This research is expected to open new avenues for creating soft robotics, mechanical metamaterials and artificial muscles.Owing to their high deformation ability, 4D printed structures have various applications in origami structures, soft robotics and deployable mechanisms. As a material with programmable molecular chain orientation, liquid crystal elastomer is expected to produce the freestanding, bearable and deformable three-dimensional structure. However, majority of the existing 4D printing methods for liquid crystal elastomers can only fabricate planar structures, which limits their deformation designability and bearing capacity. Here we propose a direct ink writing based 4D printing method for freestanding continuous fiber reinforced composites. Continuous fibers can support freestanding structures during the printing process and improve the mechanical property and deformation ability of 4D printed structures. In this paper, the integration of 4D printed structures with fully impregnated composite interfaces, programmable deformation ability and high bearing capacity are realized by adjusting the off-center distribution of the fibers, and the printed liquid crystal composite can carry a load of up to 2805 times its own weight and achieve a bending deformation curvature of 0.33 mm Liquid crystal elastomer printing methods are often limited to planar structures. In this work, authors integrate 4D printed structures with fully impregnated composite interfaces to enable programmable deformation ability and high bearing capacity by adjusting the off-centre distribution of the fibres. According to their deformation principle, shape memory materials can rapidly change from a temporary shape to their final shape at the critical temperature5. However, the disadvantage of these materials is that the deformation process is discontinuous6 and difficult to replicate7. Moreover, anisotropic materials such as liquid crystal elastomers (LCEs) are also used for 4D printing. LCEs are smart materials with high deformation ability8, relatively significant mechanical performance11 and reversible deformation process that can be prepared by direct ink writing (DIW) 4D printing13, and can respond to various external stimuli, such as light14, humidity15, and heat16. LCEs are composed of orientated liquid crystalline polymers that have high thermal shrinkage effect along the direction of the molecular chain17, and the orientations of the LCE molecular chains determine the mechanical property of the polymers19. In addition, composites are also used for 4D printing. The design method for 4D printing composite structures is inspired by the growth of pine cones22 and the movement of wheat awn23 in nature, whose deformations depend on their anisotropic expanded cell walls caused by the existence of embedded oriented stiff cellulose fibrils. Similarly, 4D printed composite structures are typically composed of two materials with different expansion coefficients distributed in gradient and can produce bending deformation under external stimulation. The deformation amplitude and direction of the composite structure can be controlled by the programmable orientation of reinforcing components, such as embedded particles24, continuous fibers25, and oriented polymer chains26. Due to the diversity of materials, 4D printing structure has various deformation stimulation conditions. Specifically, external stimuli that can induce deformation include temperature27, light29, humidity30, and electromagnetic field31. Due to their deformation performances, 4D printed structures can be widely used in various fields, such as aerospace32, soft robotics34 and artificial muscles35.4D printing is a type of additive manufacturing technology used in the fabrication of smart structures that can produce controllable deformation in response to external stimuli. Shape memory materials37. For example, 4D printed structures with deformable composites are typically thin bilayer structures because their deformation mode involves bending deformation driven by two materials with different coefficients of thermal expansion (CTEs). Hoa et al.40 prepared laminates composed of materials with different CTEs by 4D printing to realize the moldless composites manufacturing. In addition, anisotropic LCE structures are usually 1D41 or 2D structures42 because the deformation of polymers depends on the orientation degree of anisotropy and the schemes that can control the orientation of molecular chains or reinforced particles are mainly to control the movement path of the nozzle along the x and y directions12. For these reasons, most 4D printing methods for LCE structures or bilayer composites are either planar structures43 or simple shapes obtained by folding44, curling37 and accumulation45 based on planar structures, which significantly limits the shape design of 4D printed structures. Several efforts have been made to obtain more complex deformable structures by 4D printing. Guo et al.46 prepared three-dimensional LCE structures whose molecular orientation can be controlled locally, however, the voxelated structure limits the 4D printing efficiency.As a material with programmable molecular chain orientation, LCE is expected to produce the freestanding, bearable and deformable three-dimensional structure. However, 4D printing with LCEs and other active materials still faces some challenges with regard to the deformation characteristics. As widely used 4D printing materials, anisotropic materials and composite structures can produce continuous deformation, but their deformation mode is relatively simple27 reported that the mechanical properties of 4D printed precursor materials were improved after heat treatment, however, the obtained ceramic materials could not be deformed again. According to Zeng et al.47, embedding chopped or continuous fibers into polymer matrices can improve the mechanical properties while retaining the appropriate deformation capacity. Moreover, the shapes of 4D printed structures with composites or anisotropic materials is typically another factor limiting their mechanical bearing capacity. Most of the existing 4D printed LCE structures are linear or planar and can only produce tensile stress during shrinkage deformation42, which prevents them from maintaining their structural stability under the external compression forces50. Although shape memory materials can be used to prepare complex and deformable three-dimensional structures with an actuating ability, they can only produce a deformation response within a very small range near the critical temperature, and the deformation process is usually irreversible36. Therefore, the application scenarios for 4D printing are limited.Another critical challenge for 4D printed structures is their poor mechanical bearing capacity caused by the material and shape restrictions. However, efforts to improve the mechanical property of 4D printed structures typically weaken or sacrifice their deformation capacity. Liu et al.51. realized the 4D printing of the freestanding LCE structures by using multiple laser sources to cure the LCE in-situ when the nozzle moves and extrudes the liquid crystal material. However, this method has the following limitations: (i) the forming process of LCE structures depends on supporting structures; (ii) the LCE truss structures have little bearing capacity; (iii) the solidification of liquid crystal materials requires expensive high-power multiple laser sources. The composite truss with embedded and controllable off-center continuous fibers is expected to achieve the integration of the mechanical bearing capacity and deformation function simultaneously.To solve these problems, a 4D printing method for freestanding LCE composite truss structures is required. The high bearing capacity of the three-dimensional structures comes from the mechanical reinforcement in three directions, and the deformation controllability is based on the bendable trusses. Peng et al.52 and mechanical properties53 of the LCE structure. Moreover, the mechanical properties of 4D printing structures can be improved because the elastic modulus of continuous fibers is much higher than that of LCEs and other deformable polymers. In terms of the deformation performance, the difference in the CTEs of the continuous fibers and LCE matrix induces the change in the deformation mode of the pure liquid crystal from shrinkage deformation to bending deformation, which further increases the deformation capacity. Depending on the support ability of the continuous fibers, composites can be directly prepared into three-dimensional structures instead of preparing planar structures via general 4D printing, and these three-dimensional structures have improved mechanical properties. In addition, the CFDIW process allows the adjustment of the off-center position of the fiber in the composite filament, which allows for the easy control of the bending deformation direction of the composites, a better impregnation effect between fibers and liquid crystals, and production of considerable deformation in prepared three-dimensional structures.In this study, a continuous fiber direct ink writing (CFDIW) 4D printing method based on off-center continuous fiber reinforced LCEs (CFRLCEs) has been proposed. The introduction of continuous fibers can make the structure preparation process more convenient and improve the deformation capacity54. The formula materials were subjected to differential scanning calorimetry (DSC) to determine their addition reaction temperature :To verify this theoretical analysis, the composite filaments with different tensile inclination angles were 4D printed and their deformation curvatures at different temperatures were tested, as shown in Fig. x-z plane until it was vertically upwards, so that the fibers were distributed on the left side. Due to the two ends of the filament had not yet solidified, the rotational motion of the filament was not constrained. After the nozzle had fallen along an arc trajectory in the y-z plane, the end point of the fiber was finally cured using a higher-power point light source, and the off-center angle of the fibers had been adjusted  respectively, and vertical downward compressing forces are applied to trusses at the top. When the applied displacement is one fifth of the height of the structures, the shapes of the structures are shown in Fig. According to the results in Fig. −1 at 150 °C. Furthermore, high bearing and deformation capacities were simultaneously obtained in a CFRLCE truss through the design optimization of the structure. Due to its deformation ability and mechanical properties, the structures prepared by the CFDIW process are expected to be applied in the field of soft robotics with gripping functions, such as soft robotic arms or drug delivery robots.In summary, we have demonstrated a CFDIW 4D printing process for CFRLCE, which can directly print three-dimensional structures with the support of continuous fibers. The off-center position of the continuous fibers in the core-shell composite structure can be directly controlled, resulting in programmable deformation with high controllability. In this study, we realized the adjustable design of large deformation and high bearing capacity of LCE, which can carry a load of up to 2805 times its own weight, and achieved a bending deformation curvature of 0.33 mmOur future work is to explore and realize the actuating ability of CFRCLE composites, which is also the original goal of this paper. In this study, when the temperature is not high enough to cause significant deformation of the structure, the modulus of LCE decreases seriously. It leads to that although the structure has achieved bearing capacity and deformation capacity, the bearing capacity at higher temperature is not excellent. There are some methods may improve the actuating ability of composite materials, such as replacing liquid crystal materials with photoinduced deformation LCE. Some methods are expected to improve the actuating ability of the composites, such as replacing liquid crystal materials with photoinduced deformation LCE, or replacing fiber materials with continuous shape memory polymer fibers with deformation ability. Once the actuation capability is achieved, this research can be used to develop new avenues for creating soft robotics, mechanical metamaterials, and artificial muscles.−6 K−1, a tensile strength of 3.6 GPa and a tensile modulus of 131 GPa.The continuous fiber material used in this work is aramid fiber , which has an axial CTE of −2 × 10The liquid crystal ink was synthesized in one step in the ink chamber using a catalyst-free addition reaction. 1,4-bis(4-(6-(acryloxy)hexyloxy)benzoyloxy)−2-toluene , 2-Methyl-1,4-phenylene-bis(4(3(acryloyloxy)propyloxy)benzoate) , 1,4-benzenedimethylmercaptan , Benzoin dimethyl ether or benzyl dimethyl ketal , and fluorescent agent 803 C  were added to the ink chamber (the molar ratio of R6M to RM257 is 1.0: 0.3). The mixture was heated at 160 °C for 30 min to allow the formation of polymer chains by the liquid crystal monomers upon the reaction of chain extenders, and the synthesized products are shown in Supplementary Fig. The main difference between our CFDIW 4D printing equipment and existing DIW equipment involves the structure of the chamber with an off-center channel, the piston with a capillary channel, and the coupling. The heating rod and thermocouple were embedded in the chamber to heat the liquid crystal and maintain the printing temperature. First, the fiber was passed through a perforated piston, ink chamber, printing nozzle, and perforated platform. Subsequently, the powdered liquid crystal mixture was filled into the chamber and capillary hole, heated to 160 °C and stirred continuously for 30 min. During the 4D printing process, a higher curing strength is required at the filament ends. Therefore, a high-power point light source was used to irradiate it, while the rest of the filament is illuminated by an area light source. After 4D printing, the structure was put into an ultraviolet curing box to ensure uniform exposure.The liquid crystal formula was heated at 160 °C for 30 min before being cooled to room temperature to simulate the temperature changes during 4D printing. Subsequently, drops of molten liquid crystals were deposited onto a horizontally-straightened continuous aramid fiber surface, the interface between the two materials was photographed using a non-contact measuring instrument , and the wetting angle is calculated.−1. To ensure that each component reaches its clear point, we conducted DSC tests  on the R6M, RM257, and DIW ink formulation respectively.The liquid crystal monomers were heated from room temperature to 150 °C at a rate of 10 °C min0.3 g of liquid crystal formula is heated at 160 °C for 30 min, and then gradually cooled to simulate the temperature change during printing. The rheological properties were tested at different cooling stages. .α radiation with a maximum output power of 2.97 kW and an electron beam focal spot diameter of 70 μm, and the detector used was a Hypix-6000 photon direct reading detector. The Hermans orientation parameter was calculated using the azimuthal integration from Fit2D software, and the following equation is used to calculate the orientation degree of the polymer:I(θ) represents the signal intensity in different directions on the XRD pattern.To obtain the molecular chain orientation of liquid crystal components in composite trusses, the continuous fibers were stripped from the composites and ten 30 mm long LCE filaments were cut and bundled for XRD test . The anode target X-ray source used was a Cu KThe composite filament was cut into sections, and the cross section is used to observe the off-center distribution and the impregnation effect of the fibers. The SEM images were taken by a electron microscope  using a voltage of 5 kV. Before observation, the samples were sputtered with gold in vacuum for 120 s with a current of 40 mA to enhance the conductivity of their surfaces.−1.The single aramid fiber was tightened and fixed on the sample holder, and micro-droplets were prepared by dipping the fiber in the melted liquid crystals. Micro-droplets were stuck on the crosshead of the interfacial evaluation equipment , and were debonded from the single fiber by moving the sample holder with the speed of 0.12 mm sThe finite element analysis of the thermal-induced deformation process of continuous fibers reinforced LCE composites was performed by ABAQUS. The simulation included the parameters: the elastic modulus, the Poisson’s ratio and the CTE. The LCE structure in the simulation were assumed to have great thermal shrinkage property, and the initial temperature was set to room temperature (25 °C). The composite truss was modeled as a cylinder, and the cross-section of reinforced continuous fiber bundle was modeled as a circle and an off-center bow, which were used to simulate the case of low and high off-center degree, respectively. The specific shape parameters were obtained from the SEM images shown in Fig. Peer Review FileSupplementary InformationDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3


Annealing increased the paste viscosity of IRK while decreasing that of IRF. Both annealed IRK and IRF exhibited increases in the gelatinization enthalpy change and relative crystallinity. Annealed IRK gel showed higher hardness, and annealed IRF gel displayed greater springiness. Unlike native rice noodles, annealed IRK noodles exhibited denser pores, while annealed IRF noodles exhibited a looser microstructure. With increasing annealing temperature and time, both annealed IRK and IRF noodles showed enhanced tensile properties. Rice noodles made from IRF annealed at 65 °C for 12 h exhibited a fracture strain of 2.7 times that of native rice noodles. In brief, IRK and IRF exhibited different degrees of susceptibility to annealing. Annealing had more significant effects on IRF than IRK. This study highlights the possibility of using annealed IRK and IRF in rice noodles.In this study, the characteristics of indica rice kernels (IRK) and flour (IRF) annealed in different conditions were evaluated, and the quality of rice noodles made with these IRK and IRF was determined. Native IRK and IRF were annealed in deionized water at a kernel or flour to water ratio of 1:3 ( Rice sustains as a primary source of cereal crops for half of humanity and is consumed in the forms of kernels, flour, and derivatives . DespiteThe quality properties of rice noodles are mainly dependent on the textural characteristics of rice flour . HoweverAs a green physical method to modify starch, annealing (ANN) is a hydrothermal treatment that treats starch with excess water (40–80%) within a scheduled time at appropriate temperatures, which are above the glass transition temperature but below the gelatinization temperature . AnnealiAlthough studies have been reported about the annealing of rice starch, annealed rice kernels and rice flour have seldom been studied, especially their differences in properties. Compared with rice kernels, rice flour contains nearly the same components but is the product of a rice kernel with its original structure largely disrupted. We propose that annealing would have different impacts on their physicochemical properties, thereby affecting the quality of rice noodles made of them. Therefore, this study focuses on the physicochemical properties of annealed rice kernels and annealed rice flour and their effects on the quality of rice noodles. The work could be instrumental in establishing an environmentally friendly method to expand the application of annealed rice kernels and rice flour in rice noodles.Indica rice was obtained from Guilin Dingyin Food Co., Ltd. . The native indica rice contained 7.33% protein, 1.00% crude fat, 0.45% ash, 21.76% amylose content, and 74.62% total starch. Unless otherwise stated, deionized water was constantly used during the experiment. All reagents used were of analytical grade.The annealed indica rice kernels and rice flour were fabricated according to the method of Yadav et al.  with somIndica rice flour was obtained by wet milling of indica rice . SpecifiTo determine the pasting properties, 3 g of the annealed sample powders were mixed with deionized water (25 g) in the test canister using a Rapid Visco Analyzer . The obtained slurry was heated first at a rate of 12 °C/min from 50 °C to 95 °C, held for 2.7 min at 95 °C, and later cooled for 2 min to 50 °C. All the tests were operated at 160 rpm for the rotating speed of the centrifuge. The following pasting parameters were recorded: peak viscosity, trough viscosity, final viscosity, breakdown viscosity, setback viscosity, and pasting temperature .To (onset temperature), Tc (conclusion temperature), Tp (peak temperature), and ΔH  [Differential scanning calorimetry  was used to determine the thermal characteristics of the annealed rice kernels and rice flour. The powder samples (3–5 mg) combined with a triploid volume of water were placed in an aluminum pan and then balanced at room temperature overnight before being transferred to a DSC calorimeter. The pan was heated from 25 °C to 125 °C at a heating rate of 10 °C/min. The STARe software was used to calculate the  change) .An X-ray diffractometer  was used to analyze the crystalline structures of the annealed rice kernels and rice flour. The powders were placed into a saturated relative humidity chamber for 24 h to achieve a 20% moisture content . The set−1. After the annealed kernels and annealed flour were ground into powders, the blending ratio between powders and KBr was generally 0.5–2:100. The powders were first ground in an agate mortar, then KBr was added, ground, and mixed evenly, and later transferred to the tablet press. Each experiment was scanned 32 times with a resolution of 4 cm−1 [−1.An FTIR spectrometer  was used to record the FTIR spectra of the powders between 400 and 4000 cmf 4 cm−1 . OMNIC 8After the RVA test, the pastes were stored at 4 °C overnight. The texture analyzer  was used to analyze the formed gels. The texture profile analysis was performed using a P 0.5 probe with a test speed of 1 mm/s and compression tests under a strain of 50%. The textural parameters of the hydrogels were recorded .The fresh rice noodles were processed according to the flat noodle-making method described by Jia et al. . BrieflyThe tensile properties of fresh rice noodles were measured using the texture analyzer  with the A/TG probe model. The analyzer settings were a probe height of 30 cm, a pre-test speed of 3.0 mm/s, a test speed of 1.0 mm/s, an after-test speed of 3.0 mm/s, and a tensile distance of 30 mm. Tensile strength and elongation at the break of rice noodles were recorded.The scanning electron microscope  was used to observe the morphology of the freeze-dried fresh rice noodles. Fresh wet rice noodles were frozen in liquid nitrogen first, snapped immediately, and then vacuum freeze-dried for 4 d to obtain dried samples. The fractured sections were imaged.2) of the rice noodles. The obtained fresh rice noodles made from annealed kernels and annealed flour with water contents of about 65% and 68%, respectively, were placed into the NMR tube (25 mm diameter) before being transformed into the analyzer. During measurement, the analyzer settings were a maintained temperature of 32 °C and a resonance frequency of 20 MHz. The Carr–Purcell–Meiboom–Gill sequence was used to detect the mobility of water motion in samples [A low-field nuclear magnetic resonance (LF-NMR) analyzer  was used to analyze the transverse relaxation time (T samples .p < 0.05).The data obtained were processed using SPSS 16.0 software and then recorded as an average ± standard deviation. Differences were considered statistically significant at 95% , melting range (Tc–To), and gelatinization enthalpy (ΔH) of rice kernels and rice flour before and after annealing are summarized in To represents the heat stability of the crystalline structure. Compared with the native rice, both annealed rice kernels and annealed rice flour exhibited higher To, Tp, and Tc at 60–65 °C. Annealing increased the ΔH values of rice kernels and rice flour at 50, 55, 60, and 65 °C for 12 and 24 h. Rice kernels and rice flour remained essentially unchanged in To, Tp, and Tc values after annealing at 50 and 55 °C for 12 and 24 h. In contrast, as the annealing temperature increased from 60 °C to 65 °C, To and Tp increased apparently. Annealing decreased the melting range (Tc–To) from 9.92 to 6.99 and 6.19 for rice kernels and rice flour, respectively, when treated at 65 °C for 24 h, compared to the native rice.The gelatinization transition temperatures  were presented in the native indica rice, indicating the typical A-type crystalline structure. Annealing at 50–65 °C did not alter the crystalline structure, which was consistent with the previous reports [The XRD pattern spectra and relative crystallinity values of native and annealed rice kernels and flour are shown in  reports . A previous report also showed that annealing could hardly change the relative crystallinity of brown rice flour . Anneali−1 can be used to quantify the degree of short-range order of starch after annealing [−1 in −1. The increased ratio of 1047/1022 cm−1 could be due to the more ordered short-range structure and the strengthened internal structure of rice starch. Theoretically, a higher absorbance ratio indicates more significant short-range ordering in starch granules [−1 ratio is related to relative crystallinity. Annealed rice kernels exhibited a higher 1047/1022 cm−1 ratio compared with annealed rice flour and native rice, consistent with the XRD results. The ratio of absorbances at 1047/1022 cmnnealing . In Figunnealing . Native granules . The incThe texture characteristics of native and annealed indica rice gels are shown in The annealed rice flour gel had lower hardness than the annealed rice kernel gel under annealing at 50 °C, 55 °C, and 60 °C for 12 h. When annealed at 50 °C, 55 °C, and 60 °C for 24 h, with increasing annealing time, the annealed rice flour gel had a higher hardness than the annealed rice kernel gel. As the time and temperature increased, the springiness, gumminess, and resilience increased pronouncedly, which plays a crucial role in rice noodles production . MoreoveRegarding the higher hardness of annealed rice kernel gel, it is likely that annealing for 24 h could initiate the rearrangement of starch molecules, which may decrease swelling power and solubility, and this decline may promote gel hardness, consistent with the previous study about annealing starch . IncreasBased on the improved springiness, annealing temperature displayed more significant changes than annealing time in these textural features, indicating that the original binding relationship or molecular size between starch and other non-starch compounds is controlled by thermodynamic effects . Thus, tThe typical stress-strain curves of annealed rice kernel noodles and annealed rice flour noodles are shown in Native rice noodles have brittle characteristics and poor stretchability. However, in this study, annealed rice kernel noodles and annealed rice flour noodles exhibited good stretchability, which played a significant role in the rice noodles industry . As showMoreover, after rice kernels or flour annealing at 65 °C for 12 h, annealed rice flour noodles showed better fracture strain up to 110% compared with annealed rice kernel noodles, which was consistent with the texture analysis. The increased tensile properties could correspond to the increased relative crystallinity, which meant enhanced integrity of starch granules and a more ordered crystalline starch matrix . MoreoveThe microstructures of the rice noodles cross-sections with different annealing are shown in The gel network of rice noodles could be due to the gelatinization of native rice starch to a large extent, which was similar to those reported by Koh et al. , who fou2) distribution profiles could reflect the difference in the degrees of freedom. As shown in 21), and the other indicating the retention of water by the gel microstructure (T22) [Generally, LF-NMR analysis can be used to study the state, mobility, and distribution of water molecules. The transverse relaxation time (Tre (T22) .21 and T22 within the T2 relaxation time spectrum. Moreover, the increased peak height at 10–100 ms could be considered as the weakly bound water in the moisture in rice noodles. The denser network in annealed rice absorbed a certain amount of water, increasing water content and mobility. Annealed rice flour showed higher peaks than annealed rice kernels, which might be owing to the interaction between protein and starch, especially amylose molecules. Amylose is known to alter the gel network microstructure and endow a mobility-reducing entity. Annealed rice kernels could retain more amylose, thus restricting the swelling power [After annealing, all rice noodles showed two peaks at Tng power .The reason for the difference between annealed rice kernels and annealed rice flour could be the inhomogeneous morphological organization. On the one hand, rice kernels may lead to an inhomogeneous diffusion of water and heat during annealing, while rice flour exhibits a little delay in water penetration and air emission . On the In this study, annealing showed a pronounced effect on modifying the characteristics of indica rice kernels and rice flour and the quality of rice noodles. Annealed rice kernels and rice flour showed higher thermal stability, better texture properties, and increased relative crystallinity than native ones. Results also exhibited that rice flour had more susceptibility to modification than rice kernels. Rice noodles made of annealed rice flour at 65 °C for 12 h exhibited better fracture strain. Non-starch components such as proteins and lipids might have an effect on property differences in rice flour during annealing. Therefore, the annealing effects obtained in the present study are helpful in controlling the properties of rice noodles in the food processing industry.


The composite hardness is 60 HRC. Under uniaxial compression, the composite starts to deform plastically at a temperature of 700 °C and a pressure of 100 MPa. Temperatures ranging between 765 and 800 °C and an initial pressure of 150 MPa prove to be the most effective condition for composite deformation. These conditions enabled a true strain of 0.36 to be obtained without composite failure. Under higher strain, surface cracks appeared on the specimen surface. The EBSD analysis shows that dynamic recrystallization prevails at a deformation temperature of at least 765 °C; therefore, the composite can plastically deform. To increase the deformability of the composite, it is proposed to perform deformation under conditions of a favorable stress state. Based on the results of numerical modeling by the finite element method, the critical diameter of the steel shell is determined, which is sufficient for deformation of the composite with the most uniform distribution of the stress coefficient k. Composite deformation in a steel shell under a pressure of 150 MPa, at 800 °C, is experimentally implemented until a true strain of 0.53 is reached.Composites with a copper matrix attract the attention of researchers due to their ability to combine high ductility, heat conductivity, and electrical conductivity of the matrix with the high hardness and strength of the reinforcing phases. In this paper, we present the results of studying the effect of thermal deformation processing of a Сu-Ti-C-B composite produced by self-propagating high-temperature synthesis (SHS) on its ability to deform plastically without failure. The composite consists of a copper matrix and reinforced particles of titanium carbide TiC (sized up to 1.0 μm) and titanium diboride TiB Creation of new composite materials by applying the self-propagating high-temperature synthesis (SHS) technique has been successfully developed for more than 50 years ,2,3,4,5.Copper possesses high ductility, heat conductivity, and electrical conductivity . The faiIn this context, the aim of this study is to determine the temperature and load of stable plastic deformation of a Cu-Ti-C-B composite under uniaxial favorable loading and to perform an EBSD analysis of changes in the composite structure during plastic deformation.4C  was filled with the obtained powder mix. The initial compacting of the powder mix was achieved with a special snap. Then, the initial sample was immersed in an electric oven and heated up to the temperature of an exothermic reaction (1020 °С). After SHS completion, in order to eliminate porosity, the hot sample was transferred to a hydraulic press and compacted with a weight of not less than 250 MPa a. This rA Tescan Vega II XMU scanning electron microscope  was used to examine the composite structure on the cross-sectional cuts of the sandwich plates c. The lop = 0.95. The following micromechanical properties of the structural constituents of the composite were determined from the results of indentation: Vickers microhardness (НV), the contact elastic modulus (E*), the work of plastic deformation during indentation (φ), creep during indentation (СIT), the elastic recovery factor (Re), and the share of elastic strain in the total strain during indentation (HIT/E*) [IT denotes the values of indentation hardness under maximum load. The quantities φ, СIT, and Re were calculated by the following formulas:e is the work of elastic deformation during indentation which is released at unloading; Wt is the total mechanical work during indentation, which is determined by the area under the loading curve; h1 is the indentation depth corresponding to the initial point of the horizontal length of the loading curve; hp is the depth of impression after unloading; hmax is the maximum indentation depth. Determination of the micromechanical properties is necessary to identify the most plastic microconstituent that can provide plastic deformation of the composite as a whole.The micromechanical properties of the composite were determined according to GOST R 8.748-2011 (ISO 14577-1:2002) . Instrum(HIT/E*) ,40,41, w0) of 8 mm, cut out from the central part of the sandwich plates. A graphite lubricant was applied onto the specimen bases (ends) contacting surfaces with the tool. During the test, each specimen was placed in a cold furnace and heated up to a specified temperature  of 5 mm and a height  and process average strain rate (ξ*) were calculated using the following formulas:A pressure of 10 MPa was applied to the specimen heated to 700 °С, and then the readings of the punch displacement sensor were taken. By gradually increasing the load, the pressure on the specimen was changed with a step of 5 MPa until the start of punch displacement was recorded. This procedure enables one to determine the conditions under which a material starts to deform.2, sized from 0.5 to 3.0 μm), resulting from the synthesis, are the strengthening phases  and a small quantity of titanium  dissolved in its crystal lattice. Grey globular particles of titanium carbide  and black cubic particles of titanium diboride  does nosistance . TiB2 par matrix ; however2 particles, most often, there are smaller TiC particles; therefore, the second structural constituent was revealed, ”Cu + TiB2 + TiC”  with a preponderance of low-angle boundaries a–c. The 2 + TiC regions ranges between 625 and 800 HV 0.1; the average value is 760 HV 0.1. The Cu + TiB2 regions are characterized by the highest microhardness ranging from 900 to 1150 HV 0.1; the average value is 1050 HV 0.1  is currently widely used to evaluate hydrostatic stress ,49,50,51Thus, if the composite is deformed in a favorable stress state, it sustains considerable plastic strains without failure. In this connection, a specimen of the composite was tested for compression in a steel shell a. The spxu = 0 and zu = 0  was simulated by using the finite element method with the ANSYS Academic Research v. 16.2 software on the URAN cluster computer. A 3D finite element model was constructed; since the specimen and the shell were symmetric, only their quarters were simulated b. An isod uz = 0 b. The loy = 3 mm b. The frk) in the composite. The values of the coefficient are low, and this means that compressive stresses dominate in the composite during the testing. However, note that, in the simulation of compression in a shell with a diameter of 10 mm, the distribution of the values is rather nonuniform  hexagonal lattice belonging to the Р6/mmm space group, which explains why the contact elastic modulus E* is much higher in the regions containing titanium diboride particles than in the Cu+TiC regions, this being due to a larger effect of the covalent component of the TiB2 lattice, which ensures a more rigid interatomic bond. Instrumented microindentation testifies that the Cu + TiC constituent manifests the ability to deform plastically . This ismelt, sufficient for recrystallization to develop. Thus, for the Cu-Ti-C-B composite, plastic deformation is feasible due to the presence of grains with minimum dislocation density in the copper matrix. The diffuse texture of the composite matrix  consists of grains with a subcrystalline (polygonized) structure, 6% being occupied by fully recrystallized grains. As is known from ,32, two e matrix d is not This research testifies that the processes occurring in the Cu-Ti-C-B composite during thermal deformation processing are much more complex. On the one hand, heating to about 700–800 °С and higher causes recrystallization and softening in the composite, but on the other hand, diffuse processes become more active, and this may result in partial dissolution of the strengthening phases. Herewith, the contribution of precipitation hardening decreases, but there occurs solid solution hardening. Hardening and softening compete depending on the temperature and the amount of composite strain. Thus, at 700 °С, under a pressure of 150 MPa, deformation processes obviously prevail , i.e., tA further increase in the temperature to 800 °C makes diffusion processes even more active and increases the probability of partial dissolution of the strengthening phases. The alloying elements go into the copper-based solid solution, and the degree of hardening increases. Thus, several processes compete: The hardening of the solid solution increases due to its higher alloying, whereas precipitation hardening decreases due to the smaller sizes of the dispersed strengthening phases or their complete dissolution. After deformation at a temperature of at least 765 °C, recrystallized structures prevail in the composite matrix under both nonstationary uniaxial compression and favorable loading conditions . Thus, cUnder nonstationary uniaxial compression, the stresses in the composite are distributed nonuniformly and the high values of compressive stresses on the specimen surface cause cracking. Therefore, under conditions of uniaxial compression, we failed to obtain true strain without failure higher than 0.36. The finite element numerical simulation of the uniform compression of the composite under heating to 800 °C with an initial load of 150 MPa has shown that, for a favorable stress state to be implemented, it would suffice to use a 10 mm thick steel shell. The plastic deformation of the composite in the shell starts after the formation of a sufficient portion of softened grains in the copper matrix, which are fully recrystallized grains and those with a subcrystalline structure. The beginning of plastic deformation was recorded as early as at 600 °C. Evidently, dynamic recovery dominates in Portion 1, which manifests itself in the formation of a subcrystalline structure. At a temperature of at least 600 °C, the TLEC of the composite is essentially higher than that of the steel. Therefore, the composite is under additional compressive load. At temperatures exceeding 700 °C, diffusion processes become more active, the motion and interaction of dislocations in the copper matrix of the composite are easier, recrystallization processes develop, and the plastic deformation of recrystallized grains is faster  in the copper matrix and a high integral hardness (60 HRC), plastic deformation without failure is possible if certain conditions are met. Firstly, plastic deformation of the composite is ensured by the formation of a sufficient amount of a recrystallized structure with a prevalence of low-angle boundaries of copper matrix grains. This can be achieved when composite deformation is performed under uniaxial compression at a pressure of 150 MPa and a temperature ranging between 765 and 800 °C, with a true strain of 0.36. Secondly, the determining condition for the plastic deformation of the composite without surface cracking is uniform compression in a favorable stress state. The true strain of the composite has been experimentally obtained to be e = 0.53 at a deformation temperature of 800 °C under a pressure of 150 MPa.A complex analysis of the structure, micromechanical properties, and texture of a Cu-Ti-C-B SHS composite has shown that, despite a fairly large (at least 21%) number of strengthening phases (TiC, TiB


Despite abundant research on the role of Broca's area in language processing, there is still no consensus on language specificity of this region and its connectivity network.The present study employed the meta‐analytic connectivity modeling procedure to identify and compare domain‐specific (language‐specific) and domain‐general (shared between language and other domains) functional connectivity patterns of three subdivisions within the broadly defined Broca's area: pars opercularis (IFGop), pars triangularis (IFGtri), and pars orbitalis (IFGorb) of the left inferior frontal gyrus.The findings revealed a left‐lateralized frontotemporal network for all regions of interest underlying domain‐specific linguistic functions. The domain‐general network, however, spanned frontoparietal regions that overlap with the multiple‐demand network and subcortical regions spanning the thalamus and the basal ganglia.The findings suggest that language specificity of Broca's area emerges within a left‐lateralized frontotemporal network, and that domain‐general resources are garnered from frontoparietal and subcortical networks when required by task demands. •Domain‐general and ‐specific connectivity of Broca's area was investigated using meta‐analytic connectivity modeling • Language‐specificity of Broca's area arises from a left‐lateralized frontotemporal network • Domain‐general resources are garnered from frontoparietal and subcortical networks when required by task demands However, this contrast was also categorized as perception.vision (unspecified) and cognition.attention, in addition to the language domains, given that the contrast involves processing of visual stimuli, that is, pictures, and requires attention to decide when to execute the naming process (proper pictures vs. scrambled pictures). Another example is a study with a covert reading paradigm involving emotional words compared to baseline conditions , with 10,000 thresholding permutations.Convergence of co‐activations for each ROI was computed through ALE analyses using GingerALE 3.0.2  as well as conjunction analyses (language ∩ nonlanguage) were performed using the Contrast Datasets utility in GingerALE. The network identified by the contrast of language > nonlanguage is interpreted as the domain‐specific (language‐specific) network, while the conjunction of language ∩ nonlanguage is taken to reflect the domain‐general (shared between language and nonlanguage domains) network of the ROIs. The nonlanguage > language network, on the other hand, corresponds to co‐activations of the ROIs specific to nonlanguage domains. In addition to these main analyses which combine foci from all domains other than language and speech into a general nonlanguage set, exploratory analyses were conducted to identify domain‐specific and domain‐general networks of the ROIs within individual behavioral domains. The exploratory analyses were conducted to see, across different behavioral domains, whether the domain‐specific co‐activation patterns would be consistent and whether and how the domain‐general networks would differ. Given that inclusion of at least 17–20 experiments in ALE meta‐analyses has been recommended to obtain enough power for identification of small effect sizes and to ensure that the results are not overly influenced by individual studies  of 100 mm3 was used for the contrast and conjunction analyses, as applied in previous research  and temporal  lobes, but not in the parietal lobe. However, domain‐specific involvement of posterior middle and superior temporal regions showed differences among the ROIs, with IFGop co‐activating with these regions more superiorly than IFGtri and IFGorb. In addition, only IFGtri co‐activated with anterior STG and MTG as part of the domain‐specific network. The nonlanguage co‐activation networks of IFGtri and IFGorb were markedly different from those of IFGop, in which the former were predominantly left‐lateralized. While the nonlanguage co‐activation network of IFGtri included the left frontal (MFG) and parietal  cortices, that of IFGorb spanned the left frontal (MFG) and the right limbic  lobes. The domain‐general co‐activation network of IFGtri largely overlapped with that of IFGop in the left superior‐dorsal frontal  regions, but differed from that of IFGorb, which mainly involved the orbitofrontal cortex. Interestingly, the co‐activation patterns of IFGorb demonstrated a lateral‐to‐medial gradient within the left orbitofrontal cortex with gradually shifting lateral, lateral‐medial, and medial patterns for the domain‐specific, domain‐general, and nonlanguage networks, respectively.As for subcortical and cerebellar co‐activation patterns, only IFGop and IFGtri co‐activated with subcortical structures  as part of their domain‐specific networks. However, all ROIs exhibited some subcortical co‐activation primarily within the putamen and/or thalamus as part of their nonlanguage network. Additionally, IFGop also co‐activated with the bilateral caudate nuclei within its nonlanguage network. Domain‐specific networks of all ROIs showed some co‐activation with the left cerebellum as part of a larger cluster also overlapping with the fusiform gyrus. However, only IFGop exhibited distinct co‐activation with the right cerebellum within its domain‐specific network.2.5The results of contrast and conjunction analyses between language and four nonlanguage domains  for IFGop are illustrated in Figure Largely in parallel with the results of the main analyses, the domain‐specific (language > nonlanguage) co‐activation network of IFGop compared to each one of the four nonlanguage domains was generally left‐lateralized, spanning left frontal  and temporal (fusiform gyrus) structures Figure . LikewisThe co‐activation network shared between language and each behavioral domain  for IFGop revealed certain similarities and differences across domains. On the cortical territory, all domain‐general networks involved frontal regions, including IFG and MFG, while they included parietal structures  only for the cognition.attention and cognition.memory.working domains. Subcortically, particularly for the action.execution and cognition.attention domains, IFGop was associated with nonlanguage co‐activations in the basal ganglia  and the thalamus . The domain‐general network of IFGop, on the other hand, spanned the left thalamus  only for the conjunction of language with action.execution and cognition.attention, and the left caudate body with cognition.attention.3Using the MACM method, the present study investigated the difference and overlap between the language and nonlanguage networks of the left IFGop, IFGtri, and IFGorb to delineate language‐related domain‐specific (specific to language) and domain‐general (shared between language and nonlanguage domains) co‐activation networks of these ROIs. Thanks to the broad scope of the BrainMap database representing various behavioral domains, it was possible to disentangle the domain‐general and domain‐specific contributions by Broca's area and its functional connectivity network to language processing. The findings revealed a mostly left‐lateralized frontotemporal domain‐specific system for all ROIs. However, the domain‐general network was associated with a frontoparietal system that largely overlaps with the multiple‐demand network. The exploratory analyses showed that the domain‐specific network of IFGop was consistent across four behavioral domains, while its domain‐general network revealed certain differences at cortical and subcortical levels across domains. These findings show that domain‐specificity of Broca's area for language processing arises as part of a functional frontotemporal network, which may recruit additional resources from the domain‐general frontoparietal and subcortical networks depending on task demands.For all IFG ROIs, the findings revealed a largely left‐lateralized domain‐specific network (obtained using the contrast of language > nonlanguage) that spanned frontal  and temporal  regions, whereas the nonlanguage network (nonlanguage > language) exclusively involved frontoparietal regions. The domain‐general network (language ∩ nonlanguage) identified mostly left‐lateralized, frontoparietal cortices except for a single left temporal lobe cluster, involving STG and MTG, for IFGop. These findings are generally consistent with the accounts that propose a domain‐specific left frontotemporal network including parts of Broca's area that underlie language processing and that are, at least partially, distinct from domain‐general networks , it was possible to take into account extralinguistic factors that may accompany certain language tasks and that were previously associated with Broca's area such as emotional processing , posterior cingulate, medial prefrontal, and medial and lateral temporal cortices and has been associated with the brain's intrinsic activity Raichle, . PreviouAnother interface region revealed in the present study is the left orbitofrontal cortex, which demonstrated a lateral‐to‐medial gradient for IFGorb with lateral, lateral‐medial, and medial co‐activation patterns for the domain‐specific, domain‐general, and nonlanguage networks, respectively. Indeed, although the nonlanguage co‐activation network of IFGorb included several limbic structures , the only overlap between language and nonlanguage connectivity of IFGorb was observed in the left orbitofrontal cortex, with the aforementioned lateral‐to‐medial gradient. This finding is consistent with a previous meta‐analysis that associated lateral IFGorb with both emotion and semantics, and medial or opercular IFGorb with emotion alone , and only IFGop had domain‐general co‐activation with the left thalamus and putamen. Exploratory analyses showed that the domain‐general network of IFGop spanned the left thalamus  only for conjunction of language with action.execution and cognition.attention, but not with cognition.memory.working or cognition.music. Moreover, the domain‐specific networks of all ROIs showed some co‐activation with the left cerebellum, but this cerebellar involvement was part of a larger cluster overlapping with the fusiform gyrus, whereas only IFGop exhibited distinct co‐activation with the right cerebellum within its domain‐specific network. The exploratory analyses also identified this domain‐specific co‐activation of the right cerebellum with IFGop when contrasted with action.execution, cognition.attention, and cognition.music. Previous research associated the cerebello‐basal ganglia‐thalamo‐cortical system with a broad range of cognitive and sensorimotor functions including language , tasks , and modalities . This was intended as a generalization from specific tasks to language processing in general. Nevertheless, divergence, but also convergence, in the neural representation of different language functions were shown in previous research, for example, between syntax and semantics  networks shared between language and nonlanguage domains. The findings suggest that Broca's area, or Broca's complex in a broad sense, spanning the opercular, triangular and orbital parts of the left IFG, exhibits language‐specificity as part of a functional connectivity network involving a left frontotemporal system, which recruits domain‐general resources from frontoparietal multiple‐demand and subcortical  networks based on task demands. Application of MACM to compare divergence and convergence between domain‐specific and domain‐general functional networks of brain regions, as in the present study, offers significant potential for explorations of specific and shared networks for other language‐related regions and other behavioral domains.https://publons.com/publon/10.1002/brb3.3046.The peer review history for this article is available at Table SI1. Contrast and conjunction results of the language and action.execution domains for IFGop.Table SI2. Contrast and conjunction results of the language and cognition.attention domains for IFGop.Table SI3. Contrast and conjunction results of the language and cognition.memory.working domains for IFGop.Table SI4. Contrast and conjunction results of the language and cognition.music domains for IFGop.Table SI5. Contrast and conjunction results of the language and cognition.attention domains for IFGtri.Figure SI1. Contrast and conjunction results of the language and attention (nonlanguage) domains for IFGtri.Click here for additional data file.


Dendroctonus-bark beetles are natural components and key ecological agents of coniferous forests. They spend most of their lives under the bark, where they are exposed to highly toxic terpenes present in the oleoresin. Cytochrome P450 (CYP) is a multigene family involved in the detoxification of these compounds. It has been demonstrated that CYP6DE and CYP6DJ subfamilies hydroxylate monoterpenes, whose derivatives can act as pheromone synergist compounds or be pheromones themselves in these insects. Given the diversity and functional role of CYPs, we investigated whether these cytochromes have retained their function throughout the evolution of these insects. To test this hypothesis, we performed a Bayesian phylogenetic analysis to determine phylogenetic subgroups of cytochromes in these subfamilies. Subgroups were mapped and reconciled with the Dendroctonus phylogeny. Molecular docking analyses were performed with the cytochromes of each subgroup and enantiomers of α-pinene and β-pinene, (+)-3-carene, β-myrcene and R-(+)-limonene. In addition, functional divergence analysis was performed to identify critical amino acid sites that influence changes in catalytic site conformation and/or protein folding. Three and two phylogenetic subgroups were recovered for the CYP6DE and CYP6DJ subfamilies, respectively. Mapping and reconciliation analysis showed different gain and loss patterns for cytochromes of each subgroup. Functional predictions indicated that the cytochromes analyzed are able to hydroxylate all monoterpenes; however, they showed preferential affinities to different monoterpenes. Functional divergence analyses indicated that the CYP6DE subfamily has experimented type I and II divergence, whereas the CYP6DJ subfamily has evolved under strong functional constraints. Results suggest cytochromes of the CYP6DE subfamily evolve to reinforce their detoxifying capacity hydroxylating mainly α- and β-pinene to (+) and (−)-trans-verbenol, being the negative enantiomer used as a pheromone by several Dendroctonus species; whereas cytochromes of the CYP6DJ subfamily appear to retain their original function related to the detoxification of these compounds. Dendroctonus bark beetles (Curculionidae: Scolytinae) are natural components and key ecological agents of conifer forests in North and Central America, and Eurasia, as they participate in essential ecological processes, such as nutrient cycling, forest succession, and watershed regulation by the removal of old, damaged, diseased, or weakened trees  to select susceptible trees. Once in the tree, females bore into the phloem, release pheromones and compounds derived from terpene metabolism to attract males. Thereafter, both sexes copulate and excavate galleries along which the females oviposit. For a successful colonization, kairomones and pheromones integrate specific cues that facilitate mass attacks on trees. The larvae feed on phloem and develop as they construct galleries that end in pupal chambers, from which brood adults emerge. During the colonization, they must overcome the defensive mechanisms of host trees, especially the chemical constitutive and induced defenses integrated by monoterpenes (10 carbon atoms), non-volatile diterpenes (20 carbon atoms), sesquiterpenes (15 carbon atoms), and phenolic compounds present in the resin .These terpenes are toxic to bark beetles and their symbionts, which can inflict severe damage to membranous cellular structures and even result in death . The sucα-pinene, β-pinene, (+)-3-carene, β-myrcene, and R-(+)-limonene) of host trees -(−)-ipsdienol, the main pheromone in Ips spp (Dendroctonus ponderosae converts terpenes (+)- and (−)-α-pinene, (+)- and (−)-β-pinene, and (+)-3-carene into different hydroxylated enantiomers, of which only (−)-trans-verbenol, derived from (−)-α-pinene, is a pheromone in this species -- and (−)-β-pinene, (+)-3-carene, β-myrcene and R-(+)-limonene. In addition, based on the molecular interaction of these terpenes and CYPs, we predicted the conformational affinity between them. Lastly, we performed phylogenetic reconstruction, species-gene reconciliation, and functional divergence analyses to gain insight about the evolution and changes in the functional constraints of these subfamilies based on available data from Dendroctonus bark beetles.Given the diversity and functional role of CYPs in bark beetles, we hypothesized that cytochromes of CYP6DE and CYP6DJ subfamilies are involved in monoterpenes hydroxylation retain their ability to transform these compounds, regardless of whether they are involved in another function or exist other CYPs with co-responsibilities of participating in terpenes detoxification. Experimental evidence supports the participation of both subfamilies in the detoxification process and pheromone biosynthesis in  beetles . TherebyD. valens, D. rhizophagus, D. armandi, and D. ponderosae used in this study were downloaded from the NCBI GenBank . Full-length Cytochrome P450 sequences from the CYP6 family of D. mexicanus, D. frontalis and D. adjunctus were retrieved by an exhaustive search against the transcriptome assemblies of these species, which was carried out by the tBLASTn and tBLASTx with E-value cutoff ≤10−5 using the orthologs full-length sequences of CYP6DE and CYP6DJ family of species from insects mentioned above. Putative CYPs proteins were manually annotated to confirm their identity following a two-step strategy: 1) putative CYP transcripts were submitted to a BLASTp analysis against the NCBI database to determine the reference sequence with the highest identity percentage; 2) The transcripts and their corresponding reference sequence were aligned in Clustal X v.2.0 (Full-length Cytochrome P450 sequences from the CYP6 family of the species  X v.2.0 .The molecular mass (Da) and isoelectric point (pI) of the cytochromes from CYP6DE and CYP6DJ were determined with ProtParam . The sigHomo sapiens, respectively. Crystal sequences were downloaded from the RCSB-PDB . The overlapping between CYPs analyzed and crystal structures had ∼30% of identity and a coverage ∼95% in all comparisons. Prediction of secondary structure elements such as a-helix and ß-sheet, and sequences alignment were performed in the ESPript v.3.0 platform .Secondary structure elements and substrate recognition sites (SRS) of the cytochromes CYP6DE and CYP6DJ subfamilies were determined based on the cytochromes crystal structure CYP3A5 (PDB ID: 7sv2) and CYP3A4 (PDB ID: 2v0m) from platform . Based oplatform  and CYP2platform . The domAmino acid sequences of CYP6DE and CYP6DJ subfamilies, along with those of CYP6, CYP9 and CYP345 families from nine species belonging to curculionids, cerambycids, tenebrionids, and chrysomelids, were aligned in Clustal X v.2.0 using default parameters for the gap opening and extension . BayesiaDendroctonus. The CYP6DE and CYP6DJ phylogenies were inferred with BEAST2 v.2.5 as was described in Dendroctonus phylogeny was inferred by Maximum Likelihood using the cytochrome oxidase subunit-I (COI) sequences reported in http://www.atgc-montpellier.fr/, RRID:SCR_002917). The best nucleotide evolution model was GTR + G, gamma = 0.198 according to the Akaike information criterion . The reliability of the tree was evaluated with a bootstrap after 1000 permutations.A phylogenetic instability analysis was performed in MiPhy v1.1.2  to inferhttps://swissmodel.expasy.org/, RRID:SCR_018123). The crystalized structure of the CYP3A subfamily from Homo sapiens was used as template. The models were selected and validated with Ramachandran Plot in SWISS-MODEL and ERRAT in the Structural Analysis and Verification Server (SAVES) . The CYP isoforms with the highest and lowest TM-score of cytochromes CYP6DE and CYP6DJ subfamilies were overlapped with the CYP3A4 and CYP3A5 crystallized proteins, respectively in PyMOL v.2.5  . Pairwisα-pinene, (+)- and (−)-β-pinene, (+)-3-carene, R-(+)-limonene, and β-myrcene. Ligands were obtained from PubChem . Receptors and ligands were optimized using the UCSF Chimera software v.1.16  and the carbon methyl group (Cmet), whose hydrolysis give origin to verbenol and myrtenol, respectively; for (+)- and (−)-β-pinene the C2 and Cmet, that produce a β-pinene intermediary epoxide and myrtenol, respectively  if there was interaction between the terpene and the catalytic site (heme group) and 2) if the distance between the Fe ion and the carbon atom (Fe-C distance) was <6 Å . The disectively ; for limpsdienol . The hydenol  significantly greater than 0, indicate the occurrence of functional divergence.To test functional divergence after gene duplication events in isoforms of CYP6DE and CYP6DJ subfamilies, we performed type I and type II analyses based on the maximum likelihood method developed by I and θII divergence coefficients of phylogenetic subgroups from CYP6DE and CYP6DJ subfamilies, we analyzed the phylogenetic trees obtained from each subfamily in section 2.3. To define residues as divergence-related sites, we calculated the posterior probability value (Qk) considering a cutoff >0.7 for the type-I and type-II analyses   . SubgrouA, B, C) .Dendroctonus phylogeny showed that subgroups A, B and X were “founding” or “ancestral”, because of their presence in D. armandi, the species that diverged first in this bark beetle group  from D. frontalis complex species. The mapping of subgroups A, C, X, and Y within this complex showed a different evolutionary history, because these were retained in D. frontalis, subgroup A was lost in D. adjunctus, and subgroup X was missing in D. mexicanus , respectively . The firα-pinene, (+)- and (−)-β-pinene, (+)-3-carene, R-(+)-limonene, and β-myrcene, except the Dpon-CYP6DJ1 whose interactions did not involve the catalytic site. None of tested monoterpenes interacted with the catalytic site (heme group) of Dpon-CYP6DJ1 -β-pinene , except Drhi-CYP6DE4(A) and Dmex-CYP6DE(A)1 that showed the highest affinity with (+)-β-pinene (−23.06 kJ/mol) and β-myrcene (−25.03 kJ/mol) (α-pinene and (−)-β-pinene (−25.07 kJ/mol). These interactions included the residues PHE , LEU (SRS4), ALA (SRS4), THR (SRS4), GLU (SRS4) and VAL (SRS5 and SRS6) (β-myrcene] and (R)-(−)-ipsdienol; 4.7 Å  and (−)-β-pinene epoxide; 4.3 Å [Darm-CYP6DE5(A) c. (−)-β-pinene] and (−)-β-pinene epoxide; 2.8 Å  and (−)-trans-verbenol (Cytochromes from phylogenetic subgroup A formed the most stable conformations with (−)- kJ/mol) . Dfro-CYnd SRS6) . The Fe-verbenol .α-pinene (−25.16 kJ/mol), Dpon-CYP6DE2(B) with (−)-β-pinene (−24.45 kJ/mol), and Drhi-CYP6DE3(B) with (−)-α-pinene (−24.66 kJ/mol) (β-pinene] and (−)-β-pinene epoxide 4.1 Å Darm-CYP6DE6(B) c. (+)-α-pinene] and (+)-trans-verbenol; 3.9 Å [Drhi-CYP6DE3(B) c. (−)-α-pinene] and (−)-trans-verbenol (The isoform Darm-CYP6DE6(B) showed the highest affinity with (+)- kJ/mol) . These i kJ/mol) . The Fe-verbenol .β-pinene, although Dfro-CYP6DE(C)1 (−24.66 kJ/mol) and Dadj-CYP6DE(C)1 (−24.82 kJ/mol) also formed a complex with (−)-β-pinene. Dpon-CYP6DE1(C) (−24.82 kJ/mol), Dmex-CYP6DE(C)2 (−25.07 kJ/mol), and Dadj-CYP6DE(C)2 (−25.16 kJ/mol) had the highest affinity with (+)-α-pinene (β-pinene (β-pinene] and (−)-β-pinene epoxide; 4.8 Å [Drhi-CYP6DE(C)1 c. (+)-β-pinene] and (+)-β-pinene epoxide; 4.7 Å [Dpon-CYP6DE(C)3 c. (+)-β-pinene] and (+)-β-pinene epoxide; 4.4 Å [Dfro-CYP6DE(C)1 c. (−)-β-pinene] and (−)-β-pinene epoxide; 4.1 Å Dpon-CYP6DE1(C), Dmex-CYP6DE(C)2, and Dadj-CYP6DE(C)2 c. (+)-α-pinene] and (+)-trans-verbenol in three cases; 3.5 Å (Dadj-CYP6DE(C)3 and 2.6 Å  and (+)-β-pinene epoxide; 5.2 Å [Dfro-CYP6DJ(X)2-1 c. (+)-β-pinene] and (+)-β-pinene epoxide; 5.1 Å [Dval-CYP6DJ2(X) c. (+)-β-pinene] and (+)-β-pinene epoxide; 4.8 Å and 4.9 Å  and myrtenol; 3.8 Å Darm-CYP6DJ2(X) c. (−)-β-pinene] and (−)-β-pinene epoxide; 3.7 Å  and (−)-trans-verbenol in the three cases (The isoforms Dadj-CYP6DJ(X)2-2 (−26.87 kJ/mol), Dpon-CYP6DJ2(X) (−27.13 kJ/mol), Drhi-CYP6DJ2(X) (−27.04 kJ/mol), Dfro-CYP6DJ(X)2-1 (−26.83 kJ/mol), and Dfro-CYP6DJ(X)2-2 (−26.46 kJ/mol) showed the most stable interaction with (−)- kJ/mol) . Only Dfubfamily . The Fe-ee cases .α-pinene and; Dval-CYP6DJ1(Y) (−27.08 kJ/mol) Dfro-CYP6DJ(Y)1 (−24.15 kJ/mol) and Drhi-CYP6DJ1(Y) (−26.37 kJ/mol) with (+)-β-pinene (α- and β-pinene enantiomers but did not include the heme-group. Interactions included the residues ARG (SRS1), PHE (SRS1), ALA (SRS4), THR (SRS4), GLU (SRS4), VAL (SRS5), and LEU (SRS6). The LEU residue was only present in interactions of Drhi-CYP6DJ1(Y) and Dval-CYP6DJ1(Y), while ARG was only in interactions of Dmex-CYP6DJ(Y)1, which lacked the VAL residue. The GLU residue was only present in the interaction of Dval-CYP6DJ1(Y) with (+)-α-pinene, while Drhi-CYP6DJ1(Y) interacted with the same terpene but the PHE residue was absent (β-pinene] and (+)-β-pinene epoxide in both cases; 4.9 Å [Dadj-CYP6DJ(Y)1 c. (+)-α-pinene] and myrtenol; 4.3 Å [Dfro-CYP6DJ(Y)1 c. (+)-β-pinene] and (+)-β-pinene epoxide; 4.0 Å [Dval-CYP6DJ1(Y) c. (+)-α-pinene] and (+)-trans-verbenol; 3.0 Å [Dmex-CYP6DJ(Y)1 c. (−)-α-pinene] and myrtenol (The isoforms Dadj-CYP6DJ(Y)1 (−24.2 kJ/mol), Dmex-CYP6DJ(Y)1 (−24.47 kJ/mol), and Dval-CYP6DJ1(Y) (−27.08 kJ/mol) had the most stable interaction with (+)- and (−)-β-pinene . Dpon-CYs absent . The Fe-myrtenol .I = 0.999,428 ± 0.131,040 > 0, *p < 0.05)  . A total < 0.05) .II = 0.247,328 ± 0.071711> 0, *p < 0.05). A total of 54 CAASs were identified, including the positions 159 to 343 (Qk > 0.7), specifically residues 184,190,191 were in SRS2; 219 and 222-224 in SRS3; 272, 276, 280 in SRS4, and only 343 in the K-helix motif; the rest (43 CAASs) were not located in some domain or motif . Only four residues  were identified as CAASs (Qk > 0.7), and they did not fall in some domain or motif . The variation in CAASs corresponded mainly to exchanges between polar vs non-polar residues   in several species apparently has no negative effect on their fitness, since they face the same subcortical environment that is heterogeneous and changing in space and time. This confirms that physiological functions are not restricted to specific group or subfamilies of the P450 cytochromes  . Yet, alochromes .in silico analyses of CYP6DE and CYP6DJ subfamilies indicated that the cytochromes are anchored to the endoplasmic reticulum membrane, as reported for other families such as CYP4, CYP6 and CYP9s of the Dendroctonus species  and yielding products which synergize the action of pheromonal compounds or function well as pheromones  that favor massive attacks of conspecifics to overcome host resistance -α-pinene and (−)-β-pinene compared to the CYP6DE isoforms  and several SRSs, with SRS1, SRS4 and SRS5 being the most frequent. In the five subgroups, PHE, LEU, ALA, and VAL were the amino acids present in all receptor-ligand interactions –8. Theseisoforms . Interesarmigera .β-myrcene , despite myrcene is a toxic compound and abundant in mature pine tree colonized by D. ponderosae  and 3(C) isoforms form the most stable complexes with (+) enantiomers, whereas Dpon-CYP6DE2(B) with (−) enantiomers of both terpenes  due to the presence of the VAL366 residue which stabilizes the substrate binding, as observed in CYP6B1v1 and CYP6B1 of Papilio polyxenes, and CYP6B8 of H. zea  and D. valens. The evolutionary history of subgroup C is different because it emerged after the segregation of D. armandi and was retained during the diversification of Dendroctonus species. Apparently, the loss of subgroup B in the D. frontalis complex species was offset by the gain of subgroup C 1 c. β-myrcene -α-pinene to (−)-trans-verbenol is highly specific, due perhaps to the importance that (−)-trans-verbenol has as an aggregation pheromone in D. ponderosae (trans-verbenol is the result of direct hydroxylation of (−)-α-pinene in the tree oleoresin or from the verbenyl esters accumulated in the early stages of development and their subsequent release by females in the adult stage (In the case of Dpon-CYP&DE4(A), the most stable conformation was with (−)-nderosae , indepenlt stage .β-myrcene, which agrees with the production of (R)-(−)-ipsdienol in D. mexicanus. Behavioral and electrophysiology studies have demonstrated that this species produces (R)-(−)-ipsdienol which apparently acts as an aggregation pheromone (Cano-Ramírez pers. comm.). In bark beetles of the genus Ips, (R)-(−)-ipsdienol is produced by myrcene hydroxylation, which is synthetized de novo and hydroxylated by CYP9T1, 2, 3 1 is able to hydroxylate myrcene to ipsdienol.The Dmex-CYP6DE(A)1 cytochrome showed the highest affinity towards T1, 2, 3 . DendrocD. armandi has reinforced the detoxification capacity of the paralogous Darm-CYP6DE5(A) isoform, as the former showed a very stable interaction with (+)-α-pinene, where the latter presented less specific interactions with monoterpenes, despite showing preference for (−)-β-pinene. An interesting case are the results of interactions between Dpon-CYP6DE2(B) from D. ponderosae with different monoterpenes, which suggested that this isoform can interact with all tested compounds. Nevertheless, experimental evidence with this enzyme did not show functional activity on different monoterpenes and diterpenes -trans-verbenol. This could be similar to what occurs in D. ponderosae, as it has been suggested that (−)-trans-verbenol is the sex pheromone of D. rhizophagus  isoform in terpenes . The aut dilemma . Resultszophagus .D. rhizophagus that enforces subgroup A isoforms, because it has the same preferential substrate, (+)-β-pinene, whose hydroxylation produces an intermediary epoxide of β-pinene which yields myrtanal, myrtenol or perillyl alcohol. The findings with Dpon-CYP6DE1(C) and Dpon-CYP6DE3(C) isoforms from D. ponderosae are similar to those found in subgroup B, because both can hydroxylate all assayed monoterpenes. These results agree with the experimental assays performed with these isoforms  has a functional activity in isoforms .α-pinene, whereas Dpon-CYP6DE3(C) prefers (+)-β-pinene whose hydroxylation produces (+)-trans-verbenol and a β-pinene epoxide, respectively. As mentioned above, if the experimental results with the Dpon-CYP6DE2(B) isoform are correct  is a compensation to the subgroup A isoform, because subgroup B is absent. The isoforms from subgroups A and C prefer β-pinene enantiomers as substrates, whose hydroxylation yields myrtenol, myrtanal and perillyl alcohol as end products. Myrtenol has been reported in D. valens as a synergist compound of kairomones and pheromones attractive of this species  is (+)- correct , despite species .D. frontalis complex species which is an offset to the loss of subgroup B isoforms, but in D. adjunctus to subgroup A isoforms. Our findings with this species showed that the three isoforms from subgroup C (Dadj-CYP6DE(C)1,2,3 form the most stable complexes with enantiomers (+)-α-pinene and (+)- and (−)-β-pinene, whose hydroxylation produces (+)-trans-verbenol, myrtenol, and a β-pinene-epoxide. Advanced studies indicated that myrcene is an important kairomone for this species, but our findings showed that the interaction of isoforms Dadj-CYP6DE(C)1,2,3 with myrcene is not stable (β-pinene and (+)-α-pinene, respectively. The first is not involved in the chemical ecology of D. frontalis (D. mexicanus (Cano-Ramírez pers. comm.).The isoforms profit from subgroup C in the t stable . Likewisrontalis , while tD. frontalis reinforces the functional activity of the ancestral subgroup A, in D. mexicanus there is a differential preference with respect to the hydroxylated monoterpene, because the isoform of subgroup C hydroxylates (+)-α-pinene to produce (+)-trans-verbenol and the isoform from subgroup A hydroxylates myrcene producing ipsdienol, a pheromone of this species.A point that needs to be highlighted about these two bark beetles is that while subgroup C in α-pinene and (+)- and (−)-β-pinene, whose main products were (−)-trans-verbenol and myrtenol (α-pinene only by Dfro-CYP6DJ(X)2-1and 2-2. These findings showed that isoforms from subgroup X are involved mainly in the detoxification process of monoterpenes, as reported in other studies  or aggregation (D. ponderosae) pheromone (Our findings showed that isoforms from phylogenetic subgroup X had the most stable interactions with enantiomers (−)-myrtenol . The lat studies , indepenheromone  and myrtheromone .D. armandi indicates that isoforms of subgroup Y evolved in all Dendroctonus-species after divergence from this species. The isoforms which clustered in this subgroup Dadj/Dfro/Dmex-CYP6DJ(Y)1 and Dpon/Drhi/Dval- CYP6DJ1(Y), are duplicates of subgroup X and reinforce the original function of the CYP6DJ2 subfamily. In addition, the retention of this duplicate over time is also indicative that their duplication is an adaptive advantage for these bark beetles in the detoxification process.On the other side, the absence of Darm-CYP6DJ1 in α-pinene, (+)- and (−)-β-pinene, R-(+)-limonene, (+)-3-carene, myrcene, and β-phellandrene, but metabolized the cyclic monoterpene terpinolene, diterpenes (+)-(4R)-limonene, and (−)-(4S)-limonene  showed no interaction with the tested monoterpenes, which explains why this isoform recorded no functional activity in the enzymatic assays performed with monoterpenes (+)- and (−)-limonene . A detaiy CYP6AE .Dendroctonus spp. Type-I functional divergence has occurred in both subfamilies, but the amino acid patterns in phylogenetic subgroup A from the CYP6DE subfamily is more conserved compared to that in subgroups B and C. This might explain the retention of subgroup A in all analyzed Dendroctonus species (plesiomorphic condition), and the gain or loss of isoforms from subgroup B or C (apomorphic condition). The type-II functional divergence in CYP6DE subgroups is explained by the changes from polar to non-polar amino acids. In both types of functional divergence, the changes are concentrated  into regions SRS2, SRS3, SRS4, and K-helix, except 43 residues of type-II functional divergence that were not located in some domain or motif. These findings suggest that residues of apomorphic isoforms from subgroups B and C possess more versatility than residues of subgroup A isoforms, and perhaps also more specificity, with respect to the monoterpenes that can be metabolized.It has been hypothesized that genetic duplication plays an important role in functional diversity, where different selective pressures acting on different nucleotide sites of duplicate genes constrain its function, especially in motifs and functional domains . Our resD. mexicanus. A detailed analysis of the transcriptome of this species showed that isoforms of this group are not present; yet it is necessary to confirm this result by analyzing sibling species, D. vitei, or a second transcriptome of that species.In the case of the CYP6DJ subfamily, subgroup X from the CYP6DJ1 isoform is the plesiomorphic condition in these bark beetles, and is more conserved compared to the apomorphic subgroup Y. It is interesting to know that subgroup X has been lost in Dendroctonus. The fact that different subgroups are present in each species supports the birth-death model evolution of CYP genes which is the result of gene duplication and mutational changes. We recognized that subgroups B, C and Y originated as duplicates from the ancestral subgroups A and X, represent functional reinforcements of the detoxification process and could be act as an adaptive advantage in these bark beetles. In addition, our evidence suggest that these cytochromes can transform all assayed monoterpenes, but that some isoforms might preferentially metabolize some compounds and produce compounds that can act as pheromones or synergistic compounds in some species. Experimental evidence is required to confirm the activity of some isoforms from the subfamilies analyzed.Thereby, given the low residues number from CAASs (4), which did not fall in some domain or motif, we though that CYP6DE and CYP6DJ subfamilies have evolved under different selective pressures and functional constraints linked with monoterpenes detoxification through the evolutionary history of


This study concerns the analysis of navigational risk indicators as a function of the ship's domain width estimated for nine selected representative ships sailing under various hydrometeorological conditions (average and deteriorated ones) observed within the Offshore Wind Farm to be constructed within the Polish offshore zone on the Baltic Sea. For this purpose, the authors compare three types of domain parameters according to the guidelines by the PIANC, Coldwell and Rutkowski (3D). The study enabled selection of a group of ships which can be considered safe and can optionally be allowed to navigate and/or fish in the immediate vicinity and within the offshore wind farm. The analyses required the use of hydrometeorological data, mathematical models and operating data obtained with the use of maritime navigation and manoeuvring simulators. Currently, eight projects have secured contracts-for-difference (CfDs) granted by the Polish Energy Regulatory Office (ERO) as part of an administrative procedure introduced under the Offshore Wind Act. As declared by the investors, the most advanced projects should be commissioned between 2026 and 20272.The Baltic Sea has shallow waters, high average wind speeds, low wave heights and weak tides. Such conditions result in low levelized cost of energy (LCOE) values for offshore wind energy production and make the Baltic Sea a prospective area for the development of offshore wind farms (OWFs). To date, offshore wind turbines have been installed in Denmark, Germany, Sweden and Finland, yet there is no wind farm within the Polish Exclusive Economic Zone (EEZ). Poland is the last EU country at the pre-development and consenting stages; however, many pre-investment studies and survey campaigns have been carried out for several of such investments5. According to the Statistics Poland6, cargo turnover, passenger traffic and the number of ships calling at Polish seaports have increased over the past years. Apart from transport and tourism, human activity at sea is also related to the petroleum and seafood industries. When analysing the above, it becomes clear that offshore windmills installed will become navigational obstructions affecting the safety of navigation16. Therefore, it is necessary to establish safety zones for representative ships sailing in the vicinity of OWFs, assess their safety of navigation while manoeuvring within the OWF areas and estimate their so-called navigational risk indicators.The Baltic Sea is one of the busiest seas in the world, with sea transport accounting for 15% of global sea freight17.In the Baltic Sea region, different regulatory regimes are applied for vessel traffic through wind farms. For example, in Belgium and Germany, wind farms are considered maritime exclusion zones to prevent accidents or damage to turbines, whereas, in the UK and Denmark, wind farms are open for shipping, and both commercial and recreational use. In Denmark, for example, wind farms are open to transit for ships of up to 24 m in length. Such operations may only take place during the day with the VHF and AIS system being operational and activated. Seabed-disturbing activities and third-party diving activities are forbidden within offshore wind farms. Safety zones of 50 m are established around the turbines and the 500-m safety zones around offshore transformer stations remain in place. In the case of new offshore wind farms, the establishment of a corridor is being considered to make it possible for vessels of up to 45 m to travel through themIf the distance between the turbine boundary and the shipping route is less than < 0.5 nm (< 926 m), it is deemed intolerable;If the distance is between 0.5 and 3.5 nm (926–6482 m), it is deemed tolerable provided that the risk being reduced to as low as reasonably practicable (ALARP)—additional risk assessment and proposed mitigation measures required;If the distance is more than > 3.5 nm (> 6482 m), it is deemed broadly acceptable.The British requirements for safe navigation guidelines for offshore renewable energy installations  provide the following recommendations for estimating the safe distance of a turbine from the shipping route:Currently, the Polish maritime administration bodies, acting under Art. 24 in connection with Art. 47 of the Act of 21 March 1991 on maritime areas of the Republic of Poland, are considering the introduction of safety zones around structures and devices constituting elements of OWFs situated within the maritime areas of the Republic of Poland. At the moment of writing this paper, the above-mentioned legal regulations have not been developed and/or published on the official websites of the Polish maritime administration bodies.18, according to which the level of navigational risk from the OWF impacts depends on the distance between a Traffic Separation System (TSS) shipping route and the first row of wind turbines. According to the PIANC guidelines, the level of unacceptable risk will be estimated for ships to which the SOLAS Convention19 applies, and which are manoeuvred at a distance of less than 0.25 NM (463 m) and/or 500 m from the designated high-density shipping routes.General guidelines regarding the risks of navigation and safety zones in the vicinity of OWFs were presented by the World Association for Waterborne Transport Infrastructure PIANC18, the minimum distance that guarantees the safety of navigation refers to the COLREG regulations20 and is determined based on the resolutions of IMO23, MSC.137 (76)22 and MSC/Circ.105321, which address ship manoeuvrability and, in particular, the parameters of the turning circle manoeuvre and the emergency stopping (decelerating) distance. According to the PIANC guidelines, the minimum safe distance from a navigational obstacle that defines the ship’s domain should be determined using the following formulae:SDWP); expressed in meters, [m]; SDWP); expressed in meters, [m]; LOA = ship’s length overall expressed in meters, [m].According to the PIANC, ships navigating within the TSS area situated at a distance of more than 5 NM (≈ 9260 m) from the OWF can be considered to be safe in restricted sea areas. As per the PIANC guidelines24 has been widely analyzed in the existing literature concerning the safety of shipping28 and assessment of the navigational collision risk30, and is defined as the area around a vessel which is indispensable for maintaining the safety of navigation. Therefore, the navigational risk increases when any navigational obstruction appears within the ship’s domain. Most of the proposed ship’s domain models are two-dimensional (2D)31 rather than spatial (3D)32. This paper compares three domain models according to the guidelines by the PIANC, Coldwell, and Rutkowski (3D). The ship’s domain by Rutkowski (3D), which was developed based on the author’s own research, is presented in Fig. The term ‘ship’s domain’LF), length aft (SDLA), width to port (SDWP), and width to starboard (SDWS). However, due to the limited nature of our work, this paper focuses only on the analysis of two of the six parameters of the 3D model of the ship’s domain by Rutkowski12, and, in particular, the ship's domain width in the horizontal plane on the port side (SDWP) and the starboard side (SDWS) of the ship.Figure RNWP and RNWS with respect to keeping the required width for the safety of the vessel traffic lane on the ship’s port and starboard sides as estimated for a group of representative ship types which may navigate within OWF areas;determining navigational risk numeric indicators selecting a group of ships from among the representative ship types, which may pose a particular hazard to the OWF operation, and a group of ships which can be considered safe and can optionally be allowed to navigate and/or fish in the immediate vicinity and within OWFs;comparing the domain parameters for the selected representative ship types compiled according to the guidelines by the PIANC, Coldwell and Rutkowski (3D).This study focused on the following research objectives:RN)12, a risk coming from factors Ai (objects) and equal to 0 denotes full safety of navigation with respect to these factors (objects). Analogously, the higher the risk (parameter RN approximating 1), the lower the level of the safety of navigation (SN) → . Therefore, the navigational risk indicator reaching RN = 1 denotes the occurrence of such conditions and/or circumstances which are going to prevent safe navigation and may entail a 100% probability of a collision.According to the definition of navigational risk 12 and the definition of RN13, the values of which can be determined with reference to the vertical plane OX and the horizontal plane OY33. The analysis will further focus, in particular, on the components of RN defined with reference to the OY plane and in relation to objects situated on the ship’s port side (RNWP), and the ship’s starboard side (RNWS), which can be presented with the use of the following formulae:RNWP is a dimensionless value defining a component of RN with respect to keeping the required safe width of the ship's passage route  on the ship’s port side related to the possibility of the ship colliding with a navigational obstacle situated on the ship’s port side; SDWP (Ship’s Domain Width Port Side) is the ship’s domain width as measured on the ship’s port side. It is expressed in meters measured along the OY axis perpendicular to the ship’s heading (true course line TC) on the ship’s port side; dNP is the distance from the nearest hazard  measured in meters perpendicular to the ship’s heading (true course line TC) on the ship’s port side; B is the ship’s width in meters as per the ship’s particulars, the pilot card or the AIS.RNWS is a dimensionless value defining a component of RN with respect to keeping the required safe width  on the ship’s starboard side (index WS = Width Starboard Side). This parameter describes the navigational risk (estimated as ranging from 0 to 1) related to the possibility of the ship colliding with a navigational obstacle on the ship’s starboard side (Adequate Required Safe Distance from the Nearest Danger on Ship’s Starboard Side); SDWS (Ship’s Domain Width Starboard Side) is the ship’s domain width as measured on the ship’s starboard side. It is expressed in meters measured along the OY axis perpendicular to the ship’s heading (true course line TC) on the ship’s starboard side, [m]; dNS is the distance from the nearest hazard measured in meters perpendicular to the ship’s course line on the ship’s starboard side, [m].12, every ship will be safe  as long as she is the exclusive object capable of generating hazards within her domain.According to the ship’s domain definitionNWP and RNWS of the navigational risk RN, which can be referred to as the horizontal components of the navigational risk related to keeping a safe distance from the nearest danger adequately on the port and starboard sides of the ship, or, in short, the risk of keeping a safe distance from the port and starboard sides, can be depicted by means of formulas (RNWP formula dNP > SDWP) condition and (RNWS formula dNS > SDWS) condition guarantee safe navigation of the ship in relation to the objects detected on the ship’s starboard side and port side respectively. When analysing formulas NW will be limited to a range between zero and one (RNW ϵ7) only if the distance from the nearest danger on the port side (dNP) or starboard side (dNS) is either less or equal to the ship’s domain width calculated respectively for the ship’s port side (SDWP) and/or starboard side (SDWS). In all probability, assumption With reference to the horizontal plane OY distinction between Rformulas  and 4)..NWP and RN as a function of the ship’s domain parameters  and distance from the nearest navigational hazard (dN) is presented in Fig. RN factors in the horizontal plane OY in relation to the objects situated on the ship’s port and starboard sides obtained for different ship types navigating within the OWF sea area are presented below.A graphical display of Polaris Ships Bridge simulator, Version 8.0.0 Build 384 with a DP-K-Pos dynamic positioning simulator by Kongsberg Digital A.S. ;full-mission bridge) by Kongsberg Digital A.S. , andK-Sim Navigation  combined with an electronic chart system ECDIS NaviSailor 4000 by Transas, which is part of the Wärtsilä Group.For the purposes of the paper, our analysis covered nine representative ship types Table  with mat34. The information concerns the waters of the Baltic Sea along the Polish coast and may refer to the Project area. The weather parameters and hydrological conditions presented cover average values obtained during many years of research.The parameters of spatial domain models were estimated for representative ship types navigating under average hydrometeorological conditions adequate for the analysed navigable sea area and under deteriorated conditions. The weather parameters and information about the hydrological conditions prevailing in the southern Baltic Sea area as necessary for safe navigation across this basin are presented in Table 18  where COG = ship’s course over ground (B = ship’s width (beam) in meters based on the ship’s particulars, [m], ∆B = a factor showing an increase in width (beam) of the ship’s domain. The increase amounts to error MOY of the total ellipse errors δy(Bi) for all factors Bi that affect SDWS, estimated with the probability level of p = 95% (C = 2.44); in this paper, the following is assumed: ΔB = 10 m, BC = Seeming width of the ship’s trace calculated horizontally in meters [m], with wind leeway angle α [°], current deviation (drift angle) β [°], and ship’s yawing Δ[°]:For the purposes of the paper, we referred to three spatial models of the ship’s domains: the PIANC guidelinesformulas , the 2D TRmax = the ship’s transfer maximum values measured in meters as the maximum movement of the ship to the port or starboard side , observed after changing the course ∆TC ≥ 180° or after the ship’s stopping manoeuvre is completed, [m],TRneg = the ship’s ‘negative’ transfer  measured in meters, observed after on the side opposite to the general direction during the ship’s turning and/or stopping manoeuvre, also known in maritime terminology as the ‘kick’ distance on turning circle diagrams. TRneg is specified for merchant ships as a value between 1.0 and 1.5 of the ship’s breadth B (for turning circulation) or around 1.5 of the ship’s length L (for a Crash Stop (Full Ahead-Full Astern) emergency manoeuvre), [m]. tm = the period of time needed to stop the ship or change the direction of the ship’s movement by ∆TC ≥ 090° expressed in minutes based on the Pilot Card, Wheel House Poster or Turning Circle Diagrams, [min], tr = the period of time needed for the appropriate reaction, that is the right assessment of the navigational situation and giving a manoeuvre order. In practice, tr ≈ 0.5 min up to 3.0 min depending on the seafarer competence and his professional experience, [min],Drift = the total current speed value in knots (Drift = Vz) where Set = the total current (p = a factor (numeric coefficient) depending on the harmfulness of the cargo carried on board the ship. This factor (1 ≤ p ≤ 2) increases the safety margin of navigational reserve in case of an abnormal situation, which can result either in a catastrophe (disaster) or contamination of the environment. In this paper, we recommend using the following values for factor p: for ships in ballast condition without dangerous cargo or harmless charge, neutral for people and the environment: p = 1; for ships carrying a load of high harm to people and the environment, e.g. flammable substances, oil, natural gas.: p = 1.5; for ships with a very harmful load for people and the environment, e.g. radioactive substances, corrosive chemicals, explosive substances: p = 2.0,rW = a numeric coefficient (factor) correcting the width (rW) of the ship’s domain (0 ≤ rW ≤ 2), depending on her situation (privilege) according to the COLREG Rules. In this paper, we recommend the following values for factor rW: for a ship aground or at anchor: rW = 0; for ships restricted by their draught: rW = 1; for privileged ships such as vessels with restricted ability to manoeuvre  correcting the ship’s transfer (TR) parameter on turning circle in case of unexpected meteorological conditions other than those previously observed during sea trials and recorded in the Pilot Card and Wheel House Posters (currently excluded).The parameters were estimated for the turning cycle manoeuvre with the ship at full sea speed ahead (FSAH) with the rudder angle of 35° starboard and emergency stop manoeuvres by reversing the engine to full astern (FSAH-FAS and HAH-FAS). The results are presented in the further part of this paper.dmin1 = 700 m (in the case of substations) and from dmin2 = 1000 m to dmin3 = 2000 m in the case of measuring distances between individual offshore wind turbines, however our analysis has been extended to address seven different distances: 300 m, 500 m, 600 m, 700 m, 800 m, 1000 m and 2000 m. When analysing emergencies, when ships are allowed to enter the OWF area, it was assumed that they sail at an optimal (maximum) distance from any navigational hazards detected nearby and situated respectively ahead of their bows and on their port and starboard sides. Here, an assumption can be made that, in the vicinity of substations, the minimum distance from the nearest hazard will be a value defined as half of the distance between individual offshore installations, i.e. dN1 = 0.5∙dmin1 = 350 m, and for the location of wind turbines within the OWF area, this will be the distance ranging from dN2 = 0.5∙dmin2 = 500 m to dN3 = 0.5∙dmin3 = 1000 m.It has been assumed in this paper that the actual distances between individual offshore installations within the OWF area range from 18, 2D domain by Coldwell and the method by Rutkowski13 using the manoeuvring characteristics obtained by the manoeuvring simulator of the Gdynia Maritime University calculated for average and deteriorated hydrometeorological conditions.Table RN ranging from 0 to 33%  Table , dependiAs regards the 2D domain method by Coldwell and the 3D domain method by Rutkowski, navigating ship types D, E, F and I proves to be completely safe, taking into account the presence of navigational hazards situated on the ship’s port side and starboard side respectively. Moreover, the parameters of the 2D domain by Coldwell are very similar to those of the 3D domain by Rutkowski as estimated for the emergency turning circle manoeuvre performed at full speed ahead FSAH with the rudder angle of 35º starboard. Additionally, the 2D domain by Coldwell is an empirical domain estimated in the XY horizontal plane only and it does not take account of the navigational risk generated by above-water and underwater navigational obstacles. In addition, the 3D domain by Rutkowski allows for choosing the right anti-collision manoeuvre, which is performed by way of changing the course (turning circle manoeuvre) and/or changing the ship’s speed ahead (FSAH or HAH). For example, an analysis of RN as estimated for nine representative ship types with reference to navigational obstacles situated on the ship’s port side and starboard side respectively. However, a comprehensive analysis of the navigational risk in the navigable sea area analysed requires that the distribution of all navigational hazards situated within the three XYZ axes as a function of relevant parameters of the ship’s 3D domain model is studied.This paper presents the numeric indicators of navigational risk RN indicators at times assume radically different values, whereby the domain model by Rutkowski seems to be the most accurate one. To sum up, according to the 2D domain method by Coldwell and the 3D domain method by Rutkowski, navigating the following ship types: fisher ship (D), high speed water jet rescue ship (E), fishing boat (F) and z-drive prevention response tug (I), proves to be completely safe. The analyses that were conducted required the use of appropriate hydrometeorological data for the area under consideration.The paper compares three types of domain parameters according to the guidelines by the PIANC, Coldwell and Rutkowski (3D). The results obtained for The presented method can be perceived as a universal one, as it depends only on the interrelation between the ship position and the position of the detected navigational obstacle, which obstacle may be land, another ship or object , or a hydrometeorological factor generating a risk to the safety of navigation within a given navigable sea area (an open and/or restricted one).