Glass warp-knitted fabrics have been widely used as complex structural reinforcements in composites, such as wind turbine blades, boats, vehicles, etc. Understanding the mechanical behavior and formability of these textiles is very necessary for the simulation of forming processes before manufacturing. In this paper, the shear deformation mechanics of glass warp-knitted non-crimp fabrics (WKNCF) were experimentally investigated based on a picture frame testing apparatus equipped to a universal testing machine. Three commercially available fabrics of WKNCFs were tested for four cycles by the picture frame method. The aim was to characterize and compare the shear behavior of relatively high areal density fabrics during preform processing for composites. The energy normalization theory was used to obtain the normalized shear force from the testing machine data; then, the shear stress against the shear angle was fitted by cubic polynomial regression equations. The results achieved from the equations demonstrated that the in-plane shear rigidity modulus was associated with the shear angle. The effect of the shearing cycles and stitching pattern on shear resistance was also analyzed. Recently, increasing importance has been placed on composites and their promising future, according to recent market shares and many predictions ,2. The aThere are many deformation modes that can occur in the fabric in the draping process, and the entire deformation can be one or any combination of these modes . ConsequPicture frame (PF) or (trellis shear frame) is a popular apparatus that is essentially adopted to characterize the in-plane shear behavior of textile fabrics , especiaUntil now, there has not yet been a standard testing method using the picture frame; there is just a benchmarking effort on the material testing of woven composites fabrics. This effort has proven that the normalization results obtained from this method could be compared to other research results, even if they use different samples and frame sizes . There aLomov et al. demonstrated that the first shear cycle diagrams showed irregular behavior and evidence of tension in the fibers in the frame . NonetheSome of the key advantages of knitted fabrics for composite reinforcement over woven ones are: the improvement of fabric handling and matrix injection during composite processing , the acc2 using the picture frame.The essential difference in fabric architecture between NCFs and woven materials makes defect formation mechanisms rather different due to the existence of stitching yarn . So, theThe objective of this work was to characterize and analyze the in-plane shear behavior of relatively heavy areal density glass WKNCF fabrics based on a picture frame experiment. The in-plane shear rigidity moduli of fabrics were determined for four shearing cycles. For this purpose, a picture frame apparatus was set up, and three types of different glass WKNCFs were tested. The effect of the stitching pattern on the shear deformation mechanism was also observed.® company  were used for the experiments in this study. Fabrics with heavy areal densities (about 1200 g/m2) and typical stitching patterns  and LT  and chain stitching for DB (double-bias)) were characterized here. The photographs of NCF fabrics on both faces are presented in Glass warp-knitted non-crimp fabrics (glass-WKNCFs) from PGTEXThe fabrics were made from more than one set of yarns. Each yarn set  was approximately straight in its layer in the fabric plane. The stitching yarn with smaller linear density connected the layers through the fabric thickness and held adjacent layers together. The other fabric details were listed in The naming system abbreviations used by the manufacturing company for these fabrics are as following: UD denotes unidirectional, L denotes the longitudinal orientation of the fabric (0°), which is the machine production direction, T stands for the transverse orientation (90°) or cross-machine direction, and DB denotes the double-bias where the yarns are at a specific angle from the machine production direction, which is mainly (+45°/−45°). According to this naming system, the codes UD, LT, and DB become clear. The small letter “t” stands for tricot stitching, and “c” stands for chain stitching; these were added to the original name of the fabric for easily distinguishing the stitching type associated with each fabric. Moreover, all of the other fabric details are listed in Studying the deformation mechanisms of fabrics, especially shear behavior by picture frame, needs a lot of attention in order to be done carefully. For all of the material characterization tests described in the following sections, a universal testing machine  provided by the Engineering Research Center of Technical Textiles was used. The frame was mounted in a load cell  for measuring the amplifier frame displacement force, as shown in Lfabric < Lframe) in order to avoid corner buckling. The design of the frame apparatus resembled that used by UML  [The manufactured picture frame for this study was used to test in-plane shear behavior on cruciform fabric samples, where the length of the fabric was less than that of the frame  , but witThe slotted guide (sliding link) had two functions: the first one was connecting one corner of the small amplifier frame to the crosshead of the tensile testing machine , and the second one was to limit the fabric frame motion between the starting position and final deformed position i.e., between 0° and 60° (1.05 rad) of shear angle. This frame was connected to the crossheads of the tensile machine by two connectors. In addition, an extra two connectors were manufactured in order to use the same frame to other tensile testing machines. The amplifier itself would be helpful if the crosshead displacement and/or the crosshead velocity of the testing machine is limited.a displacement due to applying the tensile force a, where α is the device amplification factor; it can be calculated by the following equation:From the illustrations in a by Equation (3):The power applied to the frame From the free body diagram of the amplifier frame as shown in The free body diagrams of the link fabric frame Solving Equation (6) for By substituting in Equation (4), the net shear force applied on the fabric can be obtained by:2) with four-sided arms connecting it to the clamping areas in the frame. The 2D geometrical details of the frame are illustrated in Since the fabric sample is crucified, the sheared region by frame is square . The cutting of samples was done by “electric scissor” shown in  to ease Firstly, the frame was tested when it was empty, and the displacement-force data were recorded. Then, the fabric samples were fixed in the frame with zero tension, and the displacement-force data for the frame and fabric together were recorded. Then, the net shear force can be calculated by Equation (8) above.However, this force cannot be directly compared to the results from the other picture frame arrangements or to the results from the other shear behavior characterization methods . However, the benchmark effort  referredt was the thickness of the fabric, assuming the fabric thickness was constant during the test [From this equation, the normalized shear force was a function of the frame shear angle (θ), and in order to calculate the shear stress, we simply divide the normalized shear force by the thickness of the fabric:the test . The meathe test  are giveA = 0; then, the shear modulus G12 can be calculated from the derivative of the fitting equation determined from the data points on the curve of the shear stress versus the shear angle; the shear angle unit is in radians.The cubic polynomial function was chosen; it had potential benefits within a finite element model, and its derivative can be easily calculated and implemented into a mode . By fittIn our measurement for WKNCFs, the tricot stitch pattern for biaxial fabric could be mechanically conditioned’, and it could be experimentally proved that the second and third cycle were much more stable in characterizing the in-plane shear behavior. On the other hand, the chain stitch pattern for biaxial fabric could be conditioned just in the SC direction, but not in the ST direction, because some stitches will be broken in the first cycle. Still, the next shear cycles were implemented on the fabric to investigate the change in shear behavior.In this study, four shearing cycles were executed for each fabric sample. For each cycle, diagrams during the loading phase were registered, while the diagram during the unloading phase (returning the frame to the starting position) were not registered.”Bad tests” data were discarded from the processing, which indicates the test with extremely irregular behavior and the evidence of tension of the fibers in the frame. The normalized shear force for fabrics is given in Considering the thickness of fabric samples, the shear stress curves against the shear angle would be obtained. By fitting these curves using cubic polynomial regression, the values of Equations (11) and (12) would be obtained. The details were shown in G12 has been determined. The curves were illustrated in Then, by the derivation of these curves, the shear modulus From the curves in Essentially, the graphs started from the origin, but generally, the WKNCF fabrics were easy to deform. At the first stage of shearing (~0.17 rad), the curves were near to the zero, because the applied force was just making rovings to be closer to each other. Consequently, the spaces between rovings were diminishing without any lateral compaction. Then, in the next stage, which starts from (~0.17 rad) of shearing angle, the lateral compaction between neighboring rovings was arising gradually up to ~0.26 rad. After that, a rapid rise in the load resistance of the fabric sample was observed because rovings began to squeeze within the layer. However, the effect of the transverse roving layer was neglected.From visual observations, between the starting and final position, as shown in At the initial stage of shearing, the normalized shear force was very low due to the free rotation of rovings inside the tricot pattern, as a curve was shown in In the comparison of shear behavior between LT-t and UD-t fabric, there were no out-of-plane wrinkling, and even no local buckling occurred in LT-t fabric until the end of the shearing test (~1.05 rad), as in the photograph in For biaxial chain stitch fabric +45°/−45°, the chain-stitching pattern made the fabric behavior asymmetrical in shearing. In this case, the chain stitch would suffer from compression in one direction and from tension in the other direction. Thus, different modes of deformation were observed in the stitch compression direction for the DB-c fabric. The +45° and −45° rovings rotated toward the loading direction and therefore, they were forced to slide through the stitch loops. This sliding led to frictional resistance between the stitches and rovings. The sliding of rovings as they rotated was the reason for the low load resistance.In the curve of the first cycle in A different mechanism of deformation was detected in stitch tension direction for the DB-c fabric; where the direction of loading made the stitches under tension, this arrangement applied very high fixation to the rovings. Therefore, additional rotations were limited, and global out-of-plane wrinkling could be observed at an earlier stage in comparison to stitch compression (SC), as shown in The first break of stitches under tension appeared at an ~0.5 rad shear angle, as illustrated in By comparing the shear force between the two directions for the same fabric, it could be concluded that the shear behavior was anisotropic. This matter should be considered in establishing a good material model for such type of fabrics in order to accurately predict their total shear behavior.For the samples of UD-t, LT-t, and DB-c in SC, the in-plane shearing behavior could be analyzed from the second cycle, since the second cycle reflected the pure in-plane shear behavior, as many studies considered ,19. HoweFrom the mentioned procedure in These equations have been plotted, and the values of coefficients for all of the cycles are given in The in-plane shear rigidity modulus for glass WKNCFs fabrics based on picture frame test data were evaluated. The procedure was just depending on the picture frame shear experiment. The force-displacement results during the tests were used to obtain the normalized shear force, shear stress, and in-plane shear rigidity modulus. This modulus was a very important feature in characterizing the mechanical behavior of the reinforcement fabrics for forming the simulation of composites. The simple procedure of defining the shear modulus equation was presented based on the pure shear mechanism of the picture frame apparatus.Three types of warp-knitted non-crimp fabrics (WKNCFs) were investigated. The fabrics had two different stitching patterns, namely, tricot and chain. The cubic polynomial approximation was used to determine the shear stress equation against the shear angle; then, shear rigidity had been calculated from the derivative of the shear stress fitting equations. It was also found that the shear rigidity for fabrics with a tricot pattern increased with the shear angle, and showed the same trend in cycles with a lower shearing force. For the “chain stitching pattern under compression”, the shear rigidity was decreased in the initial stage of shearing, and afterwards, it increased rapidly in the first cycle, while it generally decreased in the next cycles. On the other hand, for the “chain stitching pattern under tension”, the shear rigidity increased up to the stage of some stitches being broken, at which point it decreased rapidly.


Ground and environmental vibrations induced by high dam flood discharge from the Xiangjiaba hydropower station (XHS) has significant adverse effects on nearby building safety and the physical and mental health of surrounding residents. As an effective approach to simulate the flow-induced vibration of hydraulic structures, the hydro-elastic experiment approach has been extensively applied and researched by Chinese scholars, but the relevant systematic research is rarely reported in international journals. Firstly, the hydraulic and structural dynamic similarity conditions that should be satisfied by the hydro-elastic model are briefly reviewed and derived. A hydro-elastic model of the XHS was further constructed using self-developed high-density rubber, and the vibration isolation system (including open trenches and flexible connects) was applied to avoid the external disturbances of pump operation, vehicle vibration and other experiments in the laboratory. Based on the data of model and prototype dynamic tests, a back propagation (BP) neural network was established to map the acceleration of the physical model to the ground in the prototype. In order to reduce the ground vibration, experiments were carried out to meticulously evaluate the ground vibration intensity under more than 600 working conditions, and the optimal operation scheme under different discharge volumes is presented here in detail. According to the prototype test data in 2013, 2014, and 2015, ground vibrations were significantly reduced by applying the presented optimal operation principle which indicates that the presented hydro-elastic approach and the vibration attenuation operation scheme were effective and feasible. Due to the need for a comprehensive utilization of water resources, many hydropower engineering projects with high dams and large reservoirs have been built or are currently under construction. The natural environment is inevitably disturbed and many environmental and ecological issues can result ,4,5,6,7 Due to the extreme complexity of the hydraulic problem in practical engineering and the impossibility of a general solution for the N–S equation, hydraulic model testing satisfying a gravity similarity criterion is an effective and frequently used method. In order to obtain a structural vibration response induced by flood discharge excitation in engineering practice, Ettema et al.  suggest It is worth pointing out that this hydro-elastic experiment technique has rarely been reported in international journals for unknown reasons, although this technology has been widely used to solve practical problems over the past 30 years and has been adequately reported in many Chinese academic journals ,30,31,322 which accounts for 97% of the whole Jinsha River basin area. The maximum height of the dam is 162 m, and the installed capacity of the XHS is 6400 MW. As shown in The XHS is the last cascade hydropower station in the lower reach of the Jinsha River. The main task of this engineering project is to generate electricity, improve navigation conditions, avoid flood hazard, and ensure irrigation water demand. Moreover, this project can also reduce sediment transport and reversely regulate the Xiluodu hydropower station in upstream reaches. The XHS controls a watershed area of 458,800 kmAs shown in 3/s (2 year flood), so it was concerning that the vibration would increase when the flood volume discharged from the dam body reached 34,800 m3/s (100 year flood) and even 48,400 m3/s (5000 year flood). Therefore, the ground vibration intensity needs to be effectively reduced. Mass incidents and even social unrest can result if this engineering problem is not handled properly.However, the surrounding ground vibration of the XHS was observed and caused strong oscillations in the doors and windows of the surrounding buildings during the flood discharging process. This vibration phenomenon and the vibration-induced noise led to fear and panic among the surrounding residents and had significantly adverse effects on the strength and safety of surrounding structures. The maximum ground acceleration reached 0.82 gal when the flood volume discharged from the dam body was only 10,000 mIn order to appropriately simulate the fluid–solid coupling system and obtain accurate and undisturbed test data, the hydro-elastic model was constructed according to both the hydraulic and structural dynamic similarity conditions, which are briefly reviewed and deduced in subsequent sections. Moreover, the vibration sensor arrangement, the dynamic test system, and the vibration isolation system are elaborated in the following analysis.The similarity of hydraulic conditions is essentially the similarity between the flow-induced dynamic excitations in prototype and scale model tests. According to a series of prototype and model tests, it is widely believed that the wall pressure induced by flow separation and diffusion when the external boundary or flow condition sharply changes is mainly influenced by the motion of a large-scale eddy with low frequency. Under the condition of a high Reynolds number, the motion of a large-scale eddy can be well simulated, and the fluctuating pressure in a prototype can thus be calculated by the fluctuating pressure measured in the model test according to the gravity similarity criterion . The dynamic load in the vibration problem of the XHS is mainly composed of fluctuating pressures in the energy dissipation zone of the stilling basin and is generated by a rapidly varied flow with strong separation and turbulent mixing. Therefore, the hydro-elastic model can be appropriately designed according to the gravity similarity criterion.The similarity of the structural dynamic condition is essentially the similarity between the dynamic behaviors of the structures in the model and prototype under flow-induced excitation. This similarity criterion is related to the structural frequencies, mode shapes, damping, etc. and includes the geometric, physical, motion, and boundary similarity conditions of the structure.(1) Geometric Condition Similarity of the StructureThe geometric similarity condition will be satisfied when the experiment model is constructed by reducing the actual structure in equal proportion. Therefore, the following similarity scales can be obtained:(2) Physical Condition Similarity of the StructureThe similarity of the physical condition requires that the mechanical properties of the structural materials and the stresses induced by external loads must be similar. It can be conveniently calculated that the following relationships should be satisfied according to the physical equations of elasticity under the condition of linear elastic deformation.When the material density scale (3) Movement Condition Similarity of the Structureu represent the acceleration, velocity, and displacement of the structure; t denotes time. Generally, the dynamic equation of the structure subjected to random excitation can be expressed as follows:E and L denote the elastic modulus and length characteristics of the structure; Considering the fluid–solid interaction effect, Equation (4) can be rewritten as: The following relationship can be deduced from Equation (5).Since the experiment model is designed according to the gravity similarity criterion, the following relationship can be obtained.Because of the geometric similarity of the structure, the following equation can be easily obtained.Substituting Equations (7) and (8) into Equation (6) yields:Considering that the liquid bulk densities  in the prototype and physical model are the same, the following equation can be given.In Equation (10), the bulk density, damping coefficient, and elastic modulus scales for the physical model are determined. (4) Boundary Condition Similarity of the StructureIn order to satisfy the boundary condition similarity, the boundary constraints in the physical model should be as close as possible to those used in practical engineering. For the design of the hydro-elastic model for the XHS, the key point is the selection of a foundation simulation range. Based on a study of foundation boundary determination of an arch dam in a hydro-elastic experiment , a suffiLλ) is set to 1:80. The spillway dam section, two stilling basins, and the foundation  are included in the hydro-elastic model. In the experiments, the flow rate is measured using the rectangular weir, and the water levels of the upstream and downstream are measured using the needle water level gauge. Comprehensively considering the scale effect and the economy cost, the geometric scale for the hydro-elastic model , which is frequently used to test the elastic modulus of different materials. Moreover, Poisson’s ratio can be ignored in the whole process of modal analysis for beams according to Euler–Bernoulli theory. This indicates that at least in this special situation, Poisson’s ratio has no effect on the structure dynamic characteristics.For the simplest situation, in order to test the elastic modulus of high-density rubber material, a cantilever beam of high-density rubber was produced, and an acceleration sensor was installed on the free end of this cantilever beam. The cantilever beam was then struck slightly by a hammer, and the periodic acceleration history with decreasing amplitude was obtained. The fundamental natural frequency of a cantilever beam is equal to the reciprocal of an acceleration period and can also be calculated by the following formula according to Euler–Bernoulli theory.M, C, and K denote mass, damping, and stiffness matrices of this MDOF system, respectively; u denote structural acceleration, velocity, and displacement, respectively; P denotes the external excitation; t represents time. Different Poisson’s ratios will lead to different stiffness matrices, which is the main cause of the errors in dynamic responses. The plane structure is taken into consideration to further investigate how much error can be generated by differences in Poisson’s ratios. Without a loss of generality, this plane structure is considered to be divided by rectangular grids. The stiffness matrix of the rectangular element Considering the more complex situation, the basic dynamic equation for the multi degree of freedom (MDOF) system can be given as follows.The 62.5% elements in the above constant matrix are very close to 1, which means that the stiffness effect generated by the material with a 0.2 Poisson’s ratio is approximately equivalent to that generated by the material with a 0.4 Poisson’s ratio. Some matrix elements also show relatively large differences from 1, which indicates that the stiffness effects generated by the materials with different Poisson’s ratios are quite different. These non-equivalent stiffness effects are illustrated in the following figure.As shown in E, ρ, and μ denote the elastic modulus, density, and Poisson’s ratio, respectively, and Subscripts 1 and 2 relate to the associated variables of the dam body and foundation, respectively. In order to focus on the vibration mode of the dam body, zero displacement and rotation constraints were applied to the front, back, left, right, and bottom surfaces of the foundation.The numerical model of the XHS and the surrounding ground could not be established due to the limited information. Thus, the numerical model of another hydraulic building was taken as an example to analyze the effect of Poisson’s ratio on the structural dynamic characteristics. In In The mode shape is also important information in modal analysis and has a significant influence on structural dynamic behavior. Therefore, a comparison between the mode shapes calculated by the numerical models with different Poisson’s ratios is given in the following figure. As shown in According to the above analysis, the first three natural frequencies and mode shapes corresponding to Poisson’s ratios of the actual material and the high-density rubber are almost equal to each other. This provides strong evidence for the conclusion that Poisson’s ratio has very limited influences on structural dynamic characteristics and the errors caused by the dissimilarity of Poisson’s ratio can be ignored in engineering practice. Therefore, it is believed that the hydro-elastic experiment technology is accurate and reliable, and can be applied to analysis of hydraulic structure vibrations induced by flood discharge in other engineering projects.The damping ratios respectively calculated by different numerical models are not given. Due to the complex spatial structure, water-stop rubber damping, and the radiation damping effect generated by fluid–structure coupling, the damping condition of the hydraulic structure is extremely complicated. This complicated damping condition cannot be accurately simulated in numerical analysis regardless of Poisson’s ratio changes, so a detailed comparison and analysis of the damping of numerical models with different Poisson’s ratios are not provided in this paper. According to the above analysis, the damping conditions corresponding to different Poisson’s ratios will be similar if the Rayleigh damping is applied due to the same mass matrix and the similar stiffness matrix.Although the above modal analysis is based on a specific engineering project, the conclusion that the Poisson’s ratio has very limited influence on the dynamic response of the hydraulic structure is believed to be generally applicable. The combined method of a hydro-elastic experiment, a prototype test, and numerical simulation has already been applied to many hydropower projects, and some reliable and beneficial results have been obtained. In All the references included in It is known that the back-propagation (BP) neural network prediction model is an effective and frequently used feedforward network with strong nonlinear mapping ability. Therefore, we used a BP neural network to establish the nonlinear mapping between the vibration accelerations measured in the hydro-elastic experiments and the prototype tests.A is obviously greater than that of other test points of the surrounding ground. Based on large-scale numerical analysis considering the unlimited surrounding ground by an infinite element technique, a general propagation law of ground vibration under various working conditions was obtained [A is located on the side near the vibration source in the ancient river channel area. Therefore, the vibration intensity of point A is greater than that of most other points in different working conditions, and the vibration level of the whole near-field will decrease if the vibration intensity of point A is reduced by the applying optimal operation scheme. Moreover, the prototype test data of this point are relatively adequate. Thus, the vibration of point A was selected as the analysis object in this study, and the BP neural network was trained to predict the vertical acceleration root mean square (RMS) of point A.Several recent studies have been focused on the spatial distribution of the ground vibration intensity under various working conditions. Detailed analyses of vibration spatial distribution under different working conditions have been provided by Lian et al.  and Lianobtained . Brieflyobtained . Point An2 and the neuron number in the input layer n1 can be expressed asThe input layer consists of 19 neurons, which represent the RMSs of the acceleration histories measured by 19 vertical acceleration sensors in the hydro-elastic model . Moreover, the number of neurons in the hidden layer can be determined on the basis of the Kolmogorov theorem. The approximate relationship between the neuron number in the hidden layer mapminmax) was applied to normalize the input data, which significantly varied. The establishment of the BP neural network and the prediction calculation were mainly based on the MATLAB neural network toolbox, which was convenient. Therefore, the number of hidden layer neurons was set as 39, and the standard BP neural network model with a network structure of 19-39-1 was established. The tan-sigmoid and linear transfer functions were used in the hidden and output layers, respectively. Moreover, the gradient descent learning algorithm with variable learning rate was applied in the model training, and the data normalization function in the MATLAB neural network toolbox , under various working conditions, should be used to train the prediction model. Therefore, more than 150 working conditions of the XHS in the flood seasons of 2013 were reproduced in the hydro-elastic experiments, and the prototype and experimental results under these working conditions were applied in the model training. The trained model was then employed to predict the vertical acceleration RMSs of point A on the basis of experiment results under several critical working conditions in 2013 as well as many working conditions in 2014. In order to conveniently compare the results of the model prediction and prototype test, the acceleration RMSs involved in the following analysis are standardized by the baseline value, which is equal to 0.10 gal. In A was arranged in a residential area where multiple interference sources exist. Thus, the disturbances of vehicle vibration, human activities, and other external noise make the prototype test results different from the prediction values. On the whole, it is considered that the predicted acceleration RMSs of point A are acceptable in engineering practice.In order to obtain a relatively accurate prediction model with good generalization ability, a large number of data, including the acceleration RMSs of the 19 test points on the hydro-elastic model (input data) and the acceleration RMSs of point In order to investigate the basic variation law of ground vibration intensity under different working conditions, the effects of the spillway gate opening, the orifice gate opening, the upstream water level, and the downstream water level on the ground vibration intensity were studied. Although numerous experiments were carried out, only the results that show relative obvious regularity and can provide useful guidance to the presentation of an optimal operation scheme are described in the following analysis.Generally speaking, the ground vibration intensity increases as discharge volume and gate opening increase. As shown in A were predicted and standardized by dividing the reference value . In In order to effectively reduce the ground vibration, a number of hydro-elastic experiments were carried out, and the corresponding acceleration RMSs of point 3/s, the vibration intensities of point A are significantly reduced when only the right stilling basin is put into operation and the flow is not discharged from the left half spillway and orifice gates. As the discharge volume increases from 15,000 to 20,000 m3/s, it can be seen in It can be seen in In the hydro-elastic experiment, ground vibrations under working conditions with 370 and 380 m upstream levels were mainly analyzed. The reason for this is that these two upstream levels are the dead storage level and the normal storage level, respectively, and the upstream levels of almost all the actual working conditions vary in the range from 370 to 380 m. According to the experiment results, similar effects on the ground vibration were generated by changing the gate opening mode in the same way regardless of the upstream water level. Moreover, two schemes of the working condition variation are considered in In order to verify the effectiveness of the aforementioned research results, the valuable data obtained by the prototype dynamic tests under different working conditions were analyzed and compared. The relatively high ground vibration intensity under relatively small discharge working conditions in 2012 was due to the fact that the flow was discharged only from orifices and the spillways were not put into operation. Following the suggestions of an optimal operation scheme , and the vibration reduction effect of synchronously open spillway (or orifice) gates were obviously verified in the prototype observation. Moreover, the following vibration variation tendencies were found: (1) relatively high vibration intensity can be generated even in a discharge range lower than 1800 m3/s if the flow is not simultaneously discharged from spillways and orifices; (2) the ground vibration intensity under working conditions with flow discharged into a single stilling basin is similar to that when the same flow is discharged into both stilling basins in a discharge range of 3500 to 10,000 m3/s. These tendencies were not reflected in the laboratory experiments. As shown in 3/s are generated when the flow is discharged only from the spillways with non-uniform (even significantly different) openings of different gates. The relatively high acceleration RMSs in the discharge range of 2500–10,000 m3/s are mainly generated under the following conditions: (1) the flow is discharged only from spillways with large and non-uniform gate openings; (2) the flow is discharged from both spillways and orifices when the orifice gates are 4, 5, or 6 m open.Due to the space limitations, the numerous practical working conditions used in 2013, 2014, and 2015 shown in  are not 3/s, respectively. Based on the optimal operation scheme, the ground vibration intensities induced by flood discharge are almost always below the range of vibrations detectable by the human body.The vibrations induced by the flood discharge (or other reasons) are always there, but we can reduce the vibration intensity such that the human body cannot detect them. Therefore, the threshold for the vibration that is perceptible by the human body should be clearly clarified, and the relationship between the vibration threshold and the acceleration RMS (or amplitude) should be analyzed. According to the Standard of Vibration in Urban Area Environment (GB 10070-1988), the vibration of a residential area at night should not exceed 67 dB , which can be regarded as the perceptible vibration threshold of the human body. The vibration acceleration RMSs obtained in the prototype test were obviously smaller than this threshold, but this does not mean that the vibration cannot be felt by the human body because the acceleration RMS was much smaller than the maximum possible acceleration. If we use the peak acceleration to represent the vibration level, the vibrations generated under many working conditions are greater than the threshold. The vibration intensity is not this intense because the vibration induced by flood discharge is extremely easy to overestimate due to the susceptibility of peak acceleration and the multiple interference sources in residential areas. Moreover, the vibration amplification effect can be generated by the high-rise building structures on the surrounding ground. Thus, the difference between the vibrations of high-rise buildings and those of ground surfaces is significant, which increases the difficulty of the accurate estimation of the vibration intensity felt by the human body. All in all, the target of the optimal operation scheme is to minimize the vibration, while the impact of ground vibration on residents is appropriately estimated based on their feedback. According to that feedback, the ground vibration generated in the working conditions used in 2012 and 2013 induces physical discomfort in many residents, and the feeling of discomfort is effectively reduced by applying the optimal operation scheme used in 2014 and 2015. According to the information provided by the management department of the XHS, the maximum flow rates in the prototype working conditions used in 2016 and 2017 were approximately 6000 and 5500 m3/s can obviously reduce the ground vibration, especially when the orifice gates are 2–3 m open. Thirdly, working conditions with synchronously and uniformly open spillway (or orifice) gates induce lower vibrations than working conditions with non-uniformly (even significantly differently) open spillways (or orifice) gates. These vibration variation laws were obviously verified in the prototype observation, which indicates that the presented hydro-elastic approach and the vibration attenuation operation scheme are effective and reasonable. A detailed optimal operation scheme was shown to reduce the ground vibration in a large discharge range of 0–30,000 m3/s, which has guiding significance in reducing the ground vibration induced by the flood discharge of the XHS under different working conditions. In this study, an improved hydro-elastic model with a vibration isolation system was constructed according to a gravity similarity criterion and structural dynamic similarity conditions. The BP neural network prediction model was applied to establish nonlinear mapping from the model vibration to the prototype ground vibration. Based on the ground vibration prediction approach combining hydro-elastic experiments and a BP neural network, the prototype ground vibration intensities under more than 600 working conditions were predicted, and the following basic laws of vibration variation can be concluded from the results. Firstly, regardless of what the spillway gate openings are, the ground vibration will be amplified when orifice gates are synchronously 5–7 m open. Secondly, the simultaneous discharge of spillways and orifices in a discharge range higher than 1800 m


Spin transport phenomena have been shown to be highly enhanced when the temperature approaches the Curie point of the material sustaining a spin flow. Here we propose a simple - yet unifying - explanation for such enhancements, based on a random-phase model accounting for the spin fluctuations within a ferromagnetic material in the paramagnetic phase. We show that pure spin currents carried by conduction electrons injected into a paramagnetic lattice of mutually interacting localized magnetic moments can be enhanced close to the Curie temperature by the exchange interaction between the lattice sites and the non vanishing spin density associated with the spin current. The latter partially aligns the magnetic moments of the lattice, generating a flow of paramagnons that contribute to the total spin current, resulting in an enhancement that can be as large as tenfold. Spintronics has already demonstrated a huge potential in consumer electronics and has stirred a technological revolution in the field of mass storage media. Spin-based devices that have already made their way to the market include giant and tunnel magneto-resistance reading heads for hard drives and non-volatile magnetic random-access memories (MRAM)3, where information is stored in the parallel or antiparallel alignment between two ferromagnetic (FM) layers.The active control and manipulation of the spin degree of freedom in solid-state systems is the goal of a branch of electronics known as spintronics, which has its foundations on the investigation of spin transport, dynamics and relaxation in electronic materials4. This phenomenon, known as spin-transfer torque (STT), can be exploited for encoding information in MRAMs in a way that holds the promise of being faster, cheaper and less power-hungry than other existing solutions5. However, the fast switching of devices relying on this encoding mechanism still requires current densities that are too high for most commercial applications. Therefore, a strategic issue in spintronics consists in finding solutions to increase the total spin that can be transferred by an electron current. Recently, a sizable enhancement of spin-dependent transport phenomena has been predicted theoretically7 and demonstrated experimentally11 for systems where spins are injected into a ferromagnetic or an antiferromagnetic material near the critical temperature. The mechanism responsible for the enhancement has been traced back to the large spin fluctuations that are thermally excited in the material approaching the ordering temperature.As much as charge currents are the key ingredients of electronics, spin-polarized currents are essential in spintronics. A spin-polarized current carries an angular momentum that can be transferred to a FM layer, inducing oscillations of its magnetization or even flipping it completelyIn the following, we show that a model based on the random phase approximation can provides a simple rationale for fluctuation-enhanced spin transfer phenomena. We evidence how a pure spin current due to carriers flowing in a lattice of disordered (paramagnetic) localized magnetic moments can be much larger than the sum of the spins individually associated with each free particle, if the material is kept at a temperature close to the Curie point. In these conditions, the lattice magnetic susceptibility is considerably enhanced as a consequence of the large spin fluctuations and, thanks to the exchange interaction, the spin accumulation associated with the spin current of mobile carriers results in a sizable magnetization of the lattice. This allows elementary lattice excitations known as paramagnons to diffuse in the solid and contribute to the total spin current.Such a phenomenon might suggest strategies to emphasize spin-dependent phenomena in solids, leading to more efficient spintronic assets, such as faster STT devices or effective architectures for the interconversion between spin and charge currents.d electrons in a paramagnetic transition metal12, in interaction with s-derived spin-polarized conduction electrons13. Our goal is to estimate the expectation value 14:Let us consider a lattice of atoms carrying disordered local magnetic moments, such as the ones associated with the V indicating the sample volume and In Eq. , \documes-d exchange interaction13:N being the number of lattice cells per unit volume and 15.The coupling between the localized and conduction electrons is assumed to be a local t with conduction electrons and its spatial Fourier transform, respectively. In the following we will consider 15, will be treated implicitly by considering the appropriate unperturbed Hamiltonian (see the next section). In Eq.  vary slowly over many lattice sites, the first term in the right-hand side of Eq.  order, small oscillations of the moments around their equilibrium direction will propagate as waves, called magnons. In a paramagnetic material, the magnetic order is partially re-established by the spin accumulation spin polarons, formed by a conduction electron dressed in a cloud of lattice moments aligned with the electron spin by the exchange interaction20. Because of the paramagnon group velocity being much smaller than the Fermi velocity, the total lattice spin dragged by each conduction electron would just be a fraction [expressed by the pre-factor in Eq. . We consider an isotropic and homogeneous system J. Because of the quenching of the angular momentum due to the crystal field, in the following we will assume S the total spin quantum number. s-d and d-d exchange coupling, respectively, and In Eq. , \docume2 in Eq.  appears mentclasspt{minimaEC defined asThe set of Eq.  is assocEC has a simple interpretation in the Weiss model25, which assumes a uniformly magnetized state with λ representing the proportionality constant between the uniform spin d-d exchange interactions. In this case, for T is below the Curie temperature defined as 26. Therefore, in the following, EC should be considered as a parameter describing the magnitude of the (average) exchange interactions between the lattice sites, rather than a quantity strictly related to the true ordering temperature of the system. However, we would also like to add that, despite the RPA is known not to be able to perfectly describe correlations close to phase transitions, it is also widely accepted as a means to capture the essential physics behind complex phenomena.λ>0, Eq.  admit a We consider solutions of Eq.  when theion, Eq.  then yieIn the long wavelength limit  an an\documEC are expressed in electron-volts. Pure Pd and Pt are paramagnetic at any temperature, but they can be turned into ferromagnets by doping with magnetic impurities such as Fe, Co or Ni24, with Curie temperatures that can be as high as d and 5d metals the high spin-orbit interaction might be comparable with the crystal-field splitting, leading to a partial unquenching of the orbital moment25. For late transition elements such as Pd and Pt, the orbital and spin moments are parallel, meaning that there might be a small net contribution due to the orbital moment to the total angular momentum carried by the enhanced spin current.Focusing our attention on Pd and Pt, where TC, in excellent agreement with the predictions previously reported by works describing spin transport by more complex models7. This conclusion is corroborated by the observation of strong enhancements of the spin Hall effect near the Curie point of NiPd8 and FePt11 alloys, which is attributed to large spin fluctuations, a condition that, according to Eq.  magnonsThis spin enhancement can only occur when carriers flow in a material kept at a temperature close to the Curie point, while spintronic devices such as MRAMs require injecting the spin current into a FM layer, where the strong exchange field strongly suppresses the fluctuations of the local moments and thus the carriers are no longer dressed with the spin excitations of the lattice. Therefore, the point is now to understand whether the spin-current enhancement provided by a paramagnet could be exploited in a device.z be the axis perpendicular to the interface, with the FM layer at z in the NM layer. It is worth noticing that, when NM = Pt and FM = Fe, the interface spin resistances of the two metals, 30)  are quite similar to each other32, thus preventing possible issues related to the conductivity mismatch for the transfer of spin-polarized electrons across the Pt-Fe interface30. Moreover, interface NM atoms are magnetically coupled to the FM material, allowing paramagnons diffusing in the NM layer to transfer angular momentum to the FM one, where magnons are excited, and to contribute to the STT33.Let us consider the interface between a FM and a NM layer. Let 34). Despite spin scattering mechanisms could transfer part of the angular momentum to the lattice, the generation of spin-torque by magnons is a well-documented phenomenon39. Therefore the injection of paramagnons into the FM material is expected to significantly contribute to the STT when the system is kept close to the NM Curie temperature.The total angular momentum deposited per unit time into the slab is equal to the total spin current multiplied by We have shown that fluctuation-enhanced spin-transport phenomena could be described by a simple random phase model where a pure spin current flowing into a lattice of disordered magnetic moments is enhanced by the exchange interaction that aligns the magnetic moments of the lattice with the spin of the carriers. The spin-current enhancement is inversely proportional to the difference between the system temperature and the critical temperature describing the strength of the exchange interaction among lattice sites, and becomes significant when the two differ by a few kelvins, in good agreement with experimental results and the predictions of models describing spin transport and fluctuations in a more complex way.


In this paper, we propose subcarrier allocation based cooperative spectrum sharing protocol for OFDM relaying networks with wireless energy harvesting. In the proposed protocol, the cognitive relay node utilizes different subcarriers to forward the primary information to obtain the spectrum access for the cognitive system transmission. The primary system consists of two parts, a primary transmitter (PT) and primary receiver (PR), and cognitive system includes a cognitive source node (CSN), cognitive destination node (CDN) and cognitive relay node (CRN). In the first phase, CRN splits a fraction of the power received from the PT and CSN transmission to decode information, while the remaining power is used for energy harvesting. Then CRN uses disjoint subcarriers to forward the signals of PT and CSN by utilizing the harvested energy in the second phase. Three parameters which consist of power splitting ratio, power allocation and subcarriers allocation are optimized in our algorithm to maximize the cognitive transmission rate with the constraint of primary target transmission rate. Numerical and simulation results are shown to give useful insights into the proposed cooperative spectrum sharing protocol, and we also found that various system parameters have a great effect for the simulation results. Comparing with 3G and 4G networks, 5G network is able to support much higher data rate, which can provide service to not just smartphones but also majority of Internet of Things (IoT) devices. However, the spectrum utilized for the 5G network communication is limited, which will cause numerous IoT devices lack of spectrum to access to the 5G network.To improve the spectrum utilization, cognitive radio (CR) allows the cognitive users (CUs) access to the licensed spectrum of the primary users (PUs) if it finds the spectrum wholly ,2,3 or sCooperative relaying can enhance the communication performance through sharing antennas with neighboring users ,8. CombiSimultaneous wireless information and power transfer (SWIPT) technology has the ability to realize simultaneous information decoding and energy harvesting by receiving radio-frequency signals ,20,21,22In the aforementioned existing SWIPT based cooperative spectrum sharing protocol, the primary and cognitive users interfere with each other, due to the fact that the cognitive relay uses the same spectrum to forward their signals. The interferences result in performance degradation for both the primary and cognitive users. To prevent the cognitive user from interfering with the primary user, in this paper, we propose a subcarrier allocation based cooperative spectrum sharing protocol with two transmission phases. The protocol requires OFDM relaying networks employing wireless energy harvesting, where the cognitive relay node utilizes different subcarriers to forward primary and cognitive signals. Specifically, in the first phase, the cognitive relay splits a fraction of the power received from the PT and CSN transmission to harvest energy. In order to implement SWIPT technology, we use the remaining power to decode information. In the second phase, the cognitive relay forwards PT and cognitive signals through utilizing disjoint subcarriers with the harvested energy in the first phase. We optimize the power splitting ratio, power allocation and subcarriers allocation for the cognitive transmission rate maximization problem with the constraint of primary target transmission rate.Firstly, to prevent the interference between the primary and cognitive systems, we propose a subcarrier allocation based cooperative spectrum sharing protocol with wireless energy harvesting for OFDM relaying networks, in which the cognitive relay uses disjoint subcarriers to forward the signals of primary and cognitive systems.Secondly, we formulate a joint resource allocation scheme aiming to maximize the cognitive transmission rate through optimizing power splitting ratio, power allocation and subcarriers allocation with the constraint of primary target transmission rate.Finally, we provide numerical and simulation results to verify the proposed cooperative spectrum sharing protocol and find out the important effects of various system variables on the simulation results.The main contributions of this work are summarized as follows:As shown in In the proposed spectrum sharing protocol, the following handshake mechanism is adopted, inspired by the classic RTS (ready-to-send) and CTS (clear-to-send) signaling mechanism. When the SNR from PT to PR is below a threshold due to path loss, shadowing, or interference, resulting in the primary achievable rate falling below a target rate, PR will seek cooperation from neighboring terminals to enhance its transmission performance by sending out a request-to-cooperate (RTC) signal, in which the target rate is also embedded. This RTC signal is then responded to by PT with an acknowledge-to-cooperate (ATC) signal. Upon receiving both RTC and ATC signals, CRN is able to estimate the channel gains of PT→CRN and CRN→PR links, and calculate accordingly whether it is able to assist the primary system to achieve its target rate by serving as a cooperative DF relay. If positive, CRN responds by sending a confirm-to-cooperate (CTC) signal to PT and PR to indicate that it can cooperate with the primary system and the primary system correspondingly switches into a two-phase DF relaying mode, with CRN being the relay node. As a reward, the cognitive system can access the primary system to transmit its data. Otherwise, both primary system and cognitive system stop transmission.k, k at PT following waterfilling approach.The primary system needs to predict its achievable rate based on the current SNR from PT to PR before deciding whether to send out the RTC signal. Without any cooperation from the cognitive system, the achievable rate of the primary system is given byWhen the achievable rate of the primary system Next, the cognitive system decides, under the current channel condition, whether it is able to assist the primary system to reach y system . If RmaxK subcarriers to transmit their signals to CRN. Thus, the signal received at CRN over subcarrier k can be denoted ask, k, k, k at CSN following waterfilling approach.The two-phase DF relaying mode is operated through two equal time transmission phases. In the first phase, PT and CSN utilize all of the CRN splits a fraction of received power with ratio ng model ,27,28,29The achievable rate of In the second phase, CRN divides the subcarriers into two disjoint sets Then in the second phase the achievable rate of Thus, after two transmission phases, the achievable rate of primary and cognitive system can be denoted asThe target is to maximize the achievable rate of the cognitive system while guaranteeing the primary system achieves its target transmission rate under the transmit power constraints, through optimizing the power splitting ratio In Equation , we can Due to the constraints in Equation , we can n method  with theWe can obtain the Lagrange dual function of the problem in Equation  as(16)g,GwhereL=α1The optimal value of 1. Obtaining optimal Taking the partial derivatives of The optimal 2. Obtaining optimal Substituting Equations (20) and (21) into Equation  and afteIn the right-hand side of Equation , we can k, which have a positive Then, all the subcarrier With the above two steps, the optimal primal variables Equation  can be fWe will show the simulation results to illustrate the performance of our proposed protocol in this section. Subcarriers number is set to be 32. The transmit power of CSN We propose a cooperative spectrum sharing protocol with two transmission phases for OFDM relaying networks with wireless energy harvesting in this paper. In the proposed protocol, CRN utilizes disjoint subcarriers to help forward the signals of primary and cognitive systems. Thus, both primary and cognitive systems will not interfere with each other to deteriorate the performance. Specifically, a fraction of the power received at CRN from the PT and CSN transmission will be split to harvest energy, and the remaining fraction of power is utilized for information decoding. CRN uses disjoint subcarriers


A low-cost inertial measurement unit (IMU) and a rolling shutter camera form a conventional device configuration for localization of a mobile platform due to their complementary properties and low costs. This paper proposes a new calibration method that jointly estimates calibration and noise parameters of the low-cost IMU and the rolling shutter camera for effective sensor fusion in which accurate sensor calibration is very critical. Based on the graybox system identification, the proposed method estimates unknown noise density so that we can minimize calibration error and its covariance by using the unscented Kalman filter. Then, we refine the estimated calibration parameters with the estimated noise density in batch manner. Experimental results on synthetic and real data demonstrate the accuracy and stability of the proposed method and show that the proposed method provides consistent results even with unknown noise density of the IMU. Furthermore, a real experiment using a commercial smartphone validates the performance of the proposed calibration method in off-the-shelf devices. An inertial measurement unit (IMU) and a camera form a widely used sensor configuration for mobile platform localization. For example, visual-inertial SLAM ,3,4,5,6 To use inertial measurements and images simultaneously, calibration of these two heterogeneous sensors is very critical. The calibration of a low-cost IMU and a rolling shutter camera has been studied for last decades in robotics and computer vision community ,17,18,19Most IMU–camera calibration methods estimate the calibration parameters with fixed noise densities of the IMU and camera measurements, which are typically handled as tuning parameters. To achieve accurate calibration, we need to know such noise densities of the IMU and camera. Fortunately, for cameras, the variation in noise densities is not large because calibration patterns  are used for corner extraction. Therefore, it is dependent on feature extraction algorithms, whose accuracy in terms of pixels can be easily evaluated and is well-known . In contTo address these problems, we jointly estimate the noise density of the low-cost IMU and the intrinsic/extrinsic calibration parameters through the graybox system identification, which estimates the unknown parameters describing the prediction of the dynamic system well ,22,23. IFor calibration, rather than finding the calibration parameters in a single optimization step, we divide the calibration process into the filtering step for initialization and the optimization step for refinement. As a result, the convergence time of our framework becomes much faster than the single optimization method. This is because it finds sub-optimal calibration parameters in the filtering step, whose computation time is more efficient than the optimization, and then uses the parameters as an initial value of optimization. Hence, the good initial estimates from filtering reduces the convergence time of optimization for the calibration problem. In fact, it is difficult to design both the calibration and noise parameter estimation problems together in the single optimization step. In the filtering step, we utilize the unscented Kalman filter (UKF) to address the strong nonlinearity of our calibration problem, and its state vector consists of the intrinsic/extrinsic calibration parameters as well as the IMU motion parameters including the position, velocity, and orientation. In the optimization step, we refine the calibration parameters with the noise density estimated from the previous filtering step, while the UKF only estimates the IMU motion including the position, velocity, and orientation.For noise identification, the optimizer estimates the noise density that attempts to make the UKF converge properly while enabling the estimation of calibration parameters by UKF. Unlike the previous graybox method , we defiIMU intrinsics: biases, scale factors, and misalignmentsCamera intrinsics: focal length, radial distortion coefficients, and rolling shutter readout timeIMU–camera extrinsics: relative rotation, translation, and time delay between an IMU and a cameraIMU noise parameters: noise density of a gyroscope and an accelerometerWe demonstrate the overall procedure of the proposed method with the input and output in The remainder of this paper is organized as follows. As mentioned in The intrinsic calibration of a camera is a well-known problem in computer vision . TherefoThe intrinsic calibration of an IMU has been performed using mechanical platforms such as robotic manipulators, which precisely moves IMU along known motion trajectories ,8,9. TheThe extrinsic calibration of an IMU and a camera has been studied for the last decade in robotics community. Mirzaei and Roumeliotis  first prJoint estimation of the intrinsic and extrinsic parameters of an IMU and a camera is efficient because it does not need to conduct calibration independently for each sensor. Furthermore, it generates more accurate results because it minimizes the intrinsic and extrinsic calibration errors simultaneously. Moreover, the joint estimation is more practical since most mobile devices are equipped with a low-cost IMU and a rolling shutter camera. The joint estimation has been introduced in , where aThe Allan variance (AV) and the non-parametric power spectral density are the classical tools used to describe noise characteristics of an IMU. Refer to  for a deOur system comprises a low-cost IMU and a rolling shutter camera, and these two sensors are rigidly connected as in M corners of the checkerboard in the image coordinate. Given the visual and inertial measurements, we formulate the calibration and noise identification as a minimization problem as follows.To generate calibration data, we sequentially obtain inertial measurements and images by capturing a checkerboard along three-axis linear and angular motion. The inertial measurements k denote time steps. We explain the aforementioned notations in detail as follows.In this section, we describe the system and measurement models for calibration as follows.We include the sensor motion parameters in the state vector. Therefore, the state vector Here, the motion state The extrinsic parameter The IMU intrinsic parameter The camera’s intrinsic parameter We describe the system model Equation  performik is the time-step of the visual measurements, while s is that of the inertial measurements.The state transition (or prediction) is sequentially performed with the inertial measurements The nonlinear system model in Equation  is defint, and the other calibration parameters are considered as constant because they are static and two sensors are rigidly connected. Note that we do not regard the bias states as smoothly time varying parameters, unlike )We also compare the prediction errors of the UKF for motion estimation with calibration parameters estimated by the Kalibr method and the proposed method. In this experiment, the states of the UKF are a position, velocity, and orientation of the IMU, and they are predicted by inertial measurements and corrected by visual measurements, which are corners of a checkerboard pattern. We record a set of inertial and visual measurements using the smartphone “Samsung Galaxy Alpha” for 60 s. The prediction errors using the Kalibr are accumulated due to the IMU noise and they result in the motion drift. However, Finally, we compare the localization accuracy with calibration parameters estimated by the Kalibr method and the proposed method. In this experiment, we capture image sequences and inertial measurements using the smartphone “Samsung Galaxy Alpha” in an outdoor vehicle driving environment. The trajectories are estimated by VINS-mono , which iThis paper proposes a robust and accurate calibration method for a low-cost IMU and a rolling shutter camera. The proposed joint calibration estimates not only the intrinsic and extrinsic parameters but also the IMU noise parameters. To improve calibration efficiency including runtime, we divide the framework into two steps. In the first step, we roughly estimate the intrinsic and extrinsic parameters through filtering while estimating the noise parameters in the optimization module. In the second step, we refine the intrinsic and extrinsic parameters via the optimization module while estimating the sensor motion in filtering. The experimental results of the synthetic data demonstrate the superiority of our framework, and, in particular, the experiments on two real-data setups validate the performance of the proposed method in off-the-shelf devices.As a result, the proposed method enhances the runtime about 73.3% and reduces IMU drift by 19.2% in comparison with those of the Kalibr method ,19. In p


Immunoglobulin A is a class of antibodies produced by the adaptive immune system and secreted into the gut lumen to fight pathogenic bacteria. We recently demonstrated that the main physical effect of these antibodies is to enchain daughter bacteria, i.e. to cross-link bacteria into clusters as they divide, preventing them from interacting with epithelial cells, thus protecting the host. These links between bacteria may break over time. We study several models using analytical and numerical calculations. We obtain the resulting distribution of chain sizes, that we compare with experimental data. We study the rate of increase in the number of free bacteria as a function of the replication rate of bacteria. Our models show robustly that at higher replication rates, bacteria replicate before the link between daughter bacteria breaks, leading to growing cluster sizes. On the contrary at low growth rates two daughter bacteria have a high probability to break apart. Thus the gut could produce IgA against all the bacteria it has encountered, but the most affected bacteria would be the fast replicating ones, that are more likely to destabilize the microbiota. Linking the effect of the immune effectors (here the clustering) with a property directly relevant to the potential bacterial pathogeneicity (here the replication rate) could avoid to make complex decisions about which bacteria to produce effectors against. Inside the organism, the immune system can fight generically against any bacteria. However, the gut lumen is home to a very important microbiota, so the host has to find alternative ways to fight dangerous bacteria while sparing beneficial ones. While many studies have focused on the complex molecular and cellular pathways that trigger an immune response, little is known about how the produced antibodies act once secreted into the intestinal lumen. We recently demonstrated that the main physical effect of these antibodies is to cross-link bacteria into clusters as they divide, preventing them from interacting with epithelial cells, thus protecting the host. These links between bacteria may break over time. Using analytical and numerical calculations, and comparing with experimental data, we studied the dynamics of these clusters. At higher replication rates, bacteria replicate before the link between daughter bacteria breaks, leading to growing cluster sizes, and conversely. Thus the gut could produce IgA against all the bacteria it has encountered, but the most affected bacteria would be the fast replicating ones, that are more likely to destabilize the microbiota. Studying the mechanisms of the immune response may uncover more such processes that enable to target properties hard to escape through evolution. Salmonella spp. and commensal E. coli) can show highly variable behaviors in the intestine, identifying which bacteria are good or bad is challenging. Besides, the overgrowth of any type of bacteria, even those that do not cause acute pathology, can impair the functionality of the microbiota. Thus the host needs mechanisms to maintain the gut microbiota homeostasis.The digestive system has a large surface area , 2, coveSalmonella . It seems however, though there is not enough data to quantitatively ensure it, that there are less long clusters than expected , and the distribution of chain lengths.We investigated if this qualitative idea holds with more realistic models. We started from a base model in which: bacteria replicate at a fixed rate; remain enchained upon replication; until the link between them breaks at a given fixed breaking rate, identical for all links; and considering that, because of the way bacteria such as q = 1), the growth rate of the number of free bacteria is lower than the replication rate. And more spectacularly, in most of the models studied , the growth rate of the number of free bacteria is non-monotonic with the replication rate: there is a finite replication rate which maximizes the growth rate of non-clustered bacteria. At very high replication rates, bacteria get trapped in more complex clusters and cannot contribute anymore to the free bacteria dynamics and thus to the next steps of the infection process. The replication rate maximizing the growth rate is of the order of the breaking rate, though its specific value depends on the details of the model. To summarize, except when q = 1, we always find that the higher the replication rate, the higher the proportion of bacteria trapped into clusters; and in many cases, the effect is even more dramatic, with the growth rate of free bacteria that may decrease with the replication rate.We find that, except in the very specific case in which subchains always escape upon link-breaking  of the immune effectors with a property directly relevant to the potential bacterial pathogeneicity (here the replication rate) avoids to make complex decisions about which bacteria to produce effectors against.S1 Text(PDF)Click here for additional data file.S1 File(ZIP)Click here for additional data file.S2 File(ZIP)Click here for additional data file.S3 File(ZIP)Click here for additional data file.S4 File(ZIP)Click here for additional data file.S5 File(ZIP)Click here for additional data file.


We present and demonstrate an efficient method for the reconstruction of profiles acquired by multifocal structured illumination microscopy (MSIM) utilizing few raw images. Firstly, we propose a method to produce nine raw multifocal images with enhanced modulation depth to accomplish the uniform illumination of the sample. Then, combing with the parameter of the arrays, we perform the standard construct reconstruction procedure of structured illumination microscopy (SIM) row by row and column by column. Finally, we combine these restored images together to obtain the final image with enhanced resolution and good contrast. Based on theoretical analysis and numerical simulations, this method shows great potential in the field of the image reconstruction of MSIM data. Therefore, it severely hinders the observation of the fine structure of biological samples. To circumvent the Abbe limit and achieve super-resolution, the past two decades have witnessed the impressive development in super resolution microscopy filed, and a variety of related techniques have come into being5 to enable measurements within spatial regimes that were previously inaccessible, such as photo-activated localization microscopy (PALM)8, stochastic optical reconstruction microscopy (STORM)11, stimulated emission depletion microscopy (STED)14, and structured illumination microscopy (SIM)18.The wave nature of visible light has hampered the development of optical microscopy in spatial resolution. The Abbe diffraction limit imposes a critical limit on the spatial resolution of optical microscopy, meaning that the maximum available resolution under a wide-field microscope is approximately equal to one-half of the fluorophores emission wavelength which remains two orders of magnitude above the size regime relevant to many molecular reactions and subcellular structures20. In addition, conventional SIM with sinusoidal illumination patterns offers the advantage which does not require additional complex sample preparation effort. However, under the circumstances of high scattering media and high light intensity, the advantages of SIM based on wide-field imaging are not obvious enough due to the optical aberrations and scattering of the sample. Utilizing point scanning to acquire images, the contrast and quality of the data can be proper maintained while it may be far too slow for monitoring many live cellular processes.As one of the mainstream super resolution microscopies, SIM applies spatially patterned illumination to elicit sample fluorescence. By frequency-mixing between the excitation pattern and fluorophore density, it visualizes high-resolution information which is inaccessible in the conventional microscope. Linear SIM can double the resolution limit of the conventional imaging system while nonlinear structured light technology can improve the performance of lateral resolution further21 is a joint Richardson-Lucy deconvolution algorithm to achieve the reconstruction of MSIM data along with enhanced resolution and good quality. However, the method needs too many images (143 images) and iterations (between 5–30 times) to accomplish the reconstruction, which is complicated and blocks its extensive application. Meanwhile, the method reported in ref.22 deconvolves the multifocal-excited, pinholed, scaled and summed (MPSS) images to achieve resolution doubling in live and multicellular organisms. In this method, to fully illuminate the sample, 120 raw multifocal images are acquired and processed to obtain a super resolution image. Although the final images show excellent quality, procedure of data process should been well taken into consideration and might consume lots of effort and time. In this paper, for the sake of image reconstruction of MSIM data, in first step we proposed a method to generate nine raw multifocal images with enhanced modulation depth, then combing with the parameter of the arrays we performed the standard construct reconstruction procedure of SIM row by row and column by column in the these images, respectively. Finally, we combined these restored images to obtain the final image with enhanced resolution and good contrast. Our method holds the merits of high efficiency and flexibility, which has great potential in the field of the reconstruction of MSIM data.MSIM, with a sparse lattice of excitation foci would dramatically increase acquisition speed and show excellent performance. MSIM could not be well achieved without proper reconstruction methods for the data profiles. The number of original images used for image reconstruction is closely related to the efficiency of the method. The method reported in ref.As a validation of principle, we created artificial MSIM data based on the standard wide-field model and processed it with the proposed reconstruction algorithm which we implemented in MATLAB. The simulations were operated on the resolution test target and the Leaf image, respectively.23. To maintain the modulation depth of the multifocal array, we set a threshold based on the maximum intensity of the array and only the parts with the amplitude above the threshold of the array is retained. As illustrated in Fig. To generate the multifocal array, we superimpose two sinusoidal stripes but orthogonal to each other as shown in Fig. To confirm the improvement of spatial resolution provided by the proposed method, we analyze and compare the simulation results, where the sample is the resolution test target . Figure 24 and Gaussian noise, which may be more close to the noise in practical experiments. Figure To illustrate the necessity of setting thresholds to generate the multifocal arrays, we analyzed the results restored by our methods where the raw images are all contaminated by a combination of Poisson noise22, the number of raw multifocal images for reconstruction is rather fewer and procedure of the reconstruction is relatively convenient to implement and operate, which is vital and suitable for the live cell imaging and monitoring along with less phototoxicity.With our method, a super resolution image can be obtained just with nine original multifocal images. Compared with methods related to reconstruction of MSIM data25. Besides, to achieve the fullest resolution improvement, the frequency of the multifocal arrays should be close to the cutoff frequency of the microscopy system.Based on wide-field microscopy, the field of view in conventional SIM is nearly equivalent to that in wide-field microscopy. Spot-scanning SIM can achieve same spatial resolution improvement as the traditional SIM, while its field of view is smaller than that of traditional SIM owning to the limitation of scanning angle of scanning device. If the scanning angle of scanning device is quite large, there would be large aberrations and distortions at the edges of the field of view resulting in degradation of resolution. Parallelization of spot-scanning SIM, MSIM could dramatically improve the efficiency of the data acquisition and realize the same resolution improvement as conventional SIM. Precise knowledge of the excitation pattern is quite imperative to MSIM in both applying digital pinholes and in image reconstruction. These effects are particularly apparent when it comes to imaging highly scattering or thick tissue samples, where the aberrations and noise produce reconstruction artefacts in the final imageTo achieve the entire illumination of the sample, successive application of nine different patterns can be realized via a single programmable spatial light modulator (SLM) with the merits of program flexibility and the moveable parts is not required. Owing to the characteristics of multifocal arrays, every single excitation focus may have a relatively high intensity and the obtained multifocal arrays might physically reject out-of-focus light and permit imaging the sample even with high scatter property. It should also be taken into consideration that the proposed approach could be applied in two-photon excitation and adaptive optics (AO) for imaging thicker samples with the proper improvement of implements.In conclusion, we proposed and demonstrated a strategy for the reconstruction of MSIM data. Meanwhile, we presented the feasible approach for the generation of multifocal arrays with considerable modulation depth which is used to maintain the final image with enhanced image contrast. With nine raw multifocal images, the proposed strategy to restore super-resolution images is of high efficiency and has great potential in live cell imaging.Iem(x) multiplies the sample fluorescence S(x), consequently eliciting fluorescence emission, which is blurred by diffraction, yielding the image Iex(x):PSFem(x) is the emission point spread function (blurred image of a point source), and ⊗ denotes the convolution operation. Fourier transformation of Eq. (OTFem(k) is the Fourier transform of the PSFem(x).In fluorescence microscopy, the illumination pattern k0 and φ are the spatial frequency and the phase of the illumination patterns, and I0 is the peak illumination intensity. By Fourier transforming Eq. . By obtaining three images with three different phases  of the illumination pattern we can obtain a system of three independent linear equations, allowing us to extract the three terms in Eq. (OTFem(k), as same as in the conventional wide-field microscopy. Consequently, it is possible to increase the resolution of the optical microscope along the pattern’s direction by a factor of approximately two in this case.The first term in Eq.  denotes s in Eq. . After tkx,y and φx,y are the spatial frequency and the phase of the two illumination patterns along the X or Y direction, respectively. Substituting the Fourier transformation of Eq.  by row by row, and obtain the image Fig. Add up the obtained images, Fig. Figure OTFem(k) of the optical system as well. Compared with the traditional fluorescence microscopy, the proposed method could improve the spatial resolution by a factor of two as the traditional SIM under the linear situation.The spatial frequency of the multifocal array is limited by the


High-intensity X-ray sources are invaluable tools, enabling experiments at the forefront of our understanding of materials science, chemistry, biology, and physics. Laser-plasma electron accelerators are sources of high-intensity X-rays, as electrons accelerated in wakefields emit short-wavelength radiation due to betatron oscillations. While applications such as phasecontrast imaging with these betatron sources have already been demonstrated, others would require higher photon number and would benefit from increased tunability. In this paper we demonstrate, through detailed 3D simulations, a novel configuration for a laser-wakefield betatron source that increases the energy of the X-ray emission and also provides increased flexibility in the tuning of the X-ray photon energy. This is made by combining two Laguerre-Gaussian pulses with non-zero net orbital angular momentum, leading to a rotation of the intensity pattern, and hence, of the driven wakefields. The helical motion driven by the laser rotation is found to dominate the radiation emission, rather than the betatron oscillations. Moreover, the radius of this helical motion can be controlled through the laser spot size and orbital angular momentum indexes, meaning that the radiation can be tuned fully independently of the plasma parameters. Conventional methods for the production of X-rays require first accelerating electrons to high energies, which involves large and costly facilities such as synchrotrons. Laser-driven accelerators4 are potentially a much more compact and less costly approach to generate the required electrons and, for some electron energies, the X-ray emission as well2.High brightness X-ray sources are of great use throughout science, from diagnosing biological samples7, in which mono-energetic 100 MeV electron beams were first obtained. Current wakefield accelerators now reach up to GeV energies with only a few centimeters of plasma as the acceleration medium11.The achievable electron energy in laser-wakefield accelerators (LWFAs) has undergone a rapid growth since the original “dream beam” experiments13. Due to the high electron energies attained in the accelerator, this emission is in the X-ray range, with typical peak photon energies up to 1–20 keV16. This has been shown to be a viable broadband high-brightness X-ray source17.Plasma wakefield accelerators not only provide high energy beams but represent a source of short-wavelength radiation as well. The transverse electric field that is naturally formed by the positive charge in the wakefield bubble causes the electrons to oscillate as they are being accelerated, which leads to the emission of betatron radiation18. This fixes the plasma density as a function of the laser parameters, thus restricting the available parameter space. Several approaches have been explored to control the amplitude of the transverse oscillations. One possibility lies in modifying the initial amplitude of oscillation by controlling the phase-space of the injected electrons, for example through colliding pulse injection19 or magnetically controlled injection20.The specific properties of the emission depend on the plasma density, electron energy and amplitude of electron oscillations. For stable laser propagation and maximum energy transfer to the electrons, it is desirable to operate under the so-called “matching” conditions21 and at an angle with the plasma channel22. These designs require good control of the laser incidence on the plasma channel. Laser drivers with duration close to the bubble size can be used to induce direct laser acceleration23 and, for longer pulses (with ps duration), self-modulated laser-wakefield acceleration has been explored as an X-ray source25 for high-density matter probing. In all of these configurations, the laser driver has a Gaussian profile, which is also the typical profile used in the vast majority of experiments in this area. Though there has been much progress, some applications of X-ray sources are still out of reach due to insufficient number of photons and would benefit greatly from increased tunability2.Alternative schemes have been proposed which modify not just the initial conditions but also the oscillation amplitude throughout the propagation of the wakefield. These include, for example, injection of the laser driver off-axis27) has received great interest after it was shown that Laguerre-Gaussian modes carry orbital angular momentum28. Several mechanisms for the production of high intensity pulses with orbital angular momentum (OAM) have been proposed29 and their interaction with plasmas is also being explored34. Recent experiments where high-intensity light pulses with orbital angular momentum (OAM) were produced35, open the way for new avenues to control laser-wakefield accelerators. Laguerre-Gaussian laser pulses have been shown to drive wakefields whose field structure is capable of accelerating positrons33. Combinations of such beams can be used to change the topology of the wakefield itself, e.g. helical wakefields driven by “light springs”34. Superposed Laguerre-Gaussian lasers have also been used, in the low-amplitude (linear) regime, to produce carefully-tailored intensity patterns36. This setup holds particular promise for developing laser-wakefield based free-electron lasers37.The field of structured light  index. In this proposed design, the combination of beams is employed to induce a rotation of the wakefields. This rotation forces the helical motion of the trapped electrons, enhancing their oscillation amplitude. This oscillation saturates with its amplitude approximately equal to the radius of the helix described by the laser lobes, which is given by the distance to the propagation axis and is larger than the bubble radius. Tuning of the oscillation amplitude (and hence of the wiggler strength parameter) is achieved by controlling this distance, which can be done by varying the laser spot size and the OAM indexes. So long as blowout occurs, the wiggler strength in our scheme does not depend sensitively on the laser intensity unlike direct laser acceleration or the scheme proposed by Wang We show, through three-dimensional particle-in-cell (PIC) simulations, that this scheme has the potential to significantly enhance X-ray generation by providing a means to increase the amplitude of oscillations of the trapped electrons compared to non-rotating wakefields driven by lasers with the same energy and duration, and similar waist. This increase is a result of the fact that in Gaussian laser-driven LWFAs the amplitude of the betatron oscillations is a fraction of the radius of the bubble, and limited by its value, whereas in the rotating wakefield scenario it is dependent on the laser spot sizes and orbital angular momentum indexes, allowing for greater flexibility.p and azimuthal orbital angular momentum (OAM) index W0 is the laser spot size, k0 is its wavenumber, z is the coordinate along the laser propagation axis, zR is the Rayleigh length and In this work, we investigate radiation emission from laser-wakefield accelerators (LWFAs) driven by multiple Laguerre-Gaussian (LG) pulses. These pulses are characterised by an electric field of the form27. Examples of these composite vortex beams are “light springs”, a combination of pulses with a helical intensity pattern38. It has been shown that these light springs can drive twisted helical wakefields, which rotate as the driver beam propagates34. If the duration of such pulses is much shorter than the helix temporal pitch, they will no longer look like a spring, instead being comprised of multiple rotating laser beam lobes  simulations were performed within the OSIRIS framework45. This avoids the need for external injection, which would require fine control of the initial beam parameters. Further simulation details are described in the Methods section.In each case, the laser driver propagates in a plasma channel with a transverse parabolic density profile matched to its spot size, given by 34), is much smaller than the electron plasma frequency In Fig. Operation in the matched regime typically favours lower densities, which means this condition is easily fulfilled, as in this simulation.From our analysis of the evolution of the laser fields in the simulation, the rotation frequency was determined to be approximately entclass1pt{minimaB134, shown in Fig. 34), which should be due to a poloidal dependence of the currents in this case.Before delving into the analysis of the electron dynamics in the different simulations, we would like to point out some distinct features of the bubbles and the structure of the fields inside them. In the composite vortex beams case (simulation A), the laser intensity lobes are bean-shaped in the transverse plane  was determined see Fig. . As expeThe radiated energy captured in the detector in Fig.  was inteThe radiated energy spectrum, integrated over the detector area, is shown in the right panel of Fig. K (the ratio between the maximum angle of deflection of the trajectory to the angular aperture of radiation), the fundamental frequency 17:rw is the amplitude of the oscillations, for (13 and the average radiated power (averaged over one period) is 17. For The dynamics of electrons undergoing betatron  oscillations is analogous to those experienced in wigglers, i.e. magnetic field devices composed of arrays of magnets of alternating polarity. Both in magnetic wigglers and plasma wigglers, information about the main properties of the radiation can be obtained from quantities such as the wiggler strength parameter 48. Nevertheless, they provide useful information on the local properties of the radiation, and experimental results have shown that the spectrum is still approximately synchrotron-like49.In laser-wakefield accelerators, wiggler emission also occurs, but the presence of an accelerating electric field in the direction of the laser propagation makes these parameters time-dependentrβ, in the rotating scenario it is approximately equal to the distance from the centre of each bubble to the propagation axis Rh. Visual inspection of the projection of the trajectories in the plane transverse to the laser propagation yields In the scenarios studied in this work, if one assumes we can interpret the spectrum in terms of the wiggler analogy, the local critical frequency is (apart from the electron density) just a function of the particle energy and amplitude of oscillation  but are a result of the distinct transverse dynamics in the rotating wakefield scenario. In particular, both the amplitude of oscillation and the azimuthal component of the perpendicular momentum are much higher in the rotating wakefields scenario compared to the other two.The second advantage of our proposed setup is that it allows greater control of the radiated energy spectrum compared to typical LWFA betatron sources. A qualitative comparison between the main features of betatron radiation from the rotating wakefields studied in this work and betatron radiation from typical laser-wakefields can be performed by inspecting the ratio between the expressions for the main parameters of the radiation in the two cases. To facilitate comparisons, in the following we present these ratios in normalised units, with frequencies normalised to 50. Furthermore, In typical LWFA betatron radiation the wavelength of the oscillation is Rh and the wavelength of the oscillation is In the rotating wakefield scenario, as the dynamics is dominated by the helical motion, the wiggler amplitude of oscillation is given by the radius of the helix The ratio between the parameters of the two scenarios,  and 7),,7), is tγ and α only. Taking the approximate average final value of γ, the wiggler strength parameter is It is interesting to note that, for the simulation parameters employed here, the fundamental frequency and the wiggler parameter for the rotating and non-rotating cases are quite different. If we approximate the initial betatron radial position in the non-rotating case to be a fraction of the laser spot size sing Eqs  and 8c)\documentFinally, the ratio between the average instantaneous radiated power γ−1/4.From this wiggler analogy, one can estimate for which parameters of the laser the betatron emission in rotating wakefields is more advantageous than in the non-rotating case, and how to tune the parameters to achieve the desired radiation properties. A more rigorous analysis of the dynamics of the electrons is required for a detailed knowledge of the radiation properties. It should be noted, however, that in these expressions it is assumed that the electron energy scales with propagation distance (or time) in the same manner in both the rotating and non-rotating scenario. Dephasing was observed to occur sooner in the rotating case compared to the non-rotating one in the simulations of the previous section. While this means that electrons injected in these cases could reach higher energies if the propagation of the laser drivers were extended, it does not follow that radiation emission would surpass that of the rotating laser scenario since the oscillation amplitude scales with An additional approximation in this analysis is that the parameters associated with the laser-driver rotation, hence the wakefield rotation, are considered constant. As depletion of the laser sets in, the wakefield group velocity and angular velocity will change.In laser-wakefields, the plasma is underdense and the initial radial position of trapped electrons is less than the bubble radius, which is approximately equal to the laser spot size under matched conditions. Furthermore, the laser spot size is typically larger than equation . Under tIn this work, the possibility of exploiting composite vortex beams to drive rotating wakefields and enhance the radiation emission from the accelerated electrons was explored. The composite vortex laser driver can lead to rotating wakefields in the plasma. The electrons trapped in these bubbles are thus forced to follow this imposed helical motion. This motion can lead to enhanced radiation emission compared to betatron radiation from typical laser-wakefield accelerators.Our simulation results show, for the earliest trapped electrons, a significant increase in the energy emitted per electron in the case of rotating wakefields compared to non-rotating wakefields driven by either non-rotating composite or Gaussian laser beam drivers. These simulations were performed with the same pulse energy for comparison purposes. We have also demonstrated that, even though the fundamental frequency of radiation in the rotating case is generally much lower than the betatron frequency, the wiggler strength parameter will be higher. For the parameters chosen here, the critical frequency was also higher than in the comparable non-rotating scenarios. While the results provided in this manuscript concern only a small fraction of the trapped electrons, they illustrate the distinct transverse dynamics observed in the rotating wakefield case. Though the amount of charge injected and the electron energy spectrum will vary with the choice of parameters, the rotating wakefields setup shown here provides an additional degree of freedom to tune the amplitude of oscillations compared to typical Gaussian-laser driven LWFAs, since it is not limited by the bubble radius, but instead is a function of the laser spot size and the OAM indexes. In some scenarios, for the same laser energy and comparable laser parameters, choosing a rotating wakefield setup driven by a composite vortex beam may provide a much more efficient and higher-frequency radiation source, albeit with higher divergence.In typical laser-wakefield scenarios the properties of the betatron radiation are determined by the plasma properties, after matching conditions are imposed. However, the characteristics of radiation emitted by the electrons accelerated in rotating wakefields can be tuned through adjusting the spot size and orbital angular momentum indexes. As these are not fixed by the matching conditions, this provides a novel capability – tuning of these radiation sources.43. In the first two simulations (A and B), the laser driver is composed of two LG pulses, each with normalised peak vector potential The three-dimensional particle-in-cell (PIC) simulations in this work were performed within the OSIRIS framework51, two macro-particles per ion are used for the electrons from the Helium atoms and ten macro-particles per ion for the Nitrogen electrons. The sample electrons for radiation post-processing were chosen randomly  early in the simulation, at The simulation box is 45. This avoids the need for external injection, which would require fine control of the initial beam parameters.In each case, the laser driver propagates in a plasma channel with a transverse parabolic density profile with a channel radius of 47. The radiated energy and spectrum are determined (incoherently) using the standard formulas from classical electrodynamics46:p is in the particles of the sample, Spixel is the detector cell area, β is the velocity of the electron normalised to the speed of light c and R is the distance from the particle position to the center of the detector cell, n is the unit vector pointing from the particle position to the center of the detector cell. The evolution of the electron sample in phasespace is obtained by recording the trajectories of these electrons during the PIC simulation. Samples of 992 1446 and 2000 macroparticles were recorded in simulations A, B and C respectively. A time-resolution of 4Δt and detector grid with t was employed. The spatial region used for the spectrum calculation was The radiation emission analysis in this work was performed using the jRad post-processing radiation codet) and the momentum bin size is Figure