esa-sceva/satcom-chunk-collection huggingface dataset:
# Ku-Band Mixers Based on Random-Oriented Carbon Nanotube Films
## 3 Results and Discussion
### Benchmarking of Mixers  
We benchmarked the conversion gain and linearity of CNT-based mixers with previously reported results from nanomaterials ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019) and conventional semiconductors ([PERSON] et al., 2019; [PERSON] et al., 2019), as shown in Figure 4, focusing on the X and Ku bands. The detailed data are summarized in Table S1 of the Supplementary Materials. From Figure 4a, we see that the conversion gain of our mixers is the best among all the nanomaterials such as graphene and MoS\({}_{2}\) in the Ku band. As for IIP3, although previously reported carbon-based mixers have better performance than that in this work, the frequency band of CNTs is too low (less than 6 GHz) and the corresponding conversion gain of graphene is lower than ours. Compared to traditional semiconductors such as silicon and III-V compounds, our mixers still have a significant gap in conversion gain. In contrast, the IIP3 of carbon nanotube-based mixers has comparable performance to conventional semiconductors. It is worth noting that the performance achieved in this work has no on-chip matching network and tuning instrument assistance; our CNT-based mixer has a better frequency conversion capability in the Ku band. Therefore, considering the conversion gain and IIP3 parameters, the frequency conversion ability of CNT-based mixers demonstrates better performance than other nano-materials in the Ku band.
# Encapsulation of Blackberry Phenolics and Volatiles Using Apple Fibers and Disaccharides
## 3 Results
### Flavor Profile of Formulated Microparticles
A change in the fiber:disaccharide ratio to 1:2 created a difference between the microparticles with trehalose and sucrose. Green and citrus flavor notes were the dominant ones for microparticles with trehalose, while in the microparticles with sucrose, only the green flavor note was dominant; the other two flavor notes were in equal ratio. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Volatiles**} & \multirow{2}{*}{**BJ**} & \multirow{2}{*}{**AF**} & \multicolumn{8}{c}{**Samples**} \\ \cline{3-10}  & & & **AF\_B** & **S\_0.5** & **S\_1** & **S\_2** & **T\_0.5** & **T\_1** & **T\_2** \\ \hline Hexanal & 0.00 & 2.63 & 2.09 & 3.46 & 6.30 & 6.92 & 3.53 & 6.84 & 7.18 \\ Heptanal & 0.24 & 2.10 & 0.27 & 1.93 & 2.29 & 2.58 & 2.58 & 2.52 & 3.01 \\ D-limonene & 0.74 & 6.49 & 11.56 & 11.71 & 11.54 & 8.82 & 9.63 & 11.93 & 15.47 \\ Citronellal & 0.07 & 0.98 & 2.19 & 2.18 & 1.80 & 1.62 & 2.68 & 1.43 & 1.41 \\ Linalo oxide & 0.62 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ Guaacool & 5.21 & 0.00 & 0.75 & 0.83 & 0.72 & 0.63 & 1.09 & 0.91 & 0.85 \\ Linalool & 3.90 & 13.49 & 11.10 & 11.16 & 8.63 & 8.31 & 11.96 & 10.44 & 8.54 \\ Phenethyl alcohol & 0.05 & 0.00 & 0.02 & 0.02 & 0.01 & 0.01 & 0.02 & 0.01 & 0.01 \\ Menthol & 0.02 & 0.00 & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 \\ Nerol & 0.07 & 0.00 & 0.04 & 0.03 & 0.02 & 0.01 & 0.03 & 0.02 & 0.02 \\ Citral & 0.57 & 0.16 & 0.45 & 0.47 & 0.33 & 0.31 & 0.56 & 0.43 & 0.45 \\ Perillyl alcohol & 0.02 & 0.00 & 0.01 & 0.01 & 0.01 & 0.00 & 0.01 & 0.01 & 0.01 \\ Eugenol & 1.04 & 0.00 & 0.11 & 0.12 & 0.07 & 0.09 & 0.14 & 0.10 & 0.11 \\ \(\beta\)-damascene & 1.19 & 0.59 & 0.83 & 0.67 & 0.57 & 0.47 & 0.76 & 0.60 & 0.56 \\ \(\alpha\)-ionone & 21.83 & 2.73 & 4.35 & 4.68 & 4.42 & 2.88 & 4.72 & 4.38 & 3.78 \\ \(\gamma\)-ionone & 29.71 & 30.57 & 137.43 & 114.14 & 89.43 & 65.43 & 147.14 & 116.86 & 93.57 \\ \(\beta\)-ionone & 25.80 & 54.60 & 106.80 & 55.50 & 51.20 & 50.90 & 73.30 & 70.20 & 73.40 \\ \hline \hline \end{tabular} AF\_B–apple fiber/blackberry microparticles; S–sucrose; T–trehalose; 0.5–ratio of apple fibers: disaccharide (1:0.5); 1—ratio of apple fibers:disaccharide (1:1); 2—ratio of apple fibers:disaccharide (1:2).  
\end{table} 
Table 7: Odor activity values (OAVs) of blackberry juice (BJ), apple fiber (AF), and formulated microparticles. Figure 2: Principal component analysis (PCA) biplot of volatile compounds in blackberry juice, apple fiber, and formulated microparticles. B—blackberry juice; AF—apple fiber; AF_B—apple fibers/blackberry microparticles; S–sucrose; T–trehalose; 0.5—ratio of apple fibers:disaccharide (1:0.5); 1—ratio of apple fibers:disaccharide (1:1); 2—ratio of apple fibers:disaccharide (1:2).
## 3 Application
### Canopy Level  
#### 3.2.1 Diurnal Changes  
Only 12 articles in the last two decades reported canopy PRI for tracking ecophysiological changes at short daily timescales. Ten studies published after 2010 illustrated the increasing applicability of PRI at the canopy scale. The correlations between PRI and ecophysiological variables were lower at the canopy than the foliar level. PRI explained 44%-74% of the variability of the actual quantum yield for broadleaved and herbaceous/crop plants but accounted for only 1%-40% of the variability of \(\Delta\)Fv/Fm' for mixed forests (Figure 5a). PRI also explained 23% and 38% of the variability of RUE for two broadleaved species under salinity stress (Figure 5d) [111]. Median \(R^{2}\) between PRI and RUE and net CO\({}_{2}\) was as high as 0.66 and 0.63, respectively, for herbaceous/crop species (Figure 5d,f). One article reported an \(R^{2}\) between PRI and the chlorophyll/carotenoid ratio of 0.65 in _Pinus sylvestris_ (Figure 5e) [117]. Two articles reported that PRI correlated well with NPQ, with a median \(R^{2}\) of 0.73 (Figure 5c). Three other articles reported slightly variable relationships between PRI and EPS for conifers (Figure 5b).  
Changes in PRI were significantly correlated with pigment contents, similar to the correlation at the foliar level (Figure 6). PRI was strongly correlated with Fv/Fm and non-photochemical quenching (qN) for shrubland at three sites in northern Europe but not for shrubland at southern sites due to the dominance of soil reflectance [62]. PRI explained a mean of 21%-46% and 21%-56% of the variability of water potential and stomatal conductance, respectively. The change in PPFD explained 86% of the change in diurnal PRI patterns for conifers [84], which demonstrated a strong effect of illumination on diurnal PRI patterns.  
Figure 5: Boxplots of the coefficients of determination of the relationships between PRI and the physiological variables at the canopy level and diurnal timescale: (**a**) Actual photochemical efficiency (\(\Delta\)F/Fm); (**b**) Epoxidation state of xanthophylls (EPS); (**c**) Non-photochemical quenching (NPQ); (**d**) Radiation-use efficiency (RUE); (**e**) Carotenoid/chlorophyll (Car/Chl); and (**f**) Net CO\({}_{2}\) uptake. Central lines represent medians, boxes represent 50% of the data, whiskers represent minima and maxima and circles represent outliers. The numbers of correlations reported in the literature are shown in brackets.
# A Data-Driven Approach for Generating Synthetic Load Profiles with GANs
## 3 Results
### Evaluation and Comparison
#### 3.2.4 Overall Model Performance of Conv1D-WGAN-GP  
The results across all datasets consistently highlight the superior performance of the Conv1D-WGAN-GP model, confirming its robustness and generalizability in synthetic time-series generation, particularly for 24 h electrical load profiles. Its design, merging the Wasserstein loss with gradient penalty (WGAN-GP) and convolutional sequence modeling (Conv1D), enables effective capturing of the local temporal dependencies while maintaining training stability--a challenge commonly faced in traditional GAN training.  
Across all four datasets, Conv1D-WGAN-GP consistently achieved the lowest average Wasserstein distance and classifier accuracy. These results are particularly noteworthy because classifier accuracy serves as a proxy for how distinguishable the generated data are from the real samples. The fact that Conv1D-WGAN-GP maintained this indistinguishability even as the dataset size scaled from a few hundred to over 100,000 samples demonstrates its strong capacity to model the underlying data distribution without overfitting or mode collapse.  
Moreover, the model achieved the smallest mean and standard deviation differences in nearly every setting. These low-level statistics suggest that the generated distributions closely match the empirical characteristics of the real data. This was further corroborated by consistently low JS divergence values, indicating tight alignment between real and synthetic distributions.  
Figure 21: Histograms of the 9 th hour for the Pig Farm dataset using Vanilla-GAN (**a**), WGAN-GP (**b**), Conv1D-GAN (**c**), and Conv1D-WGAN-GP (**d**).  
This scalability suggests that the model architecture is not overly sensitive to the volume of training data, making it suitable for real-world industrial applications, such as privacy-preserving smart meter data simulation or renewable energy forecasting augmentation.  
The stability of Conv1D-WGAN-GP training is also worth noting. The use of gradient penalty rather than weight clipping (as in classical WGANs) avoids convergence issues and contributes to more stable discriminator updates.  
Despite the shown strengths, the Conv1D-WGAN-GP model still relies on relatively simple upsampling techniques and linear activation layers within the generator. Future work could explore integrating attention mechanisms, dilated convolutions, or temporal fusion transformers to further enhance its ability to model multi-scale temporal patterns. Additionally, the model currently assumes a fixed-length (24 h) output; adapting the architecture for variable-length or multivariate time-series generation is a promising direction.
## 4 Methodology
### Geographically Weighted Regression  
We utilize geographically weighted regression (GWR) models to estimate station-level ridership. The GWR model is an extension of OLS multiple regression, which is shown as follows:  
\[y_{i}=\beta+\sum_{k=1}^{p}\beta_{k}x_{ik}+\varepsilon_{i} \tag{3}\]  
Local parameters can be estimated by introducing a geographical location factor into the regression, and the extended GWR model is as follows:  
\[y_{i}=\beta_{0}(u_{i},v_{i})+\sum_{k=1}^{p}\beta_{k}(u_{i},v_{i})x_{ik}+ \varepsilon_{i} \tag{4}\]  
where given the observation point \(i\) (\(i=1,\ 2,\ldots,n\)) with longitude/latitude coordinates \((u_{i},v_{i})\), \(y_{i}\) and \(x_{i1}\), \(x_{i2}\), \(\ldots\), \(x_{ip}\) refer to the observed values of the response variable \(y\) and explanatory variables \(x_{1}\), \(x_{2}\), \(\ldots\), \(x_{p}\) of point \(i\), and \(\varepsilon_{i}\) is the error term, following a normal distribution. \(\beta_{k}(u_{i},v_{i})\) (\(k=1,\ 2,\ldots,p\)) denotes \(p\) unknown functions related to spatial location. The geographic location calibrated by \((u_{i},v_{i})\) of each observation point \(i\) is weighted by the GWR model, and the weight is a type of distance decay function [33]. When calculating the distance matrix among stations, the Euclidean distance metric and network distance metric are assessed, and the latter considers that the travel activities always occur along the connection intermedia of the transportation network, such as metro lines and roads [26]. As the network structure of the Shenzhen Metro in 2013 was not particularly complex and there are no clear differences between the results calibrated by the network distance metric and the Euclidean distance metric, we use the Euclidean metric for simplicity of calculation. For application to other networks, the distance metric should be selected considering the network complexity, and more distance metrics related to network accessibility [34]. The determination of bandwidth will directly affect the weight function and the precision of the model, and is therefore critical. GWR4 software (GWR4 User Manual. [[http://geoinformatics.wp.st-andrews.ac.uk/download/software/GWR4](http://geoinformatics.wp.st-andrews.ac.uk/download/software/GWR4) manual.pdf]([http://geoinformatics.wp.st-andrews.ac.uk/download/software/GWR4](http://geoinformatics.wp.st-andrews.ac.uk/download/software/GWR4) manual.pdf).) is used to construct the GWR model, as it includes multiple kernel-type options and bandwidth methods. We select an adaptive bisquare kernel and use AICc to determine the bandwidth of the model, where AICc is the AIC with a correction for small sample sizes.
## 2 Transmission Line Ice Cover Monitoring System
### Multi-Dimensional Dynamic Convolution Feature Fusion Module  
In the complex scenarios of transmission lines, the application of traditional static convolutions lacks flexibility, as they remain unchanged during the network training process. This rigidity prevents adjustments according to the varying feature distributions of different input data, leading to a decline in model adaptability and poorer performance in recognizing insulators in complex scenes [13]. Additionally, the baseline model's use of cross-stage feature fusion strategies may cause feature information to become blurred or overlooked, negatively impacting the model's performance. Furthermore, it requires learning the weights and biases for feature fusion, increasing the risk of overfitting. Therefore, this paper proposes a multi-dimensional dynamic convolution feature fusion module, as illustrated in Figure 4.
## 7 Long-Range Underground Monitoring
### Technology Description
#### 7.2.4 Dashf7  
DASH7 is a LPWAN protocol specification based on ISO 18000-7 [106] which was originally used for active RFID devices. DASH7 has been modified since and now allows for communication over up to two kilometres. It operates in the 433, 868 and 915 ISM bands and can be applied for data rates between 13 and 200 kbps. The technology is represented through the DASH7 Alliance [107].  
The network consists of gateways, nodes and network management software and the topology is a star topology with gateways as central nodes [107; 108; 10].  
The technology is used in applications for smart city, smart parking, safety systems or plants monitoring systems [107]. For underground mining, the use of the technology has been described in [109] for underground event reporting and localization of miners. The authors compare the performance of DASH7 and ZigBee and introduce a multi-hop communication protocol to expand the network in a mining environment. In [110], the link performance of DASH7 in an underground environment is presented. The technology offered ranges of around 100 m in an underground environment. However, more research needs to be conducted to evaluate the performance of DASH7 LPWAN for underground usage.
## 2 Results and Discussion
### Spectrophotometric Analysis of Lyophilized Extract and Deterpenated Material
In the case of TFC, the results were between 8.3 mg RE/g DW in Amnesia Cookies and 22.0 mg RE/g DW in 24 K, while DPPH scavenging activity varied from 24.1 to 41.7 mg TE/g DW in Fresh Mountain and Venom OG, respectively. For comparative purposes, the same spectrophotometric tests were also performed on the dry infloresances of Carmagnola CS, Santhica 70, and Kompolti, which were extracted with an ethanol-water 1:1 solution. As a result, the nine commercial varieties showed an improved TPC, TFC, and DPPH profile compared to the values obtained for the original certified ones (Table 6). These findings were confirmed by literature data. For instance, [PERSON] et al. [53] indicated a TPC between 4.7 and 16.5 mg GAE/g DW for methanol:water extracts from Santhica 70 dried infloresances. Moreover, [PERSON] et al. [54] reported TPC values ranging from 9.3 to 17.1 mg GAE/g DW for Helena aerial part extracts (50% ethanol in water). This solvent:water ratio, which was also chosen in the current research to carry out the tests, guaranteed the best extraction efficiency for phenolic constituents [54]. Based on the provided outcomes, the LE and DM from the nine hemp commercial varieties could represent interesting products that could be exploited for their antioxidant properties. Interestingly, LEs, currently recognized as waste obtained during distillation, represent valuable products to be used on an industrial level.
# Research on an Improved SOM Model for Damage Identification of Concrete Structures
## 4 Experiments and Results Analysis
### Testing of Improved Algorithm Models  
In order to further verify the detection effect of the improved SOM neural network model, the classification results of the detection samples were obtained. The classification labels and sample numbers of winning neurons corresponding to honeycombs, holes, sags and cracks are shown in Table 4. Figure 11 shows the classification results of the detected samples.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Damage Type**} & **Winning Neuron** & **Sample Serial Number** \\  & **Classification Label** & **Sample Serial Number** \\ \hline Cracks & 38 & 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \\ Holes & 16 & 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 \\ Honeycombs & 23 & 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 \\ Sags & 7 & 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Test sample.  
Figure 11: Classification results of the detected samples.  
According to the analysis of Table 3 and Figure 11, the winning neuron corresponding to the test sample is consistent with the actual damage category, and the test sample corresponds to the actual sample type. The damage type corresponding to each sample can be detected based on the improved SOM neural network model.
# Skeleton Tracking Accuracy and Precision Evaluation of Kinect V1, Kinect V2, and the Azure Kinect
## 5 Discussion  
In this paper, we presented the experimental results of the general accuracy and precision of all Kinect versions obtained by measuring a plate mounted to a robotic manipulator end effector which was moved along the depth axis of each sensor. In the second experiment, we mounted a human-sized figurine to the end effector and placed it in the same positions as the test plate. In each position, we measured the relative accuracy and precision (repeatability) of the detected figurine body joints. Based on the presented data, it is safe to say that the Azure Kinect in NFOV mode is more accurate and precise in skeleton tracking than Kinect v1. Kinect v2 standard deviation values are very similar to those of the Azure Kinect; however, as is clear from Figure 18, the NFOV mode of the Azure Kinect is much more stable in terms of accuracy than Kinect v2. Furthermore, the range of the Azure Kinect is higher; it was the only sensor that could capture the figurine even behind the manipulator range; plus, the WFOV mode has a wider \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & **Pos 1** & **Pos 2** & **Pos 3** & **Pos 4** & **Pos 5** & **Pos 7** & **Pos 8** & **Pos 9** \\ \hline Azure NFOV & Avg std & 0.7955 & 1.4593 & 1.1816 & 1.2902 & 1.5918 & 1.6813 & 1.8967 & 17.5621 \\ \hline  & Min std & 0.3868 & 0.4701 & 0.5686 & 0.6996 & 0.8603 & 0.9727 & 0.96 & 8.4145 \\ \hline  & Max std & 1.7289 & 3.2511 & 3.0636 & 2.245 & 2.832 & 3.3347 & 3.499 & 28.6737 \\ \hline Azure WFOV & Avg std & 0.9367 & 1.3618 & 1.4429 & 40.1682 & 16.0603 & 44.1544 & 37.2374 & 12.419 \\ \hline  & Min std & 0.382 & 0.6155 & 0.726 & 10.6573 & 2.5789 & 14.7353 & 13.8637 & 2.7271 \\ \hline  & Max std & 2.1455 & 4.1929 & 3.3282 & 101.0889 & 62.9689 & 119.2252 & 82.6349 & 26.4784 \\ \hline Kinect 2 & Avg std & 0.5162 & 0.452 & 0.7477 & 0.5846 & 0.9744 & 1.145 & 1.8635 & 0 \\ \hline  & Min std & 0.1336 & 0.1087 & 0.2787 & 0.2575 & 0.3879 & 0.5417 & 0.6947 & 0 \\ \hline  & Max std & 2.2119 & 1.6368 & 2.4234 & 1.3069 & 2.8729 & 2.8123 & 6.6177 & 0 \\ \hline Kin 1 & Avg std & 1.3966 & 0.8655 & 0.3485 & 0.5298 & 1.18 & 1.9019 & 10.1528 & 0 \\ \hline  & Min std & 0.319 & 0.0781 & 0.0704 & 0.2106 & 0 & 0 & 0 & 0 \\ \hline  & Max std & 5.3957 & 5.7061 & 0.9518 & 1.1491 & 3.0647 & 16.9649 & 26.1015 & 0 \\ \hline Kin 1 no smooth & Avg std & 1.8913 & 0.6573 & 1.0228 & 1.2459 & 1.8447 & 4.0605 & 15.4636 & 0 \\ \hline  & Min std & 0.2877 & 0.1858 & 0.1416 & 0.234 & 0.5442 & 0.6522 & 4.2336 & 0 \\ \hline  & Max std & 12.9359 & 3.437 & 5.0265 & 6.6438 & 9.2239 & 25.2314 & 51.0188 & 0 \\ \hline \end{tabular}
\end{table} 
Table 4: Key noise data for all positions and sensors.
# An Analytical Multiple-Temperature Model for Flash Laser Irradiation on Single-Layer Graphene
## 3 Linking the Zhukovsky's Formalism and MTM: A Novel Approach  
To the best of our knowledge, there are several articles available on \"Zhukovsky's formalism and MTM\" approach [20; 21; 22], but no attempt has been carried out to link the two approaches with integral transform technique. The results are similar to the other studies but computational technique is unique, simple, and less time-consuming. It recognizes the novelty of this study. According to Ref. [20], linear Fourier equation can be written as  
\[\frac{\partial T}{\partial t}=a\frac{\partial^{2}T}{\partial x^{2}}+2b\frac{ \partial T}{\partial x}+cx\;T(x,t)+dT \tag{7}\]  
We set  
\[b=c=0 \tag{8}\]  
and  
\[a=\gamma \tag{9}\]  
and  
\[d=-\frac{G_{ep}\gamma}{K_{e}} \tag{10}\]  
In Equations (9) and (10), \(\gamma\) is the graphene thermal diffusivity.  
In case of flash laser experiments, one may write for the heat source  
\[T(x,0)\approx S_{laser}.\delta(t) \tag{11}\]  
where  
\[S_{laser}=S_{0}.exp\Big{(}-S_{1}.x^{2}\Big{)} \tag{12}\]  
with  
\[min\;\{\;S_{0},\;S_{1}\}>0 \tag{13}\]  
At the beginning of irradiation in flash laser experiments, we have the following approximation  
\[T_{e}\gg T_{p} \tag{14}\]  
Using Equation (5), we may express the electron temperature as  
\[T_{e}(x,t)=\mathrm{e}^{-\frac{G_{ep}\gamma}{K_{e}}\cdot t}.\frac{S_{laser}}{2 \sqrt{\pi\gamma t}}\;\int_{-\infty}^{+\infty}\mathrm{e}^{-\frac{(x-t)^{2}}{4 \gamma}}.\delta(\xi)d\xi \tag{15}\]  
For phonons, we consider the following heat equation, where the source term is given by a mean electrons temperature:  
\[C_{p,i}\frac{\partial T_{p,i}}{\partial t}=\frac{\partial^{2}T_{p,i}}{\partial x ^{2}}-G_{ep,i}.T_{p,i}+G_{ep,i}.\overline{T}_{e} \tag{16}\]  
A \"parallel\" is then made between the heat equation in standard form and the one in Zhukovsky form. For this, we set  
\[b=c=0 \tag{17}\]  
and  
\[a=\frac{1}{C_{p,i}} \tag{18}\]\[d=-\frac{G_{\sigma p,i}}{C_{p,i}} \tag{19}\]  
Here, \(i\) denotes different kinds of phonon branches:  
\[i=\{\ LA,\ TA,\ ZA,\ LO,\ TO,ZO\} \tag{20}\]  
The final result [20] for the phonons temperature of branch \(i\) (\(C_{p,i}\) is the heat capacity of the phonons of branch \(i\)) is  
\[T_{p,i}(x,t)=\mathrm{e}^{-\frac{G_{\sigma p,i}}{C_{p,i}}\cdot t}\cdot\frac{G_{ \sigma p,i}}{C_{p,i}}\cdot T_{e}\cdot\int\limits_{-\infty}^{+\infty}\mathrm{e} ^{-\frac{(x-i)^{2}}{4}\cdot C_{p,i}}\cdot d\xi \tag{21}\]
## 4 Discussion--Model Validation Results
### Effect of Fuel on the Injection Rate  
Equations (11)-(13) can also model the rate with different fuel origins. To demonstrate this capability, Figure 10a-c are shown. In this case, the test conditions used for graphical comparison are: 70 MPa of injection pressure, ET = 2 ms, 130 \(\upmu\)m as nozzle diameter, and a fuel temperature of 40 \({}^{\circ}\)C. RoI modeled and measured with GtL, HVO, and diesel fuels are shown.  
Figure 10 shows that the model can simulate fuel injection rates with good accuracy. Slight differences in the same order of magnitude are observed with the three fuels studied. In the first and third cases (a and c), the model subestimates the mass flow at 11.15% and 10.87%, respectively, while in case (b), the model subestimates the mass flow at 9.26%.  
Figure 10: Comparison between measured and calculated fuel injection rates with nozzle diameter 130 \(\upmu\)m, ET = 2 ms, and 70 MPa injection pressure, with GtL (**a**), HVO (**b**), and diesel (**c**) fuels.  
Figure 9: Comparative of measured vs. calculated rate with diesel fuel at 70 MPa injection pressure, ET = 1.5 ms, with nozzle diameters 150 (**a**), 130 (**b**) and 115 (**c**) \(\upmu\)m.  
These results could be justified by the differences in the correlations used for fuel property determination, as explained above in Sections 2.2.2 and 2.2.3.