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One of the key difficulties in applications of the effective media theories to real materials is the complex and "irregular" character of microstructures. However, in cases of moderate contrast between properties of the constituents, the sensitivity of the effective properties to microgeometries is much lower; it vanishes in the first approximation. The latter actually remains applicable at substantial (up to 70%–100%) contrast in properties. The effective elastic and conductive properties are considered as functions of property contrast between constituents. Whereas in the isotropic cases the Voigt–Reuss bounds provide guidance, in anisotropic cases these issues are less obvious. Two origins of effective anisotropies are discussed: (A) anisotropy of material constants and (B) geometric factors: non-random orientations of non-spherical inclusions. To the first order in contrast, the factor (A) is dominant, and factor (B) can be ignored (effective properties are independent of microgeometries, such as inhomogeneity shapes); the importance of factor (B) increases sharply with increasing contrast. For matrix composites (continuous matrices containing inhomogeneities), an interesting interplay takes place between the moderate contrast assumption and the non-interaction assumption (NIA). It shows that, in cases of moderate contrast, the NIA remains accurate at substantial concentrations. An application to monitoring fatigue of austenitic steel, whereby property contrast between the martensite and austenite phases is moderate, is discussed. Results of the second order in contrast, that are limited to the ellipsoidal inhomogeneities, are also given. [ABSTRACT FROM AUTHOR]

Data are heterogeneous when recorded in different time regimes or taken from multiple sources to some degree. Varying-coefficient models or mixture models are suitable for solving this type of problem. On one hand, existing models are quite complicated and computationally cumbersome especially for large-scale data. On the other hand, common effects among different data sources are unknown. Additionally, some existing models are unable to search the non linear relationship between response and covariates. To address these challenges, we aim at estimating common effects about non parametric regression when data are heterogeneous. Our proposed estimation method is based on basis function expansion. Adaptive basis series and fixed basis series are considered, respectively. We exploit maximin aggregation technique to get a simple non linear model, also the common effects, from all possible grouped data. The mean squared error and asymptotic distribution of the estimator are investigated. Simulation studies and real-data analysis are conducted to verify the efficiency of the estimation procedure. Comparing with ordinary least square estimator and averaging ordinary least square estimator, our proposed estimator can reduce the complexity of data sources and is more robust. [ABSTRACT FROM AUTHOR]

Discontinuous shear thickening in dense suspensions is accompanied by significant fluctuations in stress at a fixed shear rate. In this work, normal stress fluctuations are shown to have a one-to-one relationship with the formation and dissolution of local high-density regions. Namely, a burst in the force response corresponds to the spontaneous appearance of inhomogeneity. We observe that boundary conditions can significantly alter the spatiotemporal scale of these fluctuations, from short-lived to more sustained and enduring patterns. We estimate the occurrence frequency R and the average intensity Q of individual bursts/inhomogeneity events. The growth of R with the shear rate is the most rapid for the rigid boundary, whereas Q is nonmonotonic with confinement stiffness. Our results indicate that boundary conditions alter the development of inhomogeneity and thus the stress response under shear. [ABSTRACT FROM AUTHOR]

We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable. [ABSTRACT FROM AUTHOR]

In this work, the electrical and photoelectric properties of the near-surface and surface layers of silicon doped by diffusion with chromium atoms were investigated. The formation of an anomalous concentration of charge carriers in these regions, as well as an anomalously low mobility, was revealed. The specific conductivity of the near-surface layer with a thickness of 1÷5 μm turned out to be equal to (1.6÷9.9)·10³ Ohm-1·cm-1. The inhomogeneity of the crystal under study was determined by the light probe method. [ABSTRACT FROM AUTHOR]

Sprite halos are diffuse glow discharges in the D-region ionosphere triggered by the quasi-electrostatic (QES) fields of lightning discharges. A three-dimensional (3D) QES model is adopted to investigate the effect of ionospheric electron density on sprite halos. The electron density is described by an exponential formula, parameterized by reference height (h') and sharpness (β), and the local inhomogeneity has a Gaussian density distribution. Simulation results indicate that the reference height and steepness of the nighttime electron density affect the penetration altitudes and amplitudes of normalized electric fields, as well as the altitudes and intensities of the corresponding sprite halos optical emissions. A comparison of the daytime and nighttime conditions demonstrates that the daytime electron density profile is not favorable for generating sprite halos emissions. Furthermore, the pre-existing electron density inhomogeneities lead to enhanced local electric fields and optical emissions, potentially offering a plausible explanation for the horizontal displacement between sprites and their parent lightning, as well as their clustering. [ABSTRACT FROM AUTHOR]

The spectral problem of determining the optimal distribution of mechanical properties of an arbitrary inhomogeneous body taking into account damping is investigated. The optimisation problem consists in finding the maximum first natural frequency. Damping is taken into account in the framework of the linear viscoelasticity model on the basis of the complex modules concept for the standard viscoelastic body model. The functions characterising the instantaneous and long-time modules are used as control functions. The problem formulation includes isoperimetric conditions that are imposed on the control functions and determine their average volume distribution. A Relye functional is constructed, and the optimality condition, which consists in the constancy of the potential energy, is found in a variational manner. As a model problem the problems of maximisation of the first natural frequency (bending and longitudinal vibrations) of a functionally graded cantilever beam with consideration of damping are considered. Analytical expressions for the laws of variation of the instantaneous and long-range modules are obtained. It is checked that the problem in the limiting case (when the relaxation time is equal to zero) is reduced to the elastic case. To determine the optimal value of the first natural frequency, a cubic equation is constructed and solved numerically. Asymptotic formulae for determining the optimal natural frequency at small values of relaxation time are obtained. Calculations have been carried out to evaluate the optimality of the obtained solution. For example, in comparison with the case of constant modules, the gain in the value of the first natural frequency is about 27% for the case of bending.

The susceptibility of the human Red Blood Cells (RBCs) under the action of magnetic fields, either serves as a biomarker in medical tests, e.g.. Magnetic Resonance Imaging, Nuclear Magnetic Resonance, Magnetoencephalography, or it is used in diagnostic and therapeutical processes, e.g.. magnetophoresis for cell sorting. In the present manuscript we provide analytical expressions for the magnetic potential and the magnetic field strength vector, when a magnetic field is applied to a RBC, modeled as a two-layered inverted spheroid. We introduce this way in the model the biconcave shape of the RBC and its structure (membrane and cytocol) in a more realistic representation, as until now, the RBC's shape was considered either as a sphere or a spheroid. The solution inside the RBC is obtained in R-separable form in terms of Legendre functions of the first and of the second kind and cyclic trigonometric functions, by applying appropriate boundary conditions on each layer. Our results reveal a non-uniform magnetic field inside the RBC. Parametric study of the solution, for various values of the physical properties of the RBC, is also provided, demonstrating the diamagnetic or the paramagnetic property of the RBC, which is strongly related to the health condition of the blood. The obtained solution may also serve for the justification of experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how the geometrical parameter of spheroidicity, which quantifies the deviation from spherical symmetry, influences the complexity of self-gravitating, static systems. We employ the concept of complexity in self-gravitating systems as formulated by Herrera et al. (Phys. Rev. D 97, 044010, 2018) and apply it to various models of compact stellar structures, all set within the framework of the Vaidya-Tikekar (VT) background geometry. Specifically, we analyze three models: (i) the anisotropic compact stellar model by Das et al. (Gen. Relativ. Gravit. 52, 101, 2020), constrained by the Karmakar condition, (ii) the stellar model by Das et al. (Eur. Phys. J. C 84, 13, 2024) employing the VT metric ansatz under the vanishing complexity condition, and (iii) the compact stellar model using a polytropic equation of state with the VT metric ansatz (Baskey et al., New Astron. 108, 102164, 2024). These models were selected based on whether their solutions are complexity-free or not. We establish a connection between the complexity factor and the spheroidal parameter to analyze how pressure anisotropy and density inhomogeneity, as constituent components, are influenced by this geometric parameter. Our findings indicate that deviations from spherical symmetry lead to a marked increase in the complexity of the stellar structure for all the models based on VT metric ansatz. Moreover, our results indicate an inconsistent pattern in the dependence of the complexity factor ( Y TF ) and its components on spheroidicity ( K ), demonstrating that this relationship is both model-dependent and is not generic. [ABSTRACT FROM AUTHOR]

The potential of paper and paperboard as fiber-based materials capable of replacing conventional polymer-based materials has been widely investigated and evaluated. Due to paper’s limited extensibility and inherent heterogeneity, local structural variations lead to unpredictable local mechanical behavior and instability during processing, such as mechanical forming. To gain a deeper understanding of the impact of mechanical behavior and heterogeneity on the paper forming process, the Finite Element Method (FEM) coupled with continuum modeling is being explored as a potential approach to enhance comprehension. To achieve this goal, utilizing experimentally derived material parameters alongside stochastic finite element methods allows for more precise modeling of material behavior, considering the local material properties. This work first introduces the approach of modeling heterogeneity or local material structure within continuum models, such as the Stochastic Finite Element Method (SFEM). A fundamental challenge lies in accurately measuring these local material properties. Experimental investigations are being conducted to numerically simulate mechanical behavior. An overview is provided of experimental methods for material characterization, as found in literature, with a specific focus on measuring local mechanical material structure. By doing so, it enables the characterization of the global material structure and mechanical behavior of paper and paperboard.

Controlling repeated thermal cycling is one of the key mechanisms to design microstructures in the interlayer regions for narrow gap laser wire filling welding (NGLWFW) of austenite stainless steels. Herein, the optimization of process parameters for individual layers is tailored to customize the molten pool morphology during the NGLWFW process, facilitating precise control over the microstructure and, consequently, enhancing both mechanical properties and corrosion resistance of the joint. The results showed that the molten pool morphology acquired by simulation are obviously diverse from the bottom zone (BZ), middle zone (MZ) to upper zone (UZ) of the welded joint ascribed to the high heat accumulation effect, leading to the variation of microstructure. At BZ, the combination of smaller grain size and reduced dendrite spacing reduce the number of corrosion sites and promote the formation of a denser and more uniform corrosion product layer. Additionally, the diverse grain orientation, characterized by lower texture strength, facilitated a more uniform distribution of elements. Furthermore, the significantly higher content of δ-ferrite showing smallish shape disrupted the directional growth of austenite columnar grains, contributing to the excellent corrosion resistance observed at the BZ.

The authors study the effect the temperature (300–450°C) and period (0–20 min) of annealing have on the parameters (barrier height and ideality factor) and homogeneity of Au/Pt/Ti/i(n)‒In0.52Al0.48As(001) Schottky barriers. The homogeneity of the Schottky barriers is determined by analyzing the temperature dependences of their parameters in the range of 80–350 K and the Richardson plots in the Tung model. [ABSTRACT FROM AUTHOR]

A 3D problem in linear elasticity is considered for a thin inhomogeneous layer subject to transverse compression. For the first time, the effect of arbitrary vertical inhomogeneity is elucidated. Two sets of boundary conditions along the faces of the layer are adapted for modelling transverse compression. Robust asymptotic formulae involving repeated integrals across the thickness are derived for displacements and stresses. As an illustration, numerical results are presented for the elastic moduli having a transverse parabolic variation. The obtained results have a potential to be implemented in modern technology, including manufacturing and design of functionally graded materials. [ABSTRACT FROM AUTHOR]

In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous rod for modeling soft manipulators. The inhomogeneity is addressed by considering the pressure actuation as part of the rod's constitutive laws, resulting in shifting the neutral axis. This shift is investigated for a soft manipulator with three parallel fiber-reinforced actuators. Furthermore, a fiber-reinforced actuator is modeled using nonlinear continuum mechanics to extract the effect of radial pressure on axial deformation and is combined with Cosserat model. Finally, several numerical methods are employed to solve the proposed model and validated by a series of experiments. [ABSTRACT FROM AUTHOR]

The potential of paper and paperboard as fiber-based materials capable of replacing conventional polymer-based materials has been widely investigated and evaluated. Due to paper's limited extensibility and inherent heterogeneity, local structural variations lead to unpredictable local mechanical behavior and instability during processing, such as mechanical forming. To gain a deeper understanding of the impact of mechanical behavior and heterogeneity on the paper forming process, the Finite Element Method (FEM) coupled with continuum modeling is being explored as a potential approach to enhance comprehension. To achieve this goal, utilizing experimentally derived material parameters alongside stochastic finite element methods allows for more precise modeling of material behavior, considering the local material properties. This work first introduces the approach of modeling heterogeneity or local material structure within continuum models, such as the Stochastic Finite Element Method (SFEM). A fundamental challenge lies in accurately measuring these local material properties. Experimental investigations are being conducted to numerically simulate mechanical behavior. An overview is provided of experimental methods for material characterization, as found in literature, with a specific focus on measuring local mechanical material structure. By doing so, it enables the characterization of the global material structure and mechanical behavior of paper and paperboard. [ABSTRACT FROM AUTHOR]

Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang ("Exact solutions of a kdv equation with variable coefficients via exp-function method," Nonlinear Dynam., vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed. [ABSTRACT FROM AUTHOR]

The propagation characteristics of dust acoustic shock waves have been investigated in an unmagnetized nonuniform dusty plasma containing dust grains with nonadiabatic changed charges and different size, electrons and ions modeled by kappa distribution. The modified Korteweg–de Vries Burgers equation is derived by using the standard reductive perturbation technique. Numerical and theoretical analyses show that there are two different shock structures, that is, oscillatory shock structures and monotonous shock structures, in system. The results show that the dust size with power law distribution and kappa parameters have an important influence on dust acoustic shock waves. [ABSTRACT FROM AUTHOR]

ABSTRACTIn this study, Al-Zn-Mg-Cu alloy components were prepared using wire arc additive manufacturing (WAAM). Through multi-scale characterisation technology, performance testing and slow strain rate tensile (SSRT) testing, the microstructure, mechanical properties and stress corrosion cracking (SCC) susceptibility of WAAM Al-Zn-Mg-Cu components were studied, revealing the generation mechanism of inhomogeneity and anisotropy. The results show that with the increase of WAAM thermal cycles, the matrix precipitates (MPs), grain boundary precipitates (GBPs) and precipitation-free zones (PFZ) evolve in different paths and increase to varying degrees, resulting in performance decrease and increase in stress corrosion susceptibility, so the inhomogeneity is mainly attributed to differences in precipitated phases. The Inter-layer inclined to the scanning direction and the Inner-layer inclined to the building direction led to anisotropy in tensile strength and SCC behaviour, so the anisotropy is mainly attributed to the grain orientation and fracture mode.

Inhomogeneities in the near-surface region of diffusion-doped silicon with manganese atoms were studied using the local photo-EMF method and photovoltage and photoconductivity signals were detected. It has been established that the inhomogeneous region is located at a depth of 3÷35 μm from the surface of the crystal. The magnitude of photo-EMF in these layers does not change monotonically from point to point. It was revealed that the photo-EMF spectra depend on the wavelength of the irradiated light, while the shape of the areas and their shift are related to the penetration depth of laser radiation. The photo-EMF signal increases to a depth of ~25 µm from the surface, then saturates and from ~30 µm smoothly decreases and completely disappears at a depth of ~40 µm. The magnitude of the internal electric field was determined using the Tauc method. A model of the structure of the near-surface region of diffusion-doped silicon with manganese is proposed.

The paper demonstrates the analysis of the stress and strain states of an inhomogeneous structure with an axial symmetrical spheroidal inclusion in an infinite solid under a remote uniform tension load derived from the conditions of the theory of elasticity. With respect to the inhomogeneous structure, the deformations produce constraints that require a complete 3-dimensional analysis in the z, r-coordinate system. The solution generates the stress state of the inclusion and at the interface of the matrix. Spheroidal inclusions in an uniform outer tension stress field deform self-similarly to a rather elongated spheroid. With respect to the compatibility condition and depending on the different elastic moduli and Poisson's ratios in the inclusion and matrix, the solution procedure leads to a system of two linear equations with the magnitudes of the two tractions as unknowns. In this way, the solution is shortened to a twofold statically indeterminate system. The analysis performed leads to an exact solution of the general spheroidal problem in a formulation of stress concentration factors considering the different stiffness parameters of inclusion and matrix. [ABSTRACT FROM AUTHOR]

Summary: Electrical systems are traditionally modeled as homogeneous ladder networks, disregarding the inherent inhomogeneity found in real‐world systems. This can result in inaccuracies in analysis and design. The driving point impedance (DPI) is a crucial parameter for studying electrical systems, as it can be conveniently measured at the terminals. However, existing methods for calculating DPI have limitations, including increased complexity, high computational demands, convergence issues, and challenges in capturing high‐frequency effects. A new approach for computing DPI of inhomogeneous ladder networks, reducible to series and shunt impedance circuit form, is introduced in this research. The method is based on state‐space formulations and projective matrix analysis. It offers improved accuracy as compared with existing methods and can be applied to a wide range of networks. Simulation results from a six‐section mutually coupled inhomogeneous ladder network validate the effectiveness of the proposed approach. This research addresses the disregarded factors of inhomogeneity and mutual coupling within traditional approaches, presenting a significant advancement in the analysis and design of electrical systems. [ABSTRACT FROM AUTHOR]

Inhomogeneities in the near-surface region of diffusion-doped silicon with manganese atoms were studied using the local photo-EMF method and photovoltage and photoconductivity signals were detected. It has been established that the inhomogeneous region is located at a depth of 3÷35 μm from the surface of the crystal. The magnitude of photo-EMF in these layers does not change monotonically from point to point. It was revealed that the photo-EMF spectra depend on the wavelength of the irradiated light, while the shape of the areas and their shift are related to the penetration depth of laser radiation. The photo-EMF signal increases to a depth of ~25 μm from the surface, then saturates and from ~30 μm smoothly decreases and completely disappears at a depth of ~40 μm. The magnitude of the internal electric field was determined using the Tauc method. A model of the structure of the near-surface region of diffusiondoped silicon with manganese is proposed. [ABSTRACT FROM AUTHOR]

T1-weighted (T1w) MRI has low frequency intensity artifacts due to magnetic field inhomogeneities. Removal of these biases in T1w MRI images is a critical preprocessing step to ensure spatially consistent image interpretation. N4ITK bias field correction, the current state-of-the-art, is implemented in such a way that makes it difficult to port between different pipelines and workflows, thus making it hard to reimplement and reproduce results across local, cloud, and edge platforms. Moreover, N4ITK is opaque to optimization before and after its application, meaning that methodological development must work around the inhomogeneity correction step. Given the importance of bias fields correction in structural preprocessing and flexible implementation, we pursue a deep learning approximation / reinterpretation of the N4ITK bias fields correction to create a method which is portable, flexible, and fully differentiable. In this paper, we trained a deep learning network "DeepN4" on eight independent cohorts from 72 different scanners and age ranges with N4ITK-corrected T1w MRI and bias field for supervision in log space. We found that we can closely approximate N4ITK bias fields correction with naïve networks. We evaluate the peak signal to noise ratio (PSNR) in test dataset against the N4ITK corrected images. The median PSNR of corrected images between N4ITK and DeepN4 was 47.96 dB. In addition, we assess the DeepN4 model on eight additional external datasets and show the generalizability of the approach. This study establishes that incompatible N4ITK preprocessing steps can be closely approximated by naïve deep neural networks, facilitating more flexibility. All code and models are released at https://github.com/MASILab/DeepN4. [ABSTRACT FROM AUTHOR]

A rotating system that includes an initially stressed piezo-electric substrate was the subject of an analytical study of the SH waves. The substrate and vacuum bonding are in good contact with the corrugation, and the top border is treated as stress-free corrugation. About the upper barrier that is both electrically open as well as electrically short scenarios are taken into consideration. Dispersion equations for circumstances with a corrugated interface that are both electrically short as well as electrically open have been found. The SH wave characteristics through the framework suggested and circumstances dependent on different geometrical and physical factors have been investigated based on the numerical findings. The study looks at the simultaneous simulated outcomes of a number of physical factors that were produced in Mathematica 7 and include rotation, inhomogeneity, phase velocity, initial stress, and corrugated interface of SH wave distribution in a structure under discussion. The model under examination has potential applications in the creation of surface acoustic wave devices.

In this manuscript, we introduce a totally asymmetric simple exclusion process on a dynamic lattice with inhomogeneity to model motor-based long-range transport along microtubules (MTs) which exhibit cycles of growth, shortening and regrowth at their growing tips. By mean-field approximation and numerical simulations, we explore phase diagrams for the particle density near the dynamic end of the lattice as well as over the entire lattice. In particular, we find seven different phases for the density over the entire lattice and explore the corresponding phase diagram by analytical analysis. Interestingly, we find that the density may have a linear profile in part of the lattice. When the lattice has a defect, we separate the lattice into two subsystems: a right subsystem with fixed length and a defect in the middle and a left subsystem with dynamic length. When the right subsystem is in maximum-current phase, we calculate an analytical approximation of the density away from the boundaries and the defect site and the density is in association with the reduced hopping rate at the defect site; the density at the left side of the defect site serves as the effective entry rate of the left subsystem. We find that with defects, the linear profiles no longer appear at the left end of the left subsystem and only five possible phases could occur. This is a step-forward to a more comprehensive mathematical description of intracellular long-range transport of organelles along MTs with instability.

Along with the battery charge/discharge processes, the migration of the Li ions inevitably leads to an inhomogeneous distribution of the battery internal electrochemical and thermal characteristics, deteriorating the battery capacity and safety. In this work, the internal characteristics of a 20 Ah pouch LiFePO4 lithium-ion battery have been investigated based on a 3D electrochemical-thermal coupled model. It is found that the reduction of the particle size for either the cathode or anode would increase the battery capacity. Moreover, with the modulation of the thickness of cathode (Lpos) and convective heat transfer coefficient (h), the homogeneity of solid lithium concentration and temperature has been optimized. A relatively smaller Lpos and an h higher than the critical value should be adopted. From the aspect of thermal distribution, as the discharge rate increases, the irreversible reaction heat always dominates, while the proportion of ohmic heat among the total heat increases, and the high temperature region always locates on the inner sides of the tabs. The methodology proposed in this work could be applied to pouch batteries with more repeated cell units and larger sizes.

The present study investigated the inhomogeneity of microstructure and properties of hybrid laser-MIG welded 10-mm-thick 316L/AH36 joints. The study focused on the inhomogeneity of the laser zone, hybrid zone, and transition zone. The temperature field was simulated using ABAQUS and showed a higher cooling rate in the laser zone. As a result, the microstructure in the laser zone was dominated by martensite while that in the hybrid zone was composed of 84 % austenite and 16 % ferrite. The laser zone showed poorer impact toughness and corrosion resistance than the hybrid zone. However, the corrosion resistance of the whole weld was the worst. Because the inhomogeneous microstructure formed a galvanic couple that accelerated the corrosion process. This work indicated that the energy ratio (the ratio of laser to arc energy) should be considered in the welding of dissimilar thick steel to reduce the inhomogeneity in the two zones and obtain a desirable property balance among hardness, toughness, and corrosion resistance.

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young's modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson's ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated. [ABSTRACT FROM AUTHOR]

Purpose: This study analyzed the impact of initial stresses on the propagation of Love-type waves in a fiber-reinforced viscoelastic layer situated between an isotropic inhomogeneous half-space and an orthotropic viscoelastic layer. The aim of the purposed work is to investigate how various factors such as initial stresses, viscoelastic properties, thickness ratio, inhomogeneity, and reinforcement affect wave propagation in the layered structure. Methods: The separable variable method is used to obtain the displacement components for the considered layers and half-space. By applying suitable boundary conditions, the dispersion relation for Love-type wave propagation derived. The dispersion relation was then examined for different cases, considering factors such as initial stresses, viscoelastic properties, thickness ratio, inhomogeneity, and reinforcement equal to zero. Numerical computations were performed using the MATHEMATICA software, and the results were graphically depicted. Results: The study successfully obtained the dispersion curves, which illustrated the influence of various parameters on Love-type wave propagation. The results showed how initial stresses, viscoelastic properties, thickness ratio, inhomogeneity, and reinforcement affected the wave propagation behavior. Conclusion: The findings of the study confirmed the validity of the mathematical model developed in this study, as the derived dispersion relation simplified the pre-existing velocity wave equation for Love waves. The analysis of dispersion curves demonstrated the significant effects of initial stresses and other parameters on the phase and damping velocity of the Love-type wave in the fiber-reinforced viscoelastic layer. The study enhances our understanding of Love wave propagation and its practical applications in structural engineering, earthquake engineering, non-destructive testing, material science, and geophysics. [ABSTRACT FROM AUTHOR]

Solid Oxide Fuel Cell (SOFC) stacks are one of the most critical modules in industrial SOFC energy conversion systems. Although the detailed multiphysics distribution has been elaborately studied with accurate 3-dimensional (3D) models, development and validation of agile stack model is yet inadequate. Due to slow and tedious meshing and simulation, fast prototyping of stacks remains a challenge. Therefore, a 30-cell stack was tested at varied temperatures and gas flowrates and a real-time transient layer-resolved stack model is established and calibrated using the measured data, which gives a Root-Mean-Square (RMS) prediction error of 2.21% for measured voltages and 1.53 °C for measured temperatures. With layer resolution, the stack model shows the voltage, average temperature, as well as fuel and air flowrates of each cell. Moreover, the stack model reveals the relation of voltage distribution at varied fuel flowrates with temperature distribution. Furthermore, the stack model is potentially applicable to stack scaling effects, or designing Balance of Plant (BoP). [Display omitted] • An accurate layer-resolved stack model for voltage/temperature distributions. • Low computational cost of the model enabling agile and real-time applications. • Explained the role of operating conditions on flowrate inhomogeneity. • Revealed strong impact of temperature on stack voltage distribution. [ABSTRACT FROM AUTHOR]

The current study examines the behavior of an SH wave traveling over a functionally graded magneto-elastic substrate arrangement. At the substrate-vacuum interface, two irregularities with different shapes—rectangular and parabolically shaped—are considered in electrically and magnetically open cases and electrically and magnetically short cases. A study is also done on the combined impact of inhomogeneity, depth source, and irregularity. With the help of the Fourier transform, inverse Fourier transform, and perturbation technique, complex frequency relation has been derived for each type of irregular interface. The results’ key characteristics are highlighted. In order to know the impact of the parameters involved, a particular model consisting of BaTiO3- CoFe2O4 magneto-electro-elastic material has been taken. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. This calculation model could be the ideal match for laminated FGMEE structures utilized as surface acoustic wave devices since the variation of the film's magneto-electromechanical characteristics changes gradually with depth and throughout the production process (SAW). As a result, it can serve as a theoretical foundation for the design of high-performance SAW devices. [ABSTRACT FROM AUTHOR]

The propagation of light wave around planets is studied in this paper. There are planets having an atmosphere with permittivity which is high close to the planet surface and gradually decreases with elevation. Based on the results of our investigations when the light beam propagates parallel to the layers of atmosphere, its propagation direction is gradually deviating from the straight line toward higher permittivity layers. This way the light wave follows a curved route. The aim of the paper is to provide a qualitative picture for the phenomenon of light wave propagation bending around cosmic planets. Some planets have no atmosphere. Their surface is not smooth, in addition to plains there are hills and mountains with varying heights. Therefore, dielectric layers parallel to the planet surface can be considered by an equivalent average permittivity which is high at the planet surface and gradually decreases with the elevation. As its consequence the light beam tangentially incident to the planet surface deviates from the straight line and follows a curved route. Based on the results of present investigations, it is not necessary to assume that the cosmic space is curved close to a planet containing a huge mass. [ABSTRACT FROM AUTHOR]

The paper describes a method for calculating critical parameters of an inhomogeneous superconducting layer surrounded by nonsuperconducting layers. The calculation is performed using Ginzburg‒Landau equations modified for a thickness-inhomogeneous superconducting layer. The effect of adjacent nonsuperconducting layers is specified using general boundary conditions to these equations. Dependences of the critical current of a superconducting layer on the external magnetic field is calculated numerically. It is shown that for a layer of inhomogeneous thickness, in the model of which the effect of adjacent layers is introduced, an estimate of the critical current yields lower values than those for a homogeneous layer without any influence of boundaries. It is found that at a certain value of the external magnetic field, the critical current is independent of the degree of the superconducting layer inhomogeneity. In this case, the influence of adjacent layers on its superconducting state does not lead to a significant change in the value of this field. [ABSTRACT FROM AUTHOR]

This study is mainly focused on the behavior change of shear waves. These waves propagate through an inhomogeneous sandwiched water-saturated porous layer in between inhomogeneous elastic layer and inhomogeneous sandy half space under the assumption of non-local theory. Different types of inhomogeneities based on the depth of the layers have been considered in terms of elastic moduli and densities of the medium. Due to the availability of fluid in the second layer, we consider loose bonding at the interfaces in between these three layers, as fluid movement through the interfaces may be possible. A complex dispersion equation has been derived with respect to the boundary conditions. Real and imaginary parts of the dispersion equation provide us with the phase velocity of shear wave and dissipation due to loose bonding at the interfaces, respectively. This dispersion equation has been solved numerically with the help of Newton Raphson method. For validation of the present problem, the numerical solution of dispersion equation has been depicted here graphically in terms of phase velocity c c 2 of shear wave vs. non-dimensional wave number k H 1 (where k is the wave number and H 1 is the thickness of the second porous layer). Also, we discuss about the impact of depth ratios, inhomogeneity of the medium, non-local parameters, loose bonding, and porosity of the sandwiched layer on the propagation of the shear wave. [ABSTRACT FROM AUTHOR]

For large-scale device fabrication, information about film inhomogeneities is crucial for high fabrication yield. In this work, inhomogeneities in two-inch diameter heavily boron-doped nanocrystalline diamond (BNCD) films have been studied. Two BNCD films were grown using chemical vapour deposition (CVD) with different boron-to-carbon (B/C) ratios. Their superconducting properties were measured as a function of distance from the centre of the film. The critical temperature (Tc) and critical magnetic field (Hc2) decreased radially outwards from the centre for both films. Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) and scanning electron microscopy (SEM) were done on the samples to pinpoint the underlying explanation for the observed behaviour. Raman spectroscopy suggested a reduction in boron concentration and diamond purity over both films while moving radially outwards from the centre. XPS data from both films, however, did not show similar behaviours to that observed from the Raman data for the B/C ratios or diamond content. The AFM scans and SEM analysis showed a decreasing grain size further away from the film centre irrespective of the B/C ratio. This is due to the film being thinner at the edges when compared with the centre of the film. Raman analysis showed that the film with the higher B/C ratio had a higher diamond purity across the film. As expected, the film with a higher B/C ratio showed a more robust superconducting behaviour. The observed reductions in boron concentration, diamond purity, film thickness and decreased grain sizes are responsible for the diminishing superconductivity at the edge of the films.

Decreasing the freezing time of the cold storage heat exchanger was an effective way to reduce the risk of cold chain breakage and the fluctuation of cold chain temperature. A validated unsteady mathematical model of the cold storage heat exchanger was established to analyze the transient evolution of temperature, velocity, ice distribution, and heat transfer coefficient for different diameters of heat transfer tubes and coolant temperatures. The results showed that there were four stages of temperature in the cold storage heat exchanger, namely the primary cooling stage, the freezing stage, the secondary cooling stage, and the constant temperature stage. The ice fraction distribution and the heat transfer coefficient were inextricably linked to the water's natural convection. The average heat transfer coefficient decreased with decreasing coolant temperature and increasing heat transfer tube diameters. The freezing time decreased with the coolant temperature and the diameter of the heat transfer tubes decreasing. The tendency of the inhomogeneity of ice distribution first increased with the ice fraction up to 0.75 and then decreased with the ice fraction over 0.75. The inhomogeneity decreased with the coolant temperature increasing when the diameter of the heat transfer tubes was greater than 2 mm.

The microstructure and performance homogeneity of 80 mm thick ultra-wide 7B50-T7751 plate with different widths and thicknesses were studied by means of mechanical testing machine and scanning electron microscope, and the fatigue properties were compared and discussed with 7050-T7451 plate. The results show that the ultra-wide 7B50-T7751 plate has excellent mechanical properties. In L and LT directions, the tensile yield strength of 1/2 thickness reaches up to 568 MPa and 545 MPa, and the tensile strength reaches up to 612 MPa and 591 MPa, the compressive yield strength reaches up to 575 MPa and 587 MPa, the fracture toughness in L-T direction and T-L direction reaches 30.16 MPa·m1/2 and 26.47 MPa·m1/2, respectively. The ultra-wide thick plate exhibits certain anisotropy at different width positions, the performance homogeneity in LT direction tends to be better than in L direction. Performance at different width positions with 1/4 thickness shows little difference, while the performance at the edge of 1/2 thickness is better than that of the center. No obvious texture exhibits at 1/4 thickness, however, the main textures at the center of 1/2 thickness are S texture and Brass texture, and the main textures at the edge are R texture, S texture and Brass texture. When the stress ratio is 0.06, the T-L anti-fatigue crack growth rate performance of ultra-wide 7B50-T7751 thick plate is better than 7050-T7451 plate with the same thickness. The fatigue limit of LT smooth sample (Kt=1) is about 7.6% inferior than that of 7050-T7451 plate, while the fatigue limit of notch sample (Kt=3) is about 3.7% higher.

Based on the model of in-plane oscillations of inhomogeneous prestressed plates, the new inverse problems of identifying the components of the prestress tensor via acoustic response probing are considered for the plates with and without holes and inclusions; the prestress components are assumed to be functions of two coordinates. Prestresses were set as a result of solving auxiliary problems of static loading of plates by some initial mechanical load. To solve the main and auxiliary problems of calculating the plates’ displacement functions, a finite element (FE) scheme was developed based on the derived corresponding weak problem statements, implemented in the form of software systems in the FE package FreeFem++. Rectangular plates clamped along one face, both solid and having a hole or a rigid insert, were considered. Inverse problems of identification of three prestress functions depending on two coordinates are formulated on the basis of additional data about the acoustic response on the non-clamped edges of the plates as a result of considering several sets of probing loads at several frequencies. In view of the nonlinearity of the inverse problems under study, an iterative approach was developed to solve them, which combines solving the direct problems for current approximations of the desired functions and the determination of the corresponding corrections from the operator equation built at each iteration. To solve the operator equation, a projection method has been employed that allows one to present the corrections in the form of expansions in terms of some smooth given functions and reduce the problem solution to the study of ill-conditioned SLAEs with respect to sets of the expansion coefficients using the A. N. Tikhonov method. The results of computational experiments on the simultaneous identification of two-dimensional prestress fields corresponding to various types of initial actions on the considered plates are discussed.

Sprite halos are diffuse glow discharges in the D-region ionosphere triggered by the quasi-electrostatic (QES) fields of lightning discharges. A three-dimensional (3D) QES model is adopted to investigate the effect of ionospheric electron density on sprite halos. The electron density is described by an exponential formula, parameterized by reference height (h’) and sharpness (β), and the local inhomogeneity has a Gaussian density distribution. Simulation results indicate that the reference height and steepness of the nighttime electron density affect the penetration altitudes and amplitudes of normalized electric fields, as well as the altitudes and intensities of the corresponding sprite halos optical emissions. A comparison of the daytime and nighttime conditions demonstrates that the daytime electron density profile is not favorable for generating sprite halos emissions. Furthermore, the pre-existing electron density inhomogeneities lead to enhanced local electric fields and optical emissions, potentially offering a plausible explanation for the horizontal displacement between sprites and their parent lightning, as well as their clustering.

A 3D problem in linear elasticity is considered for a thin inhomogeneous layer subject to transverse compression. For the first time, the effect of arbitrary vertical inhomogeneity is elucidated. Two sets of boundary conditions along the faces of the layer are adapted for modelling transverse compression. Robust asymptotic formulae involving repeated integrals across the thickness are derived for displacements and stresses. As an illustration, numerical results are presented for the elastic moduli having a transverse parabolic variation. The obtained results have a potential to be implemented in modern technology, including manufacturing and design of functionally graded materials.