Overlap Ratio Research Articles

Optimization of the Energy Capture Performance of the Lift-Drag Hybrid Vertical-Axis Wind Turbine Based on the Taguchi Experimental Method and CFD Simulation

In order to improve the energy capture performance of vertical axis lift wind turbines in a low wind speed environment, the drag wind turbine is employed to couple with the design of existing vertical axis lift wind turbines. In contrast to the existing literature, in this work, a computational model is proposed that can simulate the interaction between the turbine and the fluid. The effects of pitch angle (β), installation angle (θ), overlap ratio (ε) and diameter ratio (DL) on the energy capture performance of hybrid vertical axis wind turbines are systematically analyzed based on Taguchi and CFD methods. The results show that under the optimized parameter combination, the peak energy capture coefficient of the lift-drag hybrid wind turbine can be increased to 0.2328, compared with 0.0309 and 0.0287 of the pure lift and drag turbine, respectively. In addition, the result of the prototype test show that the optimized hybrid wind turbine not only has a better-starting performance but also has 2.0 times the output power of that of the lift wind turbine.

An Efficient Algorithm for Distance-based Structural Graph Clustering

Structural graph clustering (SCAN) is a classic graph clustering algorithm. In SCAN, a key step is to compute the structural similarity between vertices according to the overlap ratio of one-hop neighborhoods. Given two vertices u and v, existing studies only consider the case when u and v are neighbors. However, the structural similarity between non-neighboring vertices in SCAN is always zero, and using only one-hop neighbors on weighted graphs discards the weights on each edge. Both may not reflect the true closeness of two vertices and may fail to return high-quality clustering results. To tackle this issue, we define and study the distance-based structural graph clustering problem. Given a distance threshold d and two vertices u and v, the structural similarity between u and v is defined as the ratio of their respective neighbors within a distance of no more than d. We show that the newly defined distance-based SCAN achieves better clustering results compared to the vanilla version of SCAN. However, the new definition brings challenges in the computation of final clustering results. To tackle this efficiency issue, we propose DistanceSCAN, an efficient approximate algorithm for solving the distance-based SCAN problem. The main idea of DistanceSCAN is to use all-distances bottom-k sketches (ADS) to speed up the computation of similarities. Given the ADS, we can derive the similarity between two vertices with a bounded cost of O(k). However, to ensure that the estimated similarity has an approximation guarantee, the value of k still needs to be set to as large as thousands. This brings high computational costs when computing the similarities between neighboring vertices. To tackle this issue, we further construct histograms to prune the structural similarity computations of vertices pairs. Extensive experiments on real datasets validate the effectiveness and efficiency of DistanceSCAN.

Pengaruh Ratio Overlap Sudu Terhadap Performa Turbin Air Poros Horizontal Savonius

<p><em>The Savonius air turbine has the ability to generate electricity from low-flow water sources and can be used in various types of water sources. However, the efficiency of this turbine is still low compared to other types of water turbines. Previous studies have shown that the overlap ratio of the blades can affect the turbine efficiency and power generated. Therefore, this study aims to investigate the effect of blade overlap ratio on the performance of the horizontal-axis Savonius water turbine. The purpose of this research is to study the influence of blade overlap ratio. It is hoped that the results of this study can be used as a reference in the production of horizontal-axis Savonius water turbines. </em><em></em></p>

Ion irradiation-induced nano pore/fiber formation and areal-vacancy distribution in semiconductor materials

In this study, the formation of nano-porous/fibrous structures was investigated by spot-ion irradiation on Ge and GaSb substrates to consider the formation range of nanostructures and point defects. Spot-ion irradiation was performed in a focused ion beam system with a beam diameter of 35.1 nm, which is determined by the system. The fluence and ion beam current ranged within 5 × 1019–1 × 1022 ions/m2 and 500–520 pA, respectively. All the irradiated ions were Ga+ with incident energy adjusted at 30 keV, and the angle of incidence to the surface normal was 0°. The interval of the irradiated spot ranged from 100 to 1000 nm. For line-patterned irradiations, these spots overlapped with one another at an overlap ratio of 50%, producing a 35.1 nm × 10 μm irradiated region. Result shows that nanostructured regions followed a spot interval. When an interval was shorter than 200 nm, each nanostructured spot coalesced with neighbors to form large and uniform structures. Furthermore, line-patterned irradiation indicated that the migration distance of vacancy was ∼300 nm at maximum, which is consistent with the coalescence phenomenon.

Point cloud completion in challenging indoor scenarios with human motion.

Combining and completing point cloud data from two or more sensors with arbitrarily relative perspectives in a dynamic, cluttered, and complex environment is challenging, especially when the two sensors have significant perspective differences while the large overlap ratio and feature-rich scene cannot be guaranteed. We create a novel approach targeting this challenging scenario by registering two camera captures in a time series with unknown perspectives and human movements to easily use our system in a real-life scene. In our approach, we first reduce the six unknowns of 3D point cloud completion to three by aligning the ground planes found by our previous perspective-independent 3D ground plane estimation algorithm. Subsequently, we use a histogram-based approach to identify and extract all the humans from each frame generating a three-dimensional (3D) human walking sequence in a time series. To enhance accuracy and performance, we convert 3D human walking sequences to lines by calculating the center of mass (CoM) point of each human body and connecting them. Finally, we match the walking paths in different data trials by minimizing the Fréchet distance between two walking paths and using 2D iterative closest point (ICP) to find the remaining three unknowns in the overall transformation matrix for the final alignment. Using this approach, we can successfully register the corresponding walking path of the human between the two cameras' captures and estimate the transformation matrix between the two sensors.

The crucial role of platelet stacking mode in strength and toughness of nacre

Nacre can be classified as columnar or sheet nacre based on the stacking mode of platelets, which is respectively featured by an aligned or staggered platelet arrangement. To determine the more suitable type for biomimetic modeling, the inherent structure–property relationships of both nacres were explored via mechanical tests with theoretical and numerical analyses. It is found that sheet nacre exhibits an outstanding combination of high strength and high toughness compared to columnar nacre under both tensile and compressive stresses, attributing to its staggered stacking characteristic. Under tensile stress, its effect can be quantitatively characterized by the platelet overlap ratio, with a measurement of 0.11 for columnar nacre and 0.47 for sheet nacre, where the larger ratio contributes to a higher tensile strength. Analytical and numerical models reveal that a higher overlap ratio or staggered stacking can trigger the transition from chain-like to step-like failure modes, significantly contributing to improved toughness. Under compressive stress, compared with columnar nacre’s aligned stacking, sheet nacre’s staggered platelet arrangement effectively postpones kinking failure and enhances both compressive strength and toughness. Therefore, the staggered arrangement of platelets in sheet nacre produces the more balanced mechanical properties, offering beneficial references for designing high-performance nacre-inspired materials.

A comprehensive review on design and development analysis and blade material selection of helical Savonius rotor

The helical Savonius rotor (HSR) is used as green energy generation. The accurate design of HSR is essential before installing any wind farm in a region. It has been widely employed that positive static torque coefficients of helical Savonius rotor are higher compared to conventional semicircular rotor stated by several researchers. The reason is behind that the formation of secondary vortex of fluid. It is leading by vertical vortex flow, which passes over the curve surface and creates drag force. Still now, various design have been proposed to meet peak power output through optimum geometry parameters like blade profile design, aspect ratio and overlap ratio. The selection of blade material is also the influencing parameter to improve the starting torque of the rotor. In this regards present paper is aim to study the details experimental, numerical, and analytical review on HSR and selection of blade material with minimum production cost.

A Comprehensive Investigation of the Impact of Class Overlap on Software Defect Prediction

Software Defect Prediction (SDP) is one of the most vital and cost-efficient operations to ensure the quality of software under developed. The performance of SDP heavily relies on the characteristics of experimental datasets (or say SDP datasets). However, there often exists the phenomenon of class overlap in the SDP datasets, i.e., defective modules and non-defective modules are similar in terms of values of metrics. Class overlap hinders the smooth performance as well as the use of SDP models. Even though efforts have been made to investigate the impact of overlapping instance removing techniques on the performance of SDP, many open issues are still challenging yet unknown. For example, 1) how to effectively identify the overlapping instances? 2) Whether is the phenomenon of class overlap universal in the SDP datasets? 3) What are the impacts of class overlap on the performance and interpretation of SDP models? Questions like these are very important but have not been fully explored yet. In this paper, we conduct an empirical study to comprehensively investigate the impact of class overlap on SDP. Specifically, we first propose an overlapping instances identification approach by analyzing the class distribution in the local neighborhood of a given instance. Based on the approach, we then investigate the impact of class overlap on the performance and the interpretation of seven representative SDP models. Finally, we investigate the impact of two common overlapping instance handling techniques (i.e., removing and separating techniques) on the performance of SDP models. Through an extensive case study on 230 datasets that span across industrial and open-source software projects, we observe that: i) 70.0% of SDP datasets contain overlapping instances; ii) different levels of class overlap have different impacts on the performance of SDP models. The class overlap ratio and the number of instances seriously affect the stability of the performance of SDP models; iii) class overlap affects the rank of the important feature list of SDP models, particularly the feature lists at the top 2 and top 3 ranks; IV) Class overlap handling techniques could statistically significantly improve the performance of SDP models trained on datasets with over 12.5% overlap ratios. Therefore, on the basis of these findings we suggest that future work in SDP should apply our proposed KNN method to: i) identify whether the overlap ratios of their defect datasets are greater than 12.5% before building SDP models; ii) remove the overlapping instances to find the more consistent guiding significance metrics; iii) combine RF classifier and class overlap handling techniques when reducing the efforts to review codes.

Co-combustion of pulverized coal and walnut shells in air and oxy-fuel atmospheres: Thermal behavior, synergistic effect and kinetics

In this work, the combustion characteristics of pulverized coal, walnut shells, and their blends in the oxy-fuel atmosphere (21% O2/79% CO2) and air atmosphere (21% O2/79% N2) were investigated by the thermogravimetric analyzer (TGA). The interaction between the blends was quantified by the overlap ratio (OR) and the difference between theoretical and experimental weight loss (ΔW). The results showed that the combustion characteristics of walnut shells were better than coal attributed to its higher volatile components, whereas co-combustion of walnut shells with coal could improve the reactivity of coal. The replacement of the air atmosphere with the oxy-fuel atmosphere had a negligible effect on the ignition temperature of the selected materials but generated an increase in the burnout temperature to some extent. The activation energy was calculated by using Kissinger-Akahira-Sunose (KAS) and Flynn-Wall-Ozawa (FWO) methods, and the order of reaction and pre-exponential factor of the selected samples was determined by the master plots method. The results of this study confirmed the feasibility of the co-combustion of walnut shells with coal under the oxy-fuel atmosphere and provided certain theoretical guidance to realize the operation of existing boilers in the oxy-fuel atmosphere.

Frequency‐dependent dynamic moduli prediction for general bio‐inspired staggered platelet reinforced composites

AbstractLoad‐bearing biological staggered composites, like nacre, teeth, and bone, possess an exceptional combination of material properties like high stiffness and high toughness. To date, most of the analytical research are for nacre‐like bio‐inspired staggered composites, with highly overlapped platelets. But the collagen fibril‐like staggered composites, with slender or barely overlapped platelets, are out of their scope. This motivates this work. In this paper, based on the previous research, according to the elastic‐viscoelastic corresponding principle, an analytical model for dynamic properties of general bio‐inspired staggered composites is presented. Moreover, the effect of loading frequency in a wide range is studied. The accuracy of the model is verified by comparison with existing models and finite element simulations. Besides, parametric analyses and sensitivity analysis are conducted thoroughly. The results reveal that besides the platelet concentration and the platelet aspect ratio, the platelet overlap ratio also influences the damping behavior of bio‐inspired staggered composites to a certain extent; for biological/biomimetic composites with a larger overlap ratio, higher loss modulus is possible to be achieved, and the optimal aspect ratio is mostly within [5, 30]. These findings are of great significance to the optimal design of bio‐inspired engineering materials in the future.

CFD Investigation and Optimization on the Aerodynamic Performance of a Savonius Vertical Axis Wind Turbine and Its Installation in a Hybrid Power Supply System: A Case Study in Iran

In this study, a 3D-CFD simulation on the effect of various design and operating parameters, namely the number of blades, overlap ratio, spacing size, arc angle, shape factor, presence of curtain, wind velocity, and multi-bucket rotor, on the aerodynamic performance of a Savonius vertical axis wind turbine (VAWT) is conducted. In order to evaluate the effect of each parameter, the rotor’s power coefficient (Cp) for different tip speed ratio (TSR) values and overall torque as a function of the azimuth angle are investigated. The results show that the generated power of a solid rotor with more buckets is less than that of the two-bladed rotor, and by decreasing the overlap ratio and spacing size, Cp values are enhanced. Moreover, a rotor with a larger bucket arc angle has less Cp value and total torque, in addition to shape factor, which changes the configuration of the rotor by adding arms, thus enhancing the aerodynamic performance of the prototype. Furthermore, it is shown that installing a curtain in the upstream section of the rotor improves Cp value by directing airflow. Moreover, it is observed that by increasing inlet wind velocity and, subsequently, the Reynolds number, generated power is boosted. In addition, it is noted that a suitable multi-bucket rotor configuration can boost generated power. Finally, the optimum design is achieved by using the Kriging method. Based on the optimization results, a 2-bladed Savonius VAWT with an overlap ratio of 0, spacing size of 0 (m), arc angle of 170°, shape factor of 0.5, and inlet wind velocity of 12 (m/s) at TSR = 0.37 introduces the highest efficiency.

Design of Audio-Based Accident and Crime Detection and Its Optimization

The development of transportation technology is increasing every day; it impacts the number of transportation and their users. The increase positively impacts the economy's growth but also has a negative impact, such as accidents and crime on the highway. In 2018, the number of accidents in Indonesia reached 109,215 cases, with a death rate of 29,472 people, which was mostly caused by the late treatment of the casualties. On the other hand, in the same year, there were 8,423 mugs, and 90,757 snitches cases in Indonesia, with only 23.99% of cases reported. This low reporting rate is mostly caused by the lack of awareness and knowledge about where to report. Therefore, a quick response surveillance system is needed. In this study, an audio-based accident and crime detection system was built using a neural network. To improve the system's robustness, we enhance our dataset by mixing it with certain noises which likely to occur on the road. The system was tested with several parameters of segment duration, bandpass filter cut-off frequency, feature extraction, architecture, and threshold values to obtain optimal accuracy and performance. Based on the test, the best accuracy was obtained by convolutional neural network architecture using 200ms segment duration, 0.5 overlap ratio, 100Hz and 12000Hz as bandpass cut-off frequency, and a threshold value of 0.9. By using mentioned parameters, our system gives 93.337% accuracy. In the future, we hope to implement this system in a real environment.

파라메트릭 스터디를 통한 전동식 기어시스템의 소음 및 PPTE 분석

The gear overlap ratio shows the characteristics of the spur gear and the helical gear and varies according to the torsional angle. The gear ratio, tooth width, and center distance, which are restricted in a space of performance and manufacturing and design in the gearbox, are fixed. A parametric study on modules, the number of teeth, and torsion angles was conducted to analyze the relationship between the overlap ratio and PPTE. Then, contact analysis was performed by correcting the tooth profile to improve the transmission error. Contact analysis was performed through correction of the tooth modification to improve transmission error, and the noise was analyzed according to the overlap ratio by applying a noise prediction equation.

Hidden Toe Welds in RHS-to-RHS Overlapped K-Connections

The effects of hidden toe welds on the static behavior and strength of rectangular hollow sections to rectangular hollow sections (RHS-to-RHS) overlapped K-connections is investigated. Five full-scale welded specimens with a high overlap ratio were fabricated and tested under quasistatic loading in a universal testing machine, with the existence of hidden toe welds and branch loading condition varied. The experimental results were used to validate corresponding numerical models, and a parametric study was performed thereafter. The experimental and numerical results indicate that the overlapped K-connection capacity is affected by the presence of a hidden toe weld and the branch load case but remains within a reasonable range of the capacity predicted by certain codes and guides. Considering all the branch load cases studied, the hidden toe in a partially overlapped K-connection can be left unwelded, while some modifications are suggested to current design recommendations to account for this. A new method for calculating the branch local failure limit state is proposed, which can be used to accurately predict the capacity of overlapped RHS K-connections, without considering hidden toe welds in partially overlapped K-connections.

Influence of laser parameters on corrosion resistance of laser melting layer on C45E4 steel surface

The key to further improve the corrosion resistance of the laser melting layer on steel surface is to select appropriate laser parameters. In this paper, a single factor laser melting experiment on C45E4 steel surface by using a pulsed laser beam at a wavelength of 1064 nm and electrochemical analysis were conducted to explore the influences of laser parameters including single pulse energy density, spot overlap ratio and number of laser scans on the corrosion resistance of the laser melting layers. The optimal laser parameter combination was obtained: single-pulse energy density of 3.82 J·cm−2, spot overlap rate of 80 % and 4 number of laser scans. The thickness of the optimal laser melting layer prepared with the optimal laser parameters was only 10.85 μm, and it had a maximum self-corrosion potential of 1.031 V, a minimum corrosion current of 3.451 × 10−9 A·cm−2 and a maximum charge transfer resistance of 1541.2 Ω·cm−2. During the salt spray corrosion test, the corrosion rate of the optimal laser melting layer was only one third of that of the traditional hot alkaline blackened layer with a thickness of 12.04 μm. The results showed that the corrosion resistance of the optimal laser melted layer was significantly improved compared to that of the conventional thermally alkaline blackened layer. The main reason was that the determination of the optimal single-pulse energy density, spot overlap ratio and number of laser scans in turn, made the optimal laser melting layer had a stable Fe3O4-FeO corrosion resistance structure, effectively reduced the surface roughness, microcrack density and oxidation leakage point, and prevented the C45E4 steel surface from being over-oxidized.

Adjusting microstructure and improving mechanical property of additive manufacturing 316L based on process optimization

In additive manufacturing (AM), printing defects or columnar-coarse grains due to an inappropriate process parameter often damage the mechanical properties of AM metals, which significantly reduce the quality and application fields of AM parts. In this work, the overlap ratio are optimized to adjust grain morphology and improve mechanical properties of 316L stainless steel fabricated by direct energy deposition (DED). In addition, the effects of fundamental process parameters (such as laser power, scanning speed, and overlap ratio) on the molten-pool size, density, grain morphology, and mechanical properties of DED-316L are systematically studied. By optimizing process parameters (such as overlap ratio, laser power, and scanning speed), the penetrating-columnar-grains morphology is eliminated, and a full dense (>99.9%) DED-316L with finer grains is achieved, without either adjusting the chemical composition of 316L or adding any intermediate processes (such as in-situ rolling, ultrasonic treatment, laser shock peening, or cryogenic cooling). Due to the refined grains and twinning induced plasticity (TWIP) effect, strength and plasticity of DED-316L are simultaneously enhanced. To be more specific, compared to Sample (overlap ratio-4%, laser power-720 W, scanning speed-8 mm/s) without process optimization, the tensile strength and yield strength of Sample (overlap ratio-70%, laser power-720 W, scanning speed-20 mm/s) with process optimization are individually improved by 20.3% and 18.4%, while the total elongation and uniform elongation are increased by 176.7% and 173%, respectively.

Frequency-specific brain network architecture in resting-state fMRI

The analysis of brain function in resting-state network (RSN) models, ascertained through the functional connectivity pattern of resting-state functional magnetic resonance imaging (rs-fMRI), is sufficiently powerful for studying large-scale functional integration of the brain. However, in RSN-based research, the network architecture has been regarded as the same through different frequency bands. Thus, here, we aimed to examined whether the network architecture changes with frequency. The blood oxygen level-dependent (BOLD) signal was decomposed into four frequency bands—ranging from 0.007 to 0.438 Hz—and the clustering algorithm was applied to each of them. The best clustering number was selected for each frequency band based on the overlap ratio with task activation maps. The results demonstrated that resting-state BOLD signals exhibited frequency-specific network architecture; that is, the networks finely subdivided in the lower frequency bands were integrated into fewer networks in higher frequency bands rather than reconfigured, and the default mode network and networks related to perception had sufficiently strong architecture to survive in an environment with a lower signal-to-noise ratio. These findings provide a novel framework to enable improved understanding of brain function through the multiband frequency analysis of ultra-slow rs-fMRI data.

Stress Distributions in Brazed Single-Lap Joints Under Tensile Loading

The most common method for characterizing the strength of brazed joints is uniaxial tension testing of single lap joints (SLJs). Standard interpretations depend on the assumption that the average shear stress at failure is the key metric in determining joint strength. However, it is evident from the geometry that the stress distributions must be inhomogeneous with shear lag type stress concentrations at the ends of the overlap regions. Eccentric loading causes overlap rotation and bending stresses that amplify the stress concentrations and result in geometric nonlinearity. Unfortunately, details of the distributions of normal and shear stresses on the braze needed to understand failure have not been presented. Thus, finite element analysis was used to quantify these stress distributions using 2D elastic and elasto-plastic models of monolithic stainless steel SLJs. Bending stresses and normal and shear stresses acting on the braze were determined over a wide range of overlap ratios and applied stresses. For all conditions, stresses are highly concentrated in a narrow region at overlap ends with peak normal stresses exceeding peak shear stresses. Variations in peak stresses with applied stress and overlap ratio were found to fully explain experimental joint strength data. Common interpretations based on the average shear stress at failure are found to be incorrect. Implications for testing, interpretation, and joint design are discussed.

Effects of Scanning Speed on the Polished Surface Quality of Mold Steel by Dual-Beam Coupling Nanosecond Laser

In this paper, a novel dual-beam coupled nanosecond laser was used to polish S136D mold steel. The effects of scanning speed, total fluence, spot overlap ratio, and SPSN on surface quality were analyzed. The polished surface roughness Ra without ultrasonic cleaning is too large due to slag, splash, and dust produced by laser polishing. When scanning speed is 1250 mm/min, surface roughness Ra with ultrasonic cleaning is reduced from the original surface 1.92 μm to 0.72 μm, and the surface roughness Ra is reduced by 62.50%. When the Ftot is 35.38 J/cm2, the minimum value of surface roughness Ra is 0.72 μm. If the total fluence is higher or lower, it is not conducive to reducing the surface roughness, the total fluence is higher, and there is a polished surface with SOM phenomenon. The polished surface with spot overlap ratio of 98.55% has a smooth morphology, and a minimum value of surface roughness Ra of 0.41 μm. When the specimen is inclined at a certain angle, the high-magnification camera captures color on the polished surface. It is found that the microscopic texture of molten material flow trace and polishing scanning track is obvious. Polished surface is mainly distributed with Fe, Cr, C, and O elements. The surface material processing speed per unit time is low, and the polishing surface quality is improved less. The maximum surface roughness Ra is 1.98 μm. The minimum Ra of polished surface with smoother morphology is 0.41 μm, and surface profile height is basically the same. The research results show that the new dual-beam coupled nanosecond laser polishing technology can improve surface quality of materials. This research work provides process guidance for laser polishing effect analysis and mechanism innovation.

Utility of public knowledge bases for the interpretation of comprehensive tumor molecular profiling results.

With the growing use of comprehensive tumor molecular profiling (CTMP), the therapeutic landscape of cancer is rapidly evolving. NGS produces large amounts of genomic data requiring complex analysis and subsequent interpretation. We sought to determine the utility of publicly available knowledge bases (KB) for the interpretation of the cancer mutational profile in clinical practice. Analysis was performed across patients who previously underwent CTMP. Independent interpretation of the CTMP was performed manually, and then, the recommendations were compared to ones present in KBs (OncoKB, CIViC, CGI, CGA, VICC, MolecularMatch). A total of 222 CTMP reports from 222 patients with 932 genomic alterations (GA) were identified. For 368 targetable GA identified in 171 (77%) of the patients, 1381 therapy recommendations were compiled. Except for CGA, therapy ESCAT LOE I, II, IIIA and IIIB therapy options were equally represented in the majority of KB. Personalized treatment options with ESCAT LOE I-II were provided for 35 patients (16%); MolecularMatch/CIViC allowed to collect ESCAT I-II treatment options for 34 of them (97%), OncoKB/CGI-for 33 of them (94%). Employing VICC and CGA 6 (17%) and 20 (57%) of patients were left without ESCAT I or II treatment options. For 88 patients with ESCAT level III-B therapy recommendations: only 2 (2%), 3 (3%), 4 (5%) and 6 (7%) of patients were left without options with CIViC, MolecularMatch, CGI and OncoKB, and with VICC-12 (14%). Highest overlap ratio was observed for IIIA (0.81) biomarkers, with the comparable results for LOE I-II. Meanwhile, overlap ratio for ESCAT LOE IV was 0.22. Public KBs provide substantial information on ESCAT-I/R1 biomarkers, but the information on ESCAT II-IV and resistance biomarkers is underrepresented. Manual curation should be considered the gold standard for the CTMP interpretation.