CTQ  was proposed. Three groups of factors were taken into account in the assessment of technological quality of the surface after cutting: selected surface texture parameters , results of measurements of dimensional accuracy of cut elements (length deviation LD and width deviation WD) as well as indicators of surface morphology estimated on the basis of microscopic images of the surface after cutting (deformation intensity DI and identification of cutting zones ICZ). On the basis of CTQ values determined, the cutting results of both cutting methods were compared. The analyses presented in this paper proved that the CTQ index can be effectively used to compare the results of a cutting process conducted using different methods and under different conditions. The developed CTQ index is a universal valuation tool, allowing for quantitative evaluation of features related to the technological quality of cutting process results.Despite extensive knowledge of the cutting methods described, no universal method has been developed so far for evaluating the technological quality of elements shaped by different cutting processes. The aim of the research described in this article was to fill this gap and to propose the author’s methodology for the assessment of the technological quality of the surface of X5CRNI18-10 steel shaped as a result of laser cutting and abrasive water jet cutting. A synthetic index of technological quality assessment of the surface after cutting  The operation of cutting is carried out on a very wide range of materials: from those used in technology , through mineral raw materials and derivatives , to natural biological materials . Diversity of cut materials is related to the fact that they are used in many spheres of human activity: industry, medicine, services, etc. The diversity of properties of materials to be cut makes it necessary to use different methods and ways of cutting ,2,3,4.Cutting of metals is an essential technological operation, from which the entire process of manufacturing in the machine industry usually begins. The development of cutting methods is a response to the increasing demands of new materials and the desire to increase the quality and efficiency of processes, ranging from straight cutting, through 2D cutting (in two dimensions) to 3D cutting (in three dimensions) ,6. One oThis paper focuses on a comparative analysis of the results of laser cutting (laser cutting) and abrasive water jet. These techniques have become popular in the last decade in industrial practice, which is also due to their versatility resulting from the numerical control of the cutting head motion path.A high-pressure water jet is ideal for cutting different hardnesses of steel, ensuring an even and accurate cut . A variaThe advantages of this technique include: obtaining high quality cutting surface, no structural changes of the material at the edges (no heat affected zone), no thermal deformation, high surface cleanliness, short process preparation and finishing times and high process efficiency. This method is particularly profitable for small and medium series of products ,5,14,15.Laser cutting is a process in which the energy of the photon in a form of laser beam, continuous or pulsed, causes the melting of the cut material in the cutting gap or the simultaneous melting and vaporization and burning of the cut material: metals, some ceramics or thermoplastics.Easy automation of the process and its high flexibility,Wide range of materials that can be cut (from very soft and brittle to very hard),High speed of the process,Narrow cutting gap and heat affected zone,The possibility of obtaining semi-products on dimension and contactless process resulting in the lack of tool wear,High degree of process automation,The possibility of obtaining high precision cutting,Control of energy supply to the material to be cut,High process flexibility when changing the production profile, as there is no need to change cutting tools.The advantages of laser cutting include ,16,17:EaThe laser cutting process is suitable for cutting mild steel up to about 30 mm thick. Obtaining good results above the 25 mm barrier requires high quality of all elements such as material (steel to be laser cut), gas purity, nozzle condition and beam quality. The laser cutting process requires a simultaneous, coaxial flow of gas with the laser beam. This gas is called assist gas. Its task is to blow out the resulting products  from the cutting gap.The common features of both characterized techniques—high cutting performance, wide range of cut materials and relatively high cutting precision ,16—mean The term quality can be defined as the relationship to certain characteristics of a product or service that affect the customer’s perception of it. It is the degree to which a set of inherent properties satisfies the requirements. The assessment of quality depends, among other things, on experience, knowledge, and demand for the product. This concept is subject to change as a result of human development, product and quality changes. Quality is significantly influenced by the level of awareness of employees, superiors and the degree of implementation of quality concepts within the company. The quality level is also determined by the customers. Quality is a multidimensional and interdisciplinary concept. Due to the place of shaping the quality in the manufacturing process, we can distinguish technological quality, functional quality and operational quality of the product. Technological quality changes with the use of successive technological operations from the pre-treatment operation, through the shaping treatment to the finishing treatment operation. In the case when the product has a complex structure, the assembly operations have a significant influence on the shaped quality, as a result of which the functional quality is obtained. On the other hand, after the product is handed over to the customer, the operating quality can be distinguished, which is greatly affected by the conditions and intensity of operation ,18,19,20CTQ was proposed. On the basis of CTQ values determined, the cutting results of both methods were compared, taking into account in the evaluation the parameters of the surface texture, deviations of dimensions of cut elements and the results of microscopic observations of deformation of the formed cut surface.Despite extensive knowledge of the cutting methods described, no universal method has been developed so far for evaluating the technological quality of elements shaped by different cutting processes. The aim of the research described in this article was to fill this gap and to propose the author’s methodology for the assessment of the technological quality of the surface of X5CRNI18-10 steel shaped as a result of laser cutting and abrasive water jet cutting. A synthetic index of technological quality assessment of the surface after cutting The aim of the study was to determine the most advantageous parameters of the investigated processes with respect to the assessed indices of technological quality assessment: dimensional accuracy, surface texture and results of microscopic observations of surface deformations after cutting of sheet made of X5CrNi18-10 steel ,22,23. ILaser cutting was carried out using numerically controlled Kimla FlashCUT LF 1530 6 kW –The cutting process was carried out starting from determining the position and fixing of the input material, which was a sheet made of X5CrNi18-10 steel with dimensions of 1250 mm × 2500 mm, from which workpieces of a rectangular shape 100 mm × 30 mm were cut. Then, the cutting process was programmed according to the adopted experiment plan and given unique designations.In the next stage of the study, we proceeded to measure the dimensional accuracy of the machined workpieces. For this purpose, QLR MMT digital micrometers  with measuring ranges of 25–50/0.001 mm and 50–100/0.001 mm were used. Length and width measurements were made by measuring the distance between the opposite edges of the cut objects at three locations. Measurements of the geometric structure of the surface formed in the laser and abrasive water jet cutting processes were also carried out using the multi-head measuring system Talysurf CLI 2000 from Taylor-Hobson Ltd.  . In addiPT and the cutting parameters were selected in such a way that it was possible to effectively cut the workpiece material within the entire range of variation of cutting conditions.The selected range of changes of the adjustable parameters of both cutting processes given in  resultedSa and total height of the surface St), results of measurements of dimensional accuracy of cut elements (length deviation LD and width deviation WD) as well as indicators of surface morphology estimated on the basis of microscopic images of the surface after cutting (deformation intensity DI and identification of cutting zones ICZ). An attempt was made to correlate these factors with a relation that would synthetically allow to assess the technological quality of the shaped surface. On the basis of these assumptions, a synthetic index for the assessment of the technological quality of the surface after cutting CTQ was developed, determined by the Equation (1):n denote the values after normalization. Surface texture parameters (Sa and St) placed in the numerator of Equation (1) represent recognizable features of the solid (cut surface) associated with irregularities with relatively small vertex distances in 3D. Length and width deviation (LD and WD) are a measure of the difference of the actual dimension (determined by the measurement procedure) from the assumed  dimension, resulting from the values set in the cutting machine control program. On the other hand, deformation intensity DI and identification of cutting zones ICZ determine the features of surface morphology, which are characteristic for the cutting process. These features could be evaluated by qualitative analyses of microscopic images.Three groups of factors were taken into account in the assessment of technological quality of the surface after cutting: selected surface texture parameters (arithmetic mean deviation of the surface CTQ index (1) assumes dividing the numerator by 3 to obtain the resultant value from the range of 0–1 which, when multiplied by 100%, would allow expressing the technological quality of the evaluated surface after cutting with values from the range 0–100%. Due to the occurrence of negative values in the assessment of the dimensional accuracy, it was additionally necessary to express the product of the LD and WD deviations as an absolute value. As a result, CTQ index takes higher value for smaller sum of products, corresponding to smaller values of surface texture parameters, smaller dimensional deviations and smaller surface deformations after cutting.The construction of the proposed The results of the conducted research were presented in four sections relating to surface texture analysis , dimensix, y axis): 4.8 × 4.8 mm. During the measurement, 321 profiles (y-axis) were recorded. The distance between the profiles was 15 μm. On one profile 2401 points were registered (x-axis). The distance between profile points was 2 μm. Each measurement was performed in single-pass mode. The measurement time of one area was 4024 s. Data obtained during the measurements were analyzed using specialized software TalyMap Platinum 4.0 .The results of microtopography measurements of the cut surface showed significant differences between the values of selected surface texture parameters determined in the input and output areas of the abrasive water jet and the photon flux from the material. This proves reduced efficiency of water abrasive jet action as an erosive tool in shaping of the lower part of cutting zone. It is similar in the case of laser cutting, where the curvature of the laser beam in the lower part of the cut element distorts the cut edge from the middle of the plate thickness downwards. Therefore, it was decided that the measurements of microtopography of the cut surface will be made in the lower part of the cutting zone (at a distance of 1.0 mm from the bottom edge). The surface texture was recorded on each specimen at the bottom of the cutting zone with dimensions (An overview of the surface microtopography obtained is shown in Sa–arithmetic mean deviation of the surface (μm),St–total height of the surface (μm).For each of the obtained surface microtopographies, the values of two surface texture parameters were determined:PT = 6, 8 and 10 mm for variable power P and cutting head feed rate f LASERv in laser cutting process as well as variable abrasive flow rate ṁ and cutting head feed rate f AWJv in abrasive water jet cutting process.ṁ and increasing the cutting head feed speed fv AWJ. In the case of laser cutting an increase in the cutting head feed rate fv LASER affects increase of surface texture amplitude parameters (Sa and St) of the cut surface. In the conducted study, the effect of laser cutting power P was inconclusive.The obtained results of surface texture measurements  prove thSa and St parameters prove that plate thickness PT for both cutting methods significantly affects the quality of the surface after cutting. At the smallest plate thickness PT = 6 mm in the examined range, no significant traces of the effect of concentrated energy flux were observed, which became apparent when cutting plate thickness PT = 8 and 10 mm, which increased the values of surface texture parameters.The determined values of LD = 0.609 mm was observed in the element cut from a plate of thickness PT = 8 mm by laser with power P = 4 kW and cutting head feed rate fv LASER = 30 mm/s. On the other hand, the largest positive deviation of width WD = 0.563 mm was measured in the element cut out of the plate with thickness PT = 6 mm by the laser with power P = 4 kW and cutting head feed rate fv LASER = 30 mm/s. The largest negative value of the length deviation LD = −0.236 mm was observed in the element cut from a sheet of thickness PT = 10 mm by laser with power P = 6 kW and cutting head feed rate fv LASER = 10 mm/s. On the other hand, the largest negative deviation of the width WD = −0.237 mm was determined in the case of the workpiece cut from a plate of thickness PT = 10 mm by the laser with power P = 6 kW and cutting head feed rate fv LASER = 10 mm/s. The analysis of the presented results of dimensional accuracy measurements of cut out elements showed that the lowest dimensional accuracy was obtained in the process of laser cutting. It should be noted that this process was carried out with about 10 times higher feed rate values of the cutting head in comparison with the abrasive water jet cutting process.The dimensional accuracy measurements performed in the described study allowed determination of the dimensional deviations of the workpieces after cutting. The largest positive deviation of length P, feed rate of both cutting heads fv LASER and fv AWJ and abrasive flow rate ṁ. Multivariate correlation coefficients R were determined for the models to assess model adequacy. The models were specified as first-order exponential functions without interaction and plotted as shown in The obtained measurements allowed determination of the mathematical models that informed the most favorable (in the assumed range of variability) cutting parameters, i.e., laser power fv LASER and power P during laser cutting ,For sheet thickness PT = 8 mm: laser power P = 5 kW and working head feed rate fv LASER = 10 mm/s (LASERCTQ = 92.31%),For sheet thickness PT = 10 mm: laser power P = 5 kW and working head feed rate fv LASER = 10 mm/s (LASERCTQ = 90.90%).For sheet thickness Analysis of x values  allowed PT = 6 mm: abrasive flow rate ṁ = 0.0083 kg/s and working head feed rate f AWJv = 1.66 mm/s (AWJCTQ = 90.68%),For sheet thickness PT = 8 mm: abrasive flow rate ṁ = 0.0050 kg/s and working head feed rate f AWJv = 1.66 mm/s (AWJCTQ = 96.30%),For sheet thickness PT = 10 mm: abrasive flow rate ṁ = 0.0066 kg/s and working head feed rate f AWJv = 1.66 mm/s (AWJCTQ = 99.41%).For sheet thickness However, for the abrasive water jet cutting process, the following parameter values were selected as the most favorable for the conditions under consideration:CTQ can be effectively used to determine the most favorable parameters of the cutting process. The design of the CTQ index allows taking into account other features of the analyzed surface and expanding their number, e.g., by adding parameters for evaluating the surface layer structure, surface microhardness, etc. The presented broad set of analyses showed that the developed CTQ index is a universal valuation tool, allowing for quantitative evaluation of features related to the technological quality of cutting process results.On the example of analysis of the process of laser cutting and abrasive water jet cutting of stainless steel X5CRNI18-10 it was proved that the proposed synthetic index of technological quality assessment of the surface after cutting The analyses presented in this paper in the scope of technological quality assessment of the workpieces after laser cutting and abrasive water jet cutting made it possible to formulate the following conclusions.Sa and St) is affected by decreasing the value of abrasive flow rate ṁ and increasing the cutting head feed speed fv AWJ.The obtained results of surface texture measurements of surfaces cut by the water-abrasive jet prove that the decrease in roughness amplitude parameter values  and plate thickness .In the laser cutting process the dimensional accuracy of the cut workpieces affects mostly the head feed rate fv AWJ causes deviation from perpendicularity of the surface formed. No significant effect of abrasive flow rate ṁ on the dimensional deviation was observed.In abrasive water jet cutting trends are similar, however, the dimensional deviation occurring is larger and amounts even to 0.3 mm. Additionally it was noted that increasing the head feed rate PT = 6 to 8 mm and then to 10 mm resulted in an increase in the number of surface deformations in both cutting methods.Observation of microscopic images showed that increasing the plate thickness from The surface after laser cutting was characterized by significantly higher deformation intensity (with visible division into three zones of the cut surface) compared to the surface after abrasive water jet cutting.CTQ value of the entire set of analyzed results (AWJCTQ = 99.41%) was obtained for the abrasive water jet cutting process with sheet thickness PT = 10 mm, abrasive flow rate ṁ = 0.0066 kg/s and working head feed rate f AWJv = 1.66 mm/s.The analysis showed that the most favorable (highest) CTQ index for laser cutting process (LASERCTQ = 93.85%) was obtained for sheet thickness PT= 6 mm, laser power P = 5 kW and working head feed rate fv LASER = 10 mm/s.The most favorable value of CTQ index means that it can be used to compare the results of a cutting process conducted using different methods and under different conditions.The relative (percentage) form of the


The effects of PP molecular configuration on the composite properties and cell morphology of samples were also investigated. The experimental results indicated that the application of a spherical cavity mixer with a cavity radius of 5 mm could effectively improve the mixing quality and avoid the agglomeration of WF. In addition, compared with the branched molecule, the linear molecule not only increased the melting temperature by about 10 °C, but also endowed composites with a higher complex viscosity at a shear rate lower than 100 s In recent decades, the rapid development of society not only consumed a large amount of timber and polymers, but also created innumerable waste plastics and wood, which cause serious environmental pollution and a huge shortage of forest resources ,2,3. TheAccordingly, wood–polymer composites (WPCs) have gradually replaced the application of timber, and show broad development prospects in interior decoration, architectural decoration, packaging and transportation, automobile manufacturing and other fields . In addiPrevious studies have indicated that WPCs possess the characteristics of both wood and plastic: they are water-resistant, reusable, and have a high chemical resistance and good processing characteristics . NeverthHowever, the introduction of a uniform microporous structure was found to be effective in improving the ductility while decreasing the density of composites, which is mainly attributed to the fact that the cracks inside materials were effectively suppressed by the micropores, leading to the increased growth energy ,12. As tAs a result, the cavity transfer mixer (CTM) was designed and applied to construe the foaming experimental platform with a single screw extruder. Meanwhile, PPs with different molecular configurations were chosen as the matrix, and the thermal and rheological properties of composites were characterized and analyzed. Moreover, the effect of WF content and molecular structure on the morphology of composites was also investigated, aiming to explore the evolution law of bubbles and promote the microporosization of composites.According to the previous work, the addition of WF endowed the composites with a higher apparent viscosity, which not only deformed the static mixer, but also resulted in more difficulty in the dispersion of the strong agglomeration between the WF particles. Therefore, the cavity transfer dynamic mixer with a strong shear dispersion ability was applied in the extrusion of composites with high viscosity, as shown in nS is the theoretical number of mixer striations, N is the number of circumferential cavities, and M is the number of axial cavities. The distance between adjacent cavities and other structural mixer parameters could also be denoted by N and M, which were calculated as follows:nW is the circumferential distance between adjacent cavities, zR is the radius of rotor, mL is the axial distance between adjacent cavities, bw is the minimum wall thickness between adjacent cavities, qr is the cavity radius, L is the effective rotor length. Considering the poor interfacial compatibility between WF and PP and the strong agglomeration among WF particles, the number of circumferential cavities M was set as 12, and the detailed parameters were listed in The dispersive mixing ability of a spherical cavity transfer mixer was mainly decided by the number of circumferential and axial cavities, which could be described as the number of striations ,21(1)Snqr not only led to an increased distance between adjacent cavities, it also resulted in a decreased number of axial cavities M and a decrease in the theoretical number of striations nS, which indicated that the mixer had an impaired mixing quality. Meanwhile, in order to avoid the problem of cavity interference during drilling, the minimum wall thickness was kept higher than 1.5 mm. As a result, the structural parameters of the spherical cavity mixer were determined with the qr of 5 mm, which was then fixed at the end of the screw in threaded connection.As shown in Based on the designed spherical cavity mixer shown above, the experimental platforms with/without CTM were shown in However, the decreased results of the pressure sensor shown in The PP-based WPCs mainly consisted of resin matrix, WF and other fillers. In this study, two types of PP with different molecular structures, PP1 (B8101) and PP2(B1002W), were applied as the resin matrix, both purchased from Sinopec Yanshan Petrochemical Company . The poplar WF  with a size of 150 μm, talc  with a size of 23 μm and MAH-g-PP  were purchased and used as the main fillers. In addition, the bubbles among the samples were achieved by the blowing agent Azodicarbonamide (AC), which was purchased from Selon Industrial Co . with a gas production of 220 mL/g and decomposition temperature of 160 °C.As shown in Second, the prepared WPC pellets were mixed with the foaming agent AC, and then extruded into the continuous plate with 80 mm × 8 mm rectangular section by the constructed experimental platform. Finally last, the plates were cut into specimens of certain shapes for subsequent testing.MFR is the mass flow rate of melt (g/10 min), m is the mass of splines (g), and t is the sample time interval (s). The MFR value of each sample was averaged after five repetitions.The tester RL-Z1B1, provided by Shanghai S.R.D. Scientific Instrument Co., Ltd.  was applied to measure the melt flow rate of materials, while the temperature and the load were set as 230 °C and 5 kg, respectively. The mass flow rate was calculated as follows:The rheological properties of the materials were characterized by complex viscosity (η), shear storage modulus G′, loss modulus G′′ and loss tangent (tanδ), which were conducted on a parallel-plate rheometer HAAKE MARS III, provided by Thermo Fisher Scientific Inc. (Shanghai China).The rheological tests were performed between parallel plates with the diameter of 25 mm and gap of 1 mm at 180 °C, which were also conducted in dynamic mode and nitrogen atmosphere. The frequency sweeps between 0.01 and 100 rad/s were carried out at strains within the linear viscoelastic range and the scan amplitude was 1% during testing.The thermal properties of composites were characterized by the crystallization behavior, which was measured by differential scanning calorimeter (DSC). cX of PP was calculated as follows:Hf is the heat of fusion generated during melting or crystallization, ∆Hfo is the theoretical heat of fusion of PP with 100% crystallinity  in nitrogen atmosphere. The crystallinity (209 J/g ), and ω The samples’ micromorphology was observed by a stereomicroscope SZM-45T2 provided by Sunny Optical Technology Co., Ltd . The fracture surfaces of the samples were observed by scanning electron microscope (SEM)  after tensile tests, and the fracture surfaces were coated with a thin gold layer before observation.The mechanical properties of the samples were characterized by tensile strength and flexural strength, which were both tested with a load of 5 kN and speed of 10 mm/min by the universal tester KXWW, provided by Taiding Testing Machine Manufacturing Co., Ltd . The value of each sample was averaged after five repetitions.The foaming temperature was mainly determined by the thermal properties of the composites, which were greatly affected by the molecular structure of PP ,24. As sThe melting and crystallization behaviors of composites with different WF contents were both characterized by differential scanning calorimetry (DSC), and the thermal properties are also shown in To describe the flowability of composites, MFRs of melt with different WF contents and resin matrixes were measured and shown in On the basis of the composites’ MFR, the frequency dependences of molten-state oscillatory shear moduli were also investigated and are shown in Meanwhile, the angular frequency at the intersection of storage modulus (G’) and loss modulus (G”) curves could reflect the relaxation time and weight-averaged molecular weight of PP ,30. The According to the rheological characteristic parameters, the larger molecular weight of PP1 decreased the difficulty in the formation of entanglements, which caused the much higher viscosity of PP1 compared to PP2. As shown in However, compared with linear macromolecules, the branched macromolecules had a great advantage in reducing the effect of shear action on the viscosity of resin. Therefore, with the increase in shear rate, the decrease in of PP1 viscosity was larger than that of PP2, which was more obvious in the rheological curves of the composites. In addition, both PP1 and PP2 were dominated by a viscous loss in the low-frequency region, and the loss factor was more sensitive to the movement of PP molecular chains than the movement of viscosity. The higher changing amplitude of PP1 indicated that it had a poorer stability than PP2.The mechanical strengths of composites with a different matrix were shown in Apart from their apparent quality, the dispersion state of fillers on the samples’ section was observed, by an optical microscope, to characterize the platform’s mixing effect. As shown in The mechanical properties and density of samples were both affected by the morphology of bubbles, and the sample micrographs for axial and radial sections were shown in According to the micrographs in −1 during extrusion. Thus, the higher complex viscosity of PP1-based WPCs was achieved, and samples with more uniform cell morphology were prepared. Moreover, the simulation result shown in Compared with the bubbles on the axial section, the cell morphology on the radial section was not very regular, which was mainly attributed to the velocity difference existent in the mold channel. M Favelukis et al ,32,33 foContrary to batch foaming and compression molding foaming, bubbles foamed in the flow field with large radial velocity gradient moved in the radial direction of the channel. According to the evolution process of the bubble structure on the radial section (perpendicular to Z axis) shown in (1)Compared with static mixer, CTM with a strong shear dispersion ability was more suitable for the dispersive mixing of materials with high viscosity, which was also improved by the increased radius and axial number of cavities. Meanwhile, the experimental results also demonstrated that the application of spherical CTM with the radius of 5 mm could effectively prevent the exposure of agglomerated WF on the sample surface and realize the uniform dispersion of fillers.(2)Affected by the molecular configuration, the linear molecular endowed PP1 with the triclinic crystals, which were about 10 °C higher than the trigonal crystals of PP2 with branched molecule. The smaller angular frequency of PP1 at the intersection of G’ and G” curves indicated the longer relaxation time and higher average molecular weight, which decreased the difficulty in the formation of entanglements and caused the much higher viscosity.(3)−1, which contributed to the smaller size and larger density of the bubbles. Moreover, the bubbles foamed in the shear flow field were gradually stretched into a flat ellipsoid shape and arranged along the flow direction for the radial velocity gradient.The addition of WF and linear molecular endowed PP1-based composites with higher viscosity at a shear rate lower than 100 sTo realize the microporosization of PP-based WPCs, the effects of spherical CTM and molecular configuration on the cell morphology of samples were investigated. The conclusions from this research are summarized and listed as follows:


The degree of thixotropic behaviour was evaluated by the size of the hysteresis area, and flow curves were constructed using the Bingham, Herschel–Bulkley and Casson models with respect to the plastic behaviour of the chocolate masses. According to the values of the coefficients of determination R2 and the sum of the squared estimate of errors (SSE), the models were chosen appropriately. The most suitable models are the Herschel–Bulkley and Casson models, which also model the shear thinning property of the liquids . Using the coefficients of the rheological models and modified equations for the flow velocity of technical and biological fluids in standard piping, the 2D and 3D velocity profiles of the chocolate masses were further successfully modelled. The obtained values of coefficients and models can be used in conventional technical practice in the design of technological equipment structures and in current trends in the food industry, such as 3D food printing.Chocolate masses are one of the basic raw materials for the production of confectionery. Knowledge of their rheological and flow behaviour at different temperatures is absolutely necessary for the selection of a suitable technological process in their production and subsequent processing. In this article, the rheological properties (the effect of the shear strain rate on the shear stress or viscosity) of five different chocolate masses were determined—extra dark chocolate (EDC), dark chocolate (DC), milk chocolate (MC), white chocolate (WC), and ruby chocolate (RC). These chocolate masses showed thixotropic and plastic behaviour in the selected range of shear rates from 1 to 500 s Chocolate is generally very popular worldwide and consumed across all generations. Its popularity is closely related to its overall sensory properties . In ordeBased on the introductory literature review, the following two scientific hypotheses were established. These hypotheses are not completely verifiable in the contemporary literature, so they are given due attention in this article.Chocolate masses have a plastic property with shear thinning behaviour (pseudoplastic with a yield stress).With an increasing temperature, the plastic viscosity or the consistency  and thixotropy of the chocolate masses decreases.This research includes and describes the behaviour of chocolate masses that do not contain cocoa butter substitutes. Five chocolate masses were used for the experiments—extra dark chocolate (EDC), dark chocolate (DC), milk chocolate (MC), white chocolate (WC), and ruby chocolate (RC).The EDC  contains 100% cocoa components . The DC, MC, and WC  contain 55.5%, 36.5%, and 28% cocoa components. The RC  contains 47.3% cocoa components. Further characteristics  of the chocolate masses are given in The individual chocolate masses were tempered (by the manufacturer) before distribution and used in this research in the form of chocolate drops. For completeness of sample characteristics, the specific tempering curves of chocolate masses are given in The chocolate masses were approximately the same age . Prior to analysis, the masses were stored under the same conditions in a single warehouse at 12 °C.−1) and three times at a decreasing shear strain rate (from 500 to 1 s−1) each time for 60 s. The average values of the shear stress were then used for the mathematical modelling.The rheological properties of the chocolate masses were measured using an RST CC rotary rheometer  with a cone-plate measuring geometry. The diameter of the cone was 50 mm with an angle of 2° (the standard designation is RCT-50-2). The gap between the cone and the plate was set to 0.05 mm at the narrowest point (at the tip of the cone), the gap was 0.923 mm at the edge of the cone. The measurement methodology was set appropriately, as the maximum size of the solid particles in the chocolate masses is 25 μm ,15. The −1 in 1 min, held constant at 500 s−1 in 10 s, and decreased logarithmically from 500 to 1 s−1 in 1 min. The flow measurements were performed by RST CC rotary rheometer  with cone-plate geometry equipped with an RCT-50-2 spindle (diameter of the cone was 50 mm with an angle of 2°) at the temperatures of 36, 38, 40, 42, and 44 °C. The hysteresis area was calculated with the use the corporate software, Rheo3000 .Thixotropic behaviour of five different chocolate masses was characterize by hysteresis loop test : Shear rThe dependence of the shear stress on the shear strain rate was described by three non-Newtonian (plastic) mathematical models. The first model was the Bingham rheological model :(1)τ=τ0+The second model was the Herschel–Bulkley rheological model :(2)τ=τ0+−1], K is the consistency factor [Pa·sn], n is the flow index [–], and And the third model was the Casson rheological model :(3)τ=τ0+p < 0.05).The experimental data were processed by MATLAB R2018b  and Statistica 12 . To determine a statistically significant difference between the measured values of the shear stress and dynamic viscosity at the selected temperatures of the individual chocolate masses, an ANOVA  test was performed followed by multiple comparisons using Tukey’s HSD (honestly significant difference) test  and numerical statistical analysis of the residues.2 and the sum of squared estimate of errors (SSE). The SSE is the sum of squares of the deviations of the data values from the predicted values  using the general formula:ith value of the variable to be predicted, ith value of the explanatory variable, and The degree of accuracy and suitability of the rheological models were evaluated using the coefficient of determination RIn the first phase, the mathematical description of the shear stress and shear strain rate dependence was carried out. For this purpose, the Bingham (B), Herschel–Bulkley (H–B), and Casson (C) model were used. The results of the mathematical modelling are given in K) than with the decreasing shear strain rate. With the increasing temperature for the individual samples, these values decrease [From the coefficients of rheological models, it is evident that with an increasing shear deformation rate, the chocolate masses reach higher values of plastic viscosity  flow limit ,20, withn) in the Herschel–Bulkley model confirmed the shear thinning  behaviour (n < 1) of the chocolate masses, which were not significantly affected by the temperature. With a decreasing shear strain rate, the shear thinning behaviour, especially in the MC, WC, and RC samples, was insignificant.The flow index ) prove, the used rheological models are very suitable. The Herschel–Bulkley rheological model [2 and SSE values) for the chocolate masses, although the Casson model is also used for chocolate masses in the literature [2 and SSE are given in As the high values of the coefficient of determination Ral model  seems toterature ,20,21,23Subsequently with rheological measurements, the hysteresis areas were calculated . The higThe magnitude of the hysteresis area was significantly affected by the temperature; with an increasing temperature, the value of area decreased and, thus, the degree of thixotropic behaviour of the chocolate masses. With an increasing temperature, the chocolate masses, with the exception of the RC masses, took less time to reaggregate their original structure . An incrThe compilation of the flow curves using the rheological models not only serves to determine the flow behaviour of liquids, but the values of the coefficients can be further used to model the physical-mechanical states of liquids, e.g., during their flow ,27. It iDuring tempering and other methods of processing, chocolate masses are often transported by pipelines, where the velocity profiles can be modelled using modified relationships for non-Newtonian fluids.v is the flow velocity, L is the length of the pipe, R is the radius of the pipe, and r is the distance from the pipe axis.For Newtonian fluids, the flow velocity at any point in the pipeline can be calculated according to:By modifying Equation (6), it is possible to obtain the following Equations (7)–(9), which are not widely used in the FoodTech sciences, but rather in construction materials , medicinTo calculate the flow velocity of Bingham fluids, it is necessary to adjust the relationship and introduce the appropriate coefficients of the model :(7)v=∆p n is the flow index, K is the consistency coefficient, and To calculate the flow velocity of liquids described by the Herschel–Bulkley rheological model, it is necessary to adjust the relationship and introduce the appropriate coefficients of the model :(8)v=n1+To calculate the flow velocity of liquids described by Casson’s rheological model, it is necessary to adjust the relationship and introduce the appropriate coefficients of the model :(9)v=R τD = 50 mm; the length of the pipe, L = 1 m; and the pressure drop, Δp = 10 kPa, the different flow behaviours of chocolate masses can be seen from D/2). It is certain that in the axis of the pipeline, the highest flow velocity is always the highest for real liquids.Using coefficients of the rheological models (Equations (1)–(4)) and formulas above (Equations (7)–(9)), it is possible to model the 2D velocity profiles. If we consider the standard diameter of the pipe, In the above figures, the non-Newtonian behaviour of the chocolate masses can be seen, where the flow front is typically flattened, as reported by, for example ,43. ThisFor a realistic idea and comparison of the flow properties of the samples, it is appropriate to supplement the modelling with three-dimensional velocity profiles of flowing chocolate masses. If the flow front in Based on the obtained experimental and calculated results and their discussion, it can be stated that both hypotheses were confirmed.With an increasing temperature, the plastic viscosity or the consistency  of the chocolate masses also resulted in an increase in the flow velocity of the chocolate masses in the pipe. The size of the hysteresis area decreased with an increasing temperature and, thus, the degree of the thixotropic behaviour of the chocolate masses. Thus, with an increasing temperature, the chocolate masses, with the exception of the RC masses, needed less time to reaggregate their structure.2, SSE), the Herschel–Bulkley and Casson rheological models appear to be the most suitable. The coefficients of the rheological models can be used for further modelling. For example, the 2D and 3D velocity profiles that are very well applicable in practice. The technical equations used to model the flow velocity of liquids at any point between the axis and the pipeline wall can be successfully used to model other foods and food raw materials with plastic or pseudoplastic rheological behaviour.The Bingham, Herschel–Bulkley and Casson rheological models can be successfully used to construct the flow curves of the chocolate masses. According to statistical preachers (RThe results of modelling the flow behaviour of the food and food raw materials can be used in conventional technical practice in the design of technological equipment structures and in current trends in the food industry, such as 3D food printing.


To evaluate the level of technical and tactical skills, an analysis of recordings of tournament bouts was carried out, and, based on the observations, the indices of effectiveness, efficiency, and activeness of the attack were calculated. Results: Individuals with higher fitness were more active and effective in the attack. The special efficiency indices showed significant correlations with the technical and tactical parameters. Better fighting performance was dependent on the speed of the punches, kicking range, and the results of the special fitness tests. Conclusions: To achieve greater efficiency and effectiveness of sport ju-jitsu, the training process should be based on comprehensive motor development and an optimal level of special fitness.Background: Ju-jitsu training has to be comprehensive in terms of training intensity, developing a wide range of physical fitness and learning multiple technical skills. These requirements result from the specificity of the competition characteristic of the sport form of this martial art. The aim of this study was to evaluate the aerobic capacity and special physical fitness of ju-jitsu athletes at the highest sports performance level and to determine the relationships between special fitness and the indices of technical and tactical skills. Methods: In order to determine the current level of special fitness of the athletes, a set of karate fitness tests were used, namely, the Special Judo Fitness Test and the Kickboxer Special Physical Fitness Test. Furthermore, maximal oxygen uptake (VO In Poland, modern sport ju-jitsu involves extensive competition in the form of tournaments organized by the Polish Ju-jitsu Association in the following variants: Fighting System, Duo System, and Ne Waza . This maFighting in ju-jitsu is characterized by the use of a wide range of techniques combined into specific sequences. An appropriate level of technical and tactical skills seems to be the most important element of an athlete’s success. Technical and tactical actions are used to control the fight and respond to the opponent’s attacks, while preventing counterattacks ,16,17,18A detailed literature review revealed that there is a lack of research on the analysis of the level of technical and tactical skills, especially concerning special physical fitness.The aim of this study was to evaluate the aerobic capacity and special physical fitness of ju-jitsu athletes at the highest sports performance and to determine the relationships between special fitness and the indices of technical and tactical skills. Evaluation of the correlations will demonstrate whether the level of special physical fitness determines the activeness, effectiveness, and efficiency of the attack and will enable more effective planning of sports training.2. Body mass was measured using a Tanita BC-601 body composition monitor , whereas the body height was measured using a SECA 2017 body height meter .The study was conducted on a group of 30 sport ju-jitsu athletes with the highest level of sports performance who agreed to participate in the study. The selection of the study group was purposeful and the selection criterion was training experience (at least 5 years) and level sports performance (champion level), which was assessed based on the authors’ observations and the opinion of coaches. The athletes were included in the ranking list of the Ju-Jitsu International Federation and the Polish Ju-jitsu Association, and four of them were medalists of the world championships. The mean participants’ experience in sport was 7.1 ± 2.26 years. They trained 1.5 to 2 h, 6–10 times a week. The exclusion criterion was a negative opinion of a sports physician and no consent to participate in the study. The mean age of the respondents was 25.43 ± 1.96 years, body weight was 83.74 ± 8.6 kg, and body height was 180.96 ± 4.97 cm. BMI ranged from 21.4 to 29.1 kg/m2peak) expressed in milliliters of oxygen per kilogram of body weight per minute (ml/kg/min). During the test, the levels of cardiopulmonary indices were recorded based on the breath-by-breath method using an ergospirometer . The test was performed on a treadmill . The effort began with a 4 min warm-up performed at a speed of 8 km·h −1, with a treadmill inclination angle of 1°. Thereafter, the speed was incremented by 1.0 km*h−1 every 2 mins. When the heart rate (bpm) approached the maximum level, the running speed was maintained and the load was increased by changing the angle of the treadmill by 1° every minute. The test was carried out until the participant refused to continue the test due to volitional exhaustion. The heart rate (HR) during the test was measured with a sports tester . The following indices were analyzed: pulmonary ventilation (VE), oxygen uptake (VO2), carbon dioxide production (VCO2), respiratory-exchange-ratio (RER), expiratory carbon dioxide concentration (%FECO2), the ventilatory equivalent ratio for oxygen and carbon dioxide (VE/VCO2), and heart rate (HR). Data were averaged every 30 s. The highest recorded value of oxygen uptake was considered as peak oxygen uptake [Aerobic capacity was measured using the aerobic maximal graded treadmill test . The tesn uptake .Evasive action test: In the retreat test, the subject starts from the fighting stance, moving backwards between lines 8 m apart. The track in the shape of a loop between the lines (back and forth) is covered 6 times. Execution time is measured in seconds. Equipment: stopwatch and 2 small cones that are set on lines at a distance of 8 m .Hip turning speed test: In the test of the speed (frequency) of the hip turns, each subject should be tied with a belt over his or her right hip , take a fighting stance, and twists the hips to the left. This movement will tighten the belt held by the coach at the back (control).Then the subject retracts with his or her hips. On the command “Hajime!” (“Forward!”), the participant makes 30 hip turns as quickly as possible (belt pulls are counted). The time taken to execute 30 pulls is recorded. Equipment: stopwatch and ju-jitsu belt .Speed punches test: Punches by the fighter performed from the fighting stance. Each participant performs a combination of two punches: left, straight to the head (Oi seiken jodan tsuki) and right, straight to the torso (Gyaku seiken chudan tsuki), without changing the designated distance. The targets to which the participant performs 30 such combinations  are held by a second person at a constant height. The time to complete 30 full punches is measured in seconds with an accuracy of 0.1 s. Two assistants need a stopwatch and 2 targets .Flexibility test using Mawashi Geri kick: The flexibility index = maximum range of kick/body height (cm/cm) was calculated. In the flexibility test, the maximum range (foot hit height) of the Jodan Mawashi Geri roundhouse kick was evaluated. Five measurements were taken for the preferred limb by recording the maximum score (cm) .Special Judo Fitness Test (SJFT):Special physical fitness was assessed based on selected tests taken from special fitness tests in karate, kickboxing, and judo:Before the first test, the participant performs a warm-up consisting of 5 min of jogging (moderate intensity) and a few Ippon-seoi-nage throws at a slow pace to familiarize themselves with the distance and exercise partners ,42.This test consists of three periods of effort  separated by 10 s breaks. In each period/series of throws, the thrower’s (tori) score is based on the maximum number of Ippon-seoi-nage throws on two partners (uke A and B) standing 6 m apart on the mat. Both uke A and B should have a similar body height and weight to the tori. Heart rate is measured one minute after the test. The Index in SJFT was also counted asFinal HR—heart rate recorded immediately after the testHR1 min—heart rate recorded 1 min after the testThrows—number of throws completed during the testThe body’s response to exercise was recorded using the heart rate monitor S-610i .6.Kickboxer Special Physical Fitness Test (KSPFT):Before performing the test, the participant performs a warm-up consisting of approximately 10 min of a general warm-up, followed by stretching exercises. Then the participant performs left and right straight punches on the partner’s shield from the fighting position to the head continuously for 30 s. After completing this part of the test, the participant runs 10 m in a straight line to the next station, where they perform left and right roundhouse kicks from the fighting position to the partner’s shields for 30 s to the head level. Then the participant runs back to the first shield and performs techniques for 30 s in a sequence consisting of the left straight punch, followed by the right hook to the head. After completing this part of the test, the participant runs 10 m to the target mate and performs a roundhouse kick  to the torso for 30 s. The total time of special effort during the test is 2 min (4 × 30 s), which corresponds to the duration of one round of a kickboxing bout. The tests were supervised by the authors of the present study for 3 days, two weeks before the competition, after the completion of the direct pre-competition training period. On the first day, the maximal graded exercise test was carried out. On the second day, the special fitness tests (tests 1–5 given above) were performed, whereas the KSPFT test was scheduled for the third day. Two days before the test, the training intensity was reduced to 30–40%.Analysis of bouts was performed based on digital recordings of selected tournament fights of the athletes in 2020. Three fights of each athlete were analyzed and semifinal, or final fights, were taken into consideration. The recordings were made using three cameras . The video editing program Movavi Video Editor 14 was used to process the images. The setting of the cameras allowed for continuous observation of the fighting athletes, judges, and the scoreboard. A single spreadsheet was developed as a primary research tool. The data from the spreadsheets were entered into Excel software. Then, the values of indices of technical and tactical skills were calculated for all three stages of the bout. The formulas for calculating the indices were developed based on the formulas used for judo and kickboxing ,45.a)Efficiency of the attack Effectiveness of the attack Activeness of the attack . The participant’s written consent was the inclusion criterion. The research was approved by the Bioethics Committee at the Regional Medical Chamber (No. 287/KBL/OIL/2020).p < 0.05 [The statistical analysis of the collected material was performed using the Statistica 13.1 package by StatSoft. Basic descriptive statistics were calculated: arithmetic means, 95% confidence intervals, median, minimum and maximum, first and third quartiles, and standard deviations. The consistency of the distribution with the normal distribution was verified using the Shapiro–Wilk test, whereas the relationships between individual variables were calculated using the Pearson linear correlation. The following ranges of correlation coefficient r were adopted: low up to 0.2, mild for 0.2 to 0.5, moderate for 0.5 to 0.8, and high for >0.8. The level of statistical significance was set at p < 0.05 .The activeness of the attack was calculated at a mean level of 15.49 and ranged from 13.11 to 41.12. The mean effectiveness s of the attack was 48.93, and it ranged from 45.12 to 51.23. The efficiency of the attack was at a mean level of 18.15, ranging from 16.32 to 19.82 .2peak) (People with a greater kicking range were more active (r = 0.55), efficient (r = 0.67), and effective in the attack (r = 0.73) (moderate correlation). In all three categories of the indices, higher values were achieved in the special throwing fitness test in terms of the number of completed throws. The activeness and effectiveness of the attack correlated significantly with the speed of punches. The activeness and efficiency of the attack depend on the accuracy, precision, and speed of kicks and punches, which is illustrated by the significant moderate correlations between these indices and the Kickboxer Special Physical Fitness Test. The activeness, effectiveness, and efficiency of athletes expressed by the indices of technical and tactical skills showed a strong dependence on the level of maximum oxygen uptake (VO2peak) .2peak) and the results of special fitness tests  and the indices of technical and tactical skills can be explained by the fact of a high heart rate observed in the athletes, which could be genetically or emotionally determined, and affected the final value of the index. It is also worth identifying other elements related to the level of technical and tactical skills, e.g., searching for the dependency of special efficiency on individual techniques and determining the value of the elements that were not examined (overthrows and grappling).The activeness and efficiency of the attack also depend on the accuracy, precision, and speed of kicks and punches, which is illustrated by the significant correlations between these indices and the Kickboxer Special Physical Fitness Test (KSPFT). According to Ouergui et al., a high level of combat activity directly translates into its result fight . The res2peak), in the range of r = 0.57–0.59.The activeness, effectiveness, and efficiency of the attack, expressed in terms of the level of the athlete’s technical and tactical skills, show a dependence on the level of maximum oxygen uptake  and technical skills  demonstrated in all combat phases.The training programs for ju-jitsu athletes competing in the Fighting System variant during tournaments should be focused on the development of an optimal level of special fitness. Improvements in the competitive performance of ju-jitsu athletes can be achieved by increasing the level of special endurance and quality of technique in performing throws, kicks, and strikes.Only the results of fitness tests based on the same testing methodology as in the present study were analyzed as comparative material. The literature review was made only in the field of the sport studied, i.e., sport ju-jitsu . Other forms of sport ju-jitsu  were not taken into account.


Double microlens arrays (MLAs) in series can be used to divide and superpose laser beam so as to achieve a homogenized spot. However, for laser beam homogenization with high coherence, the periodic lattice distribution in the homogenized spot will be generated due to the periodicity of the traditional MLA, which greatly reduces the uniformity of the homogenized spot. To solve this problem, a monolithic and highly integrated double-sided random microlens array (D-rMLA) is proposed for the purpose of achieving laser beam homogenization. The periodicity of the MLA is disturbed by the closely arranged microlens structures with random apertures. And the random speckle field is achieved to improve the uniformity of the homogenized spot by the superposition of the divided sub-beams. In addition, the double-sided exposure technique is proposed to prepare the rMLA on both sides of the same substrate with high precision alignment to form an integrated D-rMLA structure, which avoids the strict alignment problem in the installation process of traditional discrete MLAs. Then the laser beam homogenization experiments have been carried out by using the prepared D-rMLA structure. The laser beam homogenized spots of different wavelengths have been tested, including the wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B). The experimental results show that the uniformity of the RGB homogenized spots is about 91%, 89%, and 90%. And the energy utilization rate is about 89%, 87%, 86%, respectively. Hence, the prepared structure has high laser beam homogenization ability and energy utilization rate, which is suitable for wide wavelength regime. Gaussian Laser beam has been widely used in the field of lighting , detectiIn recent years, a lot of related research work on the method of laser beam homogenization by means of using refractive MLA have been carried out. The imaging MLA (double periodic MLAs) beam integrator system was designed by Dickey F. M. for fiber injection to obtain uniform speckle pattern at the output end of the fiber  and the Considering the problems and shortages of the previous research, a high integrated D-rMLA used to laser beam homogenization is proposed, which can be used to homogenize the laser beam with small diameter. D-rMLA is fabricated on a single substrate by double exposure and chemical etching technique. In the process of beam homogenization, the interference fringes between sub-beams are disturbed to obtain homogenized spots with high uniformity and energy utilization rate. In this paper, the method is used to carry out laser beam homogenization experiments and its feasibility is verified. The main arrangements of this paper are as follows: The principle of laser beam homogenization based on D-rMLA is shown in The beam propagation is shown in The effects of beam homogenization of double periodic MLA and D-rMLA were simulated and calculated by means of the numerical analysis software of Matlab . The beam homogenization ability of different structures of MLA is compared. The aperture, radius of curvature and array number of the sub-lens in the periodic MLA are designed as 30 μm × 30 μm, 28 μm, and 8 × 8, respectively. Diffraction distance is designed as 20 mm. According to the design parameters, the surface function Formula (3) is used to establish the MLA model, so that each microlens can be expressed numerically. Meanwhile, the transfer function of the MLA can be calculated by Formulas (4) and (5). The phase component of the MLA can be decomposed from the transfer function to calculate the phase distribution of each microlens. According to Fresnel diffraction theory, the homogenized spot with diffraction distance of 20 mm can be calculated. The three-dimensional (3D) structure of the MLA is shown in In order to compare the periodic MLAs, the side length of quadrilateral apertures of the sub-lenses in D-rMLA are designed to vary randomly from 25 μm to 45 μm, that is , 30 + 15 × rand ) μm. The array number and the average radius of curvature of the D-rMLA is 8 × 8 and 25 μm, respectively. The 3D structure of the rMLA is shown in The fabrication methods of MLA mainly include thermal reflow technique , laser dAlthough a lot of research work about the fabrication of MLA has been demonstrated, only few multi-focus MLA which consist of lens lets of different focal lengths were presented in literature. In 2012, Ferraro et al. group proposed the pyroelectric continuous printing method to fabrication graded size MLA, which has different focal lengths ,32. The 1 and M2, with random hole arrays distributed in mirror image, as shown in 1 for the first exposure is a wider crosshair with a line width of 12 μm. Furthermore, the crosshair on the mask M2 for the second exposure is a thinner crosshair with a line width of 4 μm.In order to achieve the spatial alignment of the microstructures on both sides of the glass substrate, it is necessary to prepare two masks, M1), development, dechroming, and etching. At this time, the crosshair with a line width of 12 μm is etched on the edge region which is near the structure of rMLA.Firstly, the single-sided rMLA is prepared on one side of the substrate. The process flow is shown in Secondly, another rMLA structure is fabricated on the other side of the substrate. The preparation method is described in detail in the paragraph below.The first step is the pretreatment of the substrate, including the protection of the prepared single-sided rMLA and the preparation of the mask layer namely the chromium film using chemical etching, as shown in 1 which had been etched on the substrate was aligned with the crosshair on the mask M2. In the process of exposure, the alignment marks on the mask M2 were captured with the microscope. Then the prepared rMLA was placed on the wafer supporting with the rMLA structure face down and the photoresist face up, as shown in 2 with the center wavelength of 365 nm, and the exposure time was 20 s. In the process of alignment exposure, the alignment deviation of the crosshair mark is with ±1 μm.The second step is photoresist coating and exposure. The photoresist of the type is AZ MIR—703 Photoresist (14 cp)  which was spin-coated on the glass substrate with chromium film at the speed of 4000 r/min with time of 30 s. The thickness of the photoresist was about 700 nm. In order to ensure that there is no rotation error between both sides of the substrate rMLAs after etching, alignment marks were used to align during the exposure process. The crosshair structure MThe third step is development. By the development with developer of AZ 300MIF DEVELOPER  for 35 s, the microporous structure on the mask was transferred to the photoresist, as shown in The fourth step is chromium removing. The developed substrate is put into the chromium-removing solution for about 40 s to transfer the microporous structure on the photoresist to the chromium film, as shown in 2O:HF:HNO3 = 5:2:2). In the etching process, the glass substrate is taken out every 3 min and put into the ultrasonic oscillator to clean the chemical reaction residue. The rMLA on both sides of the substrate has the same distribution of diameters and sag heights after the same etching time of 30 min, as shown in The last step is etching. The protected substrate is etched in etching solution  and D-rMLA was measured as 20 mm, and the incident spot size T0 was 4 mm. Therefore, if the size of the homogenized spot T can be measured, the half divergence angle θ of the homogenized spot at different wavelengths can be calculated by Equation (6).Firstly, the divergence angles of the homogenized spots generated by the D-rMLA of different wavelengths are measured. In the experiment, the laser beams with wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B) were irradiated to the D-rMLA, respectively. The powers of the sources of RGB laser radiation are 100 mW, 100 mW, and 30 mW, respectively. The transverse mode of the RGB laser radiation is near TEM2 is counted as T, which can be obtained by multiplying the number of pixels of the spot by the pixel size. For the laser beam with wavelength of 650 nm (R), the pixel number of homogenized spots is accounted as 2093, and the T and the full divergence angle were calculated as 15.5 mm and 32°, respectively. For the laser beam with wavelength of 532 nm (G), the pixel number was 1929, and the T and the full divergence angle were calculated as 14.3 mm and 29°. For the laser beam with wavelength of 405 nm (B), the pixel number was 1799, and the T and the full divergence angle were calculated as 13.3 mm and 26°. For the fabricated D-rMLA, the central zero order strong intensity will not be produced by the incident beams with different wavelengths. The divergence angle of the homogenized spot will change when different wavelength beams are incident. According to the grating equation (d × sin θ = λ), the longer the wavelength is, the larger the diffraction angle is.The homogenized spots of different wavelengths were captured by CCD, and the sizes of the homogenized spots were calculated by numerical analysis software MATLAB. The energy of the homogenized spots attenuates to 1/eSecondly, the uniformity of homogenized spots was tested. The homogenized spots of the laser with different wavelengths were captured after laser homogenization, as shown in in of the incident beam of 650 nm (R) is 0.98 mW, and the outgoing power Pout is 0.87 mW. The energy utilization rate is calculated as 89%. The power Pin of the incident beam of 532 nm (G) is 2.05 mW and the outgoing power Pout is 1.8 mW. The energy utilization rate was calculated as 87%. The power Pin of the incident beam of 405 nm (B) is 4 mW, and the outgoing power Pout is 3.44 mW. The energy utilization rate is calculated as 86%. Therefore, it can be concluded that the structure of D-rMLA has a high energy utilization rate. The energy loss mainly occurs in the reflection of the substrate surface, the internal absorption or scattering because of the refraction type of the fabricated D-rMLA with a continuous surface. The above three types of the energy loss are very small, so the energy utilization rate of the prepared structure is very high.Finally, the energy utilization rate is tested. The power of the incident and outgoing laser beams is measured by the power meter (accuracy of 1 μW) and the energy utilization rate is calculated by Equation (8). The power PThis paper has proposed an integrated D-rMLA fabricated by double-sided exposure technique for laser beam homogenization. The experimental results show that the uniformity of the homogenized spot for the laser beams with wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B) are 91%, 89%, and 90%, respectively. The energy utilization rate is 89%, 87%, and 86%, respectively. It is verified that the integrated D-rMLA can break the interference lattice phenomenon brought by the periodic MLA and improve the homogenization quality. Compared with the traditional double MLAs in series, the homogenizer greatly improves the system integration and can be used in laser projection, laser backlighting, and other fields.


Tilia cordata Mill.) in the conditions of the Bashkir Cis-Urals. This work aimed to analyze their assortment by diameters and compile appropriate tables. This is the first study of lime for this region. The results of the study are based on data from 69 temporary sample plots. Stands are represented by trees of 11–79 years old, not affected by thinning. They belong to the I–III growth classes and the most common goutweed forests.The paper provides studies on the structure of planted small-leaved lime (It was found, that small-leaved limes have a specific structure—coefficient of diameter variation in stands decreases with a higher average diameter, reaching 26 and 16% at 28 cm with thin and dense initial planting, respectively. The variability of tree diameters is related to the average stand diameter and is due to the initial density of the grown plantations. Correlations between the coefficients of asymmetry and excess with age and the average diameter was revealed.The verification of theoretically calculated frequencies of distribution series to empirically observed frequencies showed a discrepancy in 29 and 19% of the total number, respectively. For the remaining series of distributions, the scale and shape parameters of the Weibull function were modeled using the average, minimum and maximum diameters, standard deviation, coefficients of asymmetry and excess. This made it possible to develop stand tables for small-leaved limes depending on the average diameter. The application of forest stand structure and development regularities is an integral part of forest management planning, decision-making, scientific research. It leads to higher forest quality and productivity, determines economic efficiency. The structure of stands affects the intensity of biogeocenotic processes, the efficiency of production and deposition of organic matter, the stability and biosphere functions of forest ecosystems. The stand structure is understood as a cumulative combination of examination indicators variation, the distribution of trees by these values, their relationship at certain age stages of the forest community development.1,3) is an important indicator of a tree. It is widely used in forest inventory to calculate some stand parameters such as stem volume and aboveground biomass that cannot be measured directly. The d1,3 distribution is an indicator of the forest structure [When studying the structure of stands, the analysis of trunk diameter variation is of the greatest interest. The diameter at breast height d,3 is an tructure –4.1,3 distribution [1,3 distributions, using the example analysis of mixed Pinus ponderosa forest compartments. Paradis and Lebel [1,3 distribution model for any combination of forest species and types in Quebec (Canada), using easily accessible data from the state program for the inventory of sample areas.There is continuing interest in studying the structure of stands, despite more than a century of history –7. The sribution , includiribution . Thus, Sribution  describend Lebel  propose Tilia cordata Mill.) are not numerous [Though there is a significant amount of literature on distribution series of different tree species and natural conditions, studies on small-leaved limes  are located on the territory of Ufa city and the Ufa municipal district, located at 54°70′ north longitude and 55°90′ east longitude 150 m above sea level , medium density—from 6 to 11 thousand pieces per ha (10 plots), dense and very dense—from 11 to 20 thousand pieces per ha (7 plots). The main dendrometric characteristics of the selected plantings are shown in Table 1,3 distributions: sample size (n), arithmetic mean (X), standard deviation (S), coefficients of variation (Cv), asymmetry (As), excess (Ex), and others. By conducting a correlation analysis, the relationships between evaluation indicators and statistics of the d1,3 distribution series of trees were revealed, being approximated by the following functions:i is the minimum (dmin) and maximum (dmax), arithmetic mean (X) values of the diameters of the distribution series (in cm); bi is the coefficients of models; D is the average inventory diameter of the stand, cm.Basic statistics are calculated for all series of dmin and dmax, S, As and Ex) was compared by calculating the mean-square deviation of pairwise matched models  [i and Ci are pairwise compared data of distribution statistics calculated from models 2–4; n is the number of pairs compared, pcs.Tree diameter distribution series statistics  :4\documeTo describe these distribution series, the Pearson family curves of I–VII types were used . The num1,3 frequencies with an accuracy of up to a centimeter, expressed as a percentage of the total number of trunks of each sample plot. It has the following density function (for positive parameters γ and β):e is the Euler number (2.71…).Since there was no special software for leveling the curves of the Pearson family, a two-parameter Weibull distribution in the Statistica environment was used to calculate the expected values of dmin and dmax, S, As and Ex).Estimation accuracy of the Weibull function was verified using the Kolmogorov–Smirnov test (K–S) and the Anderson–Darlig test (AD) with a probability of 5%. After evaluating the γ and β parameters of this function, a correlation and regression analysis was performed and multiple regression models were obtained to predict them depending on the distribution statistics , while it is right-sided in the rest. it is insignificant in five plots (from 0.01 to 0.09). The coefficient of asymmetry in other compartments ranges from 0.11 to 1.93. D1,3 distributions are characterized by different density grades from − 0.97 to 5.61. Analysis of the asymmetry and excess coefficients for 34 and 13 sample plots, respectively, showed that they are beyond their twofold basic errors. This indicates the difference between the given series from the standard one. For the rest of the sample areas, the asymmetry and excess confidence estimation by the t-Student’s test, on the contrary, shows that there is no deviation of the distribution curves from the standard one .The tree diameter is the main examination indicator for studying the structure of the stand. It varies from 1 to 47 cm by sample plots. The average arithmetic value of dTo find out the regularities of the diameter distribution dynamics and its statistics, a correlation analysis was performed Table .Table 2CThe studied limes showed the following changes in the distribution series with tree aging. The relation of the asymmetry and excess coefficients with age is not expressed, but there is a tendency to decrease the asymmetry coefficient and increase the excess coefficient with increasing age. The coefficient of variation significantly decreases with the age of plantations. The standard deviation increases with aging and higher average diameters of thin and dense plantations. The value of the average tree rank for thin planting significantly correlates with the coefficient of asymmetry (r = − 0.624) and the minimum diameter of the tree in the distribution series (r = 0.717). The identified relationships made it possible to create models 1–3), presented in Table , presentThe data in Table dmin (27–101%), dmax (16–19%) and S (18–21%). A similar test for the coefficients of asymmetry and excess demonstrated several times greater differences: up to 535% for As, up to 1817% for Ex. Differences in the distribution series depending on the density of forest plantation can be visually estimated from Fig. Checking the statistics of the distribution series according to formula 4 using the developed models 1–3, Table , Table 3dmin 7–101%, dThe given data indicate that diameters in thin plantations vary greatly compared to dense and very dense stands. Meanwhile, medium dense plantations have an intermediate position of variability. With average diameters of 8–14 cm, the variability is closer to dense and very dense stands, and with large diameters (22–28 cm)—to thin. With higher average stand diameter, the variability of trees in thickness decreases, reaching values of 26 and 16% at 28 cm with thin and dense initial planting, respectively.The use of Pearson curves to approximate the tree distribution series by diameter showed that the type I function provides more satisfactory description for 46 of the 69 sample plots, types II and VII for 7 plots, type IV for 6 sample compartments, type VI for the rest. This indicates the heterogeneity of the tree distribution by their size with the age of stands. The verification of theoretically calculated frequencies of distribution series to empirically observed frequencies by the B.S. Iastremskii criterion proved to be relevant for 49 applied models (71%). Figure It shows that trees of the smaller diameter classes are more frequent in young stands and their number decreases with age. At the same time, as the forest grows, the frequency of large diameter trees increases, shifting the curve to the right. With a higher average diameter of the stand, the distribution curves stretch, they become less steep and less elongated upwards in the center, approach the abscissas axis more slowly when moving away from the middle, and become the closest to the standard distribution.Due to the small number of samples of medium, dense and very dense plantations, insignificant correlations between the coefficients of asymmetry and excess with the average diameter of stands Table , as wellmin, dmax, S, As, and Ex)  Table .Table 4CThe data in Table Both models presented have high F scores (p < 0.0001) and explain 99 and 96% of the variability, respectively.The coefficients obtained for the Weibull function were used to estimate the evolution of the diameter distribution in planted stands of small-leaved lime depending on the class of the average diameter (one-centimeter diameter class), the calculated values of which are given in 1,3, being the main forest inventory indicator, change the place of the average tree, the reduction numbers by rank, the minimum and maximum diameters, the concentration of the trunk number percentage in the diameter class, the standard deviation value, asymmetry and excess of the series, which is consistent with other studies [Planted stands of small-leaved limes in distribution series by d studies , 4, 6.1,3 distribution series. This is consistent with the view of Bachioua [The use of Pearson curves made it possible to effectively describe the dBachioua , who conBachioua  showed a1,3 distributions and modeling the probability-density function, which conforms to the research of Diamantopoulou et al. [The discrepancy between the theoretically calculated frequencies of the distribution series and the empirically observed frequencies of the Pearson curves and the two-parameter Weibull function  indicates the complex nonlinear nature of the d1,3 distributions [1,3 distributions in this study.Many authors report that the Weibull function is widely used in many forestry applications to model dibutions , 22, becibutions , 29, 30.ibutions , 30. In ibutions , 17, 18.dmin and dmax are similar to those observed by Binoti et al. [dmax and γ. Linear models that link the parameters β and γ to the main distribution statistics show very high determination coefficients . It is noted that their performance deteriorates as the average value of d1,3, asymmetry and excess of the distribution series increases, which is consistent with studies by Lima et al. [The correlation analysis results obtained between the two parameters (γ and β) of the Weibull function and the characteristics of i et al. . Except Diameter distribution models can be useful in describing and analyzing the stand structure, age distribution, growth and yields. They can be employed in assessing the stand stability and calculating a number of trees in each diameter class to plan forest management activities, reveal previous violations, predict successions of forests and land biomass reserves, etc. , 4, 12. The given paper analyzes the diameter distribution of small-leaved limes in forest plantations. Lime plantations were found to have certain features in the structure due to the even age, planting density and biological characteristics as a shade-tolerant specie. There is regularity in variation coefficient changes. It significantly decreases with the age of plantations. The experimental material revealed correlations between the coefficients of asymmetry and excess with the age and average diameter of small-leaved lime.The analysis of the numerical characteristics and models of the structure of plantings by diameter gives grounds to consider the initial density of the grown plantations as the determining factor.The analysis of tree distribution by diameter classes using the Pearson curves and the Weibull function provided the best processing of the experimental material. The simplicity of algebraic manipulation and the ability to take various forms of distribution curves make Pearson curves and the Weibull function a useful tool for forestry models.In fact, this is the first study of this type for planted stands of small-leaved lime. The obtained data of the compiled distribution series of the total number of trunks by diameter class are recommended for describing and analyzing the structure of stands, for forest management (conducting various logging operations), development of forest inventory standards , assessing sustainability, environmental factors, inventory, etc.


Voltage-gated potassium channels of the Kv7.x family are involved in a plethora of biological processes across many tissues in animals, and their misfunctioning could lead to several pathologies ranging from diseases caused by neuronal hyperexcitability, such as epilepsy, or traumatic injuries and painful diabetic neuropathy to autoimmune disorders. Among the members of this family, the Kv7.2 channel can form hetero-tetramers together with Kv7.3, forming the so-called M-channels, which are primary regulators of intrinsic electrical properties of neurons and of their responsiveness to synaptic inputs. Here, prompted by the similarity between the M-current and that in Kv7.2 alone, we perform a computational-based characterization of this channel in its different conformational states and in complex with the modulator retigabine. After validation of the structural models of the channel by comparison with experimental data, we investigate the effect of retigabine binding on the two extreme states of Kv7.2 (resting-closed and activated-open). Our results suggest that binding, so far structurally characterized only in the intermediate activated-closed state, is possible also in the other two functional states. Moreover, we show that some effects of this binding, such as increased flexibility of voltage sensing domains and propensity of the pore for open conformations, are virtually independent on the conformational state of the protein. Overall, our results provide new structural and dynamic insights into the functioning and the modulation of Kv7.2 and related channels. The region encompassing segments S1–S4 forms the voltage sensing domain (VSD), with positively charged residues in S4 comprising the main voltage sensor. The S5–S6 region forms the pore domain that contains a P-loop that imparts Kulin CaM . The cenulin CaM . VSD actulin CaM , passingulin CaM   genes are related to the onset of diseases such as epilepsy, benign familial neonatal convulsions (BFNC) or neonatal epileptic encephalopathy , peripheUnfortunately, RTG was withdrawn from the market due to safety issues associated with retina and skin discoloration . NonetheThe binding mode of RTG onto KCNQ2 (featuring an activated VSD and a closed pore—AC) was confirmed by the determination of a cryo-EM structure . The druOverall, our work confirms the high potential of computational methods in this field  and provhttps://www.ebi.ac.uk/Tools/msa/clustalo/). Regarding the AO and RC states, as no experimental structure of KCNQ2 in these conformations was available at the time of this investigation, we used as templates the corresponding structures of the KCNQ1 channel previously published by http://molprobity.biochem.duke.edu/) , and the modelling was restricted to the transmembrane region of the channel (residue ARG75 to GLN323 in each monomer), amounting to 249 aminoacids per monomer and including helices S0 to S6. The models were generated using the Prime tool  of the Mke.edu/) .Apo proteins. MD simulations of the AO, RC, and AC models of KCNQ2 in explicit phospholipid membranes at 310 K were performed using Amber18  molecules in the inner leaflet, consisting of an equal number of C4-PO4- and C5-PO4- mono-protonated PIP2 molecules with stearoyl and arachidonoyl conjugations at the sn-1 and sn-2 position. The PIP2 parameters were taken from  applied to protein Cα atoms. The protein restraints were then gradually removed over 50 ns, and 9 replicas of production MD, each of 100 ns in length, were conducted for each model (yielding 1 μs for each state) using a step size of 2 fs, constant pressure periodic boundary conditions, anisotropic pressure scaling and Langevin dynamics. Note that, as in (−1 Å−2) between each K+ ion and the 8, 4, 4, and 4 oxygen atoms of residues T277, I278, G279 and Y280 respectively. On top of these runs, for each model and each replica we performed 100 ns additional MD simulations in the absence of restraints. Therefore, for each state we generated a production trajectory corresponding to ∼2 μs of simulated time. Amber18  and the  Amber18 . Namely, Amber18  and embe Amber18 . A TIP3Pken from . No PIP2t, as in , productRTG-KCNQ2 complexes. Multicopy simulations of the RTG-KCNQ2 complexes derived from docking calculations (vide infra) were performed using the same settings as for the simulations of the unbound channel. Force field parameters of the ligand were derived from the GAFF  as well as to the experimental structures of the KCNQ2 channel in the AC state, as well as of its complex with RTG .Root Mean Square Fluctuations (RMSF). The flexibility of the protein was evaluated in terms of RMSF calculations, performed on each trajectory with the atomicfluct command of the AmberTools. The fluctuations were evaluated after alignment of the Pore domain to the average conformation extracted from the corresponding MD trajectory.Identification of the putative binding site of retigabine. Since no experimental structure of RTG in complex with KCNQ2 was available when this investigation was performed, the putative  binding site of RTG on the Pore-forming domain of the channels was identified based on the findings in  structures for molecular docking, a cluster analysis was performed on the cumulative trajectory generated by concatenating the 10 independent trajectories generated for each state. We performed two different cluster analyses, using either the Cα atoms of the protein or all heavy atoms of the residues around each of the four putative binding sites of retigabine. In this way, we obtained structures differing both in their overall architecture and as well as in the conformations of the putative binding site of retigabine. As metric, we used the dRMSD calculated over the selections above , with cut off set to 2 Å. These structural clusters were further analysed as described below.Volume and druggability calculations. Druggability calculations were performed using the f-pocket  were evaluated using CAVER3.0  approach  and non-bonded  terms of the force field. As customary, we employed the single-trajectory approach, in which only simulations of the complex are employed to generate the ensemble of conformations of the receptor and of the ligand by simply removing the appropriate atoms  and a non-polar one .te atoms . This coThe electrostatic solvation free energy was calculated using the implicit solvent model developed by Nguyen et al.  igb = 8.conf) was not evaluated as it is notoriously difficult to evaluate with accuracy  was unavailable, and the more reliable template was the AC cryo-EM structure of the KCNQ1 ion channel (PDB ID: 5VMS), featuring a high sequence similarity with KCNQ2 . The AC ectively , indicatectively . As expeThe AO and RC states were built using as templates the new and refined models of the KCNQ1 channel in the corresponding structures . Also inα-RMSDs from the initial structure stable around 4 Å  as a reference. The distribution of the protein Cis state . As expeis state . Note this state . To obtaThe results indicate a decreasing structural variability for the AO, AC, and RC states  and confNext, we analysed the features of the binding site of the anticonvulsant drug RTG, targeting KCNQ2-5 channels . Since tAlong this line, we first assessed if and to what extent the precise geometry of the binding site hosting RTG in the experimental structure is reproduced during the MD simulations of the AC, AO, and RC conformational states of KCNQ2. As can be seen in However, it is worth noticing that also the AO state, starting from a conformation distant 3.6 Å from the experimental geometry , also assumed a non-negligible fractions of bound-like conformations.fpocket . We notice that, on average, the affinity of the ligand is higher towards the channel in the AO state than the RC one . While experimental binding geometries were recovered also in the simulations of the RTG-RC complexes , they weAs we don’t know if the binding mode of RTG is fully conserved across the different states of the channel, in the following we discuss our results in terms of average structural and dynamical, properties across the stable trajectories of the complexes. This allows evaluating our findings on the effect of RTG binding on KCNQ2 free of any experimental bias. First, we found that binding of RTG alters the dynamics of the channel; namely, it slightly rigidifies the Pore domain, and moreover, it increases the flexibility of the VSD domains with respect to the unbound protein, particularly in the AO state . This reFinally, we investigated if and to what extent the binding of RTG alters the morphology of tunnels leading from the center of KCNQ2 (beneath the selectivity filter) to its cytoplasmic gate. To this end, we run the software CAVER  on the rWhile the limitations of our approach do not allow to assess the long-term effects of RTG binding on KCNQ2, the early steps of channel opening induced by ligand binding caught by our analysis shed light on the mechanism of action by this compound. Overall, our findings support an allosteric mechanism in which binding of RTG to the channel would promote its transition towards the AO conformational state. Such conformational transition could occur, according to our data, without the need for drastic rearrangements of RTG within the binding site recently validated by Li and co-workers .+ current regulating neuronal excitability. Because of their fundamental role in regulating cellular excitability, this channel in its heterotetrameric form with KCNQ3 is implicated in several human disease conditions, including epilepsy, pain, migraine, arrhythmias, sensory dysfunction, and metabolic illnesses. The KCNQ2/KCNQ3 opener retigabine represents an attractive compound for the treatment of these diseases. Structural information about the molecular interactions of this compound with KCNQ2 along the conformational cycle (the various states) of the channel can be highly informative to drug design efforts.KCNQ2 is a main molecular determinant of the M-current, a widespread KHowever, apart the recent cryo-EM structure of AC KCNQ2, alone and in complex with RTG (unavailable when this work was undertaken), to date there are no KCNQ2 structures available in the RC and AO states. For these reasons our efforts were aimed at generating models of all three states and characterise their dynamics and interaction with RTG. Conformations extracted from the molecular dynamics simulations were used to dock RTG into the AO and RC states and compared with the experimental structure of the KCNQ2 in the AC state complexed with RTG. All the generated models of both the apo structures in various states as well as the complexes with RTG were subjected to MD simulations, for a total simulated time of ∼50 μs. The analysis of the trajectories confirmed the stability of the apo structures as well as the AO and RC structures complexed with RTG. Our results on the effect of binding of one RTG molecule to the AO and RC states are in line with experimental findings on the channel in the AC state bound to four drug molecules. Overall, our data suggest that RTG can bind to the same site of the channel, and maintaining the same orientation, independently of the KCNQ2 (and thus Pore domain) conformation/state. Furthermore, our simulations of the RTG-bound states unveil a tendency of the channel towards increased flexibility of the VSD domains and sampling of conformations corresponding to an open Pore, which are also in line with experiments. The excellent agreement of our simulations with the experimental AC state structure gives trust into our modelling approach and confidence that the new models of the AO and RC states of this channel are reliable, allowing to uncover new insightful details on the interaction of this channel with RTG.