SEARCH · Search NASA

Results for “Velocity Model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗

DOE OSTI2020

Determining the ballistic threshold velocity for a composite structure using multiple failure models

A composite structure, such as a laminated composite panel, for example, comprises one or more layers or “plies” embedded in a matrix material or otherwise fixed together in an arrangement, commonly referred to as a “stack up.” Each material in the structure has a corresponding material failure model (MFM) defining the physical characteristics of that material. A ballistic threshold velocity computing device obtains the MFMs for each material in the composite structure, generates a predicted ballistic velocity threshold velocity for each MFM, and then generates a parametric model to compute a composite ballistic velocity threshold velocity for the composite structure.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A Tidal Hydrodynamic Model for Cook Inlet, Alaska, to Support Tidal Energy Resource Characterization

Cook Inlet in Alaska has been identified as a prime site in the U.S. for potential tidal energy development, because of its enormous tidal power potential that accounts for nearly one-third of the national total. As one important step to facilitate tidal energy development, a tidal hydrodynamic model based on the unstructured-grid, finite-volume community ocean model (FVCOM) was developed for Cook Inlet to characterize the tidal stream energy resource. The model has a grid resolution that varies from about 1000 m at the open boundary to 100–300 m inside the Inlet. Extensive model validation was achieved by comparing model predictions with field observations for tidal elevation and velocity at various locations in Cook Inlet. The error statistics confirmed the model performs reasonably well in capturing the tidal dynamics in the system, e.g., R2 > 0.98 for tidal elevation and generally > 0.9 for velocity. Model results suggest that tides in Cook Inlet evolve from progressive waves at the entrance to standing waves at the upper Inlet, and that semi-diurnal tidal constituents are amplified more rapidly than diurnal constituents. The model output was used to identify hotspots that have high energy potential and warrant additional velocity and turbulence measurements such as East Foreland, where averaged power density exceeds 5 kw/m2. Lastly, a tidal energy extraction simulation was conducted for a hypothetical turbine farm configuration at the Forelands cross section to evaluate tidal energy extraction and resulting changes in far-field hydrodynamics.

16 TIDAL AND WAVE POWER↗

DOE OSTI2023

Theoretical investigation of braking of tearing mode rotation by resistive walls in ITER

The locking of the 2/1 tearing mode to the resistive wall in the ITER tokamak (15 MA inductive scenario 2) is investigated theoretically using a cylindrical asymptotic matching model. The model takes into account the fact that ITER plasmas will effectively be surrounded by two walls; the inner blanket module layer with a time constant of about 23 ms, and the outer vacuum vessel with a time constant of about 380 ms. The model also takes cognizance of the fact that neither the blanket module layer nor the vacuum vessel can be accurately described as “thin” walls (in the ordinarily accepted sense). The model incorporates changes in both the plasma poloidal and the toroidal angular velocity profiles, in response to the electromagnetic braking torque that develops at the rational surface, because it turns out that neoclassical poloidal flow-damping is not strong enough to completely suppress changes in the poloidal velocity. Finally, the model accurately calculates changes in the poloidal and toroidal plasma angular velocity profiles by evolving the full angular equations of motion, taking the electromagnetic braking torque, plasma inertia, plasma viscosity, and poloidal flow-damping into account. The time required for the 2/1 tearing mode to grow from a small amplitude to a sufficient one to lock to the walls is found to be about 3.5 s. As a result, the critical full radial island width at which wall locking is triggered is found to be about 9% of the plasma minor radius.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Atomic Iron and Nickel in the Coma of C/1996 B2 (Hyakutake): Production Rates, Emission Mechanisms, and Possible Parents

Abstract Two papers recently reported the detection of gaseous nickel and iron in the comae of over 20 comets from observations collected over two decades, including interstellar comet 2I/Borisov. To evaluate the state of the laboratory data in support of these identifications, we reanalyzed archived spectra of comet C/1996 B2 (Hyakutake), one of the nearest and brightest comets of the past century, using a combined experimental and computational approach. We developed a new, many-level fluorescence model that indicates that the fluorescence emissions of Fe I and Ni I vary greatly with heliocentric velocity. Combining this model with laboratory spectra of an Fe-Ni plasma, we identified 22 lines of Fe I and 14 lines of Ni I in the spectrum of Hyakutake. Using Haser models, we estimate the nickel and iron production rates as Q Ni = (2.6–4.1) × 10 22 s −1 and Q Fe = (0.4–2.8) × 10 23 s −1 . From derived column densities, the Ni/Fe abundance ratio log 10 [Ni/Fe] = −0.15 ± 0.07 deviates significantly from solar abundance ratios, and it is consistent with the ratios observed in solar system comets. Possible production and emission mechanisms are analyzed in the context of existing laboratory measurements. Based on the observed spatial distributions, excellent fluorescence model agreement, and Ni/Fe ratio, our findings support an origin consisting of a short-lived unknown parent followed by fluorescence emission. Our models suggest that the strong heliocentric velocity dependence of the fluorescence efficiencies can provide a meaningful test of the physical process responsible for the Fe I and Ni I emission.

Bromley, S. J. (ORCID:0000000321108152)↗

DOE OSTI2025

Exploring the interaction between the MW and LMC with a large sample of blue horizontal branch stars from the DESI survey

The Large Magellanic Cloud (LMC) is a Milky Way (MW) satellite that is massive enough to gravitationally attract the MW disc and inner halo, causing significant motion of the inner MW with respect to the outer halo. In this work, we probe this interaction by constructing a sample of 9866 blue horizontal branch (BHB) stars with radial velocities from the DESI spectroscopic survey out to 120 kpc from the Galactic centre. This is the largest spectroscopic set of BHB stars in the literature to date, and it contains four times more stars with Galactocentric distances beyond 50 kpc than previous BHB catalogues. Using the DESI BHB sample combined with SDSS BHBs, we measure the bulk radial velocity of stars in the outer halo and observe that the velocity in the Southern Galactic hemisphere is different by 3.7σ from the North. Modelling the projected velocity field shows that its dipole component is directed at a point 22 deg away from the LMC along its orbit, which we interpret as the travel direction of the inner MW. The velocity field includes a monopole term that is –24 km s –1 ⁠, which we refer to as compression velocity. This velocity is significantly larger than predicted by the current models of the MW and LMC interaction. This work uses DESI data from its first 2 yr of observations, but we expect that with upcoming DESI data releases, the sample of BHB stars will increase and our ability to measure the MW–LMC interaction will improve significantly.

Galaxy: evolution↗

DOE OSTI2023

Frozen Hydrometeor Terminal Fall Velocity Dependence on Particle Habit and Riming as Observed by Vertically Pointing Radars

Vertically pointing Ka-band radar measurements are used to derive fall velocity–reflectivity factor ($V$ t = $aZ$$^{b}_{e}$) relations for frozen hydrometeor populations of different habits during snowfall events observed at Oliktok Point, Alaska, and at the Multidisciplinary Drifting Observatory for the Study of Arctic Climate (MOSAiC). Case study events range from snowfall with highly rimed particles observed during periods with large amounts of supercooled liquid water path (LWP > 320 g m –2 ) to unrimed snowflakes including instances when pristine planar crystals were the dominant frozen hydrometeor habit. The prefactor a and the exponent b in the observed $V$ t –$Z$ e relations scaled to the sea level vary in the approximate ranges 0.5–1.4 and 0.03–0.13, respectively (reflectivities are in mm 6 m –3 and velocities are in m s –1 ). The coefficient a values are the smallest for planar crystals (a ~ 0.5) and the largest (a > 1.2) for particles under severe riming conditions with high LWP. There is no clear distinction between b values for high and low LWP conditions. The range of the observed $V$ t –$Z$ e relation coefficients is in general agreement with results of modeling using fall velocity–size (υ t = αD β ) relations for individual particles found in literature for hydrometeors of different habits, though there is significant variability in α and β coefficients from different studies even for a same particle habit. Correspondences among coefficients in the $V$ t –$Z$ e relations for particle populations and in the individual particle υ t –$D$ relations are analyzed. Furthermore, these correspondences and the observed $V$ t –$Z$ e relations can be used for evaluating different frozen hydrometeor fall velocity parameterizations in models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Force Balance Model Assessment for Mechanistic Prediction of Sliding Bubble Velocity in Vertical Subcooled Boiling Flow

The bubble sliding after departing from nucleation site is frequently observed in flow boiling systems and, the crucial impact on wall heat transfer has been evidenced through many experiments. As a result, the heat transfer modeling associated with sliding bubble has become one of the subjects of great attention in CFD boiling heat transfer community. The modeling efforts are primarily aimed at improving the existing Heat Flux Partitioning (HFP) model via the implementation of sliding bubble-induced heat transfer. The performance of HFP model depends inherently on the fidelity of sub-models used to predict the fundamental bubble parameters (e.g., bubble departure/lift-off diameter). In the same context, the accurate prediction of sliding bubble parameters (e.g., sliding bubble growth, sliding bubble velocity) is essential to achieving the successful heat transfer modeling associated with sliding bubble. Of many sliding bubble parameters, this paper deals with the sliding bubble velocity. Specifically, the force balance model was assessed in view of the sliding bubble velocity prediction. The parametric effect of key sub-models (e.g., drag force, bubble growth models) used in the force balance equation was investigated. The experimental data from Maity (2000) and Yoo et al. (2016) were used for demonstrating the model predictive performance. It was found that the force balance model proposed in this study was able to predict well the bubble sliding velocity based on the accurate prediction of bubble growth during sliding. The predictive performance was proven with the experimental data measured under various subcooled boiling conditions of both water and refrigerant (NOVEC-7000) flowing upward in vertical channels.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Numerical simulations of membrane distillation systems with actively heated membranes

Membrane distillation (MD) is a thermal desalination process that is gaining attention for treating hypersaline brines. One recent approach uses composite membranes with a thermally conductive layer that delivers heat to the membrane–feed interface, where it drives evaporation. Though this increases single-pass recovery, it comes with the challenge of promoting lateral heat conduction through the thin membrane. Herein, we develop a 3D, computational fluid dynamics (CFD) model that simulates conjugate heat, mass, and momentum transport in the feed channel and composite membrane. We then use the CFD to verify a simpler numerical model that approximates the feed velocity field analytically. We validate the numerical model experimentally, and use it to investigate the impacts of the conductive layer thickness, feed channel geometry, and operating conditions on temperature and concentration polarization, permeate production, and specific energy consumption. Overall, we find that lateral heating increases permeate production at the expense of increased concentration polarization. In extreme cases, the concentration increases more than four-fold along the membrane surface. Furthermore, we show however, that the feed flow rate and conductive layer thickness can be tailored to mitigate concentration polarization, for only a small reduction in permeate production.

42 ENGINEERING↗

DOE OSTI2025

Modeling of melting and erosion in high velocity microparticle impacts

High velocity collisions can cause melting, a situation involving elasticity, plasticity, and phase transformations in tandem, which is very challenging for mechanical modeling. Here, this paper advances the use of smoothed particle hydrodynamics (SPH) simulations for this complex situation, investigating stainless steel microspheres impacting a tin substrate. After extensive validation against a range of mechanical and geometrical measurements of experimental impacts, the model provides a detailed, quantitative view of melt volume production over a broad range of impact velocities. It also enables direct decomposition of the impact energy partitioning, including analysis of the energy absorbed by plasticity in the impactor, the system kinetic energy, and the adiabatic heating of the substrate in addition to the melting itself. Since these quantities are not available experimentally, SPH modeling substantially enhances the quantitative understanding of such impacts. Finally, the model speaks to the phase characteristics of the ejecta formed during impact, confirming the experimental inference that the ejected material likely contains a significant fraction of solid material.

Constitutive modeling↗

DOE OSTI2020

Pervasive low-velocity layer atop the 410-km discontinuity beneath the northwest Pacific subduction zone: Implications for rheology and geodynamics

Regional triplication waveforms of five intermediate-depth events are modeled to simultaneously obtain the compressional (P) and shear (SH) wave velocity structure beneath northwestern Pacific subduction zone. Both the P- and SH-wave velocity models for three different sub-regions show a low-velocity layer (LVL) with a thickness of ~55-80 km lying above the 410-km discontinuity with a ~900 km lateral extent from the Japan Sea to the northeastern Asian continental margin. With the dihedral angle approaching to zero around 400 km, a minute amount of melt atop the 410-km discontinuity caused by the hydrous slab might completely wet olivine grain boundaries and result in a low seismic velocity layer in this specific subduction zone. This mechanism suggests that the 410-LVL is a low viscosity zone that would partially decouple the upper mantle from the transition zone. We infer that the widespread 410-LVL provides evidence for a water-bearing mantle transition zone beneath the western Pacific subduction zone.

58 GEOSCIENCES↗

DOE OSTI2024

Geophysical and Environmental Monitoring Data, and Subsurface Flow Modelling Results for Chicken Bone Meadow, Mt. Snodgrass, Crested Butte, CO

This dataset includes geoelectrical monitoring data acquired between October 2021 and November 2022, soil moisture and temperature data, groundwater data obtained from borehole SNIB covering the period from June 2021 to September 2022, and hydrological modelling results. The data were acquired to investigate how variations in bedrock type and topography, and vegetation cover control subsurface flow dynamics. To provide insights into the subsurface flow dynamics and their controls, a monitoring transect was installed at the Chicken Bone Meadow, Mt. Snodgrass, Crested Butte, CO, measuring the spatio-temporal variations of soil moisture, soil and snow temperature, subsurface electrical resistivity variations, and groundwater dynamics. Field data are organized in a folder structure, with Electrical Resistivity Tomography (ERT) data being provided as one file per measurement, and data of the soil moisture and temperature sensors being provided as text files covering the entire monitoring period. The ‘Locations.csv’ file contains the location of all sensors, given in NAD83 – UTM Zone 13N. ERT monitoring data has been processed to filter data based on reciprocal errors (data with errors > 30% were removed), a linear error model was fitted to each survey, and to ensure a constant set of measurements for time-lapse inversion, filtered data were interpolated and assigned a 100% measurement error. Soil moisture and temperature data were acquired at 15 min intervals, and averaged to provide 1h data. Weather data and borehole data (groundwater depth, conductivity and temperature) were acquired at 30 min intervals, and are provided as daily measurements; all measurements are averaged, except of precipitation values, which are given as daily accumulation. The hydrological model was set up along the ERT monitoring transect, and net infiltration was used as surface boundary condition and derived from the weather data. Four different results are provided, (1) results for a parameterization using hydraulic permeability and porosity as derived from the ERT data through petrophysical relationships, and (2) three simplified model results, using 1 to 3 geological layers above the bedrock. Modelling was performed using PFLOTRAN, and for each model the PFLOTRAN input files are provided. The result files include weekly hydrological modelling results (e.g., saturation, velocities, pressures), as well as the model parameterization. The dataset additionally includes a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Implications of Sound Velocities of Natural Topaz on the Seismic L–Discontinuity

Compressional and shear wave velocities of topaz have been measured by ultrasonic interferometry in a multi-anvil apparatus up to 13 GPa at room temperature. By fitting the measured velocities under pressure to finite strain equations, the elastic moduli of topaz and their pressure derivatives were obtained, yielding K S0 = 165.5 (25) GPa, K S ' = 2.9 (1), G 0 = 116.5 (17) GPa, and G' = 1.0 (1). Modeling of the velocity profiles of subducted sediments suggests that at 8 GPa (~240 km depth) the P- and S- wave velocities of the subducted sediments exhibit a first order increase of 10% and 11%, respectively. Furthermore, the comparison between seismic observations and velocity contrasts of sediment + MORB model at 240 km shows dehydration of a 1.5–3.9 km thick sediment layer can potentially contribute to the seismically observed Lehmann discontinuity in Tonga, Japan, Philippine Sea, South America, Indonesia, and South Shetland subduction zones.

36 MATERIALS SCIENCE↗

DOE OSTI2025

An efficient hybrid downscaling framework to estimate high-resolution river hydrodynamics

Flow depth and velocity are the most important hydrodynamic variables that govern various river functions, including water resources, navigation, sediment transport, and biogeochemical cycling. Existing high-resolution flow depth simulations rely on either computationally expensive river hydrodynamic models (RHMs) or data-driven models with formidable training costs, whereas data-driven modeling of flow velocity has rarely been explored. Here, using the hybrid Low-fidelity, Spatial analysis, and Gaussian process learning (LSG) model, we developed a downscaling approach to construct high-resolution flow depth and velocity from a two-dimensional (2-D) RHM simulation at coarse resolution. The LSG models were trained and tested in an urban watershed in Houston using two different hurricane-driven flood events. The high-resolution (as fine as 30 m resolution) and low-resolution (mostly 1000 m resolution) meshes include 664 724 and 14 536 grid cells, respectively. The results showed that through downscaling, the simulation errors were reduced to less than one-fourth and one-third of the errors of the low-resolution 2-D RHM for flow depth and velocity, respectively. Our analysis further revealed that the dominant uncertainty sources of the downscaled hydrodynamics are different, with flow velocity dominated by the dimensionality reduction error, which we reduced by using a regionalized training procedure. The downscaling approach achieves an 84-fold acceleration in computational time compared to the high-resolution 2-D RHM, making high-fidelity ensemble flood modeling feasible. More importantly, the developed method provides an opportunity to couple large-scale hydrodynamical processes with local physical, chemical, and biological processes in river models.

Tan, Zeli [Pacific Northwest National Laboratory (↗

DOE OSTI2020

A Comparative Study of Two BAM Designs for Friction Sensitivity Testing of Explosives

A new commercial design of BAM friction tester that utilizes a programmable servo motor was tested in comparison to the traditional cam-driven model. Displacement and velocity profiles were analyzed for both designs; significant differences were found between the two designs, most notable of which is that the traditional cam-driven unit has plate velocities that can be 50–75 % greater than those seen on the servo-driven model. Five energetic materials were also tested on each machine, including PETN, RDX, HMX, CL-20, and HNAB. Finally, results from the servo-driven model generally showed slightly less sensitivity when compared to the cam driven model, though the magnitude of the difference is not significant enough to require modification of safe handling procedures for the materials tested.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2023

Can we observe the ion-neutral drift velocity in prestellar cores?

Given the low-ionization fraction of molecular clouds, ambipolar diffusion is thought to be an integral process in star formation. However, chemical and radiative-transfer effects, observational challenges, and the fact that the ion-neutral drift velocity is inherently very small render a definite detection of ambipolar diffusion extremely non-trivial. Here, we study the ion-neutral drift velocity in a suite of chemodynamical, non-ideal magnetohydrodynamic (MHD), two-dimensional axisymmetric simulations of prestellar cores where we alter the temperature, cosmic-ray ionization rate, visual extinction, mass-to-flux ratio, and chemical evolution. Subsequently, we perform a number of non-local thermodynamic equilibrium (non-LTE) radiative-transfer calculations considering various idealized and non-idealized scenarios in order to assess which factor (chemistry, radiative transfer, and/or observational difficulties) is the most challenging to overcome in our efforts to detect the ion-neutral drift velocity. We find that temperature has a significant effect in the amplitude of the drift velocity with the coldest modelled cores (T = 6 K) exhibiting drift velocities comparable to the sound speed. Against expectations, we find that in idealized scenarios (where two species are perfectly chemically co-evolving) the drift velocity ‘survives’ radiative-transfer effects and can in principle be observed. However, we find that observational challenges and chemical effects can significantly hinder our view of the ion-neutral drift velocity. Finally, we propose that HCN and HCNH + ⁠, being chemically co-evolving, could be used in future observational studies aiming to measure the ion-neutral drift velocity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

High-resolution lithospheric structure of continental China from joint inversion of surface wave and gravity data

The lithospheric structure of continental China has been previously determined by seismic travel time tomography, surface wave tomography, and joint inversion of body wave and surface wave data. However, due to the inherent limitations of seismic data, the lithospheric structure of continental China is still not well resolved in the shallow part and in some regions where the station coverage is relatively sparse. In this study, we aim at improving the lithospheric structure by joint inversion of seismic surface wave data and satellite gravity data to take advantage of the uniform distribution and complementary strength of the gravity data. Here, the empirical relationship between velocity and density is used as a bridge for joint inversion of surface wave and gravity data. The joint inversion shear-wave velocity Vs (density) model, named as USTClitho1.0g, can fit both surface wave and gravity data well. This high-resolution Vs model can better fit the active airgun source seismic arrival times and better delineate some features in continental China, such as the velocity contrast across the north–south gravity lineament (NSGL), the lithosphere thinning in eastern China, the crustal footprint of the Hainan mantle plume, the likely magma chamber beneath volcanos in northeast China, the middle-lower crust low velocity layer beneath the Tibetan plateau, and the tearing of subducted Indian mantle lithosphere. Our joint inversion Vs model can provide a reference model for geosciences in continental China and surrounding areas.

58 GEOSCIENCES↗

DOE OSTI2026

Code for the manuscript "Lagrangian Attention Tensor Networks for Velocity Gradient Statistical Mode

We disclose a python/pytorch implementation of the physics-informed machine learning algorithm described in "Lagrangian Attention Tensor Networks for Velocity Gradient Statistical Modeling", LA-UR-24-30678. Direct numerical simulation (DNS) of ubiquitous turbulence phenomena is computationally infeasible for realistic flows. As a result, reduced modeling for turbulent flows aim to reduce the number of resolved scales while retaining accurate representations of the small-scale physics. The dynamics of the velocity gradient tensor (VGT) is a key ingredient in reduced or subgrid turbulence models. The evolution equation for the VGT involves nonlocal terms, requiring closure modeling. This implementation of the novel methodology of Lagrangian Attention Tensor Networks (LATN), utilizes a structured representation of the history of the VGT to inform a physics-informed machine learning algorithm. This addition of structured memory terms is shown to outperform previous models when trained and evaluated on DNS data.

Livescu, Daniel [LANL]↗