Spectral Code Research Articles

Physical conditions in two high-redshift H2-bearing GRB-DLAs, 120815A and 121024A

ABSTRACT The gamma-ray burst (GRB) afterglows provide a unique opportunity to study the interstellar medium (ISM) of star-forming galaxies at high-redshift. The GRB-DLAs (damped Lyman-α absorbers) contain a large neutral hydrogen column density, N(H i), and are observed against the GRB afterglow. A large fraction of GRB-DLAs show presence of molecular hydrogen (H2) which is an indicator of star-formation. Hence it is important to study those GRB-DLAs which have H2 lines to decipher and understand their physical conditions. The GRB-DLAs 121024A and 120815A, situated at redshift 2.30 and 2.36, respectively, are two such important H2-bearing GRB-DLAs. Besides H2, these two GRB-DLAs also show many metal lines. In this work we have carried out a detail numerical study on the H2 lines, as well as on those metal lines, in GRB-DLAs 121024A and 120815A self-consistently. We use the spectral synthesis code cloudy for this study. This modelling helps us to determine the underlying physical conditions which give rise to such lines and hence to understand these two GRB-DLAs in much more detail than any other previous investigation. We find that the hydrogen densities for these two H2-bearing DLAs are ≥60 cm−3. Moreover our study infers that the linear sizes are ≤17.7 pc for these two GRB-DLAs, and the mean gas temperatures averaged over the cloud thickness, are ≤140 K. Overall, we find that these two H2-bearing GRB-DLAs are denser, cooler, and smaller compared to those without H2.

Comparison of Numerical Methods for Modeling the Wave Field Effects Generated by Individual Wave Energy Converters and Multiple Converter Wave Farms

This numerical study compares the wave field generated by the spectral wave action balance code, SNL-SWAN, to the linear-wave boundary-element method (BEM) code, WAMIT. The objective of this study is to assess the performance of SNL-SWAN for modeling wave field effects produced by individual wave energy converters (WECs) and wave farms comprising multiple WECs by comparing results from SNL-SWAN with those produced by the BEM code WAMIT. BEM codes better model the physics of wave-body interactions and thus simulate a more accurate near-field wave field than spectral codes. In SNL-SWAN, the wave field’s energy extraction is modeled parametrically based on the WEC’s power curve. The comparison between SNL-SWAN and WAMIT is made over a range of incident wave conditions, including short-, medium-, and long-wavelength waves with various amounts of directional spreading, and for three WEC archetypes: a point absorber (PA), a pitching flap (PF) terminator, and a hinged raft (HR) attenuator. Individual WECs and wave farms of five WECs in various configuration were studied with qualitative comparisons made of wave height and spectra at specific locations, and quantitative comparisons of the wave fields over circular arcs around the WECs as a function of radial distance. Results from this numerical study demonstrate that in the near-field, the difference between SNL-SWAN and WAMIT is relatively large (between 20% and 50%), but in the far-field from the array the differences are minimal (between 1% and 5%). The resultant wave field generated by the two different numerical approaches is highly dependent on parameters such as: directional wave spreading, wave reflection or scattering, and the WEC’s power curve.

Discovery of a Remarkably Powerful Broad Absorption-line Quasar Outflow in SDSS J135246.37+423923.5

Abstract Broad absorption-line (BAL) features in quasar spectra reveal an unambiguous signature of energetic outflows from central supermassive black holes, and thus, BAL quasars are prime targets for investigating the potential process of luminous quasar feedback on galaxies. We analyzed the rest-UV spectrum of an “overlapping trough” iron low-ionization broad absorption-line quasar (FeLoBAL) SDSS J135246.37+423923.5 using the novel spectral synthesis code SimBAL and discovered an extraordinarily fast and energetic BAL outflow. Our analysis revealed outflow velocities reaching with a velocity width of , which is the largest FeLoBAL outflow velocity measured to date. The column density of the outflow gas is log with the log kinetic luminosity (erg s−1), which exceeds the bolometric luminosity of the quasar and is energetic enough to effectively drive quasar feedback. The energy estimate for the outflow is far greater than the estimates from any BAL object previously reported. The object also shows “anomalous reddening” and a significant scattered component that we were able to model with SimBAL. We found the first definitive case for radiation filtering in an additional zero-velocity absorption component that required an absorbed continuum to produce the particular absorption lines observed (Mg ii, Al iii, and Al ii) without also producing the high-ionization lines such as C iv.

Stellar age gradients and inside-out star formation quenching in galaxy bulges

Radial age gradients hold the cumulative record for the multitude of physical processes driving the build-up of stellar populations and the ensuing star formation (SF) quenching process in galaxy bulges and, therefore, potentially sensitive discriminators between competing theoretical concepts on bulge formation and evolution. Based on spectral modeling of integral field spectroscopy (IFS) data from the CALIFA survey, we derived mass- and light-weighted stellar age gradients (∇(t⋆, B)ℒ, ℳ) within the photometrically determined bulge radius (RB) of a representative sample of local face-on late-type galaxies that span 2.6 dex in stellar mass (8.9 ≤ log ℳ⋆, T ≤ 11.5). Our analysis documents a trend of decreasing ∇(t⋆, B)ℒ, ℳ with increasing ℳ⋆, T, with high-mass bulges predominantly showing negative age gradients and vice versa. The inversion from positive to negative ∇(t⋆, B)ℒ, ℳ occurs at log ℳ⋆, T ≃ 10, which roughly coincides with the transition from lower-mass bulges whose gas excitation is powered by SF to bulges classified as composite, LINER, or Seyfert. We discuss two simple limiting cases for the origin of radial age gradients in massive late-type galaxy bulges. The first one assumes that the stellar age in the bulge is initially spatially uniform (∇(t⋆, B)ℒ, ℳ ≈ 0), thus the observed age gradients (∼ − 3 Gyr/RB) arise from an inside-out SF quenching (ioSFQ) front that is radially expanding with a mean velocity vq. In this case, the age gradients for massive bulges translate into a slow (vq ∼1–2 km s−1) ioSFQ that lasts until z ∼ 2, suggesting mild negative feedback by SF or an active galactic nucleus (AGN). If, on the other hand, negative age gradients in massive bulges are not due to ioSFQ but primarily due to their inside-out formation process, then the standard hypothesis of quasi-monolithic bulge formation has to be discarded in favor of another scenario. This would involve a gradual buildup of stellar mass over 2–3 Gyr through, for instance, inside-out SF and inward migration of SF clumps from the disk. In this case, rapid (≪1 Gyr) AGN-driven ioSFQ cannot be ruled out. While the ℳ⋆, T versus ∇(t⋆, B)ℒ, ℳ relation suggests that the assembly history of bulges is primarily regulated by galaxy mass, its large scatter (∼1.7 Gyr/RB) reflects a considerable diversity. This calls for an in-depth examination of the role of various processes (e.g., negative and positive AGN feedback, bar-driven gas inflows) with higher-quality IFS data in conjunction with advanced spectral modeling codes.

Design and performance of spectral efficient modified new diagonal code for a spectral amplitude code-optical code division multiple access system

Our study contains performance and design of a spectral amplitude code-optical code division multiple access (SAC-OCDMA) system using proposed modified new diagonal (MND) code. The proposed MND code has advantages as very low cross-correlation value compared to other code sequences. Also the code has a short length for the higher code weight value. Furthermore, due to its enormous code property, it also introduces very low multiple access interference. Thus the MND code-based SAC-OCDMA system permits a higher number of users. The MND code construction method is also explained, which is very easy using diagonal matrices. Based on the theoretical analysis, bit error rate (BER) performance of MND code AND-subtraction scheme compare with conventional codes is better than random diagonal code, Pascal’s triangle matrix code (PTMC), and multidiagonal (MD) code, which makes it spectral efficient. It provides 5 dB lower BER compared to MD code and PTMC for 90 users. Simulation of the MND code-based system for four users with 2 Gbps data rate has been successfully demonstrated using the AND-subtraction scheme and the direct detection scheme.

Performance enhancement of multiple access 3D-OCDMA networks using a pascal triangle codes

In this paper, a novel Three Dimensional Pascal’s Triangle Zero Cross Correlation (3D-PTZCC) code is proposed for non coherent Spectral Amplitude Coding Optical Code Division Multiple Access systems with a spectral/time/spatial combination and direct detection at the level of the receiver. The proposed code is based on (1D-PTZCC) and (2D-PTZCC) codes using Pascal’s Triangle rule. Its structure can minimise the receiver complexity of 3D-Perfect/Multi Diagonal (3D-PD/MD) and 3D-Perfect Difference (3D-PD) codes. The simulation results prove that systems using the proposed code can support a high data rate, high signal power and large number of simultaneous users with less power consuming. The code can save the received power by around − 5.5 dBm and − 3.7 dBm and the system capacity can be enhanced by 4.7 and 3.85 times compared to the systems using (3D-PD/MD) and (3D-PD) codes.

Performance improvement of multi access OCDMA system based on a new zero cross correlation code

In this paper, a novel zero cross correlation (ZCC) code is proposed for spectral amplitude coding-optical code division multiple access (SAC-OCDMA) systems. The code construction method starts from the identity matrix and has several benefits summarized in both the code simplicity and flexibility. The proposed code presents also an adapted (or accepted) code length for SAC-OCDMA systems and a high SNR value that reaches respectively 3.18 and 1.84 times of the system capacity comparing to other existed codes such as modified quadratic congruence (MQC) and modified double weight (MDW) codes.

Hoki: Making BPASS accessible through Python

We now know that a large number of stars are born in multiple systems. Additionally, more than 70% of massive stars are found in close binary systems, meaning that they will interact over the course of their lifetime. This has strong implications for their evolution as well as the transients (e.g supernovae) and the potential gravitational wave progenitors they produce. Therefore, in order to understand and correctly interpret astronomical observations of stellar populations, we must use theoretical models able to account for the effects of binary stars. This is the case of the Binary Population and Spectral Synthesis code (BPASS), which has been a staple of the field for over 10 years. As is the case for most other theoretical models, the data products of BPASS are large, varied and complex. As a result, their use requires a level of expertise that is not immediately accessible to a wider community that may hold key observational data. The goal of hoki is to bridge the gap between observation and theory, by providing a set of tools to make BPASS data easily accessible and facilitate analysis. The use of Python is deliberate as it is a ubiquitous language within Astronomy. This allows BPASS results to be used naturally within the pre-existing workflow of most astronomers.

R-matrix electron-impact excitation data for the C-like iso-electronic sequence

Context. Emission and absorption features from C-like ions serve as temperature and density diagnostics of astrophysical plasmas. R-matrix electron-impact excitation data sets for C-like ions in the literature merely cover a few ions, and often only for the ground configuration. Aims. Our goal is to obtain level-resolved effective collision strength over a wide temperature range for C-like ions from N II to Kr XXXI (i.e., N+ to Kr30+) with a systematic set of R-matrix calculations. We also aim to assess their accuracy. Methods. For each ion, we included a total of 590 fine-structure levels in both the configuration interaction target and close-coupling collision expansion. These levels arise from 24 configurations 2l3nl′ with n = 2−4, l = 0−1, and l′ = 0−3 plus the three configurations 2s22p5l with l = 0−2. The AUTOSTRUCTURE code was used to calculate the target structure. Additionally, the R-matrix intermediate coupling frame transformation method was used to calculate the collision strengths. Results. We compare the present results of selected ions with archival databases and results in the literature. The comparison covers energy levels, transition rates, and effective collision strengths. We illustrate the impact of using the present results on an Ar XIII density diagnostic for the solar corona. The electron-impact excitation data is archived according to the Atomic Data and Analysis Structure (ADAS) data class adf04 and will be available in OPEN-ADAS. The data will be incorporated into spectral codes, such as CHIANTI and SPEX, for plasma diagnostics.

A locally field-aligned discontinuous Galerkin method for anisotropic wave equations

In magnetized plasmas of fusion devices the strong magnetic field leads to highly anisotropic physics where solution scales along field lines are much larger than perpendicular to it. Hence, regarding both accuracy and efficiency, a numerical method should allow to address parallel and perpendicular resolutions independently. In this work, we consider the eigenvalue problem of a two-dimensional anisotropic wave equation with variable coefficients which is a simplified model of linearized ideal magnetohydrodynamics.For this, we propose to use a mesh that is aligned with the magnetic field and choose to discretize the problem with a discontinuous Galerkin method which naturally allows for non-conforming interfaces.First, we analyze the eigenvalue spectrum of a constant coefficient anisotropic wave equation, and demonstrate that this approach improves the accuracy by up to seven orders of magnitude, if compared to a non-aligned method with the same number of degrees of freedom. In particular, the results improve for eigenfunctions with high mode numbers.We also apply the method to compute the eigenvalue spectrum of the associated anisotropic wave equation with variable coefficients of flux surfaces of a Stellarator configuration. We benchmark the results against a spectral code.

The Strength of the 2175 Å Feature in the Attenuation Curves of Galaxies at 0.1 < z ≲ 3

Abstract We update the spectral modeling code MAGPHYS to include a 2175 Å absorption feature in its UV to near-IR dust attenuation prescription. This allows us to determine the strength of this feature and the shape of the dust attenuation curve in ∼5000 star-forming galaxies at in the COSMOS field. We find that a 2175 Å absorption feature of ∼1/3 the strength of that in the Milky Way is required for models to minimize residuals. We characterize the total effective dust attenuation curves as a function of several galaxy properties and find that the UV slopes of the attenuation curve for COSMOS galaxies show a strong dependence on star formation rate (SFR) and total dust attenuation (A V ), such that galaxies with higher SFR and A V have shallower curves and vice versa. These results are consistent with expectations from radiative transfer that attenuation curves become shallower as the effective dust optical depth increases. We do not find significant trends in the strength of the 2175 Å absorption feature as a function of galaxy properties, but this may result from the high uncertainties associated with this measurement. The updated code is publicly available online (following acceptance).

An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables

AbstractWe derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term‐by‐term balance in the kinetic, internal, and potential energy budgets, ensuring an energy‐consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit‐explicit time stepping algorithm.

MicrIO: an open-source autosampler and fraction collector for automated microfluidic input-output.

Microfluidic devices are an enabling technology for many labs, facilitating a wide range of applications spanning high-throughput encapsulation, molecular separations, and long-term cell culture. In many cases, however, their utility is limited by a 'world-to-chip' barrier that makes it difficult to serially interface samples with these devices. As a result, many researchers are forced to rely on low-throughput, manual approaches for managing device input and output (IO) of samples, reagents, and effluent. Here, we present a hardware-software platform for automated microfluidic IO (micrIO). The platform, which is uniquely compatible with positive-pressure microfluidics, comprises an 'AutoSipper' for input and a 'Fraction Collector' for output. To facilitate widespread adoption, both are open-source builds constructed from components that are readily purchased online or fabricated from included design files. The software control library, written in Python, allows the platform to be integrated with existing experimental setups and to coordinate IO with other functions such as valve actuation and assay imaging. We demonstrate these capabilities by coupling both the AutoSipper and Fraction Collector to two microfluidic devices: a simple, valved inlet manifold and a microfluidic droplet generator that produces beads with distinct spectral codes. Analysis of the collected materials in each case establishes the ability of the platform to draw from and output to specific wells of multiwell plates with negligible cross-contamination between samples.

The Multi-slit Approach to Coronal Spectroscopy with the Multi-slit Solar Explorer (MUSE)

Abstract The Multi-slit Solar Explorer (MUSE) is a proposed mission aimed at understanding the physical mechanisms driving the heating of the solar corona and the eruptions that are at the foundation of space weather. MUSE contains two instruments, a multi-slit extreme ultraviolet (EUV) spectrograph and a context imager. It will simultaneously obtain EUV spectra (along 37 slits) and context images with the highest resolution in space (0.″33–0.″4) and time (1–4 s) ever achieved for the transition region (TR) and corona. The MUSE science investigation will exploit major advances in numerical modeling, and observe at the spatial and temporal scales on which competing models make testable and distinguishable predictions, thereby leading to a breakthrough in our understanding of coronal heating and the drivers of space weather. By obtaining spectra in four bright EUV lines (Fe ix 171 Å, Fe xv 284 Å, Fe xix 108Å, Fe xxi 108 Å) covering a wide range of TR and coronal temperatures along 37 slits simultaneously, MUSE will be able to “freeze” the evolution of the dynamic coronal plasma. We describe MUSE’s multi-slit approach and show that the optimization of the design minimizes the impact of spectral lines from neighboring slits, generally allowing line parameters to be accurately determined. We also describe a Spectral Disambiguation Code to resolve multi-slit ambiguity in locations where secondary lines are bright. We use simulations of the corona and eruptions to perform validation tests and show that the multi-slit disambiguation approach allows accurate determination of MUSE observables in locations where significant multi-slit contamination occurs.

The impact of star formation sampling effects on the spectra of lensed z > 6 galaxies detectable with JWST

ABSTRACT The upcoming James Webb Space Telescope (JWST) will allow observations of high-redshift galaxies at fainter detection levels than ever before, and JWST surveys targeting gravitationally lensed fields are expected to bring z ≳ 6 objects with very low star formation rate (SFR) within reach of spectroscopic studies. As galaxies at lower and lower star formation activity are brought into view, many of the standard methods used in the analysis of integrated galaxy spectra are at some point bound to break down, due to violation of the assumptions of a well-sampled stellar initial mass function (IMF) and a slowly varying SFR. We argue that galaxies with SFR ∼ 0.1 M⊙ yr−1 are likely to turn up at the spectroscopic detection limit of JWST in lensed fields, and investigate to what extent star formation sampling may affect the spectral analysis of such objects. We use the slug spectral synthesis code to demonstrate that such effects are likely to have significant impacts on spectral diagnostics of, for example, the Balmer emission lines. These effects are found to stem primarily from SFRs varying rapidly on short (∼Myr) time-scales due to star formation in finite units (star clusters), whereas the effects of an undersampled IMF is deemed insignificant in comparison. In contrast, the ratio between the He ii- and H i-ionizing flux is found to be sensitive to IMF-sampling as well as ICMF-sampling (sampling of the initial cluster mass function), which may affect interpretations of galaxies containing Population III stars or other sources of hard ionizing radiation.

Simulation of Boiling Two-Phase Flow in a Helical Coil Steam Generator Using the Spectral Element Code Nek-2P

To enable the design of a light water small modular reactor, the boiling flow inside a helical coil steam generator has been simulated with the two-fluid model in Nek-2P. Nek-2P is the multiphase branch of the spectral element code Nek5000. Details of the implementation of the two-fluid model and the included closure models are discussed. The presented closure models include interactions for momentum, heat, and mass transfer between phases. Models for the drag, lift, and turbulent dispersion forces are included. The complete model is fully consistent in the limits of both phasic volume fractions approaching zero and is able to simulate flows of dispersed vapor, continuous liquid, dispersed liquid, continuous vapor, or any combination thereof. The closure models and their implementation in Nek-2P have been validated by comparing to experimental data for a boiling flow, demonstrating excellent agreement. Results from the simulation of the helical coil indicate strong phasic separation driven by the effects of buoyancy and inertia. Significant differences were observed in the results compared to simulations performed using Star-CCM+, although these differences were somewhat expected.

Modeling of parasitic oscillations in smooth-wall circular symmetric dielectric-loaded gyrotron beam ducts

The self-consistent simulation of the electron beam interaction was performed in the presence of a lossy dielectric layer in the smooth-wall beam duct of a gyrotron oscillator. For this purpose, the linear and spectral code TWANGlinspec was extended. In this code, the local transverse structure of the TE mode is adapted to the solution of the complex cold dispersion relation of an infinite, homogeneous, dielectric coated cylindrical waveguide. Before considering the realistic situation, the validity of the TE pure mode (Ez = 0) assumed in TWANGlinspec had to be assessed for SiC or BeOSiC materials. The effect of the dielectric layer on the parasitic starting current is large for parasitic oscillations localized at the end of the beam duct and in the so-called spacer region. For the realistic case, the geometry of the dual frequency gyrotron for the Tokamak à Configuration Variable was considered, and the effect of a dielectric layer was numerically investigated. The electron beam velocity spread was also included in the simulations. The result is that in such conditions, the parasitic oscillation starting currents are increased above the operating beam current. The observation of these spurious modes would therefore not be expected.

Nonlinear Evolution of a Steep, Focusing Wave Group in Deep Water Simulated With oceanwave3d

Abstract Steep, focusing waves can experience fast and local nonlinear evolution of the spectrum due to wave–wave interactions resulting in energy transfer to both higher and lower wavenumber components. The shape and kinematics of a steep wave may, thus, differ substantially from the predictions of linear theory. We have investigated the role of nonlinear interactions on group shape for a steep, narrow-banded, directionally spread wave group focusing in deep water using the fully nonlinear potential flow solver, oceanwave3d. Exact second-order correction of the initial conditions has been implemented together with a novel third-order approximate correction based on a Stokes-type formulation for surface elevation combined with a scaling argument for the third-order velocity potential. Four-phase separation reveals that the third-order scheme provides a good estimate for the third-order superharmonics. A quantitative assessment of numerical error has also been performed for the spatial and temporal discretization, including energy conservation, a reversibility check, and validation against previous simulations performed with a higher-order spectral (HOS) code. The initially narrow-banded amplitude spectrum exhibits the formation of “sidelobes” at angles of approximately ±35deg to the spectral peak during the simulated extreme wave event, occurring in approximately ten wave periods, with a preferential energy transfer to high-wavenumber components. The directional energy transfer is attributed to resonant third-order interactions with a discussion of the engineering implications.

Verification and validation of large eddy simulation with Nek5000 for cold leg mixing benchmark

Large eddy simulation (LES) of an experimental benchmark investigating buoyant mixing among two fluids is developed for verification and validation. Flow physics involve a completely closed system where after a valve is opened, two initially stationary fluids with different densities are allowed to mix. The Boussinesq approximation and low-Mach equations are coded into spectral element code Nek5000 to predict the buoyancy forces, and miscibility is accounted for using the advection-diffusion equation for concentration. Due to computational costs of higher order solutions, current analysis consists of initial flow development after the valve is opened. Minor differences between the models and Schmidt number are found within the turbulent spectrum and time integrated quantities. Moreover, solutions for higher polynomial orders are compared to quantify error due to spatial discretization. Error estimates using a posteriori spectral derivation of truncation and quadrature error are also calculated. Validation with particle image velocimetry (PIV) reveals good prediction of both average and fluctuating components of the primary flow within the cold leg but less accurate results in the downcomer. It is concluded that instabilities due to resolving more of the interface using the high molecular Schmidt number is essential for accurately predicting this type of flow.

Spectral element applications in complex nuclear reactor geometries: Tet-to-hex meshing

The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a tet-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYS ICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.