esa-sceva/satcom-chunk-collection huggingface dataset:
# Performance Prediction and Design of Stratospheric Propeller
## 6 Result and Discussion  
### Airfoil Performance of FX-63  
The blade element performance was required to design and predict the performance of the propeller. A CFD simulation was applied to obtain the lift and drag coefficient curves of the FX63 airfoil for different Reynolds numbers and angles of attack (AOA). The range of Reynolds numbers changed from 1000 to 100,000, and the AOA changed from \(-5^{\circ}\) to \(15^{\circ}\). The lift and drag coefficient curves are presented in Figures 7-9.  
The polynomial fitting method in MATLAB was used to interpolate the lift and drag coefficient curves, when the Reynolds number increased from 1000 to 1,000,000. The airfoil lift and drag coefficient curves at \(Re\) = 8000 and 200,000 are presented in Figures 10 and 11, respectively. The polynomial curves were in good agreement with the CFD data. The polynomial equations are reported below the figures.  
\[C_{L}=\left\{\begin{array}{cc}0.0009\alpha^{3}{+}0.004\alpha^{2}+0.114\alpha+ 0.289&-5\leq\alpha\leq-2\\ -0.0003\alpha^{3}{+}0.003\alpha^{2}+0.102\alpha+0.283&-2\leq\alpha\leq 1\\ 3.8\times 10^{-6}\alpha^{4}-4.5\times 10^{-5}\alpha^{3}-3.7\times 10^{-3}\alpha^{2}+ 0.103\alpha+0.282&1\leq\alpha<15\end{array}\right. \tag{27}\]  
\[C_{D}=\left\{\begin{array}{cc}-0.001\alpha^{3}-0.007\alpha^{2}-0.016+0.047&-5 \leq\alpha\leq-2\\ -0.0001\alpha^{3}{+}0.001\alpha^{2}{+}0.003+0.062&-2\leq\alpha\leq 1\\ 4.2\times 10^{-7}\alpha^{4}+2.1\times 10^{-5}\alpha^{3}+3.7\times 10^{-4}\alpha^{2}+ 3.3\times 10^{-3}\alpha+0.061&1\leq\alpha<15\end{array}\right. \tag{28}\]  
\[C_{L}=\left\{\begin{array}{cc}-0.0002\alpha^{3}-0.003\alpha^{2}+0.103\ \alpha+0.759&-5\leq\alpha\leq-2\\ -3\times 10^{-5}\alpha^{3}-0.001\alpha^{2}+0.108\ \alpha+0.764&-2\leq\alpha\leq 1\\ 4.7\times 10^{-6}\alpha^{4}-9.3\times 10^{-5}\alpha^{3}+6.0\times 10^{-5} \alpha^{2}+0.104\alpha+0.769&1\leq\alpha<15\end{array}\right. \tag{29}\]  
\[C_{D}=\left\{\begin{array}{cc}-1.4\times 10^{-5}\alpha^{3}{+}0.0001\alpha^{2}+0.00 1\ \alpha+0.018&-5\leq\alpha\leq-2\\ -5.6\times 10^{-6}\alpha^{3}{+}0.0001\alpha^{2}+0.001\ \alpha+0.018&-2\leq\alpha\leq 1\\ 2.0\times 10^{-6}\alpha^{4}-3.2\times 10^{-5}\alpha^{3}+3.0\times 10^{-4} \alpha^{2}+0.001\alpha+0.018&1\leq\alpha<15\end{array}\right. \tag{30}\]  
Figure 8: FX63 airfoil performance for \(Re\) = 10,000–100,000.  
Figure 9: FX63 airfoil performance for \(Re\) = 100,000–1,000,000.
Sensors_**2013**, _13_, 7250-7278; doi:10.3390/s130607250  
Sensors  
ISSN 1424-8220  
www.mdpi.com/journal/sensors  
Article  
An Integral Model for Target Tracking Based on the Use of a WSN  
[PERSON] \({}^{1,\ast}\), [PERSON] \({}^{2}\), [PERSON] \({}^{3}\), [PERSON] \({}^{1}\)  
and [PERSON] \({}^{1}\)  
\({}^{1}\) DISCA, Universitat Politecnica de Valencia, Camino de Vera s/n, Valencia 46022, Spain;  
E-Mails: [EMAIL_ADDRESS] (J.-C.C.); [EMAIL_ADDRESS] (P.M.)  
\({}^{2}\) DCS, Instituto Tecnologico de Leon, Guanajuato 37290, Mexico;  
E-Mail: [EMAIL_ADDRESS] (C.L.R.)  
\({}^{3}\) DCS, Instituto Tecnologico de Mexicali, Mexicali, Baja California 21396, Mexico;  
E-Mail: [EMAIL_ADDRESS] (A.D.-R.)  
* Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS];  
Tel.: +34-9-6387-7007; Fax: +34-9-6387-7579.  
Received: 6 March 2013; in revised form: 10 April 2013 / Accepted: 23 May 2013 /  
_Subscribed: 3 June 2013_  
**Abstract:** The use of wireless sensor networks (WSN) in tracking applications is growing at a fast pace. In these applications, the sensor nodes discover, monitor and track an event or target object. A significant number of proposals relating the use of WSNs for target tracking have been published to date. However, they either focus on the tracking algorithm or on the communication protocol, and none of them address the problem integrally. In this paper, a comprehensive proposal for target detection and tracking is discussed. We introduce a tracking algorithm to detect and estimate a target location. Moreover, we introduce a low-overhead routing protocol to be used along with our tracking algorithm. The proposed algorithm has low computational complexity and has been designed considering the use of a mobile sink while generating minimal delay and packet loss. We also discuss the results of the evaluation of the proposed algorithms.  
**Keywords:** wireless sensor network; intruder tracking and detection; mobile sink
# An Empirical Approach for Extreme Behavior Identification through Tweets Using Machine Learning
## 3 Materials and Methods
### Data Collection and Preparation
#### 3.1.3 Feature Extraction  
Sentiment analysis on text usually requires hand written feature derived from word-level (e.g., airstrike, terrorist), word-level \(n\)-gram (e.g., doing_good, good_job), character level \(n\)-gram (e.g., b, be, beh, av, ave beha, behave), POS tags (e.g., noun, adjective, verb), word cluster (e.g., maybe, probably, prob collapse to the same cluster), hashtag (e.g., #Afghanistan, #[PERSON]), emoticon (e.g., \(\copyright\), \(\copyright\)), user tags (e.g., @[PERSON]), abbreviations (e.g., WTH, ASAP, ROFL) and elongated words (e.g., yummy, hurrah). Machine learning algorithm needs a numerical picture in the form of a feature vector that enables the model to perform mathematical and statistical investigation. In feature building phase, text data requires to be converted into a manageable representation that is understandable by the algorithm. For this purpose, a feature vector is constructed (i.e., Term Frequency-Inverse Document Frequency) where weighting scheme is applied in order to calculate the score of each token in the corpus. It is defined as:  
\[\text{Term Frequency (TF)}=\frac{\text{frequency of term t in a tweet}}{\text{total terms in tweets}} \tag{1}\]  
\[\text{Inverse Document Frequency (IDF)}=\frac{\text{total tweets}}{\text{number of tweets having a term t}} \tag{2}\]  
\[\text{TF}-\text{IDF(t,d)}=\text{TF(t,d)}\times\text{IDF(t,d)} \tag{3}\]  
Here, \(t\) represents a term in a tweet and \(d\) represents a tweet (usually termed as document in text documents).
## 3 Results
As reported in Table 2, at optimal cut-off ([PERSON]'s index), RFF (n. estimators = 500, depth = 5) showed the best performance (accuracy 82.4%, precision 83.4%, TPR 96.2%, AUROC 0.82, Figure 1), outperforming LR (accuracy 77.9%, precision 80.1%, TPR 96.2%, AUROC 0.81), and KNN (n. of neighbors = 5) (accuracy 73.6%, precision 76.5%, TPR 96.2%, AUROC 0.67). In Figure 1, ROC curve for RFF (box A), LR (box B) and KNN (box C) models was reported. In Figure 2 calibration diagnostic has been plotted for RFF; PFS roughly happened with an observed relative frequency consistent with the forecast value, showing an acceptable calibration curve. We would expect the match between predicted frequencies and observed frequencies to increase with a larger dataset. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Youden’s Index Cut-Off** & **Accuracy (\%)** & **TPR (\%)** & **Precision (\%)** & **AUROC** \\ \hline LR & 0.77 & 77.9 & 96.2 & 80.1 & 0.81 \\ \hline RFF & 0.62 & 82.4\% & 96.2 & 83.4 & 0.82 \\ \hline KNN & 0.84 & 73.6 & 96.2 & 76.5 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Algorithms Performance. In bold the algorithm with the best performance on 10-fold cross validation. Accuracy, Recall, Precision and AUROC for RFE, were significantly better than other algorithms’ ones.
## 2 Literature Review
### Decision-Making Methods
#### 2.2.4 Combinatorial Distance-Based Assessment  
Proposed by [PERSON] et al. in 2016 [37], it evaluates the desirability of alternatives using Euclidean and taxonomic distances. The primary metric is the Euclidean distance between the alternatives and the negative ideal solution, while the secondary metric is the Taxicab distance. The alternative farthest from the negative ideal solution is deemed the most desirable. The method is implemented as follows:  
1. Definition of the decision matrix \(X=\left[X_{ij}\right]_{nxm}\);
2. Normalization of the decision matrix: \[n_{ij}=\left\{\begin{array}{l}\frac{X_{ij}}{max_{i}X_{ij}}\text{ {\it if }}j\in N_{b};benefit\\ \frac{min_{i}X_{ij}}{X_{ij}}\text{ {\it if }}j\in N_{c};cost\end{array}\right\}\] (26)3. Calculating the weighted normalized decision matrix: \[r_{ij}=w_{j}.n_{ij};\ 0<w_{j}<1;\ \sum_{j=1}^{m}w_{j}=1\] (27) 4. Determine the ideal negative solution (point): \[ns=\left[ns_{j}\right]_{1 xm};ns_{j}=min_{i}r_{ij}\] (28) 5. Calculate the Euclidean and taxicab distances of the alternatives with respect to the negative ideal solution: \[E_{i}=\sqrt{\sum_{j=1}^{m}\left(r_{ij}-ns_{j}\right)^{2}}\] (29) \[T_{i}=\sum_{j=1}^{m}\left|r_{ij}-ns_{j}\right|\] (30) 6. Construct the relative evaluation matrix \(Ra=\left[h_{ik}\right]_{nxm}\): \[h_{ik}=\left(E_{i}-E_{k}\right)+\psi\left(T_{i}-T_{k}\right)\] (31)  
\(\psi\) is a threshold function to recognize the equality of the Euclidean distances of two alternatives:  
\[\psi(x)=\begin{cases}1\ \text{if}\ \left|x\right|\geq\tau\\ 0\ \text{if}\ \left|x\right|<\tau\end{cases} \tag{32}\]  
\(\tau\) is the threshold that can be set by the decision-maker. Its value can be between 0.01 and 0.05; usually \(\tau\) = 0.02 is used.
7. Calculate the evaluation score for each alternative: \[H_{i}=\sum_{k=1}^{n}h_{ik}\] (33) The alternatives are ranked according to the degressive values of Hi.
# Spinning Reserve Capacity Optimization of a Power System When Considering Wind Speed Correlation
## 5 Analysis of Examples
### The Impact of Wind Speed Correlation on Spinning Reserve under Different Wind Power Capacities  
Figure 2a-d shows the up and down spinning reserve capacities with different wind speed correlations, in which the wind power installed capacities are 180 and 360 MW, and the confidence level \(\beta\) is 0.9.  
Figure 2 illustrates that the wind speed correlation has a greater influence on the spinning reserve capacity with the increase of the wind power installed capacity. In particular, the wind power forecast error will increase with time, and the wind output with positive correlation is more fluctuating; therefore, the difference in the spinning reserve capacity between the positive and the negative correlation becomes greater with time. Meanwhile, the up spinning reserve is more easily affected by the wind speed correlation than the down spinning reserve. Therefore, it is necessary to consider the influence of wind speed correlation on spinning reserve in the power system with the large-scale wind power integration.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Spinning Reserve (MW)**} & \multicolumn{8}{c}{**Time/h**} \\ \cline{3-11}  & & **15** & **16** & **17** & **18** & **19** & **20** & **21** & **22** & **23** & **24** \\ \hline \multirow{2}{*}{High correlation} & Up & 248.5 & 244.5 & 216.1 & 242.7 & 219.5 & 235.9 & 223.6 & 263.2 & 243.3 & 204.5 \\  & Down & 173.8 & 162.2 & 165.6 & 137.6 & 185.8 & 137.6 & 128.7 & 170.6 & 151.6 & 111 \\ \hline \multirow{2}{*}{Moderate correlation} & Up & 230.7 & 237.6 & 214.7 & 233.4 & 210.6 & 224.4 & 222.4 & 247.1 & 215.4 & 192.5 \\  & Down & 164.9 & 150.7 & 159.9 & 116.2 & 159.4 & 127.7 & 122.3 & 157.5 & 140.1 & 92.2 \\ \hline \multirow{2}{*}{Low correlation} & Up & 217.5 & 214.7 & 211.7 & 224.7 & 194.9 & 212.9 & 211.3 & 233.5 & 193.8 & 179.9 \\  & Down & 152.9 & 134.8 & 152.7 & 101.9 & 146.3 & 116.7 & 115.1 & 149.2 & 121.9 & 88.7 \\ \hline \multirow{2}{*}{No correlation} & Up & 212.7 & 206.7 & 210.9 & 220.9 & 190.4 & 208.9 & 210.5 & 228.8 & 188.6 & 172.1 \\  & Down & 146.2 & 129.7 & 149.9 & 97.5 & 138.8 & 112.2 & 109.5 & 142.8 & 107.5 & 85.1 \\ \hline \multirow{2}{*}{Negative Correlation} & Up & 201.3 & 196.6 & 209.3 & 213.9 & 181.8 & 197.2 & 201.3 & 219.2 & 178.8 & 166.7 \\  & Down & 134.6 & 118.1 & 145.8 & 86.5 & 117.2 & 110.9 & 98.8 & 137 & 94.2 & 83.88 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of the spinning reserve under different wind speed correlations.
# The Montreal Experience: A Retrospective Study Part I--Basic Principles and Treatment Algorithm
###### Abstract  
CONTEXT: Authors have refined myopia control strategies (MCS) from their experience treating more than 800 children who were followed at the Montreal School of Optometry Clinic (CUV). They developed a treatment algorithm known as the Montreal Experience (ME). Contrary to many other MCS, treatment modalities are selected after careful evaluation of a patient's parameters (rate of progression, age of myopia onset, corneal parameters, pupil area), the risk factors for ocular pathology (growth charts), and taking into account the patient's lifestyle and potential compliance. This represents a customized approach for each patient. PURPOSE: To evaluate the efficacy of MCS used following ME algorithm; the primary outcome relates to axial length progression over 24 months. METHODS: This is a retrospective study, conducted after approval of University IRB. Data were extracted from the file of each patient who: (1) consulted CUV between January 2017 and December 2018 and (2) were kept under the same MCS (same design/concentration). Clinical population is composed of 298 patients (35% Caucasian; 45% Asian; 20% others), with a median age of 11 (range 5-18). The treatment options were orthokeratology (OK-4 designs; \(N=140\)), multifocal soft contact lenses (SMCL; 5 designs; \(N=128\)), and low-dose atropine (LDA 0.01% to 0.25%; \(N=42\)). RESULTS: Results are analyzed through sophisticated statistical models, designed for this purpose. At the end of a stepwise selection process that sequentially removed model terms that were not statistically significant, nine model terms remained: month, modality, the interaction of month and modality, refraction (SEQ), the interaction of SEQ and modality, gender, age, the interaction of age and month, and the interaction of age and modality. A total of 298 files were kept for analysis. Participant age varied from 9.7 to 12.5 years old. Baseline AL varied from 24.9 to 25.3 mm and SE refraction was \(-3.7+1.7\) D on average. This study population was divided between Caucasian (34%), Asian (44%), and other ethnic origins (22%). Overall results indicate that results vary according to modality and months only. There is no statistical difference based on age, gender, and SEQ. All methods used were effective to slow the natural AL growth. Evolution was the lowest when using smaller treatment zones OK lenses (0.249 mm) and the highest (0.376 mm) for those treated with LDA. This OK advantage was statistically significant versus other modalities at 1 and 2 years. CONCLUSION: The Montreal Experience reveals that personalized MCS may be effective to manage myopia efficiently. It shows AL evolution comparable to the documented natural evolution of emmetropes, especially when using customized or smaller treatment zone OK lens design. Future work on other populations will confirm this tendency.  
myopia; control; orthokeratology; soft multifocal lenses +
Footnote †: journal: Medical Imaging
# Performance Evaluation of Reinforced Recycled Aggregate Concrete Columns under Cyclic Loadings
## 3 Parametric Investigation
### Influences of \(f_{y}\) and \(\rho_{\mathrm{s}}\)
The strain compatibility can be assumed between concrete and longitudinal steel reinforcement, leading to:  
\[\varepsilon_{\mathrm{c}}=\varepsilon_{\mathrm{s}}\ \rightarrow\ \frac{\sigma_{\mathrm{c}}}{E_{ \mathrm{c}}}=\frac{\sigma_{\mathrm{s}}}{E_{\mathrm{s}}}\ \rightarrow\ \sigma_{\mathrm{c}}=\frac{E_{\mathrm{c}}}{E_{\mathrm{s}}}\sigma_{\mathrm{s}}= \alpha_{\mathrm{cs}}\sigma_{\mathrm{s}}, \tag{6}\]  
where \(\varepsilon_{\mathrm{c}}\) and \(\varepsilon_{\mathrm{s}}\) are the strain of concrete and longitudinal steel reinforcement, respectively; \(\sigma_{\mathrm{c}}\) and \(\sigma_{\mathrm{s}}\) are the stress of concrete and longitudinal bars, respectively; \(E_{\mathrm{c}}\) and \(E_{\mathrm{s}}\) are the elastic modulus of concrete and steel, respectively; and \(\alpha_{\mathrm{cs}}\) is equal to the ratio of \(E_{\mathrm{c}}/E_{\mathrm{s}}\). A relationship between the axial load ratio and the stress level of longitudinal bars can be obtained:  
\[ \begin{array}{l}n=\frac{N}{J_{\mathrm{cp}}A}=\frac{\sigma_{\mathrm{c}}A_{ \mathrm{c}}+\sigma_{\mathrm{s}}A_{\mathrm{s}}}{J_{\mathrm{cp}}A}=\frac{\pi_{ \mathrm{s}}\alpha\sigma_{\mathrm{s}}(A-A_{\mathrm{s}})+\sigma_{\mathrm{s}}A_{ \mathrm{s}}}{J_{\mathrm{cp}}A}=\frac{\sigma_{\mathrm{s}}[\alpha_{\mathrm{cs}} A+(1-\alpha_{\mathrm{cs}})A_{\mathrm{s}}]}{J_{\mathrm{cp}}A}\\ \sigma_{\mathrm{s}}=\frac{nJ_{\mathrm{cp}}A}{\alpha_{\mathrm{cs}}A+(1-\alpha_{ \mathrm{cs}})A_{\mathrm{s}}}\ \Rightarrow\ \frac{nJ_{\mathrm{cp}}A}{\alpha_{\mathrm{cs}}A+(1-\alpha_{ \mathrm{cs}})\left[\begin{array}{c}A_{\mathrm{s}}\end{array}\right]}=\left[ \begin{array}{c}\sigma_{\mathrm{s}}\downarrow\end{array}\right]\end{array}  \tag{7}\]  
where \(A_{\mathrm{c}}\) and \(A_{\mathrm{s}}\) are the sectional area of concrete and longitudinal bars, respectively; and \(A=A_{\mathrm{c}}+A_{\mathrm{s}}\). It can be seen from Equation (7) that given a certain axial load ratio and strength class of concrete, increasing the steel ratio (\(\rho_{\mathrm{s}}\)) led to a decrease in the stress level of steel reinforcement. Consequently, more stress would be transferred and sustained by the concrete, which accelerated its damage in cyclic loading. The ductility of RRC columns thus decreased with increasing the area ratio of steel reinforcement.
# A Wearable Sonification System to Improve Movement Awareness: A Feasibility Study
## 4 Evaluation of the Wearable Auditory Feedback System  
Four participants took a standing balance test for this pilot study. Standing balance tests were conducted to establish the effectiveness of the wearable system, particularly in evaluating how accurately the IMU unit captures rotation around the x-axis in the sagittal plane and rotation about the z-axis in the frontal plane. The IMU sensor was attached to the sternum of each participant and calibrated, as mentioned in the last section. The sensors were configured with a sampling rate of 10 Hz. The auditory feedback was provided to the participant via headphones through an audio interface that converted the digital signal from the Max software into an analog signal (see Figure 4). The test conditions were as follows:  
* Test 1: the participant stood on one leg with open eyes, and no audio feedback was provided.
* Test 2: the participant stood on one leg with eyes closed, and no audio feedback was provided.
* Test 3: the participant stood on one leg with their open opens, and audio feedback was provided.
* Test 4: the participant stood on one leg with eyes closed, and audio feedback was provided.  
Each test was conducted for 60 s, a timeframe specifically chosen to gather sufficient data for statistical analysis. This approach helps mitigate the impact of noise and potential errors in the data collection process, thereby enhancing the reliability of the experimental results.
# Numerical and Experimental Investigation of Recycled Brick Coarse Aggregate Concrete
## 2 Materials and Methods  
### Materials  
Ordinary concrete consists of cement, coarse aggregate, sand, water, and other materials. The cement used here was 42.5 grade ordinary Portland cement. The sand was local medium sand with a fineness modulus of 2.36, and the average particle size was 0.35-0.5 mm. Coarse aggregate included NCA and RBCA. First, waste red bricks were collected from construction waste sites. Second, the red brick was broken by a small jaw crusher in the laboratory. Finally, the crushed aggregate was screened, cleaned, and dried to obtain RBCA with a 5-20 mm particle size range. The NCA was ordinary gravel with a 5-20 mm particle size range. Table 1 describes the physical properties of the aggregates. Figure 1 shows the RBCA production process, including the collection site of the waste red bricks, the crushing process, and the crushed coarse aggregate with particle sizes of 10-20 mm and 5-10 mm. Compared with natural aggregate, the red brick aggregate is a flake with high water absorption, and micro-cracks can be observed on the aggregate surface.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Raw Material** & **Apparent Density/(kg/m3)** & **Bulk Density/(kg/m3)** & **Water Absorption/\%** & **Crush Value/\%** \\ \hline RBCA & 2190 & 990 & 18.61 & 32.9 \\ NCA & 2769 & 1543 & 1.45 & 14.8 \\ Medium sand & 2689 & 1655 & 0.51 & / \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical properties of aggregate.  
in a standard curing chamber with 95% humidity and a temperature of 20 \(\pm\) 2 \({}^{\circ}\)C for 28 days. The mechanical test was carried out after 28 days of curing time. Figure 3 shows a typical RBCA concrete specimen.
## 6 Conclusions
\begin{tabular}{l l} _GDL_ & Gas diffusion layer \\ _HOR_ & Hydrogen oxidation reaction \\ _MEA_ & Membrane-electrode assembly \\ _MPL_ & Microporous layer \\ _ORR_ & Oxygen reduction reaction \\ _PEM_ & Polymer electrolyte membrane \\ _PDE_ & Partial differential equation \\ Symbols & \\ \(C\) & Total interstitial gas concentration [mol/m\({}^{3}\)] \\ _C\({}_{n,m}\)_ & Water concentration on the surface area of the membrane at the anode side [mol/m\({}^{3}\)] \\ _C\({}_{0,\alpha}\)_ & Water concentration on the surface area of the membrane at the cathode side [mol/m\({}^{3}\)] \\ _D\({}_{i}\)_ & Diffusivity of O\({}_{2}\), H\({}_{2}\), and H\({}_{2}\)O in the gas mixture [m\({}^{2}\)/s] \\ _D\({}_{i,ref}\)_ & Diffusivity of \(i\) at reference conditions [m\({}^{2}\)/s] \\ _D\({}_{d}\)_ & Knudsen diffusion coefficient [m\({}^{2}\)/s] \\ _D\({}_{\lambda}\)_ & Diffusion coefficient of dissolved water [m\({}^{2}\)/s] \\ _D\({}_{w}\)_ & Water diffusion coefficient related to the water activity [m\({}^{2}\)/s] \\ \(F\) & [PERSON]'s constant (96,485 C mol\({}^{-1}\)) \\ _H\({}_{ad}\)_ & Water ab-/desorption enthalpy [/mol] \\ _H\({}_{ac}\)_ & Evaporation/condensation enthalpy [/mol] \\ \(J\) & Flux [A/m\({}^{2}\)] \\ \(L\) & Layer thickness [m] \\ _M\({}_{w}\)_ & Molar mass of water [kg/mol] \\ _M\({}_{md,dry}\)_ & Molar mass of water [kg/mol] \\ _N\({}_{electro}\)_ & The net transport water caused by electro-osmotic drag \\ _N\({}_{diffusion}\)_ & The net transport water caused by back-diffusion [mol/(s-cm\({}^{2}\))] \\ \(P\) & Absolute gas pressure [Pa] \\ _P\({}_{ref}\)_ & Reference pressure (1 atm, 101,325 Pa) \\ _P\({}_{sat}\)_ & Saturation water vapor pressure [Pa] \\ _P\({}_{a}\)_ & Gas pressure in anode gas channel [Pa] \\ _P\({}_{c}\)_ & Gas pressure in cathode gas channel [Pa] \\ \(R\) & Gas constant (8.31446 J/mol K) \\ _RH_ & Relative gas humidity [-] \\ _RH\({}_{a}\)_ & Relative humidity in anode gas channel [-] \\ _RH\({}_{c}\)_ & Relative humidity in cathode gas channel [-] \\ _S\({}_{H2O}\)_ & Source term of hydrogen \\ _S\({}_{O2}\)_ & Source term of oxygen \\ _S\({}_{electron}\)_ & Source term of electrons \\ _S\({}_{proton}\)_ & Source term of protons \\ _S\({}_{matter}\)_ & Source term of water \\ _S\({}_{\lambda}\)_ & Dissolved water reaction rate [mol/m\({}^{3}\)s] \\ _S\({}_{T}\)_ & Heat source [W/m\({}^{3}\)] \\ _S\({}_{ml}\)_ & Reduced liquid water saturation [-] \\ \(T\) & Absolute temperature [K] \\ _T\({}_{ref}\)_ & Reference temperature [K] \\ _T\({}_{st}\)_ & Stack temperature [K] \\ _T\({}_{a}\)_ & Temperature of anode plate and GC [K] \\ _T\({}_{c}\)_ & Temperature of cathode plate and GC [K] \\ U & Open voltage of single fuel cell [V] \\ _V\({}_{W}\)_ & Molar volume of liquid water [m\({}^{3}\)/mol] \\ _V\({}_{m}\)_ & Acid equivalent volume of membrane [m\({}^{3}\)/mol] \\ \(a\) & Active surface area density [1/m] \\ _a\({}_{bg}\)_ & Liquid-gas interfacial area density prefactor [1/m] \\ \(i\) & Electrochemical reaction rate [A/m\({}^{3}\)] \\ _i\({}_{0}\)_ & Exchange current density [A/m\({}^{2}\)] \\ _k\({}_{i}\)_ & Water absorption/desorption transfer coefficient [m/s] \\ \end{tabular}