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Benchmarking the PCMCI Causal Discovery Algorithm for Spatiotemporal Systems

Causal discovery algorithms construct hypothesized causal graphs that depict causal dependencies among variables in observational data. While powerful, the accuracy of these algorithms is highly sensitive to the underlying dynamics of the system in ways that have not been fully characterized in the literature. In this report, we benchmark the PCMCI causal discovery algorithm in its application to gridded spatiotemporal systems. Effectively computing grid-level causal graphs on large grids will enable analysis of the causal impacts of transient and mobile spatial phenomena in large systems, such as the Earth’s climate. We evaluate the performance of PCMCI with a set of structural causal models, using simulated spatial vector autoregressive processes in one- and two-dimensions. We develop computational and analytical tools for characterizing these processes and their associated causal graphs. Our findings suggest that direct application of PCMCI is not suitable for the analysis of dynamical spatiotemporal gridded systems, such as climatological data, without significant preprocessing and downscaling of the data. PCMCI requires unrealistic sample sizes to achieve acceptable performance on even modestly sized problems and suffers from a notable curse of dimensionality. This work suggests that, even under generous structural assumptions, significant additional algorithmic improvements are needed before causal discovery algorithms can be reliably applied to grid-level outputs of earth system models.

54 ENVIRONMENTAL SCIENCES↗

Employment of CB models for non-linear dynamic analysis

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

Klein, M. R. M.↗

A hybrid porous model for full reactor core scale CFD investigation of a prismatic HTGR

Three-dimensional (3-D) Computational Fluid Dynamics (CFD) analysis of a whole nuclear reactor core is a tremendous challenge due to the large geometric volume and complex structures. Here, this research presents a hybrid porous (HP) model to simplify a prismatic High Temperature Gas-cooled Reactor (HTGR) core, so 3-D CFD investigation can be performed on a full reactor core scale. In the HP model, the prototypic small coolant channels in the nuclear fuel blocks are lumped together to form multiple equivalent large coolant channels, and then the porous medium flow model is applied to each of them. Therefore, heat transfer in fuel blocks is computed by a hybrid combination of solid energy and porous flow energy equations. The similarity between the HP model and prototypic model is achieved by deriving the porous flow permeability, inertial resistance factor, and artificial thermophysical properties. Compared with the widely used whole porous (WP) flow model, the HP model preserves more realistic geometric structures, and therefore more accurate physical processes. The General Atomics' Modular High Temperature Gas-cooled Reactor (MHTGR) design was chosen as a prototype to demonstrate the methodology. Simulations were performed using the prototypic CFD model and HP model at steady-state forced circulation, steady-state natural circulation, and transient conditions that correspond to normal operation, extended period of pressurized cool down, and short-term transients after reactor shutdown, respectively. The comparison shows good agreement between the HP model and prototypic model in the maximum fuel temperature, average solid temperature, and helium flow rate, which demonstrates the potential applicability of the HP model for a full reactor core scale simulation in the future. As a benefit, the HP model reduces the mesh quantity by a factor of 50 from a prototypic model. Correspondingly, the computation time was reduced by a factor of at least 30.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Spectra of low-mass helium star models and the type Ic supernova SN 1987M

The question of whether the low-mass helium star models reproduce the helium-poor Type Ic spectrum of SN 1987M is investigated by comparing the theoretical spectrum from the 3.3-solar-mass model of Shigeyama et al. (1990) to observations of SN 1987M reported by Filippenko et al. (1990). The results indicate a number of positive correlations between the observed and the computed spectra. In both types of spectra, Ca II, O I, and Mg I emission lines dominate at late times, and, if extensive composition mixing is imposed, good fits can be made to the shapes of the emission features and good agreement can be found with the observed ratio of the forbidden and IR triplet blends of Ca II. The former indicates that the 3.3-solar-mass model predicts the proper density/velocity structure, and the latter indicates that the computed temperature structure is consistent with the observation though the lines are too strong relative to the continuum. This result is roughly independent of the He abundance. The computed and observed spectra are consistent with a small Ni-56 production in contrast to Type Ia thermonuclear events whose spectra are dominated by Fe-group lines at late times.

Swartz, Douglas A.↗

PORFLOW modeling of Vadose zone flow and transport for the E-area intermediate level vault

In support of the E-Area Performance Assessment, a two-dimensional model of water flow and radionuclide transport through the E-Area Intermediate Level Vault (ILV) and local vadose zone has been developed using the PORFLOWTM software. The purpose of the model is to calculate flux to the water table for radionuclides eluted from the ILV during its operational life, the period of institutional control, and times following site closure. Results of model calculations will be used by a three-dimensional PORFLOW model of transport through the aquifer to determine radionuclide concentrations at a hypothetical 100 meter well and at the site boundary where contaminated groundwater could be assessed by members of the public following site closure. While newly developed, the model structure closely follows that used in the 2008 PA while incorporating a refined computational mesh, updated material properties for the vadose zone soil and vault concrete, revised infiltration rates, and new solid-liquid distribution coefficients. The model also addresses degradation of concrete hydraulic properties by blending soil and concrete water retention curves over a 500 year period. That is, the hydraulic properties of ILV concrete start out as fresh concrete at the time of site closure and degrade to soil properties over a 500 year time period. This approach has not been used previously in E-Area PA’s. The model has been used to calculate water flow through the ILV vadose zone and, on a trial basis, transport of a limited number of radionuclides from the waste region inside the ILV to the water table. Figure ES-1 provides a view of the model and an example of water flow after the concrete has substantially degraded. Figure dimensions are in centimeters. The red area in the left hand side figure is the waste disposal region within the ILV. Colored bands in the figures indicate different soil and concrete regions. Figure ES-2 shows a calculation of flux to the water table (mol/yr) for U-234 and its one-year half-life decay chain (U-234 → Th-230 → Ra-226 → Pb-210). Pb-210 flux is too small to show on the same scale used for Th-230 and Ra-226 in Figure ES-2. The model has also been used to make a preliminary evaluation of the release of tritium from TPBAR disposal containers that will be place in the ILV. A separately calculated tritium release rate as a function of time was used as a source in the PORFLOW model. The TPBAR disposal schedule and tritium release rate differ from the values used in the 2008 PA. Results from these initial trial runs are compared to calculations made for the 2008 PA ILV analysis. In brief, a new PORFLOW model of flow and transport through the ILV vadose zone has been developed and tested. The model is ready to be used for PA calculations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A Macroalgal Cultivation Modeling System (MACMODS): Evaluating the Role of Physical-Biological Coupling on Nutrients and Farm Yield

Offshore aquaculture has the potential to expand the macroalgal industry. However, moving into deeper waters requires suspended structures that will present novel farm-environment interactions. Here, we present a computational modeling framework, the Macroalgal Cultivation Modeling System (MACMODS), to explore within-farm modifications to light, seawater flow, and nutrient fields across time and space scales relevant to macroalgae. A regional ocean model informs the site-specific setting, the Santa Barbara Channel in the Southern California Bight. A fine-scale hydrodynamic model predicts modified flows and turbulent mixing within the farm. A spatially resolved macroalgal growth model, parameterized for giant kelp, Macrocystis pyrifera , predicts kelp biomass. Key findings from model integration are that regional ocean conditions set overall farm performance, while fine-scale within-farm circulation and nutrient delivery are important to resolve variation in within-farm macroalgal performance. Therefore, we conclude that models resolving within-farm dynamics can provide benefit to farmers with insight on how farm design and regional ocean conditions interact to influence overall yield. Here, the presence of repeating longlines aligned with the mean current generate flow diversions around the farm as well as attached Langmuir circulations and increased turbulence intensity. These flow-induced phenomena lead to less biomass in the interior portion of the farm relative to the edges. We also find that there is an effluent “footprint” that extends as much as 20 km beyond the farm. In this regard, MACMODS can be used to not only evaluate farm design and cultivation practices that maximize yield but also explore interactions between the farm and ecosystem in order to minimize impacts.

54 ENVIRONMENTAL SCIENCES↗

The high latitude circulation and temperature structure of the thermosphere near solstice

NCAR thermospheric-general-circulation-model (TGCM) computations of solar-maximum thermospheric neutral-gas temperature and circulation around the December solstice are presented and discussed. The TGCM uses a 5 x 5-deg grid and 24 constant-pressure layers, corresponding to altitudes of about 97-500 km. The results are mapped as electron-density contours, polar plots, cylindrical equidistant projections, meridional cross sections, and F-region polar plots comparing the TGCM predictions with DE-2 satellite observations. The significant differences between summer and winter high-latitude F-region winds are attributed to the ion drag momentum associated with magnetospheric convection. The TGCM wind predictions follow the same pattern as the satellite measurements but are too small; possible model corrections are considered.

Roble, R. G.↗

A New Method for Estimating the Single Scattering Phase Functions of Regolith Grains

Hapke's photometric model has been widely used in solar system remote sensing applications for nearly two decades. Recently, Hapke extended his model to describe the coherent-backscatter opposition effect and multiple-scattering by particles with anisotropic single particle phase functions (SPPF's). A practical difficulty for retrieving Hapke's model parameters from typical planet, satellite, and asteroid photometry data sets is that the model employs a large number of adjustable parameters (at least eight) that can be reliably constrained only for a small number of planetary data sets in which both disk-resolved and whole-disk observations are available from opposition to very large phase angles. The present work aims to reduce the number of adjustable parameters and preserve (or even enhance) the model's accuracy and usefulness by expressing Hapke's parameters in terms of more fundamental physical properties on which they mutually depend. The most difficult part of this task, described here, is to develop a simple method for computing the effective SPPF for structurally complex regolith grains from optical constants, grain-size distribution, and average regolith porosity. The development of light-scattering models for irregularly shaped particles is a large, complex subject and many sophisticated methods, such as Discrete Dipole Approximation (DDA) and Monte-Carlo simulations, have been explored elsewhere. Many of these methods are computationally intensive and probably impractical for routine substitution in Hapke's model. Here, progress is reported in developing a practical, semi-empirical method for estimating the directional scattering behavior (i.e. SPPF) of irregular regolith grains. The method employs Optical Transfer Function (OTF) techniques to model how the structural complexity of regolith particles broaden and attenuate the angular distribution of scattered light relative to that expected from ideal spherical particles of equivalent size and composition.

Helfenstein, P.↗

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Samareh, Jamshid A.↗

Predicting the Structure of the Solar Corona During the December 4, 2002 Total Solar Eclipse

The solar magnetic field plays a key role in determining coronal. The principal input to MHD models is the observed solar magnetic field. 3D MHD models can be used to compare with eclipse and coronograph images, SOHO images (LOSCO, EIT), Ulysses and WIND spacecraft data, and interplanetary scintillation (IPS) measurements. MHD computations can tell us about the structure of the corona. Eclipses can help us to verify the accuracy of the models. 4 December, 2002 total eclipce: visible in the southern hemisphere (South Atlantic, southern Africa, Indian Ocean, and Australia). Total in center Angola is at 06:00 UT.

Mikic, Zoran↗

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.

Volakis, J. L.↗

Physics-based Entry, Descent and Landing Risk Model

A physics-based risk model was developed to assess the risk associated with thermal protection system failures during the entry, descent and landing phase of a manned spacecraft mission. In the model, entry trajectories were computed using a three-degree-of-freedom trajectory tool, the aerothermodynamic heating environment was computed using an engineering-level computational tool and the thermal response of the TPS material was modeled using a one-dimensional thermal response tool. The model was capable of modeling the effect of micrometeoroid and orbital debris impact damage on the TPS thermal response. A Monte Carlo analysis was used to determine the effects of uncertainties in the vehicle state at Entry Interface, aerothermodynamic heating and material properties on the performance of the TPS design. The failure criterion was set as a temperature limit at the bondline between the TPS and the underlying structure. Both direct computation and response surface approaches were used to compute the risk. The model was applied to a generic manned space capsule design. The effect of material property uncertainty and MMOD damage on risk of failure were analyzed. A comparison of the direct computation and response surface approach was undertaken.

descent and landing↗

Visualization and validation of twin nucleation and early-stage growth in magnesium

The abrupt occurrence of twinning when Mg is deformed leads to a highly anisotropic response, making it too unreliable for structural use and too unpredictable for observation. Here, we describe an in-situ transmission electron microscopy experiment on Mg crystals with strategically designed geometries for visualization of a long-proposed but unverified twinning mechanism. Combining with atomistic simulations and topological analysis, we conclude that twin nucleation occurs through a pure-shuffle mechanism that requires prismatic-basal transformations. Also, we verified a crystal geometry dependent twin growth mechanism, that is the early-stage growth associated with instability of plasticity flow, which can be dominated either by slower movement of prismatic-basal boundary steps, or by faster glide-shuffle along the twinning plane. The fundamental understanding of twinning provides a pathway to understand deformation from a scientific standpoint and the microstructure design principles to engineer metals with enhanced behavior from a technological standpoint.

36 MATERIALS SCIENCE↗

Structure-Property Relationships of Bismaleimides

The purpose of this research was to control and systematically vary the network topology of bismaleimides through cure temperature and chemistry (addition of various coreactants) and subsequently attempt to determine structure-mechanical property relationships. Characterization of the bismaleimide structures by dielectric, rheological, and thermal analyses, and density measurements was subsequently correlated with mechanical properties such as modulus, yield strength, fracture energy, and stress relaxation. The model material used in this investigation was 4,4'-BismaleiMidodIphenyl methane (BMI). BMI was coreacted with either 4,4'-Methylene Dianiline (MDA), o,o'-diallyl bisphenol A (DABA) from Ciba Geigy, or Diamino Diphenyl Sulfone (DDS). Three cure paths were employed: a low- temperature cure of 140 C where chain extension should predominate, a high-temperature cure of 220 C where both chain extension and crosslinking should occur simultaneously, and a low-temperature (140 C) cure followed immediately by a high-temperature (220 C) cure where the chain extension reaction or amine addition precedes BMI homopolymerization or crosslinking. Samples of cured and postcured PMR-15 were also tested to determine the effects of postcuring on the mechanical properties. The low-temperature cure condition of BMI/MDA exhibited the highest modulus values for a given mole fraction of BMI with the modulus decreasing with decreasing concentration of BMI. The higher elastic modulus is the result of steric hindrance by unreacted BMI molecules in the glassy state. The moduli values for the high- and low/high-temperature cure conditions of BMI/MDA decreased as the amount of diamine increased. All the moduli values mimic the yield strength and density trends. For the high-temperature cure condition, the room- temperature modulus remained constant with decreasing mole fraction of BMT for the BMI/DABA and BMI/DDS systems. Postcuring PMR-15 increases the modulus over that of the cured material even though density values of cured and postcured PMR were essentially the same. Preliminary results of a continuous and intermittent stress relaxation experiment for BMI:MDA in a 2:1 molar ratio indicate that crosslinking is occurring when the sample is in the undeformed state. Computer simulation of properties such as density, glass transition temperature, and modulus for the low- temperature cure conditions of BMI/MDA and BMI/DABA were completed. The computer modeling was used to help further understand and confirm the structure characterization results. The simulations correctly predicted the trends of these properties versus mole fraction BMI and were extended to other BMI/diamine systems.

Tenteris-Noebe, Anita D.↗

Single-Molecule Kinetics of Styrene Hydrogenation on Silica-Supported Vanadium: The Role of Disorder for Single-Atom Catalysts

We report a theoretical approach for the study of supported atom catalysis is developed based on recent advances in the study of single-molecule kinetics. This view is particularly useful in exhibiting the role of disorder in single-atom and single-site catalysts on amorphous supports. The distribution of passage times (or waiting times) through a complex catalytic network originating from a set of coupled active sites is described by a probability distribution function (PDF), f(t), that reflects the local environment of the reaction center. An efficient algorithm is developed based on the linear algebra of the Markov transition matrix that produces f(t) or its moments. The kinetics of the hydrogenation reaction of styrene on an organovanadium(III) catalyst supported on amorphous silica is studied. A kinetic model consisting of three intertwined catalytic cycles emanating from three chemically distinct active sites is proposed to describe the chemistry. Density functional theory (DFT) calculations are employed to determine the free energy barriers of the reactions, which are used to construct the rate coefficient matrix. The disorder induced by the amorphous support material is divided into a low-dimensional short-range component reflecting the covalent structures near the reaction center and a weaker long-range component modeling the bulk randomness. The results are computed and analyzed for a wide range of concentration values and disorder scenarios. The unusual structure in the f(t) PDF is found to occur for certain cases that reveal the contribution of multiple catalytic pathways acting in concert.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On Efficient Multigrid Methods for Materials Processing Flows with Small Particles

Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. Multigrid methods are known for their superior efficiency in representing/resolving different levels of physical details. The efficiency is achieved by employing interactively different discretizations on different scales (grids). To assist optimization of manufacturing conditions for materials processing with numerous particles (e.g., dispersion of particles, controlling flow viscosity and clusters), a new multigrid algorithm has been developed for a case of multiscale modeling of flows with small particles that have various length scales. The optimal efficiency of the algorithm is crucial for accurate predictions of the effect of processing conditions (e.g., pressure and velocity gradients) on the local flow fields that control the formation of various microstructures or clusters.

Thomas, James↗

Atomistic Method Applied to Computational Modeling of Surface Alloys

The formation of surface alloys is a growing research field that, in terms of the surface structure of multicomponent systems, defines the frontier both for experimental and theoretical techniques. Because of the impact that the formation of surface alloys has on surface properties, researchers need reliable methods to predict new surface alloys and to help interpret unknown structures. The structure of surface alloys and when, and even if, they form are largely unpredictable from the known properties of the participating elements. No unified theory or model to date can infer surface alloy structures from the constituents properties or their bulk alloy characteristics. In spite of these severe limitations, a growing catalogue of such systems has been developed during the last decade, and only recently are global theories being advanced to fully understand the phenomenon. None of the methods used in other areas of surface science can properly model even the already known cases. Aware of these limitations, the Computational Materials Group at the NASA Glenn Research Center at Lewis Field has developed a useful, computationally economical, and physically sound methodology to enable the systematic study of surface alloy formation in metals. This tool has been tested successfully on several known systems for which hard experimental evidence exists and has been used to predict ternary surface alloy formation (results to be published: Garces, J.E.; Bozzolo, G.; and Mosca, H.: Atomistic Modeling of Pd/Cu(100) Surface Alloy Formation. Surf. Sci., 2000 (in press); Mosca, H.; Garces J.E.; and Bozzolo, G.: Surface Ternary Alloys of (Cu,Au)/Ni(110). (Accepted for publication in Surf. Sci., 2000.); and Garces, J.E.; Bozzolo, G.; Mosca, H.; and Abel, P.: A New Approach for Atomistic Modeling of Pd/Cu(110) Surface Alloy Formation. (Submitted to Appl. Surf. Sci.)). Ternary alloy formation is a field yet to be fully explored experimentally. The computational tool, which is based on the BFS (Bozzolo, Ferrante, and Smith) method for the calculation of the energetics, consists of a small number of simple PCbased computer codes that deal with the different aspects of surface alloy formation. Two analysis modes are available within this package. The first mode provides an atom-by-atom description of real and virtual stages 1. during the process of surface alloying, based on the construction of catalogues of configurations where each configuration describes one possible atomic distribution. BFS analysis of this catalogue provides information on accessible states, possible ordering patterns, and details of island formation or film growth. More importantly, it provides insight into the evolution of the system. Software developed by the Computational Materials Group allows for the study of an arbitrary number of elements forming surface alloys, including an arbitrary number of surface atomic layers. The second mode involves large-scale temperature-dependent computer 2. simulations that use the BFS method for the energetics and provide information on the dynamic processes during surface alloying. These simulations require the implementation of Monte-Carlo-based codes with high efficiency within current workstation environments. This methodology capitalizes on the advantages of the BFS method: there are no restrictions on the number or type of elements or on the type of crystallographic structure considered. This removes any restrictions in the definition of the configuration catalogues used in the analytical calculations, thus allowing for the study of arbitrary ordering patterns, ultimately leading to the actual surface alloy structure. Moreover, the Monte Carlo numerical technique used for the large-scale simulations allows for a detailed visualization of the simulated process, the main advantage of this type of analysis being the ability to understand the underlying features that drive these processes. Because of the simplicity of the BFS method for e energetics used in these calculations, a detailed atom-by-atom analysis can be performed at any point in the simulation, providing necessary insight on the details of the process. The main objective of this research program is to develop a tool to guide experimenters in understanding and interpreting often unexpected results in alloy formation experiments. By reducing the computational effort without losing physical accuracy, we expect that powerful simulation tools will be developed in the immediate future, which will allow material scientists to easily visualize and analyze processes at a level not achievable experimentally.

Bozzolo, Guillermo H.↗

The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: Boeing Helicopters airframe finite element modeling

Mathematical models based on the finite element method of structural analysis, as embodied in the NASTRAN computer code, are routinely used by the helicopter industry to calculate airframe static internal loads used for sizing structural members. Historically, less reliance has been placed on the vibration predictions based on these models. Beginning in the early 1980's NASA's Langley Research Center initiated an industry wide program with the objective of engendering the needed trust in vibration predictions using these models and establishing a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process. Emphasis in this paper is placed on the successful modeling of the Army/Boeing CH-47D which showed reasonable correlation with test data. A principal finding indicates that improved dynamic analysis requires greater attention to detail and perhaps a finer mesh, especially the mass distribution, than the usual stress model. Post program modeling efforts show improved correlation placing key modal frequencies in the b/rev range with 4 percent of the test frequencies.

Gabel, R.↗