With the further transformation of The Large Sky Area Multi-Object Fiber Spectroscopic Telescope, the new generation of fiber positioner robot chooses a 4 mm hollow cup motor with minimum phase inductance. Because the load of the fiber positioner robot is constant and the inertia of the motor is very small, an open loop positioning control method based on Space Vector Pulse Width Modulation is proposed, and the specific open loop parameters are directly tuned by relevant experimental strategies. The critical factors of the open loop driving mode are discussed in detail from four aspects: subdivision, fundamental frequency, wave generation mode and peak current. Based on the actual fiber positioner robot, the hardware driver and assessment platform are built. The positioning tests show that the method proposed is practical and effective, and meets the precision positioning demand of the new generation optical fiber positioner robot. With the further transformation of the astronomical telescope LAMOST project, the panel is designed to be smaller and the number of positioner robots increases to 5000, hence the mechanical design of fiber positioner robots  motor, because of its superior speed performance in a wide range of speed regulation, it is widely used in many speed regulation applications.Throughout the whole field of theta-phi optical fiber positioners, the classical stepper motor10, based on FOC (Field-oriented control) or other control methods to form a position closed loop negative feedback control system to meet the demands of precision positioning. This is also the control scheme selected by SDSS-V Sloan Astronomical observation system11.sensored closed loop control, the encoder is usedsensorless closed loop control, divided into two categories according to the principle of detecting rotor position:13 uses BEMF model to estimate the rotor position; the theoretical application scenario is that rotor spins at medium or high speed, when there is a fair adequate BEMF to estimate the rotor position. But when motor is in zero speed or low speed, i.e., there is no BEMF or BEMF signal will be very weak, a series of rotor position estimation algorithms based on BEMF model, e.g. SMO16, Adaptive methods17, State Observer18 and AI  methods21, will not be applicable.The BEMF (back electromotive force) method23 depends on the motor convex polarity model24 (decomposing the angle information between 0 to 25 (distinguishing north or south pole information).The HFI (high-frequency injection) methodsBut in the precision positioning control field, there are two closed loop control schemes for BLDC motor: sensored and sensorless.The method based on the BEMF model is applicable to the green part of the Fig. However, the selected miniature 4 mm hollow cup motor does not have a 4 mm encoder matching its size as the position feedback unit in a closed loop position control system, and the inner rotor of the motor is composed of a whole magnet without convex polarity. Additionally, its ironless windings has no characteristic of inductance saturation.On the other hand, the carrier frequency of PWM (Pulse Width Modulation) in conventional closed loop control are limited by phase current sampling and the execution of complex algorithms, especially in sensorless control algorithm will be lower. As far as the current microcontroller is concerned, the PWM carrier frequency is usually at dozens of kHz in closed loop. For the miniature hollow cup motor with minimum coil inductance, the short freewheeling time is hard for closed loop control system to improve the carrier frequency. Here is the dilemma: when the carrier period is too long and the current acquisition device in the closed loop controller is about to collect current and other feedback information, the freewheeling in inductance has been just over, then the whole closed loop control will not be conducted correctly.On account of the fiber positioner robot is basically a constant torque load for the motor, and the inertia of 4 mm BLDC is small , and run complex control algorithm in software. The carrier frequency of PWM can be easily raised to hundreds of kHz, which is very advantageous for miniature hollow cup motors with minimum coil inductance (e.g. the coil inductance of 4 mm motor we chosed is only 37 uH). Furthermore, robust positioning performance and strong reliability can be achieved simply. An open loop method is applied to the controller design of fiber positioner robot. And open loop driving parameters are regulated by experimental strategy and the specific effects of each parameter are discussed in detail. In order to assess the effectiveness of the positioning system, the positioning test is carried out on universal toolmaker’s microscope. The results reveals that the open loop positioning system satisfies the positioning requirements of the new generation LAMOST. And the hollow cup motor itself is more efficient than the stepper motor, reducing the heat dissipation of the whole system, creating a better thermal condition for the whole spectrum environment, decreasing the harmful effect of the positioning drive system to the seeing of astronomical observation.26 is the most important part of digital vector control system. In voltage modulation, there is only one switch in each group of bridge arms  read the vector information stored in the FLASH at the end of the previous positioning operation. I.e., after every time of optical fiber positioner robot finishing the positioning task, the last positioning vector executed will be written into the FLASH of the MCU for storage. When the next power-on run, the controller reads the last vector stored before from FLASH and takes it as the output of the initial positioning vector at current task, so that the rotor continues a new positioning and running from the position where it stopped last time.r—The motor phase resistance, After the initial positioning of the motor rotor, the stator current vector The three-phase coordinate system makes an equal amplitude clarke transformation to the According to equation , we can p is the pole pairs), we haveThe mechanical power of the motor is Then formula of electromagnetic torque can be given by:In view of stator flux The current equation in the 27:Substituting the equation  into 9 yThe first part in equation  is the eConsidering a very short time N vectors in one turn of dragging motor, and after the TIM2 commutation N times, the magnetic field of the stator rotates one whole turn. In each TIM2’s count cycle of n times, in which n is determined by the experiment according to the specific load. Among them, the PWM fundamental frequency f is the reciprocal of TIM1’s base cycle, i.e., n is an integer, n is, the greater the motor output torque will be, and the corresponding phase current increases. By conducting experiments, the value of n is continuously regulated to fullfil the task of successfully dragging the load of motor.The SVPWM module Fig.  mainly cConsidering the fluctuation of the load torque at different starting positions actually, the following rules are made about the definition of the motor dragging the load successfully Fig. : commandn is the critical value to be tested yeilding the break-away torque.If the load torque of the motor varies according to the starting position, the differential fluctuation is t, where a is a constant coefficient and do not care its detailed value. The b is a certain constant coefficient. Then Since n by degree till find out the reliable value of n under the n as Bying commanding the positioner to run as Fig. n decreases accordingly.As When In the open loop driving strategy, the torque fluctuation is inevitably introduced. In view of this, it is discussed from the following aspects to optimize it: subdivision, PWM fundamental frequency, wave generation mode.We can observe from the results Fig.  that:As Experiment platform Fig. : \documeThe experiment settings are as follows: the clock frequency of the generator TIM1 is 144 MHz, its cycle count value ion Fig.  to keep entclass1pt{minimaWith the increase of subdivision, the phase current When there are only six vectors in a rotation period, it is apparently that the phase current appears to be ladder-like of six steps, that is, the current pulsation will be stimulated at each vector commutation, causing the ripple of output torque. Therefore, the mechanical system would be not smooth enough, and noise will be greater. With no doubts, a larger subdivision is recommended in practical application. Based on this, we use 96 subdivision.The results from Fig. Keep the stator magnetic field speed same  values as an evaluation indicator, reflecting the signal quality, defined as: Record SNR reflecting signal quality would be better with the increase of fundamental frequency.It can be seen clearly that the phase current ripple deceases with the increase of the fundamental frequency Fig. , and thi(a) In asymmetric SVPWM, voltage vectors are synthesized by three basic vectors: (b) In a 5-segment SVPWM, the voltage vector is synthesized by three basic vectors: (c) In 7-segment SVPWM, voltage vectors are synthesized by four basic vectors: For the above three modes of wave generation, under the same 9 V bus voltage, This section discusses the effect of asymmetric SVPWM, five-segment SVPWM and seven-segment SVPWM on the open loop positioning control proposed. SNR and AC RMS (Root Mean Square) of current are used for assessment. According to equation , there aV =12.33 mw, multiplying by 10000, which will become a considerable amount. In that case, we tend to apply asymmetric wave generation mode.From the Table Analyze the single phase equivalent circuit shown in Fig. r is phase resistance of 14.85 ohm; The full response expression of the first-order circuit in the Fig. M and us. Considering the theoretical time required for the phase current to reach 0.632According to equation , we can It can be seen that with the increase of high level counting value, the peak value of phase current increases gradually. When the maximum high level of TIM1 is 2000, it has far exceeded 359, but in practice, the peak value of phase current is still only 288 mA, which does not reach the steady phase current 349.91 mA  Clamp the optical fiber positioner robot to the universal toolmaker’s microscope with the fixture.(b) Adjust sliding rails in the direction of XYZ, so that the markpoint can be obtained by camera.(c) The clockwise and counterclockwise alternating command is transmitted to the phi axe to spin (d) After each positioning operation, the coordinate position of the markpoint is identified and recorded.The clockwise and counterclockwise alternating positioning test is used to locate The model of digital universal toolmaker’s microscope we operated is 19JC whose division value is 1 um in direction movement of X,Y and division value of Z-axis keeps 0.5 um. And the overall measurement accuracy is 1 um. Since the 19JC’s extent of automation and efficiency are not that high, manual measurement,adjustment and visual aiming are still necessary. The essential procedure of positionintg experiment are as follows:ded Fig. .Figure 2The RMS value of the whole positioning error is 146 um, and the modal error is 158 um. Considering gear backlash, machenical and assembly error, and not all reliable mechanical connections used in the new generation positioner robot, especially for an adhesive means adopted, it can be concluded that the open loop positioning control proposed has achieved excellent positioning precision and meets the engineering demands.In this paper, an open loop precision positioning control method based on SVPWM is proposed, and the regulation process of every aspect and the specific influence involved are discussed in details. To some degree, the positioning control method could be improved furtherly with better IC (Integrated Circuit) selection, especially for maximum number of subdivisions and fundamental frequency. Take the MCU STM32F302K8U6 we used for example, the highest clock frequency of the generator timer is 144 Mhz, which is quite high. When adopting a carrier frequency of 576 kHz, its cycle count value kHz Fig. , \documeAs for the maximum number of subdivisions, when the number of subdivisions increases continuously with same carrier frequency, the more voltage vectors would be generated in same count cycle, and the high-level values of some voltage vectors in the vector table will decrease gradually to a certain extent, where the time wasted by mosfet would yield an assignable impact. Similarly, the maximum number of subdivisions is still subject to the inherent features of mosfet, here we no longer analyse unnecessary detail. If try a MCU with higher frequency timer and certain mosfet with more ideal on-off edges and shorter dead time, it is credible to achieve higher subdivisions and fundamental frequency.Compared to the closed loop control limited by the current sampling and mathematical calculation of the feedback loop, the PWM carrier frequency of open loop method proposed is able to be as high as 576 kHz Table , which iIn view of the open loop positioning control method proposed in this paper, there are still some optimation, a reasonable acceleration and deceleration curve in the starting stage under the premise of ensuring the robust output torque can further decease the heat loss. In addition, it is possible to develop an ultra-miniature 4 mm BLDC motor encoder to apply a closed loop positioning control in the future.


Kink deformation is often observed in materials with laminated layers. Graphite composed of stacked graphene layers has the unique laminated structure of carbon nanomaterials. In this study, we performed the interlayer deformation of graphite under compression using a simulation of molecular dynamics and proposed a differential geometrical method to evaluate the kink deformation. We employed “mean curvature” for the representativeness of the geometrical properties to explore the mechanism of kink deformation and the mechanical behaviors of graphite in nanoscale. The effect of the number of graphene layers and the lattice chirality of each graphene layer on kink deformation and stress–strain diagrams of compressed graphite are discussed in detail. The results showed that kink deformation occurred in compressed graphite when the strain was approximately equal to 0.02, and the potential energy of the compressed graphite proportionately increased with the increasing compressive strain. The proposed differential geometric method can not only be applied to kink deformation in nanoscale graphite, but could also be extended to solving and predicting interlayer deformation that occurs in micro- and macro-scale material structures with laminated layers. Graphite that is composed of stacked graphene layers has the unique laminated structure of carbon nanomaterials. Although graphene that consists of a hexagonal pattern of carbon atoms has extremely excellent mechanical behavior, natural graphite with laminated graphene is soft and easy to deform under high pressure due to the weak van der Waals (vdW) interaction force between the adjacent graphene layers . When dec axis. However, the deformation of graphite has not been described by exact quantitative figures, and there is no explanation of the relationship between the shape of it and force. Especially, the deformation mechanism of laminated structures was still not clarified clearly enough up until now.According to the unique deformation phenomena in laminated structures, the concept of the kink band was proposed by , where tThe establishment of a general deformation theory based on a differential geometric method is expected to elucidate the deformation mechanism in laminated structures, e.g., graphite in the present work. To investigate kink deformation in micro-buckled graphite with laminated graphene layers, in the following parts, we build two kinds of atomic simulation models: armchair graphite and zigzag graphite. Both kinds of graphite incorporate 20, 30, 40, 50, or 60 atomic layers, and we performed the compression test on each type of graphite using MD simulation at first. Then, we proposed a differential geometric method to evaluate the mean curvature of each graphene layer in each type of graphite. Next, we discussed the geometrical properties of unique deformation and studied the relationship between the distributions of mean curvature and potential energy. Lastly, we summarized the remarkable conclusions.x direction . The interaction was evaluated using the adaptive intermolecular reactive empirical bond-order (AIREBO) potential , where ton force ; the thiS. We introduced mean curvature, defined by atomic configuration, so that we could characterize out-of-plane deformation with quantification. It should be sufficient to approximate the normal vector m using the normal vector of the plane I–J–K. Here we assumed local Cartesian coordinates O–w was parallel to the normal vector m.To evaluate the out-of-plane deformation of graphene from plane to curved surface, we proposed a differential geometry method to calculate the mean curvature tensor using the atomistic configuration. During the compression process, each graphene layer, modeled as a 2D plane, initially deformed to a 3D curved surface due to the out-of-plane deformation. Thus, this 2D–3D transition generated folds and kink deformations in the graphite. However, in general, the mean curvature of the differential was used to describe the shape of a folding non-individual body. The structure of graphene is made up of discrete carbon atoms, in which each atom is connected with three adjacent atoms via C–C covalent bonds. As shown in S could be expressed as:Thus, the curved surface S, we have the following conditions.R with rotation angle w direction was introduced.R, if only the rotation angle in the principle direction was rotated, the curvature tensor Since the atom O ditions.κ11uI2+2κEquation  helped uEquation .(6)κP=κH is the average value of the principal curvature components The mean curvature The deformation behavior of graphite under compression depends on the external force and its internal structure. In this section we discuss the effect of compressive strain, the number of graphite layers, and the lattice chirality of the graphite within the layered structure mentioned in z direction to become obvious; the mountain and valley shapes could be observed clearly when the compressive strain From the results obtained using armchair graphite with 40 graphene layers under compression, as shown in To deeply discuss the effect the number of graphene layers has on micro-buckled graphite, we listed and compared the deformation shapes of armchair graphite with different number of graphene layers when the compressive strain was n = 20, as shown in n = 50, as shown in n = 60 as shown in According to the derived Equation , we calcDuring the compressive process, each graphene layer was generated by out-of-plane deformation. We picked the bottom layer (To discuss the relationship between the mean curvature and site potential energy in detail, we plotted In this work, in order to investigate the interlayer deformation of micro-buckled graphite and to establish a general methodology for evaluating the kink deformation of compressed laminated structures, we performed compression tests on armchair and zigzag graphite with different numbers of laminated graphene layers using MD simulation. We proposed a differential geometric method using mean curvature to explore the relationship between geometrical and mechanical properties. From the compression tests, not only the kink deformation but also the delamination were observed, and different kinds of deformation patterns appeared in the graphite according to the different chiralities of the graphite and different number of graphene layers. We concluded that the kink deformation in graphite started from the position of delamination and the growth of kink deformation weakened the growth of delamination. We also showed the relationships between compressive stress and compressive strain, and between site potential energy and compressive strain to investigate the structural effect on the material properties of graphite. Moreover, according to the calculated mean curvature, we found that the concentration of compressive stress and site potential energy were generated at almost the same locations in all of the analytical models. Lastly, we should note that the calculation of site potential energy and mean curvature using the proposed differential geometric method could be extended and used for solving and predicting the interlayer deformation that occurs in micro and macro materials with laminated layers.


Korean river design standards set general design standards for rivers and river-related projects in Korea, which systematize the technologies and methods involved in river-related projects. This includes measurement methods for parts necessary for river design, but does not include information on shear stress. Shear stress is one of the factors necessary for river design and operation. Shear stress is one of the most important hydraulic factors used in the fields of water, especially for artificial channel design. Shear stress is calculated from the frictional force caused by viscosity and fluctuating fluid velocity. Current methods are based on past calculations, but factors such as boundary shear stress or energy gradient are difficult to actually measure or estimate. The point velocity throughout the entire cross-section is needed to calculate the velocity gradient. In other words, the current Korean river design standards use tractive force and critical tractive force instead of shear stress because it is more difficult to calculate the shear stress in the current method. However, it is difficult to calculate the exact value due to the limitations of the formula to obtain the river factor called the tractive force. In addition, tractive force has limitations that use an empirically identified base value for use in practice. This paper focuses on the modeling of shear-stress distribution in open channel turbulent flow using entropy theory. In addition, this study suggests a shear stress distribution formula, which can easily be used in practice after calculating the river-specific factor T. The tractive force and critical tractive force in the Korean river design standards should be modified by the shear stress obtained by the proposed shear stress distribution method. The present study therefore focuses on the modeling of shear stress distribution in an open channel turbulent flow using entropy theory. The shear stress distribution model is tested using a wide range of forty-two experimental runs collected from the literature. Then, an error analysis is performed to further evaluate the accuracy of the proposed model. The results reveal a correlation coefficient of approximately 0.95–0.99, indicating that the proposed method can estimate shear-stress distribution accurately. Based on this, the results of the distribution of shear stress after calculating the river-specific factors show a correlation coefficient of about 0.86 to 0.98, which suggests that the equation can be applied in practice. Understanding fluid interaction is very important in almost all studies of open channel flows. Shear stress is used and applied in hydraulics, hydrology, fluid mechanics, and in various fields, and is one of the most important mechanical factors . It is aLeighly  proposedKeulegan  and JohnFor these reasons, this study focuses on theoretical and statistic methods, which are probability and entropy concepts. Combining these, a useful method can be developed to explain the shear stress profile in open channel flows.A probabilistic method of shear stress distribution in open channel flows using entropy concepts has been studied. Bonakdari et al.  comparedFor the past few decades, entropy theory has been applied in the field of river hydraulic geometry and fluvial hydraulics. The entropy concept was introduced in hydraulics by Chiu  with ShaSince then, various entropy-related research has been carried out. Chiu et al. ,30 appliShear stress has to be estimated to determine flow characteristics. Considering the importance in an open channel, the complete evaluation is highly difficult due to the complexity of the cross-section and the various hydraulic parameters. The research related to the shear stress is based on empirical outcomes. That being so, it is difficult to apply the equations generally. Therefore, the current Korean river design standards use simple and obtainable tractive force and critical tractive force, which can be obtained through empirical methods instead of shear stress.The objective of this study, therefore, is to model shear stress distribution using entropy theory, verify the model using twenty-one experimental datasets obtained from Song’s experimental data , and to The variable Considering every state, the average value of information hannon’s  entropy The probability distribution of maximizing the entropy produces more information from already acquired basic knowledge. To solve the PDF, i.e., the available information of variable Therefore, the PDF The entropy concept can be applied to the shear stress using Equation (5) from Shannon’s entropy as:The available information for Then, average information can be expressed as:Arranging the independent constraint conditions can be given as:Therefore, PDF Substituting Equation (9) into Equations (10) and (11) can be constructed as follows:We apply the cumulative probability function to fluid flow using Equation (14), and Equation (13) will become Equation (14) by applying the PDF as:mum) see .The  by Chiu ,38 to exSolving Equation (14) can be written as:Open channel flow also uses the constraint conditions of Equations (6) and (7). Substituting Equation (13) into Equation (6) is given as:Substituting Equation (18) into Equation (15) and rearranging it results in another proposed mean shear stress distribution formula as:By inserting Equation (16) into Equation (15) we have:Equation (20) is the last proposed model for boundary shear stress distribution. Generally, Normally when laminar and turbulent flows coincide, they can be written as:Boundary shear stress from Equation (22) can be expressed as follows: when there is shear stress at the bed, Tractive force means the running water force when the silt on the river bed is moved by water. The commonly used tractive force  and (23) have an advantage, but their accuracy is suspect. The reason for this is that the energy gradient is actually a difficult factor to estimate. As can be seen in Equation (22), the measured point velocity of the whole cross-section is required for shear stress to reach each gradient. In other words, the velocity gradient  and (20) with a wide range of slope, discharge, and sediment flow conditions, experimental data from Song  were selProposed shear stress distribution was used to estimate the entropy parameter For first (uniform), second (accelerating non-uniform), third (decelerating non-uniform) and fourth (unsteady) flow conditions , the proIn From From From If the main parameters of Therefore, in other words, if the river-specific factor Song data were used to prove the utility of shear stress distribution when the river-specific factor Using Equation (17) based on the data, is the results were displayed graphically to calculate the river-specific factor for each flow state. Unsteady flow was divided into four cases according to the gradient, and equilibrium We now put the equilibrium The RMSE is a measure of the residual, which is the difference between the values simulated by the model and actual observed values. The RMSE enables simulative power to be integrated into a single unit of measurement. The RMSE of the model’s simulation for the estimated variable The determined shear-stress distribution was compared with those measured by Song. The determined RMSE values were very low from 0.000245 to 0.001108 as shown in Basically, the steady flow shows a high correlation coefficient value and proves the utility of the shear-stress distribution equation. However, the unsteady flow shows a lower mean correlation value compared to the steady flow. Looking at the results of the unsteady flow in detail, note that not all areas are observed with low correlation, but with high and low correlation. This indicates that the low correlation coefficient value from the unsteady flow is the error caused by the observation of the data. In practice, using point shear stress values calculated based on accurate observations can reduce error and have higher correlation coefficient values.Based on the advantages of being able to express and easily obtain shear stress distribution by entropy shear stress distribution using equilibrium The proposed equation has proved to show reasonable results. From Using the estimated boundary shear stress and mean shear stress from all forty-two runs, entropy parameter The aforementioned discussion delineates that an entropy-based model on shear stress is able to describe the characteristics of shear stress from the frictional force caused by viscosity and fluctuating fluid velocity in an open channel turbulent flow. The proposed equation has proved to show reasonable results.Based on the parameters calculated, the mean values of the correlation coefficient in the results of the shear stress distribution equation for each flow were 0.9708 for the uniform flow, 0.9867 for the non-uniform flow (accelerating), 0.9471 for the non-uniform flow(decelerating), and 0.8604–0.9212 in the unsteady flow for each gradient. Based on these results, it was confirmed that the shear stress distribution formula using river-specific factors can be available in practice.Of course, part of the unsteady flow shows lower correlation coefficient values, but the correlation coefficient values are error generated from observations. When measuring the distribution of point shear stress for practical use, the conclusions based on accurate observations are determined to reduce the error further and obtain high accuracy shear stress distributions and results.However, there are some minor limitations to this study. Some observed data, such as shear stress distribution and vertical depth from the bed, should be known in order to estimate the model. In other words, there needs to be some information in order to use this model. In addition, the basic shape of the model depends on the PDF of shear stress and Equation (21). This is important because in complex flows such as unsteady flows, it can be difficult to show the distribution exactly, especially if the maximum velocity occurs below the water surface. The model is based on probability and statistics and does not consider basic hydraulics in the beginning, but only depends on constraints and data. Because the accuracy of the observed data can affect the correlation value of the distribution equation, accurate point shear stress data must be obtained for use in practice.Although the tractive force and critical tractive force formulas used in the current Korean river design standards are simple to obtain, the tractive force is a formula using a factor that is difficult to obtain, which makes it difficult to calculate the exact value. In addition, critical tractive force is a value obtained empirically, which also has the disadvantage of difficulty in calculating the exact value. However, in order to use the existing shear stress formula, shear stress can be calculated only with the energy gradient, a factor that is very difficult to obtain, so Korea’s river design standards use tractive force and critical tractive force instead of shear stress.Therefore, using the entropy concept, this study has proposed shear stress distribution and boundary layer shear stress, which can be applied in open channel flows. To determine how well the shear stress model fits with the observed data, Song’s data were used. From this aspect, this paper validated the model with a wide range of forty-two runs of experimental data published in the literature. The results show the utility and reliability of Equations (19) and (20), in which the mean shear stress is considered, then using the qualified shear stress distribution, the shear stress distribution over the whole flow depth of open channel turbulent flows is shown.Furthermore, based on the equations’ proven utility and reliability, this paper has proposed a method that can easily be used in practice by obtaining river-specific factor T if point shear stress is given. We suggest that the contents of tractive force and critical tractive forces with shortcomings in terms of accuracy in the Korean river design standards are revised to the shear stress distribution method presented in this study. The results of the distribution of shear stress after the calculation of river-specific factor T were also considered to be highly correlated, and thus it was determined that the method could be used in practice.However, there is no best entropy parameter T value for every run. This means that we need to somewhat reach an agreement with solutions. To improve this, very precise methods must be applied in order to enhance the results. One of these methods can be an optimum technique. Optimization techniques such as genetic algorithms or harmony searching can be applied for finding better solutions to these kinds of problems, where we might even be getting closer to what we are seeking.T) and the unknown boundary shear stress or mean shear stress.There have been very few studies about shear stress in open channels recently. It seems that there are only few models that can estimate shear stress distribution. Some of the models require parameters that are difficult to calculate or even obtain, or even have hypotheses that eventually reach the limit of the formula. Other models have many parameters to estimate, but the features of the proposed model have only two parameters, the entropy parameter . Nevertheless, in future research, our model has to be compared with some shear stress models.The analysis has limitations but the results appear to be useful. If the point shear stress in the open channel and vertical depth from the bed are given, the shear stress distribution can be estimated simply from the model, which will show high availability when designing or managing the open channel. In addition, the boundary shear stress can be estimated easily without the energy gradient when calculating the boundary shear stress in an open channel.


This paper explores the uniaxial tensile creep response of acrylic-based pressure-sensitive adhesive (PSA), which exhibits a unique multi-phase creep response that does not have the classical steady-state region due to multiple transitions caused by several competing mechanisms: (i) cavity nucleation and growth in the interior of the adhesive material of the PSA system, as well as at the interfaces between the PSA and the substrate; (ii) fibrillation of the bulk adhesive, and (iii) interfacial mechanical locking between the adhesive and the bonding substrate. This results in multiple regimes of strain hardening and strain softening, evidenced by multiple regions of steady-state creep, separated by strong transitions in the creep rates. This complex, multi-phase, nonlinear creep response cannot be described by conventional creep constitutive models commonly used for polymers in commercial finite element codes. Accordingly, based on the empirical uniaxial tensile creep response and the mechanisms behind it, a new mechanistic model was proposed. This is capable of quantitatively capturing the characteristic features of the multiphase creep response of single-layered PSA joints as a function of viscoelastic bulk properties and free energy of the PSA material, substrate surface roughness, and interfacial surface energy between the adhesive and substrate. This is the first paper to present the modeling approach for capturing unique multi-phase creep behavior of PSA joint under tensile loading. Sosson Creep of PSA-bonded joints under tensile loading appears to depend not only on the PSA material itself but also on the substrate that the PSA is bonded to. Hait and Barthel proposed a model for evaluating the effect of substrate surface roughness on adhesive bonding under tensile loading . Their mzz direction, as shown in xx, yy, and xy, loading along the peel direction (zz) shows the most damage for this kind of adhesive joint structure. In practice, this kind of loading can be caused by external multiaxial loading and initial curvature (warpage) mismatch of bonding substrates. Even the residual stress from a small geometric mismatch can pose a hazard for the creep performance of the PSA layer in a long-term application. In summary, the published data on creep of PSA joints focus mostly on the understanding of shear creep performance. In contrast, the creep resistance to loading in the out-of-plane loading direction , as well as substrate properties (such as surface free energy and surface roughness). The utilization of such modeling is not only for design and virtual testing but also, for real-time prognostic health management (PHM). PHM application requires continuously updated predictions of the residual creep life of adhesive joints and is enabled by using such models as “digital twins” by continuously re-calibrating them with real-time in situ data .zz) direction. The size of the PSA bond line was The test specimen consists of two rigid T-shaped aluminum substrates bonded with a single-layered PSA, as shown in in study .A creep result, which consists of multiple steady-state (secondary creep) regions separated by sharp peaks and transitions in the creep rates, under test conditions of 50 kPa and 70 °C, is shown in These transitions in the creep curve are believed to be a result of the same underlying physics that produced the transitions in the tensile stress–strain tests reported elsewhere . The mulCavitation and growth of bulk and interfacial cavities were extensively discussed in our previous paper .These meThe creep performance is not only influenced by the loading conditions but also affected by the geometry of the joint. For example, the creep resistance of the joint increases as the PSA layer thickness decreases. α) of adhesive to fit the data from experiments and/or literature. However, the thickness of adhesive does not always help the creep resistance of a PSA joint—it is the result of constant competition between the actual bonding area and geometric confinement of the PSA joint. The aspect ratio of the area to the thickness of the adhesive layer (and hence the geometric confinement in the adhesive layer) decreases as the thickness of the adhesive layer increases. Thus, a thicker PSA joint can creep faster because its stress field is dominated by the deviatoric part, in comparison to a thinner PSA joint under the same loading condition. The empirical part of this study does not include the effect across many adhesive thicknesses due to the limitation of sample availability. However, the predictive model has the capability built in to capture the effect of adhesive thickness on creep by calibrating the parameter of penetration depth (yR). As an example, The choice of substrate affects the interfacial cavitation process and hence alters the creep response, just as it was seen to affect the stress–strain response . The keyous work , but theCreep deformation is modeled using the same “block” model that was used to model the stress–strain response in PSA joints in our previous work . The defiC, as shown in x, z), as described by the equations below [i, iC is the parabolic value of block i, and W0 and H0 are the initial width and height of the same block i and The creep deformation model is adapted from Yamaguchi’s “block” model . Yamagucns below .(1)x=XiMost of the PSAs of interest in this study are highly ductile and capable of cavitation and fibrillation and can deform by more than 1000% of their original shape. Therefore, Green’s strain is used to describe the stretched PSA as it is accurate over large strains. The specific form of the Green strain tensor and the corresponding velocity gradient for this 2D problem were defined in our previous study .In the current block model , The PSA is lightly cross-linked and is modeled with a standard linear viscoelastic model, as discussed in our previous paper . The strThe resulting evolution of creep deformation is highly dependent on the history of the stress components. Therefore, to obtain the full history of the deformation process, the initial stress ramp-up process, shown in zz component of the deviatoric stress tensor, The same standard linear constitutive model is used for the bulk PSA, both during the initial ramp-up phase and also during the subsequent constant stress creep phase. The constitutive equations for each phase (displacement-controlled ramp and stress-controlled creep processes) are shown in Equations (3) and (4), respectively:response , G2 is tThe stress levels used in this study for creep testing are typically lower than those encountered in the stress–strain testing reported in our previous paper on stress–strain response . Howeverith cavity, Cavity-induced creep deformation is best modeled with two separate deformation regions centered around a typical cavity. One is the far-field slow deformation region, which is in the bulk adhesive, far from the cavity. The other is the near-field rapid deformation region, which is in the region near the cavity, especially when the cavity is in the initial rapid growth stage. Therefore, we assign different viscosities, fined by : (5)Ri˙=When the cavity size is large enough, the growth rate of the cavity decreases. The deformation rate of the bulk adhesive in the near-field of the cavities becomes similar to that of the bulk adhesive in the far-field. This means fined by (6)R˙=R4The growth of the interfacial cavity, which was extensively discussed in our previous publication , is contThe total stress during the stress ramping up process is: In the constant stress creep phase, the total stress is held constant from the last step of the stress ramp up of Phase I. Stress component In this model, due to the use of rate-dependent viscosity, the near-field viscosity in the vicinity of the cavities is much lower than the viscosity in the rest of the bulk far-field area. This value is highly dependent on the expansion rate at each time step. For simplicity, to fit experimental data, the near-field viscosity is 0.1% of the far-field viscosity for the duration of creep.zz direction and is maintained constant during the entire creep deformation. The hydrostatic part of the stress field dominates over the deviatoric part during the initial stages of the creep deformation due to the high geometric confinement. However, it starts decreasing as the stresses start relaxing due to cavity initiation. By the end of the transition phase, more than 90% of the hydrostatic stress is released. In contrast, the z-component of the deviatoric stress starts to increase as the cavitation initiates and the rate of increase slows down towards the end of the transition phase  and a cThe predictive mechanistic creep model discussed in this paper is capable of reproducing many features found in the experimental creep response of PSA-bonded assemblies, especially the multiphase nature of the creep response due to the constant competition between softening (due to cavitation) and hardening (due to fibrillation processes). However, some simplifications and approximations in the modeling algorithm (listed below) induce some discrepancies between the experiments and the model predictions.(1)The actual cavitation mechanism is based on the balancing of stress level and the evolution of defect size due to the mass diffusion process. The model in this paper simplifies the physics of the phenomenon and uses the local deviatoric strain level as a proxy for the cavitation criterion.(2)The interfacial friction and critical energy release rate are assumed to be linearly dependent on the surface free energy. This assumption is based on literature data reporting a linear dependence between peel-strength and surface free energy of the polymeric substrate.(3)Some of the model predictions, e.g., the effect of adhesive properties (modulus and viscosity), have not been verified by empirical studies, due to the limitations of available test results. Additional verification of these model predictions will be conducted in future studies.(4)zz-direction deformation is the same for each fibril, but the stresses in each fibril will vary depending on the fibril location.Due to the complex stress distribution in the force-controlled creep phase, average stress is used for determining the evolution of the strain. In reality, the (5)Additional experiments are needed to understand the non-monotonic dependence on the substrate surface roughness and to investigate the effects of temperature-dependent material properties and interfacial interaction between PSA and substrate.(6)The differences in the effective viscoplastic material properties between the near-field and far-field adhesive materials around a cavity are not clearly distinguished.(7)The transverse stresses due to Poisson’s ratio mismatch between substrate and PSA are not explicitly included in the “block” model. Some inaccuracies of the model prediction may be caused by this inadequacy.The predictive model in this study is only applicable for tensile (peel) loading, not for shear.Multiphase creep response is observed when joints between rigid substrates, bonded with highly ductile single-layered PSA, are subjected to tensile (peel) loading. The transitions in the creep curve are the result of competition between mechanisms of softening due to cavitation and stiffening due to fibrillation, during the deformation and debonding process. The interplay of these mechanisms is highly dependent on the adhesive properties and surface properties of the bonding substrate.A predictive mechanistic model, which is based on mechanisms of interfacial and bulk cavitation, the growth of cavities, fibrillation, and interfacial mechanical locking, is presented to capture the tensile creep response of single-layered PSA/substrate joints. This predictive model shares a similar modeling technique with the stress–strain model presented elsewhere  but uses


In this study, multi-objective optimization of mechanical properties in friction-stir-welding of AH12 1050 aluminum alloy is performed using a combination of the response surface method and multi-objective particle swarm optimization algorithm. The process parameters are considered as tool pin diameter, shoulder diameter, rotational speed, feed speed, and tool tilt angle. The heat-affected zone’s yield strength, fracture strain, impact toughness, and hardness on the advancing and retreating sides are selected as the objective functions. Threaded and simple conical pins are utilized to evaluate the effect of the pin geometry on the specimen mechanical properties. Optimization model outputs are in agree with the obtained experimental results. The effects of process parameters on the mechanical properties of the friction-stir-welded sheets are studied. Results reveal that the lower rotational speed and higher feed speed improve the material strength and hardness. Moreover, the microstructural analysis demonstrates that the proposed methodology can achieve a fine-grained structure with the minimum defects. Improvement in the material flow is observed for the threaded cylindrical pin compared with the conical pin due to the geometric shape of the tool pin leading to more functional mechanical properties. It is found that the combination of the response surface methodology and the multi-objective particle swarm algorithm led to the modeling and optimization of the process with outstanding accuracy and low experimental cost. As shown in Fig. 2. Since the welding process in FSW is simultaneously performed by rotational and linear motions, the formed distortion and residual stress are reduced compared to the conventional welding processes. As the FSW process does not contain melted metal, the temperature of this process is lower than fusion welding, which reduces the thermal gradient in the welding zone and improves the mechanical properties and welding quality3.Friction stir welding (FSW), which involves making the joint without melting the parts, was introduced in 1991 by The Welding Institute (TWI)4 investigated the parameters affecting the FSW of high-speed and medium–carbon steel. After finding the optimum welding parameters, the strengths of the joints have been determined by mechanical tests as well as hardness variations and microstructures examination. They compared the results with the strengths of the base materials. Leon and Jayakumar5 studied the effect of process parameters on the tensile strength, microstructure, and stiffness in the FSW of aluminum 6061. The changes in mechanical properties have been compared with the base metal. The key role of the tool rotational speed and welding speed on joint characteristics has been revealed. They reported that the tensile properties and impact strength of the FSW joints have been improved duo to the higher hardness and fine microstructure. Yousef et al.6 utilized an artificial neural network (ANN) to model the FSW parameters on the mechanical properties of aluminum sheets. They combined the influence of feed speed and pin rotational speed on the mechanical properties of welded aluminum sheets and achieved a good performance of ANN model. Sandaram and Muragan7 investigated the effect of pin geometry in the FSW of 2024 and 5083 aluminum alloys. They used five different tool pin profiles and four process parameters to create a predictive response surface model for ultimate tensile strength and tensile elongation. Results revealed that joints fabricated using a tapered hexagon tool pin profile achieve the highest tensile strength and tensile elongation. In contrast, the straight cylinder tool pin profile gives the lowest tensile strength and tensile elongation. Ghaffarpour et al.8 analyzed the effect of FSW process parameters on the 5083 and 6061 aluminum alloys joint mechanical properties. By using the response surface design methodology, they optimized the maximum tensile strength of the welding process and compared the results with those of the experimental test. Moreover, they studied the formability of welded sheets by using the limit dome height test. Yuvaraj et al.9 studied the effect of FSW process parameters on the tensile strength using the desirability function approach. The FSW parameters such as tool offset, pin profile and tilt angle have been considered for the experiments. Based on the ANOVA analysis, they revealed that the tilt angle of the tool has been the most controlling factor for improving the tensile properties of the joint, followed by tool pin profile and tool offset. Marimuthu and Pandiyarajan10 optimized the FSW process using four effective parameters and two objective functions. Optimization was performed using the desirability function approach and examining more efficient parameters in the process. The Box-Behnken three levels and three factors have been used to classify the number of experiments. Jangra et al.11 investigated rotational and feed speeds, tool pin profile, and tool shoulder diameter. They conducted several experiments on two similar sets, AA 6082-T6 and cryogenic treated AA6082 to compare the optimization results. A combined approach of Taguchi method, grey relational analysis, and entropy measurement method have been developed to find an optimal single setting of process parameters for two response characteristics. By examining four effective parameters, Verma et al.12 optimized the ultimate tensile strength and elongation percentage in aluminum alloy friction welding using genetic multi-objective optimization algorithm (MOGA) and hybrid genetic multi-objective optimization algorithm (HMOGA). Rotational speed, welding speed, and tilt angle have been used as input variables. They found that HMOGA provided better results than MOGA. In the aforementioned study, multi-objective optimization was performed using statistical methods, such as the desirability function.Several studies have been conducted on FSW technology for similar and dissimilar alloys. Sahin13, including genetic algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO), and artificial bee colony (ABC). The complexity of GA is more than PSO in principle for the same work. ACO is a time-consuming method, and the convergence time is also uncertain. ABC has a slow convergence rate, easy to fall in local optimum, and is difficult to find the best out of available feasible solutions. PSO is widely employed to solve the continuous problems because of the simplicity of concept and fewer parametric settings than other population-based optimization algorithms15.Most problems in nature have several (possibly conflicting) objectives to be satisfied. Some of the nature-inspired optimization algorithms have been used frequently in engineering optimization problemsAlthough, in the mentioned studies up to two objective functions are considered, in the present study, the FSW process of 1050 A-H12 aluminum is optimized using five objective functions and five influential design parameters. In addition, a multi-objective particle swarm optimization algorithm (MOPSO) is utilized known as a metaheuristic algorithm. The high convergence speed and relative simplicity of PSO make it a perfect candidate for the multi-objective optimization problems. The five objectives for optimization are considered as yield strength, impact toughness, failure strain, and hardness of the heat-affected zone on the advancing and retreating sides. The process parameters include pin diameter, shoulder diameter, rotational speed, feed speed, and tool tilt angle. After preparing test samples, tensile, impact, and hardness tests are conducted. A relation between the parameters and objective functions is estimated using the available data and the response surface method. Finally, the optimal solutions are obtained, and the predictions are compared with the experiments.16. The choice of surrogate functions to estimate the actual performance is crucial. These functions can be defined as polynomials or sums of various basis functions .The response surface method (RSM) is an approach for building approximations of objectives based on observations in the design space. This approach is functional when gradient-based methods failns analyses are conducted and p = 1; 2; …; ns, then a second-order polynomial model has the following formyp)), personal best , and Global Best 21.Figure Xi,(t)), current velocity ), the distance between the current and personal best positions, and the distance between the current position and the global best position. Therefore, the new velocity vector ) for particle i is calculated based on the following equation:w is the inertia weight parameter. r1 and r2 are the random vectors between 0 and 1, used in maintaining group diversity. C1 and C2 are the cognitive and social parameters (acceleration parameters), respectively. Selecting the appropriate value for these parameters accelerates the convergence of the algorithm and prevents premature convergence in the local optima. The new position of the particle is obtained from Eq.  is added to the PSO algorithm. The MOPSO flowchart is shown in Fig. Determining the parameters required for implementing the algorithm (MOPSO).The initial population is created.The best personal memory of each particle is determined.The undominated members of the population are stored in the repository and sorted based on their crowding distance.Each particle is selected a leader from among the repository members and performed its movement.The best personal memories of each particle are updated.New undominated members are added to the repository.The dominated members of the repository are removed. If the termination conditions are not met, the algorithm is repeated from 5 onwards.MOPSO is a generalization of the PSO algorithm used to solve multi-objective problemsIf the new personal best dominates the best personal memory, then the new personal best replaces the current personal best memory.If the new personal best is dominated by the best personal memory, then nothing will be done.If neither of them dominates each other, then one is randomly considered as the best position vector.The following considerations can be made to determine the best vector of personal best memory:Different experimental design methods are studied based on the degree of effective parameters as well as the number of effective parameters and responses. Taguchi experimental design method was employed for the DOE Table .Table 1TThe used sheets were made of A-H121050 aluminum alloy with 5 mm thickness. The chemical composition and the base mechanical properties of this alloy are provided in Tables 23. Based on the studies performed on the welding of aluminum alloys, the most common shapes of the pin are threaded cylindrical and conical24.Hot work steel H13 was used to fabricate the tools with diameters of 14, 16, and 18 mm, as it is the best material for welding aluminum parts25 to obtain a more functional joint. In addition, the slant angle of the conical pin was considered 75°. Figure The required tools are fabricated double-sided (one side of the threaded cylinder and the other side of a simple cone) to investigate the thread effects. All shoulders were prepared with a concave angle of 5°The fabricated specimens are provided from the welded parts for tensile test using a 15-ton DeghatAzma universal machine at room temperature. The cross-head velocity is adjusted 2 mm/min to satisfy the quasi-static condition. The specimen geometry all utilized relations are considered in accordance with ASTM E8. Tensile tests are conducted up to specimen failure to determine the elastic behavior and plastic and failure properties.The specimens hardness at the points located in the heat-affected zones (HAZs) on the advancing and retreating sides (HAZ Adv. and HAZ Ret.) was measured using a Shegarf Abzar hardness testing apparatus based on Rockwell B . The tests were conducted by applying a 100 kgf force in 10 s in accordance with ASTM-E18.The specimen required for the impact test was prepared according to ASTM E23 with a V-notch. The impact properties were evaluated using a 200 J Santam Charpy impact test machine. The specimens were carefully placed on the support by a special tool to ensure that the V-notch was in the right place related to the impact hammer. The welded specimens are prepared for tensile and impact tests by using the wire-cut machine as shown in Fig. 3 + H2O). Subsequently, the transverse cross-sections of the parts were analyzed using scanning electron microscopy (SEM).The samples were fabricated in accordance with ASTME3-01. The specimens were mounted and sealed and polished using 200 to 5000 sandpapers. The samples were then etched with a 2.5% chlorine solution  and two optimal samples are compared using microstructural tests to evaluate the weld quality. Excessive heat causes a coarse-grained structure and reduces the weld strength. The grain shape and size are the functions of material heat and flow. Due to the frictional contact between shoulder and work surface, heat is generated during the rotation of the tool, and the material undergoes a severe deformation at high temperature of the joint with the pin rotational movement. Thus, small and coaxial recrystallized grains are formed. The pin shape can adjust the material flow and causes fine graining. Once an optimal pin is employed, the forging forces in the welding zone are increased. This implies an improvement in material microstructures.Figure Figure Lower heat is generated in the optimal samples owing to low rotational speed and high feed speed. In low-quality samples, more heat is generated due to the higher rotational speed and lower feed speed. Figure The formed holes are observable in the upper third of the weld, which is affected by the tool shoulder and forging force. Excessive heat also causes some welding layers to oxidize, as shown in Fig. 27.Figure By dividing the welding section into three parts, we can see that the main stirring zone is placed in the upper third of the weld, affected by the tool shoulder. In this region, before two parts are forged, a paste state is formed in the joint parts, and the particles penetrate each other. The lower two-thirds of the weld is affected by the pin. In this area, the metal is extruded from the front to back of tool; therefore, stirring is less than one-third of the upper. As stated before, it can be concluded that fine-grained and flawless structures are occurred at lower temperatures, and coarser and weaker structures are produced at higher temperatures.However, it should be noted that in addition to rotational and feed speeds that cause heat changes, other factors such as the tool penetration depth could also affect the heat production. For example, in b10, despite the low rotational speed and high feed speed, heat is obtained lower than others due to the lower tool penetration depth into the workpiece. Hence no appropriate mechanical connection is formed, and the lower strength and hardness values for this sample are achieved. In the c17 sample, although the high rotational speed and the low feed is utilized, due to the reduction of the penetration depth of the tool, heating is reduced to the optimal level and a joint with the desired strength and mechanical properties can be obtained.In addition to the tool penetration depth, the tilt angle also affects the heat production and, as a result, the formation of microstructure and desirable or undesirable mechanical properties. This is evident in the comparison of the results of b6 and b18. In these two samples, increasing the tool tilt angle is reduced the mechanical properties Fig. .The lower rotational speed and higher feed speed are generated lower heat; consequently, the material strength and hardness are improved.Based on the metallographic analysis, the proposed model is desirable for achieving a fine-grained structure with minimum defects and optimal mechanical properties for samples fabricated at low temperatures.In addition to the rotational and feed speeds, which could change the generated heat, other factors such as the tool penetration depth affect heat production. For example, in b10, despite the low rotational speed and high feed speed, heat production is low due to the low tool penetration depth into the workpiece, preventing the formation of a proper mechanical connection. Therefore, the strength and hardness values for this sample are low. In addition, in the c17 sample, although the rotational speed is high and the feed is low, it still results from the reduction of the penetration depth of the tool, heating is reduced to the optimal level, and a joint with the desired strength and mechanical properties can be observed.Improvement in the material flow is observed for the threaded cylindrical pin compared with the conical pin due to the geometric shape of the tool pin leading to more functional mechanical properties.Increasing the tool tilt angle is reduced the mechanical properties by comparing the results of b6 and b18.The combination of the response surface methodology and the multi-objective particle swarm algorithm led to the modeling and optimization of the process with outstanding accuracy and low experimental cost.In this study, multi-objective optimization of the objective functions including yield strength, impact toughness, fracture strain, and hardness in HAZ on the advancing and retreating in frictional stir welding of 1050A-H12 aluminum was performed using the response surface method and MOPSO method. In addition, the effects of pin and shoulder diameter, pin geometry, rotational and feed speeds, and tilt angle on the above objectives were investigated, and the following results were obtained.Supplementary Information.


Sensitive responsiveness refers to parents’ ability to recognize and respond to infants’ cues and has been linked to parental empathy. Additionally, oxytocin (OT) and vasopressin (AVP) are hormones important for sensitivity and empathy. The aim of this study is to test the links between dispositional empathy along with changing OT and AVP levels and responsiveness to a life-like doll in couples and to verify whether these factors are predictors of responsiveness to a child’s cues. Exploratory analyses include predictors of sensitive responsiveness: polymorphisms of OXTR, AVPR1a and CD38 genes, personal characteristics and relational factors. The project employs standardized experimental settings that can be used with non-parents and the assessment of parental sensitive responsiveness towards their child. The participants are couples expecting their first child (111) and childless couples (110). The procedure involves caretaking of a life-like doll. Salivary samples and questionnaire data are collected in a planned manner. In the second part, the expectant couples are invited for the assessment of their sensitivity to their own child (Free Play episodes). Parental sensitivity is assessed using the Ainsworth Sensitivity Scale. This paper presents an interdisciplinary research project that reaches beyond the questionnaire measurement, considering many factors influencing the dynamics of adult–infant interaction. Sensitive responding refers to parents’ ability to appropriately recognize infants’ behavioral and emotional cues and to respond during interaction in a well-timed, reciprocal and mutually rewarding manner . It is oSensitivity to distress is a particularly important dimension of parental responsiveness . One of In family psychology, empathy is viewed as an essential component of the childrearing process, although it is rarely studied in the context of personal attributes of mothers and fathers, including those who start their journey to parenthood . AlthougEmpathy is a multidimensional construct, which includes the tendency to experience empathic emotions ; empathic concern for others—sympathy (other-oriented) as well as taking the perspective of others (other-oriented cognitive empathy)) ,13. OtheThe infant cry is a stimulus coming from a child that evokes strong emotional reactions, activating both appetitive and aversive reactions  in parenIn the HEART research project (HORMONALLY mediated EMPATHY role for AFFILIATIVE RESPONSE towards infant TEARS), we test which empathic dimensions are predictors of sensitivity in parental roles, operationalized as sensitive responsiveness towards infant crying in couples expecting their first child.We expand earlier research on empathy by including measures of oxytocin (OT) and vasopressin (AVP) as hormones important in close relationships, and also in the context of parental roles ,24,25. BSince OT and AVP levels are central to our research questions, we also include single-nucleotide polymorphisms (SNPs) within human OXT–AVP pathway genes , OXT receptor (OXTR) and ADP-ribosyl cyclase CD38)) as distant predictors of hormonal levels and their changes, empathy and responsiveness towards child signals. Recent studies on CD38 revealed that this transmembrane protein elaborates on the release of the OT . Moreover some transcription factors may be also involved in OT expression in the brain ) and therefore may be associated with social functioning . The selected SNPs have been previously reported to have an impact on social behavior  and othe) as distIn the presented project, psychological predictors of sensitive responding towards a child’s cues refer to individual characteristics , and the assessment of important relationships  . In thisReferring to the attachment framework, the HEART project focuses on sensitive responsiveness, displayed by the couple in parental roles . The main aim of the proposed study is to test the link between dispositional empathy and sensitive responsiveness to infant crying—a signal that evokes parental physiological, emotional, cognitive and behavioral responses. Going beyond previous research on mothers , responsThe HEART project methodologically reaches beyond self-report measurement, and combines personality as well as genetic and endocrine measures, stressing the importance of individual differences for the functioning of couples in the context of parental roles. There is a need for studying empathy and parental sensitivity in couples. Personality, hormonal and couple relationship factors are examined as predictors of responsiveness towards infant crying. To test the individual differences in parental sensitive responsiveness, we implement an experimental design with the use of a life-like doll to be used with expectant and non-expectant couples  and the subsequent assessment of sensitive responding towards own child for the couples that participated in the study during pregnancy. With this design, we are able to control many factors influencing the dynamics of adult–infant interaction. Affective states experienced by participants evoked by a crying signal will also be examined in the context of personality, hormonal and couple predictors. To the best of our knowledge, the project also constitutes the first attempt to include retrospectively assessed parental attitudes in the family of origin along with genetic factors and levels of OT and AVP in their prediction of sensitive responsiveness towards infant crying.The primary aim of the HEART study  and relational factors  predict sensitive responsiveness towards infant crying, independently and through hormonal mediation.Although the main goal of the current study is to examine the predictive effects of empathy and hormonal factors on sensitive responsiveness to infant crying in a standardized setting before the birth of the couples’ own child, we also aim to test whether these factors are predictors of responsiveness to their own child’s cues. Therefore, we plan to continue the research in the sample of expectant couples to examine sensitive responsiveness in mothers and fathers towards their own children aged 6–12 months.The HEART project employs standardized experimental settings for the assessment of parental sensitive responsiveness that can be used with non-parents and—in a later stage of the project—the assessment of parental sensitive responsiveness towards their own child. The participants are couples living in the northern part of Poland. Only couples with a relationship lasting at least 2 years and with previous cohabitation can participate. Due to the need for homogeneity of the sample, only heterosexual couples participate in the study.The procedure involves caretaking of a life-like doll, which cries as programmed during the interaction with a caregiver. This standardized procedure creates a unique opportunity to observe responsiveness to infant distress signals, which is difficult to obtain in observations of free play with a child . TherefoAll parts of the project are conducted in the laboratory with a two-way mirror and cameras situated in the Institute of Psychology at the University of Gdansk furnished as an infant room. Another laboratory room for gathering questionnaire data and storage of the salivary samples is arranged in the Institute of Psychology. Each session takes place during the same time of the day in order to avoid the influence of diurnal variations concerning hormone secretion .t-test for independent samples and the effect size was measured with Cohen’s d.In total, 597 couples received an invitation  to participate in the study. A third of the couples (34.51%) did not respond to the invitation, 148 (24.79%) did not meet the inclusion criteria, 22 (3.69%) of the couples refused to participate, and one couple resigned during the examination. A final sample of 221 couples  participated in the study. The background information collected through the registration form was obtained from 171 couples not participating in the study. Their characteristics compared with the study group are listed in Couples expecting their first child were contacted via antenatal schools in the Pomeranian area and social media. Non-expectant couples were recruited via announcements at the University of Gdansk and social media. In order to be included, all participants had to be in the age range 22–35 years. Only couples with a relationship lasting at least 2 years and with previous cohabitation could participate. Exclusion criteria for both partners were tobacco consumption, drug use, pharmacological treatment such as glucocorticosteroids or selective serotonin reuptake inhibitors, alcohol and psychoactive substance addiction. All participants had to declare general good health. The two groups (expectant vs. non-expectant) should not have significantly differed from each other on sociodemographic characteristics. Additionally, the inclusion criteria for the postpartum session were participation of the whole family (both parents and their first child), age of the infant between 6 and 12 months and absence of developmental disorder diagnosis. The recruitment process is presented in The participants were asked not to consume spicy and salty foods, alcohol, coffee and tea as well as foods with high sodium levels in the 24 h prior to the session and sampling. Upon arrival at the lab, and 30 min prior to the observation of the first person in the couple, two salivary samples were collected from each partner to measure basal salivary OT and AVP, and to gather genetic material for genotyping of polymorphisms in OXTR, AVPR1a and CD38 genes. Next, each partner started to fill in the psychological questionnaires on the computer, and after filling in the first questionnaire, one of the partners, in random order, was assigned to participate in a 10 min episode with a life-like doll for the assessment of the participant’s sensitive responsiveness, while the other continued to fill in the questionnaires. Next, the same 10 min episode with a subsequent partner followed. Then, the third 10 min episode with the couple (couple’s sensitivity) was conducted. Each session was followed by filling in the PANAS-X in Polish  and someThe infant simulator  is a doll resembling a real infant in physical appearance, size and weight (2.95 kg). It makes breathing, burping, giggling, suckling and crying sounds and needs to be cared for like a real infant. The doll used in the project was a Caucasian female or male infant  dressed in a long-sleeved sleeper and a blanket, thus creating the impression of holding a real baby. The simulator was equipped with software enabling pre-programming of its behavior using schedules based on real infants. Additionally, thanks to electronic wristbands, the noises of the simulator could depend on the care provided (option responsive to care) or could be pre-set independently of the care provided (pre-set option).Since our study was observational and the infant simulator served as a stimulus for assessment of the sensitivity, a pre-set option  was chosen in order to provide equal session conditions for all participants. The infant was crying with a varying frequency. The cry began in the third minute with around 30 s of mild fussing and then became full-blown crying for 4 min. The infant simulator stopped crying in the last minute of the session. All participants received the same instruction: “Please, take care of this infant until I come back. The whole room is at your disposal”. The doll was given to men to encourage their engagement in the task . The procedure took place in a laboratory furnished like an infant room equipped with a crib, a car seat/carrier, a sofa, an armchair, a baby changing table and numerous accessories placed all over the room: a bottle, a blanket, clothes, diapers, board books and toys . Thus, participants had the opportunity to behave as in a real caregiving situation.The participants from the expectant group were invited to the subsequent session when their child was between 6 and 12 months old. Every family came to the same room arranged to allow playing with the child. One of the parents was asked to play with his/her child as usual for a few minutes (free play procedure). At the same time, the second parent filled in the questionnaires. Then, they swapped places. Sensitivity during the episode with the child was rated using the observational scale  and self-reportedly with the Parental Responsiveness Scale SRR; ,49). Mor. Mor49])Dispositional empathy was assessed using the Empathic Sensitiveness Scale . SWE isSelf-report. For the subjective assessment of sensitive responsiveness, the Polish adaptation of the My Emotions Scale , the InfThe Parental Responsiveness Scale SRR; ,49) is u is u49])Observation. The Ainsworth Sensitivity Scale  was usedSaliva samples for the evaluation of OT and AVP levels were collected from participants by applying salivettes and subjected to the process of lyophilization in order to increase the stability of hormones and ensure that the concentration of OT and AVP exceeded the limits of detection and quantification of the radioimmunoassay (RIA) test ,57,58. T® Analyzer , which utilizes matrix-assisted laser desorption/ionization time-of-flight mass spectrometry for qualitative nucleic acid analysis.On the basis of a literature search, we selected 10 single-nucleotide polymorphisms (SNPs) in OXTR and CD38, and 2 simple sequence repeats (SSRs) in AVPR1a. Genotyping of 10 SNPs was performed with the use of the MassARRAYAttachment style. We used a short version of the Experience in Close Relationships—Revised . The scTemperament. The short version of the Formal Characteristics of Behavior—Temperament Inventory  was usePerceived partner empathy. The perception of a partner’s empathy was assessed with the Perceived Partner’s Empathy Scale . The unRelationship satisfaction. We used a scale that comes from the RELATionship Evaluation Questionnaire ,64 and iThe participants retrospectively assessed the behaviors of each of their parents (separately mother and father) using the Family of Origin (RP) , which rFor our primary aim, testing the direct and indirect (through oxytocin and vasopressin) effect of dispositional empathy on responsiveness to infant crying, with The data analysis will be carried out using R  with thecentiles ,73,74. FThe project collects novel data from 442 Polish women and men using a secure web-based environment at the University of Gdansk, Poland. Access to data during the research period is restricted to project members  given access to the data. All members of the research team have signed a confidentiality agreement.Personal information is processed in accordance with the Polish Personal Information Protection Act based on European legislation. All the data are coded and a separate participant identification code list used to link the data and biological specimens is stored until the end of the research project in a separate location in order to secure the personal information. Results will be mainly published in peer-reviewed international journals in accordance with the project description and agreements within the consortium. There will be no personal identification of participants in scientific communications.https://osf.io/z5682/, accessed on 22 January 2020).Written informed consent regarding all collected data  is obtained from the participants. They are also reminded that participating in the study is voluntary, that they can withdraw from it at any time without consequences and that their data are stored anonymously and securely. All consent forms and related documentation given to the participants were approved by the Ethics Committees and can be requested from the authors. The research protocol received ethical approval by the Independent Bioethics Committee for Scientific Research at Medical University of Gdańsk, Poland (permission #NKBBN/154/2017) and the Ethics Committee at the Institute of Psychology, University of Gdańsk, Poland (permission #4/2016) and (permission#6/2018), and is in accordance with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. The study is registered in the Open Science Framework , and focus on the crying signal. Using this design, we are able to control many factors influencing the dynamics of adult–infant interaction. Affective states experienced by participants evoked by a crying signal are also examined in the context of biological and psychological predictors. Additionally, we examine parental sensitive responsiveness of couples towards their own child’s cues in follow-up assessments, which uniquely enables exploration of the predictive validity of the experimental design with a life-like doll.Therefore, HEART explores the issues essential for the quality of family life and children’s development. We seek answers to questions about the bases or roots of the role of empathy in displaying sensitivity towards children’s needs and thus in creating adult–child bonds. Sensitive parental behaviors in response to babies’ signals have an impact on the formation of proper bonds, the development of the child’s social cognition and emotional regulation ,75. The The study has some limitations. The study design might facilitate participation of couples who are well educated or highly involved in their future parenthood , which might limit the possibilities for generalization. In the second part of the study, it is not possible to invite a control group, due to the specificity of the research measures including, the Ainsworth Sensitivity Scale and Parental Responsiveness Scale. Additionally, hormonal measurement requirements limit the heterogeneity of the sample as only healthy couples who were not taking particular medications and psychoactive substances participated in the studies. The experimental procedure with a life-like doll yields some risk that particular participants will not consider this controlled situation realistic. However, exploration of individual differences in this standardized setting will give the opportunity to examine characteristics that are associated with lack of engagement and low response to the experimental cues. The experimental situation as well as the subsequent observation of the free play with the participants’ own children might not be long enough to examine individual differences in parental sensitivity. However, similar designs have been successfully implemented before .The HEART project enables testing of the predicted positive impact of dispositional empathy and hormonal factors—OT and AVP—on parental sensitivity in a controlled experimental design , which constitutes a major strength. The large sample, including both expecting and non-expecting couples, gives the opportunity to test the impact of parental role activation on responsiveness towards infant crying. In a standardized setting, use of a life-like doll enables manipulation of a child’s cues that might elicit sensitive responsiveness. The research design uniquely combines psychological  measures with biological assessments. Measures have been translated into Polish to examine sensitive responding subjectively, through self-reported emotional reactions towards infant crying, and objectively, through observation of participants’ behaviors. Finally, the postpartum session is designed to examine sensitive responsiveness towards participants’ own children’s cues (objectively and subjectively with a new measure) in the group of formerly expectant couples, which provides the possibility to test the predictive validity of the study’s experimental procedure. Therefore, HEART results might be clinically used to design interventions and programs for parents  to support and develop their skills in sensitive responding towards child cues.


The massive amount of diffraction images collected in a raster scan of Laue microdiffraction calls for a fast treatment with little if any human intervention. The conventional method that has to index diffraction patterns one-by-one is laborious and can hardly give real-time feedback. In this work, a data mining protocol based on unsupervised machine learning algorithm was proposed to have a fast segmentation of the scanning grid from the diffraction patterns without indexation. The sole parameter that had to be set was the so-called “distance threshold” that determined the number of segments. A statistics-oriented criterion was proposed to set the “distance threshold”. The protocol was applied to the scanning images of a fatigued polycrystalline sample and identified several regions that deserved further study with, for instance, differential aperture X-ray microscopy. The proposed data mining protocol is promising to help economize the limited beamtime. CompareA salient feature of Laue microdiffraction is its sensitivity to the local misorientation inside the illuminated volume ,11, moreThe rotation-free feature of Laue microdiffraction renders it suitable for in-situ or ex-situ mechanical experiments ,20,21,22https://gitlab.esrf.fr/micha/lauetools, accessed on 16 February 2022). The standard treatment is in essence a trial-and-error process that usually suffers from inefficiency, especially for the raster scanned diffraction patterns which has to be treated one by one. Therefore, any additional information concerning the scanned microstructure would facilitate the process, for example, Örs et al. [Despite the wealth of information behind Laue microdiffraction pattern, the interpretation is not straightforward since the wavelength or index pertaining to each diffraction peak is not known a priori. Standard treatment involves modulating the orientation and calibration parameters to minimize the discrepancy between the simulated and experimental diffraction pattern, and has been implemented in software such as XMAS  and Laues et al.  used thes et al.  suggesteIn a word, the indexation of diffraction peaks is the key to the full interpretation of diffraction pattern. Nevertheless, in certain circumstances, full interpretation of diffraction patterns is unnecessary or fast parallel computing capabilities are unavailable, thereby necessitating the development of indexation-free approach towards on-the-fly analysis of raster scanned diffraction patterns. Zhou et al.  proposedIn the present work, we demonstrated the application of unsupervised machine learning algorithms to the raster scanning Laue microdiffraction images of the fatigued polycrystalline copper. Substantial dislocation structures will grow in copper after the cyclic loading , deterio9 cycles with a frequency of 10 Hz.The diffraction images were collected from raster scanning of fatigued polycrystalline copper.  The sample was designed in accordance with the ASTM/E606 standard. The Laue raster scanning over the sample was performed in beamline 4B of Pohang Light Source . The raster scanning was over a on peaks a.The original Laue microdiffraction pattern has 1024 × 1024 pixels. Although one can directly use the full gray levels of images to segment the grid points from a theoretical point of view, it is neither practical nor necessary to handle such huge amount of data, thus necessitating a feature extraction process to reduce the diffraction patterns into a manageable number of latent features. The extracted features would subsequently lay foundation for grid segmentation.To begin with, each image needed to be normalized to eliminate systematic errors. Normalization was accomplished by subtracting the mean gray level from the gray level and dividing by the standard deviation of the gray levels, in accordance with McAuliffe et al. .Then, since the background occupying the majority of Laue pattern contained nothing other than noise, a moderate resolution coarsening could speed up the image processing and smooth the noise . In thisA number of algorithms serve to extract features for further grid segmentation. Song et al.  applied Conceivably, increasing the number of latent features A quantitative metric of the resemblance between the original and restored image is the normalized cross-correlation (NCC) coefficient:Further reduction of Another candidate for factorization is non-negative matrix factorization (NMF) which has been used in processing electron microscopy images ,38. In oThe PCA is in essence the singular value decomposition (SVD) of the data matrix We applied the PCA to the data matrix it-Learn , and disit-Learn , therefoTo sum up, the pipeline for feature extraction consisted of (i) pixel agglomeration with HAC algorithm and subsequently (ii) factorization of data matrix via PCA. It should be noted that neither of the step was indispensable. The design of the pipeline was a compromise between the computational capacity and the integrity of the information. Indeed, although PCA could reduce the size of data with less loss of information, it was computationally more expensive than pixel agglomeration by HAC; in this regard, HAC algorithm should be implemented in the first place to reduce the data to a size handleable by PCA.After extracting HAC algorithms can operate in two modes: (i) by specifying the number of clusters; (ii) by specifying the distance threshold above which the grid points would not be merged, and the number of clusters will be determined automatically. In the stage of feature extraction, we used the first mode, and here we used the second mode for the segmentation of grid. The rest of the setting was the same as in feature extraction and not recapitulated herein.Indeed, the choice of distance threshold was rather subjective. In two extreme cases, too small distance threshold might lead to the maximum of te score , Calinskte score , and Davte score  of the cThe three indices have not reached a consensus on the optimum number of clusters. Both figures were mosaic, especially Herein, we presented a statistics-oriented criterion to decide the optimal distance threshold. In the community of material scientists, the grain size distribution  in a polycrystal has long been recognized as lognormal as a rule of thumb . Recentlith cluster as (1)Calculate the logarithms of the number of grid points (2)Normalize (3)Calculate the maximum absolute difference between the empirical cumulative distribution function Denoting the number of grid points in the In this sense, smaller KS distance indicates better lognormality of the distribution. (1)in cluster 324, the spots were slightly streaked due to the penetration of the X-ray; the distinctively high silhouette coefficients indicated that the diffraction patterns in cluster 324 shared high resemblance compared to patterns in other clusters.(2)in cluster 67, the spots were elongated unidirectionally implying that one slip system was predominantly activated; the more distant from cluster 324 the more blurred the spots.(3)in cluster 111, some spots were multidirectionally streaked implying the activation of multiple slip systems; some spots were highly blurred or even indiscernable suggesting innegligible amount of statistically stored dislocations (SSDs) in the illuminated volume.The diffraction patterns of subgrid B in The progressively blurring of spots from the interior (cluster 324) to the border (cluster 111) of the grain conveyed a picture of dislocation pile-up in which the mobile dislocations became sessile at the grain boundaries and obstructed the dislocation emitted from the interior of grain. The pile-up of primary dislocations led to the activation of other slip systems, resulting in multidirectionally streaked spots Both steps used the HAC algorithm since HAC algorithm could exploit the 2D connectivity in both the pixels of the diffraction patterns and the grid points of the raster scanning to ensure the continuity of segments and save the computation time.(2)A statistics-oriented criterion was proposed as a guideline to set the distance threshold in HAC algorithm which determined the number of segmentations, which yielded at least in our case more realist results than conventional criterion.In analogy to the preceding work ,32,35,38The application of machine learning to raster scanning diffraction images is a case-by-case issue. The proposed protocol, which was useful in our case, has the potential to be applied in other cases, and help economize the limited beamtime.