dataesr/scientific-paragraphs-categorization huggingface dataset:
85) and Per(V res R , 84. 15) are respectively the 15. 85 th and 84. 15 th percentiles of the distribution of radial velocity residuals: V res R = V GDR2 R -V GB R. The lower and upper 1-σ 9 CU6GB, SIM, RAVE, APOGEE and GES (Sect. 5. 2). 10 standing for ground-based. D. Katz et al. :  Gaia Data Release 2 Properties and validation of the radial velocities uncertainties on the precision are calculated as: low σ GB V R = √ 2π e -0. 5 0. 1585 × 0. 683 N V res R ( Ṽres R -Per(V res R , 15. 85)) (5) upp σ GB V R = √ 2π e -0. 5 0. 1585 × 0. 683 N V res R (Per(V res R , 84. 15) -Ṽres R ) (6) where Ṽres R is the median of the radial velocity residuals and N V res R the number of radial velocity residuals. The second dataset is made of all the stars with a radial velocity published in Gaia DR2 and is hereafter referred to as the full dataset.
With this dataset, the estimator of the precision is the median of the radial velocity uncertainties (Sect. 5. 1. 2): σ Full V R = ˜ V R (7) and the lower and upper 1-σ uncertainties on the precision are calculated as: low σ Full V R = π 2N V R (˜ V R -Per( V R , 15. 85)) (8) upp σ Full V R = π 2N V R (Per( V R , 84. 15) -˜ V R ) (9) where N V R is the number of individual radial velocity uncertainties and ˜ V R , Per( V R , 15. 85) and Per( V R , 84. 15) respectively the median, 15. 85 th and 84. 15 th percentiles of the distribution of radial velocity uncertainties. The radial velocity uncertainty, V R , is function of the standard deviation of the time series of transit radial velocities. The precision derived from the full validation dataset is therefore proportional to the scatter of the transit radial velocities.
Although the full dataset is made of the 7. 2 million stars, the effective temperature, surface gravity and metallicity are known respectively for only 1. 3, 0. 4 and 0. 4 million stars (from a compilation of ground-based catalogues). The assessment of the radial velocity precision as a function of these parameters is therefore limited to these sub-samples. To compare the estimates of the precision derived with the robust dispersion of the residuals (Eq. 4) on the one hand and with the median of the radial velocity uncertainties (Eq. 7) on the other hand, both estimators were applied to the same subset of CU6GB stars. Figure  26  shows the external (relying on the residuals) and internal (relying on the uncertainties) precisions as a function of G ext RVS magnitude. Within the uncertainties, the two estimators of the precision are in good agreement.
The two validation datasets and the two estimators of the precision are complementary, in the sense where they are sensitive to different aspects. The stars in the GB dataset have been selected on the basis of multiple ground-based observations to be as clean as possible of radial velocity variables. The full dataset contains all the 7 224 631 stars of the Gaia DR2 spectroscopic catalogue, which includes a proportion of undetected multiple and variable stars, even if the filters applied on the suspected SB2 and on the radial velocity uncertainty (Sect. 4) should have removed the bulk of the large amplitude velocity variables. Furthermore, the GB based precision includes a contribution from the ground-based catalogues themselves. For the ground-based velocities derived from high-resolving power echelle spectrograph (like in the CU6GB catalogue), this contribution is very small.
Precision versus magnitude Figure  27  shows the precision, estimated from the robust dispersion of the radial velocity residuals (Eq. 4), as a function of the external G ext RVS magnitude, for the ground-based catalogues included in the GB validation dataset. Figure  28  shows the precision, estimated from the median of the radial velocity uncertainties (Eq. 7), as a function of the external G ext RVS magnitude, for the full dataset. The precision derived using the CU6GB sample reaches ∼200-250 m s -1 for the stars with G ext RVS ∈  [4, 8]  mag, close to the precision obtained with the full dataset for G ext RVS ∈  [4, 8]  mag: ∼ 220 -350 m s -1. This is about 3 to 5 times more precise than the pre-launch specification, which was 1 km s -1. In this range of magnitude, the Gaia DR2 radial velocity precision is limited by the precision of the calibrations and in particular of the wavelength calibration.
From G ext RVS ∼ 5 mag, some spectra begin to be saturated. The proportion increases with decreasing magnitude and as a consequence the radial velocity precision deteriorates (Fig. 28 ). The estimation of the bright stars precision using Xhip, RAVE and APOGEE is limited by the internal uncertainties of these catalogues. Beyond, G ext RVS ∼ 9 mag, the CU6GB and APOGEE samples show similar behaviours. At G ext RVS = 11. 75 mag, the APOGEE and RAVE stars yield similar Gaia DR2 precisions of 1. 4-1. 5 km s -1. The precision derived with the full sample is slightly lower, i. e. 1. 8 km s -1 , probably because of the larger proportion of unfiltered radial velocity variables. RVS magnitude and number of transits (the different curves), respectively for the GB validation dataset (top) and for the full dataset (bottom).
Precision versus effective temperature Figure  30  presents the Gaia DR2 precision as a function of the external G ext RVS magnitude and effective temperature (the different curves), respectively for the GB validation dataset (top) and for 1. 3 million stars from the full dataset with known T eff (bottom). The radial velocity precision improves as the effective temperature decreases. This is the direct consequence of the evolution of the morphology of the spectra with temperature. As it decreases, the weak neutral lines become on average stronger, carrying more information to derive the radial velocity. This is illustrated by Fig. 31  which compares the spectra of a HIP46933 (T eff = 4487 K, log g = 4. 22, [Fe/H] = -0. 24 dex;  Adibekyan et al. 2012)  and HIP84551 (T eff = 6517 K, log g = 4.
The sub-library used by the software module determineAP includes a synthetic spectra with T tpl eff = 6500 K, but none with T tpl eff = 6750 K. Therefore, stars which have been processed with a T tpl eff = 6750 K template all had atmospheric parameters included in the compilation of ground-based catalogues. Those processed with a T tpl eff = 6500 K template are in majority not included in the ground-based compilation and their templates has been selected by determineAP. The stars whose templates have been selected by determineAP suffer from a larger template mismatch than those included in the ground-based compilation, which explains the swapping of some curves. At G ext RVS = 11. 75 mag, the precision estimated from the full sample is ∼ 3. 7 km s -1 at T tpl eff ∼ 6500 K, ∼ 2. 6 km s -1 at T tpl eff ∼ 6750 K, ∼ 1.
Precision versus surface gravity As shown by Fig. 33  and 34 , overall, at the faint end, the radial velocity precision improves as the, stellar and template, surface gravities decrease. The effect is more clearly visible in the full sample, which benefits from a much larger statistics and therefore more precise estimates of the precision. Stars processed with a template with surface gravity log g = 3. 5 show lower performance. This is the consequence of a larger mismatch between the templates and the observed RVS spectra. In the reduced library used by the software module determineAP, there is a single synthetic spectra with T tpl eff = 6000 and a single one with 6500 K, both having a surface gravity of 3. 5. The restricted library also contains 2 solar metallicity templates with an effective temperature of 5500 K and surface gravities of 3.
Precision versus metallicity Figure  35  presents the radial velocity precision as a function of the external G ext RVS magnitude and metallicity (the different curves), estimated using the full dataset. As expected, as the metallicity increases, the metallic lines get stronger and the radial velocity precision improves. Yet, over the metallicity range probed in Fig. 35, i. e. ∼ [-2. 0, 0. 5] dex, the precision is only weakly sensitive to metallicity (e. g. compared to the sensitivity to temperature). The limited number of very metal-poor stars, with known metallicities in our compilation of groundbased catalogues, prevents to assess a reliable precision below [Fe/H] = -2 dex. Figure  36  shows the individual radial velocity residuals of the GB validation stars. Stars more metal-poor than -2 dex mostly show (absolute) residuals smaller than 4 km s -1.
Template selection in future Gaia releases In Gaia DR2, the 280 million spectra to process, the available processing power and the tight processing schedule have imposed a limit of 28 spectra to the library of templates used by the software module determineAP. In the subsequent Gaia releases, the elaborated analysis of Bp, Rp and RVS spectra (for the brightest stars) should provide precise atmospheric parameters for most RVS stars  (Bailer-Jones et al. 2013; Recio-Blanco et al. 2016) , reducing the mismatch between templates and observed spectra and improving the radial velocity performances.
Conclusion Gaia DR2 contains median radial velocities for 7 224 631 stars brighter than G RVS = 12 mag and with effective temperatures in the range [3550, 6900] K. These stars offer a full sky coverage and a completeness with respect to the full second Gaia data release of 77. 2%, for stars with G ≤ 12. 5 mag. The accuracy of the radial velocities has been assessed by comparison to several ground-based catalogues. The medians of the radial velocity residuals vary from one catalogue to another, but do not exceed a few 100s m s -1. In addition, Gaia DR2 radial velocities present a positive trend with magnitude, starting around G RVS = 9 mag and raising up to ∼ 500 m s -1 at G RVS = 11. 75 mag. The radial velocity precision has been assessed both by comparison with groundbased catalogues and using the distribution of Gaia radial velocity uncertainties.
For bright stars with G RVS in  [4, 8]  mag, the radial velocity precision is in the range 200-350 m s -1. At the faint end, G RVS = 11. 75 mag, the precisions are respectively 1. 4 and 3. 7 km s -1 for T eff = 5000 and 6500 K. Beyond Gaia DR2 several catalogues are already planned 11. Each one should include refined data treatments, new functionalities, new products and for the radial velocities a fainter processing limit. Gaia DR3 should include radial velocities for stars down to G RVS = 14 mag, while Gaia DR4 aims at reaching the limiting magnitude of the Radial Velocity Spectrometer: G RVS = 16. 2 mag.
Figure23presents the median radial velocity residuals as a function of the stars velocity. The residuals of the Gaia DR2 versus RAVE velocities decrease by about 600-700 m s -1 from +25 km s -1 to -125 km s -1 and show a symmetric behaviour at positive velocities. The small number of high velocity stars in our validation datasets prevents from deriving precise median residuals outside [-175, +175] km s -1 , whereas the pipeline derives radial velocities in the range [-1000, +1000] km s -1. The individual radial velocity residuals (Figure24) provide a view on a broader velocity intervals. The individual residuals do not show any strong offset or trend over the interval[-400, 400]  km s -1. The fastest validation star has a radial velocity of 552. 6 km s -1 in our RAVE list and 553. 5 km s -1 in Gaia DR2.
Figure29presents the radial velocity precision as a function of G ext RVS magnitude and number of transits (the different curves), respectively for the GB validation dataset (top) and for the full dataset (bottom). As expected, the precision improves with the number of transits. For example, at G ext RVS = 11. 75 mag, the precision estimated using the full dataset, improves from ∼ 2. 2 to ∼ 0. 9 km s -1 , between 4 and 37 transits.
Acknowledgements. This work has made use of results from the  European Space Agency (ESA) space mission Gaia , the data from which were processed by the  Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The Gaia mission website is http://www. cosmos. esa. int/gaia. Most of the authors are current or past members of the  ESA Gaia mission team and of the Gaia DPAC  and their work has been supported by the  French Centre National de la Recherche Scientifique (CNRS) , the  Centre National d'Etudes Spatiales (CNES) , the  Agence Nationale de la Recherche , the  Région Aquitaine , the  Universit/'e de Bordeaux , the  Utinam Institute of the Université de Franche-Comté , and the  Institut des Sciences de l' Univers (INSU) ; the  Science and Technology Facilities Council  and the  United Kingdom Space Agency ; the  Belgian Federal Science Policy Office (BELSPO)  through various  Programme de Développement d' Expériences Scientifiques (PRODEX)  grants; the  German Aerospace Agency (Deutsches Zentrum fur Luft -und Raumfahrt e.
V. , DLR); the  Algerian Centre de Recherche en Astronomie, Astrophysique et Géophysique of Bouzareah Observatory ; the  Swiss State Secretariat for Education, Research, and Innovation  through the  ESA PRODEX programme , the  Mesures d' Accompagnement , the  Swiss Activités Nationales Complémentaires , and the  Swiss National Science Foundation ; the  Slovenian Research Agency  (research core funding No. P1-0188 ). This research has made use of the SIMBAD database (Wenger et al. 2000) developed and operated at  CDS, Strasbourg, France.
g. misorientations) and deformation parameters. The drawback of a vast, non-representative set of possible solutions is overcome by using well-established, crystallographic microstructural information as inequality constraints. The framework is applied to f. c. c. b. c. c. lattice constants of a high-resistance maraging steel. Due to the multiplicity of the solutions the focus is not laid on specific solutions, but rather on the implications the new framework has in comparison with the prevalent theory. However, to obtain specific solutions, a free and open-source Matlab program with a user-friendly GUI has been developed. Finally, the fields of applications for optimized crystallographic sets are discussed.
, 2014). This work follows an object-oriented programming (OOP) approach where each crystallographic set has a class structure and suitable methods have been implemented for the flexible manipulation (sorting, reducing etc. ) of the full set of solutions. This way, solutions, not fulfilling a given set of constraints as elaborated subsequently, can be discarded in a stepwise manner, thus enabling an iterative optimisation. Again it is emphasized that here we do not provide an exemplary solution, but visualize realizations of a reasonably constrained solution space (discussed subsequently), due to the multiplicity of the solutions. However, optimal solutions (with respect to any available crystallographic property) may be easily obtained with the freely available Matlab toolbox. 1  Therein the selection constraints and lattice parameters of the transformation can be set.
The program also allows to write all the invariant habit plane solutions (consisting of all its crystallographic properties/parameters such as active slip systems, accumulated shear increments, habit plane orientation, orientation relation etc. ) of the currently reduced set into a text file. It was noticed that the well-known linear-dependence of slip deformations (c. f. linear dependence of vectors) plays a significant Fig. 6. of selected habit plane solutions dependent on the larger of the two accumulated shears, i. e. the sum of shear deformation increments of a single slip system (right column) as well as the sum of the accumulated shear deformation increments of both slip systems (left column). Top-row:new treatment. Bottom-row: classical treatment. In both cases the results indicate that for most solutions one shear deformation is substantially larger than the other.
Discussion In this work a link between the phenomenological theory of martensite crystallography and crystal plasticity has been established in a large strain formalism. The key idea is to use an incremental formulation as in crystal plasticity for an incremental lattice orientation update of the martensite in combination with a suitable cost function from the phenomenological theory of martensite crystallography. The framework is not restricted to the cubic crystal system, but can be used for any lattice type. The consequence for the generalization at hand is that there exists rather a range of possible solutions instead of only one exact solution. Therefore, here ad hoc no optimal solution is suggested by the algorithm. However, it would be easily possible to find a solution that is optimal to any choice of specified crystallographic parameter, by setting stricter bounds on the selection constraints using the freely available Matlab GUI.
The database-like approach for habit plane solutions, encompassing the "crystallographic set" through an object-oriented programming approach, enables an optimized selection of a crystallographic set for lath martensite based on the available constraint data. The presented framework permits to conduct sensitivity studies (visualization of the phase space of the theory) on various microstructural parameters, all included in a crystallographic set, which has proven to play a key-role for the formation and stability of the microstructure. Note that in Equation (  10 ) it is assumed that the stretch contribution of the Bain strain is independent of the stretch contributions of the shear deformations U S (see Equation (  12 )). In principle the approach presented here would allow to study whether a part of the Bain stretch comes from the shear deformations.
The set of solutions obtained by the current approach now could be correlated/ fitted with these blurry maxima in the pole figures of single grains to obtain a good local fit. The benefit of this procedure is that given the set of solutions, the information of active deformation mechanisms that were involved in the transformation, is fully characterised. Although not treated here, the program is also useful in the case of systems with microstructural features for which a set of crystallographic constraints are very distinct and well-defined (much better defined than in the case of dislocated martensite), such as certain precipitates. If these precipitates additionally have a considerable size the program can be used to search for invariant habit plane solutions in a very restricted solution space.
Acknowledgements Financial support by the  Austrian Federal Government  (in particular from  Bundesministerium für Verkehr, Innovation und Technologie and Bundesministerium für Wissenschaft, Forschung und Wirtschaft ) represented by  Österreichische Forschungsfürderungsgesellschaft mbH and the Styrian and the Tyrolean Provincial Government , represented by  Steirische Wirtschaftsfürderungsgesellschaft mbH and Standortagentur Tirol , within the framework of the  COMET Funding Programme  is gratefully acknowledged.
The modelling of crop rotations has also been common in the field of agricultural economics with work regarding sequential cropping being mainly to understand influences on decision-making; therefore focusing on short timescales and at the farm management level  (Dury et al. , 2012; Caldwell and Hansen, 1993). Many dynamic global vegetation models (DGVMs), commonly used to study the effects of climate change, simulate a single crop per year, both for individual sites and gridded simulations. This may be due in part to some global observation datasets such as  (Sacks et al. , 2010)  reporting only one growing period per year for most crops  (Waha et al. , 2012). MIRCA2000  (Portmann et al. , 2010)  include different cropping calendars for different regions, however rice and wheat are divided equally between the kharif and rabi seasons, when in reality wheat is only grown during the rabi season  (Biemans et al.
(2015 Garrigues et al. ( , 2018) )  to illustrate and evaluate the sequential cropping method implemented in JULES. The method is summarized by Fig. 1  and described in Sect. 3. We aim to show that the method is able to produce two crops in a single growing period and therefore provide a better representation of the real land surface at Avignon than previously possible using the crop model, rather than perform a detailed tuning exercise. Avignon is chosen because it has been observed and documented over several years  (2001 to 2014) , growing a range of crops throughout this period. The continuous measurements of surface fluxes provided by this dataset are a unique resource for evaluating land surface models (LSMs) and for testing and implementing crop rotations in LSMs. Garrigues et al. (2015)  use this dataset to evaluate LSM simulations of evapotranspiration using the interactions between soil, biosphere, and atmosphere scheme (ISBA) LSM  (Noilhan and Planton, 1989)  specifically, the version from  Calvet et al.
, 2015). These parameters are used to define the overall effect of the photoperiod on the crop called the relative photoperiod effect, RP E described by Equation  2. In these simulations, as in  (Osborne et al. , 2015) , the effect of photoperiod is not included i. e P sens is set to 0 and therefore RPE is equal to 1. 0. RP E = 1 -(P -P crit )P sens (2) The RPE is then used to calculate the rate of crop development described by Equation  3. dDV I dt =          T eff T Temr for -1 ≤ DV I < 0 ( T eff T T veg )RP E for 0 ≤ DV I < 1 T eff T Trep for 1 ≤ DV I < 2 (3) where T T emr is the thermal time between sowing and emergence, T T veg and T T rep are the thermal time between emergence and flowering and between flowering and maturity respectively. These are calculated using a temperature climatology from the driving data and sowing dates from observations or a reliable dataset to ensure that the crop reaches maturity on average by the harvest date, the values used in these simulations are given in Tables  4  and 5.
(  2004 )). This RCM simulation is one of an ensemble of simulations produced for the EU-HighNoon FP7 project for the whole of the Indian subcontinent (25 N, 79 E-32 N, 88 E) for the period 1991-2007. The HighNoon simulations are described in detail in previous publications such as  Kumar et al. (2013)  and  Mathison et al. (2013 Mathison et al. ( , 2015)). HadRM3 provides more regional detail to the global data with lateral atmospheric boundary conditions updated 3-hourly and interpolated to a 150 s timestep. These simulations include a detailed representation of the land surface in the form of version 2. 2 of the Met Office Surface Exchange Scheme (MOSESv2. 2; Essery et al. (2001) ). JULES has been developed from the MOSESv2. 2 land surface scheme and therefore the treatment of different surface types is consistent between the RCM and JULES  (Essery et al.
, 2001; Mathison et al. , 2015). Sowing dates are prescribed using climatologies calculated from the observed dataset,  Bodh et al. (2015) , from the government of India, Ministry of Agriculture and Farmers welfare. Thermal times are calculated using these climatological sowing and harvest dates from  Bodh et al. (2015)  and a thermal climatology from the model simulation as described in  Osborne et al. (2015) , the values used in the simulations here are provided in Table  5. In the JULES point simulations only wheat is irrigated, the settings used for this are provided in Table  1  (column 'India settings').
India observations Crop yield observations from the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT, 2015)) provides seasonal yields for each crop for comparison with the point simulations. We also show average crop yield observations from  Ray et al. (2012a)  for three, 5-year periods between  1993 and 2007 (1993-1997, 1997-2003, 2003-2007)  via  Ray et al. (2012b). These data are based on previous publications  Monfreda et al. (2008)  and  Ramankutty et al. (2008)  and include the period of the point simulations which are from 1991-2007. We show both of these datasets to highlight that there is a range in the estimates of yield for this region. 6 Results.