esa-sceva/satcom-chunk-collection huggingface dataset:
# Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control
## 4 A Priori Bounds for CIA Decompositions
### Connection to Decomposition Algorithm and Optimization Problem  
As a last step in this chapter, the previous results are related to (MIOCP) and the decomposition Algorithm 1.  
**Remark 2** (**Arbitrary close approximation of (OCP) solution**).: _We could extend Algorithm 1 with an outer loop that checks if \(\Phi^{\mathrm{opt}}\) is sufficiently close to \(\Phi^{\mathrm{rel}}\), and if not, we would refine the grid \(\mathcal{G}_{\omega}\). In [29], an arbitrary close approximation of the (OCP) solution has been deduced with this procedure and based on (CIA). With the assumption of \(\Phi(\cdot)\), \(c(\cdot)\) being continuous and that there exists a feasible trajectory \(\mathbf{x}\) for (OCP), it follows that for any \(\epsilon>0\) there exists a grid \(\mathcal{G}_{\omega}\), with grid size \(\Delta_{\max}\), such that there is a feasible trajectory \(\{\mathbf{y}(t)\}_{t\geqslant\mathcal{G}_{\omega}}\) with:_  
\[|\Phi(\mathbf{x}(t_{f}))-\Phi(\mathbf{y}(t_{f}))|\leq\epsilon,\] \[\|\mathbf{c}(t_{j},\mathbf{x}(t_{j}))-\mathbf{c}(t_{j},\mathbf{ y}(t_{j}))\|\leq\epsilon.\]  
_The proof uses the sum-up rounding scheme that derives the binary control approximation with \(\theta^{\bullet}_{\mathrm{CIA}}\leq Const(n_{\omega})\Delta_{\max}\)[35; 41], where \(Const(n_{\omega})\) is a constant depending on \(n_{\omega}\). In case we extend Algorithm 1 with the refinement procedure, and if (CIA) or (SCIA) are chosen to be elements of \(S^{\mathrm{CIA}}\), the same approximation result holds._  
**Corollary 5** (**Solution accuracy of differential states of Algorithm 1**).: _Let \(\theta^{\bullet}_{\mathrm{SCIA},\max}\), \(\theta^{\bullet}_{\mathrm{SCIA},1}\) be the optimal objective values of (SCIAmax) and (SCIA1), respectively. Consider the setting of Theorem 1. In particular, let the regularity assumptions (17d), (17c), and essential boundedness of \(\mathbf{f}\) be true. Assume that \(\mathbf{x}\) and \(\mathbf{y}\) are the solutions of the IVP (2b) and (2c), where \(\mathbf{x}\) is based on a given \(\mathbf{a}\), and \(\mathbf{y}\) is based on Algorithm 1. Let \(\mathcal{G}_{\omega}\) be the applied grid. It follows for \(t_{i}\in\mathcal{G}_{\omega}\) that:_  
\[||\mathbf{y}(t_{i})-\mathbf{x}(t_{i})||_{j}\leq\Big{(}||\mathbf{y}_{0}- \mathbf{x}_{0}||_{j}+\theta^{\bullet}_{\mathrm{SCIA},j}\Big{)}e^{L(t_{i}-t_{0 })},\qquad j\in\{\max,1\}. \tag{24}\]  
Proof.: The claim is a direct result of Corollary 2.  
We have deliberately chosen the tightest bound from the previous corollaries, but could also use others. The received grid-specific rounding error bounds aim primarily at approximating the differential states. With (\(\lambda\)CIA) or Lipschitz continuity of the objective, there are also tools to discuss the rounding error of the objectives. The recombination heuristics work in the area of objective approximation and, hence, are to be discussed next.
# Optimization of Signal Detection Using Deep CNN in Ultra-Massive MIMO
## 2 Materials and Methods
### Traditional Method
#### 2.2.1 Zero Forcing Detector  
Zero forcing was an early concept in channel estimation. By detecting signals, this type of estimation is classified as a one-dimensional (1D) estimator, which means that the channel estimation is performed using test cycles. In one dimension, whether frequency or time, (ZF) signal detection reduces the amount of squared error between the received signal and the estimated value. As a result, it is possible to find \(\widetilde{X}_{ZF}\) signal detection by  
\[\hat{H}_{ZF}=\text{argmin}_{H_{ZF}}\|Y-H_{ZF}X\|\|^{2} \tag{5}\]  
On the other hand, the signal detection can be written in the following form:  
\[\widetilde{X}\ =H^{\dagger}Y \tag{6}\]  
All transmitting and receiving antennas, the impulse response signals are encapsulated and presented in the form of a matrix by  
\[\widetilde{X}_{ZF}=YH^{H}(HH^{H})^{-1} \tag{7}\]  
In this formulation, \((*)^{H}\) is designated as the conjugate transpose of the matrix, and \((*)^{-1}\) pertains to the inverse of the matrix.
## 3 Results  
### The Use of UV Radiation to Remove Selected Dyes  
UV radiation without the addition of a catalyst proved ineffective in removing all analyzed dyes (Figure 2). UV radiation primarily acts through direct photolysis, breaking the chemical bonds in the dye molecules. Its effectiveness depends on the ability of a given dye to absorb UV light. The addition of a TiO\({}_{2}\) catalyst significantly improved the degradation efficiency of Indigo Carmine. Indigo Carmine strongly absorbs UV radiation, leading to the direct photolysis of chromophoric systems and rapid decolorization. When UV radiation is absorbed by these molecules, the UV energy excites electrons within the molecular structure of the dye. This leads to the breaking of double bonds in aromatic rings or other functional groups within the dye molecule. Meanwhile, the catalyst, under UV radiation, generates hydroxyl radicals and excited-state electrons. These radicals are strong oxidizers that can further degrade the dye molecules by breaking chemical bonds such as -C=C- in unsaturated bonds or -N=N- in azo rings [31].  
In contrast, the removal of Allura Red AC increased from 8.52% to 42.5%. No statistically significant difference was observed at different time points. However, UV radiation had the least impact on the removal of Tartrazine. The efficiency decreased upon the introduction of the catalyst. UV can partially break azo -N=N- bonds and aromatic rings, but the reaction is slow.  
This study also examined the effect of catalyst dosage on the removal efficiency of Indigo Carmine, which demonstrated the highest removal effectiveness (Figure 3). A fivefold increase in dosage resulted in an increase in removal efficiency from 82% to 95% after 30 min.  
Studies on the removal of Indigo Carmine from aqueous solutions using UV radiation were also conducted by [PERSON] and [PERSON] (2022) [32]. They achieved an average removal efficiency of 98% for this dye with a relatively short UV exposure time of 25 min (pH = 2.5). The dose of the TiO\({}_{2}\) catalyst and the pH played a significant role. [PERSON] et al. (2016) [4] reported that UV-irradiated TiO\({}_{2}\) alone achieved 93.3% color removal within one hour of reaction time. On the other hand, the study by [PERSON] et al. (2015) [33] demonstrated that, within 60 min of the photocatalytic reaction, 95% degradation of Indigo Carmine was achieved at 25 \({}^{\circ}\)C under acidic pH, with an optimal catalyst dose of 0.75 g/L and an IC concentration of 5-10 mg/L.
# A Survey of Precision Formation Relative State Measurement Technology for Distributed Spacecraft
## 1 Introduction  
With the continuous exploration of space, spacecraft formation flying has become a hot topic in the aerospace field [1]. The spacecraft formation utilizes a variety of sensors to form a \"large virtual spacecraft\" to complete high-precision and high-complexity space missions that cannot be completed independently by a single spacecraft [2]. While saving costs, it improves sensitivity and reliability, greatly optimizes the overall performance of the spacecraft system and expands the application field.  
Depending on the closeness of the dynamics between the formation spacecraft, as shown in Table 1, formation flying can be divided into precision formation, cooperative formation, and knowledge formation. Precision formations apply relative measurement and precision control techniques to maintain the formation shape and position for long periods of time, with specific applications that include virtual telescopes and synthetic aperture radars. Due to the increasing difficulty of space tasks, precise spacecraft relative measurement technology, as the cornerstone of formation control and the key to autonomous relative navigation, faces many challenges. In view of this key technology, this paper outlines the current research status of distributed spacecraft precision formationprojects and analyzes the technical characteristics and application scenarios of relative state measurement technology, such as GNSS, radio, laser, vision, and new composite technologies. The optimization method and development trend of the relevant technologies are further elaborated.
## 3 Results and Data Analysis
### Distribution Pattern of Wind Pressure Coefficient at \(0^{\circ}\) Wind Angle  
(1) Figure 3 shows the cloud chart of wind pressure coefficients of the north wall at \(0^{\circ}\) wind angle with different sizes. As can be seen from Figure 3, the substantial proportion of the surface area on the north wall of the solar greenhouse with five sizes experiences positive pressure. The wind pressure coefficient in the central zone is relatively high, whereas it decreases significantly in the surrounding areas. It is remarkable that the wind pressure coefficient in the central region consistently remains above 0.6. As the height of the wall increases, there is a corresponding rise in the extent of regions experiencing positive wind pressure. To assess the effect of varied north wall height on its wind pressure coefficient, we selected data points at heights of h/2 plotting curve, capturing one point every 0.5 m, resulting in a total of 121 data points, as presented in Figure 4. Remarkably, the north wall positive wind pressure coefficient value exhibited an increase as the height increased.  
(2) The cloud chart of wind pressure coefficients at the rear roof, as presented in Figure 5, elucidates that the majority of the rear roof heights of five sizes exhibit wind pressure coefficients around 0. Notably, a discernible pattern of increased negative wind pressure is observed along the east, west, and front boundaries. Comparative analysis of the cloud chart of wind pressure coefficients at various sizes indicates a positive correlation between solar greenhouse size and the areas where the absolute value of the negative wind pressure coefficient is around 0, with the span at 16 m coming out of the wind pressure coefficient greater than 0.2.  
(3) Figure 6 illustrates a cloud chart of wind pressure coefficients for a range of front roof sizes, totaling five different configurations. Within these front roofs, specific regions exhibit absolute wind pressure coefficient values below 0.4, and the extent of these regions diminishes as solar greenhouse size increases. Concurrently, there was an evident increase in wind suction per unit area as size expands, indicating a direct correlation between size and wind suction. Moreover, areas featuring absolute wind pressure coefficient values within the 0.4-0.6 range expand with increasing size. In addition, the concentration of wind suction is most pronounced around the crest of the front roof. Intriguingly, as the spans increase from 8 m to 16 m, the extreme value of negative wind pressure coefficient undergoes a gradual transition from \(-\)1.8 to \(-\)2.4.  
Figure 4: Wind pressure coefficient curve at h/2 height of north wall with different sizes.  
Figure 3: Cloud chart of wind pressure coefficients on the north wall of solar greenhouse with five different sizes under 0\({}^{\circ}\) wind angle.  
Figure 5: Cloud chart of wind pressure coefficients on the rear roof of solar greenhouses with five different sizes under 0\({}^{\circ}\) wind angle.  
Figure 6: _Cont._
# Experimental Study of See-Saw Mode Nano-Vibration on Orifice-Type Restrictors
## 2 Materials and Methods
### Time-Domain Results of Restrictors' Vibration  
Figure 8 shows the vibration measurement results of the double-ring- and double-U-grooved-style restrictors under 0.5 MPa and no gas where A is the vibration displacement. The data in the picture were 5 KHz high-pass filtered so that low-frequency interference signals would not overwhelm the high-frequency ones.  
Figure 8 also shows that the amplitude of the vibration signal changed significantly under an air-supply pressure of 0.5 MPa. Although the amplitude was very small (<1 nm), it was evident, indicating that the air-supply pressure significantly affected the amplitude. To further examine the relationship between air-supply pressure and vibration, the time-averaged vibration amplitudes, Aa, at 5.12 s, at different positions, are listed in Table 1 (P1-P7 are for the double-ring-grooved, and P1(U)-P7(U) are for the double-U-grooved)  
Figure 7: Block diagram of the measurement process.  
as plotted in Figure 9. When the air-supply pressure gradually increases, the vibration is mainly increased.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Gas Source (MPa)** & **P1** & **P2** & **P3** & **P4** & **P5** & **P6** & **P7** & **P1(U)** & **P2(U)** & **P3(U)** & **P4(U)** & **P7(U)** \\ \hline No gas & 0.21 & 0.29 & 0.26 & 0.28 & 0.18 & 0.17 & 0.18 & 0.39 & 0.35 & 0.32 & 0.45 & 0.33 \\
0.1 & 0.55 & 0.39 & 0.69 & 0.61 & 0.16 & 0.16 & 0.14 & 1.94 & 2.01 & 2.14 & 2.17 & 0.59 \\
0.2 & 0.71 & 0.43 & 0.81 & 0.68 & 0.18 & 0.18 & 0.16 & 2.16 & 2.52 & 2.25 & 2.34 & 0.68 \\
0.3 & 0.97 & 0.57 & 0.87 & 0.70 & 0.21 & 0.20 & 0.19 & 2.87 & 2.96 & 2.72 & 2.99 & 1.93 \\
0.4 & 1.10 & 0.74 & 0.89 & 0.88 & 0.24 & 0.21 & 0.20 & 3.21 & 3.37 & 3.49 & 3.42 & 2.03 \\
0.5 & 1.42 & 1.64 & 1.29 & 1.31 & 0.27 & 0.26 & 0.24 & 5.12 & 4.98 & 5.37 & 5.51 & 3.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Time-averaged amplitude \(A_{a}\) under different air-supply pressures (nm).  
Figure 8: Time-domain vibration data under 0.5 Mpa and no gas: (**a**) double-ring-grooved; and (**b**) double-U-grooved.
## 2 Concept and Configuration of the Proposed System  
Figure 1 shows the configurations of the proposed precast rocking walls incorporating tension-compression and shear steel energy dissipaters (PRW-TSD). The rocking wall in the system consists of two or more precast concrete wall panels spliced together. Each wall panel has a polyvinyl chloride duct embedded in the center for unbonded post-tensioning (PT) strands to connect the foundation. The wall panels are erected with a grouting layer between them and the foundation, without any connecting reinforcements except the PT strands. Several tension-compression energy dissipaters, called miniature bar-type structural fuses (MBSFs) [30; 31], are set across the horizontal joints between the wall panels and the foundation. Simultaneously, the precast wall panels are connected to each other by shear energy dissipation plates (SEDPs) at the vertical joints between the wall panels. During an earthquake, the horizontal joint between the wall panel and the foundation (wall-footing joint) will open and close in an alternating fashion due to the rocking behavior, and the MBSFs will produce tension-compression alternative deformation. In addition, since the two sides of the vertical gap between the two adjacent wall panels move conversely due to the seismic action, the SEDPs will deform in a shear mode. Therefore, during the rocking behavior of the precast walls under seismic loading, the MBSFs and SEDPs can dissipate earthquake-input energy by tension-compression and shear plastic deformations, respectively. As a result, the precast wall panels are protected, with little or no damage caused by the earthquake. Moreover, the MBSFs and SEDPs can also help to adjust the lateral stiffness and load-bearing capacity of the PRW-TSD system together with the prestressing tendons. The prestressing force generated by the PT strands improves the self-centering capacity and reduces the residual drift of the system under earthquake actions. The PRW-TSD system is constructed by dry connections, which eliminate complex steel bar alignment work and concrete pouring at construction sites. The working labor is also reduced due to the convenient and speedy construction process. Note that the MBSFs and SEDPs are all mounted onto the external sides of the wall panels, which are easy to repair and replace after earthquakes.  
Figure 1: Configurations of the PRW-TSD system.
## 2 Materials and Methods
### Parameter Calibration Experimental Design
#### 2.5.2 Single-Factor Test Design  
Based on materials with similar mechanical properties and the results of multiple preliminary tests [23; 37], the parameter ranges for the discrete element simulation of FTB were defined, as presented in Table 2. A single-factor test was applied to examine the effect of each parameter on the maximum shear force of FTB [23; 39].  
The single-factor test was designed in the EDEM discrete element simulation software, with maximum shear force as the evaluation index. Parameters \(x_{1}\) to \(x_{6}\) were each tested at five levels, as detailed in Table 3. During the simulations, the median value among the five levels, namely the third level, was set as a constant.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Particle contact radius \(x_{1}\)/mm & 1.2\(\sim\)2.0 \\ Normal stiffness per unit area \(x_{2}\)/(N\(\cdot\)m\({}^{-3}\)) & 1.0 \(\times\) 10\({}^{7}\)–9.0 \(\times\) 10\({}^{8}\) \\ Tangential stiffness per unit area \(x_{3}\)/(N\(\cdot\)m\({}^{-3}\)) & 1.0 \(\times\) 10\({}^{7}\)–9.0 \(\times\) 10\({}^{8}\) \\ Critical normal stress \(x_{4}\)/Pa & 1.0 \(\times\) 10\({}^{6}\)–90.0 \(\times\) 10\({}^{6}\) \\ Critical tangential stress \(x_{5}\)/Pa & 1.0 \(\times\) 10\({}^{6}\)–90.0 \(\times\) 10\({}^{6}\) \\ Bonding radius \(x_{6}\)/mm & 1.2–2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters of discrete elements of FTB.  
Figure 8: Shear test of FTB. 1. Shear blade. 2. FTB sample. 3. Base platform.
# A Study on the Softening Shear Model of the Energy Pile-Soil Contact Surface
## 3 Results
### Softening Shear Model of Pile-Soil Contact Surface under Large Shear Displacement Conditions  
#### 3.5.1 Constitutive Equation  
For ultra-long piles, when the relative displacement of the pile-soil contact surface is larger than the ultimate displacement of the soil body around the pile, the pile-soil contact surface will slip, and its shear strength is reduced from the peak strength to the residual strength, and the softening phenomenon occurs. Through the previous analysis of the deformation mechanism of the energy pile, it can be found that there is a situation in which the pile-soil displacement becomes larger under the heating condition, which indicates that it is necessary to adopt the softening load transfer function to reflect the change characteristics of the pile-soil contact surface friction. In this paper, according to the mechanical characteristics of energy piles, a segmented softening function is proposed, which can consider the unloading process of energy piles in the upper part of the pile in the heat dissipation process and in the lower part of the pile in the heat extraction process. Moreover, the unloading process adopts the linear elasticity equation, and the slopes of the equations are equal to the initial slopes of the function. Figure 15 shows the curve of the softening shear model for pile-soil contact surface.  
\[\tau=\begin{cases}\tau_{p}\frac{s(a+cs)}{(a+bs)^{2}}&(0\leq s\leq s_{r})\\ \tau_{r}&(s>s_{r})\end{cases} \tag{10}\]  
In the equation, \(\tau\) is the shear stress, \(\tau_{p}\) is the peak strength and \(\tau_{r}\) is the residual strength at the pile-soil contact surface, kPa. \(s\) is the shear displacement, \(s_{p}\) is the displacement corresponding to the peak strength and \(s_{r}\) is the displacement corresponding to the residual strength, mm. \(a\), \(b\) and \(c\) are the fitting parameters.
# Lagrangian Modeling of Marine Microplastics Fate and Transport: The State of the Science
###### Abstract  
Microplastics pollution has led to irreversible environmental consequences and has triggered global concerns. It has been shown that water resources and marine food consumers are adversely affected by microplastics due to their physico-chemical characteristics. This study attempts to comprehensively review the structure of four well-known Lagrangian particle-tracking models, i.e., Delft3D--Water Quality Particle tracking module (D-WAQ PART), Ichthyoplankton (Ichthyop), Track Marine Plastic Debris (TrackMPD), and Canadian Microplastic Simulation (CaMPSim-3D) in simulating the fate and transport of microplastics. Accordingly, the structure of each model is investigated with respect to addressing the involved physical transport processes (including advection, diffusion, windage, beaching, and washing-off) and transformation processes (particularly biofouling and degradation) that play key roles in microplastics' behavior in the marine environment. In addition, the effects of the physical properties (mainly size, diameter, and shape) of microplastics on their fate and trajectories are reviewed. The models' capabilities and shortcomings in the simulation of microplastics are also discussed. The present review sheds light on some aspects of microplastics' behavior in water that were not properly addressed in particle-tracking models, such as homo- and hetero-aggregation, agglomeration, photodegradation, and chemical and biological degradation as well as additional advection due to wave-induced drift. This study can be regarded as a reliable steppingstone for the future modification of the reviewed models.  
microplastics; fate; transport; particle tracking; marine environment +
Footnote †: journal: Marine Science and Engineering
## 1 Introduction
Additionally, the magnetic properties of ferrite precipitates enable rapid magnetic separation and potential reuse as catalysts, demonstrating significant engineering advantages [31]. However, the application of the ferrite process in treating high-concentration PVA, particularly from 3D printing wastewater, remains under-explored. The interactions between PVA and iron oxides during the ferrite process present both opportunities and challenges [32; 33; 34]. While PVA may interfere with the formation of crystalline ferrite structures, it might also promote the formation of novel composite materials with enhanced removal capabilities. Understanding these interactions and optimizing process parameters is crucial for developing effective treatment strategies for high-concentration PVA wastewater. This study proposes a multi-step ferrite process specifically designed for treating high-concentration PVA wastewater from 3D printing applications. The primary objectives of this research are to evaluate the efficiency of an H\({}_{2}\)O\({}_{2}\)-modified ferrite process for removing high-concentration PVA, to investigate the formation mechanisms and properties of magnetic precipitates generated during the treatment process, and to explore the potential reuse of these precipitates as functional materials. We hypothesize that the introduction of H\({}_{2}\)O\({}_{2}\) pre-oxidation will enhance the conventional ferrite process through improved pH regulation and partial oxidative degradation of PVA molecules, thereby facilitating more effective subsequent ferrite formation and PVA removal. Additionally, we posit that PVA concentration will significantly influence the crystalline structure and magnetic properties of the formed precipitates, potentially leading to tailorable magnetic materials. The key contributions of this study to scientific knowledge include the development of an effective treatment approach for high-concentration PVA wastewater that addresses a growing environmental challenge posed by the 3D printing industry, elucidation of the interaction mechanisms between PVA and iron oxides during the modified ferrite process,and demonstration of a resource recovery strategy that transforms waste constituents into potentially valuable magnetic materials. This integrated approach represents an important advancement in sustainable wastewater treatment, aligning with circular economy principles by converting treatment byproducts into resources.