esa-sceva/satcom-chunk-collection huggingface dataset:
# Protection of Buried Pipelines from High-Speed Train Vibrations with Expanded Polystyrene Geofoam
## 4 Discussion  
In the present work, a cost-efficient mitigation measure utilizing EPS backfill for buried pipelines subjected to vibrations induced by HST passage has been examined. This problem was investigated by performing a numerical parametric study utilizing ABAQUS finite-element software. Regarding pipe response, the numerical model was partially validated with available experimental data regarding the use of EPS for buried pipe protection under traffic loads [19; 23] due to a lack of available data for train moving loads. Nonetheless, the employed numerical methodology has been extensively validated in some authors' previous studies (e.g., [13; 26]) with in situ measurements of HST passage without the presence of pipelines.  
Low-density EPS19 was used as a backfill material above the pipe. Furthermore, the impact of the pipe material and geometry on its deformations and the diameter change has been investigated by comparing steel and polyethylene pipelines with varying dimensions. The implementation of this low-density backfill has contributed to reducing the vibrations level on the top of both steel and, especially, polyethylene pipelines. In order to examine the efficiency of the examined mitigation measure, the passage of Thalys HST with three  
Figure 17: (**a**) Vertical and (**b**) horizontal diameter change for a steel pipe with \(D=250\) mm for thickness equal to 3 mm; and (**c**) vertical and (**d**) horizontal diameter change for thickness equal to 9 mm.  
different velocities has been investigated. To compare the results among the unprotected and protected pipes, commonly used indicators in the field of traffic-induced vibrations have been used, while the vertical and horizontal deformations, i.e., pipe ovalization, have also been compared.  
The main findings of the present investigation could be summarized as follows:  
* Implementing an EPS layer between the track and the buried pipeline substantially reduces HST-induced vibrations.
* The insertion loss at the center frequencies of the lower 1/3 octave bands is constant and independent from the HST passing velocity.
* The reduction in the vibrations level strongly depends on the thickness of the EPS layer.
* The material and dimensions of the pipe affect the results both for unprotected and protected cases. Thick steel pipes are less vulnerable; thus, the implementation of EPS may not be needed.
* The transient and residual deformations of polyethylene pipes are higher compared to those of steel pipes. Hence, the efficiency of the application of the EPS layer is more pronounced in this case.
# Effect of Marine Coolant Additives on Cavitation Erosion-Corrosion of Diesel Engine Cylinder Liner
## 4 Conclusions  
This study was conducted to analyze the effect of nitrite-based additives on the cavitation erosion and corrosion damage of DCI through electrochemical experiments and cavitation erosion tests. The following conclusions were as follows:  
1. The corrosion current density measurements showed that the nitrite-based additive effectively served as a corrosion inhibitor against chloride ions;
2. In the presence of the nitrite-based additive, during cavitation erosion attack, the soft spherical graphite was preferentially removed, and small craters formed, acting as stress concentration regions. Subsequently, fatigue cracks initiated and grew from the surrounding areas of the small craters, leading to the coalescence of adjacent craters, which developed into larger craters;
3. In the absence of the nitrite-based additive, DCI exposed to chloride ions exhibited a significant acceleration in crater damage due to the interaction between cavitation erosion and corrosion;
4. The ultrasonic vibration cavitation erosion test used in this study can create an environment similar to the cavitation bubbles that occur in diesel engines. However, it has limitations in accurately replicating the actual operating conditions of the engine. In particular, it is challenging to fully replicate, under laboratory conditions, the vibration characteristics of the cylinder liner and the coolant flow conditions that vary with engine load and rotational speed. To overcome these limitations, validation experiments using actual engines are necessary, and this represents a critical task to be addressed in future research.  
Conceptualization, I.-C.P.; methodology, W.-S.J. and I.-C.P.; software, W.-S.J. and I.-C.P.; validation, W.-S.J. and I.-C.P.; formal analysis, W.-S.J. and I.-C.P.; investigation, W.-S.J. and I.-C.P.; resources, W.-S.J. and I.-C.P.; data curation, W.-S.J. and I.-C.P.; writing--original draft preparation, W.-S.J. and I.-C.P.; writing--review and editing, I.-C.P.; visualization, W.-S.J. and I.-C.P.; supervision, I.-C.P.; project administration, W.-S.J. and I.-C.P.; funding acquisition, I.-C.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The raw data supporting the conclusions of this article will be made available by the authors upon request.  
**Conflicts of Interest**: The authors declare no conflicts of interest.
# Substructuring of a Petrol Engine: Dynamic Characterization and Experimental Validation
## 2 Full FEM Engine Modelling  
The FEM model of the entire engine created by means of the commercial code Altair Hypermesh [16] is shown in Figure 1. Tetrahedral quadratic elements were used to model components such as the engine crankcase, cylinder head, crankshaft, gearbox, etc., whereas quadrilateral quadratic surface elements were used to model thin elements such as the exhaust pipe or the oil pan. Bar elements were used to model the bolts that connect the various components. The average element size was set to 3-6 mm. The final full FEM model comprised nearly \(5.7\times 10^{6}\) elements and \(4.7\times 10^{6}\) nodes.  
In order to validate the full FEM model, two frequency response function (FRF) analyses were performed: one for the vertical bending and one for the lateral bending. An FRF analysis consists of the application of a unitary force in a given node, followed by measurements of the related accelerations in different nodes of the model. Such relevant points selected for the FRF analyses of the engine are shown in Figure 2 for both the vertical and the lateral bending load case. These numerical analyses replicated the experimental tests previously performed and the results are compared in the following section.  
Figure 1: FEM model of the engine with all its sub-components.  
The FEM model was imported in the MSC Nastern to calculate the modal basis of the engine up to a frequency of 1500 Hz (the Lanczos algorithm was used for such a purpose). A damping coefficient equal to 0.03 was considered for all the structural elements. Subsequently, the modal basis was imported in the Siemens LMS Virtual Lab environment, with input and output points defined for either the vertical (Figure 2a) or lateral (Figure 2b) bending. Finally, FRF and modal-based frequency response analyses were performed to calculate the accelerations at the relevant points.  
A free-free condition was simulated in all the presented cases. As a matter of fact, the engine mounts are capable of decoupling the dynamic engine behavior from the supporting structure in the whole frequency range considered.  
Moreover, the impact of the crankcase-gearbox bracket shown in Figure 3 on the acceleration levels at the previously mentioned relevant points was assessed. Such evaluation was needed to understand whether the impact on the dynamic behavior of the engine was necessary, since its removal would have a positive impact on cost reduction.  
Figure 2: Full FEM model with details of the relevant points for the FRF analyses for load cases of (**a**) vertical bending and (**b**) lateral bending.
## 3 Results and Discussion
### Leachability of manure Blends through the Soil
#### 3.3.3. Leaching of Metals  
Figure 6 compares the release of major elements from all soil combinations in the leachates. The application of manure to the soil increased significantly the amounts of Ca and Mg dissolved in water, principally attributed to the high contents of soluble calcite and dolomite minerals in manure (Figure 1). Upon addition of biochar, it can be seen that the extractability of Ca was reduced, suggesting that the surface or porosity of biochar provided retention sites for this element. By comparison, the leachability of K was greatly intensified with a higher amount of biochar, due to the high concentrations of the soluble forms of sylvite and arcanite in this (Figure 1).  
Regarding the leaching behavior of heavy metals from the materials studied, Table 6, presenting the cumulative concentrations in liquid effluents, indicates that only Sr, Zn and  
Figure 5: Variation of COD with time in biochar/manure/soil leachates.  
Figure 6: Cumulative concentration of major elements in biochar/manure/soil leachates.  
Mn were extracted in considerable amounts, of 413-1145, 145-487 and 215-462 ug/kg, respectively. The higher extractability of Sr suggests that this element was associated with organic matter, or salts dissolved in the water effluents [5]. In the presence of biochar in the mixtures, heavy metal levels in the leachates were significantly reduced by about 50-70% (Cu by 50%, Mn by 54%, Sr by 64%, Zn by 70%). Toxic metals Cr, Co, Hg and As were not quantified at all in the extracts, being below detection limits, and Pb, which is known to have calcium or organic affinity [11], was very low, implying no risk to the environment. All measured values were below the legislation limits of EC [46]. Possible reasons for the low reachability of metals from the biochar may be their bounding in stable oxides, phosphates or aluminosilicates, such as quartz, hematite, whitlockite magnesium, albite and vezouvian (Figure 1), or other mechanisms, including electrostatic attraction, competition between elements or complexation [47].
###### Abstract  
Oxidative stress, a physiological process that can damage cells, is known to affect various aspects of oral health. Oxidative stress can influence dental implant longevity and health. Assessing biomarkers of oxidative stress in saliva is beneficial for diagnosing and tracking the progression of oral diseases. A study is made of salivary oxidative stress in patients with dental implants with or without periodontitis. The study consisted of the following groups: Group1 (healthy without dental implants); Group 2 (subjects undergoing periodontal maintenance without dental implants); Group 3 (healthy patients with implants older than six months); and Group 4 (patients undergoing periodontal maintenance with implants older than six months). A complete examination of the oral cavity was made in each patient and a questionnaire was used to assess habits of hygiene, quality of life, and information about the implants. The following parameters were recorded in unstimulated whole saliva: ferric reducing antioxidant power (FRAP), Trolox equivalent antioxidant capacity (TEAC), cupric reducing antioxidant capacity (CUPRAC), advanced oxidation protein products (AOPP), and total proteins (TP). A total of 160 patients were studied, with 40 patients per group. The mean oxidative stress biomarker values obtained in the patients without implants and with implants were FRAP 0.590 \(\pm\) 0.514 and 0.588 \(\pm\) 0.334 mmol/L (_p_ = 0.974); TEAC 0.320 \(\pm\) 0.223 and 0.315 \(\pm\) 0.172 mmol/L (_p_ = 0.879); CUPRAC 0.286 \(\pm\) 0.216 and 0.288 \(\pm\) 0.151 mmol/L (_p_ = 0.956); AOPP 456.04 \(\pm\) 789.75 and 430.65 \(\pm\) 752.05 mmol/L (_p_ = 0.838); and TP 73.90 \(\pm\) 50.83 and 70.36 \(\pm\) 56.93 mg/dL (_p_ = 0.684), respectively. No substantial variations were noted in the salivary oxidative stress biomarker levels between patients with controlled periodontal disease and/or dental implants compared to healthy individuals.  
oxide stress; dental implants; antioxidant capacity; saliva; oxidative stress biomarkers
# Model Based Robust Predictive Control of Ship Roll/Yaw Motions with Input Constraints
## 3 Main Result
### Design of Robust Model Predictive Controller for Rolllyaw with Saturation Constraints
\begin{array}{c}\prod=\left[\begin{array}{cc}\prod_{11}&\prod_{12}\\ \prod_{21}&\prod_{22}\\ \end{array}\right]\\ =\left[\begin{array}{cc}\left\|\mathbf{A}+\mathbf{BK}\right\|_{\mathbf{U}/\delta}^{2}- \frac{\mathbf{U}}{\delta}+\frac{Q+K^{T}RK}{\delta}&*\\ \frac{\mathbf{U}}{\delta}(A+BK)&\frac{\mathbf{U}-\lambda\mathbf{I}}{\delta}\\ \end{array}\right]=\left[\begin{array}{ccccc}-\frac{\mathbf{U}}{\delta}+\frac{Q +K^{T}RK}{\delta}&*&*\\ 0&\frac{-\lambda\mathbf{I}}{\delta}&*\\ A+BK&I&-\left(\frac{\mathbf{U}}{\delta}\right)^{-1}\\ \end{array}\right]\\ =\left[\begin{array}{ccccc}-\frac{\mathbf{U}}{\delta}+\frac{K^{T}RK}{\delta}&* &*&*\\ 0&\frac{-\lambda\mathbf{I}}{\delta}&*&*\\ A+BK&I&-\left(\frac{\mathbf{U}}{\delta}\right)^{-1}&*&*\\ \frac{\mathbf{Q}}{\delta}&0&0&-\frac{\mathbf{Q}}{\delta}&*\\ \frac{\mathbf{K}}{\delta}&0&0&0&-\frac{\mathbf{R}}{\delta}\\ \end{array}\right]\leq 0\\ \end{array}  \tag{20}\]  
By multiplying \(\left[ \begin{array}{ccccc}\mathbf{V}&0&0&0&0\\ 0&\delta&0&0&0\\ 0&0&1&0&0\\ 0&0&0&\delta&0\\ 0&0&0&0&\delta\\ \end{array} \right]\) on both sides of the inequality Equation (20), and setting \(\mathbf{V}:=\mathbf{U}^{-1}\delta\), \(\mathbf{Y}:=\mathbf{K}\mathbf{V}\), \(\sigma:=\lambda\delta\), one can obtain the equivalent LMI as follows,  
\[\left[ \begin{array}{ccccc}-\mathbf{V}&0&*&*&*\\ 0&-\lambda\delta\mathbf{I}&*&*&*\\ (A+BK)\mathbf{V}&\delta\mathbf{I}&-\mathbf{V}&*&*\\ \mathbf{QV}&0&0&-\mathbf{Q}\delta&*\\ \mathbf{R}\mathbf{K}\mathbf{V}&0&0&0&-\delta R\\ \end{array} \right]=\left[ \begin{array}{ccccc}-\mathbf{V}&0&*&*&*\\ 0&-\sigma\mathbf{I}&*&*&*\\ \mathbf{AV}+\mathbf{BV}&\delta\mathbf{I}&-\mathbf{V}&*&*\\ \mathbf{QV}&0&0&-\delta\mathbf{Q}&*\\ \mathbf{RV}&0&0&0&-\delta R\\ \end{array} \right]\leq 0,\]  
which is exactly the inequality (19). The variable \(\sigma\) or \(\lambda\) is associated to input-state-stability [32]; it is worth noting that smaller \(\lambda\) means better control performance [33]. Besides, our optimization objective is to minimize \(\sigma\), which is denoted by  
\[ \begin{array}{c}\min\sigma\\ s.t.\ \delta\leq\delta_{0}\\ \end{array}  \tag{21}\]  
where \(\delta_{0}\) is the optimal \(\delta\) obtained in the previous time instant. The input saturation constraints of the controller should be considered. It is assumed that control inputs satisfy \(\left|u_{j}(k+i|k)\right|\leq U_{j},j\in\{1,\cdots,m\}\). Referring to [34], the input saturation constraints of the controller are guaranteed by the following LMI  
\[\left[ \begin{array}{cc}\mathbf{C}&\mathbf{Y}\\ \mathbf{Y}^{T}&\mathbf{V}\end{array} \right]\geq 0, \tag{22}\]  
where \(C\) is a diagonal matrix, and the \(j\)-th element satisfying \(C_{jj}\leq U_{j}^{2}\). The \(H_{\infty}\)-type MPC online real-time optimization problem considering linear state feedback control law can be summarized as follows [33]:  
\[ \begin{split} OP:&\min_{V,Y,\mathbf{\beta},\sigma},\\ s.t.&(\ref{eq:1}),(\ref{eq:2}),(\ref{eq:3}),(\ref{eq:4}) \end{split}  \tag{23}\]
## 5 Experimental Results and Discussion
### Implementation of the Decoupling Inverse Compensator SDIHC
Table 5 shows the RMSE and \(e_{w}\) of different compensators. It can be found that the results without decoupling and inverse stiffness-dependent submodules lead to the worst accuracy because the coupling between parallel PAMs play a significant role in the system behaviors. The SDIHC algorithm successfully completed hysteresis compensation and decoupling, and the RMSE of the compensation results was no more than 1.56 mm. As for the hysteresis compensation effect of the SDIHC compensator, the maximum width ratio \(e_{w}\) of the hysteresis loops with different stiffness states after applying the SDIHC compensator was within the range of [0.58%, 2.33%], clearly lower than the experimental results before compensation in Section 2. To further validate the SDIHC, a desired signal \(y_{1d}=y_{2d}=y_{3d}=abs[40\sin(0.04\pi t)+5]\) mm with \(p_{0}=0.6\) bar is tracked in Figure 13. The steady-state error with the proposed SDIHC was within the range of [\(-1.33\) mm, 1.25 mm]. It can be observed that the proposed compensator provided an effective method for precise end position control of the pneumatic soft manipulator. Figure 12: Inverse compensation results. (**a**) \(p_{0}=0.7\) bar, \(y_{1d}-y_{1}\); (**b**) \(p_{0}=0.7\) bar, \(\ldots\); (**c**) \(p_{0}=0.7\) bar, \(y_{1d}-y_{3}\); (**d**) \(p_{0}=1.5\) bar, \(y_{2d}-y_{1}\); (**e**) \(p_{0}=1.5\) bar, \(y_{2d}-y_{2}\); (**f**) \(p_{0}=1.5\) bar, \(y_{2d}-y_{3}\); (**g**) \(p_{0}=2.3\) bar, \(y_{3d}-y_{1}\); (**h**) \(p_{0}=2.3\) bar, \(y_{3d}-y_{2}\); (**i**) \(p_{0}=2.3\) bar, \(y_{3d}-y_{3}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{5}{c}{**SDIHC Compensator**} & \multicolumn{2}{c}{**Individual Hysteresis Compensator**} & \multicolumn{2}{c}{**PID-Based Compensator**} \\ \hline
**Group** & \(\mathbf{e_{w}}\) **(\%)** & **RMSE (mm)** & \(\mathbf{e_{w}}\) **(\%)** & **RMSE (mm)** & **(\%)** & **RMSE (mm)** \\ \hline (a) & 0.58 & 0.21 & 6.12 & 2.31 & 2.89 & 3.01 \\ (b) & 0.87 & 1.09 & 7.13 & 7.55 & 3.51 & 4.33 \\ (c) & 1.02 & 1.21 & 6.78 & 8.53 & 4.03 & 4.96 \\ \hline \end{tabular}
\end{table} 
Table 5: RMSE and \(\mathbf{e_{w}}\) comparisons of different compensation methods.
## Materials and Methods
### Scenarios Development  
We utilized the existing data-set, the LULC change projection scenarios, developed by [PERSON] et al., [49], based on four future socioeconomic scenarios (A1B, A2, B1, and B2) documented in the IPCC SRES [65; 66; 47]. The IPCC SRES describes alternative developments driven by forces of greenhouse gas emissions, including population, economics, technological innovation, and energy use (Figure 2). The scenarios comprised of qualitative descriptions of future conditions, often referred to as narrative storylines, and quantitative modeling, including projections of land use. The two reasons to adopt the dataset are: (1) The SRES scenarios were down-scaled using an Integrated Assessment Model in combination with a Future Land Use Simulation Model (FLUS) [60], Landsat-based land use historical trajectory, and expert knowledge. Hence, a finer resolution of LULC could match better with the ecological processes. (2) The changes in the built-up that are ignored in the IMAGE were calibrated in the data set, which can reflect the reality of economic development in our study area better.  
Although the narrative storylines of the four scenarios have been described in detail [48; 49], here we emphasize some key characteristics of each scenario. A was used to represent an economic emphasis, and on the contrary, B indicates an environmental protection; 1 denotes globalization, and 2 denotes a regional orientation.  
Figure 2: Overview of the data flow in the Terrestrial Ecosystem Simulator-Land Use/land Cover model (TES-LUC). (**a**) is driving factors, including biophysical and socioeconomic variables. (**b**) is the land use allocation module; (**c**) is Terrestrial Ecosystem simulator. Note: Land use allocation module (**b**) is redrawn according to [PERSON] et al., [49]; (**c**) is modified from [PERSON] et al., [56]; the coupling relationship is drawn based on [PERSON] et al., [67]. The ellipses on the right are modified from a Framework for Assessing Multiple Ecosystem Responses to Land-Use Change [68].  
* A1B: Low population growth; High gross domestic productivity (GDP) growth; Sprawling urban expansion; Rapid technological innovation; Energy sector--Balanced; Active management of resources.
* A2: High population growth; Low GDP growth; Sprawling urban expansion; Slow technological innovation; Energy sector--Fossil fuels; Low resources protection.
* B1: Low population growth; High GDP growth; Compact urban expansion; Rapid technological innovation; Energy sector--Renewable; Protection of biodiversity.
* B2: Medium population growth; Medium GDP growth; Compact urban expansion; Medium technological innovation; Energy sector--Mixed; Protection of biodiversity.
## 4 Experimental Results and Discussion
### Experimental Setup and Evaluation Metrics
#### 4.1.5 The Hidden Layers of the OCC Network  
To analyze the optimal structure of the OCC network, we have trained the network with the different number of hidden layers. The experimental results are shown in Table 2. We can see that the \(\Delta E_{mean}\) becomes stable from three to eight hidden layers, while the testing time will increase as the number of layers increase. According to experimental results, we set the number of hidden layers at 3.
## Appendix A
\begin{array}{c}-16k_{1}^{2}\alpha_{1}\mu\sin^{2}\left( \frac{\beta_{n}L_{1}}{2\sqrt{\alpha_{1}}}\right)\\ -8k_{1}\beta_{n}\sqrt{\alpha_{1}}R_{1}R_{2}(R_{2}^{2}-R_{3}^{2})\sin(2k_{2}L_{ 2})\sin\left(\frac{\beta_{n}L_{1}}{\sqrt{\alpha_{1}}}\right)\\ -2\beta_{n}^{2}(R_{1}^{2}-R_{2}^{2})(R_{2}^{2}+R_{3}^{2})\cos(2k_{1}L_{1})\\ +2\beta_{n}^{2}(R_{2}^{2}+R_{3}^{2})[R_{1}^{2}+R_{2}^{2}-2R_{2}^{2}\cos\left( \frac{\beta_{n}L_{1}}{\sqrt{\alpha_{1}}}\right)]\\ -2\beta_{n}^{2}(R_{2}^{2}-R_{3}^{2})(R_{2}^{2}-R_{1}^{2})\cos(2k_{2}L_{2})\\ -2\beta_{n}^{2}(R_{2}^{2}-R_{3}^{2})(R_{2}^{2}+R_{1}^{2})\cos(2k_{1}L_{1})\cos (2k_{2}L_{2})\\ +4\beta_{n}^{2}(R_{2}^{2}-R_{3}^{2})R_{2}^{2}\cos\left(\frac{\beta_{n}L_{1}}{ \sqrt{\alpha_{1}}}\right)\cos(2k_{2}L_{2})\\ -4\beta_{n}^{2}R_{1}R_{2}(R_{2}^{2}-R_{3}^{2})\sin(2k_{1}L_{1})\sin(2k_{2}L_{2}) \end{array} \right\},\] (A15a)\[\Omega_{n}^{(2)}=\frac{-2A_{11}^{2}a_{2}R_{2}\sqrt{\alpha_{2}}}{\left[\eta(\beta_{n }^{3}-4k_{2}^{2}\alpha_{2}\beta_{n})\right]}\left\{ \begin{array}{c}4B_{n}k_{2}^ {2}(R_{2}^{2}+R_{3}^{2})\alpha_{2}\cos(\frac{\beta_{n}L_{2}}{\sqrt{\alpha_{2}}} )\\ +8B_{n}-4B_{n}k_{2}^{2}(R_{2}^{2}+R_{3}^{2})\alpha_{2}\\ +4C_{n}k_{2}^{2}(R_{2}^{2}+R_{3}^{2})\alpha_{2}\sin(\frac{\beta_{n}L_{2}}{ \sqrt{\alpha_{2}}})\\ -2C_{n}\beta_{n}^{2}R_{3}^{2}\sin(\frac{\beta_{n}L_{2}}{\sqrt{\alpha_{2}}})- \xi C_{n}\end{array} \right\}, \tag{15b}\]  
\[\Omega_{n}^{(3)}=4A_{11}^{2}D_{n}\frac{a_{3}R_{2}^{2}R_{3}\sqrt{\alpha_{3}}}{ \beta_{n}\eta}\sin(\frac{\beta_{n}L_{3}}{\sqrt{\alpha_{3}}}), \tag{15c}\]  
and  
\[\mu=(R_{1}^{2}+R_{2}^{2})(R_{2}^{2}+R_{3}^{2})+(R_{1}^{2}-R_{2}^{2})(R_{2}^{2}- R_{3}^{2})\cos(2k_{2}L_{2}), \tag{16a}\] \[\delta=\beta_{n}^{2}\bigg{[}(R_{3}^{2}-R_{2}^{2})\cos(2k_{2}L_{2})+(R_{3}^{2}+ R_{2}^{2})-2R_{3}^{2}\cos(\frac{\beta_{n}L_{2}}{\sqrt{\alpha_{2}}})\bigg{]}, \tag{16b}\]  
\[\xi=2\beta_{n}k_{2}(R_{2}^{2}-R_{3}^{2})\sqrt{\alpha_{2}}\sin(2k_{2}L_{2}), \tag{16c}\]  
\[\eta=R_{2}^{2}(R_{1}+R_{3})^{2}\cos^{2}(k_{2}L_{2})+(R_{2}^{2}+R_{1}R_{3})^{2} \sin^{2}(k_{2}L_{2}), \tag{16d}\]  
Summing up the above derivations, the temperature field in each layer of the one-dimensional composite system is given by  
\[T_{j}(x,\ t)=\Theta_{nh,j}(x,\ t)+\Theta_{h,j}(x,\ t)+T_{end},\ j=1,\ 2,\ 3, \tag{17}\]