dataesr/scientific-paragraphs-categorization huggingface dataset:
R, where R denotes the elastic rotation operator. Introducing this expression in the definition of the velocity gradient, one may obtain: L = R ̇. R -1 + e °+ R. F ̇p. (F p ) -1. R -1 , where e ° is an objective measure of the elastic strain rate. In the following simulations, Jaumann derivative will be used for convenience reasons as it is implemented in ABAQUS FEM software. The total strain rate is the symmetric part of the velocity gradient. Its additive decomposition into elastic and plastic parts leads to the following expression of the plastic strain rate: D p = D -e °. For FLD determination, it is common to apply the load in the principal directions of anisotropy, leading to a null elastic spin. A simplified formulation of the material laws, close to the small strain formulation, may then be used.
Different localization indicators may then be constructed to predict localization. In this paper, the out-of-plane strain rate ratio is used as a strain localization measure. Localization is predicted when this ratio exceeds a userpredefined value  [18] : 𝑆 𝑀𝐾 = 𝜖 33 𝐵 𝜖 33 𝐴 (5) It can be shown that the value of this threshold may be taken in a range of, for example, 5 to 10 and that its choice should not influence strain localization predictions as strain rate evolves exponentially in zone B near localization. Predictions are then not sensitive to this parameter, but high values of the threshold may lead to numerical instabilities. Different methods may be set up to implement the M-K model, from purely analytical developments to FEM simulation. In this paper, this second choice has been favored and ABAQUS software has been used for numerical applications.
In this procedure, strain localization is expected to appear in zone presenting an initial thickness defect. The fully 3D finite transformation framework is implemented in ABAQUS FEM software. This implementation is versatile and easily adaptable to a large class of materials including elasto-plastic or visco-plastic behaviors. This numerical procedure allows strain localization predictions using material parameters commonly available from datasheets without being sensitive to damage parameters identification strategies. Experimental and numerical procedures are then applied and compared on St14 mild steel. A set of original experimental results is proposed in this paper. Both give close results for sheets presenting initial defect ration of 0. 95. Relative errors between experimental and numerical results are 10%, 22% and 8% respectively for uniaxial tension (UT), plane tension (PT) and equibiaxial expansion (EE).
For shorter exposure durations, the method is able to constrain minimum elevations. The main advantage of the method is that it is only slightly sensitive to erosion: even if the preservation state of the surface is unknown, the bias on the computed elevation remains lower than 1500 m in most cases. The approach can also be applied to previously exposed surfaces that have subsequently been buried, in order to reconstruct the paleo-elevation of a given surface over time ranges of ∼0 to 8 Ma (using the 26 Al-10 Be pair) and ∼0 to 12 Ma (using the 10 Be-21 Ne pair). Data comparison -We tested the method using the multiple cosmogenic nuclides dataset available for the western arid tropical Andes. The altitudes computed using the cosmogenic nuclide concentrations agree within uncertainties with the reported sampling altitudes over a range of 0 to more than 4000 m, illustrating the applicability of the method.
Altitudes computed under the assumptions of continuous exposure or steady state erosion yields best fits that are statistically in agreement and close to the 1:1 line for both the 26 Al-10 Be and the 21 Ne-10 Be dataset. The 21 Ne-10 Be inventories in samples that have been exposed for more than 5 Ma yield elevations that are several hundreds of meters below their present-day elevations (∼1000 m). This may result from a post 10 Ma uplift of the West Andes, or from an unrecognized exposure underwater, or below a soil cover. Implications -This study may also have implications in other fields that rely on multiple cosmogenic nuclide measurements. The same approach might notably be used to compute the depth of exposure of samples located below the rock surface or underwater. This study may also help to improve the accuracy of the common burial dating method that uses multiple radioactive cosmogenic nuclides.
, 2005). However, these exploratory works had to address several important limitations, notably because a method based on the measurement of only one nuclide corresponds to a mathematically underdetermined system: this approach thus requires the use of surfaces that have not been affected by erosion, and for which the duration of paleo-exposure can be independently and accurately measured with high precision  (Blard et al. , 2006). Such a combination of favorable conditions is rarely fulfilled in nature, making the method difficult to apply. Here we present a novel approach for using and interpreting datasets of multiple-cosmogenic nuclides measured in the same rock samples. We show that, when the exposure time is long enough (typically > 500 ka), the isotopic ratio of two cosmogenic nuclides with contrasting half-lives, along with their respective concentrations, allows calculation of precise and accurate elevations.
Under the most favorable conditions, the method enables altitudes to be derived with a precision (<500 m) that is useful for most geological applications. The strength and main advantage of this new technique is that its accuracy is only slightly sensitive (bias from this assumption is less than 1000 m) to the amount of erosion that has affected the exposed paleosurface, a parameter that is generally unknown. We tested the method on an existing dataset of samples collected in the arid part of the Western Andes, using bedrock and detrital samples in which pairs of cosmogenic nuclides ( 10 Be-21 Ne and 26 Al-10 Be) had been measured in previous studies  (Kober et al. , 2007; Nishiizumi et al. , 2005; Placzek et al. , 2010; Ritter et al. , 2018a). The calculated altitudes are in good agreement with the present-day elevation of the samples, suggesting both that the method is adequate and that the altitude change of the Central Andes has been limited over the last hundreds of thousands of years.
General theory: determining altitudes from paired-cosmogenic nuclides All of the calculations (i. e. simulations and data interpretations) presented here were performed using the parameters summarized in Table  1. Scaling factors were computed using the CREp calculator (https://crep. otelo. univ-lorraine. fr /#/)  (Martin et al. , 2017). In a companion paper  (Blard et al. , 2019) , we provide a Mat-lab© code, (Paleoaltitude. m), which allows paleoaltitudes to be computed from any dataset of cosmogenic nuclides (either the 26 Al-10 Be or the 10 Be-21 Ne pair), under both assumptions of continuous exposure and erosion (see  Blard et al. , 2019  for the mathematical description of the used algorithm). This code also plots data and simple exposure curves (ratio of two cosmogenic nuclides vs concentration of one cosmogenic nuclide) for variable altitudes in the same diagram.
5A ), while it requires ∼3 Ma for the 10 Be-21 Ne pair (Fig. 5B ). This modeling also shows that the response time of the registered altitude is shorter in the case of uplift than in the case of subsidence (Fig. 5 ). This is due to the exponential increase in production rate with elevation, which gives a larger weight to the nuclides produced at high elevation. 3. Testing the method against the existing 10 Be-21 Ne-26 Al dataset from Atacama.
Data description In order to evaluate the accuracy of this new paleoaltimetric method as well as its overall uncertainty in real conditions, we tested this approach on an existing dataset of samples, in which multiple cosmogenic nuclides have been measured ( 26 Al and 10 Be, or 21 Ne and 10 Be). For this, we selected datasets from a geological setting that fulfilled the following criteria: i) samples have presumably been exposed at the surface for a sufficiently long and continuous duration ( 100 ka); ii) rocks have remained at the same sampling elevation without any significant elevation change during the exposure history; and iii) the dataset covers a quite large altitudinal range, from sea-level to several thousand of meters. For this initial test, we chose the Atacama desert, a very arid region of the Western Tropical Andes that meets the required geological and geomorphological criteria: i) rainfall is extremely low (<10 mm w.
e. yr -1 ), making long exposure (>1 Ma) possible  (Dunai et al. , 2005; Ritter et al. , 2018b) , ii) several lines of evidence suggest that no altitudinal change greater than 1000 m has occurred since 5 Ma  (Garzione et al. , 2008; Kar et al. , 2016) , and iii) the steep west-east topographic gradient gives access to an altitudinal range from 0 to 5000 m. We consider here all published datasets that have reported measurements of cosmogenic nuclides pairs ( 26 Al-10 Be and 10 Be-21 Ne) from surface samples collected in the Atacama desert:  (Kober et al. , 2007; Nishiizumi et al. , 2005; Placzek et al. , 2010; Ritter et al. , 2018a Ritter et al. , , 2018b)). Table  S1  presents the main characteristics of these samples (nature, lithology, sampling coordinates). The dataset includes a total of 68 samples for the 26 Al-10 Be pair and 43 samples for the 10 Be-21 Ne pair.
On the other hand, a few samples plot below or on the left of their respective exposure curves, suggesting that these samples have been affected by periods of burial or recently exhumed. Importantly, the majority of the samples are located on their corresponding elevation-curves, suggesting that the dataset was not affected by any significant elevation change since the initiation of exposure. For a more precise comparison, we also inverted all of the data to compute paleoelevations using the altimetry method, following the mathematical approach described in  (Blard et al. , 2019). Ta- ble S2 displays the detailed results and Fig. 7  is a plot of these computed elevations vs sampling elevations. Since we do not have any a priori knowledge of the amount of erosion that affected these samples, the two extreme cases of continuous exposure and steady-state erosion were considered (Fig.
7A  and B ). Sample exposures that did not satisfy the conditions to compute elevations are not plotted on Fig. 7. Among the 43 21 Ne-10 Be samples, elevations could not be calculated for only 2 samples. In the case of the 68 26 Al-10 Be samples, mean altitudes could not be calculated for 18 samples in the case of continuous exposure, and 10 in the case of steady-state erosion. This difference mainly results from the shorter integration times of the 10 Be-26 Al dataset (0. 55 ± 0. 28 Ma) compared to those of the 21 Ne-10 Be dataset (1. 22 ± 0. 60 Ma). Fig. 7  plot shows that there is a first order good agreement between the computed elevations and the sampling elevations. The two extreme scenarios of continuous exposure and steady-state erosion yield quite similar results, indicating that the method is robust, whatever our knowledge of the surface preservation state.
Best-fit regression lines were computed, along with their parameter uncertainties at the 2-sigma confidence level. In the case of the 26 Al-10 Be dataset, the best-fit regression curves lie slightly below the 1:1 line, both for the continuous exposure ( y = (0. 78 ± 0. 31) • x + (10 ± 600), R 2 = 0. 50, p-value < 6 ×10 -6 ) and the steady-erosion case ( y = (0. 70 ±0. 39) • x +(670 ± 770), R 2 = 0. 39, p-value < 10 -3 ). This slight divergence with the 1:1 line is due to a group of 6 samples that today stand between 2300 and 3800 m, but that yielded computed elevations 1000 to 2000 m below their present position. This bias may result from unrecognized recent exhumation of samples that spent most of their exposure histories more than 50 cm below the rock surface (see section 4. 1 below). However, if these 6 points are excluded, the agreement between the sampling and the computed elevation is excellent, indicating that the method is robust and accurate, even when using a large dataset that was not specifically sampled for paleoaltimetric purposes.
The 21 Ne-10 Be dataset yields best fits that are statistically in quite good agreement with the 1:1 line: y = (1. 12 ± 0. 21) • x -(800 ± 610), R 2 = 0. 83, p-value < 2 × 10 -13 in the case of continuous exposure, and y = (1. 42 ± 0. 21) • x -(760 ± 540), R 2 = 0. 83, p-value < 6 × 10 -16 , in the case of steady-erosion. The samples that are not aligned on the 1:1 line are those from the Quillagua-Llamara Soledad paleoake shorelines  (Ritter et al. , 2018a) , which are located at low elevations (∼1000 m) and yield underestimated computed elevations (ranging from -1500 to 500 m). Several possibilities might be proposed to explain the fact that many of the shorelines samples of  Ritter et al. (2018a)  yielded computed altitudes lower than their present-day elevations: i) A significant part of the exposure may have started and occurred below the lake surface, or below soil cover that has been removed during the upper Pleistocene; ii) We did not consider the muogenic production in the equation.
If an unknown process has recently exhumed the rock, there is a risk that the actual altitude of exposure will be significantly underestimated using the paleoaltimetry method (Fig. 3 ). This important aspect should be kept in mind during sampling and any evidence that suggests the sporadic presence of loess, soils or any cover should be considered before sampling a paleosurface on a fresh outcrop. The possibility of landslides should likewise be carefully assessed. A potential depth-meter. If the altitude of exposure is wellknown, the position of the simple exposure curve may also be turned into a sensitive and precise depthmeter  (Gosse and Phillips, 2001). If exposure is sufficiently long ( 100 ka), the paleoaltime-Fig. 7. Sampling against elevations calculated with the paired cosmogenic nuclides method considering A) continuous exposure and B) steady-state erosion, for the whole Atacama dataset (data from  Kober et al.
For a material that has exposed under steady-erosion conditions before burial, the equation that must be used to compute the burial age t burial is: P 1 N 1 e -λ 1 •t burial - P 2 N 2 e -λ 2 •t burial = λ 1 -λ 2 f (9) If nuclides 1 and 2 are both radioactive, equation (  9 ) has no analytical solution and must be numerically solved to determine t burial. For the particular case of a cosmogenic nuclides pair with only one radioactive isotope, such as 10 Be-21 Ne, equation (  9 ) simplifies and can be analytically solved: A Matlab© code, (Burial. m), computing burial ages taking into account the altitude of the preburial exposure episode is available in a MethodsX companion paper  (Blard et al. , 2019). t burial = -1 λ • ln.
Acknowledgements Careful and constructive reviews by  Greg Balco  and  Derek Fabel  helped us to improve the submitted manuscript. Authors are grateful for stimulating discussions with  Vincent Regard ,  Sébastien Carretier ,  Raphaël Pik ,  Julien Charreau  and  Jérôme Lavé. Alice Williams  carefully checked the English quality of the manuscript. This is CRPG contribution n • 2689.
For fire safety studies in nuclear installations, IRSN uses the SYLVIA software. The SYLVIA two-zone model was developed by IRSN to simulate a full ventilation network, fire scenarios in a highly confined and mechanically ventilated facility, and airborne contamination transfers inside nuclear installations. In order to take into account the different sources of uncertainty coming from initial and boundary conditions as well as from model parameters, the SYLVIA software is associated with the SUNSET statistical software. However, such a use of SYLVIA software has a major drawback: it requires a large number of runs and a significant statistical analysis what is not always compatible with the requirements of safety assessments in terms of deadlines. To overcome this difficulty, IRSN is currently developing an expert system based on a SYLVIA database.
This approach allows deriving the most likely diagnosis or prognosis in a very short time, but also deriving a more complex form of reasoning intertwining prognostic and diagnostic inferences. The proposed expert system is based on the Bayesian Belief Network (BBN) methodology and consists in two steps: First, a large database obtained from SYLVIA runs allows the estimation of Conditional Probability Tables. Then, a message passing algorithm is used to exploit dynamically this data base. The illustrating example is based on the study of pressure effects due to fire scenarios in nuclear facilities and the database is made up of 1,600,000 runs of the SYLVIA software. The goal of this paper is to detail the methodology and process to carry out an expert system for fire safety studies, and is supported by one example showing how it can be used as a decision support tool for fire safety analysis in nuclear area.
Introduction The SYLVIA software system  [1]  has been developed by the Institut de Radioprotection et de Sûreté Nucléaire (IRSN) to simulate a full ventilation network, fire scenarios in a highly confined and ventilated facility, and airborne contamination transfers inside nuclear installations. This software is based on a two-zone approach and is used by IRSN for fire safety studies. To evaluate the impact of uncertainties, the SYLVIA software is coupled to the SUNSET statistical tool  [2]  also developed by IRSN. This coupling makes it possible to directly carry out a set of parametric studies and then measure the impact on some selected responses. A typical use of the SYLVIA/SUNSET coupling is to perform a Monte Carlo simulation in which a set of variables, known as study parameters, is modeled by random variables.
The results obtained from a Monte Carlo simulation constitute a database linking parametric configurations determined by the set of values assigned to the study parameters and uncertainties to the corresponding results. However, the direct use of this database in the context of a safety assessment encounters two main difficulties: -The database is necessarily very limited considering the possible configurations. The SYLVIA simulations constituting the database represent a small percentage of the possible parametric configurations. This is due to the combinatorial explosion of the configurations as a function of the possible values taken for each parameter and the number of parameters considered. For instance, if we consider 16 parameters and each of them can take only 3 values, the number of combinations of values is 3 16 , i.
e. approximately 43 million configurations. -The database is not specific to the characteristics of a safety assessment. It is necessary to extract from the database the information compatible with the specificities of the case of interest. For example, a safety assessment can focus more specifically on large volumes, high heat release rates, etc. and seek to discriminate configurations compatible with safety issues, such as maximum gas temperature, maximum pressure, etc. in a compartment. To meet this dual challenge, it is necessary to be able to correctly update the information contained in the database by integrating the characteristics of each safety assessment. One solution is to develop an expert system. This approach allows deriving in a negligible time prognostic and diagnostic like inferences, but also more complex forms of reasoning intertwining prognostic and diagnostic inferences.
To achieve this aim, a large SYLVIA results database has to be built. In a first section, we will describe the methodology used to create an expert system from a consequent SYLVIA database. Then, we will detail how we have established an expert system corresponding to a case of application dealing with the study of pressure effects due to a fire in an enclosure. In the last section, a practical use of the expert system will be analyzed, illustrating the interest of this expert system-like approach as a support tool for both training and safety assessment.
The expert system An expert system is a tool that aims to simulate the cognitive mechanisms of an expert, in a particular field. This is one of paths leading to artificial intelligence. More precisely, an expert system in artificial intelligence is defined as a computer program that has the ability to represent and reason on knowledge. In fire safety, it is useful to be able to quickly discern the configurations at risk of an installation. The idea behind the expert system approach is to make the most benefit of the SYLVIA software to build a database covering a wide range of configurations, and then to use the expert system reasoning abilities to discern configurations of this database useful to one specific case of interest. An expert system can be divided into three separated components  [3] , as shown in Fig.
The knowledge base In our case, the generic information is implicitly contained in the computer code. Thus, the first step to develop an expert system is to transcribe numerically the knowledge related to the different physical phenomena modelled by the code. Since the computation time is short enough to perform many calculations, our approach consists in building a database, which relates to the case studied -such as the pressure effects in a compartment -by performing a stratified Monte-Carlo study by a Latin Hypercube Sampling (LHS) method  [4]. This Monte Carlo study is carried out by varying the input parameters of the calculation code in the study area under consideration. Thus, if we want the expert system to be able to answer to queries for volume ranges between 100 and 500m 3 , we will model this parameter by a random variable between 100 and 500m 3 in the Monte-Carlo simulation.
This way, we can build a large database made of SYLVIA calculations. This database is made up of all the data corresponding both to the parameters and outputs. Then, this database can be interpreted as a numerical transcription of the generic knowledge carried by the SYLVIA code. In a formal way, the SYLVIA software can be seen as a mapping of the parameters domain to the responses domain (see Fig. 2 ). This can be written: Ri = S(P1, … , PN) ( 1 ) where Ri is any response of interest, Pj, the parameters and S, the SYLVIA software acting as a transfer function. The principle followed to establish the SYLVIA knowledge base consists in transcribing the transfer function S into numerical tables (one for each response). In order to carry out this transcription of SYLVIA into numerical tables (see Fig.
The Peatross & Beyler law  [12]  is a linear regression as a function of oxygen volume fraction available for combustion close to the fuel: χ= 0. 1X -1. 1 ( 11 ) where χ is the correction factor to be applied to HRR in open atmosphere and X the oxygen volume fraction close to the fuel. In SYLVIA software, the flame is supplied by oxygen available in the zone where the flame is located. In the case where the interface height is in the flame area, this oxygen volume fraction is calculated from the oxygen volume fractions of the two zones, by a weighting ratio of the flame lengths crossing the lower and upper zones. Yield of soot. Soot being involved in the malfunction of electrical equipment, the yield of soot (ratio of the produced mass of soot to the pyrolysed mass of fuel) is a parameter of the study.