esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Performance Analysis  
In this section, we analyze the BER performance of the RIS-assisted SHTLC system. From [31], we can obtain the average BER of the DF relay system as  
\[P_{BER}=P_{s-p}+P_{p-t}-2P_{s-p}P_{p-t} \tag{14}\]  
where \(P_{s-p}\) and \(P_{p-t}\) denote the BER of the satellite-to-HAP link and the HAP-to-terrestrial link, respectively [32]. \[P_{s-p}=\frac{q^{p}}{2\Gamma(p)}\int_{0}^{\infty}\exp(-q\gamma)\gamma^{p-1}F_ {s-p}(\gamma)d\gamma \tag{15}\]\[P_{p-t}=\frac{q^{p}}{2\Gamma(p)}\int_{0}^{\infty}\exp(-q\gamma)\gamma^{p-1}F_{p-t} (\gamma)d\gamma, \tag{16}\]  
where \(p\), \(q\) are the modulation parameters for different modulation methods. For example, \(p=0.5\) and \(q=0.5\) is CBFSK; \(p=0.5\) and \(q=1\) is CBPSK; \(p=1\) and \(q=0.5\) is NBFSK; and \(p=1\) and \(q=1\) is DBPSK. The BER of the satellite-to-HAP link is obtained as follows by transforming the exponential function in Equation (15) into the Meijer G-function and substituting it into Equation (9):  
\[P_{s-p}=\frac{p^{q}\Gamma}{4\Gamma(p)}\sum_{k=0}^{N_{E}(\beta-1)}c_{k}\overline {\gamma}^{-\frac{N_{E}+N_{E}+k}{4}}\int_{0}^{\infty}\gamma^{\frac{N_{E}+N_{E}+ k}{4}}+p-1G_{0,1}^{1,0}\left[q\gamma\left| \begin{matrix}-\\ 0\end{matrix} \right.\right]G_{1,3}^{2,1}\left[\frac{N_{E}\sqrt{\gamma/ \gamma_{\overline{\gamma}}}}{B}\left| \begin{matrix}\Delta_{1}\\ \Delta_{2}\end{matrix} \right.\right]d\gamma \tag{17}\]  
Using the integral property of the Meijer G-function, the closed expression for the BER of the satellite-to-HAP link is obtained as  
\[P_{s-p}=\frac{C}{16\pi\Gamma(p)}\sum_{k=0}^{N_{E}(\beta-1)}c_{k}(q\overline{ \gamma})^{-\frac{N_{E}+N_{E}+k}{4}}G_{3,6}^{4,3}\left[\frac{N_{E}^{2}}{16B^{2 }q\overline{\gamma}}\left| \begin{matrix}\Delta_{3}\\ \Delta_{4}\end{matrix} \right.\right] \tag{18}\]  
where \(\Delta_{3}=\frac{1}{2}-\frac{N_{E}a+N_{E}+k}{4},1-\frac{N_{E}a+N_{E}+k}{4},1- p-\frac{N_{E}a+N_{E}+k}{4}\), and \(\Delta_{4}=\frac{N_{E}a-N_{E}-k}{4},\frac{1}{2}+\frac{N_{E}a-N_{E}-k}{4},\frac {k+N_{E}-N_{E}a}{4},\frac{1}{2}+\frac{k+N_{E}-N_{E}a}{4},-\frac{N_{E}a+N_{E}+k }{4},\frac{1}{2}-\frac{N_{E}a+N_{E}+k}{4}\). The Gauss-Laguerre quadrature formula [33] can be used to transform Equation (16) into  
\[ \begin{array}{rl}P_{p-t}&=\frac{q^{p}}{4\Gamma(p)}\int_{0}^{\infty}\gamma^{ -\frac{1}{2}}\exp(-\gamma)\exp(\gamma-\gamma q)\gamma^{p-\frac{1}{2}}\left[ \[PERSON]\left(\frac{\gamma-N_{E}\mu\overline{\gamma}}{\sqrt{2N_{E}\mu^{\prime}}} \right)-\[PERSON]\left(\frac{-N_{E}\mu}{\sqrt{2N_{E}\mu^{\prime}}}\right)\right]d \gamma\\ &=\sum\limits_{m=1}^{n}H_{m}g(a_{m})\\ \\ & g(a_{m})=\frac{q^{p}}{4\Gamma(p)}e^{a_{m}-qa_{m}}a_{m}{}^{p-0.5} \left[\[PERSON]\left(\frac{a_{m}-N_{r}\mu\overline{\gamma}}{\sqrt{2N_{r}}\overline{ \gamma}\sigma}\right)-\[PERSON]\left(\frac{-N_{r}\mu}{\sqrt{2N_{r}}\sigma}\right) \right]\\ \\ & H_{m}=\frac{\Gamma(n+1/2)a_{m}}{n!(n+1)^{2}\left[L_{n}^{-0.5}(a_{m}) \right]^{2}}\end{array}  \tag{19}\]  
where \(a_{m}\) is the m-th root of the generalized Laguerre polynomial \(L_{n}^{-0.5}(x)\). Finally, the closed expression of the BER for the RIS-SHTLC system is obtained by bringing Equations (18) and (19) into Equation (14). \[
## 4 Recent Advancements in Applications
### Precision Agriculture  
MMSs are highly useful for monitoring and maintaining agricultural production. Data collected by MMSs can be analyzed to address a variety of applications, including harvest estimation [121], yield mapping and monitoring [122], crop classification [123], irrigation planning and monitoring [124], water stress monitoring [125], and pest detection [120]. In precision agriculture applications, similar to NRM, UAVs are often the most favorable platform. This is because an orthogonal (nadir) view is typically the best direction to collect detailed and comprehensive information from a higher perspective, enabling more accurate and efficient data analysis for improved agricultural management. The integration of MMSs and UAVs enhances the ability to monitor crops, optimize resource use, and support sustainable farming practices.
# The Development of Teleoperated Driving to Cooperate with the Autonomous Driving Experience
## 3 Designs and Developments
### Overall Designs
ROS tools enable real-time latency monitoring. If the measured delay surpasses safety thresholds, the fallback controller overrides teleoperation inputs and initiates automated braking via a dedicated actuator. All components are synchronized through ROS nodes and topics across the communication channel. ROS and Autoware System Architecture  
This study implements a dual-mode driving platform capable of switching between autonomous and teleoperated control. The system architecture is built on the Robot Operating System (ROS) framework, with core autonomous functionalities handled by Autoware modules, such as localization, perception, planning, and control. In parallel, a 5G-based teleoperation channel enables remote intervention. Real-time network latency is continuously monitored, and when communication delay exceeds predefined thresholds, a fallback mechanism engages autonomous braking to maintain safety. Figure 2: System architecture of autonomous driving and 5G teleoperation components. Figure 3 shows the ROS/Autoware system-level architecture used in the prototype. The architecture integrates sensor data acquisition (e.g., LiDAR, camera), localization, path planning, and control nodes. A custom teleoperation module handles remote command reception, while a fallback controller ensures safe maneuvering under degraded network conditions. Communication across modules is managed via ROS topics and services.
## 2 Methods
### Trajectory Clustering
#### 2.2.3 Parameter Determination  
In the incremental DBSCAN algorithm, there are three important parameters that need to be set: Eps, MinPts, and TWW. Eps is the distance threshold of similar trajectories, MinPts is the minimum number of trajectories to form clusters, and TWW is the time window width used to maintain the cluster state. The setting method of the three parameters is outlined below.  
1. Setting of Eps The trajectory distance can be obtained by Equation (3). When \(D^{*}(A,B)<\)Eps, the two trajectories are similar. Due to the large volume trajectory data and usual navigation on customary routes, a small Eps setting does not affect the formation of trajectory patterns. On the contrary, if the Eps is set too large, some trajectories that do not belong to one cluster will be merged into one. Eps was set to 0.1 in this paper; that is, 90% of the short trajectory points could find the nearest point on the long trajectory and they could group into a cluster. Through experiments, 0.1 was an appropriate setting value and could distinguish the trajectory pattern as far as possible and allowed for the existence of some noise points.
2. Setting of MinPts and TWW  
Figure 6: Continuous trajectories stream using sliding window model. Each cell represents a trajectory. The gray cells are the expired trajectories that have been removed from the cluster. The green cells are the removed trajectories that will be removed from the current cluster. The blue cells are the processing trajectories that have been absorbed to the current cluster. The yellow cell are the inserted trajectories that will be absorbed to the current cluster. The width of the sliding window represents the length of time. Trajectories within the sliding window are the dataset to generate the current cluster.  
There is interaction between MinPts and TWW. If MinPts is set too small, many debris trajectories are generated, and a stable maritime traffic pattern would not be formed. If MinPts is set too large, it increases the time for maritime traffic pattern formation. Therefore, the setting of MinPts should be the minimum TWW. The number of clusters could reach a relatively stable state. MinPts was determined by setting different MinPts and looking at the change in the number of clusters when TWW was infinite. Subsequently, the MinPts setting that made the number of clusters stable at the earliest time, and the length of time to reach this stable state, were selected as the setting of TWW.
## 4 Results and Discussion
### The Results of the Numerical Analysis  
The results of the numerical tests are presented in Figures 10 and 11.  
The numerical analysis shows that the maximum equivalent stresses at a temperature of \(-20\)\({}^{\circ}\)C (1.8879 MPa) are about 30% higher than those at a temperature of \(20\)\({}^{\circ}\)C (1.3135 MPa). This is due to the known effect of the reduced the elasticity of materials (increasing stiffness) at lower temperatures.  
Moreover, we have shown that the failure of a cuff in a vehicle could be expected at almost the same point where it was experimentally proven, because the maximal equivalent von Mises stress appears there. The maximal equivalent stresses are, however, smaller than the boundary of the breakage of test material. The failure, namely the breakage of a cuff, is a consequence of material fatigue due to a large number of oscillations, as well as the impact of various (ambient) temperatures during the oscillations of a cuff. Therefore, it is important to know the appropriate fatigue damage parameters of the material, as the effective prediction of fatigue life at different temperatures is of great significance for the timely replacement of cuffs and extension of the service life of them.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \begin{tabular}{c} **Sample** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Vehicle** \\ **Brand** \\ \end{tabular} & \begin{tabular}{c} **Region of** \\ **Use** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Kilometers** \\ \end{tabular} & \begin{tabular}{c} **Testing** \\ **Temperature** [\({}^{\circ}\)C] \\ \end{tabular} & \
\begin{tabular}{c} **Temperature at** \\ **the Moment of** \\ **Failure** [\({}^{\circ}\)C] \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Oscillations to** \\ **the Failure** \\ \end{tabular} \\ \hline
9 & Volkswagen & north & 298,545 & \((-14.1)\div(-15.1)\) & \(-14.1\) & 1,554,906 \\
10 & Volkswagen & north & 320,148 & \((-4.1)\div(-13.7)\) & \(-13.7\) & 1,822,630 \\
11 & Volkswagen & north & 332,874 & \((-10.1)\div(-14.3)\) & \(-14.3\) & 1,795,112 \\
12 & Renault & north & 274,121 & \((-4.1)\div(-12.4)\) & \(-12.4\) & 1,981,989 \\
13 & Renault & south & 298,745 & \((-10.1)\div(-18.9)\) & \(-13.3\) & 4,427,388 \\
14 & Volkswagen & south & 334,584 & \((-12.7)\div(-18.4)\) & \(-18.4\) & 3,541,361 \\
15 & Ford & south & 225,121 & \((-10.2)\div(-20.5)\) & \(-20.1\) & 4,745,626 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The results of testing cuffs at temperatures from \(-4\)\({}^{\circ}\)C to \(-20\)\({}^{\circ}\)C.  
Figure 11: _Cont._  
Figure 10: Equivalent von Mises stresses in longitudinal cross-section of a cuff (isometric view) at different temperatures: (**a**) at \(-20\)\({}^{\circ}\)C; (**b**) at \(20\)\({}^{\circ}\)C.
## 4 QoS Controller Implementation
### Operational Modes
* _Autonomous mode:_ Finally, the proposed QoS controller can also work in an autonomous mode, which seeks the best trade-off between latency and hitrate for each subscriber (Figure 6c). The controller works according to two hitrate thresholds, \(\hat{\mathcal{H}}_{low}\) and \(\hat{\mathcal{H}}_{high}\) and one latency threshold \(\hat{\mathcal{L}}\). At startup, the subscribers' QoS is set to 0: if the observed hitrate is lower than \(\hat{\mathcal{H}}_{low}\), the controller increases the QoS to QoS 1. At this point, a new hitrate and latency estimation is performed: if the new hitrate has not exceeded \(\hat{\mathcal{H}}_{high}\) and the estimated latency is still below the threshold (suggesting good network conditions), the controller increases the QoS to QoS 2. Otherwise, if \(\mathcal{H}>\hat{\mathcal{H}}_{high}\) and the latency is above the threshold, the controller sets the QoS back to QoS 0. Similarly, the QoS level is downgraded from QoS 2 to QoS 1 if \(\mathcal{L}>\hat{\mathcal{L}}\). Note that depending on the network conditions and on the values given to the three thresholds used, there could exists loops between two adjacent QoS states. To avoid such issue, the controller tracks the QoS node of each subscriber and forces it to QoS 1 if loops are detected.
# Computer Simulations of Dual-Antenna Microwave Ablation and Comparison to Experimental Measurements
## 3 Results
### Influences of Blood Perfusion on MWA Results  
In clinical procedures, the perfusion of liver tumors varies depending on the location and size of their growth [38]. In order to improve the clinical applicability of the dual-antenna MWA simulation model, the effects of different blood perfusion rates on temperature distribution and coagulation zone were systematically simulated and analyzed. These data were obtained by changing the value of \(\omega_{\text{b}}\) in the MWA model. The results showed that as perfusion increased, the temperature and the coagulation volume decreased. As shown in Figure 6, in the early stages of the ablation procedure, there was a subtle difference in the temperature increase of the liver tissue. However, as the time increased until the end of ablation treatment, the temperature differences were significant. Compared to the case without perfusion, the temperature drop of P1 at 480 s was approximately 5.87 \({}^{\circ}\)C, 8.26 \({}^{\circ}\)C, and 14.75 \({}^{\circ}\)C for \(\omega_{\text{b}}=1.0\) kg/(m\({}^{3}\cdot\)s), \(\omega_{\text{b}}=1.5\) kg/(m\({}^{3}\cdot\)s), and \(\omega_{\text{b}}=3.0\) kg/(m\({}^{3}\cdot\)s), respectively.  
According to Table 5, the volume of the coagulation zone was reduced by 18.4%, 25.4%, and 42.5% for \(\omega_{\text{b}}=1.0\) kg/(m\({}^{3}\cdot\)s), \(\omega_{\text{b}}=1.5\) kg/(m\({}^{3}\cdot\)s), and \(\omega_{\text{b}}=3.0\) kg/(m\({}^{3}\cdot\)s), respectively. Therefore, if the effects of blood perfusion are not considered, the predicted coagulation zone volume will inevitably be larger than the actual one.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Spacing** & **40 W** & **50 W** & **60 W** \\ \hline
20 mm & 70 & 34 & 28 \\
30 mm & 110 & 90 & 80 \\
40 mm & 240 & 210 & 190 \\ \hline \end{tabular}
\end{table}
Table 4: Time for the coagulation zone fusion under different heating parameters (in seconds).
## 6 Discussion
### Geothermometry  
Different thermometer methods can be used to deduce the temperature of equilibrium of the examined serpentinized ultramafics (Supplementary Materials, Table S10). These methods include olivine-spinel thermometry using the calibrations described in [76; 77], as well as Al in orthopyroxene-olivine-spinel thermometry [75]. The obtained average temperature of the studied serpentinized peridotites using the olivine-spinel thermometry [77] method was 781 \({}^{\circ}\)C, which is lower than the average temperature (852 \({}^{\circ}\)C) calculated using the calibration described in [76]. On the other hand, the average temperatures of the studied serpentinized peridotites calculated using the calibrations described in [75] (Al content in the orthopyroxene) was 859 \({}^{\circ}\)C, similar to the estimated average in [76]. In comparison with Pan-African forearc periodtites using the calibration described in [77], the estimated average temperature of the studied serpentinized peridotites (781 \({}^{\circ}\)C) is very similar to those found in Um Khariga (778 \({}^{\circ}\)C) [78]. In addition, the average temperature of the examined rocks obtained using Al in orthopyroxene thermometry (859 \({}^{\circ}\)C) is close to the average of Um Khariga peridotites (984 \({}^{\circ}\)C) using the same calibration.  
Figure 10: (**a**) Al\({}_{2}\)O\({}_{3}\)/SiO\({}_{2}\) vs. MgO/SiO\({}_{2}\) in the studied ultramafic samples. Abyssal peridotite, primitive mantle, and depleted mantle are from [44; 46; 67], respectively. Mariana forearc and forearc are from [44; 61], respectively. The thick yellow line represents a terrestrial array [71]. (**b**) Zr vs. Nb diagram from [68]; (**c**) Mg# versus Cr# binary diagram from [1]; partial melting degree is from [72]. (**d**) 100 Cr# vs. TiO\({}_{2}\) of the examined spinels (Cr- and Al-spinel). Boninites, MORB, forearc peridotites, and depleted and highly depleted peridotites are obtained from [28; 73; 74; 75], respectively. The pink field represents fresh Cr-spinels of the Egyptian Eastern Desert [22].
## 3 Results
### Efficiency of Categorizations by AI Using Different Sets of Information--A Comparative Analysis  
The accuracy of categorizations based on different sets of information is summarized in Table 15.  
The best categorization by OSA severity was achieved using BMI, gender, age, neck circumference and data from the Berlin and Epworth questionnaires (71%). The second most efficient prediction was based on BMI, gender, age and applying the Berlin and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Categorization Based on:** & **Correct Categorization** & **Non-OSA Prediction** & **OSA Prediction** \\ \hline BMI, age and gender & 81\% & 80.55\% & 81.25\% \\ \hline Berlin questionnaire & 62\% & 19.44\% & 85.93\% \\ \hline Epworth questionnaire & 75\% & 58.33\% & 84.37\% \\ \hline BMI, age, gender and data from the Berlin and & 83\% & 77.77\% & 85.93\% \\ \hline \hline \end{tabular}
\end{table}
Table 14: Accuracy of categorisation tests based on different information sets. OSA: obstructive sleep apnoea; BMI: body mass index.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Categorization Based on:** & **Correct Categorization** & **Non-OSA Prediction** & **Mild OSA Prediction** & **Moderately** \\  & & & & **OSA Prediction** \\ \hline BMI, age and gender & 64\% & 75\% & 56.25\% & 59.37\% \\ \hline Berlin questionnaire & 61\% & 72.22\% & 50\% & 59.37\% \\ \hline Epworth questionnaire & 56\% & 52.77\% & 96.87\% & 18.75\% \\ \hline Berlin and & 63\% & 80\% & 53\% & 53.12\% \\ \hline BMI, age, gender, and Berlin & 69\% & 80.55\% & 59.37\% & 65.62\% \\ \hline BMI, age, gender, Berlin and & & & & \\ Epworth questionnaire and & 71\% & 80.55\% & 65.62\% & 65.62\% \\ \hline neck circumference & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 15: Summary table of accuracy of categorisations based on different sets of information. OSA: obstructive sleep apnoea; BMI: body mass index.  
Epworth questionnaires (69%), followed by prediction based on BMI, gender, and age (64%). The least efficient categorization by severity of OSA was based on questionnaires alone. Surprisingly, the best predictor of mild OSA was the Epworth questionnaire (96.87%), followed by BMI, gender, age, data from the Berlin and Epworth questionnaires, and neck circumference (65.62%). The questionnaires alone and in combination gave an efficiency of less than 60% for predicting mild OSA. For the prediction of moderate-severe OSA, BMI, gender, age and data from the Berlin and Epworth questionnaires with or without neck circumference gave the same results. The least reliable result for predicting moderate-severe OSA was obtained with the Epworth questionnaire alone (18.75%).
## 2 Fundamentals
### Optimisation Approaches for Nozzle Systems  
The challenges of optimising a nozzle system to achieve optimal heat transfer by forced convection have already been described by [PERSON] [6]. [PERSON] [7] and [PERSON] [8] recommend the following three lengths as a basis for the nozzle design:  
* Hydraulic diameter of the nozzle \(D_{hyd}\);
* Nozzle-to-strip distance, nozzle height \(H\);
* Nozzle-to-nozzle distance, nozzle pitch \(s\).  
All three parameters are strongly interrelated. To optimise the nozzle system, it is essential to keep one of the three parameters constant and adapt it to the boundary conditions of the technical specifications. Otherwise, reducing all parameters would lead  
Figure 2: Flow conditions in the impingement jet.  
to an increase in forced convective heat transfer due to the increasingly shorter flow path of the fluid. In case of a constant nozzle height, the following estimates result for the remaining two parameters:  
\[D_{hyd,opt}\approx\frac{1}{5}\cdot H \tag{3}\]  
\[s_{opt}\approx\frac{7}{5}\cdot H \tag{4}\]  
For round nozzles, the nozzle diameter is equal to the hydraulic diameter. In case of slot nozzles, where the slot length is significantly greater than the slot width \(W\), the hydraulic diameter is calculated using \(D_{hyd}=2\ W\). When optimising the nozzle opening area and nozzle pitch, the relative opening area \(A_{rel}\) is used to enable comparisons between different systems. The relative opening area describes the ratio of the absolute nozzle opening area \(A_{nozzle}\) to the area of the nozzle body \(A_{total}\). The optimum values for the area of relative nozzle opening are the analytically determined suggested values [7].  
\[\text{Round nozzle field}:\ A_{rel,opt}\approx 1.52\% \tag{5}\]  
\[\text{Slot nozzle field}:\ A_{rel,opt}\approx 7.18\% \tag{6}\]  
In addition to optimising for a defined heat transfer coefficient, it is also necessary to consider the effectiveness of the overall system. The area-related fluid power \(P_{f}^{\prime\prime}\) is used for this purpose. It is defined according to Equation (7):  
\[P_{f}^{\prime\prime}=\Delta p\cdot C_{c}\cdot u\cdot A_{rel} \tag{7}\]  
with  
\(\Delta p\)  
as the nozzle outlet pressure related to atmospheric pressure in Pa;  
\(C_{c}\)  
as the contraction coefficient;  
\(u\)  
as the flow velocity in m/s.  
The contraction coefficient is calculated by dividing the contracted nozzle cross-section by the nozzle opening area. It is important to examine the coefficient for each specific nozzle in advance. The equations used to evaluate the effectiveness and efficiency of a nozzle system demonstrate that accurate temperature and pressure measurements, as well as a precise investigation of the flow conditions, are necessary for a holistic analysis.
## 2 Materials and Methods
### Jet-Cleaning 3D CFD Modeling
#### 2.1.2 Performance Index for Jet-Cleaning Models  
There are three main performance index parameters in the jet cleaning model [29], namely the peak wall shear stress \(\tau_{\text{max}}\), action area \(A_{\text{eff}}\), and cleaning water consumption \(Q_{\text{total}}\). The peak wall shear stress \(\tau_{\text{max}}\) is the maximum tangential stress generated when the jet impacts the wall, and it directly determines the stripping ability of the jet on the sediment and other dirt. In the numerical model, \(\tau_{\text{max}}\) reflects the comprehensive effect between jet energy, turbulence intensity, and boundary layer interaction, which is the key mechanical parameter to evaluate the efficiency of jet cleaning, and the specific calculation Formula (1) is shown as follows.  
\[\tau_{\text{max}}=\mu\left(\frac{\partial u}{\partial y}\right)_{\text{wall}} \tag{1}\]  
where \(\mu\) is the fluid viscosity, and \(u\) is the fluid velocity.  
The action area \(A_{\text{eff}}\) refers to the effective area where the shear stress \(\tau\) exceeds the critical stripping threshold \(\tau_{0}\) of sediment and other dirt in a single jet operation, which directly reflects the size of the cleaning range of the aerated jet [29]. The calculation Formula (2) is shown as follows.  
\[A_{\text{eff}}=\iint_{\Omega}H(\tau-\tau_{0})dA \tag{2}\]  
where \(\text{H}(\tau-\tau_{0})\) is the Heaviside step function expressed as follows:  
\[\begin{cases}\text{H}(\tau-\tau_{0})=1,\;\tau\geq\tau_{0}\\ \text{H}(\tau-\tau_{0})=0,\tau<\tau_{0}\end{cases} \tag{3}\]  
Water consumption \(Q_{\text{total}}\) is the amount of water consumed per unit of time, which directly reflects whether aerated jet cleaning is water efficient. In the numerical model, \(Q_{\text{total}}\) is obtained by integrating the jet outlet flow with the effective cleaning time.  
\[Q_{\text{total}}=v_{\text{j}}\cdot A_{\text{j}}=v_{\text{j}}\cdot\frac{\pi d_ {\text{j}}^{2}}{4} \tag{4}\]  
where \(A_{j}\) is the nozzle outlet cross-sectional area and \(d_{j}\) is the nozzle inlet diameter.  
The Formulas (1)-(4) described above are all reflected in the jet cleaning numerical model, i.e., the relevant evaluation indexes can be directly obtained through the jet cleaning model to facilitate the subsequent workflow requirements.