esa-sceva/satcom-chunk-collection huggingface dataset:
## 1 Introduction
[15; 16] numerically and experimentally investigated the influence of placing a PCM slab at the back side of the evaporator in a refrigerator and  
Figure 1: Pressure-enthalpy diagram of a refrigeration cycle with performance improvement by (**a**) raised evaporator pressure or (**b**) increased sub-cooling degree. reported the PCM to maintain the temperature for longer time in absence of power supply, leading to improved performance compared to the conventional systems. [PERSON] et al. [17] placed a novel air heat exchanger, containing PCM that melts at 5 \({}^{\circ}\)C, near an evaporator inside a cold room, comparing the thermal behaviour with and without PCM, and reported maintenance of thermal conditions of the stored products, reduced number of ON/OFF cycles (six cycles by thirteen cycles) with PCM in the room. Despite of the abovementioned studies, the integration of PCM into the heat exchangers of refrigeration cycles is a topic not deeply investigated in the literature. Furthermore, previous attempts of PCM integration into refrigeration cycles involves introducing extra components, which would lead to complexity in assembling of the system, or a need for an extra space. This study investigates for the first time a novel three-fluid refrigerant-PCM-water heat exchanger (RPW-HEX), all in a single component. The RPW-HEX was directly integrated into a vapour compression system, replacing the conventional evaporator, and it was connected to an external heat transfer fluid (HTF) loop, which simulates the heat source (thermal load). This ALL-IN-ONE component provides double benefits, i.e., it works as a heat exchanger and as a TES module, and it is able to take advantage of the PCM high energy storage density and isothermal energy supply that would lead to peak shifting and peak shaving in the refrigeration cycle. Experiments were performed based on three modes. The first two modes treat the RPW-HEX as a TES tank, testing the charging and discharging of PCM. The third mode treats it as a heat exchanger medium among three fluids, which attests for ability to cover energy demand while storing extra cold energy, when the compressor is ON, and to release the stored cold energy when the compressor goes OFF. Finally, a parametric study is carried out on the influence of compressor power, evaporation temperature set-point, HTF inlet temperature and HTF flow rate on the RPW-HEX.
## 3 Signal Quality Assessment
We distinguish the results between constellations and devices in consecutive panels and between the satellites by different colors. What one can read from the figure is that, despite the fact that \(C/N_{0}\) presented in Figure 6 were averaged in \(1^{\circ}\) bins, the values may still exhibit relative noise nature (e.g., code on GPS L1 of Xiaomi Mi 8 for \(C/N_{0}\) in the range of 10-25 dB-Hz). However, if we carefully inspect Figure 6, we note that the smartphone code noise demonstrates a clear dependency on a signal strength. Recalling the results of the elevation-dependent quality of code observations that were given in Figure 5, we may conclude that the \(C/N_{0}\) weighting scheme should be considered as superior to the elevation-dependent one. However, this will be validated in the positioning experiment in the next section. We also discover that the \(C/N_{0}\) series of Xiaomi Mi 9 are of a different nature when compared to those of Xiaomi Mi 8 and Huawei P30. For the latter devices, we noticed that generally the highest noise corresponds to the signals with the lowest strength (up to 20 dB-Hz). Some small local peaks may be also detected as in the case of GLONASS signals of Huawei P30 around 35 dB-Hz. However, when it comes to the Xiaomi Mi 9 smartphone, we see that the noisiest observations are those with \(C/N_{0}\) fitting the range of 20-30 dB-Hz. This is another finding, after the highest signal noise that proves a dissimilar performance of Xiaomi Mi 9 with respect to the other analyzed smartphones. Figure 6: \(C/N_{0}\)-dependent quality of code observations on GPS L1, Galileo E1, BDS B1, and GLONASS G1 frequency bands in 1 st, 2 nd, 3 rd, and 4 th rows, respectively. The results corresponding to different smartphones are distinguished by columns. Different colors represent different satellites. Code residuals were computed as the observations that were double differenced in a time domain. The values are averaged for particular satellites in 1 dB-Hz bins.
## 2 Materials and Methods
### Reagents, Solvents and Materials  
Resveratrol 99.0% (3,4',5-trihydrocaystilbene, C\({}_{14}\)H\({}_{12}\)O\({}_{3}\), RSV) from TCI Chemicals (Tokyo, Japan), quercetin dihydrate 99.0% (3,3',4',5'7'-pentahydroydroflavone, C\({}_{15}\)H\({}_{14}\)O\({}_{9}\), QR) from BioChemika-Fluka (Buchs, Switzerland), trans-ferulic acid 99.0% (4-hydroxy-3-methoxycinnamic acid, C\({}_{10}\)H\({}_{10}\)O\({}_{4}\), FERA) from Sigma-Aldrich (Shanghai, China), retinol 95% (vitamin A, C\({}_{20}\)H\({}_{30}\)O, Retinol, RTN) from Sigma-Aldrich (Buchs, Switzerland), and \(\upalpha\)-Tocopherol 95.5% (vitamin E, C\({}_{29}\)H\({}_{50}\)O\({}_{2}\), \(\upalpha\)-Tocopherol, \(\upalpha\)-TOC) from Sigma-Aldrich (Darmstadt, Germany) were used as active ingredients (Figure 1). Coconut oil, cetyl alcohol, borax, and cera alba (excipients) were purchased from Chemco (Athens, Greece). For the preparation of the new formulation (cold cream), one of the raw materials used was resveratrol, which originated from the extract of grape (_Vitis vinifera_) and Japanese acacia (_Polygynum cuspidatum_). The extract is sold under the brand name Regener Life Resveratrol(r) (Company: Natural Factors, Coquitlam, BC, Canada, purchased from a local pharmacy) in 500 mg capsules with 250 mg of pure and natural trans-resveratrol.  
Figure 1: Chemical structures of RSV, FERA, QR, RTN, and \(\upalpha\)-TOC.  
The solvents for the mobile phase or for processing the samples were of high purity and suitable for use (HPLC grade). More specifically, methanol (CH\({}_{3}\)OH, MeOH) (Chem-Lab, Zedlegem, Belgium), acetonitrile (ACN) (Honeywell, Charlotte, NC, USA), and ethanol (CH\({}_{3}\)CH\({}_{2}\)OH, EtOH) (Honeywell) were used. Water was ultrapure for HPLC (18.2 M\(\Omega\) cm resistivity) and produced through a purification system (B30, Adrona SIA, Riga, Latvia).  
Formic acid (CH\({}_{2}\)O\({}_{2}\), FA) Sigma-Aldrich (Darmstadt, Germany) and trifluoroacetic acid (C\({}_{2}\)HF\({}_{3}\)O\({}_{2}\), TFA), Sigma-Aldrich (Darmstadt, Germany), were utilized to adjust the pH, while the final diluent of the samples consisted of MeOH-ACN-F.A. 50:50:0.2 \(v/v/v\).  
Phosphate-buffered saline (PBS) pH 7.4 was prepared by dissolving 8.0 g NaCl, 1.44 g Na\({}_{2}\)HPO\({}_{4}\), 0.24 g KH\({}_{2}\)PO\({}_{4}\) (Merck, Darmstadt, Germany), and 0.20 g KCl (Chem-Lab nv, Zedlegem, Belgium) in 1 L of distilled water. For the in vitro permeability experiments, a dialysis tubing cellulose membrane (flat width 43 mm) was obtained from Sigma-Aldrich (Darmstadt, Germany).
## 5 Discussion
### Distillation Methods
#### 5.2.1 Selection of Feature to Distillate  
During the training of the student network guided by the teacher network, it is necessary to select distilled features. In this paper, the available features for selection include semantic mask features \(F_{seg}\), line features \(F_{line}\), and vertex features \(F_{pqr}\). We aimed to ensure that the student network learns effective feature representations, and thus conducted ablation experiments to investigate different feature combinations.  
Table 3 presents the experimental results of different feature combinations during the distillation process. The student network achieved the best learning performance when using the semantic mask feature \(F_{seg}\), line feature \(F_{line}\), and vertex feature \(F_{pqr}\) simultaneously. The results demonstrated that all three features have a positive impact on building polygon extraction. The combination of these three features outperformed any pairwise  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Distillation** & **Dice Loss** & **OA** & **IoU** & \(\mathrm{P_{50}^{IoU}}\) & \(\mathrm{P_{50}^{Boundary}}\) & **Batch Time** & **Params** \\ \hline Baseline & & & 90.88 & 62.37 & 52.50 & 45.71 & **0.84s** & **74.29M** \\ Ours & \(\surd\) & & 91.37 & 64.63 & 54.11 & 51.98 & 0.88s & **74.29M** \\ Ours & \(\surd\) & \(\surd\) & **92.28** & **66.54** & **56.01** & **54.19** & 0.90s & **74.29M** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Ablation experiments.  
combination, indicating their complementary nature and collective contribution to building polygon extraction.
## 5 System Equilibrium Analysis under Arbitrary Transmission Limit  
### System Balance Equation  
The authors in [44] analyzed the system equilibrium point of the random access procedure without considering the following data transmission procedure and ACB scheme. In [21], the system equilibrium is derived asymptotically for joint optimization of random access and data transmission under a large transmission limit (\(Q\geq 9\)). Compared to [21], this section would provide a more rigorous system equilibrium analysis under arbitrary transmission limit \(Q(Q\geq 1)\).  
Apparently, when the system with uniform distributed traffic converges to the equilibrium state, there must be \(X_{i}=X_{j}\), \(\forall i,j\) and \(Z_{i}=Z_{j}\), \(\forall i,j\). Let\(f\) denote the one-shot success probability in each cycle, according to Equation (24) we can derive that:  
\[\begin{array}{ll}X_{i}[2]&=\frac{1}{W_{BO}+1}\sum\limits_{k=i-(W_{BO}+1)}^{i -1}(X_{k}[1]-Z_{k}[1])\\ &=\frac{1}{W_{BO}+1}(W_{BO}+1)(X_{i-1}[1]-Z_{i-1}[1])\\ &=X_{i-1}[1]-Z_{i-1}[1]\\ &=\lambda(1-f)\end{array} \tag{31}\]  
where \(\lambda\) is the average number of new arrivals. Therefore, in a recursive way, we can have the following equation:  
\[\begin{array}{ll}X_{i}[q]&=X_{i-1}[q-1]-Z_{i-1}[q-1]\\ &=\lambda(1-f)^{q-1},\hskip 56.905512 pt2\leq q\leq Q\end{array} \tag{32}\]Omitting the time subscript \(i\), the system balance equation is derived as follows:  
\[\begin{array}{ll}X&=\sum\limits_{q=1}^{Q}X[q]\\ &=\sum\limits_{q=1}^{Q}\lambda(1-f)^{q-1}\\ &=\lambda\frac{1-(1-f)^{Q}}{f}\end{array} \tag{33}\]  
**Remark 3**: _According to Equations (31)-(33), we can find that the components of devices in each cycle are the same with and without backoff scheme. Therefore, the uniform backoff scheme has no impact on the system performance except delay. Then according to the definitions in Subsection 4.2, the performance metrics in equilibrium state are computed as:_  
\[\begin{array}{ll}P_{S}&=1-(1-f)^{Q}\\ \begin{array}{ll}U&=\frac{\sum\limits_{q=1}^{Q}\lambda(1-f)^{q-1}f}{\sum \limits_{q=1}^{Q}\lambda(1-f)^{q-1}f}\\ &=\frac{\sum\limits_{q=1}^{Q}\lambda(1-f)^{q-1}f}{\sum\limits_{q=1}^{Q}\lambda (1-f)^{q-1}f}\\ &=\sum\limits_{q=1}^{Q}\lambda(1-f)^{q-1}f\end{array} \tag{34}\]  
_where \(L\) is the reserved resource blocks and \(\frac{1+(W_{B0}+1)}{2}\) is the average delay caused by backoff._
# Shear Strength Analysis and Slope Stability Study of Straight Root Herbaceous Root Soil Composite
## 4 Discussion
### Factors Affecting Slope Stability  
Numerous factors affect slope stability, including internal factors, such as the rock and soil properties and geological conditions, and external factors, such as hydrogeological conditions, weathering, earthquakes, and human factors. The stability of shallow slopes can be enhanced by planting vegetation, amongst other methods. Slopes with plant roots on their surfaces are more stable than those with root systems at the foot or top of the slope [47]. The reinforcement effect of plant roots improves slope stability and reduces the range of influence of the sliding surface. Factors affecting slope stability include the root content, root burial depth, and slope angle.  
[PERSON] et al. employed numerical analysis to reveal that the safety coefficient of slopes was substantially influenced by the plant spacing. The stability of slopes with a plant spacing of 5 m was consistent with that of bare slopes [47]. [PERSON] et al. observed tree spacing to improve slope stability [34; 48]. Although these studies confirm that an increase in the cohesive force provided by plant roots reduces slope instability, high-density herbaceous plants are often planted on roadbed slopes. As the root content of the surface soil increases, the frictional force at the root-soil interface transfers the shear stress of the shallow soil to the deep soil, improving the soil strength of shallow slopes.  
[PERSON] et al. found that the root depth and the resulting increase in the cohesive force enhance slope stability [35; 48], which is consistent with our results. The root content of plants increased cohesion, and a deeper root burial depth increased the slope safety coefficient. [PERSON]'s model considers 2.1 m as the critical depth of the main root. In contrast, our calculation model focused on shallow slopes planted with herbaceous plants, with a maximum root depth of 0.6 m. Most sliding surfaces are located 1 m or more below the surface [49]. The root system only reinforces the soil when the root burial depth reaches the soil layer below the sliding surface.  
Our model parameters were observed to influence slope stability. Poisson's ratio had a negligible effect on the safety coefficient, while the elastic modulus only influenced slope deformation and displacement [34; 50]. The slope angle significantly affected the safety coefficient of the slope, namely, the safety coefficient decreased as the slope angle increased. These results indicate that the root content and root burial depth affected slope stability, which is consistent with previous research. For example, [PERSON] et al. found that the slope safety coefficients for different root structures decreased with an increase in the slope, while [PERSON] et al. observed that plant roots increased the safety coefficient [47; 51].
## 2 Dynamic Model of the Feed System
### Dynamic Equations of Ball Screw System  
The vibration characteristics of the feed system are affected by three harmonic forces \(F_{x}\sin(\omega t)\), \(F_{y}\sin(\omega t)\) and \(F_{z}\sin(\omega t)\). In order to investigate the vibration characteristics of the feed system, the dynamic model is simplified as a nine degrees-of-freedom mass  
Figure 5: Bending deformation of screw shaft.  
spring-damping model, as shown in Figure 6. The dynamic equations can be written as follows:  
\[\left\{\begin{array}{l}m_{\text{W}}\ddot{\bar{\delta}}_{Wx}+c_{x}\Big{(}\dot{ \delta}_{Wx}-\dot{\delta}_{SNx}\Big{)}+F_{\text{sn}x}=F_{x}\sin(\omega t)\\ k_{Sx}(\delta_{SNx}-\delta_{Sx})+c_{x}\Big{(}\dot{\delta}_{SNx}-\dot{\delta}_{Sx} \Big{)}=F_{\text{sn}x}+c_{x}\Big{(}\dot{\delta}_{Wx}-\dot{\delta}_{SNx}\Big{)} \\ m_{S}\ddot{\delta}_{Sx}+2c_{x}\dot{\delta}_{Sx}+F_{Ax}+F_{Dx}=c_{x}\Big{(}\dot{ \delta}_{SNx}-\dot{\delta}_{Sx}\Big{)}+k_{Sx}(\delta_{SNx}-\delta_{Sx})\\ m_{\text{W}}\ddot{\bar{\delta}}_{Wy}+c_{y}\Big{(}\dot{\delta}_{Wy}-\dot{\delta} _{SNy}\Big{)}+F_{\text{sn}y}=F_{y}\sin(\omega t)\\ k_{Sy}\big{(}\delta_{SNy}-\delta_{Sy}\big{)}+c_{y}\Big{(}\dot{\delta}_{SNy}- \dot{\delta}_{Sy}\big{)}=F_{\text{sn}y}+c_{y}\Big{(}\dot{\delta}_{Wy}-\dot{ \delta}_{SNy}\Big{)}\\ m_{S}\ddot{\delta}_{Sy}+2c_{y}\dot{\delta}_{Sy}+F_{Ay}+F_{Dy}=c_{y}\Big{(}\dot{ \delta}_{SNy}-\dot{\delta}_{Sy}\big{)}+k_{Sy}\big{(}\delta_{SNy}-\delta_{Sy} \big{)}\\ m_{W}\ddot{\bar{\delta}}_{Wz}+c_{z}\Big{(}\dot{\delta}_{Wz}-\dot{\delta}_{SNz} \Big{)}+F_{\text{sn}z}=F_{z}\sin(\omega t)\\ k_{Sz}(\delta_{SNz}-\delta_{Sz})+c_{z}\Big{(}\dot{\delta}_{SNz}-\dot{\delta}_{ Sz}\Big{)}=F_{\text{sn}z}+c_{z}\Big{(}\dot{\delta}_{Wz}-\dot{\delta}_{SNz} \Big{)}\\ m_{S}\ddot{\delta}_{Sz}+c_{z}\dot{\delta}_{Sz}+F_{Az}=c_{z}\Big{(}\dot{\delta}_ {SNz}-\dot{\delta}_{Sz}\Big{)}+k_{Sz}(\delta_{SNz}-\delta_{Sz})\end{array}\right. \tag{56}\]  
where \(\delta_{Wx}\), \(\delta_{Wy}\) and \(\delta_{Wz}\) are the displacement of worktable along the \(x\), \(y\) and \(z\) directions; \(\delta_{SNx}\), \(\delta_{SNy}\) and \(\delta_{SNz}\) are the displacement along the \(x\), \(y\) and \(z\) directions caused by the bending deformation of screw shaft; \(\delta_{Sx}\), \(\delta_{Sy}\) and \(\delta_{Sz}\) are the displacement of the screw shaft along the \(x\), \(y\) and \(z\) directions; \(m_{W}\) and \(m_{S}\) are the mass of the worktable and screw shaft, respectively; \(k_{Sx}\), \(k_{Sy}\) and \(k_{Sz}\) are the stiffness of screw shaft along the \(x\), \(y\) and \(z\) directions; \(F_{\text{sn}}\) and \(F_{A}\) are the restoring force functions of the screw-nut interface and angular contact ball bearing, respectively, which are given by \(F_{\text{sn}}=F_{L\text{sn}}+F_{L\text{sn}}\), \(F_{A}=F_{LA}+F_{RA}\); \(c_{x}\), \(c_{y}\) and \(c_{z}\) are the damping constants of the feed system, respectively, their damping ratio is calculated by the half power bandwidth method. In this paper, the damping ratios along the \(x\), \(y\) and \(z\) directions are assumed to be \(\xi_{x}=\xi_{y}=0.0434\), \(\xi_{z}=0.0483\), respectively [32].
## 5 The Proposed Protocol
### PDFH and SDFH Selection Utilizing the MPA
#### 5.2.1 The Initialization Phase  
During the initialization phase of the MPA, a set of input parameters needs to be configured, which includes the following:  
1. Number of search agents (_SAs_): This parameter represents the number of DFGMS within a certain DFG eligible to participate in the DFH selection process (_Nc_).
2. Dimension (_Dim_): This parameter defines the number of RMs utilized in our research; its specific value is set at 5.  
Figure 7: The selected PDFHs utilizing the MPA for the proposed protocol.  
3. Maximum number of iterations (_Max_Iter_): This parameter involves iteratively running the algorithm to determine the most appropriate DFH node. In our proposed protocol, _Max_Iter_ is defined as 500. 4. Lower and upper and bounds (_LB_ and _UB_): The _LB_ and _UB_ are set to 0 and 1, respectively. Specifically, our proposed protocol utilizes a normalization technique to define these boundaries at 0 and 1. This choice arises from the lack of precise information regarding the UB and LB of the three RMs employed in our study. To ensure equal treatment and establish uniformity among these metrics, we opted for normalization. As a result, all values are confined within the standardized range of [0, 1]. 5. Positions: This parameter comprises an array of IDs corresponding to the DFGMs located within a DFG, utilized to identify the optimal DFH's ID. 6. Main parameters of MPA: The authors in [43] have defined these parameters (i.e., _FADs_ and _P_), which have the values of 0.2 and 0.5, respectively. Interestingly, these values are retained and unchanged in our study. The following are the initial values that will be subject to updates in subsequent phases. \[Top\_predator\_pos= [0 0 0 0 0],\ Top\_predator\_fit=\infty\] \[\overrightarrow{StepSize}=\begin{array}{c}SA_{1}\\ SA_{2}\\ \vdots\\ SA_{Nc}\end{array}\begin{bmatrix}0\\ 0\\ \vdots\\ 0\\ \vdots\\ 0\end{bmatrix}\begin{bmatrix}0\\ 0\\ \vdots\\ 0\end{bmatrix}\begin{bmatrix}0\\ 0\\ \vdots\\ 0\end{bmatrix}\begin{bmatrix}0\\ 0\\ \vdots\\ 0  
Assuming that a RM is in the \"\(m\)\" row and is in the \"\(n\)\" column, we can say that \(RM_{scatl}\) reflects the scaled RM version of the original RM after normalization.  
\[RM_{scatl}=\frac{RM_{m,n}-RM_{n(min)}}{RM_{n(max)}-RM_{n(min)}}, \tag{21}\]  
where \(m\) values are located in [1, \(N_{c}\)], \(n\) has five values (1, 2, 3, 4, and 5), \(RM_{m,n}\) stands for the original value of RM that requires normalization, and \(RM_{n(\max)}\) and \(RM_{n(\min)}\) are the maximum and minimum values of the RM in the same column, respectively.
# Enhancing Freeway Traffic Capacity: The Impact of Autonomous Vehicle Platooning Intensity
## 2 Conceptual Framework
### Headway Consideration  
The time headway can be formulated as in Equation (4), where \(h_{d}\) represents the distance headway and \(v\) represents the speed limit in an equilibrious traffic flow.  
\[h_{t}=\frac{h_{d}}{v} \tag{4}\]  
In line with previous research [4], to ensure safety, the distance headway of a set of vehicles (j) can be determined using Equation (5), taking into account various factors. These factors include the speed of the leading vehicle \(v_{lead}\), the speed of the following vehicle \(v_{follow}\), the deceleration of the leading vehicle \(b_{lead}\), the deceleration of the following vehicle \(b_{follow}\), the length of the leading vehicle \(h_{lead}\), the measurement error of position \(h_{error}\), the safety buffer distance that the driver maintains from the leading vehicle after braking \(h_{buffer}\), and the reaction time of the j set of vehicles \(\tau_{j}\). When considering these parameters, Equation (5) formulates the appropriate distance headway for ensuring safety between vehicles in the \(j\) set.  
\[h_{dj}=\frac{v_{follow}^{2}}{2b_{follow}}+v_{follow}\tau_{j}-\frac{v_{lead}^ {2}}{2b_{lead}}+h_{buffer}+h_{error}+h_{lead} \tag{5}\]Equation (5) seeks to show the relative safety condition according to which the braking distance of the following vehicle does not exceed the distance from the rear of the leading vehicle after braking.
## 5 Computational Experiments and Numerical Results
### Time Complexity Analysis  
The time complexities of the methods, such as _UP_, _OI_, _CP_, and _SP_, are analyzed for comparison to the initial method, _FF_. The corresponding data is followed. The time complexity of the proposed LR-based solutions (_UP_, _OI_, _CP_, and _SP_) is \(O(N|T|||I||S|log|T|I||S|)\). The Lagrange dual solution is determined by Sub-problems (3)-(8). The time complexity is the worst of sub-problems, which is \(O(|T|I||S|log|T|I||S|)\) of SUB1 in parallel processing by divide-and-conquer algorithms. Each sub-problem required \(O(|T||I||S|log|T|I||S|)\) time minimum coefficient among servers. The Lagrange dual solutions could be obtained after a maximum number of iterations \(N\), and the time complexity is \(O(N|T||I||S|log|T|I||S|)\). The convergence is achieved in a small number of iterations (about 600) shown in Figure 5. However, the time complexity of the Brute force is \(O(2^{|T|^{3}|I|^{3}|S|^{3}|\Pi|})\) with the total combination of decision variables. The complexity of _FF_ is \(O(|T||I||\Pi||S|)\) with the sequential screening method. Furthermore, the proposed algorithms (_UP_, _OI_, _CP_, and _SP_) can be set as the output results at any complete iteration. Thus, the time can be controlled in practice.
## 3 Results and Discussion
### Calibration of Critical Stress and Critical Distances
This issue requires additional investigation in other materials to analyze the relationship between the two critical distances under compressive loading conditions. Moreover, the deviations of the critical stress values derived from the experimental calibrations through the MTS and the MS criteria are about 9% and 16% for PMMA and GPPS, respectively, which are quite acceptable. Figure 10: Variations of compressive stress versus the distance from the notch tip: (**a**) PMMA; (**b**) GPPS. \begin{table}
\begin{tabular}{c c c c c} \hline
**Material** & \(r_{c}\) **(mm) MTS Criterion** & \(\sigma_{c}\) **(MPa) MTS Criterion** & \(d_{c}\) **(mm) MS Criterion** & \(\sigma_{c}\) **(MPa) MS Criterion** \\ \hline PMMA & 0.26 & \(-181.1\) & 0.97 & \(-165.2\) \\ GPPS & 0.37 & \(-101.4\) & 1.78 & \(-84.7\) \\ \hline \end{tabular}
\end{table} 
Table 3: Main mechanical properties of the two polymers tested under compression.