esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Rotational Flow Control
### Example: Centrifugo-Pneumatic Siphon Valves  
In prior publications, we compared different rotationally actuated valves schemes for LoaD systems through a more general digital twin approach [73; 78]. It turns out that normally-closed centrifugo-pneumatic (CP) siphon valves with a compression chamber of volume \(V_{\rm C}\) that is initially sealed by dissolvable-film (DF) membrane offer many operational benefits; amongst them are wide tunability of the critical spin rate \(\Omega\) (5), high operational robustness, and flexible configurability in real space as well as in the frequency domain.  
Figure 1 illustrates the basic operating principle of a CP-DF siphon valve structure \(\Gamma\) located at a radial position R with respect to the axis of rotation at \(\tau=0\). In a (hypothetical) priming procedure, a liquid volume \(U_{\rm Iso}\) is first loaded to completely fill the tiny isoradial channel; as a result, a gas volume \(V_{0}\) composed of a main compression chamber of volume \(V_{\rm C,0}\), an inbound segment of volume \(A\cdot Z\), and tiny outlet features with negligible volume contributions \(V_{\rm out}/V_{0}\ll 1\) is cut off from the inlet that is open to atmosphere at \(p_{0}\) (Figure 1a, typical dimensions in the Appendix A). The actual pressure \(p_{0}^{\prime}\) in the enclosed gas might deviate from the ambient pressure \(p_{0}\), e.g., due to filling dynamics. Then, the remainder of \(U_{0}\) is added to the open inlet reservoir. At the retention rate \(\omega=\Omega\), the outer meniscus has progressed in the radially inbound section of cross section \(A\) and axial length \(Z\) to the crest point at \(R_{\rm crest}=R-Z\) (Figure 1b).  
This high-pass, CP-DF siphon valve opens above \(\omega=\Omega\) once sufficient liquid \(U_{DF}\) has entered the outer chamber to cover the local DF membrane at \(R_{DF}\) (Figure 1c). Strictly speaking, there is a release rate \(\Omega^{*}>\Omega\) needed for displacing \(U_{DF}\) from the inbound section terminated at \(R_{\rm crest}\) into the outer chamber to open the valve. This offset is usually very small and can be calculated from (5) by substituting \(U_{0}\) by \(U_{0}^{\prime}=U_{0}-U_{DF}\); for the sake of simplicity, and unless otherwise mentioned, we assume \(\Omega^{*}\approx\Omega\). Figure 1d displays a multi-segmented design of the core structure \(\Gamma\) used later for advanced optimization.  
Inserting \(p_{\rightarrow}=p_{0}\) and \(p_{\leftarrow}=p_{V}\) (2), we obtain the following:  
\[\Omega=\sqrt{\frac{p_{0}\cdot(V_{\rm C}/V-1)}{\varrho\cdot\overline{\tau} \Delta r}} \tag{6}\]  
for the critical retention rate \(\Omega\) (5) of CP-DF siphon valves with \(V=V_{\rm C}-A\cdot Z\).
# On the Use of Bright Scatterers for Monitoring Doppler, Dual-Polarization Weather Radars
## 3 Results
### On the Very Stable Characteristic of the 1 st Doppler Moment (Mean Radial Velocity)
#### 3.3.1 Central Location of the Radar Reflectivity: Three Location Parameters  
Three location parameters that describe the central location of the distribution of the radar reflectivity over the selected five days are shown in Tables 2 and 3 for horizontal and vertical polarization, respectively. The 2 nd column shows the Log of the mean value, while the 3 rd column shows the mean value of the log-transformed values: Since the algebraic average is always greater than (or equal to) the geometric average, it is obvious that the Log of the mean value is larger than  
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Date**} & **DN = 128** & **DN = 127** \\  & **Mean Rad. Vel. = 0 m/s** & **Mean Approaching Vel. = 0.06 m/s** \\ \hline
5 January 2015 & 249 & 39 \\
9 February 2015 & 2 & 286 \\
10 February 2015 & 286 & 2 \\
13 October 2016 & 35 & 253 \\
18 January 2017 & 6 & 282 \\ \hline \end{tabular}
\end{table}
Table 1: Daily number of occurrences (temporal resolution is 5 min) of the mean radial velocity values for the high resolution Monte Lema radar cell on Cimetta that hosts the tall tower.  
the mean of the Log. However, it should be noted that the two central location values only differ by a fraction of dB; this, in turn, implies the presence of a point target with a large radar cross section (\"bright\" scatterer). The last column shows the log-transformed median. It is easy to derive the Log-transformed ratio between the average and median reflectivity: It is simply the difference between the values in column 2 and those in column 4. The five values of the horizontal polarization range from 0.03 dB (10 February 2015) to 0.39 dB (5 January 2015), which is typical of a Rice distribution that has a much larger contribution from the point target than from the background. The five values of the vertical polarization range from \(-1.15\) dB (10 February 2015) to 0.47 dB (18 January 2018), and are not compatible with a Rice distribution; they instead indicate a probability distribution function that is skewed to the left.
## 2 Basic Theory and Calculation Method
### [PERSON]'s Solution  
[PERSON] used the mirror source-sink method, assumed that the surface is free, the soil is isotropic, and incompressible. The analysis steps are as follows and in Figure 3:First step: The existence of the original surface is ignored, and the half-space problem is transformed into the internal gap problem of full space. Under the action of a source gap, stress field changing, there will be the normal stress \(\sigma_{0}\) and the shear stress \(\tau_{0}\) at the original surface position.  
Second step: A sink is set at the mirror position of the source gap above the original surface; there is a volume expansion of the same size at the sink position. The sink expansion will produce a normal stress \(-\sigma_{0}\) of the same value and opposite direction and a shear stress \(\tau_{0}\) of the same value and same direction at the original surface position. Therefore, under the action of source and sink, the normal stress on the original surface can be offset, which does not exist in practice.  
Third step: Under the action of source and sink, a shear stress \(-2\tau_{0}\) of twice the value and opposite direction is supposed at the original surface position and the corresponding displacement field of the surface shear stress below the surface at each point can be obtained.  
Final step: The displacements generated by the above three steps at any point below the surface are \(S_{1}\), \(S_{2}\), and \(S_{3}\), respectively. The displacement solution of the practical problem is \(S=S_{1}+S_{2}+S_{3}\).  
Based on above steps, [PERSON] deduced the expression of surface displacement caused by tunnel construction is as in Equation (8):  
\[\left\{\begin{array}{l} S_{x0}=-\dfrac{v_{\text{loss}}}{2\pi} \dfrac{x}{x^{2}+H^{2}}\Bigg{[}1+\dfrac{y}{(x^{2}+y^{2}+H^{2})\dfrac{1}{2}} \Bigg{]}\\ S_{y0}=\dfrac{v_{\text{loss}}}{2\pi}\dfrac{1}{\dfrac{1}{(x^{2}+y^{2}+H^{2}) \dfrac{1}{2}}}\\ \hskip 14.226378 pt S_{z0}=\dfrac{v_{\text{loss}}}{2\pi}\dfrac{H}{x^{2}+H^{2}} \Bigg{[}1+\dfrac{y}{\dfrac{1}{x^{2}+y^{2}+H^{2})\dfrac{1}{2}}}\\ S_{x0}(y\rightarrow\infty)=-\dfrac{v_{\text{loss}}}{\pi}\dfrac{(x^{2}+y^{2}+H^{ 2})}{x^{2}+H^{2}}\\ S_{z0}(y\rightarrow\infty)=\dfrac{v_{\text{loss}}}{\pi}\dfrac{H}{x^{2}+H^{2}} \end{array}\right. \tag{8}\]  
Figure 3: Analysis steps of mirror source–sink method.  
where \(V_{loss}\) is stratum loss. Contrastive Equation (8) can be found:  
\[\left\{\begin{array}{l} S_{x0}(y)=S_{x0}(y\rightarrow\infty)\times \frac{1}{2}\times\left[1+\frac{y}{(x^{2}+y^{2}+H^{2})\frac{1}{2}}\right]\\ S_{20}(y)=S_{z0}(y\rightarrow\infty)\times\frac{1}{2}\times\left[1+\frac{y}{(x ^{2}+y^{2}+H^{2})\frac{1}{2}}\right]\\ \end{array}\right.. \tag{9}\]
## 4 Results
### Optimal Parameter Settings for the Individual Performance Measurements
#### 4.1.1 Printing Time
This is also confirmed from the results showing that the 1400 mm/min printing speed was interacting with the 0.3 mm layer thickness and with the 0\({}^{\circ}\) build orientation which generates the shortest mean printing time. It can be interpreted that one process parameter is less affected by another parameter if the lines on an interaction effect plot are close to parallel lines. Overall, the interaction effects existing in the ASTM D695 case are weaker than those of other design cases although the interaction effects are statistically significant. For example, the layer thickness for the ASTM D695 design affects less the relationship between the build orientation and the printing time, relatively, than the layer thickness for other designs. The above main interaction effects of the process parameters on the printing time may result from the characteristic of FFF that stacks the material layer by layer. In the fabrication process of each layer, the nozzle moves back to the default position when the deposition of one layer is completed, and then the next layer is filled. In other words, the nozzle movement time increases as the number of layers increases. This can be a plausible reason for the impacts of the process parameters that increase printing time. When the layer thickness decreases, the total number of required layers for the print increases since more layers should be deposited for the same dimensions. Moreover, the number of layers increases when the 90\({}^{\circ}\) build orientation is used. For example, ASTM D638, ASTM D695, and ASTM D3039 have 16 layers, 64 layers, and 16 layers, respectively, when they are fabricated at the 0\({}^{\circ}\) build orientation; they increase to 48 layers, 127 layers, and 64 layers at the 90\({}^{\circ}\) build orientation. Consequently, the build orientation at 90\({}^{\circ}\) negatively affects the printing time. Table 7 shows the printing time of each parameter combination for all the design cases, which are estimated by the prediction model only including the significant factors. In summary, the same process parameter settings are associated with a minimum printing time regardless of the design cases; the parameter combination of 0.3 mm (layer thickness), 0\({}^{\circ}\) (build orientation), and 1400 mm/min (printing speed) provides the minimum printing time for each design case. Therefore, these parameter settings can ensure the shortest printing time to fabricate outputs using CFR-PEEK if the operational objective of the additive manufacturing is only only minimize printing time. Figure 5: Main effect plots of the significant factors for printing time. (**a**) ASTM D638; (**b**) ASTM D695; (**c**) ASTM D3039. Figure 6: Interaction effect plots of the significant factors for printing time. (**a**) ASTM D638; (**b**) ASTM D695; (**c**) ASTM D3039.
## 2 Method Development  
### Overview  
Figure 1 provides an overview of the method. As shown, the citation network was converted into an unweighted network with papers as nodes and citation relationships as links (Step 1 in Figure 1). Because core papers always constitute the largest component, direct citation is the most effective means of detecting research frontiers. In fact, not all papers are closely related to the target fields of nanocarbons. Papers having no citations as the largest component were considered digressional and were ignored in this study (Step 2 in Figure 1). The network was then divided into several clusters [41, 42] using the topological clustering method [42] (Step 3 in Figure 1). Topological clustering is a clustering method based on the graph structure of a network, and here we use a modularity maximization. Here, a cluster is a module in a citation network and is a group of papers in which the citation relations are divided using a modularity (\(Q\) value) maximization method and are densely aggregated [42]. The modularity maximization method appreciates network partitioning such that the intracluster is dense and the intercluster is sparse. The modularity maximization method determines an optimal partitioning pattern by extracting the partitioning pattern that maximizes the modularity by a greedy algorithm. \(Q\) is an evaluation function of the degree of coupling within a cluster and between clusters and is given below.  
\[Q=\sum_{i}\left(e_{ii}-a_{i}^{2}\right) \tag{1}\]  
Here, \(e_{ii}\) is the ratio between the number of links connected to nodes belonging to the same cluster \(i\) and the number of links in the entire network. Additionally, \(a_{i}^{2}\) is the expected value of the ratio between the number of links of \(e_{ii}\) and the total number of links.  
Next, an emerging paper was defined, features were extracted from the cited networks, and the constructed machine learning model was evaluated (Step 4). Emerging papers were defined as papers that were ranked in the top 5% of the dataset each year and whose citations increased for three years after publication. Step 4 will be described in detail after the following task definition. Using the predicted emerging paper results, the topics of the clusters were further analyzed to address the emergence by area and paper (Step 5 in Figure 1).
## 3 Results and Discussion
It is also important to note that the cultivated plant species differ in their requirements for K. Winter rapeseed exhibits the highest K uptake, while potatoes have the lowest requirements. Therefore, in the case of potatoes, the introduction of K through BAs resulted in only a slight increase in the amount of this element in the soil, compared to the control. It is worth noting that the experiment was conducted on haptic luvisol soil with a silt granulometric composition. Such soil is inherently well-drained, which may lead to substantial leaching of K from the applied BAs [52; 53]. Leaching losses of potassium (K) may have reached 22% and 16% of the applied K in sandy loam and loamy soils, respectively, in submerged moisture conditions [54]. For this reason, substituting K fertilization with BAs may prove insufficient, particularly in conditions of increased rainfall or in soils with good drainage. A better alternative might be to split the planned doses over time to provide nutrients to plants throughout the entire growing season. However, this requires further research. The absence of increased salinity, despite the high content of soluble salts in the BAs introduced into the soil, may indicate the leaching of potentially soluble nutrients. However, such changes in field conditions are difficult to capture and require detailed laboratory studies. Additionally, in other research where the effects of the same BAs on the soil were observed in controlled conditions, no significant increase in the Ca, Mg, K, and Na cations in the soil solution was found. However, a substantial increase in the concentration of these elements was noted in the seeds of spring rapeseed [11]. This may support the theory that the application of BAs induces an increase in Ca, Mg, K, and Na content in plant biomass. Changes in soil environmental properties that occur as a result of neutralizing soil acidity and the toxic effects of Al\({}^{3+}\) contribute to better crop yields and nutrient uptake [22]. The application of BAs, similar to liming, also affects other soil properties, including its structure and biological characteristics. In general, an increase in the activity and abundance of soil microorganisms is a result of applying BAs, primarily due to the increase in pH [34; 37]. The introduction of BAs, especially in acidic soils, improves conditions for the activity of nitrifying and ammonifying bacteria [55]. Although BAs do not contain N, their application can promote the mineralization of large reserves of organic N in the soil, improving its availability for cultivated plants. The application of BAs often enhances soil nutrients and plant nutrient uptake, thereby increasing crop biomass and yields [24]. Furthermore, the increase in plant biomass resulting from improved soil conditions leads to a greater accumulation of nutrients, particularly Ca, Mg, and K, which are subsequently absorbed by the plants. This may indicate a dependency on these factors. Additional studies are necessary, particularly regarding other elements in BAs, including heavy metals.
## 3 Results  
### Climate Anomalies  
We first analyzed the temporal evolution of JAS climatic and vegetation-related anomalies from 2000 to 2022 (Figure 2). Based on the temporal series, this study defined a year as experiencing a CHD event if the T2m anomaly exceeded one standard deviation (STD) and, simultaneously, the magnitude of the negative SM anomaly also exceeded one STD. Using this definition, we identified three CHD years: 2003, 2013, and 2022 (Figure 2a). The magnitude of climatic and vegetation-related anomalies of the three CHD years are shown in Table 1.  
Among the three CHD years, 2022 experienced the strongest CHD event, with an average positive T2m anomaly of 1.33 K and an average negative SM anomaly of \(-0.05\) m\({}^{3}\) m\({}^{-3}\). The CHD events in 2003 and 2013 were weaker. The average positive T2m anomalies in 2003 and 2013 were 0.68 K and 0.61 K, respectively, and their average negative SM anomalies were about \(-0.01\) m\({}^{3}\) m\({}^{-3}\) and \(-0.02\) m\({}^{3}\) m\({}^{-3}\), respectively. These hot and dry conditions also resulted in positive anomalies in VPD, with 2022 being the strongest (3.84 hPa), followed by 2013 (1.96 hPa) and 2003 (0.83 hPa). Simultaneously, DSR showed positive anomalies in the years 2013 and 2022, with amplitudes of 13.38 W m\({}^{-2}\) and 21.27 W m\({}^{-2}\), respectively, while the year 2003 showed a slightly negative anomaly in DSR (\(-1.02\) W m\({}^{-2}\)).  
Figure 3 further shows the spatial distribution of climatic anomalies for the three CHD years. During the strongest CHD year of 2022, the entire YRB was concurrently characterized by very high T2m and notably low SM across all grid points. Additionally, relatively high VPD and DSR were also observed throughout the YRB. In 2003, the higher T2m anomalies were mainly concentrated in the coastal provinces of the YRB, and meanwhile, these provinces also had lower SM, higher VPD, and increased DSR. In 2013, the climate anomalies in the YRB were similar to those in 2022, but the intensity was weaker, especially with opposite signals observed in the western and southern grid points of the YRB. The different distributions of climate anomalies among these three CHD years may lead to varying responses in regional GPP.  
Figure 2: Temporal series of climatic and vegetation-related JAS anomalies from 2000 to 2022. Panel **(a)** is for 2 m air temperature (T2m, units: K) and soil moisture (SM, units: m\({}^{-3}\) m\({}^{-3}\)), and the red and blue dashed lines represent one standard deviation of T2m and SM, respectively. The stars in **(a)** represent the identified CHD years: 2003, 2013, and 2022. Panel **(b)** is for vapor pressure deficit (VPD, units: hPa) and downward solar radiation (DSR, units: W m\({}^{-2}\)), and panel **(c)** is for the two GPP products (GPP\({}_{\text{GOSIF}}\) and GPP\({}_{\text{FluxSat}}\), units: gC m\({}^{-2}\) day\({}^{-1}\)) and Enhanced Vegetation Index (EVI\({}_{\text{MODIS}}\), unitless).
## 2 Data and Methods  
### Study Area  
Mongolia spans 41\({}^{\circ}\)35\({}^{\prime}\)-52\({}^{\circ}\)09\({}^{\prime}\) N in latitude and 87\({}^{\circ}\)44\({}^{\prime}\)-119\({}^{\circ}\)56\({}^{\prime}\) E in longitude, with an area of 1.565 million km\({}^{2}\). It has an average elevation of 1580 m AMSL, which gradually increases from east to west (Figure 1). The country has a variety of land features, including vast semi-desert and desert plains, grassy steppe, and mountains. Most of the places (52%) experience arid climatic condition, which can be further categorized into hyper-arid (5.13%), arid (6.74%), and semiarid (40.13%) environments [12]. Mongolia receives relatively low precipitation, although there is high variation in its spatial distribution. As per the station data, the annual rainfall ranges from 50 to 150 mm in desert and semi-desert areas, while precipitation in other regions ranges from 250 to 400 mm. The region receives most of its rainfall (about 85%) in the growing season (May-September) [39]. The annual mean temperature in Mongolia is around 0 \({}^{\circ}\)C, with a north-south gradient ranging from \(-8\) to 6 \({}^{\circ}\)C. However, it experiences highly fluctuating temperatures across different seasons in the year. The maximum temperature in winter (November-April) remains between \(-30\) and \(-40\)\({}^{\circ}\)C in many regions and as low as \(-48\)\({}^{\circ}\)C in the mountains. In summer (June-August), temperatures rise sharply and reach as high as 40 \({}^{\circ}\)C in some places such as the South Gobi. The major land use types include alpine tundra (3.0%), mountain taiga (4.1%), mountain steppe and forest steppe (25.1%), grass steppe (26.1%), desert steppe (27.2%), and desert (14.5%) [40]. Generally, forest steppe has the highest productivity, followed by the steppe, desert steppe, and desert zones. There are 3191 taxa of vascular plants belonging to 684 genera of 108 families documented in the flora of Mongolia [41].  
Figure 1: Territory of Mongolia, its locations in Asia, distribution of observation sites, and land coverage.
## 3 The Case of Finite Exchangeable Sequences
### Exact Finite Representation as a Mixture of Urn Sequences
Note that due to the random permutation, we obtain a random sequence, even though \(x\) is deterministic. Now we can state the result, after Kallenberg [12], but using our own notations:  
**Theorem 9** (Urn representation). : _Let \(X=(X_{1},\ldots,X_{n})\) be a finite exchangeable sequence of random variables, each \(X_{i}\) taking values in a measurable space \(S\). Then \(X\) can be represented as a mixture of urn sequences. Formally, there exists a probability measure \(\mu\) on \(S^{n}\) (mixing measure), such that for any \(A\subseteq S^{n}\)_  
\[\Pr(X\in A)=\int_{S^{n}}\Pr\big{(}\,\sigma_{x}(x)\in A\,\big{)}\,d\mu(x)\]  
_holds, where \(\sigma_{x}\in\Sigma_{n}\) is a uniform random permutation, drawn independently for every \(x\in S^{n}\)._  
Observe that Theorem 9 shows a direct analogy to Theorem 1, replacing the i.i.d. Bernoulli sequence with a finite urn sequence, giving us the finite length analogy of [PERSON]'s Theorem. In the special case when \(S=\{0,1\}\), using the hypergeometric distribution formula (4), we can specialize it to the following result, resembling the conditional independence form of de Finetti's Theorem, given in Theorem 2:  
**Theorem 10**. : _Let \(X_{1},X_{2},\ldots,X_{N}\) be a finite sequence of \(\{0,1\}\)-valued exchangeable random variables. Then there exists a random variable \(\eta\), taking values in \(\{0,1,\ldots,N\}\), such that for every \(n\in[N]\) and \(k\in\{0,1,\ldots,n\}\), the following holds:_  
\[\Pr\left(\sum_{i=1}^{n}X_{i}=k\ \ \big{|}\ \ \eta=K\right)=\frac{\binom{K}{k} \binom{N-K}{n-k}}{\binom{N}{n}}. \tag{5}\]  
_Furthermore, \(\eta\) is given as the number of ones in the sequence, representing the empirical distribution:_  
\[\eta=\sum_{i=1}^{N}X_{i}.\]  
Theorem 10 says: given that the length-\(N\) exchangeable sequence contains \(K\) ones, it behaves precisely as an urn sequence that contains \(K\) ones. This also provides a simple algorithm to generate the exchangeable sequence: first pick \(\eta\) from its distribution, and whenever \(\eta=K\), then generate an urn sequence with \(K\) ones. The distribution of \(\eta\) (the mixing measure) can be obtained as the empirical distribution of ones in the original sequence. The sequence generated this way will be statistically indistinguishable from the original.