pattern on small propellers. A large number of different serration were realized by varying height, width and teeth distribution. The idea is to find the optimal serration geometry in terms of acoustic requirements and to highlight the role of teeth number.Results shows a sensible reduction in the noise propeller signature. Serration effects seems to depend strongly from the polar angle identifying different region of operation. Spectral Analysis points out that the serration affect the low frequency region and even the tonal component of aerodynamic noise. Statistical analysis shows a departure from a gaussian distribution and an effect of damping on distribution tails.

A New k-Distribution Scheme for Clear-Sky Radiative Transfer Calculations in Earth’s Atmosphere. Part I: Thermal Infrared (Longwave) Radiation

Abstract A new k-distribution scheme of longwave radiation without the correlated-k-distribution assumption is developed. Grouping of spectral points is based on the line-by-line (LBL)-calculated absorption coefficient k at a few sets of reference pressure pr and temperature θr, where the cooling rate is substantial in a spectral band. In this new scheme, the range of k(pr, θr) of a band is divided into a number of equal intervals, or g groups, in log10(kr). A spectral point at the wavenumber ν is identified with one of the g groups according to its kν(pr, θr). For each g group, a Planck-weighted k-distribution function Hg and a nonlinearly averaged absorption coefficient k¯g⁡(p,θ) are derived. The function Hg and the absorption coefficient k¯g⁡(p,θ) constitute the new k-distribution scheme. In this k-distribution scheme, a spectral point can only be identified with a g group regardless of pressure and temperature, which is different from the correlated-k distribution scheme. The k-distribution scheme is applied to the H2O, CO2, O3, N2O, and CH4 absorption bands, and results are compared with LBL calculations. To balance between the accuracy and the computational economy, the number of g groups in a band of a given gas is chosen such that 1) the difference in cooling rate is <0.1 K day−1 in the troposphere and <1.0 K day−1 in the stratosphere and 2) the difference in fluxes is <0.5 W m−2 at both the top of the atmosphere and the surface. These differences are attained with 130 g groups, which is the sum of the g groups of all five gases.

Numerical ranges of model operators and Clark measures

Let ϑ and η be inner functions with two spectral points on the unit circle T. Assuming ϑ(0)=η(0)=0, let ϑ0=ϑ/χ and η0=η/χ. Generalizing former results in [15] we prove that coincidence of some tangent polygons to the numerical ranges W(S(ϑ0)) and W(S(η0)) are already sufficient for coincidence of the model operators S(ϑ0) and S(η0). Instead of exponential representations of analytic self-maps of the upper half-plane, we rely here on Cauchy transforms of Clark measures associated with ϑ and η. Relaxing the assumptions yielding uniqueness, conditions are given also for the existence of multipliers between the model spaces H(ϑ) and H(η).

A Comparative Approach to Screen the Capability of Raman and Infrared (Mid- and Near-) Spectroscopy for Quantification of Low-Active Pharmaceutical Ingredient Content Solid Dosage Forms: The Case of Alprazolam.

Content uniformity is a critical attribute for potent and low-dosage formulations of active pharmaceutical ingredient (API) that, in addition to the formulation parameters, plays pivotal role during pharmaceutical development and production. However, when API content is low, implementing a vibrational spectroscopic analytical tool to monitor the content and blend uniformity remains a challenging task. The aim of this study was to showcase the potentials of mid-infrared (MIR), near-infrared (NIR), and Raman spectroscopy for quantitative analysis of alprazolam (ALZ) in a low-content powder blends with lactose, which is used as a common diluent for tablets produced by direct compression. The offered approach might be further scaled up and exploited for potential application in the process analytical technology (PAT). Partial least square and orthogonal PLS (OPLS) methodologies were employed to build the calibration models from raw and processed spectral data (standard normal variate, first and second derivatives). The models were further compared regarding their main statistical indicators: correlation coefficients, predictivity, root mean square error of estimation (RMSEE), and root mean square error of cross-validation (RMSEEcv). All statistical models presented high regression and predictivity coefficients. The RMSEEcv for the optimal models was 1.118, 0.08, and 0.059% for MIR, NIR, and Raman spectroscopy, respectively. The scarce information content extracted from the ALZ NIR spectra and the major band overlapping with those from lactose monohydrate was the main culprit of poor accuracy in the NIR model, whereas the subsampling instrumental setup (resulting in a non-representative spectral acquisition of the sample) was regarded as a main limitation for the MIR-based calibration model. The OPLS models of the Raman spectra of the powder blends manifested favorable statistical indicators for the accuracy of the calibration model, probably due to the distinctive ALZ Raman pattern resulting in the largest number of predictive spectral points that were used for the mathematical modeling. Furthermore, the Raman scattering calibration model was optimized in narrower scanning range (1700-700 cm-1) and its prediction power was evaluated (root mean square error of prediction, RMSEP = 0.03%). Thus, the Raman spectroscopy presented the most favorable statistical indicators in this comparative study and therefore should be further considered as a PAT for the quantitative determination of ALZ in low-content powder blends.

The water vapor foreign-continuum in the 1.6 µm window by CRDS at room temperature

Water vapour foreign-continuum absorption cross-sections, CF, are measured for the first time at room temperature in the 1.6 µm transparency window, of importance for atmospheric applications. The measurements are performed by cavity ring down spectroscopy (CRDS) at 15 selected spectral data points. These data, covering the 5700–6640 cm−1 spectral range, are derived from the variation of the absorption signal during pressure ramps of humidified air up to 1 atm with a typical 1% water vapour relative concentration. The foreign-continuum absorption was obtained as the excess of the measured loss rate compared to the sum of the loss rate measured with dry air, the local water monomer contribution and the self-continuum absorption. CF values were derived from the linear dependence of the foreign-continuum absorption with the product of the partial pressures of water vapour and air. The semi-empirical MT_CKD CF values are found significantly underestimated in the centre of the window.

Non-invasive MRI quantification of cerebrospinal fluid dynamics in amyotrophic lateral sclerosis patients

BackgroundDeveloping novel therapeutic agents to treat amyotrophic lateral sclerosis (ALS) has been difficult due to multifactorial pathophysiologic processes at work. Intrathecal drug administration shows promise due to close proximity of cerebrospinal fluid (CSF) to affected tissues. Development of effective intrathecal pharmaceuticals will rely on accurate models of how drugs are dispersed in the CSF. Therefore, a method to quantify these dynamics and a characterization of differences across disease states is needed.MethodsComplete intrathecal 3D CSF geometry and CSF flow velocities at six axial locations in the spinal canal were collected by T2-weighted and phase-contrast MRI, respectively. Scans were completed for eight people with ALS and ten healthy controls. Manual segmentation of the spinal subarachnoid space was performed and coupled with an interpolated model of CSF flow within the spinal canal. Geometric and hydrodynamic parameters were then generated at 1 mm slice intervals along the entire spine. Temporal analysis of the waveform spectral content and feature points was also completed.ResultsComparison of ALS and control groups revealed a reduction in CSF flow magnitude and increased flow propagation velocities in the ALS cohort. Other differences in spectral harmonic content and geometric comparisons may support an overall decrease in intrathecal compliance in the ALS group. Notably, there was a high degree of variability between cases, with one ALS patient displaying nearly zero CSF flow along the entire spinal canal.ConclusionWhile our sample size limits statistical confidence about the differences observed in this study, it was possible to measure and quantify inter-individual and cohort variability in a non-invasive manner. Our study also shows the potential for MRI based measurements of CSF geometry and flow to provide information about the hydrodynamic environment of the spinal subarachnoid space. These dynamics may be studied further to understand the behavior of CSF solute transport in healthy and diseased states.

Genetic Analysis of Milk Production Traits and Mid-Infrared Spectra in Chinese Holstein Population.

Simple SummaryUsually, spectral data are used as predictors to predict milk components, animal characteristics, and even reproductive status. Another innovative way to use spectral data involves considering spectral wavenumbers as traits and then analyzing from the genetic perspective. In this study, we considered milk spectral data directly as traits, then detected the influence of some non-genetic factors on spectral wavenumbers and estimated the genetic parameters of spectral points. The result of the present study could be used as a management tool for dairy farm and also provides a further understanding of genetic background of milk mid-infrared (MIR) spectra. In future, milk spectral data could be applied more effective. For example, some sub-clinical diseases might be detected based on the difference between the expected and observed values of the spectral traits. In addition, we could also use genetic correlation between wavenumbers and a trait of interest, which are difficult and expensive to measure, to apply for the genetic improvement of dairy species.Milk composition always serves as an indicator for the cow’s health status and body condition. Some non-genetic factors such as parity, days in milk (DIM), and calving season, which obviously affect milk performance, therefore, need to be considered in dairy farm management. However, only a few milk compositions are used in the current animal selection programs. The mid-infrared (MIR) spectroscopy can reflect the global composition of milk, but this information is currently underused. The objectives of this study were to detect the effect of some non-genetic factors on milk production traits as well as 1060 individual spectral points covering from 925.92 cm−1 to 5011.54 cm−1, estimate heritabilities of milk production traits and MIR spectral wavenumbers, and explore the genetic correlations between milk production traits and 1060 individual spectral points in a Chinese Holstein population. The mixed models procedure of SAS software was used to test the non-genetic factors. Single-trait animal models were used to estimate heritabilities and bivariate animal models were used to estimate genetic correlations using the package of ASReml in R software. The results showed that herd, parity, calving season, and lactation stage had significant effects on the percentages of protein and lactose, whereas herd and lactation stage had significant effects on fat percentage. Moreover, the herd showed a significant effect on all of the 1060 individual wavenumbers, whereas lactation stage, parity, and calving season had significant effect on most of the wavenumbers of the lactose-region (925 cm−1 to 1200 cm−1), protein-region (1240 cm−1 to 1600 cm−1), and fat-regions (1680 cm−1 to 1770 cm−1 and 2800 cm−1 to 3015 cm−1). The estimated heritabilities for protein percentage (PP), fat percentage (FP), and lactose percentage (LP) were 0.08, 0.05, and 0.09, respectively. Further, the milk spectrum was heritable but low for most individual points. Heritabilities of 1060 individual spectral points were 0.04 on average, ranging from 0 to 0.11. In particular, heritabilities for wavenumbers of spectral regions related to water absorption were very low and even null, and heritabilities for wavenumbers of specific MIR regions associated with fat-I, fat-II, protein, and lactose were 0.04, 0.06, 0.05, and 0.06 on average, respectively. The genetic correlations between PP and FP, PP and LP, FP, and LP were 0.78, −0.29, and −0.14, respectively. In addition, PP, FP, and LP shared the similar patterns of genetic correlations with the spectral wavenumbers. The genetic correlations between milk production traits and spectral regions related to important milk components varied from weak to very strong (0.01 to 0.94, and −0.01 to −0.96). The current study could be used as a management tool for dairy farms and also provides a further understanding of the genetic background of milk MIR spectra.

Isolated spectral points of a linear relation

We characterize the isolated points of the spectrum, the poles of the resolvent and the Riesz points of a bounded and closed linear relation on a Banach space. The found results include and generalize some known characterizations in the frame of bounded operators.

Dielectric Properties of Pulsed Laser Deposited Nanoscale CeNi5 Thin Films

Dielectric properties of pulsed laser deposited, nanoscale CeNi5 alloy layers, on glass or SiO2 substrate are described using the complex dielectric function. The UV–Vis–NIR spectral behavior of this function is studied separately for its real part e1 (the dielectric constant or dielectric permittivity), and for its imaginary part e2 (the dielectric loss function). The layers were obtained from grinded CeNi5 bulk powder using short, modulated laser pulses. The absolute reflectance of the obtained nanoscale alloy layers was measured at the 632.8 nm wavelength of a liquid nitrogen cooled and stabilized He–Ne source. This value was further used to renormalize the relative differential reflectance spectroscopy measurements performed in the UV‒Vis‒NIR domain. The obtained absolute reflectance spectra were processed using the Kramers–Kronig formalism, so that the real and imaginary parts of the complex dielectric function could be computationally determined, also leading to the calculation of the electron loss functions –Im e–1 and –Im(1 + e)–1. The behavior of these functions near the spectral inflexion points was determined using appropriate theoretical considerations. The variation of the dielectric functions was explained, electron density of states and the shape of the energy bands were inferred. This study reveals the layer thickness and deposition substrate dependent optical and electrical properties of the produced nanoscale CeNi5 structures.

Fast multiline spectral reshaping algorithm for active vibration control

Multiline spectral vibration (or noise) is very common in rotating machinery like motor, gearbox, compressor, propeller, etc. Active reshaping of these vibrations is one of the most important branches for active vibration control, which may find application in fields of sound quality control, psychoacoustics, military camouflage, etc. The traditional filtered-reference LMS is the most popular structure for multiline spectral reshaping control. However, with the increase of spectral lines, vibration sources and observation points (feedback channels), the traditional structure will have extremely heavy computational complexity, especially for the system whose dynamic of secondary path is complex, since it requires two long filters for every single spectral line and secondary path to adjust the reference signals. In this study, we propose a fast-multiline spectrum reshaping algorithm for active vibration control. We first construct an equivalent system of the traditional multiline spectrum reshaping algorithm by introducing two extra control branches, which is able to improve the convergence property of the system. Then, we generate a group of pre-phase-scheduled reference signals using the phase information at certain frequencies of the secondary paths instead of using filters. Afterwards, we conduct a theoretical analysis of computational complexity of multiline spectrum reshaping and fast multiline spectrum reshaping algorithms. Finally, we carried out two case studies based on the FEMilS test-bed to verify the effectiveness of the proposed algorithm. The results show that the proposed algorithm performs an accurate residual vibration control with uniformed convergence speed and reduced computational complexity.

Resonant states 0+ of the Boron isotope 8B from the Jost-matrix analysis of the partial cross-sections

The available [Formula: see text]-matrix parametrization of experimental data on the excitation functions for the elastic and inelastic [Formula: see text] scattering at the collision energies up to 3.4[Formula: see text]MeV is used to generate the corresponding partial-wave cross-sections in the states with [Formula: see text]. Thus, obtained data are fitted using the semi-analytic two-channel Jost matrix with a proper analytic structure and some adjustable parameters. Then the spectral points are sought as zeros of the Jost matrix determinant (which correspond to the [Formula: see text]-matrix poles) at complex energies. The correct analytic structure makes it possible to calculate the fitted Jost matrix on any sheet of the Riemann surface whose topology involves not only the square-root but also the logarithmic branching caused by the Coulomb interaction. In this way, two overlapping [Formula: see text] resonances at the excitation energies [Formula: see text] and [Formula: see text][Formula: see text]MeV have been found.

Structural and Functional Sensing of Bio-Tissues Based on Compressive Sensing Spectral Domain Optical Coherence Tomography.

In this paper, a full depth 2D CS-SDOCT approach is proposed, which combines two-dimensional (2D) compressive sensing spectral-domain optical coherence tomography (CS-SDOCT) and dispersion encoding (ED) technologies, and its applications in structural imaging and functional sensing of bio-tissues are studied. Specifically, by introducing a large dispersion mismatch between the reference arm and sample arm in SD-OCT system, the reconstruction of the under-sampled A-scan data and the removal of the conjugated images can be achieved simultaneously by only two iterations. The under-sampled B-scan data is then reconstructed using the classic CS reconstruction algorithm. For a 5 mm × 3.2 mm fish-eye image, the conjugated image was reduced by 31.4 dB using 50% × 50% sampled data (250 depth scans and 480 spectral sampling points per depth scan), and all A-scan data was reconstructed in only 1.2 s. In addition, we analyze the application performance of the CS-SDOCT in functional sensing of locally homogeneous tissue. Simulation and experimental results show that this method can correctly reconstruct the extinction coefficient spectrum under reasonable iteration times. When 8 iterations were used to reconstruct the A-scan data in the imaging experiment of fisheye, the extinction coefficient spectrum calculated using 50% × 50% data was approximately consistent with that obtained with 100% data.

Correct Solvability and Representation of Solutions of Volterra Integrodifferential Equations with Fractional Exponential Kernels

For abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space, the correct solvability of initial value problems is studied and the spectral analysis of operator functions being symbols of these equations is performed. This makes it possible to represent strong solutions of the equations under consideration as series in exponentials corresponding to spectral points of the operator functions. The equations in question are abstract forms of linear partial integrodifferential equations arising in the theory of viscoelasticity and in a number of other important applications.

Property $$(UW_\Pi )$$ and Perturbations

Property \((UW_\Pi )\) holds for a bounded linear operator \(T \in B(X),\) defined on a complex infinite dimensional Banach space X, if the poles of the resolvent of T are exactly the spectral points \(\lambda \) for which \(\lambda I-T\) is upper semi-Weyl. In this paper, we discuss the relationship between property \((UW_\Pi )\) and other Weyl type theorems. The stability of property \((UW_\Pi )\) is also studied under nilpotent, quasi-nilpotent, finite-dimensional or compact perturbations commuting with T.

Jost-matrix analysis of the resonance 5He∗(3 2+) near the dt-threshold

Partial cross-sections of the [Formula: see text] and [Formula: see text] collisions in the quantum state [Formula: see text] near the [Formula: see text]-threshold, taken from an available [Formula: see text]-matrix analysis, are fitted using the semi-analytic multi-channel Jost matrix with proper analytic structure and some adjustable parameters. Then the spectral points are sought as zeros of the Jost matrix determinant (which correspond to the [Formula: see text]-matrix poles) at complex energies. The correct analytic structure makes it possible to calculate (analytically continue) the fitted Jost matrix on any sheet of the Riemann surface whose topology involves not only the square-root but also the logarithmic branching caused by the Coulomb interaction. As a result of such an analytic continuation, it was found that the previously established [Formula: see text]-resonance (at [Formula: see text]) and its shadow pole (at [Formula: see text]) both are split in overlapping pairs. Apart from studying the properties of a specific nuclear state, it is also proved for a general multi-channel problem that the Coulomb forces change the topology of the Riemann surface as well as destroy the so-called mirror symmetry of the [Formula: see text]-matrix.