dataesr/scientific-paragraphs-categorization huggingface dataset:
We thank the  MRF  staff for their support. This work was supported by  EUROfusion Enabling Research  project  TRiCEM, Tritium Retention in Controlled and Evolving Microstructure. This work has been carried out within the framework of the  EUROfusion Consortium  and has received funding from the  Euratom  research and training programme 2014-2018 and  2019-2020  under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the  European Commission. We acknowledge funding by the  RCUK   Energy Programme  (Grant No. EP/T012250/1 ).
Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer (SOL) of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted ohmic L-mode discharges on the tokamak à configuration variable (TCV) tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from five diagnostic systems from the outboard midplane (OMP) to the divertor targets-giving a total of 45 one-and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models-GBS, GRILLIX and TOKAM3X.
already been used to test boundary turbulence simulations in basic plasma physics devices  [24] [25] [26]  and limited tokamak plasmas  [17]. In this paper, we extend these previous works to the validation of edge turbulence codes in diverted tokamak geometry, with the goal of guiding the development of the models and assessing how close simulations are to reproducing realistic plasma behaviour. For this purpose, a diverted, ohmic L-mode scenario has been developed on the tokamak à configuration variable (TCV)  [27] , performed in both toroidal magnetic field directions. Thanks to the large suite of edge/SOL diagnostics available on TCV, an extensive experimental dataset has been collected, allowing for a stringent assessment of the simulation-experiment agreement. We refer to this scenario and dataset as the TCV-X21 validation reference case.
A dynamic repository is provided at https://github. com/SPCData/TCV-X21, which will be updated with the results of future comparisons against the reference case (this is encouraged, to provide an evolving picture of the state-of-the-art of divertor modelling). We additionally provide a static repository for the version used in this paper at https://doi. org/10. 5281/zenodo. 5776286, and a web-interface to the processing routines at https://mybinder. org/v2/gh/SPCData/TCV-X21/HEAD?labpa th=tcv-x21. ipynb. Throughout this paper, wherever extended analyses are available through the repository, we indicate this via a file-path relative to the root of the TCV-X21 repository. The remainder of this paper is organised as follows: we first outline our validation methodology in section 2, following the methodology in Ricci et al 2015  [25].
Experimental scenario In this work, we developed an experimental scenario in TCV for the validation of boundary turbulence codes. TCV is a medium size tokamak (R axis = 0. 88 m) with nominal vacuum toroidal magnetic field of B φ,axis 1. 45 T equipped with 16 independently-powered shaping coils providing extreme plasma shaping capabilities  [27]. The experimental scenario, referred to as the TCV-X21 reference scenario, is a lowersingle-null L-mode ohmic plasma. A poloidal cross-section showing the magnetic flux surfaces of this scenario, obtained from the LIUQE magnetic reconstruction code  [49] , can be seen in figure  2  together with the set of diagnostics used to collect the experimental dataset. The discharges were performed in deuterium and at a reduced toroidal field of B φ,axis 0. 95 T.
In general, we categorise the experimental uncertainty into three sources. The first is Δe fit , the uncertainty related to fitting experimental data to a model. The second is Δe dia , due to inherent characteristics of the diagnostics, e. g. uncertainties in the effective ion collection surface of LPs. Finally, the third is Δe rep , the uncertainty related to the reproducibility of the observable assessed by comparing repeated discharges, typically performed in separate experimental sessions. Then, the total experimental uncertainty is evaluated reconstructed by LIUQE and the diagnostics used to gather the dataset. We indicate the location of the wall-embedded Langmuir probes at the high-field-side and low-field-side divertor targets (HFS-LP and LFS-LP-red and blue circles), the reciprocating divertor probe array (RDPA-black L-shaped structure) and its swept area (black watermark box), the Thomson scattering system (TS-orange squares), the fast horizontal reciprocating probe (FHRP-solid and watermark boxes in purple), the far infrared interferometer (used to estimate the line-average density, FIR-cyan), the field-of-view of the infrared system (IR-green), and the position of the top valve used to fuel the plasma (magenta).
Reciprocating divertor probe array The reciprocating divertor probe array (RDPA) installed at the bottom of TCV (see figure  2 ) provides 2D measurements of a variety of quantities by combining a fast, vertical linear motion and a radial array of 12 rooftop Mach probes  [57]. A typical RPDA plunge takes approximately 350 ms and its Mach probes are operated in three different modes: sweepbias, J sat , and V fl. The quantities obtained in this way are timeaverages of n e , T e , V fl , V pl , M and time histories of J sat and V fl. The time histories are used to estimate mean and fluctuation profiles of J sat and V fl , as well as the skewness and kurtosis of J sat. The vertical positions Z of the RDPA dataset are translated to the coordinate system Z -Z X , where Z X is the vertical X-point position determined by LIUQE.
Since the start of this project, new versions of the codes with extended models have been developed-these are discussed in section 6. 5. The codes employ different sheath boundary conditions at the magnetic presheath entrance near the divertor targets. The details of the boundary conditions used for each code are given in appendix A, with the key differences summarised here. For GBS, the parallel ion velocity u is set to c s. In GRILLIX and TOKAM3X, corrections for the E × B drift (both codes) and curvature drift (TOKAM3X only) are included in the u boundary condition, and the drift-corrected ion velocity is set to c s to allow supersonic transients to be freely advected across the boundaries (see appendix A and reference  [7, 66] ). For the electron and ion temperatures, GBS enforces ∇ T = 0, while in GRILLIX and TOKAM3X sheath heat transmission factors are used.
Conversely, the T e and V pl profiles are much broader than the experimental profiles. This is likely due to the reduced heat conductivity, which changes the ratio between the parallel and perpendicular heat fluxes. Since the plasma potential is related to the electron temperature, it will also be broadened. Of the three codes, GBS is the only code which predicts a significantly-non-zero V fl , but the predicted profiles do not match the experiment. At least for the reversed-field case, this could be a consequence of the profile broadening. For GRILLIX, the density at the targets is too low, while the shape is loosely recovered, except for the PFR peak observed at the LFS in forward-field. The SOL T e profile is matched well at both targets and in both field directions, while in the PFR the T e profile drops off too sharply.
Summary and conclusions The predictive capabilities of divertor turbulence simulations were rigorously assessed via a validation against a series of dedicated diverted TCV discharges in both forward and reversed field direction. The discharges were performed at a lower toroidal magnetic field than typical for TCV (0. 95 T vs 1. 45 T) to decrease the computational cost, thus allowing direct, full-size simulations of the experimental scenario. Moreover, the discharges were carried out in low density, sheath-limited conditions, designed to reduce the effect of the neutrals, which are currently not included in the simulations. The discharges were repeated several times to improve the statistics of the experimental measurements and to investigate the effect of toroidal field reversal. An extensive experimental dataset, which we refer to as TCV-X21, was collected for the purpose of validating the codes, which includes a broad range of 1D and 2D measurements of fluctuation and time-averaged quantities at the OMP, at the DE, throughout the divertor volume, and at the target plates.
The validation dataset is provided in an open repository, as a reference for future validations and to allow benchmarking of boundary turbulence simulations. Full-size simulations of the TCV-X21 reference case, in both toroidal field directions, were performed by three separate edge turbulence modelling groups, using the GBS, GRIL-LIX and TOKAM3X codes. The simulations were flux-driven, meaning that the plasma profiles, turbulence and transport were evolved self-consistently. As such, the simulations were validated against the full set of experimental measurements, including both mean profiles and fluctuations. The only tunable physics parameters in these simulations were the position and strength of the density source and of the temperature or power source. The source positions were chosen to approximately match the positions of ohmic power deposition and neutral ionisation, and the rates were adjusted to approximately match the experimental OMP density and temperature (or power) at the position of the separatrix.
This validation shows that the TCV-X21 reference case developed in this work allows for the rigorous validation and bench-marking of turbulence simulations. The results of this first validation indicate that turbulence simulations are already providing a promising match to the experiment, which can be further improved by targeted development of the codes. This validation methodology can be extended to other codes since the TCV-X21 reference data has been publicly released. Additionally, similar validations could be performed at more challenging plasma parameters, with neutral physics included, in more complex magnetic geometries, at larger magnetic field strengths and on larger machines. Continued validation of turbulence simulations over a broad parameter space will accelerate the development of the codes, to improve their usefulness for interpreting results from existing machines, and eventually to enable predictive simulations of future fusion reactors.
Acknowledgments This work has been carried out within the framework of the  EUROfusion Consortium  and has received funding from the  Euratom  research and training programme 2014-2018 and  2019-2020  under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the  European Commission. This work was supported in part by the  Swiss National Science Foundation. This work was partly supported by the  U. S. Department of Energy  under Grant No. DE-SC0010529. This work was completed within the framework of the  EUROfusion Enabling Research   ENR-MFE19. EPFL-02 , led by  Christian Theiler. It was supported by the  EUROfusion Theory Simulation Verification  and  Validation  project  3 , led by  Patrick Tamain. This work was supported by a Grant from the  Swiss National Supercomputing Centre (CSCS)  under project IDs s1126, s1129, s1028 and s882.
Acknowledgements We gratefully acknowledge  Nantes Université , the  Centre National de la Recherche Scientifique (CNRS)  for financial support. KEK thanks the " Ministère de l'Enseignement Supérieur et de la Recherche Scientifique de Côte d'Ivoire"  for a visiting grant in France. We acknowledge  Julie Hémez  ( CEISAM, Nantes Université ) for HRMS analyses.
Acknowledgments: The authors thank the technical department of ICPEES and more particularly  Christophe Sutter  (Electronic engineer) and  Michel Wolf  (Assistant Mechanical Engineer) as well as all the administrative staff of ICPEES for their support. The authors would also like to thank the entire staff of the  MICA Carnot Institute  for the quality of the exchanges and the animation of this network of laboratories as well as the interdisciplinary thematic institute "Hierarchical and functional materials for health, environment and energy" ( ITI HiFunMat ).
Phase-Field Simulations Phase-field simulations of the PTO nanowires are performed with the help of the FEniCS software package  [38]. The evolution of the polarization vector field P i to its equilibrium fashion is governed by the relaxation equation: -γ ∂P i ∂t = δ δP i F(P i , u ij , ∂ i ϕ)dV. ( 2 ) where the energy density is taken as a function of electric potential ϕ and the strain tensor u ij , obtained from the stress-dependent energy given by Equation (  1 ) by the Legendre transformation  [39]. Equation (  2 ) is closed by the Poisson equation which takes into account electrostatic effects: ε 0 ε i ∇ 2 ϕ = ∂ i P i , (3) and by the linear equation of elasticity: s -1 ijkl ∂ j u kl -Q ijkl P k P l = 0. (4) The value of the parameter γ is taken equal to one, as it is not crucial for the static case.
Coefficients k 2 , k 4 , a, b, c and ρ are the shell model fitting parameters. The multi-scale model with 23 independent parameters was originally developed to study bulk properties of PTO  [48] , and it was then successfully used to describe the behavior of surfaces, interfaces, and nanoparticles without including any additional coefficients  [11, 49, 50]. The PTO wires are constructed from elementary perovskite unit-cells centered on Ti atoms with axes along pseudocubic directions (x, y and z axes lie along the [100], [010], and [001] directions, respectively). In addition, we consider that all surface faces consist of PbO planes. Molecular dynamics simulations with the atomistic model are carried out using the DL-POLY package  [51]  in a box with periodic boundary conditions. The nanowires extend along the z axis and they are surrounded by enough empty space to avoid any possible interaction between periodic replicas.
This discrepancy is a consequence of the smaller equilibrium volume of the model and is related to the LDA database used to fit model parameters. It is well known that the volume and volume-dependent properties are underestimated when using the LDA approximation for the exchange-correlation functional in first-principle calculations which, in turn, lead to the significant underestimation of the polarization and transition temperatures. In bulk, for instance, the model gives a tetragonal ground state with the lattice parameter a = 3. 859 Å, a tetragonal distortion c/a = 1. 043, and the spontaneous polarization P = 0. 54 C m -2 , while the experimental data are a = 3. 90 Å, c/a = 1. 065, and P = 0. 75 C m -2 , respectively. The underestimation of the static structural properties is translated via the adjusted model to the finite temperature behavior.
Funding: This research was financially supported by the  European Union   H2020-MSCA-RISE EN-GIMA  and MELON actions. S. K. acknowledges the support from the  Alexander von Humboldt Foundation. The work of V. M. V. was supported by  Terra Quantum AG  and, in part, by the  Fulbright Foundation. F. D. R. and M. S. acknowledge the support from  CONICET  (No. PUE-IFIR 2017-2022 N0076 ).
Briefly, MIBEL is located on the periphery of Europe and has a fairly low interconnective capacity with the rest of the European electricity market  (Loureiro et al. , 2019). Therefore, MIBEL's market is relatively limited, and its domestic electricity systems are likely to be highly reliant on each other to manage their respective instantaneous electricity demand and supply. Another important characteristic of the Spanish electricity system is that it has one of the largest installed capacities of wind generation in Europe. Furthermore, Spain is one of the European countries with the greatest potential for producing electricity from solar PV and, according to data published in Red Eléctrica de España (REE), the capacity of installed solar PV power surged exponentially in 2020. The main goal of this research is to study the impact of electricity imports and exports (hereafter, inflow and outflow, respectively), and of wind and solar PV power, on the Spanish day-ahead electricity price.
By assessing the MOE of wind and solar PV on an hourly basis,  Benhmad and Percebois (2018)  concluded that, in Germany, the MOE does vary in magnitude throughout the 24 h of the day. Indeed, the study of  Lagarde and Lantz (2018)  highlighted that the higher electricity prices are in Germany, the higher the MOE and volatility in electricity prices. Conversely, in some other countries, the MOE was found to be negligible or even non-existent. For instance, an analysis of hourly data in the Czech Republic found no evidence of the MOE from solar PV power  (Luňáčková et al. , 2017) , and in a study of Slovakia  (Janda, 2018) , it was negligible. These conclusions can be explained in part by the low intensity of solar radiation in both countries, and the prominent role of nuclear power in Slovakia.
Data analysis This paper used high-frequency hourly data from the Spanish electricity system and each hour is studied individually (hence 24 models were estimated). Studying each hour individually created a framework that significantly reduced both strong seasonality, and any autocorrelation in the estimations. Strong autocorrelation was not anticipated in this analysis for two main reasons. Firstly, in this empirical analysis it was assumed that there were no interrelations between the independent variables. The electricity produced from wind power and solar PV is highly intermittent and unpredictable, so it is unnecessary to consider its relationship with other explanatory variables (such as electricity consumption or electricity inflow and outflow). Secondly, as the MOE is assessed in each hour individually, bids for the day-ahead electricity price at 1 a.
m. of day d are not submitted at the same time as bids for 1 a. m. of day d -1, for instance. This method of assessing the MOE meant the possibility of strong autocorrelation in the wholesale electricity price time series was greatly reduced. The data originated from the REE -ESIOS Sistema de Información del Operador del Sistema and the timespan studied was from 1 May 2015 to 31 December 2020. All available data for the period was studied, totalling 2072 observations for each of the 24 hourly estimations. The database included the day-ahead electricity price (PRICE, = C/MWh); the forecast consumption of electricity (CONS, MWh); the forecast electricity production from wind power (WIND, MWh); the forecast of electricity production from solar PV power (SOLAR, MWh); electricity inflow (INFLOW, MWh); and electricity outflow (OUTFLOW, MWh).
Conclusions Increased levels of generation from wind and solar PV power in the electricity generation mix has provoked a profound restructuring of electricity markets and a complete rethinking of strategies for market participants. One of the restructuring measures has been to increase the capacity of interconnections and, as a consequence, it has become extremely important to evaluate the impact of electricity flows on electricity prices. With this in mind, this paper analysed the impact of electricity inflow and outflow, as well as of wind and solar PV power, on the mean of Spanish day-ahead electricity prices and their volatility. The data was analysed on an hour-by-hour basis, with each hour of the day being assessed individually, from 1 May 2015 to 31 December 2020. The MOE was confirmed for both wind and solar PV power in almost all hours of the day.
(2017) applied the ANN technique for the purpose of assessing the plasticity index of clay soil stabilized with lime. A total of 280 plasticity index values were collected from various data sets recorded by a number of researchers from the literature. These values were utilized in the ANN method which turned out to be a quite e cient approach in predicting the plasticity index of sand-treated clayey soil stabilized with lime. With regard to Sari  Ahmed et al. (2018) , they carried out a study in order to examine the affect of y ash on the behavior of high-plasticity clay soils using the ANN method. For this, 29 y ash -stabilized soils were utilized for developing models intended to predict the consistency limits. The liquid limit and the amount of y ash to be used were taken as input factors and the plasticity index as output parameter.
These researchers revealed that the ANN technique is highly e cient in predicting the plasticity index (PI) of clay soils stabilized with y ash. In this context, Jasim et al. (2019) applied the ANN technique to predict the plasticity index of soils in Baghdad, the capital city of Iraq, and also used an experimental database. As for Akbay  Arama et al. (2021) , they developed and implemented models based on the ANN method for predicting the plasticity index of very highly plastic clayey soils. In addition, some empirical relationships were employed to evaluate the plastic limit and plasticity index from the liquid limit. It is worth emphasizing that the data used in the models were obtained from experimental consistency tests that were carried out on various clay soils from the city of Istanbul, in Turkey.
Data construction In this study, the results of the experimental tests that were conducted on 38 samples of sand-treated soil were collected for the purpose of developing an ANN model capable of predicting the plasticity index. It should be noted that these data were gathered from several research studies available in the literature. In ( ) addition, a total of 197 plasticity index values found in the literature were randomly divided into three categories : the rst category was for training (70%), the second one for testing (15%), and the third one (15%) for the validation of the analysis model. All the data involved in this model are shown in Table  1 , while the statistical data-collection parameters are presented in Table  2. The database obtained is clearly presented in the plasticity chart and is illustrated in Fig.
ANN model development The ANN models depend on various parameters such as the associated topology (number of inputs, number of outputs, and number of hidden layers) ; they also depend on the learning parameters like the transfer function, the number of learning cycles, and the maximum error  (Taleb Bahmed et al. , 2017). In this study, the Matlab simulation program was employed to develop the ANN model using the backpropagation training algorithm. The minimal error was obtained by applying Eq. 3, while the mean relative error could be determined by means of Eq. 4  (Kellouche et al. , 2021). It should be noted that the best performance was obtained when the structure of the ANN model included three layers : one input layer, one hidden layer, and one output layer. It is useful to recall that each layer consists of a number of neurons.
MER(%) = ∑ N i = 1 E N (4) Where : N the number of specimen. f ( σ) = 1 ( 1 + e -σ ) (5) Where : f the activation function ; σ weighting function. 2019 ) ; these results are not included in the training database. This was done for the purpose of predicting the plasticity index from the input parameters such as the liquid limit, plastic limit, and percentage of sand. Based on the results obtained (Table  3 ), it could be noted that the overall average error between the experimental results and the values predicted by the ANN model was equal to 2. 48%. This small error value allowed concluding that the proposed model is quite accurate. This model can be used as a reliable tool for the prediction of plasticity index (PI) of clay soils treated with sand. 3. Experimental Procedure.