dataesr/scientific-paragraphs-categorization huggingface dataset:
Input physics: Core-helium burning stars To explore the transition towards the core-helium burning phase of low-mass stars, we used the MESA stellar evolution code  (Paxton et al. 2011 (Paxton et al. , 2013 (Paxton et al. , 2015 (Paxton et al. , 2019)) , version 15140 1. The use of the MESA code enables us to study the internal rotation of red clump stars (low-mass stars in the core-helium burning phase), since the GENEC code does not routinely follow the rotational evolution of stars after the helium flash. Moreover, using two evolutionary codes with different implementations of rotational effects enables us to verify that the results obtained about the AM transport efficiency in stars ascending the RGB are not too sensitive to the specific code that is used. Rotation in MESA was treated following  Heger et al.
(2000) , and we refer to that work for further details. Although the treatment of rotation in MESA is purely diffusive, while it is an advecto-diffusive process as treated in GENEC, we verified that the results and conclusions derived in this work are independent of the code used. This is due to the fact that AM transport by meridional currents and the shear instability is negligible in the type of evolved stars that we study in this work. The equation used in MESA to follow the evolution of the AM transport is ∂Ω ∂t m = 1 j ∂ ∂m t (4πr 2 ρ) 2 jD ∂Ω ∂m - 2Ω r ∂r ∂t m 1 2 dln j dln r , ( 2 ) where j is the specific angular momentum. The remaining variables are defined as in Eq. (  1 ). The additional viscosity ν add is added linearly in the diffusion coefficient D in the first term. For consistency with our GENEC models, we only account for transport of AM by the shear instability and meridional circulation (in addition to ν add ) in radiative regions.
Afterwards, the models enter the stable core-helium burning phase (when the mass fraction of central helium drops below ∼0. 9) and spend more than ∼85 % of their burning time with a roughly constant radius of R ∼ 10-11 R. This corresponds to ∼100 Myr. The models with an additional viscosity of ν add ∼ 10 5 cm 2 s -1 spend most of their core-helium burning time with a core rotation rate that agrees with the upper end of the data bulk for red clump stars, which corresponds to Ω core /2π ∼ 150 nHz <Ω core >/2π [nHz] Radius [R ⊙ ] ν add =1. 5x10⁴ ν add =1x10⁵ ν add =5x10⁵ Fig. 10. Evolution of the core rotation rate as a function of the stellar radius. All models have an initial mass of 1. 2 M and an initial velocity of 5 km s -1 (P ini = 12 days) and were computed with MESA. Different values for the additional viscosity are used in each model, as indicated in the figure in units of cm 2 s -1.
Global behaviour of the AM redistribution In the previous section, the efficiency of AM redistribution was determined for red giants in the hydrogen-shell and core-helium burning phases. Now we compare our results to those obtained in previous works for subgiants and secondary clump stars. In line with our work, the additional viscosity needed to satisfy the constraints on eight subgiants has been obtained in previous works  (Eggenberger et al. 2019b; Deheuvels et al. 2020). For two of these subgiants located close to the end of the main sequence, asteroseismic data are consistent with the fact that they are rotating as solid bodies. Because of this,  Deheuvels et al. (2020)  could only estimate a lower boundary on the additional viscosity, high enough to ensure the compatibility with asteroseismic constraints on core and surface rotation rates.
Conclusions We studied the efficiency with which AM must be redistributed in stellar interiors to match the constraints on the core rotation rate of red giants in the hydrogen-shell and core-helium burning phases. To do this, we computed stellar evolution models including an additional viscosity with the GENEC and MESA stellar evolution codes. With this approach, we inferred a mean value of the diffusion coefficient that transports angular momentum. We compared our models to a data set of roughly 900 red giants obtained by  Mosser et al. (2012)  and  Gehan et al. (2018) , including red giants in the hydrogen shell-burning phase close to the base of the RGB and more evolved low-mass stars in the corehelium burning phase. We did not aim to model each star individually, but to investigate the behaviour of the efficiency needed to match the constraints on their core rotation rates.
Acknowledgements. F. D. M. , P. E. , G. M. and S. J. A. J. S. acknowledge funding by the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation program  (grant agreement No. 83925 , project  STAREX ). G. B acknowledges fundings from the  SNF AMBIZIONE  grant No. 185805  (Seismic inversions and modelling of transport processes in stars).
Statistical analysis Statistical analysis was performed with R (version 4. 1) using the phyloseq package (version 1. 36. 0) (23). We ensured a minimal depth of 50 000 reads per sample, that discarded 3 of 79 available HC samples (consequently, only 76 HC samples were used for downstream analyses). We performed a rarefaction at lowest sample depth for human and murine data sets independently, resulting in 56 219 reads/sample and 62 463 reads/sample respectively. To compare microbiotas diversity and composition, we assessed alpha-diversity by Shannon index, beta-diversity by Bray-Curtis dissimilarity index which was visualized through principal component analysis (PCoA). Permanova test was performed to track the effect of clinical conditions on distances between samples. Differentially abundant taxa were identified using DESeq2 method (24) (version 1.
To track trends in our data sets that were not significant due to our relatively small sample size, we looked for the 16 most relevant biomarkers from the overall literature (raw p-values, no log2FoldChange cutoff). In our human data set, besides our signature, we found that Bacteroidetes and Proteobacteria phyla, Bacteroides, Desulfovibrio genus, and Ruminococcus gnavus species showed the same trend as the literature (Figure  4B ). Similarly, Bacteroides and Lactobacillus genera were found coincidently in our mouse dataset (Figure  4C ). Overall, we shared nine human biomarkers and seven murine biomarkers among the 16 biomarkers we commonly found. We then established a universal panel of biomarkers including our finding according to i) the signature obtained in at least three human studies, ii) the common signature between human and mouse studies, and iii) the disease activity, as established by at least one study in our present work and two other studies  (14, 25).
We minimized this bias through our unsupervised analysis, which was able to define patients with SLE according to their dysbiosis. It seems important to note that the exact composition of clusters may differ if samples are added or removed from the dataset and is sensitive to methodological choices, notably to distance metric and clustering linkage strategy. Also, patients with SLE were enrolled while already being diagnosed and treated. Thus, we did not investigate the impact of treatment on SLE-associated dysbiosis because we did not have their stool samples before the beginning of treatments, and the small size of our cohort precludes any definitive conclusions and warrants further studies. In our murine study, because of the unavailability of disease activity score in mice due to the small number of animals, we only compared these data to those of patients with SLE in comparison to HCs.
In order to comply with present and future stringent environmental policies, engine manufacturers have to improve engine design and control to achieve combustion with high dilution ratios. The use of CFD simulations with complex combustion chemistry remains prohibitive, and alternatives to assess quickly the laminar flame speeds at local grid cell conditions (temperature, pressure, equivalence ratio, and dilution ratio) are desired, such as empirical correlations. Whereas these correlations should ideally be obtained from experimental measurements, comprehensively validated kinetic models can help extend databases to conditions that cannot be achieved practically. Hence, the present study proposed a reduced kinetic mechanism, containing 593 species and 3698 reactions, for one gasoline surrogate, namely Toluene Reference Fuel with Ethanol addition (TRFE).
It is obtained by first compiling sub-mechanisms from the literature for the four components (isooctane, n-heptane, toluene, and ethanol) with updates of some key rate constants, and then is reduced for 1-D flame speed computations. The model was first validated against recent experimental laminar flame speed measurements of TRFE/air/diluent mixtures for various temperatures, pressures, equivalence ratios, and dilution ratios and then employed to extend the experimental database for the TRFE surrogate to higher dilution ratios and temperatures. A new formalism, including new mathematical expressions for the reference and dilution terms, and the temperature exponent are proposed. This new formalism exhibits improved abilities in fitting the laminar flame speeds, especially at high dilution ratios and in very fuel-lean and fuel-rich conditions.
Deficiencies of these expressions originate from the lack or the limited set of experimental data at these unusual conditions. However, this situation can nowadays be fixed through kinetic modeling. The aim of the present work is to propose new expressions for the laminar flame speed   correlation, especially for the reference   , temperature exponent, and dilution terms. These new formulations will then be applied to a Toluene Reference Fuel with Ethanol addition (TRFE) emulating a commercial gasoline fuel for which an experimental   database is available. This latter will then be extended through kinetic modeling, employing a kinetic mechanism specifically herein developed and validated for this surrogate. Finally, correlation parameters will be derived and the adequacy of the proposed empirical correlation will be discussed.
Gasoline Table  2  compares the properties of the surrogate and the commercial fuels. Thereafter, we will refer to this specific surrogate using the abbreviation ''TRFE''. Di Lorenzo et al. [25]  measured the laminar flame speeds of TRFE in air (N 2/ O 2 = 79%/21% by volume), without and with the dilution of synthetic EGR in a spherical combustion vessel equipped with a double-view Schlieren configuration, enabling to constantly assess the anisotropy of the propagating flame. The synthetic EGR composition was set to 74. 16% N 2 , 13. 62% CO 2 , and 12. 22% H 2 O on a molar basis. The authors defined the EGR ratio as  EGR ∕( fuel +  air +  EGR ), and this definition has been adopted hereafter. Data were collected over a large set of conditions: equivalence ratios ranging from 0. 85 to 1. 40, temperatures of 373, 423, and 473 K, pressures between 1 and 5 atm, and EGR ratios of 0, 10, and 20%.
Identified missing reactions were adopted a The parameters for duplicated species and reactions are replaced by the parameters from the sub-mechanism with the highest value in priority. from the LLNL 2011 mechanism. Thermochemical and transport data for each species were inherited from their parent mechanisms. The list of sub-mechanisms used in the initial construction of the detail mechanism and their relative priorities is shown in Table  3. Despite that Aramco Mech 3. 0 is a recent model, rate coefficients of some reactions potentially sensitive for laminar flame speeds predictions have been the focus of even more recent publications. Hence, the original rate constants for these reactions were updated. They mainly consist in reactions of the C 2 -C 3 sub-mechanism. For example, Xiong et al.
The Direct Relation Graph method with Error Propagation (DRGEP) followed by a full sensitivity analysis is applied for the reduction procedure, as implemented in Chemkin Pro software  [48]. TRFE/air/EGR mixtures are considered for the reactants and the matrix of initial conditions is as follows:  = 0. 8-1. 1-1. 4,   = 1000 K,   = 1-5 bar and EGR ratio = 0-20%-50%. This matrix, applied to zero-dimensional constant volume calculations, covers a wide range of temperature (1000-3000 K) and pressure (1-17 bar) to emulate the conditions encountered throughout the reaction zone of 1-D flames, where the high-temperature combustion chemistry relevant to flame conditions is favored. Target properties were ignition delay time (IDT), maximum heat release rate, maximum integrated heat release, maximum mole fractions for H, OH, HO 2 , and CH 3 radicals, with a maximum error tolerance of 5%.
Validation of the reduced model Before using MACDIL Mech. to extend the database published by Di Lorenzo et al. for the TRFE surrogate fuel, it is tested and validated against experimental laminar flame speeds measurements available in the literature for TRF and TRFE fuels. The PREMIX code  [49]  included in the CHEMKIN Pro software  [48]  was employed to perform the laminar flame speed calculations. A 20 cm wide domain and fine grid control parameters (GRAD=0. 1 and CURV=0. 1) were used to ensure freely propagating flames as well as grid-independent results. Thermal diffusion (Soret effect) was included. Mixture average transport was used instead of multi-component transport to reduce computational time. Comparisons have been performed (included in the Supplementary Material) and showed that the simplified mixture-average calculations are in very close agreement with the multi-component flame speeds, with absolute differences ranging from 0.
Validation on pure component and TRF mixtures In a first attempt to validate the model, the ability of MACDIL Mech. to predict the laminar flame speeds of the four components has been assessed. These comparisons are provided in the Supplementary Material. The model exhibits an overall good agreement for the four fuels, although laminar flame speeds predicted for isooctane and ethanol are close to the lower bound of the experimental uncertainties. Fig. 5 (a) displays the comparison between the present predictions and the experimental data of Mannaa et al. [50]  obtained for a TRF surrogate at different initial pressures and in a wide equivalence ratio range (0. 8-1. 6). The experimental data were obtained by monitoring the outward propagation of spherical flames in a heated combustion vessel.
investigated the effect of an increase of the pressure on the fundamental laminar flame speed of the TRFE surrogate. The pressure was varied between 1 and 5 bar. Fig. 6(d ) compares the experimental measurements at 473 K with the model predictions at the upper pressure. Unlike the observation at atmospheric pressure, MACDIL Mech. overestimates the laminar flame speeds on the fuel-lean side whereas a much better agreement is obtained for  = 1. 2 and 1. 3. The maximum flame speed is still predicted by the model to occur around  = 1. 1, but experimental data rather suggest an optimum at a slightly higher equivalence ratio. The LLNL 2011 model qualitatively agrees with the MACDIL Mech. computations, but its predicted laminar flame speeds are slower than the MACDIL ones even though the opposite trend was observed at atmospheric pressure.
This observation suggests that the pressure dependence of the laminar flame speed is more pronounced in this model. Fig. 8  displays the dependence of   to the pressure according to the two models and the experimental measurements for near stoichiometric mixtures ( ≈ 1. 1). Both experimental and numerical data exhibit a non-linear decay with the pressure, which is in line with the asymptotic theory that predicts   to be proportional to   , with  between -1 and -0. 5. The experimental trend is well captured by MACDIL Mech. , but the LLNL 2011 over-predicts the pressure dependence. Hence, while the LLNL 2011 computed laminar flame speeds are higher than that by MACDIL Mech. , an inversion is detected for pressure around 2. 5 atm and they are lower above this threshold. Effect of EGR addition.
slightly overestimates the laminar burning velocity. Nevertheless, the model computes an overall pressure and temperature dependence that are weakly, if none, sensitive to the EGR dilution ratio, which is consistent with the experimental observations despite the narrow experimental temperature and pressure ranges. The effect of the EGR dilution ratio at constant temperature and pressure on the laminar flame speed of TRFE is displayed in Fig. 9(a). Over the range (0%-20%) investigated by Di Lorenzo et al. , both a qualitative and quantitative agreement is observed between the experimental data and the computations using MACDIL Mech. and LLNL 2011. However, although the measurements might suggest a linear dependence of the laminar flame with the dilution ratio, this observation must be mitigated by the limited set of data and the uncertainties associated.
The MACDIL mechanism on the contrary predicts a nonlinear relationship between the two quantities (  and EGR ratio). In spite of the lack of experimental data at temperatures above 473 K, calculations with MACDIL Mech. are nonetheless displayed in Fig. 9(a)  as they show that the dilution effect is temperature dependent, with a stronger dependence at high temperatures. Indeed, one can clearly see that as the dilution ratio increases, the effectiveness of the diluent in reducing the laminar flame speeds decreases:   ∕  = -300, -220, and -120 cm/s for   = 0. 1, 0. 3, and 0. 5, respectively at 723 K. The EGR employed by Di Lorenzo et al. is a ternary mixture (CO 2/ H 2 O/N 2 ), and therefore the overall effect observed is a combination of the thermal and chemical effects of the three components.
Experimental The knowledge of the dilution effectiveness of the three pure diluents and the mixture enable assessing the validity of the linear mixing rule proposed earlier  (14) , at least for this mixture and fuel. According to the mixture rule, the dilution effectiveness of the EGR mixture is calculated to be 3. 56 from the experimental values of the three components, which is very close to 3. 41 according to the experimental measurements. Using the data based on the model predictions, an estimation of 3. 52 is derived, which is even closer to the value, 3. 56, obtained with the mechanism. Therefore, it may be possible to quickly calculate the dilution effectiveness of an arbitrary diluent mixture, providing the dilution effectiveness of neat diluents, which could greatly simplify the estimation of   for complex mixtures and extend the validity range of the empirical correlation.
Generation of the database and determination of the correlation parameters The reduced kinetic mechanism MACDIL Mech. described in the previous section has been used to extend the experimental database of Di Lorenzoet al. [25]. The final database for the laminar flame speeds of TRFE/air/EGR mixtures covers fresh gas temperatures between 373 and 973 K, pressures from 1 to 50 bar, equivalence ratios from 0. 4 to 2. 0, and EGR dilution ratios between 0 and 80%. Correlation parameters were obtained by minimizing the Root Mean Squared Error (RMSE), √ ∑ (𝑆 𝐿,𝑖,𝑐𝑜𝑟𝑟 -𝑆 𝐿,𝑖,𝑑𝑎𝑡𝑎 ) 2 𝑛. and are given in Table  5. The reference temperature   , the reference pressure   , and the reference EGR ratio were arbitrarily fixed at 473 K, 1 bar, and 0%, respectively. Parameters for the reference flame speed (Eq.
Effect of temperature and pressure Fig. 11 (a) displays the temperature dependence of the laminar flame speed according to the four correlations as well as the experimental and computed (MACDIL Mech. )   without EGR addition for near stoichiometric fuel/air mixtures at atmospheric pressure. The Gülder and the Yahyaoui correlations overestimate the experimental and computed data on the whole temperature range considered (373-973 K), which is consistent with the previous observations of Fig. 10. The PRISME correlation is in excellent agreement with the low-temperature measurements, but its predictions are lower than the MACDIL computations above 600 K. The present correlation, as expected, matches the MACDIL Fig. 10. Laminar flame speeds of TRFE/air mixtures at 473 K, 5 bar and diluted in 20% EGR: comparison between experimental data  [25] , MACDIL Mech.
In addition to equivalence ratio dependency, the MACDIL Mech. and the experimental data indicate that dilution effectiveness could also depend on temperature and pressure and vice versa. [25] , MACDIL Mech. calculations, literature correlations  [25, 52, 53]  and the present correlation. ranges investigated, experimental measurements indicate that the  and P dependence depends on the dilution ratio, which is confirmed by the MACDIL Mech. computations. Therefore, this effect must be included in the final correlation. The dilution ratio dependence of the temperature and pressure dependences can also be formulated as a  and P dependence of the dilution effectiveness, thus preventing the modification of two terms but only one. This was achieved by introducing a simple  and P power dependence in the dilution effectiveness expression, Eq.
Conclusion The laminar flame speeds of a TRFE surrogate and their dependences on parameters such as equivalence ratio, temperature, pressure, and dilution ratio have been investigated. The limited set of experimental data for TRFE/air EGR mixtures motivated the development of a reduced mechanism, referred to as the MACDIL Mech. , that contains 593 species involved in 3698 reactions. It was formulated by compiling state-of-art sub-mechanisms from the literature for each surrogate component (isooctane, n-heptane, toluene, and ethanol), with updates for key reaction rate constants based on recent theoretical and experimental studies. The resulting model was finally reduced using a DRGEP-SA method based on 0-D computations and then successfully validated against the experimental measurements available for the TRFE/air EGR mixtures in the whole [, T, P,   ] domain.
The MACDIL Mech. was then used to expand the database of laminar flame speeds for the TRFE surrogate of interest to higher temperatures, pressures, and dilution ratios. This newly expanded database (including both experimental and computed data) was next employed as a training set to derive the optimized coefficients of a new empirical correlation, the MACDIL correlation. The formulation of this new correlation has been herein devised, with the following new features: 1. the laminar flame speed reference term adopts a dual Gaussian formulation in which the different parameters are related to physical quantities along the   - curve, thus enabling to capture the different -dependences of the fuel-lean and fuel-rich branches; 2. the temperature exponent formulation similarly adopts a two-Gaussian expression, preventing unrealistic overestimations of the laminar flame speeds at over-lean and over-rich conditions, i.
Some improvements of the correlation formulation are still required, especially for the dilution ratio/pressure combined effect on the laminar flame speed. Likewise, the optimization of the correlation parameters would benefit from a larger experimental database, covering a larger T, P, and dilution ratio range. Nevertheless, the new correlation can be implemented in CFD codes to provide more accurate estimations of laminar flame speeds than existing correlations, and thus improve simulations of turbulent flames at highly EGR-diluted regimes.
Acknowledgments This work was supported by  Agence Nationale de la Recherche, France  [ ANR-15-CE22-0014 ]. The authors thank  Dr. Marco Di Lorenzo ,  Prof. Pierre Brequigny , and  Prof. Fabrice Foucher  from the  PRISME lab  for communicating the experimental data. We thank  Dr. Giampaolo Maio  and  Dr. Stephane Chevillard  for using MACDIL correlation in CFD simulations. We thank  Dr. Lucia Giarracca  for using MACDIL Mech. in kinetic modeling.