dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2018a,b). In this study, the data from the VIMES test are used for the dynamic modeling for Sc t. Combined with experimental research, the Large -Eddy Simulation (LES) can provide more insights into the turbulence phenomena; however, it is not realistic to apply it for simulating the gaseous behavior in a real containment vessel because of the necessity of high computational cost and time. Röhrig et al. (2016)  performed the LES and RANS on a light gas stratification breakup by a vertical jet in the small-scale vessel conducted by  Deri et al. (2010)  at the CEA. This research concluded that the LES yields a decent prediction of the characteristic erosion process. Moreover, they mentioned that the RANS approaches manage to capture the overall behavior though with a notable lack in accuracy, indicating the improvement of the RANS accuracy is required.
Sarikurt and Hassan (2017)  used the LES methodology on the IBE-3 in the PANDA facility and investigated the flow structures for the interaction of a buoyant jet and a stratified layer. The research summarized that understanding the interaction mechanism will help quantify the turbulent mass transfer of the gas component. In this study, we performed the LES to obtain detailed turbulence properties in the interaction region, such as turbulence fluctuation and turbulent mass flux. This paper phenomenologically discusses the interaction behavior between a vertical jet and stratification. The capability of the dynamic modeling for Sc t in RANS is shown based on a phenomenological understanding. The VIMES experimental data are used to validate the LES and RANS. The remainder of the paper is organized as follows: Section 2 describes the VIMES apparatus with the initial and boundary conditions and the brief experimental results; Section 3 presents the numerical and boundary conditions, including the turbulence model, mesh, and discretization schemes, and explains the validity confirmed by various perspectives (i.
Initial and boundary conditions All experiments in this paper were performed under the condition of iso-thermal. Gas temperature in the initial and inlet conditions was approximately 288. 15 (± 5. 0) deg-K. The binary gas of air and helium was injected to build up the initial density stratification, as shown in Fig. 2(a). The injection flow rate was 105 ± ( 6. 0) L/min. The molar fractions of helium and air were 70% and 30%, respectively. The injection duration was 420 s. Consequently, the density stratification was formed above 1. 0 m. The maximum value of the helium molar fraction reached approximately 60% at the top of the test vessel. A horizontal bar attached to each data point in Fig. 2 (a) indicates the standard deviation taken from nine experiments conducted with the same initial conditions, showing that the helium molar fraction was measured with an error of less than 3%.
CFD result Table  1  summarizes the simulation case in this study. The LES was performed only for Case 1. The calculated period was limited only to 62 s from the start of the upward jet injection to save computational cost and time. The statistical processing was performed with the data of 30 s to 62 s, which corresponded to the period of the PIV measurement in the VIMES experiment. For RANS in Case 1, the constant value of Sc t was set to 0. 85 and 8. 5. The first value was decided based on the previous studies that simulated the same kind of stratification erosion process by several jet types  (Kelm et al. , 2019 , Studer et al. , 2018 , and Ishay et al. , 2015). The second one was set to validate the effect of the forcible suppression of the turbulent mixing. The Sc t value for the other cases was set only to 0.
Conclusion We phenomenologically discussed herein the interaction behavior between a vertical jet and density stratification by investigating the turbulence properties obtained with the LES. For RANS, we focused on the turbulent Schmidt number Sc t because the change of Sc t directly operates on the turbulent diffusion coefficient D t and the production term in the transport equations of the turbulent kinetic energy and its dissipation ratio by buoyancy force. We applied the constant Sc t values of 0. 85 and 8. 5. The first value was selected based on the previous studies, while the second value was for forcibly suppressing the turbulence mixing. The dynamic modeling for Sc t was applied. The experimental data obtained with the VIMES apparatus were utilized as the    In conclusion, the dynamic modeling for Sc t is a useful and practical approach to improve the prediction accuracy on the stratification breakup behavior by a vertical jet.
Acknowledgments The authors acknowledge  Mr. Wakayama ,  Mr. Kurosawa ,  Mr. Yanai ,  Mr. Kawakami ,  Mr. Yamaki  of  Nuclear Engineering Co. (NECO) , and  Mr. Ohmiya  of  KCS  corporation for performing the experiment together. The experimental data used to validate the CFD analysis were acquired with the support of the  Nuclear Regulation Authority (NRA), Japan.
2016). It is also necessary that the different cosmological probes in Euclid use a consistent and well-defined framework for forecasting and that the tools used for such forecasts are rigorously validated and verified. These forecasts will then provide the reference for the performance of Euclid to the scientific community. Forecasting in this context refers to the question of how well Euclid will perform when using the survey data to distinguish the standard cosmological model from simple alternative dark energy scenarios, given its current, up-to-date specifications. This paper represents the outcome of an intense activity of comparison among different and independent forecasting codes, from various science working groups in the Euclid Collaboration. This work was conducted by a group known as the inter-science taskforce for forecasting (IST:F) and it presents the results of the code comparison for forecasts based on Fisher-matrix analyses.
The comparison presented here has involved several different codes. Therefore, rather than providing a single open source code, in a specific programming language, we grant a validation stamp for all the codes that took part in the code comparison and satisfied the requirements. These are listed in Sect. 4. 1. Since the Red Book the Euclid baseline survey and instrument specifications have been updated according to the progress in our knowledge of astrophysics, and in the evolution of the design of the telescope and instruments. In this paper we also update the Red Book forecasts by including some of these changes, which directly impact the statistical precision with which Euclid can constrain cosmological parameters. Such effects include changes to the survey specifications, changes to the instrument that impact the populations of galaxies probed, and changes in the understanding of astrophysical systematic effects.
Impact of neutrinos In the presence of massive neutrinos, the definition of the linear growth rate in Eq. (  25 ) needs to be modified to allow for a dependence on both redshift and scale, f (z, k), even at the linear level. To handle such dependencies in a semi-analytical way, approximations to the growth rate f (z, k) as a function of the neutrino fraction f ν = Ω ν,0 /Ω m,0 have been developed. One approach is the fitting formulae of  Kiakotou et al. (2008) , where f (z, k; f ν , Ω DE,0 , γ) ≈ µ ν (k, f ν , Ω DE,0 )Ω γ m (z) , (39) with µ ν (k, f ν , Ω DE,0 ) ≡ 1 -A(k)Ω DE,0 f ν + B(k) f 2 ν -C(k) f 3 ν , (40) and the functions A(k) , B(k), and C(k) have been obtained via fits of power spectra computed using the Boltzman code CAMB  (Lewis et al. 2000). Fig. 1  shows the effect of massive neutrinos on f in the linear regime, as ratios between the massive and massless neutrino cases, that it is to say that we show the function µ ν (k), which is independent of redshift.
This section aims at describing the implementation and code comparison among the different codes and represents our main deliverable: we include detailed instructions in Appendix A for the reader who may want to validate another Fisher Matrix forecast code; we make publicly available the recipe used, the reference output Fisher matrices, and plotting routines to reproduce your own comparison plot, in the form of Fig. 3 , to check that your own code is validated. In Sect. 4. 1 we describe the codes used in our comparison, in the WL, GC and XC cases. As the comparison was done among codes which had been already partially developed before this work, and was motivated by several codes providing different results in both amplitude and orientation, code ownership belongs to the authors who developed them.
We have however encouraged all code owners to make these codes publicly available: CosmoSIS and CosmoMathica (used to produce the input files for this work) are already publicly available, the authors of four codes (FisherMathica, SOAPFish, CCCPy, TotallySAF) have expressed intention to make them publicly available, five codes (BFF, fishMath, CosmicFish, CarFisher and STAFF) can be available upon request. Requests can be made directly to the authors, as listed below in Sect. 4. 1. In Sects. 4. 2 and 4. 3 we describe specific implementation steps regarding the galaxy clustering and weak lensing code comparisons, in particular the construction of the background cosmological quantities, the implementation of the survey geometry and galaxy sample properties, and the perturbed quantities, in order to construct the observed power spectrum.
We give specific and detailed information on the parameters we vary, and the calculation of the derivatives entering the Fisher matrix. We also describe how we implement non-linear corrections and how we project our Fisher matrices to derive constraints on commonly used dark energy and gravity parameters, such as w 0 , w a and γ. We define the different cases we use to validate our codes and finally show the results of the code comparison, that is to say how well the codes match. In Sect. 4. 4 we repeat this procedure for the probe combination case. Overall, we find very good (percent level) agreement between the different codes for all cases. In Sect. 4. 5 we comment on critical lessons we learnt during the code comparison validation, and give some advices for writing a Fisher matrix code for cosmology from scratch.
Now it also includes the non-linear modelling described in this work. It interfaces with CAMB to produce matter power spectra files, and with a F90 routine for the computation of scale independent growth factor and growth rate. The projection onto the final parameter space is performed by a separate module, that enables one to choose different settings (e. g. k-, zor µ-intervals) without the need to rerun the Boltzmann code for power spectra production. FisherMathica is a Fisher matrix code written by Santiago Casas in Mathematica in a modular way, including packages for different applications. Based on the code used in  Amendola et al. (2012) , it has been used for forecasts of modified gravity and dark energy  (Casas et al. 2016 (Casas et al. , 2017 (Casas et al. , 2018)). The particular advantage of this code is flexibility in terms of cosmological parameters.
It accepts any basis and can convert between them, such as A s versus σ 8 or ω m,0 versus Ω m,0. It can accept also new parameters, which can be useful for extended models of modified gravity. The CosmologyTools package takes care of computing Hubble functions, distances, coordinate and unit transformations, analytical growth rate equations and other cosmological observables. The publicly available CosmoMathica package  19  deals with the interaction with common codes in the cosmological community, such as the Boltzmann codes CLASS and CAMB and its modified gravity version MGCAMB,  Eisenstein & Hu (1998)  transfer functions, the Coyote Cosmic Emulator  (Heitmann et al. 2014 ) and other fitting formulas for non-linear power spectra. CosmoMathica has been used to produce the input files for this work.
The FisherGC package takes care of the galaxy clustering Fisher matrix, by computing the derivatives of the power spectrum with respect to the shape parameters and with respect to the redshift dependent parameters. It reads the GC specifications for different surveys from given text files and computes all needed quantities for the Fisher matrix. The integration settings are very flexible and are the ones provided by the Mathematica NIntegrate function. The FisherWL package computes the kernels, the window functions and the C( ) functions for weak lensing. It also includes several models of intrinsic alignment. The Fisher matrix is calculated in a parallelised way for each of the parameters and redshift bins. The UsefulTools package takes care of input/output, creation of tables, Fisher ellipses plots and post-processing.
It contains many useful matrix and vector operations that are needed to analyse and interpret Fisher matrices results. Finally, the code can be called interactively using Mathematica notebooks or from the command terminal, using. m file scripts. fishMath is a code that computes galaxy clustering forecasts, written in Mathematica by Elisabetta Majerotto. A previous version of it, which did not include forecasts on shape parameters, was used in various papers to produce forecasts  (Laureijs et al. 2011; Majerotto et al. 2012; Bianchi et al. 2012) , and more recent versions of it have been used to make various cross-checks for other papers  (Sapone et al. 2013; Sapone et al. 2014; Majerotto et al. 2016). The code allows one to switch from linear modelling to the two different parameterisations of non-linear modelling.
It consists of different modules, so that it is possible, for example to start by producing the Fisher matrix or to read the Fisher matrix from a file and marginalise it or project it over the preferred parameters. It also computes errors on parameters and the FoM for dark energy. SOAPFish is a code implemented using a combination of Python 3 and Mathematica 10. 0. 0. 0, by Domenico Sapone. It is a modified and improved version of the code used in  Sapone et al. (2009 Sapone et al. ( , 2010))   2011 ) and  Sapone & Majerotto (2012) , where the authors forecasted the sensitivity with which the next generation of surveys will measure the cosmological parameters with different cosmological models. The code is divided into cells and three main parts. The first one specifies the values of the cosmological parameters and the survey properties, such as survey area, number of bins and error on redshift.
The code can also provide the input files and produce the visualization plots. CCCP (Camera's Code for Cosmological Perturbations) is a code developed by Stefano Camera and has been used as a standalone code, or in order to compute either angular power spectra only or Fisher matrices only, in various analyses (e. g. Camera & Nishizawa 2013; Camera et al. 2015a,b,c; Bonaldi et al. 2016). At the time of the present code validation, it is written in Mathematica 11. 2. 0. 0 and it is kept updated from version to version. It consists of two main routines: (i) one calculating cosmological background and perturbation quantities for a given set of cosmological parameters; and (ii) another computing the Fisher matrix for the parameters of interest. The former routine employs, whenever is possible, analytical expressions to avoid interpolations and the propagation of numerical errors.
Moreover, it has utilities implementing the SteM derivatives, with and without accuracy checks. It can be run as a single jupyter notebook, from the computation of the observables, to the derivatives, to the final Fisher matrices and the corresponding parameter constraints. CosmicFish is a Fisher matrix code written in the Fortran90 and Python languages by Marco Raveri and Matteo Martinelli. It is interfaced with CAMB_sources and its generalizations are based on common CAMB modifications, such as MGCAMB  (Zhao et al. 2009; Hojjati et al. 2011)  and EFTCAMB  (Hu et al. 2014; Raveri et al. 2014). CosmicFish uses as primary parameters for ΛCDM cosmology the set {Ω b,0 h 2 , Ω c,0 h 2 , h, n s , log 10 10 A s , (w 0 , w a , γ)} with the parameters in parentheses added when considering extensions to ΛCDM.
Numerical derivatives are computed with with respect to these parameters, with the options of either 3 or 5 points stencil. Finally it projects the results on the common parameter basis combining the original Fisher matrix with a Jacobian matrix. CosmicFish has been used in previous works to investigate the information gain given by past and future cosmological surveys  (Raveri et al. 2016b) , as well as to obtain forecasts for proposed CMB missions  (Abazajian et al. 2016 ). Also, a preliminary validation of the code was done reproducing results available in the literature at the time of the code release  (Raveri et al. 2016a ). The version validated in this paper contains key features and calculations not available in the current public code, e. g. the effect of intrinsic alignments and the possibility of working in the common parameter basis.
These new features will be included in the next update of the public version of this code. CosmoSIS is a publicly available cosmological parameter estimation code 20   (Zuntz et al. 2015). It has a modular structure and this enables the use of existing codes for observable predictions, and different experimental likelihoods, written in different languages, like Fortran90, Python and C/C++. The public version of CosmoSIS provides a standard library with different modules for the Boltzmann solver, like CAMB  (Lewis et al. 2000; Howlett et al. 2012) , CLASS (Lesgourgues 2011a;  Blas et al. 2011; Lesgourgues 2011b; Lesgourgues & Tram 2011) , or MGCAMB  (Zhao et al. 2009; Hojjati et al. 2011 ), the background quantities, or nuisance parameters (like the galaxy bias, and intrinsic alignments). More importantly for us, it also contains a sampler that computes Fisher matrices.
CosmoSIS runs as a pipeline. Some modifications have been made to the standard implementation by Isaac Tutusaus and Martin Kilbinger for the purposes of this paper, and the pipeline used works as follows: the Boltzmann solver used (CAMB) uses A s instead of σ 8 , fixing A s to a dummy value and adding a third module into the pipeline to rescale the matter power spectrum. Afterwards the fourth module is added to take into account the non-linear correction to the matter power spectrum, and the fifth to consider the intrinsic alignments. Two more modules are needed to load the distribution of galaxies, n(z), and apply the galaxy bias model to the power spectrum. The projection to the C i j ( ) values is performed for each of the considered observables, adding the intrinsic alignment power spectra and finally the full covariance matrix for the observables is computed.
Once this is done, the Fisher matrix sampler calls the pipeline iteratively for all the variations of the parameters required to compute the numerical derivatives, and finally the Fisher matrix. Two derivative methods are available (3-point and 5-point stencils) with a user-defined step size per parameter. CosmoSIS has been widely used in the literature to analyse real data  (Abbott et al. 2018a,b; Baxter et al. 2019) , and to compute forecasts  (Harrison et al. 2016; Park et al. 2016; Olivari et al. 2018). STAFF (Shear Tomography Accuracy from Fisher Forecast) is a Mathematica code developed by Vincenzo F. Cardone for the code comparison challenge. It comes as a single notebook (staff ) performing all the necessary steps to output the final Fisher matrix, or as three separate notebooks for intermediate computations, namely pscalc for the estimate of the matter power spectrum and its derivatives, cijdercalc to obtain the shear, photometric galaxy clustering, and cross-correlation power spectra and derivatives, and fmcalc for the Fisher matrix evaluation.
The main virtues of STAFF are its simplicity and versatility which allows the user to quickly modify the code for any non standard cosmological model of interest. Unfortunately, being written in Mathematica, the code is slower than some others, and hence it is not ideal from this point of view. Nevertheless, the most time consuming step is when computing the matter power spectrum and its derivatives and this operation needs only to be performed once. This is because since the semi-analytical approach implemented for the derivatives of the different power spectra of interest make it possible to express all of them as operations on the matter power spectra. Table  6  presents a summary the forecasting codes involved in the comparison, including: name: label or name of the code; contact: contact person(s) for the corresponding code; -GC s : whether the code has been validated to forecast galaxy clustering from the spectroscopic survey; -GC ph : whether the code has been validated to forecast galaxy clustering from the photometric survey; -WL: whether the code has been validated to forecast cosmic shear weak lensing from the photometric survey; -XC (GC ph ,WL) : whether the code has been validated to forecast cross-correlations between galaxy clustering and weak lensing, both from the photometric survey;.
Galaxy clustering code comparison In this section we describe the procedure to compare the cosmological forecasts for GC measurements from the Euclid spectroscopic galaxy sample that are predicted by the different codes described in Sect. 4. 1. All codes employ the recipe described in Sect. 3. 2. The Fisher matrix for GC is given by Eq. (  91 ) and it depends on the model for the observed galaxy power spectrum given by Eq. (  87 ), and on the characteristics of the Euclid survey encoded in the effective volume, given by Eq. (  90 ). Here, we describe additional issues to take care of when implementing this recipe. If the reader wishes to compare and validate their own GC Fisher matrix code for Euclid GC, they should follow these instructions in order to do so. As part of the code-comparison process, all codes were adapted to use common inputs.
(32) , and the values of σ 8 (z) from our input files (see Sect. A. 2 for details). The latter can be computed using the galaxy bias factors listed in Table  3  and the same values of σ 8 (z). -The pure matter power spectrum normalised by σ 2 8 (z), P δδ (k, z)/σ 2 8 (z). Although these redshift-independent ratios are again given as input files (see Sect. A. 2), they can be estimated directly from the output of any Boltzmann code (e. g. Lewis et al. 2000 or Lesgourgues 2011a ). -The "no-wiggles" power spectrum, which we obtain using the formulae of  Eisenstein & Hu (1998). The necessary ratios of P nw (k, z)/σ 2 8 (z) are treated as inputs to the codes (see Sect. A. 2). -The absolute error in the distances expressed in terms of the redshift errors σ 0 = 0. 001, given by Eq. (  75 ). -The residual shot noise term is represented by P shot (k, z), which is set to zero at the reference cosmology.
Results of the code comparison In this section we compare the output of the six codes capable of estimating cosmological forecasts for GC measurements described in Sect. 4. 1. These are BFF, CarFisher, fishMath, FisherMathica, SOAPFish, and TotallySAF. We have compared the results of these codes for each of the cases summarised in Table  7. The main conclusion of this exercise is that all codes are able to provide consistent cosmological forecasts for Euclid. In Fig. 2 , top-left panel, we show the relative difference between the full marginalised errors of the four shape parameters produced by the six codes considered in the current comparison. To produce this plot-and all the similar plots henceforth-we compare, for the constraint on each cosmological parameter, the performance of each code to the median of the constraints obtained by the set of all the available codes.