dataesr/scientific-paragraphs-categorization huggingface dataset:
Assessment of the simulation The test matrix of the database is used to assess the simulation procedure. For this assessment, the "true" values of transition temperatures and upper shelf used to compute the accuracy e are here the values obtained from the fitting of the database (Tab. 2). Table  3  and Figure  3  present the results of the 10,000 computations of transition temperatures and upper shelf with the test matrix of the database. The mode of sampled transition temperatures is close to these obtained by overall data base: for the transition temperatures, the accuracy values are smaller than the standard deviation. The main part of uncertainty on transition temperatures comes from the precision which is primally in relation with the data scatter in the transition domain. We assume that the accuracy values are small enough compared to usual experimental errors to conclude that the simulation procedure is satisfactory.
Definition of the reference case The determination of the accuracy needs the definition of a reference case with "true" values of transition temperatures and upper shelf. The database values cannot be considered as true because of the size of the population and the imperfections in its modelling. So, we have defined "true" values as the results of the simulation with a test matrix with a large number of specimens (600) distributed on 7 test temperatures between -90 and +100 °C (Tab. 4). We assume that the values resulting of the simulations with this test matrix (Tab. 5) are the true values from which the accuracy of the other test matrices is evaluated. As the reference case represents the "truth", its accuracy is equal to 0 and its uncertainty is equal to its precision. It is interesting to note that the skewness and Kurtosis coefficient indicate that the transition temperatures and, to a less extent, the upper shelves distributions are nearly symmetric and mesokurtic.
The values of these parameters are given in Table  13. An upper bound of the uncertainties on each  transition temperature is defined by increasing the parameter c k in such a way that the data corresponding to the highest uncertainty amplitude a k is on the parabolic function plot (dotted lines in Fig. 10 ). The values of the corresponding c k parameters (c k upper bound) are also given in Table  13. Equation (  6 ) can be checked by applying it to previous simulation results not used for the parameters tuning. We have taken the case of the first run for the "RCC-M" matrix which have a test matrix shift of 0. 67. The uncertainties given by equation (  6 ) and of the simulation are found to be in good agreement (Tab. 14). i i-1 i-1 i i i-1 3 Distributions of transition temperaturesT28, T41, T56 and T68 have been determined using numerical simulations based on a random sampling of Charpy data.
-Uncertainties are approximatively inversely proportional to the squared root of the number of specimens. -An empirical equation to estimate the uncertainties is proposed. It is a function of the number of specimen and of the shift of the test matrix. This work was partly funded by SOTERIA, a project of the European Union's Horizon 2020 research and innovation programme. The author thanks all the contributors to the database and, in particular, the members of the fracture mechanics laboratory of the SRMA at CEA Saclay.
According to the collision cross section data, the corresponding parameters can be calculated, and the critical breakdown field strength can be obtained from the ionization coefficient and the attachment coefficient. At present, the data of the collision cross section of gas are limited and are constantly replenished and improved. It is difficult to measure and calculate the collision cross section, which is an important factor that hinders the new gas research. The current micro-parameter calculations are based on some assumptions and simplifications. There is still a need for further research and exploration on the microscopic calculation of gas discharge to macroscopic processes. (2) Extinguishing performance: Gas arc performance can be obtained through the interruption test in the laboratory or the circuit breaker equipment.
ACKNOWLEDGEMENTS This study was supported by a  Chaire d'Excellence Junior University Sorbonne Paris Cité, USPC  (to MB), the  Israeli Science Foundation  ( ISF-NSFC 2525/17 , to AS), the  European Union  ( H2020   Eureka!Eurostars NANOSCALE  (to MO and AS). Our collaborative research on TIRF and SAF was further financed by a  French-Israeli ImagiNano CNRS-LIA grant  (to AS & MO), the  Agence Nationale de la Recherche  ( ANR-10-INSB-04-01 , grands investissements FranceBioImaging, FBI, to MO), the  Université Paris Descartes  (invited professorship during the academic year 2017-18, to AS) and the  French Ministère des Affaires Etrangères  ( Chateaubriand Senior Fellowship  to AS). The authors thank  Dana Khanafer  for help with Fig. 2C. The Oheim lab is a member of the C'nano  IdF and Ecole de Neurosciences de Paris (ENP)  excellence clusters for nanobiotechnology and neurosciences, respectively.
ACKNOWLEDGMENTS We thank  Juliette Monsel  and  Jens Schulenborg  for useful comments on the manuscript. This research was supported in part by the  National Science Foundation  under Grant No. NSF   PHY-1748958  (RS and JS), the  Knut and Alice Wallenberg Foundation  and the  Vetenskapsrådet, Swedish VR (JS and FH) , the  Ramón y Cajal program   RYC-2016-20778 , the  Spanish Ministerio de Ciencia e Innovación  via grant No. PID2019-110125GB-I00  and through the  "María de Maeztu" Programme for Units of Excellence in R&D   CEX2018-000805-M (RS) , and the  French Agence Nationale de la Recherche  under the  programme "Investissements d'avenir "  ANR-15-IDEX-0002  (RW).
Modeling of Heat Dissipation in Flexible NW LEDs To better understand how heat is dissipated from the flexible LED to the heat sink, the temperature distributions inside the device were simulated using 3D finite-element analysis with the Comsol Multiphysics software heat-transfer module  [50]. Steady-state temperature field distribution was calculated, and material parameters were taken from the Comsol Multiphysics standard material library. In particular, the parameters for bulk GaN were used to simulate the NWs. It should be noted that modifications of thermal properties were theoretically predicted  [51]  and experimentally observed  [52]  in GaN NWs compared to bulk. However, these modifications took place for NW diameters smaller than the phonon mean free pass, which is around 100 nm in GaN at room temperature  [53].
Funding: This work was financially supported by  EU ERC project NanoHarvest  (grant no. 639052 ), the  ITN Marie Curie project INDEED  (grant no. 722176 ), by the  Indo-French Centre for the Promotion of Advanced Research (IFCPAR/CEFIPRA  project no. 6008-1 ), and by the  Labex GANEX  (grant no. ANR-11-LABX-0014 ).
ACKNOWLEDGMENTS We acknowledge the financial support received from the  Cross-Disciplinary Program on Instrumentation and Detection of the CEA , the  French Alternative Energies and Atomic Energy Commission. We are grateful to  Dr P. Jonnard  from the  LCPMR laboratory at Sorbonne Université  for reviewing this article so attentively. We also thank  Dr N. Clavier  from  ICSM/LIME laboratory at the CEA  for providing us with spherical uranium oxide microparticles.
Many different equations ranging from simple empirical to semi-analytical solutions of the Richards equation have been proposed for quantitative description of water infiltration into variably saturated soils. The sorptivity, S, and the saturated hydraulic conductivity, K s , in these equations are typically unknown and have to be estimated from measured data. In this paper, we use so-called characteristic time (t char ) to design a new method, referred to as the characteristic time method (CTM) that estimates S, and K s , from one-dimensional (1D) cumulative infiltration data. We demonstrate the usefulness and power of the CTM by comparing it with a suite of existing methods using synthetic cumulative infiltration data simulated by HYDRUS-1D for 12 synthetic soils reflecting different USDA textural classes, as well as experimental data selected from the Soil Water Infiltration Global (SWIG) database.
ω is the contribution of the gravity component to the infiltration process Then, one could calculate I grav by rearranging the Equation 13 and putting W = 0. 5 as below: 𝐼 grav = 𝑆 CTM-I √ 𝑡 grav 0. 5 (27) Finally, when t grav and I grav values were predicted as above, Equation 21 can be used to determine K s by setting ω = 0. 5, t char = t grav , and I char = I grav. Figure  4  briefly shows the flowchart of how CTM-I and CTM-K s should be used to ensure accurate prediction of both S and K s. A script written in Python applying the CTM is provided as supplemental material. The Appendix also provides the script in text format. A script written in MATLAB or scilab also could be provided upon to request.
In the case of CF2 and CF3, the "lsqnonlin" function is used to predict S and K s. We truncated simulated infiltration curves to obtain infiltration curves of different durations from 5 min to 10 h, corresponding to a typical infiltration measurement window derived from the Soil Water Infiltration Global (SWIG) database  (Rahmati, Weihermüller, Vanderborght, et al. , 2018; Rahmati, Weihermüller, & Vereecken, 2018). We used a variable infiltration duration in order to assess the capability of CTM in finding the characteristic time and infiltration independently of the duration of the infiltration experiments. In addition to the analysis mentioned above, we also used synthetic data with measurement noise as well as experimental data selected from SWIG database  (Rahmati, Weihermüller, Vanderborght, et al.
The error was first defined for the infiltration rate and then propagated to the cumulative infiltration. This approach only considers the measurement error and not errors caused by violation of the underlying theoretical assumptions such as the presence of soil layering, nonuniform infiltration, and infiltration in (dead-end) macropores. In the case of experimental data, we selected 1D infiltration data available in the SWIG database obtained from infiltration experiments using a zero-water potential imposed at surface. In overall, 614 infiltration data were selected for final analysis. As no independent measurements of K s and S are reported in SWIG for the selected data, we estimated these values using the QEI formulation  (Latorre et al. , 2015) , which we consider as a benchmark for comparison with the estimates from other approaches.
Evaluation of the estimated hydraulic parameters The accuracy of the CTM and other selected methods was evaluated using the RMSE and  Nash and Sutcliffe (1970)  efficiency, E, criteria between measured and predicted K s and S values: RMSE = √ ∑ ( 𝑋 m -𝑋 p ) 2 𝑛 (33) 𝐸 = 1 - ∑ ( 𝑋 m -𝑋 p ) 2 ∑ (𝑋 m -Xm ) 2 (34) where X m and X p are the logarithmic values of known and predicted parameters (S and/or K s ), respectively. In the case of the SWIG database, the predictions provided by the QEI model were considered as the known values. The values of RMSE near zero denote a great accuracy, whereas E takes values in the interval [-∞, 1]. A value of E equal to unity shows a perfect match and an E value of zero means that the average of the observed values is as good as predicted values. Negative E values mean that the model is worse for prediction than taking only the mean of the observed values.
Evaluating the CTM over experimental data Up to this point in the study, the CTM method was tested and verified over synthetic data obtained from HYDRUS-1D. Experimental data obtained in field campaigns are usually noisy and not perfect. Although we added some random noises over those synthetic data to evaluate the method performance over the noisy data as well, such a noise addition will not represent other important error sources such as soil layering, nonuniform infiltration, and infiltration in (dead-end) macropores. Therefore, a performance evaluation over experimental data is yet required. However, experimental data usually lack the true values of TA B L E 5 Average RMSE and  Nash and Sutcliffe (1970)  efficiency (E) criteria between logarithms of known and predicted saturated hydraulic conductivity (K s ) and soil sorptivity (S) values using the characteristic time method (CTM), Sharma method (SH), and nonlinear curve fitting method of two-(CF2) and three-term (CF3) equations over experimental data of the Soil Water Infiltration Global (SWIG) database As a conclusion of the above, we used field experimental data taken from the SWIG database  (Rahmati, Weihermüller, Vanderborght, et al.
, 2013). The CTM method avoids all these shortcomings outlined above. Its sole complexity involves the use of an iterative process that is necessary since the knowledge of the transition time between transient and steady regime depends on unknown values of S and K s. Despite this difficulty, no fits are required, and the computation involves only simple algebraic operations. Its adaptation to all types of datasets (encompassing a part of the transient state or including both transient and steady states) makes it a useful tool. In addition to its advantages, our study demonstrates its efficiency in reaching its goal. All these aspects make the CTM method a promising method for the estimation of S and K s.
The accuracy of K s and S predictions using CTM showed no dependency on the duration of infiltration. We also evaluated the performance of the CTM in a comparison with other methods over noised synthetic data, as well as experimental data selected from the SWIG database  (Rahmati, Weihermüller, Vanderborght, et al. , 2018; Rahmati, Weihermüller, & Vereecken, 2018) , to verify the usage of the CTM with real noised data. The results showed that even with noised and experimental data, the CTM still was better than CF2 and CF3, showing considerably higher accuracy, particularly in the case of K s predictions. The CTM method was also comparable with the classical method of SH owing to the advantage of no arbitrariness in selection of data for accurate predictions of S and K s. Further research is needed to corroborate the estimated values of S and K s using CTM with independently determined values of S and K s.
The system generates astigmatism 3x as shown on the simulated displacement fringes of the optical surface in Fig. 3  right. Simulations of the deformation are performed using the FEA software PATRAN/NASTRAN. We used a tetrahedral mesh with a minimum of 80000 elements to have an accurate simulated deformation. Zerodur is modelled with a Young's modulus of 90. 6 GPa, a density of 2. 53 g/cm 3  and Poisson ratio of 0. 24  [35]. The model is constrained in its centre along the z-axis, in the 3 translational degrees of freedom and forces are applied on a square area on the back surface external border (Fig. 3 middle ). To generate the additional coma 3x we need to break the symmetry of the deformation process, while keeping the same combination of forces to generate the astigmatism 3x (Fig. 3 left ).
Results A complete characterisation of the prototype surface is performed; the optical quality of the mirror is characterised in the three spatial frequency domains, as described in Section 2. 1. The assessment of the LoF SFE and MidF SFE is validated with the phase map acquisition from interferometric measurement performed on the complete polished surface of 58 mm in diameter, the number of pixels on this diameter is 870. Figure  11  shows the phase maps at 50 mm and 22 mm diameter computed with the Intelliwave software from the interferometric fringe image (Fig. 10 right ). The measurement on the 50 mm diameter is added to provide an insight on how the process is expected to scale for the larger clear aperture diameter OAPs. On the clear aperture of 22 mm, the number of pixels is 330 corresponding to a maximal spatial frequency of 165 c/p, which covers the LoF and MidF domains.
X i¼m i¼1 ∂S V; P ð Þ ∂P i dP i ¼ À X j¼n j¼1 ∂S V; P ð Þ ∂V j dV j ð3Þ with dV j : tolerances on each variable; dP i : tolerances on system parameters. While the system is continuous, the same equations are found at every particular instant. Thus, for a system defined with m parameters and n variables, the previous equations are the same at z instants (the chosen z time instants should be greater than the number of parameters and variables). Therefore, the following matrix equation can be deduced: see this equation at the bottom of the page. It can be presented in this simplified form: A Â dP ¼ B Â dV: ð4Þ The next step is to complete matrices A and B numerically. Thus, to perform the physical behavior of the mechatronic system, multi-domain tools or languages can be used such as Matlab/Simulink, Bond Graph or Modelica.
As the compliance with mathematical modeling should be guaranteed, the Modelica language including a mathematical description of the models  [17] [18] [19] [20]  has been selected. In parallel, as the Dymola tool implements Modelica while providing a graphical interface, it will be chosen as the multidisciplinary modeling tool. It is commonly used for the modeling and simulation with major applications in virtual prototyping. The target values of variables are given with the Modelica simulation. We extract variables in z instants and insert them in the matrices A and B. After obtaining the complete matrix formulation, it can be solved in two ways: -With regards to the requirements: knowing the acceptable deviation on the behavior of each variable (dV), the admissible tolerances of parameters (dP) can be searched.
Modeling and simulation Figure  2  shows a simple model of a DC motor using Modelica language with the Dymola tool. This model is used to evaluate the variables in the nominal case. Variables curves in Figure  3  are given via Modelica simulation. Using Dymola, the number of time intervals is 500 for one second by default. While all the curves of variables are periodic (continued repetition of part) with a period equal to 2 s, the chosen number of instants is z = 500 Â 2 =1000. For each chosen instant in time, the target variables have been retrieved from these curves to apply the approach.
First, in order to determine the shape of nanoparticles specifically, the simulation results were compared with the experimental results for the spherical and disk-like shape nanoparticles. Also, extinction spectra for nanoparticles were obtained by using MNPBEM simulation programme depending on the near field coupling between disk-like nanoparticles and the near field coupling between spherical nanoparticles. It was observed that, the experimental data fits the theoretical results for the disk-like nanoparticles. The extinction simulation spectrum of disk-like shape Au nanoparticles is displayed in Figure  4  and it was noticed that these theoretical results are very similar to that deposited experimentally at 2 × 10 -3 mbar Ar ambient gas pressure. The diameter, height, and the interparticle distances of disk-like shaped Au nanoparticles are determined to be 115 nm, 15 nm, and 40 nm, respectively.
Therefore, simulated LSPR band is more uniform and narrower. Although LSPR band in the simulation is shifted a few nm because of the consideration of experimental result, both results are in well agreement (LSPR peak is presented with red dot line in Figure  3 ). The diameter and interparticle distances for spherical nanoparticles were taken to be 115 nm and 40 nm in average (Figure  2a ), respectively, measured by AFM. The extinction spectrum was obtained by using MNPBEM simulation program is presented in Figure  5. Because of authors' knowledge, the multipoles are induced on the individual particles due to the near field coupling between the larger spherical nanoparticle. Also, the larger sized nanoparticles lead to higher modes for the electrons confined in nanoparticles (nanoparticle size ≥ 100 nm)  [2]  and no homogenous electric field is created, and therefore, electron cloud not move homogeneously.
It was observed that, the experimental data fits the theoretical results for the disk-like nanoparticles. The extinction simulation spectrum of disk-like shape Au nanoparticles is displayed in Figure  4  and it was noticed that these theoretical results are very similar to that deposited experimentally at 2 × 10 -3 mbar Ar ambient gas pressure. The diameter, height, and the interparticle distances of disk-like shaped Au nanoparticles are determined to be 115 nm, 15 nm, and 40 nm, respectively. Theoretical background for MNPBEM implies that the extinction efficiency is inversely proportional to the distance between Au nanoparticles. Since the disk-like shape nanoparticles have the larger size and the near field interparticle coupling, LSPR peak have consequently shifted toward the IR region.
The diameter and interparticle distances for spherical nanoparticles were taken to be 115 nm and 40 nm in average (Figure  2a ), respectively, measured by AFM. The extinction spectrum was obtained by using MNPBEM simulation program is presented in Figure  5. Because of authors' knowledge, the multipoles are induced on the individual particles due to the near field coupling between the larger spherical nanoparticle. Also, the larger sized nanoparticles lead to higher modes for the electrons confined in nanoparticles (nanoparticle size ≥ 100 nm)  [2]  and no homogenous electric field is created, and therefore, electron cloud not move homogeneously. The charge distribution on nanoparticle surface is inhomogeneous and the high multipolar charge distribution is excited  [2]. Therefore, two peaks are formed in an extinction spectrum and LSPR peak obtained from simulation is located at a wavelength that is shorter than what we have obtained from the experimental work.
Acknowledgments: The result of the investigation is a part of a project that has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie  grant agreement No  778156. This work was supported partly by the  Scientific and Technical Research Council of Turkey (TUBITAK)  under Grant No. 1649B031503748  and  Scientific Research Projects Coordination Unit of Selçuk University , Project No. 15201070  and  15301020. Serap Yi  git Gezgin would kindly like to thanks for a scholarship given by the  Scientific and Technical Research Council of Turkey (TUBITAK)  under Grant No. 1649B031503748.
3c ) to separate the sample from the hydraulic oil, and placed in the confining chamber (see Fig. 4a ). The shear and normal displacements are measured via LVDTs and lateral strain gauge, respectively. The pressures are monitored by transducers with accuracy of AE0. 1 MPa. The above experimental data can be recorded in a data acquisition center. (2) Step 2: Apply confining stress (P c ) as isotropic stress by injecting silicon oil into the confining chamber at a rate of 0. 5 MPa/min, which is equivalent to s n applied on the preexisting fracture. (3) Step 3: Apply axial force (F i ) to the desired level by running the axial servo pump at a rate of 1 mL/min under constant normal stress, which results in a path that can be approximated as strain-controlling fashion  (Carey et al. , 2015; Frash et al.
Acknowledgments The financial support by the  National Key Research and Development Program of China  (Grant No. 2018YFC0809601 ), the  National Natural Science Foundation of China  (Grant No. 51779252 ), the  Major Technological Innovation Projects of Hubei, China  (Grant No. 2017AAA128 ), and the  Key Projects of the Yalong River Joint Fund of the National Natural Science Foundation of China  (Grant No. U1865203 ) for this work are gratefully acknowledged.