esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussion
### Comparison of Methods
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **L** & **a** & **b** & **C** \\ \hline \multirow{4}{*}{Average} & \multirow{4}{*}{LBR} & L-A (37.94) \(<\) L-A\({}^{*}\) (40.02) & a-A (36.01) \(>\) a-A\({}^{*}\) (34.03) & b-A (\(-70.23\)) & b-A\({}^{*}\) (\(-70.23\)) & C-A (\(79.16\)) \(>\) C-A\({}^{*}\) (78.31) \\  & & L-M (38.12) \(<\) L-M\({}^{*}\) (40.08) & a-M (36.23) \(>\) a-M\({}^{*}\) (33.92) & b-M (\(-70.01\)) & C-M (\(78.45\)) \(>\) C-M\({}^{*}\) (78.06) \\  & & L-Z (39.45) \(>\) L-Z\({}^{*}\) (38.96) & a-Z (36.45) \(>\) a-Z\({}^{*}\) (33.64) & b-Z (\(-69.45\)) \(=\) b-Z\({}^{*}\) (69.45) & C-Z (\(77.00\)) \(<\) C-Z\({}^{*}\) (77.43) \\ \cline{2-6}  & \multirow{4}{*}{LBP} & L-A (35.40) \(<\) L-A\({}^{*}\) (77.61) & a-A (46.72) \(>\) a-A\({}^{*}\) (43.93) & b-A (\(-78.12\)) \(=\) b-A\({}^{*}\) (\(-78.12\)) & C-A (\(91.21\)) \(>\) C-A\({}^{*}\) (89.79) \\  & & L-M (34.77) \(<\) L-M\({}^{*}\) (37.59) & a-M (47.04) \(>\) a-M\({}^{*}\) (43.90) & b-M (\(-78.10\)) & C-M (\(78.10\)) \(<\) C-M\({}^{*}\) (89.75) \\  & & L-Z (34.00) \(<\) L-Z\({}^{*}\) (36.32) & a-Z (47.52) \(>\) a-Z\({}^{*}\) (43.50) & b-Z (\(-77.56\)) \(=\) b-Z\({}^{*}\) (\(-77.56\)) & C-Z (\(88.44\)) \(<\) C-Z\({}^{*}\) (89.09) \\ \hline \multirow{4}{*}{Standard} & \multirow{4}{*}{LBR} & L-A (5.27) \(<\) L-A\({}^{*}\) (6.58) & a-A (8.89) \(<\) a-A\({}^{*}\) (10.77) & b-A (9.62) \(=\) b-A\({}^{*}\) (9.62) & C-A (12.22) \(<\) C-A\({}^{*}\) (12.93) \\  & & L-M (6.90) \(>\) L-M\({}^{*}\) (6.79) & a-M (9.14) \(<\) a-M\({}^{*}\) (10.75) & b-M (9.70) \(=\) b-M\({}^{*}\) (9.70) & C-M (12.25) \(<\) C-M\({}^{*}\) (12.98) \\ \cline{1-1}  & & L-Z (9.73) \(>\) L-Z\({}^{*}\) (7.67) & a-Z (9.67) \(<\) a-Z\({}^{*}\) (10.69) & b-Z (9.74) \(=\) b-Z\({}^{*}\) (9.74) & C-Z (11.88) \(<\) C-Z\({}^{*}\) (12.99) \\ \cline{1-1} \cline{2-6}  & \multirow{4}{*}{LBP} & L-A (3.40) \(<\) L-A\({}^{*}\) (4.49) & a-A (5.70) \(<\) a-A\({}^{*}\) (7.08) & b-A (3.42) \(=\) b-A\({}^{*}\) (3.42) & C-A (5.47) \(<\) C-A\({}^{*}\) (5.72) \\ \cline{1-1}  & & L-M (4.67) \(>\) L-M\({}^{*}\) (4.57) & a-M (5.88) \(<\) a-M\({}^{*}\) (7.01) & b-M (3.46) \(=\) b-M\({}^{*}\) (3.46) & C-M (5.65) \(<\) C-M\({}^{*}\) (5.67) \\ \cline{1-1}  & & L-Z (7.97) \(>\) L-Z\({}^{*}\) (5.82) & a-Z (6.46) \(<\) a-Z\({}^{*}\) (6.77) & b-Z (4.24) \(=\) b-Z\({}^{*}\) (4.24) & C-Z (6.39) \(>\) C-Z\({}^{*}\) (5.77) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the simulated color parameters for the sapphires.
# Search and Rescue in a Maze-like Environment with Ant and Dijkstra Algorithms
## 3 Search and Rescue in Maze-like Environments  
### Modeling the Problem  
#### 3.1.1 Indoor Search and Rescue Operations: A Maze Exploration Problem  
By the very nature of the intended application domain, the environment for an indoor search-and-rescue operation is (at least partly) unknown. The problem of searching for a victim (locating a specific position in the environment, reaching it and maintaining and updating the path from that position to return to the point of entry) in such an environment is often, and aptly, modeled as a maze-solving problem. The randomness of the maze walls can represent the random placement of obstacles in the area of interest. Therefore, the task  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Reference** & **Cost Function** & **Alg.** \\ \hline ✓ & [93] & Distance, Gas Concentration & **D, ACO** \\  & [96] & Energy & **D** \\  & [97] & Distance & **D** \\ ✓ & [98] & Energy, Difficulty, Distance & **D** \\ ✓ & [99] & Distance & **FD** \\ ✓ & [100] & Distance & **D, ACO** \\ ✓ & [101] & Distance & **D** + others \\ \hline \hline \end{tabular}
\end{table}
Table 2: Research using deterministic and heuristic path-planning strategies; (✓) indicates maze-like environments with obstacles. The used algorithms are **D**ijsktra (**D**), **F**loyd**-**D**ijsktra (**FD**), **Ant** Colony **O**ptimization (**ACO**); _others_ refers to a combination of sweep and savings.  
of maze solving is essentially a path-planning problem in an unknown environment. The main issues associated with maze solving include redundancy in the found path [40; 41; 86], and premature convergence while finding local optima [74; 103]. Several studies have attacked these problems using different path optimization techniques.  
Therefore, we used a collection of mazes with different layouts, sizes and complexities. The mathematical model and a measure capturing the complexity of these mazes are presented in Section 4.1.1.
# Detecting Small Anatomical Structures in 3D Knee MRI Segmentation by Fully Convolutional Networks
## 5 Conclusions  
This work attempted to use annotated knee MRI images by Sunnmore MR-Klinikk to explore two types of encoder-decoder architecture FCNs, including U-net and DeepLabv3 plus. Based on FCN, some neural network variants are proposed, which uses U-net as the basic network, ASPP to capture the multi-scale feature of images, and atrous depthwise separable convolutions to reduce the number of parameters in the encoder. The decoder utilises trilinear interpolation without parameters to implement upsampling instead of deconvolution. This architecture enables us to use a larger patch size and achieves relatively high segmentation accuracies on small structures without the sacrifice of accuracies on large structures. In addition, the training time is significantly reduced from hours to minutes on one epoch.  
For U-net architecture, we use four types of blocks, including residual blocks, residual SE blocks, dense blocks, and dense SE blocks, to replace the standard convolution blocks in the original network. The experiments show that the segmentation accuracies of small structures are improved with SE structures. For DeepLabv3 plus variants, SE structures also help improve the small structure detection and, compared with U-Net, they require fewer parameters, run faster, and perform better in terms of average accuracy. In conclusion, DeepLabv3 plus networks with SE block better capture structural features in MRI segmentation.  
Conceptualization, M.S. and L.L.; methodology, M.S. and L.L.; software, L.L.; validation, M.S.; formal analysis, M.S.; investigation, M.S.; resources, C.P.S.K. and K.-I.G.; data curation, C.P.S.K. and K.-I.G.; writing--original draft preparation, M.S. and L.L.; writing--review and editing, M.S. and I.A.H.; visualization, L.L.; supervision, I.A.H.; project administration, I.A.H.; funding acquisition, I.A.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Norwegian University of Science and Technology.  
Not applicable.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The authors declare no conflict of interest.
# Heat Capacity of Drained Peat Soils
## 2 Materials and Methods
### Specific Heat Capacity Measurements
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Site** & **Site\_JD** & **Soil** & **Thickness** & **Soil Type** & **C** & **N** & **CN** & **AC** & \(\rho_{b}\) & \(\rho_{p}\) & \(P_{o}\) \\
**Coordinates** & **Site\_JD** & **Layer** & **(cm)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline N 53.6306 & Site1 & P1 & 00-15 & Moorsh & 39.00 & 3.30 & 11.82 & 19.24 & 0.3441 & 1.6626 & 0.7930 \\ E 22.7388 & & P2 & 45–50 & Reed & 43.27 & 2.71 & 15.97 & 13.52 & 0.1620 & 1.5997 & 0.8987 \\  & & P3 & 75–80 & Reed & 48.88 & 2.40 & 20.37 & 10.75 & 0.1350 & 1.5693 & 0.9140 \\ \hline N 53.6082 & Site2 & P4 & 00–15 & Moorsh & 42.06 & 2.99 & 14.07 & 19.01 & 0.3397 & 1.6601 & 0.7954 \\ E 22.6349 & & P5 & 45–50 & Reed & 44.63 & 2.83 & 15.77 & 11.58 & 0.1559 & 1.5784 & 0.9012 \\  & & P6 & 75–80 & Reed & 45.04 & 2.11 & 21.35 & 10.95 & 0.1489 & 1.5715 & 0.9052 \\ \hline N 53.6507 & Site3 & P7 & 00–15 & Moorsh & 40.05 & 3.10 & 12.92 & 21.15 & 0.3047 & 1.6837 & 0.8190 \\ E 22.5779 & & P8 & 22–32 & Alder & 43.41 & 3.07 & 14.14 & 13.26 & 0.1944 & 1.5969 & 0.8783 \\  & & P9 & 45–60 & Alder & 42.06 & 3.36 & 12.52 & 14.85 & 0.1894 & 1.6144 & 0.8827 \\  & & P10 & 75–80 & Alder & 40.03 & 2.81 & 14.25 & 17.46 & 0.2204 & 1.6431 & 0.8659 \\ \hline N 53.7007 & Site4 & P11 & 05–15 & Moorsh & 38.95 & 2.63 & 14.81 & 19.78 & 0.1803 & 1.6686 & 0.8919 \\ E 22.6456 & & P12 & 15–30 & Seedge & 41.12 & 2.34 & 17.57 & 16.15 & 0.1785 & 1.6287 & 0.8904 \\  & & P13 & 40–50 & Seedge & 49.50 & 2.92 & 16.95 & 10.60 & 0.1326 & 1.5676 & 0.9154 \\ \hline N 53.7023 & Site5 & P14 & 00–10 & Moorsh & 26.39 & 2.00 & 13.20 & 31.59 & 0.2507 & 1.7985 & 0.8606 \\ E 22.4130 & & P15 & 10–20 & Moorsh & 27.90 & 2.10 & 13.29 & 25.04 & 0.2307 & 1.7264 & 0.8664 \\  & & P16 & 50–60 & Reed & 47.64 & 3.20 & 14.89 & 10.01 & 0.1443 & 1.5611 & 0.9076 \\ \hline N 54.6987 & Site6 & P17 & 0–10 & Moss & 50.56 & 1.10 & 45.96 & 2.00 & 0.0587 & 1.4730 & 0.9601 \\ E 17.5210 & & P18 & 10–20 & Moss & 51.96 & 1.40 & 37.11 & 2.50 & 0.0702 & 1.4785 & 0.9525 \\ \hline  & & Min & 26.39 & 1.10 & 11.82 & 2.00 & 0.0587 & 1.4730 & 0.7930 \\  & & Max & 51.96 & 3.36 & 45.96 & 31.59 & 0.3441 & 1.7985 & 0.9601 \\  & & AVG & 42.36 & 2.58 & 18.16 & 14.97 & 0.1911 & 1.6157 & 0.8832 \\ \hline \hline \end{tabular} C—organic carbon content, N—total nitrogen content, AC—ash content, \(\rho_{b}\)—soil bulk density, \(\rho_{p}\)—particle density, \(P_{o}\)—porosity.  
\end{table} 
Table 1: Sites coordinates and soil basic properties.
# Strength Prediction Model for Cohesive Soil-Rock Mixture with Rock Content
###### Abstract  
Fault fracture zones, characterized by high weathering, low strength, and a high degree of fragmentation, are common adverse geological phenomena encountered in tunneling projects. This paper performed a series of large-scale triaxial compression tests on the cohesive soil-rock mixture (SRM) samples with dimensions of 500 mm \(\times\) 1000 mm to investigate the influence of rock content \(\mathrm{P_{BV}}\) (20, 40, and 60% by volume), rock orientation angle \(\alpha\), and confining pressure on their macro-mechanical properties. Furthermore, a triaxial numerical model, which takes into account \(\mathrm{P_{BV}}\) and \(\alpha\), was constructed by means of \(\mathrm{PFC^{3D}}\) to investigate the evolution of the mechanical properties of the cohesive SRM. The results indicated that (1) the influence of the \(\alpha\) is significant at high confining pressures. For the sample with an \(\alpha\) of 0\({}^{\circ}\), shear failure was inhibited, and the rock blocks tended to break more easily, while the samples with an \(\alpha\) of 30\({}^{\circ}\) and 60\({}^{\circ}\) exhibited fewer fragmentations. (2) \(\mathrm{P_{BV}}\) significantly affected the shear behaviors of the cohesive SRM. The peak deviatoric stress of the sample with an \(\alpha\) of 0\({}^{\circ}\) was minimized at lower \(\mathrm{P_{BV}}\) (<20%), while both the deformation modulus and peak deviatoric stress were larger at high \(\mathrm{P_{BV}}\) (>60%). Based on these findings, an equation correlating shear strength and \(\mathrm{P_{BV}}\) was proposed under consistent \(\alpha\) and matrix strength conditions. This equation effectively predicts the shear strength of the cohesive SRM with different \(\mathrm{P_{BV}}\) values.  
202515843
## 3 Elasto-Plastic Constitutive Model
### Construct of Elasto-Plastic Constitutive Model of UGM  
Based on the plastic increment theory of classical elasto-plastic theory, the elasto-plastic constitutive model of UGM was constructed by the SMP yield function, non-associated flow rule and plastic strain hardening law. Then, the elasto-plastic stiffness matrix shown in Equation (9) is obtained:  
\[D^{ep}_{ijkl}=\left[\begin{array}{cccccc}K+\frac{4}{3}G-m_{11}^{p}&K-\frac{2} {3}G-m_{12}^{p}&K-\frac{2}{3}G-m_{13}^{p}&0&0&0\\ K-\frac{2}{3}G-m_{21}^{p}&K+\frac{4}{3}G-m_{22}^{p}&K-\frac{2}{3}G-m_{23}^{p}&0&0 &0\\ K-\frac{2}{3}G-m_{31}^{p}&K-\frac{2}{3}G-m_{32}^{p}&K+\frac{4}{3}G-m_{33}^{p}&0 &0&0\\ 0&0&0&2G&0&0\\ 0&0&0&0&2G&0\\ 0&0&0&0&0&2G\end{array}\right] \tag{9}\]  
where, \(K\) is the bulk modulus, \(G\) is the shear modulus of elasticity; \(m_{ij}\) is the plastic section. This elasto-plastic matrix includes 15 parameters which are acquired from load-decreasing tests, isobaric tests, and repeated load tests. A user-defined material (UMAT) subroutine was developed for the revised SMP model implemented in the numerical simulation [12; 31; 32]. The flowchart of the UMAT subroutine is shown in Figure 2.  
Figure 2: Flowchart of the UMAT subroutine.
# C1 DR-Net: Channel-Time Dense Residual Network for Detecting Crew Overboard Behavior
## 2 Overview of CTDR-Net  
Our Channel-Time Dense Residual Network (CTDR-Net) can be seen in Figure 1. The process of overboard behavior usually lasts for 2-4 s, and a camera with a frame rate of 25 fps can collect approximately 50-100 frames of images. We use a sparse sampling method with a two-frame interval to extract video frame sequences, which are input into the model for recognition. This method can reduce the number of input images and the computational complexity of the model. We set the size of the model input to \(3\times 32\times 224\times 224\), where 32 represents the input frame sequence. According to the analysis of the duration and characteristics of the overboard behavior, it can be concluded that 32 frames of images can contain more than half of the overboard behavior information.  
When crew members are overboard, they are often obscured, which increases the difficulty of feature extraction. DR-Net is designed to extract features from the input  
Figure 1: Illustration of our CTDR-Net.  
image. It uses \(7\times 7\times 3\) convolution and \(3\times 3\times 3\) maximum pooling to extract the base features and reduce the dimensionality of the input data. DR-Net employs two dense blocks and transition convolutional layers to improve the feature extraction capability and compress the features to reduce the number of parameters. Two residual blocks are adopted to enhance the deep feature extraction capability, which can reduce the risk of network overfitting.  
We introduce the CTAM in the middle of the two residual blocks to filter out the background noise and increase the key feature extraction capability. The fully connected layer combined with softmax activation function is used to realize crew overboard behavior detection. We adopt the LeakyReLU activation function to enhance the robustness and generalization ability of the network and the cross-entropy loss function and back propagation algorithm to optimize the model parameters, which can improve the detection accuracy of crew overboard behavior.
## 3 Methodology
### YOLOv5 Network  
The backbone network, neck network, and detect network are the three main components of YOLO5s framework. These networks included the Focus module, the CBL module, the CSP module, the SPP module, the Concat module, and the Upsample module. Figure 6 depicts the network structure of the YOLO V5s. The YOLO5 network model has a high detection accuracy and a high inference rate, with the fastest detection rate of up to 140 frames per second. The size of the YOLOv5 pre-trained weight is 90% smaller than the size of the YOLOv4 pre-trained weight, indicating that the YOLOv5 model is suitable for deployment to embedded devices for real-time detection. The PyTorch framework is accessible and easy to train the dataset with compared to the Darknet framework used in YOLO V4. Other performance improvement features of YOLO v5 include easy integration of computer vision technologies, quick model training, and easy environment configuration. YOLO5s, YOLO5m, YOLO5l, and YOLOv5x are the four architectures that make up the YOLO5 architecture, respectively. The distinctive features of YOLO5 architectures are the depth multiplier control model and the size of the convolution cores. Both YOLO5s and YOLO5l have depth multiples of 0.33 and 1, respectively. The recognition model had to adhere to strict real-time performance and lightweight requirements because the study's focus was the detection and classification of seven different objects, of which there were three crop types and four weed species. Therefore, after careful examination and analysis of the accuracy, efficiency, and size of the detection model, the weed detection system for precise and real-time laser-based killing in fields was made by using the YOLO5s model [43].
## 2 Materials and Methods
### Description of Gas Analysers
#### 2.1.1 Innova  
The INNOVA 1314 (LumaSense Technologies A/S, Ballerup, Denmark) is a multi-gas analyser based on PAS. The sensing principle is an application of the photoacoustic effect that is a phenomenon that the excitation of gas molecules via absorbing electromagnetic radiation generates acoustic signals, and the amplitude of which is proportional to the gas concentration [16]. INNOVA consists of a broadband infrared lamp and multiple narrowband optic filters mounted on a mechanical chopper wheel. Measurements are performed semi-continuously in three primary steps: (1) filling a built-in measurement chamber with a fixed amount of gas samples, (2) determining the concentration of each target gas in the sample based on PAS, and (3) removing the gas sample from the measurement chamber. Due to partially overlapped spectral absorption wavelength, NH\({}_{3}\) measurements can be strongly affected by water vapour applying the PAS measuring technique [17]. To overcome the issue, INNOVA integrated an algorithm to compensate for this interference. According to the calibration report provided by the manufacturer, measurement bias induced by 2 vol% water vapour concentration was negligible (NH\({}_{3}\) reading contribution <0.06 ppm\({}_{\text{v}}\)).
## 3 Results and Discussion
### Relationship between PAH and Trace Metals Concentrations and Household Characteristics
#### 3.2.1 PAHs  
Compared to residences located in suburban areas, houses in urban areas were found to exhibit significantly higher concentrations of Anthracene (26.2 vs. 16.1 ng/g, \(p\) < 0.05) and other PAHs derived from combustion processes (Flut, Pyr, B[a]A, Chr, B[b]F, B[k]F, B[a]P, Ind \(\kappa\omega\) B[ghi]P), referred to hereafter as COMPAHs, such as B[a]P (8.5 vs. 5.8 ng/g). This is in agreement with the literature, as it has been reported that proximity to combustion sources such as vehicle exhaust emissions is probably the most important factor affecting the accumulation of PAHs in indoor dust [2; 7; 35]. The age of the house was found to affect both the Pyr (75 vs. 114 ng/g, \(p\) < 0.05) and all the B2 PAH (87 vs. 140 ng/g, \(p\) < 0.05) concentrations, with the houses that have been built in the last 20 years presenting lower concentrations than the older ones. Houses on the ground floor presented higher concentrations of Flut, B[a]A, Chr, B[b]F, Ind, D[ah]A (\(p\) < 0.05), which are known to originate from combustion processes.  
Both the B2 PAH and COMPAH concentrations were considerably higher in the houses with an attached garage. Especially for BaP a significant difference was noticed (13.6 vs. 6.2 ng/g, \(p\) < 0.05). The existence of a metro or tram station nearby (\(<\) 200 m) was associated with increased concentrations of COMPAHs (479 vs. 217 ng/g, \(p\) < 0.05), especially those of B[a]A, B[a]P, Ind and D[ah ]A. This is probably due to the heavy traffic and the parking stations that are located close to such stations. The presence of a carpet in the house was associated with increased concentrations of Nap (1319 vs. 209 ng/g, \(p\) < 0.05), while the habit of residents wearing shoes inside their home was associated with higher concentrations of COMPAHs (475 vs. 221 ng/g, \(p\) < 0.05), as well as B2 PAHs (191 vs. 73 ng/g), especially those of B[a]P, Pyr, Chr, D[ah]A and B[ghi].
## 5 The Proposed Protocol
### Communication Overhead of the Proposed Protocol
\[E_{RSNs}(NL_{C},d)=E_{elec}\times NL_{C}. \tag{45}\]  
Consequently, the energy dissipated for the disjoin message is calculated as follows:  
\[E_{disjoin}=C\times E_{TCHs}+N\times E_{TCHs}+N\times E_{RSNs}. \tag{46}\]  
Thus, the energy dissipated in the steady-state phase (\(E_{Steady}\)) is as follows:  
\[E_{Steady}=(N-C)\times E_{TSNs}+E_{CHs}+E_{disjoint}. \tag{47}\]  
Consequently, the total energy dissipation each round, which includes the setup and steady-state phases, can be determined using Equations (35) and (45):  
\[E_{Round}=E_{Setup}+E_{Steady}. \tag{48}\]  
Dealing with Data Fusion Impairments: More Optimized Data Fusion Techniques Including Building Occlusion Management, Devices/Links Failures and Recovery, Device Deployment Redundancy, Redundant Coverage, and Data Redundancy  
In addition to being used and improved for energy dissipation and communication effectiveness, data fusion grouping approaches in the IoT may also be used to deal with concerns regarding building occlusion, device/link failures, and data redundancy. These factors are essential for networks to continue operating with stability and reliability. The use of self-healing mechanisms in the proposed protocol is noteworthy. These mechanisms relate to the system's capacity to autonomously identify, diagnose, and fix malfunctions without the need for human interaction. In fact, in large-scale or remote IoT deployments, where manual intervention is difficult and expensive, self-healing methods are very helpful. The network initiates repair procedures and may even need to reorganize its structure to accommodate the modifications when the proposed protocol automatically identifies possible failures and evaluates the data to determine the root cause of the problem. The next subsections will have more detail.
## 3 Results
### Adsorption in an Anthracite-Sand Filter with PAC  
The adsorption of organic substances present in the water fed into the filter with PAC proceeded at different rates, depending on sorbent doses and flow rates. Changes in absorbance A over time for PAC doses of 1, 2, 3 and 4 g and flows of 0.8, 1.0, 1.5 and 2.2 mL/s are shown in Figures 7-10. The solid line in these Figures represents the calculation results obtained using model (2), (3), (4). The adsorption capacity of PAC, at a dose of 1 g, becomes exhausted much faster than at higher doses. If the absorbance \(A_{0}\) in the feed is higher at a higher PAC dose than at a lower one, then the curves intersect (Figure 8, doses: 3, 4 g) or the curve for a 4 g dose lies above the curve for a 3 g dose (Figure 9). Figure 5: Model (9) fit—theoretical _Pe_ vs. measured _Pe_ as an apparent sorbent density function \(\rho_{p,sorb}\). Figure 6: Model (9) fit—theoretical _Pe_ vs. measured _Pe_. Figure 7: Fitting the adsorption model (solid line) to test results (points) for different PAC doses at \(Q=0.8\) mL/s. Figure 8: Fitting the adsorption model (solid line) to test results (points) for different PAC doses at \(Q=1.0\) mL/s. Figure 10: Fitting the adsorption model (solid line) to test results (points) for different PAC doses at \(Q=2.2\) mL/s. Figure 9: Fitting the adsorption model (solid line) to test results (points) for different PAC doses at \(Q=1.5\) mL/s. Data for the adsorption models (2), (3) and (4) and the calculated model parameters are summarized in Table 2.  
The experimental results made it possible to establish a relationship between the diffusive Nusselt number (\(Nu\)) (equivalent to the Sherwood number \(Sh\)), the \(Re\) number and the apparent sorbent density (\(\rho_{p,sorb}\)) as:  
\[Nu=0.1587\cdot\text{Re}^{0.6244}\cdot\left(\frac{\rho_{p,sorb}}{\rho_{0,p,sorb }}\right)^{1.8370} \tag{13}\]  
\[Nu=\frac{\frac{k\cdot a_{m}}{c}\cdot\rho_{p,sorb}\cdot\left(d_{50}\right)^{2}} {D_{m}} \tag{14}\]  
\[\text{Re}=\frac{\frac{V_{x}}{c}\cdot 4\cdot R_{h}}{v_{w}}=\frac{V_{x}^{*} \cdot 4\cdot R_{h}}{v_{w}} \tag{15}\]  
Figure 6:0  
Figure 6:1  
where:  
\(k\)--mass transfer rate constant across a water-sorbent interface (m/s);  
\(a_{m}\)--specific outer surface of sorbent particles (m\({}^{2}\)/g PAC);