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DOE OSTI2023

Assessing Clouds Using Satellite Observations Through Three Generations of Global Atmosphere Models

Abstract Clouds are parameterized in climate models using quantities on the model grid‐scale to approximate the cloud cover and impact on radiation. Because of the complexity of processes involved with clouds, these parameterizations are one of the key challenges in climate modeling. Differences in parameterizations of clouds are among the main contributors to the spread in climate sensitivity across models. In this work, the clouds in three generations of an atmosphere model lineage are evaluated against satellite observations. Satellite simulators are used within the model to provide an appropriate comparison with individual satellite products. In some respects, especially the top‐of‐atmosphere cloud radiative effect, the models show generational improvements. The most recent generation, represented by two distinct branches of development, exhibits some regional regressions in the cloud representation; in particular the southern ocean shows a positive bias in cloud cover. The two branches of model development show how choices during model development, both structural and parametric, lead to different cloud climatologies. Several evaluation strategies are used to quantify the spatial errors in terms of the large‐scale circulation and the cloud structure. The Earth mover's distance is proposed as a useful error metric for the passive satellite data products that provide cloud‐top pressure‐optical depth histograms. The cloud errors identified here may contribute to the high climate sensitivity in the Community Earth System Model, version 2 and in the Energy Exascale Earth System Model, version 1.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1996

Bubble Dynamics on a Heated Surface

In this work, we study the combined thermocapillary and natural convective flow generated by a bubble on a heated solid surface. The interaction between gas and vapor bubbles with the surrounding fluid is of interest for both space and ground-based processing. On earth, the volumetric forces are dominant, especially, in apparatuses with large volume to surface ratio. But in the reduced gravity environment of orbiting spacecraft, surface forces become more important and the effects of Marangoni convection are easily unmasked. In order to delineate the roles of the various interacting phenomena, a combined numerical-experimental approach is adopted. The temperature field is visualized using Mach-Zehnder interferometry and the flow field is observed by a laser sheet flow visualization technique. A finite element numerical model is developed which solves the two-dimensional momentum and energy equations and includes the effects of bubble surface deformation. Steady state temperature and velocity fields predicted by the finite element model are in excellent qualitative agreement with the experimental results. A parametric study of the interaction between Marangoni and natural convective flows including conditions pertinent to microgravity space experiments is presented. Numerical simulations clearly indicate that there is a considerable difference between 1-g and low-g temperature and flow fields induced by the bubble.

Kassemi, Mohammad↗

DOE OSTI2025

Gluon unpolarized, polarized, and transversity GPDs from lattice QCD: Lorentz-covariant parametrization

We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) H g , E g , H ˜ g , E ˜ g , H g T , E g T , H ˜ g T , E ˜ g T in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-0 and spin- 1 2 hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

New Architecture to Support Integration and Processing of Seismic Data from Heterogeneous Sources

The Geophysical Monitoring Program (GMP) at Lawrence Livermore National Lab (LLNL) maintains a database and supporting infrastructure for geophysical data used in support of the Nuclear Detonation Detection mission. This database includes data from multiple sources, many of which do not distribute data to the public or for which there is no automated means of access. For example, Figure 1 shows (left) the distribution of waveform data in our database by source. The Incorporated Research Institutions for Seismology Data Management Center (IRISDMC) is our major source of waveform data and those data may be retrieved at will using the Federated Digital Seismograph Networks FDSN web Application Programming Interface (API). However, the next 6 most important sources of waveform data have no or only limited automated access to waveforms. As Figure 1 (right) shows, it is very common for waveform records associate with an event in our database to come from two or more sources, and in some cases data come from 10 sources. This diversity of data sources drives our need for efficient and correct integration of metadata, parametric data, and waveform data.

58 GEOSCIENCES↗

DOE OSTI2024

Description of FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment

The urgency to deliver fusion power is growing now more than ever, with increasing pressure for both public programs and private companies to meet milestones timelines and overcome significant remaining technical challenges to ensure growth of a nascent fusion industry in time to meet rapidly growing clean energy demands. With incredible advancements in computation and years of investment in fusion model development and validation, integrated modeling is poised to fill a key role in accelerating the timeline to a fusion pilot plant (FPP). Future fusion pilot plants will operate in regimes far beyond current experience, and device design will rely on physics-based prediction and extrapolation. Many concepts will also rely on simulation to assess safety (shielding, tritium management, materials activation and lifetimes), economics and scalability before the decision to build. Importantly, integrated simulation can be used to reveal and solve the complexities of system integration that may otherwise not be apparent in physical components or models developed in isolation. New experimental test facilities that produce relevant conditions to validate and resolve key technical challenges for various subsystems (materials, blankets, fuel cycle, etc.) have been repeatedly called for by the fusion community but are not yet realized. Integrated modeling has an important role in identifying realistic load conditions (thermal, electromagnetic, plasma, neutron and photon loads, etc.) and defining the components and experiments for these test facilities in order to ensure meaningful validation that sufficiently reduces modeling uncertainties and technical risk for the full integrated reactor. The Fusion REactor Design and Assessment (FREDA) SciDAC project is building a component-based integrated modeling framework & data structure to enable self-consistent, multi-fidelity, iterative optimization workflows for the fusion reactor design process. FREDA aims to shorten the time to viable designs by providing a set of flexible workflows to support the various stages of the design process using an integrated model hierarchy, ranging from the simple analytic descriptions to the highest fidelity, theory-based plasma and engineering modeling developed by the fusion and fission communities. These tools are expected to be needed for timely support of FPP design in the milestone program and in the FIRE collaboratives. The plasma simulation backbone of FREDA is IPS-FASTRAN with newly developed coupled Core-Edge Pedestal-SOL (CESOL) workflows, which is being extended to the far-SOL region up to the plasma facing components. FREDA incorporates the FERMI engineering modeling suite and will enable self-consistent evaluation of the thermal shields, limiters, blanket, magnets, and other surrounding structures with predictions of temperatures, erosion, dpa, activation, tritium generation and transport, creep, corrosion, material degradation, etc. Parametric generation of 3D CAD enables rapid iteration of component geometry in response to plasma and loading specifications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Retrofit Energy Analysis and Central Thermal modeling (REACT) v1.0

REACT is a website designed to simplify the analysis and decision-making process for retrofitting existing central plant heating and cooling systems with advanced heat pump technologies. The tool evaluates the technical and economic viability of replacing traditional boilers with various options including water-to-water or air-to-water heat pumps, which can provide efficient and lower-cost heating and cooling. It allows users to compare current central plant configurations with retrofit scenarios, assessing energy consumption, life-cycle costs, and environmental impact. Retrofitting traditional boiler and chiller systems with water-to-water or air-to-water heat pumps can significantly reduce energy consumption and lower lifecycle costs. The REACT provides: User-Friendly Tools: A user friendly web interface for quick, intuitive analysis accessible to non-experts. Advanced Modeling: A Python-powered engine for detailed parametric studies, optimization, and research applications. Comprehensive Analysis: Lifecycle cost evaluation, energy consumption modeling, and environmental impact assessment. Visual Insights: A variety of plots to visualize system performance and design trade-offs. The engine for the website (REACT) bases on several Python libraries, and the website will be hosted on an ETA server.

Kim, Donghun [Lawrence Berkeley National Laborator↗

DOE OSTI2020

A viscoelastic model for seismic attenuation using fractal mechanical networks

SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.

Geochemistry & Geophysics↗

NASA NTRS2003

Precipitation Processes Developed During ARM (1997), TOGA COARE (1992) GATE (1974), SCSMEX (1998), and KWAJEX (1999): Consistent 3D, Semi-3D and 3D Cloud Resolving Model Simulations

Real clouds and cloud systems are inherently three-dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D) have been used to study the response of clouds to large-scale forcing. IN these 3D simulators, the model domain was small, and the integration time was 6 hours. Only recently have 3D experiments been performed for multi-day periods for tropical clouds systems with large horizontal domains at the National Center of Atmospheric Research (NCAR) and at NASA Goddard Space Center. At Goddard, a 3D cumulus Ensemble (GCE) model was used to simulate periods during TOGA COARE, GATE, SCSMEX, ARM, and KWAJEX using a 512 by 512 km domain (with 2-km resolution). The result indicate that surface precipitation and latent heating profiles are very similar between the 2D and 3D GCE model simulation. The major objective of this paper are: (1) to assess the performance of the super-parametrization technique, (2) calculate and examine the surface energy (especially radiation) and water budget, and (3) identify the differences and similarities in the organization and entrainment rates of convection between simulated 2D and 3D cloud systems.

Tao, W.-K.↗

DOE OSTI2025

Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements

The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parametrized quantum circuits that often contain substantially fewer gates than Trotter circuits. Here we report an improved version of the method, which we call AVQDS(T), by porting the tiling efficient trial circuits with rotations implemented simultaneously technique. The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. Here we perform benchmark noiseless AVQDS(T) simulations of quench dynamics in local spin models and compare with an alternative adaptive variational approach on quantum resource requirement. Quantum dynamical simulations implementing realistic noise channels are also reported. Finally, we propose a way to substantially alleviate the measurement overhead of AVQDS(T) while maintaining high accuracy by synergistically integrating quantum circuit calculations on quantum processing units with classical calculations using, e.g., tensor networks to evaluate the quantum geometric tensor. We showcase that this approach enables AVQDS(T) to deliver more accurate results than simulations using a fixed ansatz of comparable final depth for a significant time duration with fewer quantum resources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Nonlinear Loss Engineering in Near‐Zero‐Index Bulk Materials

Transparent conducting oxides (TCOs) show unprecedented optical nonlinearities in the near infrared wavelength range, where the real part of their linear refractive index approaches zero. More specifically, the Kerr nonlinearities of these materials have sparked widespread attention due to their magnitude and speed. However, due to the absorptive nature of these nonlinear processes, it is of fundamental interest to further investigate the imaginary component of the nonlinear index. The present work studies the nonlinear optical absorption properties of aluminium‐doped zinc oxide (AZO) thin films in their near‐zero‐index (NZI) spectral window. It is found that the imaginary part of the refractive index is reduced under optical excitation such that the field penetration depth more than doubles. An optically induced shift of the NZI bandwidth of ≈120 nm for a pump intensity of 1.3 TW cm −2 is also demonstrated. Looking into the optically induced spectral redistribution of the probe signal, local net gain is recorded, which is ascribed to a nonlinear adiabatic energy transfer. The present study adds key information about the fundamental interplay between real and imaginary nonlinear indices in NZI media, while advancing parametric amplification as viable direction for loss compensation.

36 MATERIALS SCIENCE↗

NASA NTRS1976

Post sunset behavior of the 6300 A atomic oxygen airglow emission

A theoretical model of the 6300 A OI airglow emission was developed based on the assumptions that both the charged and neutral portions of the Earth's upper atmosphere are in steady state conditions of diffusive equilibrium. Intensities of 6300 A OI emission line were calculated using electron density true height profiles from a standard C-4 ionosonde and exospheric temperatures derived from Fabry-Perot interferometer measurements of the Doppler broadened 6300 A emission line shape as inputs to the model. Reaction rate coefficient values, production mechanism efficiencies, solar radiation fluxes, absorption cross sections, and models of the neutral atmosphere were varied parametrically to establish a set of acceptable inputs which will consistently predict 6300 A emission intensities that closely agree with intensities observed during the post-sunset twilight period by an airglow observatory consisting of a Fabry-Perot interferometer and a turret photometer. Emission intensities that can only result from the dissociative recombination of molecular oxygen ions were observed during the latter portion of the observational period. Theoretical calculations indicate that contamination of the 6300 A OI emission should be on the order of or less than 3 percent; however, these results are very sensitive to the wavelengths of the individual lines and their intensities relative to the 6300 A OI intensity. This combination of a model atmosphere, production mechanism efficiencies, and quenching coefficient values was used when the dissociative photoexcitation and direct impact excitation processes were contributing to the intensity to establish best estimates of solar radiation fluxes in the Schumann--Runge continuum and associated absorption cross sections. Results show that the Jacchia 1971 model of the upper atmosphere combined with the Ackerman recommended solar radiation fluxes and associated absorption cross sections produces theoretically calculated intensities that more closely agree with the observed intensities than all the other combinations.

Smith, R. E.↗

NASA NTRS2004

Gas-phase production of single-walled carbon nanotubes from carbon monoxide: a review of the hipco process

The latest process for producing large quantities of single-walled carbon nanotubes (SWNTs) to emerge from the Rice University, dubbed HiPco, is living up to its promise. The current production rates approach 450 mg/h (or 10 g/day), and nanotubes typically have no more than 7 mol % of iron impurities. Second-generation HiPco apparatus can run continuously for 7-10 days at a time. In the HiPco process nanotubes grow in high-pressure, high-temperature flowing CO on catalytic clusters of iron. Catalyst is formed in situ by thermal decomposition of iron pentacarbonyl, which is delivered intact within a cold CO flow and then rapidly mixed with hot CO in the reaction zone. Upon heating, the Fe(CO)5 decomposes into atoms that condense into larger clusters. SWNTs nucleate and grow on these particles in the gas phase via CO disproportionation: CO + CO --> CO2 + C (SWNT), catalyzed by the Fe surface. The concentration of CO2 produced in this reaction is equal to that of carbon and can therefore serve as a useful real-time feedback parameter. It was used to study and optimize SWNT production as a function of temperature, pressure, and Fe(CO)5 concentration. The results of the parametric study are in agreement with current understanding of the nanotube formation mechanism.

Review↗

NASA NTRS1993

Hypersonic panel flutter in a rarefied atmosphere

Panel flutter is a form of dynamic aeroelastic instability resulting from the interaction between motion of an aircraft structural panel and the aerodynamic loads exerted on that panel by air flowing past one of the faces. It differs from lifting surface flutter in the sense that it is not usually catastrophic, the panel's motion being limited by nonlinear membrane stresses produced by the transverse displacement. Above some critical airflow condition, the linear instability grows to a limit cycle . The present investigation studies panel flutter in an aerodynamic regime known as 'free molecule flow', wherein intermolecular collisions can be neglected and loads are caused by interactions between individual molecules and the bounding surface. After collision with the panel, molecules may be reflected specularly or reemitted in diffuse fashion. Two parameters characterize this process: the 'momentum accommodation coefficient', which is the fraction of the specularly reflected molecules; and the ratio between the panel temperature and that of the free airstream. This model is relevant to the case of hypersonic flight vehicles traveling at very high altitudes and especially for panels oriented parallel to the airstream or in the vehicle's lee. Under these conditions the aerodynamic shear stress turns out to be considerably larger than the surface pressures, and shear effects must be included in the model. This is accomplished by means of distributed longitudinal and bending loads. The former can cause the panel to buckle. In the example of a simply-supported panel, it turns out that the second mode of free vibration tends to dominate the flutter solution, which is carried out by a Galerkin analysis. Several parametric studies are presented. They include the effects of (1) temperature ratio; (2) momentum accommodation coefficient; (3) spring parameters, which are associated with how the panel is connected to adjacent structures; (4) a parameter which relates compressive end load to its value which would cause classical column buckling; (5) a parameter proportional to the pressure differential between the front and back faces; and (6) initial curvature. The research is completed by an investigation into the possibility of accounting for molecular collisions, which proves to be infeasible given the speeds of current mainframe supercomputers.

Resende, Hugo B.↗

DOE OSTI2022

Systematic exploration of heavy element nucleosynthesis in protomagnetar outflows

ABSTRACT We study the nucleosynthesis products in neutrino-driven winds from rapidly rotating, highly magnetized and misaligned protomagnetars using the nuclear reaction network SkyNet. We adopt a semi-analytic parametrized model for the protomagnetar and systematically study the capabilities of its neutrino-driven wind for synthesizing nuclei and eventually producing ultra-high energy cosmic rays (UHECRs). We find that for neutron-rich outflows (Ye < 0.5), synthesis of heavy elements ($\overline{A}\sim 20-65$) is possible during the first $\sim 10\, {\rm s}$ of the outflow, but these nuclei are subjected to composition-altering photodisintegration during the epoch of particle acceleration at the dissipation radii. However, after the first $\sim 10\, {\rm s}$ of the outflow, nucleosynthesis reaches lighter elements ($\overline{A}\sim 10-50$) that are not subjected to subsequent photodisintegration. For proton-rich (Ye ≥ 0.5) outflows, synthesis is more limited ($\overline{A}\sim 4-15$). These suggest that while protomagnetars typically do not synthesize nuclei heavier than second r-process peak elements, they are intriguing sources of intermediate/heavy mass UHECRs. For all configurations, the most rapidly rotating protomagnetars are more conducive for nucleosynthesis with a weaker dependence on the magnetic field strength.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

BLASIM - A computational tool to assess ice impact damage on engine blades

A portable computer code called BLASIM is developed at NASA LeRC to assess the ice impact damage on aircraft engine blades. In addition to the ice impact analyses, the code is also capable of carrying out static, dynamic, resonance margin and flutter analyses. The blade can be solid, hollow, superhybrid or composite material. An optional preprocessor (input generator) is also developed to generate input to the code through interactive process. The blade geometry can be defined either by a series of airfoils at discrete input stations or by a finite element grid. The code employs a coarse fixed finite element mesh with triangular plate finite elements and has quick turnaround time. The ice piece is modeled as an equivalent spherical object and has the velocity opposite to that of the aircraft with direction parallel to the engine axis. For the local impact damage assessment, the impact force is considered as a distributed load acting over a region around the impact point and the average radial strain of the finite elements along the leading edge is taken as a measure of the local damage. To estimate the damage at the blade root, the impact is considered to be an impulse and a combined stress failure criteria is employed. Parametric studies for local and root ice impact damage, and post-impact dynamics are discussed for solid and composite blades.

Reddy, E. S.↗

DOE OSTI2020

Multidimensional simulations of Mckenna-driven flow tube configuration: Investigating non-ideality in NO x formation flow tube experiments

Multidimensional simulations have been conducted to simulate atmospheric pressure, flat-flame/McKenna-burner-driven-flow tube experiments targeted to obtain NO x speciation data for predicting/analyzing syngas combustion emissions. In a prior work, we demonstrated the impacts of multidimensional transport on post flame region prediction departures from those assuming unidimensional flow/transport conditions. In this work, we develop and utilize a multidimensional laminar reacting flow solver to simulate the fully coupled flame and post flame regions to further elucidate the impacts of the earlier unidimensional modeling assumptions on interpreting post flame NO x experimental data. The model is used to simulate a lean, premixed syngas/air flame and its associated post flame regions within a cylindrical flow-tube-like arrangement. The combustion process takes place under atmospheric condition with trace amount of NO x seeding fed into the inlet gas stream. The spatial evolution of NO x species (NO and NO 2 ) in the flame and in the post-combustion zone suggests two distinct regions: 1) a region encompassing the flame structure itself; and 2) a post flame region in which the temperature decays due to both axial and radial transport processes. The predictions show that for the conditions studied, a pulsatile flow field exists due to the formation of an expanding and contracting recirculation zone in the outer periphery of the flow tube. By resolving the nature of the flow, the resulting time-averaged temperature and species concentrations show improved agreement with existing experimental measurements. The flow-field interaction results in radial inhomogeneities in the NO 2 profiles with the maximum concentration offset from the flow centerline. The location of the peak in NO 2 is coupled with radial temperature gradients from wall cooling effects and their significant influence on NO/NO 2 interconversion kinetics, producing notable NO 2 accumulation in regions near the wall. Geometrical configurations capable of suppressing/minimizing the pulsatile nature are also investigated and the results are compared. Other experimental configurations could be considered in parametric simulations to determine the optimal configuration that would minimize non-idealities in the observations. The work shows the value in performing such computations in advance of settling on a particular design for flow tube/flow reactor experiments.

42 ENGINEERING↗

DOE OSTI2024

Parametrization of Generalized Parton Distributions from 𝑡-Channel String Exchange in AdS Spaces

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) that is valid for all skewness. Our approach leverages conformal moments, representing them as the sum of spin-𝑗 nucleon 𝐴-form factor and skewness-dependent spin-𝑗 nucleon 𝐷-form factor, derived from 𝑡-channel string exchange in AdS spaces consistent with Lorentz invariance and unitarity. This model-independent framework, satisfying the polynomiality condition due to Lorentz invariance, uses Mellin moments from empirical data to estimate these form factors. With just five Regge slope parameters, our method accurately produces various nucleon quark GPD types and symmetric nucleon gluon GPDs through pertinent Mellin-Barnes integrals. Our isovector nucleon quark GPD is in agreement with existing lattice data, promising to improve the empirical extraction and global analysis of nucleon GPDs in exclusive processes, by avoiding the deconvolution problem at any skewness, for the first time.

QCD phenomenology↗

NASA NTRS2006

Structural Configuration Analysis of Crew Exploration Vehicle Concepts

Structural configuration modeling and finite element analysis of crew exploration vehicle (CEV) concepts are presented. In the structural configuration design approach, parametric solid models of the pressurized shell and tanks are developed. The CEV internal cabin pressure is same as in the International Space Station (ISS) to enable docking with the ISS without an intermediate airlock. Effects of this internal pressure load on the stress distribution, factor of safety, mass and deflections are investigated. Uniform 7 mm thick skin shell, 5 mm thick shell with ribs and frames, and isogrid skin construction options are investigated. From this limited study, the isogrid construction appears to provide most strength/mass ratio. Initial finite element analysis results on the service module tanks are also presented. These rapid finite element analyses, stress and factor of safety distribution results are presented as a part of lessons learned and to build up a structural mass estimation and sizing database for future technology support. This rapid structural analysis process may also facilitate better definition of the vehicles and components for rapid prototyping. However, these structural analysis results are highly conceptual and exploratory in nature and do not reflect current configuration designs being conducted at the program level by NASA and industry.

Mukhopadhyay, V.↗