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The present topic is devoted to investigating the effects of semi four-cusped hypocycloid irregularity on torsional surface waves in an initially stressed anisotropic porous medium situated between two anisotropic nonhomogeneous semi-infinite spaces. The irregularity manifests as a semi-fourcusped hypocycloid at the interface where the layer and the lower semi-infinite space are separated. It is assumed that the directional rigidities, density and initial stress vary in the upper and lower semi-infinite spaces in an exponential and hyperbolic manner, respectively. A closed form for the torsional wave dispersion equation is presented. Additionally, the velocity equation is found in the case of no irregularity. The study demonstrates that heterogeneity of lower semi-infinite space, initial stress and directional rigidities of both semiinfinite spaces, as well as of porosity of the layer have a favourable effect on the phase velocity of torsional surface waves. However, the heterogeneity of the upper semi-infinite space, ratio of directional rigidities and initial stress of the layer and irregularity parameter have a negative impact. It has also been observed that, in the case of a uniform media, the velocity equation reduces to the conventional equation for the Love wave.

The anisotropy interfacial energy changes the growth tendency of dendrites in different directions during solidification, when the growth tendency in a specific direction appears or disappears, the transition of dendrite orientation will happen. In this study, three-dimensional simulations of anisotropic α‐Mg dendrite were conducted by changing the anisotropic interface energy in the phase field model. The variation in the preferred growth direction of equiaxed dendrite in α‐Mg was analyzed by controlling the anisotropic function of the interfaces. The changes in the growth direction of dendrites on different dendrite planes and the distribution of solute were investigated. The dendrites of α‐Mg equiaxed crystals mainly grow in ⟨112‾0⟩ and ⟨112‾3⟩ directions, and the transition of dendrite orientation depends on ⟨112‾0⟩ direction. When ⟨112‾0⟩ direction branching disappears, α‐Mg dendrite is transformed from 18 branches to 12 branches. The solute distribution at the front of the dendrite boundary changes significantly with the growth trend. Differences in the degree of solute distribution affect the solid-liquid interface and change the microstructure of the material.

Crown ether is widely used in water purification because of its ring structure and good selective adsorption of specific heavy metals. However, its high cost and difficulty in recycling limit the purification of heavy metals in water. The anisotropic [2,4]-dibenzo-18-crown-6-modified bamboo pulp aerogel (DB18C6/PA) is successfully synthesized by microwave irradiation and directional freezing technology. The physical and chemical properties of DB18C6/PA are analyzed by FTIR, XPS, SEM, TEM, TGA, surface area and porosity analyzers. Single or multivariate systems containing Pb2+, Cu2+ and Cd2+ are used as adsorbents. The effects of the DB18C6 addition amount, pH, initial concentration and adsorption temperature on the adsorption of DB18C6/PA are systematically explored. Pseudo-first-order kinetic models, pseudo-second-order kinetic models and the isothermal adsorption models of Langmuir and Freundlich are used to fit the experimental data. The adsorption selectivity is analyzed from the distribution coefficient and the separation factor, and the adsorption mechanism is discussed. The results show that anisotropic DB18C6/PA has the characteristics of 3D directional channels, high porosity (97.67%), large specific surface area (103.7 m2/g), good thermal stability and regeneration (the number of cycles is greater than 5). The surface has a variety of functional groups, including a hydroxyl group, aldehyde group, ether bond, etc. In the single and multivariate systems of Pb2+, Cu2+ and Cd2+, the adsorption process of DB18C6/PA conforms to the pseudo-second-order kinetic model, and the results conform to the Freundlich adsorption isothermal model (a few of them conformed to the Langmuir adsorption isothermal model), indicating that chemical adsorption and physical adsorption are involved in the adsorption process, and the adsorption process is a spontaneous endothermic process. In the single solution system, the maximum adsorption capacities of Pb2+, Cu2+ and Cd2+ by DB18C6/PA are 129.15, 29.85 and 27.89 mg/g, respectively. The adsorption selectivity of DB18C6/PA on Pb2+, Cu2+ and Cd2+ is in the order of Pb2+ >> Cu2+ > Cd2+.

Numerical modeling of acoustic-elastic media is helpful for seismic exploration in the deepwater environment. We propose an algorithm based on the staggered grid finite difference to simulate wave propagation in the interface between fluid and transversely isotropic media, where the interface does not need to consider the boundary condition. We also derive the stability conditions of the proposed method. Scholte waves, which are generated at the seafloor, exhibit distinctly different propagation behaviors than body waves in ocean-bottom seismograms. Numerical examples are used to characterize the wavefield of Scholte waves and discuss the relationship between travel time and the Thomsen parameters. Thomsen parameters are assigned clear physical meanings, and the magnitude of their values directly indicates the strength of the anisotropy in the media. Numerical results show that the velocity of the Scholte wave is positively correlated with ε and negatively correlated with δ. And the curve of the arrival time of the Scholte wave as a whole is sinusoidal and has no symmetry in inclination. The velocity of the Scholte wave in azimuth is positively related to the polar angle. The energy of the Scholte wave is negatively correlated with the distance from the source to the fluid-solid interface. The above results provide a basis for studying oceanic Scholte waves and are beneficial for utilizing the information provided by Scholte waves.

We obtain the solutions of Einstein’s field equations for an anisotropic fluid in a static spherically symmetric metric with off-diagonal elements. We also study the pioneer anomaly with the help of the obtained solutions. First, we derive analytical solutions to study sudden change in gravity in the radial and tangential directions of a non-homogeneous gravitational system by considering Π as a constant. Then we find other solutions by considering Π as a function of r in the space of gravitating object. We extend our solutions in the numerical limits to verify the unusual behavior of gravity at larger distances for the inhomogeneous system. We show a sudden increase in radial pressure for 𝑟𝜖[0, 20] as well as the tangential pressure for 𝜃𝜖[0, 𝜋], which may be treated as a factor of pioneer anomaly. We obtain the anomalous acceleration 2.493 × 10−11𝑚/𝑠 2 at a distance of 20 AU from the Sun, which has better accuracy than other theoretical calculations when it is compared to the observed value. We also derive an expression for cosmological constant in terms of 𝑟. We establish that the cosmological constant is a function of 𝑟, which seems to be variable but its variability diminishes for large values of 𝑟. The results of this study are interesting and quite new. The selected spherically symmetric metric with off-diagonal elements provides a modified method to observe the phenomena of general relativity.

In this article, we introduce anisotropic mixed-norm Herz spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and investigate some basic properties of those spaces. Furthermore, we establish the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}). Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces are also gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces HK˙q→,a→α,p(Rn)H{\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and HKq→,a→α,p(Rn)H{K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}), on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators.

In this work, a parameter identification software for the data-driven hyperelasticity frameworks proposed by Dal et al. (Journal of the Mechanics and Physics of Solids 179, 105381, 2023), and Tikenoğullarıet al. (Journal of the Mechanics and Physics of Solids 181, 105453, 2023) is introduced. These data-driven hyperelasticity frameworks allow direct incorporation of experimental data into the constitutive model with the usage of B-splines, removing the requirement of a predetermined mathematical formula for the strain–energy density function. Three isotropic and two dispersion-type anisotropic data-driven formulations are embedded in the software. Additionally, three established models from the literature are included for comparison purposes. An optimization procedure is employed to identify the control points, also referred to as material parameters. This process involves tailoring the model to best fit data obtained from uniaxial tension, triaxial shear, pure shear, and (equi)biaxial tension experiments. The model calibration phase incorporates the normalization condition and the polyconvexity condition is enforced through the control points of the B-splines in order to ensure a stable constitutive response.

Flexible, stretchable, and sensitive multidirectional sensing systems that can decouple different mechanical inputs and identify multidirectional signals are crucial for dynamic human signal perception and intelligent human–computer interaction. Most reported multidirectional sensors are suitable for discriminating in‐plane deformation directions, and the sensing materials are difficult to balance between stretchability and mechanical strength. Here, a segmented embedded structure strategy inspired by the interlaced structure of cartilage is proposed. This strategy combines soft and hard materials in a topological and zipper‐shear chain manner and balances the performance of reinforced composites with flexibility and high toughness. In the case of segmented embedded hydrogels (SEHs), a wearable multidirectional sensing system that can decouple and identify planar strain/pressure is constructed. The multidirectional sensing system exploits the inherent anisotropy and layered structure design of composites to decouple the sensing functions. Supported by machine learning algorithms, the high accuracy demonstration of the multidirectional sensors in typical multidirectional motion joint posture monitoring and recognition confirms their potential in practical applications such as personal health sensing and human–computer interaction. [ABSTRACT FROM AUTHOR]

This study proposes a novel anisotropic model based on fractal theory for three-dimensional (3D) rough surface reconstruction to improve the large error associated with isotropic models. The proposed model comprises a fractal-based two-dimensional (2D) contour curve, a conversion operator and a coefficient vector ratio. The effects of the virtual random curve and fractal-based 2D contour curve in the conversion operator are discussed. The largest height ratio of the virtual contour curve and the measured surface discrete point curve of each column are used in the coefficient vector ratio. The rough surface is also smoothed using a five-point cubic smoothing algorithm. Compared with the isotropic model, the proposed model resembles the measured surface more closely with an average fitting error reduction of 49.84% and 64.7% before and after smoothing, respectively. The surface exhibits horizontal and vertical textures that can be controlled by the fractal dimension and roughness in the X and Y directions. Additionally, an asperity contact model is established and analysed. The proposed modelling method for anisotropic 3D rough surface contact condition is more consistent with the measured surface model. The transverse and longitudinal textures of the anisotropic surface can be changed by the fractal dimension and fractal roughness in the X and Y directions. This research provides insights into characterising 3D rough surfaces of high-precision gears and improving nominal contact area accuracy. [ABSTRACT FROM AUTHOR]

[Display omitted] The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the J 1 x - J 1 y - J 2 model, which contains anisotropic nearest-neighbor couplings J 1 x , J 1 y and the next nearest neighbor coupling J 2 . For small J 1 y / J 1 x , by tuning J 2 , a direct continuous transition between the AFM and valence bond solid phase is observed. With growing J 1 y / J 1 x , a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM–VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL–VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems. [ABSTRACT FROM AUTHOR]

Conductive hydrogels (CHs) are promising candidates for wearable devices. However, it remains challenging for traditional CHs to realize a combination of self‐adhesive and skin‐comparable performances. Herein, a stretch‐induced orientation strategy was demonstrated to achieve this goal. The hydrogel was fabricated from poly(vinyl alcohol), aluminum sulfate, tannin acid, and deionized water, which exhibited skin‐comparable elastic modulus (26.3 kPa), stretchability (180%), and water content (87.6%). Meanwhile, it had anisotropic properties. For instance, the mechanical and anisotropy ratios between parallel and orthogonal directions were 1.77 and 2.02, respectively. Furthermore, the presence of free ions within regular conductive channels imparted stable conductivity (gauge factor of 2.2 within 200% strains), fast response (0.2 s), and low detect limit (a strain of 0.2%). Additionally, the existence of catechol groups from tannin acid enabled self‐adhesion ability (adhesion strength of 73.9 kPa). All of these merits show promising potential in wearable devices and electronic skins. [ABSTRACT FROM AUTHOR]

This article reports the direct observation of the fracture of individual poly‐ether‐ketone‐ketone (PEKK) spherulites. A single layer of PEKK spherulites was obtained by bonding a PEKK film in‐between two sandblasted Ti alloy plates using an autoclave. The crack of an individual PEKK spherulite was achieved by opening the Ti/PEKK/Ti sandwich using a double cantilever beam test. The fracture morphology of the PEKK spherulite was characterized using scanning electron microscopy and atomic force microscopy. It was found that under tensile stress the crack of the individual spherulite propagates along the middle plane and crosses the nucleation core. This is due to the symmetric radial structure of the spherulite. Moreover, it was found that the fracture surface morphology at the core of the spherulite is strongly influenced by the local crystalline structure, which is anisotropic and determined by the initial nucleation growth direction. As a result, the area fraction experiencing plastic deformation during the fracture of PEKK spherulites at different orientations may vary by an order of 10. Our results show the important role of the initial nucleation growth direction on the mechanical properties of the polymer crystals and may provide a new approach to the design of high‐performance polymer materials with tailored crystalline structures. [ABSTRACT FROM AUTHOR]

CdS‐based materials are extensively studied for photocatalytic water splitting. By incorporating Ag+ into CdS nanomaterials, the catalyst's charge carrier dynamic can be tuned for photo‐electrochemical devices. However, photo‐corrosion and air‐stability of the heterostructures limit the photocatalytic device's performance. Here, a one‐pot, single molecular source synthesis of the air‐stable AgCdS ternary semiconductor alloy nanostructures by heat‐up method is reported. Monoclinic and hexagonal phases of the alloy are tuned by judicious choice of dodecane thiol (DDT), octadecyl amine (ODA), and oleyl amine (OLA) as capping agents. Transmission electron microscope (TEM) and powder X‐ray diffraction characterization of the AgCdS alloy confirm the monoclinic and hexagonal phase (wurtzite) formation. The high‐resolution TEM studies confirm the formation of AgCdS@DDT alloy nanorods and their shape transformation into nano‐triangles. The nanoparticle coalescence is observed for ODA‐capped alloys in the wurtzite phase. Moreover, OLA directs mixed crystal phases and anisotropic growth of alloy. Optical processes in AgCdS@DDT nano‐triangles show mono‐exponential decay (3.97 ± 0.01 ns). The monoclinic phase of the AgCdS@DDT nanorods exhibits higher electrochemical hydrogen evolution activity in neutral media as compared to the AgCdS@ODA/OLA alloy nanocrystals. DDT and OLA‐capped alloys display current densities of 14.1 and 14.7 mA cm−2, respectively, at 0.8 V (vs RHE). [ABSTRACT FROM AUTHOR]

Elastomers and composites made thereof have wide applications, e.g., in automobile, aerospace, and civil engineering. Predicting fracture in such materials is crucial for efficient design and optimum utilization. These materials are oftentimes hyperelastic and anisotropic in nature and in general subjected to mixed mode loading rather than merely pure modes. Soft biological tissues can also be considered anisotropic hyperelastic materials. Computational modeling helps in studying the role of different sources influencing mixed-mode fracture. A unifying thermodynamically consistent anisotropic phase field formulation for modeling the mixed-mode fracture of hyperelastic soft materials like elastomers, elastomeric fiber-reinforced composites, and soft biological tissues at finite strains is proposed and formulated. To model the mechanical response of anisotropic hyperelastic materials subjected to mixed-mode loading, a coupled Neo-Hookean model with orthotropic anisotropy is adopted considering volumetric-deviatoric and a tension-compression decomposition. For modeling the complex crack initiation and propagation, a phase field method based on a power law criterion is adopted by considering a single order parameter as the damage variable. This model is suitable for capturing the overall response of soft fiber-reinforced elastomeric composites as well as soft biological tissues. The proposed model is validated by conducting fracture tests on (a) silicone elastomers, (b) unidirectional fiber-reinforced elastomeric composites, (c) natural rubber reinforced with black carbon, and (d) brain tissue reinforced with axons. The results obtained are compared with experimental and numerical investigations from literature. [ABSTRACT FROM AUTHOR]

To evaluate the mechanical behavior and the load transfer mechanisms of a geosynthetic-reinforced pile-supported (GRPS) embankment under traffic load, an analytical model is developed based on elastodynamic theory, and its solution is derived rigorously. Since the present model is continuum based, the displacement and stress distributions in the embankment can be obtained analytically. Additionally, the present model takes the anisotropic property of the reinforced layer into consideration. The governing equations of the model are solved by introducing Fourier expansions of the field variables and making use of the theory of differential equations. With the boundary and interface conditions, the solution of the system is determined. The influences of some critical parameters are investigated. Here we show the load velocity has a significant influence on the response of the system, especially when it approaches the critical point. The present results suggest that the maximum efficiency of a single pile Max{EPi} at v = 100 m/s is almost 2 times higher than its value at v = 1 m/s. Some other parameters, such as pile cap spacing, embankment height, and the stiffness ratio between subsoil and piles, also affect the distributions of EPi , while the total pile efficiency EP only depends on the supporting properties. Some practical suggestions are also presented based on the parametric studies. [ABSTRACT FROM AUTHOR]

This work aims to determine the effect of stresses caused by dislocation networks placed at the interface of a semiconductor heterostructure of the thin GaAs/Si system. In this case, we use a mathematical modeling by Fourier series expansion to numerically simulate the stresses for the two cases of isotropic and anisotropic elasticity in order to predict the mechanical behavior of the heterostructure in the presence of interfacial dislocations while respecting well-defined stress boundary conditions. The elastic stress relaxation is reached for a layer thickness threshold of the GaAs deposit on the Si substrate not exceeding 5 nm. [ABSTRACT FROM AUTHOR]

In this study, the anisotropy of Ti-35Nb-15Zr (at%) fabricated in situ using laser powder bed fusion (LPBF) was investigated for the first time. The effects of varying laser powers on the anisotropic microstructure and mechanical properties were investigated. The equiaxed grains growing in the horizontal section were finer than the β-columnar grains growing in the vertical section, and the grain size increased from 8.8 to 10.47 μm as the laser power increased. The difference in microstructure generally resulted in higher nanohardness in the horizontal Sect. (7.12, 6.70, and 6.49 GPa at 250, 275, and 300 W laser power, respectively) than in the vertical Sect. (5.41, 5.56, and 5.38 GPa at 250, 275, and 300 W laser power, respectively). The yield strength (1223.48 ± 27.67 MPa) and ductility (6.77 ± 0.48%) of the samples were both higher in the horizontal direction. The Young's modulus of the samples in the horizontal direction, which reached as low as 72.82 ± 0.77 GPa, were lower than those in the vertical section, with a minimum of 77.59 ± 1.89 GPa. With increasing laser power, the yield strength in the horizontal direction, Young's modulus, and yield strength in the vertical direction increased, whereas the yield strength in the vertical direction decreased. In particular, the Ti-35Nb-15Zr alloy exhibited better cellular activity than cast Ti6Al4V. All samples formed dense, bone-like apatite layers on the surface in different directions, demonstrating the great potential of the LPBF Ti-35Nb-15Zr alloy as an implant. [ABSTRACT FROM AUTHOR]

Due to the continuous increase in power density and power consumption, thermal management has become a crucial issue in electronic devices like integrated circuits. Polymer‐based thermal conductive composites possess excellent thermal and mechanical properties, making them ideal materials for thermal management in the modern microelectronic industry. In this work, we present a combination of filler hybridization strategy and 3D‐printing technology to synergistically enhance the thermal conductivity of graphite microplatelets (GMP)/alumina (Al2O3)/zinc oxide (ZnO)/polydimethylsiloxane (PDMS) composite (o‐GAZP). When the content of GMP reaches 4.5 vol%, the 3D‐printed composite material exhibits a directional thermal conductivity of up to 4.51 W m−1 K−1. This value is significantly higher than the thermal conductivity of a randomly mixed GMP/Al2O3/ZnO/PDMS composite (1.98 W m−1 K−1). The remarkable thermal conductivity can be attributed to the anisotropic structural design, which benefits from the orientation of GMP and the creation of a multi‐scale dense structure through filler compounding. Additionally, the presence of Al2O3 and ZnO effectively separates the GMP particles, preventing the formation of electron transfer pathways and improving the electrical insulation performance of the composites. Furthermore, the impact of the anisotropic structural design on the thermal conductivity of the composites was verified through finite element simulation. This study demonstrates that constructing efficient thermally conductive and electrically insulating pathways by densely packing highly oriented two‐dimensional anisotropic graphite‐based fillers with uniformly dispersed thermally conductive and electrically insulating fillers is a simple and effective method to enhance the composites' thermal conductivity, electrical resistivity, and mechanical properties simultaneously. These findings hold great potential for various scalable thermal‐related applications. By implementing this approach, composites can exhibit excellent thermal conductivity, high electrical resistivity, and superior mechanical performance. [ABSTRACT FROM AUTHOR]

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In this paper, we study the evolution of the gradient flow minimizing the anisoperimetric ratio of convex plane curves. It is shown that for any closed embedded initial curve, which is smooth and convex, the flow exists for all time and the evolving curves converge smoothly to a homothety of boundary of the Wulff shape, which is determined by anisotropic function. [ABSTRACT FROM AUTHOR]

Image-based motion-analysis systems typically place markers on the bodies of interest. The error in determining segment attitude from these markers is a function the marker position errors, the number of markers, and the spatial distribution of the markers. The spatial distribution includes two factors: the mean square distance of these markers to their geometric center, and the degree of anisotropy in the marker distribution. The purposes of this study were to: (1) present a metric which quantifies the marker spatial distribution (anisotropic to isotropic) and (2) examine the influence of marker distribution on the accuracy of rigid body attitude determination. To test the influence of the marker distribution on body attitude determination 1000 criterion attitudes were determined. These attitudes then had to be estimated for two marker sets for which the marker distribution metric, noise levels, and root-mean-square distance of the markers were systematically varied. Anisotropic marker distributions were shown to negatively affect the accuracy of attitude determination. The influence of anisotropic marker distributions on attitude accuracy could be blunted by increasing the number of markers, increasing the root-mean-square distance of markers from their geometric center, and reducing noise levels. These results have implications for the measurement of the attitudes of body segments. For example, the ability to have a large spatial distribution of markers and a large number of markers to maximize the measurement accuracy of segment attitude is different for a small segment such as the fifth metacarpal compared with the thigh. [ABSTRACT FROM AUTHOR]

In this work, an anisotropic constitutive model for equilibrium swelling of cellulose-reinforced salt-sensitive hydrogels is proposed and its capability is verified using the experimental data. This model is able to predict the swelling behavior of salt-sensitive hydrogels reinforced with fibers in different types of orientation such as perfectly aligned, uniform in-plane, and uniform volumetric. The model is implemented numerically in the finite element method framework. Several related parameters i.e., swelling ratio, principal stretches, true concentration of counter-ion and co-ion, and salt concentration are investigated both analytically and through finite element method (FEM). Good agreement between the analytical and numerical results indicates that the model can be used for simulating more complex structures including multi-layer strips and sheets. The results show that adding cellulose fibers to the hydrogel's medium leads to a significant enhancement in the strength of the material while preserving the inherent flexibility of the hydrogel. [ABSTRACT FROM AUTHOR]

Two types of additive manufacturing (AM) techniques, fused filament fabrication (FFF) and selective laser sintering (SLS), were employed to fabricate specimens from three widely used AM polymers: polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), and polyamide (PA): the first two using FFF and PA using SLS. The single‐edge notch bending (SENB) test was employed to measure the mode‐I fracture toughnesses of bulk and AM specimens in three directions relative to the printing direction. Unlike their bulk counterparts, AM polymers exhibited anisotropic fracture toughness. The degree of anisotropy in FFF‐PLA was much larger than FFF‐ABS and SLS‐PA. The smallest fracture toughness value for each AM polymer was achieved along the transverse printing direction. Different AM techniques affect fracture toughness differently. For instance, FFF is shown to increase PLA's plastic deformation, while SLS reduces PA's ductility. The decrease in fracture toughness is consistently observed when transitioning from bulk polymers to AM ones, reaching as much as 75%. This study provides insights into the fracture toughness of AM parts made via popular plastics, which are crucial for designing structural parts using FFF and SLS processes. Highlights: Additively manufactured polymers always exhibit some anisotropic fracture toughnessDifferent additive manufacturing techniques affect the fracture toughness differentlyFused filament fabrication increases polylactic acid's plastic deformationBut selective laser sintering reduces polyamide's ductility [ABSTRACT FROM AUTHOR]

As theoretical research further develops, coding metasurfaces have been widely studied and applied due to their uniqueness in digital characterization and sequence arrangement. In this work, based on highly conductive graphene‐assembled film (GAF), an ultralight anisotropic broadband coding metasurface (ABCM) is proposed. The GAF ABCM consists of 16 units with specific phase responses and enables complete metal substitution. By arranging the unit cells in a specific order, the GAF ABCM realizes the functions of anomalous reflection, polarization conversion, and radar cross‐section (RCS) reduction. Results validate that the GAF ABCM has a measured 10 dB normal incidence backward RCS reduction within the working frequency band of 7–18 GHz, which fully covers the X‐band and Ku‐band for radar application. Furthermore, due to the lightweight property of GAF, the density of the GAF ABCM is only 0.06 g/cm3 (surface mass density of 0.038 g/cm2). All results indicate that the lightweight GAF metasurface is promising in radar stealth and communication fields. [ABSTRACT FROM AUTHOR]

The unsteady Helmholtz type equation of anisotropic functionally graded materials (FGMs) is considered in this study. The study is to find numerical solutions to initial boundary value problems governed by the equation. A combined Laplace and boundary element method is used to solve the problems. The analysis derives a boundary-only integral equation that is used to compute the numerical solutions. The analysis also results in another class of anisotropic FGMs of applications. Some problems are considered. The numerical solutions obtained are accurate and consistent. [ABSTRACT FROM AUTHOR]

Objective Both the classical Dupuit model and the modified Dupuit model including infiltration are influenced by Dupuit's assumption and have potential systematic errors. Building a numerical model of well flow in an unconfined aquifer by characterizing the three-dimensional or axisymmetric two-dimensional (2D) flow is an essential approach to verify the performance of Dupuit-type models. Methods In this study, a 2D numerical model is proposed for the steady state well-flow in an unconfined aquifer, in which the control equation of seepage in the cylindrical coordinates is transformed equivalently to the Cartesian coordinates through parameter transformation, and the sectional 2D modelling is implemented via the MODFLOW finite-difference grid of cubic blocks. In the numeric model, the water level in the pumping well is a given condition, the flux across the seepage face is estimated by difference equation according to Darcy's law, the phreatic surface is identified by the treatment of dry and wet cells in MODFLOW, and the pumping rate is determined from the water debug calculation. Results Fine grids are constructed innumerical models of typical cases to obtain high-precision results, in which the relative error of the backwards estimated pumping rate is no more than 0.2%. This numerical model is used to check the Dupuit-type well-flow models. As indicated, the groundwater level estimated from the analytical formulas generally agrees well with the numerical modelling results, except that near the well, where the analytical solution underestimates the groundwater level due to ignoring the waterjump and the errors depend on the anisotropic permeability of the aquifer. When infiltration exists, the flow in the vicinity of watershed does not follow Dupuit's assumption. However, the estimated groundwater level on the watershed by modified Dupuit well-flow equation has a low level of relative error, which is less than 1%. Conclusion This numerical method is simple and practical however it is also influenced by limitations in MODFLOW.

Cu6Sn5-xAg alloys (x = 0, 3, 6; %, mass fraction) were synthesized using Ag as a dopant through a high-temperature melting technique. The microstructure of the alloy was analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), and other equipment, while the hardness of the alloy was measured to investigate the impact of Ag addition on the structure and microstructure of the Cu6Sn5 intermetallic compound. This study explored the influence of varying Ag contents on the properties of Cu6Sn5 intermetallic compounds, with calculations based on first principles revealing the mechanical properties and density of states of η′-Cu6Sn5 and its Ag-doped systems. The results indicated that Cu6Sn5-xAg alloys predominantly existed in three distinct forms, all exhibiting large masses without any impurities or precipitates. First-principle calculations demonstrated that Ag substitution in certain sites suppressed the anisotropy of the Young’s modulus of Cu6Sn5, particularly in the Cu1, Cu3, Sn1, and Sn3 positions, while the effect was less significant at the Cu2, Cu4, and Sn2 sites. The introduction of Ag through doping enhanced the covalent bonding within the η′-Cu6Sn5 structure, promoting the formation of a stable (Cu, Ag)6Sn5 structure.

Electrospun fibers of amorphous or low-crystallinity polymers typically exhibit a low molecular orientation that can hamper their properties and application. A key stage of the electrospinning process that could be harnessed to mitigate the loss of orientation is jet rigidification, which relates closely to the solvent evaporation rate. Here, we establish quantitative Raman methods to assess the molecular orientation and crystallinity of weakly crystalline poly(2,6-dimethyl-1,4-phenylene oxide) fibers with varying diameters. Our findings demonstrate that solvent volatility can be leveraged to modulate the orientation and crystallinity through its impact on the effective glass transition temperature (T g,eff) of the polymer jet during the electrospinning process. Specifically, a highly volatile solvent yields a higher and more sustained orientation (median ⟨ P 2⟩ of 0.53 for diameters < 1.0 µm) because its fast evaporation rapidly increases T g,eff above room temperature. This vitrification early along the jet path promotes the formation of an oriented amorphous phase and a moderate fraction of strain-induced crystals. Our data reveals that a high T g is a crucial parameter for reaching high orientation in amorphous or low-crystallinity polymer systems. Graphical Abstract This is a visual representation of the abstract. [ABSTRACT FROM AUTHOR]

Comprehensive Summary: With high water content, excellent biocompatibility and lubricating properties, and a microstructure similar to that of the extracellular matrix, hydrogel is becoming one of the most promising materials as a substitute for articular cartilage. However, it is a challenge for hydrogel materials to simultaneously satisfy high loading and low friction. Most hydrogels are brittle, with fracture energies of around 10 J·m−2, as compared with ∼1000 J·m−2 for cartilage. A great deal of effort has been devoted to the synthesis of hydrogels with improved mechanical properties, such as increasing the compactness of the polymer network, introducing dynamic non‐covalent bonds, and increasing the hydrophobicity of the polymer, all at the expense of the lubricating properties of the hydrogel. Herein, we develop a hydrogel material with anisotropic tubular structures where the compactness gradually decreases and eventually disappears from the surface to the subsurface, achieving a balance between lubrication and load‐bearing. The porous layer with hydrophilic carboxyl groups on the surface exhibits extremely low friction (coefficient of friction (COF) ∼0.003, 1 N; COF ∼0.08, 20 N) against the hard steel ball, while the bottom layer acts as an excellent load‐bearing function. What is more, the gradual transition of the tubular structures between the surface and the subsurface ensures the uniform distribution of friction stress between a lubricating and bearing layers, which endows the material with long‐lasting and smooth friction properties. The extraordinary lubricious performance of the hydrogels with anisotropic tubular structure has potential applications in tissue engineering and medical devices. [ABSTRACT FROM AUTHOR]

The flexibility and controllability of 3D printing technologies have made them popular for creating integrated wearable sensors. However, producing sensors with 3D anisotropic response is still difficult with current printing materials and techniques. To address this challenge, digital light process (DLP) printing technology with blading function to fabricate 3D anisotropic pressure and strain sensors is used. By applying blading‐induced shearing force, nanoalignment of carbon nanotubes (CNTs) in each layer is achieved, while the continuous liquid interface production of the DLP printing process facilitates good electrical communication between adjacent microlayers. The constructed 3D sensor displays high tensile and pressure responses up to 40 MPa and the ability to detect pressure changes in all directions. Additionally, the resistance anisotropy ratio range is adjustable. Finite‐element method (FEM) simulation shows that the relative change in resistance has an anisotropic distribution that aligns well with experimental results. The work would offer a new way to create 3D anisotropic pressure/strain sensors for advanced flexible and stretchable sensing applications. [ABSTRACT FROM AUTHOR]

Comprehensive Summary: With high water content, excellent biocompatibility and lubricating properties, and a microstructure similar to that of the extracellular matrix, hydrogel is becoming one of the most promising materials as a substitute for articular cartilage. However, it is a challenge for hydrogel materials to simultaneously satisfy high loading and low friction. Most hydrogels are brittle, with fracture energies of around 10 J·m−2, as compared with ∼1000 J·m−2 for cartilage. A great deal of effort has been devoted to the synthesis of hydrogels with improved mechanical properties, such as increasing the compactness of the polymer network, introducing dynamic non‐covalent bonds, and increasing the hydrophobicity of the polymer, all at the expense of the lubricating properties of the hydrogel. Herein, we develop a hydrogel material with anisotropic tubular structures where the compactness gradually decreases and eventually disappears from the surface to the subsurface, achieving a balance between lubrication and load‐bearing. The porous layer with hydrophilic carboxyl groups on the surface exhibits extremely low friction (coefficient of friction (COF) ∼0.003, 1 N; COF ∼0.08, 20 N) against the hard steel ball, while the bottom layer acts as an excellent load‐bearing function. What is more, the gradual transition of the tubular structures between the surface and the subsurface ensures the uniform distribution of friction stress between a lubricating and bearing layers, which endows the material with long‐lasting and smooth friction properties. The extraordinary lubricious performance of the hydrogels with anisotropic tubular structure has potential applications in tissue engineering and medical devices. [ABSTRACT FROM AUTHOR]

Anisotropic layered porous ceramics are crucial to satisfy the demand for devices with directional functions. However, challenges, such as complicated preparation processes and difficulties in regulating the oriented structure, severely limit their application. Here, multilayered mullite ceramics (MLMCs) with specific porosities and strongly anisotropy properties, were prepared by designing porous thin-layered units and an interlayer layout, in combination with a simple gel-casting. Benefiting from the suitable slurry properties, the samples did not show obvious defects, and a perfect bonding was observed between the layers. The optimized MLMCs exhibited a porosity of 65.12%, the differences in compressive and flexural strengths of 14 (± 0.7) and 5 (± 0.2) MPa in different pressure directions respectively, and the anisotropy factor of thermal conductivity up to 0.98, as well as exhibited good high temperature thermal insulation properties. Ultimately, the MLMCs formed transverse heat conductor and longitudinal heat insulation heat-transfer patterns, with promising applications in thermal insulation. [ABSTRACT FROM AUTHOR]

Some results on modeling and observation of infrasound propagation in the atmosphere in a presence of mesoscale and anisotropic wind velocity and temperature fluctuations are presented. The theoretical model of infrasound scattering from anisotropic wind velocity and temperature inhomogeneities of the atmosphere is developed. With this model, the appearance of the stratospheric, mesospheric, and thermospheric arrivals of the infrasound signals in the acoustic shadow zones is explained. The analytic relation between the wave field of the scattered infrasound signal and the vertical profile of the effective sound speed fluctuations is obtained. Using this relation, the vertical profiles of the fluctuations within the upper stratosphere (25–55 km) and the lower thermosphere (105–140 km) were retrieved from the waveforms and travel times of the signals recorded in the acoustic shadow zones. The theoretical frequency spectrum of the infrasound wavefield reflected from the fine-scale layered structure of the atmosphere is obtained and compared with the spectra of the observed stratospheric arrivals. [ABSTRACT FROM AUTHOR]

In this paper, we propose to study the existence of entropy solutions for the strongly nonlinear anisotropic elliptic equation Au + H(x,u, ∇u) = f in Ω, where f belongs to L¹(Ω), A is a Leray-Lions operator and H is a nonlinear lower order term with nonstandard growth with respect to |∇u| (i.e., such that |H(x, s, ξ)| ≤ c(x) + b(|s|) ∑i=1N |ξi|...), but without assuming the sign condition H(x, s, ξ)s ≥ 0. A concrete example is given to illustrate the existence result. [ABSTRACT FROM AUTHOR]

Elongated ellipsoidal liquid crystal microdroplet reorientation dynamics are discussed in this paper for biosensor applications. To investigate the effect of elongated droplets on nematic liquid crystal droplet biosensors, we simulated a model of a liquid crystal droplet using ellipse geometry. Director reorientation is examined in relation to the elongated droplet shape. In addition, we examined aspect ratio as a factor affecting biosensor response time in relation to surface viscosity and anchoring energy. Finally, the findings suggest that the aspect ratio should be taken into account when designing biosensors. These results can be used to develop more effective biosensors for a variety of applications. This model then predicts the director reorientation angle, which is dependent on the anchoring energy and surface viscosity. This model further suggests that both surface viscosity and homeotropic anchoring energy play an important role when it comes to the director reorientation angle. We developed and applied a nonlinear unsteady-state mathematical model utilizing torque balance and Frank free energy according to the Leslie–Ericksen continuum theory for simulating elongated nematic liquid crystal biosensor droplets with aqueous interfaces. Using the Euler–Lagrange equation, a transient liquid crystal–aqueous interface realignment is modeled by changing the easy axis when surfactant molecules are added to the interface. The realignment at the surface of the droplet is assumed to be driven by the effect of the surfactant, which causes an anchoring transition. According to the results, the response time of the biosensor depends on the aspect ratio. Therefore, the elongation has the potential to control biosensing response time. The result of our study provides a better understanding of director reorientation in elongated liquid crystal droplets in biosensing applications through the numerical results which are presented in this paper. [ABSTRACT FROM AUTHOR]

In the pursuit of advanced functional materials, the role of low-dimensional van der Waals (vdW) heterointerfaces has recently ignited noteworthy scientific interest, particularly in assemblies that incorporate quasi-2D graphene and quasi-1D nanocellulose derivatives. The growing interest predominantly stems from the potential to fabricate distinct genres of quasi-2D/1D nanoarchitecture governed by vdW forces. Despite the possibilities, the inherent properties of these nanoscale entities are limited by in-plane covalent bonding and the existence of dangling π-bonds, constraints that inhibit emergent behavior at heterointerfaces. An innovative response to these limitations proposes a mechanism that binds multilayered quasi-2D nanosheets with quasi-1D nanochains, capitalizing on out-of-plane non-covalent interactions. The approach facilitates the generation of dangling bond-free iso-surfaces and promotes the functionalization of multilayered materials with exceptional properties. However, a gap still persists in understanding transition and alignment mechanisms in disordered multilayered structures, despite the extensive exploration of monolayer and asymmetric bilayer arrangements. In this perspective, we comprehensively review the sophisticated aspects of multidimensional vdW heterointerfaces composed of quasi-2D/1D graphene and nanocellulose derivatives. Further, we discuss the profound impacts of anisotropy nature and geometric configurations, including in-plane and out-of-plane dynamics on multiscale vdW heterointerfaces. Ultimately, we shed light on the emerging prospects and challenges linked to constructing advanced functional materials in the burgeoning domain of quasi-3D nanoarchitecture. [ABSTRACT FROM AUTHOR]

We obtain the solutions of Einstein's field equations for an anisotropic fluid in a static spherically symmetric metric with off-diagonal elements. We also study the pioneer anomaly with the help of the obtained solutions. First, we derive analytical solutions to study sudden change in gravity in the radial and tangential directions of a non-homogeneous gravitational system by considering Π as a constant. Then we find other solutions by considering Π as a function of r in the space of gravitating object. We extend our solutions in the numerical limits to verify the unusual behavior of gravity at larger distances for the inhomogeneous system. We show a sudden increase in radial pressure for 𝑟𝜖[0, 20] as well as the tangential pressure for 𝜃𝜖[0, 𝜋], which may be treated as a factor of pioneer anomaly. We obtain the anomalous acceleration 2.493 × 10-11𝑚/𝑠2 at a distance of 20 AU from the Sun, which has better accuracy than other theoretical calculations when it is compared to the observed value. We also derive an expression for cosmological constant in terms of 𝑟. We establish that the cosmological constant is a function of 𝑟, which seems to be variable but its variability diminishes for large values of 𝑟. The results of this study are interesting and quite new. The selected spherically symmetric metric with off-diagonal elements provides a modified method to observe the phenomena of general relativity. [ABSTRACT FROM AUTHOR]

This article addresses challenges associated with anisotropic functionally graded media that are governed by the transient diffusion-convection equation. The authors seek to obtain numerical solutions for these problems by utilizing a combination of Laplace transform and boundary element method. To achieve this, a boundary integral equation is derived and a standard boundary element method is used to obtain numerical solutions, which are then inversely transformed using the Stehfest formula to obtain solutions in the time variable. The problems studied include those involving compressible or incompressible flow and media with quadratic, exponential, and trigonometric gradients. The findings suggest that the approach used to transform the variable coefficients equation into the constant coefficients equation is valid and the mixed Laplace transform and boundary element method is a simple and effective means of obtaining numerical solutions. The accuracy of the numerical solutions is also confirmed, and the impact of material anisotropy and inhomogeneity on the solutions is highlighted, suggesting that accounting for these factors is crucial for experimental studies. Additionally, the symmetry of solutions for symmetric problems is also verified for further validation of the numerical solutions. [ABSTRACT FROM AUTHOR]

Spinal cord injury (SCI) results in massive neuronal death, axonal disruption, and cascading inflammatory response, which causes further damage to impaired neurons. The survived neurons with damaged function fail to form effective neuronal circuits. It is mainly caused by the neuroinflammatory microenvironment at injury sites and regenerated axons without guidance. To address this challenge, a ferrofluid hydrogel (FFH) was prepared with Ferric tetrasulfide (Fe3S4), carboxymethyl chitosan, and gold. Its internal structural particles can be oriented in a magnetic field to acquire anisotropy. Moreover, Fe3S4 can release hydrogen sulfide (H2S) with anti-inflammatory effects under acidic conditions. Regarding in vitro experiments, 0.01g/ml Fe3S4 FFH significantly reduced the inflammatory factors produced by LPS-induced BV2 cells. Oriented and longer axons of the induced neural stem cells loaded on anisotropic FFH were observed. In vivo experiments showed that FFH reduced the activated microglia/macrophage and the expression of pro-inflammatory factors in SCI rats through the NF-κB pathway. Moreover, it significantly promoted directional axonal regrowth and functional recovery after SCI. Given the critical role of inhibition of neuroinflammation and directional axonal growth, anisotropic Fe3S4 FFH is a promising alternative for the treatment of SCI.

Specific finite detail modeling of the human body gives a capable primary enhancement to the prediction of damage risk through automobile impact. Currently, car crash protection countermeasure improvement is based on an aggregate of testing with installed anthropomorphic test devices (i.e., ATD or dummy) and a mixture of multibody (dummy) and finite element detail (vehicle) modeling. If an incredibly easy finite element detail version can be advanced to capture extra statistics beyond the abilities of the multi-body structures, it might allow advanced countermeasure improvement through a more targeted prediction of overall performance. Numerous research has been done on finite element analysis of broken femurs. However, there are two missing pieces of information: 1- choosing the right material properties, and 2- designing a precise model including the inner structure of the bone. In this research, most of the chosen material properties for femur bone will be discussed and evaluated.