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• A novel model for investigating the vehicle-induced fatigue damage of fastener clips in high-speed railway is established. • An efficient dynamic solution and an iterative method are introduced into the vehicle-track (VT) dynamic interaction. • The spatial variability of the fastener is characterized in the VT system by combining the random field expansion method. • The stochastic fatigue damage evolution of the fastener clips and its impact on the VT system have been revealed. To investigate the vehicle-induced fatigue damage evolution of fastener clips and their impact on the vehicle-track (VT) system, a numerical dynamic model is established to achieve probabilistic evaluation. The "rain flow" counting method is adopted to describe the stress cycles of the hazard area of the clips, and the S-N curve is used to predict the fatigue life of the clips. The solution of the dynamic equation of motion is obtained by the time-domain Green's function method, which is an effective method to improve computational efficiency. A versatile iterative algorithm is adopted to solve the nonlinear system considering the damaged clips. In the probabilistic evaluation framework, a novel random field method is employed to depict the spatial variability of clips' strength. The applicability of the model established in this work in aspects of expressing random damage of fasteners and evaluating the dynamic behavior of the system is demonstrated by different numerical examples. The results show that the dynamic responses of the train and track system significantly exacerbate as the number of train cycles increases, which is closely related to the variability and non-uniform damage of the fasteners. The probability of cumulative damage to the fasteners induced by the train follows a three-stage rule, and the fatigue damage of the non-uniform fastener system caused by the train is greater than that of the uniform situation. In addition, the short wave components of track irregularity will significantly exacerbate the damage to fasteners and therefore degrade the status of the railway line. As the driving speed increases, the damage to the fasteners also increases, but the impact of vehicle speed on the fastener damage is smaller than that of track irregularity, especially in the range of fatigue damage greater than 0.9. Therefore, maintaining the geometric smoothness of the track, controlling the uniformity of the mechanical properties of the fasteners, and reducing the driving speed are feasible measures to extend the service life of the fastener system, thereby ensuring the operation of high-speed trains. [ABSTRACT FROM AUTHOR]

Cylindrical radiation of individual pulses is studied and strong differences from spherical radiation are highlighted. Prior to this study, the class of available analytical solutions for cylindrical radiation was rather limited. It included (i) a well-known solution for a steady-state, time-harmonic line source and (ii) the solution for a delta-pulse line source. The first of these has no analytical counterpart for individual pulses. By means of the second (actually the Green's function) a more general class of line source solutions can be formulated, but each one is in the form of an integral that has to be evaluated numerically and requires tedious preparation of a singular integrand, making it difficult to achieve perfect accuracy. In the present paper, use is made instead of a particular family of analytically-exact (linear) solutions that has been developed recently. It is used to assess the accuracy of solutions obtained numerically by the method of characteristics (MoC), which is then applied to more general sources than those amenable to analytical treatment. The MoC analysis is specially formulated to reduce the influence of terms involving the reciprocal of the radius (such terms are numerically unmanageable close to the origin). It is found that the qualitative behaviour of waves radiating from the surface of a cylinder of finite radius can depend strongly on the duration of the initiating disturbance and that this can be interpreted in a convolution-like manner. After validation, the numerical method is coupled with a conventional MoC analysis of planar wave propagation and is used to simulate the reflection and radiation of an initially planar wavefront arriving at a flanged duct exit. The numerical representation is one-dimensional in both domains – (x , t) inside the duct and (r , t) outside it. Although its use implies identical behaviour in all radial directions in the external domain, the solution is found to be in close agreement with circumferential-average values from a CFD solution that simulates azimuthal variations as well as radial variations. Whilst being less comprehensive than the CFD simulation, the MoC analysis has the important practical benefit of making highly efficient use of human and computational resources. By comparing the MoC and CFD solutions, it is found that the nominally-cylindrical radiation from the duct approximates closely to radiation from a line source a small distance inside the duct (not at the exit plane). An approximate location of the effective source is quantified. • Cylindrically-radial unsteady flow is solved numerically by the method of characteristics. • Close agreement is demonstrated with a new analytical solution for pulses propagating cylindrically. • Waves radiating cylindrically from a duct exit are coupled with uniaxial, internally-propagating waves. • A strong correlation is demonstrated with a CFD analysis of fully-coupled behaviour. • A new end-correction is identified and quantified for waves radiating cylindrically from a duct exit. [ABSTRACT FROM AUTHOR]

• A mathematical analogy established between steady-state heat conduction and thermal inclusion in plane elasticity. • A complete set of Eshelby tensors for thermal and elastic fields expressed in explicit analytical form. • All the closed-form solutions elegantly unified in an algebraic expression for both interior and exterior fields. • Present model is flexible, effective and versatile for arbitrarily shaped inclusions with any eigen-temperature gradients. • The heat and stress concentrations investigated around the inclusion boundary. The existence of inclusions or inhomogeneities may disrupt heat flow, resulting in increased stresses and temperature fluctuations at the material interface. Analyzing the thermo-elastic fields surrounding such microstructures is crucial for unveiling the intricate failure mechanisms within materials. Based on the method of Green's function and contour integral, this work presents a complete set of explicit analytical solutions for thermal and elastic fields of an arbitrary polygonal inclusion subjected to linearly varying eigen-temperature gradients or thermal eigenstrains. In contrast to the previous studies on potentials showing analogy with anti-plane elasticity, a mathematical analogy of Green's functions between steady-state heat conduction and thermal inclusion for plane elasticity is accordingly established. By employing the linear interpolation of the nodal eigen-temperature gradients or eigenstrains, the work further extends the traditional isoparametric element idea to the thermos-elastic inclusions, and proposes a novel isoparametric inclusion model to solve arbitrarily shaped inclusions with any distributed eigen-temperature gradients. Unlike the finite element method, which requires meshing for both the matrix and inclusion, the present model exhibits efficiency, flexibility, and versatility with the mesh discretization only conducted inside the inclusion domain. The inclusion based isoparametric method may have potential applications in mechanical engineering and material science for analyzing the thermo-structural behavior of various microstructures. [ABSTRACT FROM AUTHOR]

Efficient and rapid detection of hydrogen during transport can effectively prevent gas leaks and explosions. Inspired by the successful synthesis of biphenylene network (BPN) monolayer, the electronic structure and sensing characteristics of nanodevices with metal Sc-decorated BPN monolayer for different concentrations of H 2 are investigated by using density-functional theory in combination with the nonequilibrium Green's function approach theoretically and systematically. Calculated electron localization functions, charge transfers, energy band structures, projected densities of states, charge difference densities and adsorption energies revealed that the adsorption of H 2 by metal Sc-modified BPN monolayer are all chemisorbed. Furthermore, compared to the original BPN transport device, the modification of Sc metal enhances electronic transport while preserving the anisotropy of the electron transport along the zigzag and armchair directions. The metallicity gradually enhanced with increasing concentration of Sc adsorbed by BPN. Interestingly, the BPN-Sc system exhibits a pronounced negative differential resistance (NDR) effect along the armchair direction, and it achieves switching ratios of 3.65 × 105 and 1.98 × 105 for its D-5H 2 and D-1H 2 devices. In addition, the maximum rectification ratio of the D-1H 2 device in the armchair direction reaches ∼107 at low hydrogen concentration. Critically, the short recovery time (0.1 μs) demonstrates that the device can be reused when adsorbing individual H 2. These results indicate the potential use of BPN with adsorbed Sc in the domain of gas sensitivity, especially for applications in detecting low concentration H 2 leakage sensors, providing a theoretical basis. [Display omitted] • The BPN-Sc system exhibits a pronounced negative differential resistance (NDR) effect along the armchair direction. • The maximum rectification ratio of the D-1H2 device in the armchair direction reaches ∼107 at low hydrogen concentration. • The short recovery time (0.1 μs) demonstrates that the device can be reused when adsorbing individual H 2. [ABSTRACT FROM AUTHOR]

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior knowledge about the solution structure of a problem and can thus be directly applied to a large class of problems. However, training the parameters of the networks may sometimes be slow. In order to improve on DeepONets for approximating the wave equation, we introduce the Green operator networks (GreenONets), which use the representation of the exact solution to the homogeneous wave equation in term of the Green's function. The performance of GreenONets and DeepONets is compared on a series of numerical experiments for homogeneous and heterogeneous media in one and two dimensions. [ABSTRACT FROM AUTHOR]

The local discontinuous Galerkin (LDG) method on a Shishkin mesh is studied for a one-dimensional singularly perturbed reaction-diffusion problem. Based on the discrete Green's function, we derive some improved pointwise error estimates in the regular and layer regions. For the LDG approximation to the solution itself, the convergence rate of the pointwise error in the regular region is sharp. For the LDG approximation to the derivative of the solution, the convergence rate of the pointwise error in the whole domain is optimal. We establish also optimal pointwise error estimates in the case that the regular component of the exact solution belongs to the finite element space. Numerical experiments are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

• A high-efficient model for vehicle-track-soil dynamic interaction based on hybrid solution method. • Cyclic calculation boundary and multi-time-step strategies are integrated into the hybrid model. • The proposed hybrid model can evaluate the vehicle-track-soil performance efficiently without losing accuracy. To meet the demand for dynamic analysis of railway engineering structures accurately, the numerical model considering the coupled vibrations of the vehicle, track and substructure becomes a research tendency. However, it generates low-efficiency risk due to high degrees of freedom of the model. In this paper, a hybrid integration method based on the implicit scheme and Green's function is introduced and combined with the cyclic calculation method and the multi-time-step solution method to optimize the dynamic procedure for high-efficient solution of vehicle-track-soil (VTS) dynamic interaction. The VTS system is divided into two sub-models: vehicle-rail sub-model and the track slab-soil sub-model. The compatibility between two sub-models is maintained by the equilibrium mechanism of the fasteners' interaction forces. Through detailed validation, discussion and numerical studies, the feasibility and efficiency of the proposed model combing the hybrid integration method and two optimized dynamic solution strategies are fully demonstrated in the dynamic assessment of VTS dynamic interaction. [ABSTRACT FROM AUTHOR]

The present paper studies Love-type wave propagation in a fluid-saturated fractured poro-viscoelastic layer sandwich between a coated elastic layer and a non-homogeneous anisotropic Voigt-type viscoelastic half-space. The interfaces between the layers and the half-space are considered as sliding contacts with two different sliding parameters. An impulsive point source is located at a varying depth in the intermediate poro-viscoelastic layer in the form of the Dirac-delta function. The vertical non-homogeneity in the half-space is assumed to be a combination of linear and exponential functions that vary with depth in the medium. Using the Fourier transforms and Green's functions, the equations of motion, in the form of partial differential equations, are solved analytically. An appropriate boundary condition is used to accomplish this. The closed form of the complex dispersion equation has been obtained by assuming that the wavenumber is in the form of a complex quantity. The validity of our model has been examined using several specific cases and compared to the classical Love wave equation. Numerical and graphical analyses of dispersion and displacement were performed using MATLAB software. It has been found that a single porous medium has a higher Love-type phase velocity than a double porous medium. Additionally, the sliding parameters increase the range of wavenumber when there is no phase velocity. An inverse relationship was found between the depth of the point source and the particle displacement in the coated layer. In addition to contributing to our understanding of geophysical phenomena and subsurface explosions, these findings may provide insight into the inner structure of the planet. • Layered media with sliding contacts are introduced. • The coupled Green's function approach is used for Love-type dispersion. • Wavenumbers for non-existence of phase velocity increase with sliding parameters. • An inverse relationship is found between the depth of the point source and the particle displacement in the coated layer. [ABSTRACT FROM AUTHOR]

This manuscript aims to study the effectiveness of two different levels of fractional orders in the frame of Caputo-Hadamard (CH) -derivatives on a special type class of delay problem supplemented by Dirichlet boundary conditions. The corresponding Hadamard fractional integral equation is derived for a proposed CH -fractional pantograph system. The Banach, Schaefer, and Krasnoselskii fixed point theorems (FPT s) , are used to investigate sufficient conditions of the existence and uniqueness theorems for the proposed system. Furthermore, the Green functions properties are investigated and used to discuss the Ulam-Hyers (UH) stability and its generalized by utilizing nonlinear analysis topics. Finally, three mathematical examples are provided with numerical results and figures by using Matlab software to illustrate the validity of our findings. [ABSTRACT FROM AUTHOR]

Consider the quadratic finite element method over a regular family of uniform tetrahedral partitions for the three-dimensional Poisson equation. Utilizing properties of the bubble function and estimates for discrete Green's function, we derive a pointwise superconvergent estimate for the finite element approximation in the sense of L ∞ -norm. Furthermore, the L 2 -norm superconvergent estimate is also provided. A numerical example is presented to demonstrate the accuracy of the theoretical results. [ABSTRACT FROM AUTHOR]

• Green's function of two-layer coating structure provides a theoretical basis for analysis of multicoating problem. • Analytical expressions, expressed as elementary functions, can be easily converted into numerical calculation codes. • Those solutions are the basis for analyzing the two-layer coating under distributed loading with numerical integration. The study of multi-layer coating structure is an important problem in the fields of machinery and materials. In this paper, a two-dimensional theoretical solution of the orthotropic double-coated substrate structure under the normal line force of the free surface is derived. The method in this paper is mainly aimed at orthotropic materials and falls within the scope of linear elasticity. Based on the general solution of two-dimensional orthotropic materials, the harmonic functions with undetermined constants corresponding to each region are constructed. With the equilibrium conditions, surface boundary conditions and interface continuity conditions, the full-field analytical solution (Green's function) expressed in elementary functions is determined with the method of mirror images, which is valuable to solve the full field analytical expression of layered structures for the linear elasticity problem. Compared with the existing theories, the effectiveness and accuracy of the method are verified. In the future, Green's function of the paper is the basis for the numerical integration of distributed loads, which can be used as the code basis for the development of special software to study ultra-precision coatings. [ABSTRACT FROM AUTHOR]

• Developing a nondestructive approach for the critical pressure of functionally graded combined shells with hydrostatic pressure. • Equivalent model of hydrostatic pressure for functionally graded combined shells is proposed. • The validity of the developed computational model is verified by numerical examples. • The effects of power-law exponents, geometric parameters, boundary conditions on critical pressure are discussed. This paper describes a unified nondestructive semi-analytical formulation for the critical pressure of underwater functionally graded combined shells subjected to external hydrostatic pressure. The structural model of combined shells is constructed from the first-order shear deformation theory, Voigt mixing law, and virtual spring technology. The admissible displacement functions are uniformly expressed with Legendre polynomials along the generatrix direction and Fourier series along the circumferential direction. The Kirchhoff-Helmholtz boundary integral equation is discretized by using the Legendre-Gauss spectral boundary element method, and the external acoustic field model is derived by expanding the Green's function, sound pressure, and displacement of combined shells with one-dimensional Fourier transformation. The linear elastic material theory is applied to deduce the work done by the hydrostatic pressure. The key technology to predict the critical pressure is to create an accurate equivalent model of the hydrostatic pressure. Through solving the final coupled governing equation, the critical pressure is obtained from the linear relationship between the hydrostatic pressure and the square of natural frequency. The convergence and correctness are verified by comparison with the results from published papers and numerical methods. The effects of different hydrostatic pressures, power-law exponents, geometric parameters, and boundary conditions on the critical pressure are investigated in several examples. Computed results can provide security guidance for the nondestructive prediction of underwater functionally graded combined shells at the beginning of engineering application design. [ABSTRACT FROM AUTHOR]

• A mathematical modeling of the time-dependent behavior of polymer-based piezoelectric composites is developed. • The modeling is based on the piezoelectric time-dependent Green's functions. • The Mori-Tanaka model is adopted to derive the coupled dynamic localization tensor. • A trapezoidal numerical scheme is adopted for computing the direct and inverse Volterra product. • The time-dependent behavior is estimated for different shapes of inclusions and different loadings. In the time domain, a new straightforward micromechanical modeling is developed to predict the time-dependent behavior and the macroscopic coupled response of polymer piezoelectric composite materials. The modeling is based on the dynamic electroelastic Green's tensor allowing the derivation of convolution localization equations in Stieltjes space. The Mori-Tanaka micromechanical model is adopted to derivate the dynamic electroelastic localization tensor. The presented modeling leads to an expression of the time-dependent effective electroelastic properties directly in the time domain, without an iteration procedure, through convolution products in Stieltjes space. It allows the prediction of the time-dependent behavior and the coupled macroscopic response while taking into account the constituent properties, volume fractions, and shape of inclusions. In implementing the expression of the effective behavior, one has to go through the computation of direct and inverse tensorial convolution products. A trapezoidal numerical scheme is adopted for this sake. Many numerical results are presented, and for the sake of validation, a comparison is made with the ones obtained based on the Laplace transform approach as well as with experimental and numerical results. [ABSTRACT FROM AUTHOR]

[Display omitted] Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking the P 4 / nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions. [ABSTRACT FROM AUTHOR]

We perform a posteriori error analysis in the supremum norm for the quadratic discontinuous Galerkin method for the elliptic obstacle problem. We define two discrete sets (motivated by Gaddam, Gudi and Kamana [1]), one set having integral constraints and other one with the nodal constraints at the quadrature points, and discuss the pointwise reliability and efficiency of the proposed a posteriori error estimator. In the analysis, we employ a linear averaging function to transfer DG finite element space to standard conforming finite element space and exploit the sharp bounds on the Green's function of the Poisson's problem. Moreover, the upper and the lower barrier functions corresponding to continuous solution u are constructed by modifying the conforming part of the discrete solution u h appropriately. Finally, numerical experiments are presented to complement the theoretical results. [ABSTRACT FROM AUTHOR]

Photo-supercapacitors are combined devices that incorporate a photovoltaic cell as a light harvester unit to an electrical double layer capacitor where the charge carriers could be stored for further applications. Density functional theory calculations were performed to explore the electronic structure properties behind the mechanisms of electron communication between the interface of the solar cell material and the energy storage device. A hybrid perovskite was used to model the solar cell, while different carbon allotropes were considered as the molecular model of supercapacitor electrode. The communication of the perovskite with carbon is highly selective to the interaction of inorganic/organic termination and the carbon allotrope. Non-equilibrium Green's functions revealed the electron transmission behavior among the hybrid perovskite and the carbon allotropes, showing that the transport of charge carriers from the solar cell could be tuned with the adequate selection of the carbon allotrope. Quantum capacitance calculations were also performed to shed light into the intrinsic storage properties that the composite material may present. It shows that PbI and organic terminations in perovskite play a lead role to improve electronic charge retention, and consequently the inherent capacitance properties of the systems. This study also represents a combined theoretical/experimental work, in which an experimental methodology based on TEM graphics and XRD patterns allows to identify the inorganic/organic terminations in a hybrid perovskite solar cell material. This methodology could be implemented as a tool to tailor materials intended to improve the overall efficiency of a photo-supercapacitor device. • DFT calculations reveal the origin of electron transport at ETL interfaces. • Electron density between perovskite and carbon suggests sites for electron transport. • Perovskites with organic termination present low probability for electron transport. • Perovskites with inorganic PbI-termination induce charge carriers mobility at the ETL. • Simulated current-voltage profiles show a steady electron diffusion at the interface. [ABSTRACT FROM AUTHOR]

• The exact solution of three-dimensional multilayer structure with arbitrary thickness under point load is derived. • The analytical method can clearly predict the critical load of interface shear delamination failure. • The stresses and displacements of the substrate, adhesive, and adherend are presented by explicit closed-form expressions. Explicit closed expressions of stresses and displacements of an adherend and an adhesive provide researchers and designers with insight into the effects of variable parameter properties on structural performance. Through potential theory method, the Green's functions of a double-coated structure under normal point load are solved using the mirror image method, where the mirror image rule satisfies the recursion law of the Fibonacci sequence. The stress distribution of the multilayer structure under the action of point load is presented in the form of an infinite series with a fast convergence rate. A guideline for the design of coating thickness and material parameters to reduce interfacial stress is developed (reduce adhesive thickness, reduce elastic modulus of adherend, increase elastic modulus of adhesive). The accuracy of the exact solution is demonstrated through comparison with contact analytical solutions. In addition, the critical load of interface shear delamination failure is predicted. The stresses and displacements of the adherend and the adhesive are presented with the solutions, which can serve as a reference for researchers and designers. [Display omitted] [ABSTRACT FROM AUTHOR]

• Exact solution of the problem of Eshelby's inhomogeneity in strain gradient elasticity theory. • Green's function technique and integral equation developed for arbitrary boundary conditions. • Analytical expressions of mean strain inside inclusion. • Analytical expressions of effective elastic properties with strain gradient. • Effect of the scale parameter, the contrast of elastic behavior and the volume fraction of inhomogeneity. A new micromechanical approach to deal with the problem of Eshelby's inhomogeneity is developed for the prediction of the effective properties of composite materials according to the strain gradient elasticity theory. The method is based on the Green's function technique leading to an integral equation of the heterogeneous elastic problem. Within the simplified strain gradient elasticity theory, the integral equation for an infinite heterogeneous medium subjected to non-homogeneous boundary conditions is acquired. Thanks to this integral equation, the exact solution of Eshelby's inhomogeneity problem is detailed for spherical inhomogeneity and isotropic elastic behavior. From the expression of strain localization relations, the effective elastic properties of a two-phase composite material are then predicted through Mori Tanaka's homogenization scheme. To test the relevance of the suggested approach, its predictions are compared with results issued from some reference models and experimental data. [ABSTRACT FROM AUTHOR]

In this paper, a near-field thermophotovoltaic (TPV) system with a dual TPV cell design is considered and studied numerically. The fluctuational electrodynamics accompanied by the dyadic Green's function are utilized for calculating the radiation heat flux. The generated photocurrent and the conversion efficiency are obtained by solving the photon-coupled charge transport equations. It was discovered that the addition of the second TPV cell to the system, increases the generated photocurrent of the system due to the absorption of the low-energy photons and generation of the electron-hole pairs. By increasing the gap size between the emitter and Si TPV cell from 50 nm to 1 μm, the generated photocurrent decreases because of the reduction of the near-field thermal radiation effects. Finally, the tandem nano-gap TPV system shows higher conversion efficiency compared with the single Si TPV cell for different values of the vacuum gaps, and the gap size of d 1 = 200 nm is the optimum gap size due to the improvement of the conversion efficiency of the system. [ABSTRACT FROM AUTHOR]

We propose two efficient numerical algorithms, Bernoulli uniform collocation method and Bernoulli Chebyshev collocation method for solving 3 r d -order Lane-Emden-Fowler boundary value problems. To avoid singularity at x = 0 , we transform the concerned problem into its integral form. By using the Bernoulli collocation method, the resulting integral equation is converted into a system of nonlinear equations to be solved numerically by any suitable iteration method. The error bound of the algorithm and the existence of a unique solution of the problem are also discussed. The high accuracy and efficiency of the proposed method are shown by comparing the results of L ∞ and L 2 errors of several examples. Moreover, the numerical results of our method are compared with the results obtained by the other known techniques. [ABSTRACT FROM AUTHOR]

• A method is proposed to account for the variability of materials in the displacement generated by changes in fluid pressure. • The results obtained by the proposed method agree well with the statistical solution obtained via Monte Carlo simulation. • Due to uncertainties, the subsidence caused by uniform pressure change can be up to 27% higher than the deterministic value. • The proposed method can be as much as 30 times faster than the Monte Carlo simulation. The present work proposes a stochastic statistical method, called Green-FOSM, to consider the uncertainties associated with the mechanical properties of rocks that form geological profile. This method intended to help improve the decision-making process associated with production of oil and gas, the extraction of water, and the storage of CO 2 or natural gas. The novelty of the method lies in the use of the Green's function approach, which, together with the FOSM method (first-order second moment method), is used to propagate uncertainties associated with the material to the displacement field of the geological formation. Furthermore, using the concepts of stochastic grid and autocorrelation function, the proposed method allows the consideration of the spatial variability of the random variables that represent these mechanical properties. This method is applied to a 2D model subject to two processes of pore pressure changes (depletion only and depletion combined with injection) with different levels of correlation and variability. The statistical results obtained by the proposed method agree well with the results obtained using Monte Carlo simulation. In problems with more than 1500 random variables, the relationship between the CPU times demonstrates that the proposed method is up to 30 times faster than the Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The molecular system-level detection of H 2 and NH 3 gas using an electrically doped Adenine bio-molecular gas sensor has been proposed and investigated using Density Functional Theory (DFT) combined with Non-Equilibrium Green's Function (NEGF) formalisms. First-principles calculations were applied and the structures and electronic properties of the Adenine gas sensor have calculated. This sensor reveals that the current-voltage response and conductivity of the bio-molecules increased evidently after the adsorption of these gas molecules. The Adenine sensor offers approximately 1800 times and 3300 times better current response during H 2 and NH 3 adsorption respectively. The significant gap between Highest Occupied Molecular Orbital (HOMO) and Lowest Un-occupied Molecular Orbital (LUMO) indicates the system's thermodynamic stability. Therefore, we hope that the Adenine monolayer could be a room temperature H 2 and NH 3 sensor with high selectivity and sensitivity and fast response and recovery time. Therefore, we hope that the Adenine monolayer will be a good candidate forH 2 and NH 3 work-function-type gas sensors. [Display omitted] • Ultra-low-voltage Adenine bio-molecular gas sensor is proposed for the first time. • First-principles approach is applied to explore theoretically gas sensor properties using adenine molecules. • Extremely sensitive and thermos-dynamically stable sensor evaluated to predict the case of NH 3 and H 2 adsorption. • Good current-voltage response, conductivity, and HOMO-LUMO gap are observed for the Adenine sensor. [ABSTRACT FROM AUTHOR]

Two-dimensional diamane with outstanding properties is promising for advanced nanodevice applications, whereas a comprehensive understanding of phonon-limited mobility as well as the prediction of device performance limit is still lacking. Here we report on phonon-limited mobility simulation in fluorinated diamane monolayer using first-principles calculations, with consideration of both elastic and inelastic phonon scattering processes based on Boltzmann transport equation. We construct sub-7 nm fluorinated diamane metal-oxide-semiconductor field-effect transistors (MOSFET) to investigate their quantum transport properties by first-principles calculations based on density functional theory coupling with the non-equilibrium Green's function formalism. Our findings show that fluorinated diamane mobility is concentration-dependent, with the electron and hole mobility reaching as high as 4390 and 10100 cm2V−1s−1, respectively, at the 1014 cm−2 carrier concentration. Our simulations reveal that the key figures of merits (FOMs) of fluorinated diamane MOSFETs are benchmarked against the International Technology Roadmap for Semiconductors (ITRS) standards for high-performance (HP) and low-power (LP) applications, showing superior potential compared to the most reported 2D materials. The simulated results demonstrate that the on-current, delay time, and power-delay product meet the ITRS requirements for HP and LP applications, including devices constructed with nano-scale channel length (≥3 and 5 nm) respectively. Finally, we show that the performance of a 32-bit ALU based on fluorinated diamane MOSFETs is comparable with emerging beyond-CMOS devices. Thus, our results shed light on the electronic properties of fluorinated diamane, making it superior to serve as a channel material in the post-silicon era. [Display omitted] • The phonon-limited mobility of monolayer fluorinated diamane is calculated. • The electron/hole mobility is 4390/10100 cm2V−1s−1 at concentration of 1014 cm−2. • Quantum transport properties of fluorinated diamane MOSFETs are simulated. • The FOMs indicates fluorinated diamane is suitable for sub-5nm applications. [ABSTRACT FROM AUTHOR]

• Novel mathematical model for deriving semi-analytical Green's function solutions. • First time on the coupled horizontal and rocking vibrations in poroelasticity. • Anisotropic and layered poroelastic half-space via Biot's poroelastodynamic theory. • Handling layering via the powerful and stable dual variable and position method. • Soil-structure interaction (SSI) via a novel integral least-square approach. The coupled horizontal and rocking vibrations of a rigid circular disc resting on a transversely isotropic (TI) and layered poroelastic half-space is solved by a newly developed semi-analytical method for the first time. The poroelastic medium is modelled via Biot's poroelastodynamic theory. The Green's function corresponding to the horizontal uniform and vertical linearly changing patch loads on the surface of the layered half-space are first derived by virtue of the cylindrical system of vector functions and dual variable and position method. To solve the dynamic interaction, the influence function by the ring load is then introduced and calculated via the method of superposition. Together with the mixed boundary-value conditions, the dynamic horizontal, rocking, and coupling compliances are finally solved by a novel discretization scheme and an integral least-square approach. The developed fundamental solutions are verified by comparing with existing solutions in the purely elastic and poroelastic media. Numerical examples are presented to investigate the influence of poroelastic properties on the coupled vibration characteristics, which could be useful to the dynamic design of foundation on the saturated soil. It should be emphasized that the effect of the coupling compliance must be considered since its contribution can be as large as 26%, compared to the diagonal compliances. [ABSTRACT FROM AUTHOR]

This paper focuses on the analysis of nonlinear physical phenomena without losing their natural properties and reduces computational difficulties in numerically capturing the behaviour of nature governed by nonlinear coupled Burgers equations with source functions. To achieve this, an implicit backward differentiation formula-spline (BDFS) method is proposed, which does not need linearization or tensor product. In the case of linearization, it is quite probable to get away from nature of the problem under the consideration of various assumptions. Then, without any linearization, the given problem through the BDFS scheme is converted to a system of nonlinear and linear difference equations. Unlike traditional approaches, the BDFS method leads to a procedure that requires neither linearization nor any other transformation process. The current approach reduces the computational cost and the need for storage space as it does not require any matrix or tensor product. Notice that the Newton and Thomas algorithms have been implemented to solve the nonlinear and linear parts of the resulting system at each iteration, respectively. Here, the convergence analysis of the present method is also discussed theoretically. Several examples are considered to illustrate the effectiveness of the current method. [ABSTRACT FROM AUTHOR]

• Applying stress on the S-hyperdoped silicon can change the electronic structure of the material obviously and lead to the insulator-to-metal transition (IMT). • The IMT will occur when the conduction band comes very close to the intermediate-band and the electron filling in the conduction band increases under the critical stress. • The critical stresses for the IMT are different in different directions due to the nonuniform distribution of dopant. In this work, the effect of the stress on the electronic structure and electronic transport properties of S-hyperdoped silicon, which is an intermediate-band (IB) photovoltaic material, was studied in detail by combining the density functional theory and nonequilibrium Green's function methods. We found that applying stress on the material could lead to the insulator-to-metal transition (IMT), which is crucial for improving the performance of the IB material. Under the critical stress for the IMT of the material, the IB and the conduction band (CB) have not been fully merged together, which is slightly different from the dopant-concentration-induced IMT. The critical stress exhibits direction-dependent property for material with nonuniform distribution of dopant, and it is smaller in the direction that shows lower dopant density. [ABSTRACT FROM AUTHOR]

• A method is proposed for the dynamic analysis of a class of high-order beams with vibration absorbers. • Deriving the Green's function of a given linear differential operator of order n is the key-step of the method. • The method applies in the frequency domain providing solutions for beams of relevant engineering interest. • A case study involving a coupled bending-torsion beam is selected to illustrate the method. • The method is validated employing the theory of distributions and a standard exact approach. In this work, a general method is proposed to solve a wide class of high-order boundary value problems governing the dynamics of beams equipped with vibration absorbers. The method relies on one-dimensional beam theories and theory of generalized functions to model the reaction forces of the absorbers. The key step consists in deriving, via Laplace transform, the Green's function of a linear differential operator of any order n , which involves even-order terms and constant coefficients. Next, the Green's function, obtained in exact and elegant analytical form, serves as a basis to derive the exact solutions of boundary-value problems of order n governing the frequency response of beams with absorbers, under concentrated/distributed loads. Remarkably, the solutions are derived for any order n of the boundary-value problem, providing the exact frequency response of beams of relevant engineering interest as composite beams, twisted beams, coupled bending-torsion beams and multiple-beam systems including any number of beams; moreover, they are readily implementable for any number/positions of absorbers and loads. To illustrate the method, a case study is selected: a boundary value problem of order n = 10 governing the frequency response of a coupled bending-torsion beam with asymmetric cross section and no warping effects. For this problem, an additional validation of the proposed analytical framework is obtained by the theory of distributions, while a comparison with an exact classical approach demonstrates correctness and advantages for applications with multiple absorbers. [ABSTRACT FROM AUTHOR]

This paper surveys a new class of electromagnetic materials. The emphasis is on the bianisotropic medium; a complex material which has never been applied in antenna design. In this context, we investigate the behavior of the magnetoelectric elements of the gyrotropic reciprocal bianisotropic medium used as a grounded substrate by studying their effects on the input impedance and mutual coupling of a printed dipole antenna. Numerical integrative equation calculations are carried out using the spectral method of moments (SMoM) based on the analytical derivation of the appropriate spectral Green's functions for the considered dipole configuration. The obtained results reveal a change in the sign of the real part of the input impedance. This is mainly due to the complex property of the considered medium. The medium has also minimized the input impedance ∼4 times (1kΩ); this can help in device matching. This medium has shown a significant impact on the input impedance as well as the antenna array coupling. The design miniaturization possibility is an important result of this research in the design of antenna arrays. [ABSTRACT FROM AUTHOR]

It is notable that, the nonlocal reaction-diffusion equation carries math and computational physics to the core of extremely dynamic multidisciplinary studies that emerge from a huge assortment of uses. In this investigation, a totally new methodology for building a locally numerical pointwise solution is given by the agent the reproducing kernel algorithm. This is done utilizing a couple of generalized Hilpert spaces and their corresponding Green functions. The proposed calculation algorithm is applied to certain scalar issues problems to figure the arrangement solutions with Dirichlet constraints. By applying the procedures of the Gram–Schmidt process, orthonormalizing the basis, and truncating the optimized series, the approximate solutions are drawn, tabulated, and sketched. Introduced mathematical outcomes not only show the hidden superiority of the algorithm but also show its accurate efficiency. Finally, focused notes and futures planning works are mentioned with the most-used references. [ABSTRACT FROM AUTHOR]

The potential flow theory is a reliable tool widely-used in ocean engineering to solve the fluid hydrodynamic problems such as the wave hydrodynamic problems. The Rankine source and its image about the seabed is often chosen as the Green's function to solve the potential flow problems for its simple form, easy singular-integral treatment and few boundary conditions in the boundary integral equations. However, traditionally, the boundary element method based on it is only executed in the time domain by time stepping technique which requires lots of computation due to the time domain form of the damping zone's boundary condition. To apply this Green's function in frequency domain, this paper derived a parameterized frequency-domain formula for the boundary condition of the damping zone, and successfully applied the Rankine source and its image about the seabed in frequency domain. This paper's work possesses a great potential to promote the efficiency in solving the potential flow problems. • Derived a parameterized frequency-domain formula for the boundary condition of the damping zone. • With the formula, the boundary element method using the Rankine source and its image about the seabed as the Green's function can be implemented rapidly and effectively in the frequency domain rather than traditionally in the time domain. • Applicability, accuracy and efficiency of this new method to solve the potential flow problems were presented. [ABSTRACT FROM AUTHOR]

• The thermal conductivity of double-walled carbon nanotubes is investigated. • Both ballistic and quasi-ballistic phonon transports are analyzed. • The influence of van der Waals interactions on phonon transports is revealed. Assembling single-walled carbon nanotubes (SWCNT) into multiwalled carbon nanotubes (MWCNT) reduces the intrinsically high thermal conductivity of individual SWCNTs. Typically, this reduction can be explained by structural imperfections, e.g., defects, and van der Waals (vdW) intertube interactions between the constituent SWCNTs are considered to have negligible impacts on the reduction. However, intertube interactions should alter the transport characteristics of low-frequency phonons responsible for heat conduction, which implies that intertube interactions may also reduce the thermal conductivity of MWCNTs when low-frequency phonons modulated by intertube interactions participate in the overall heat conduction. In this study, by applying a combination of the atomistic Green's function method and nonequilibrium molecular dynamics simulation to double-walled carbon nanotubes (DWCNT) with different chiral configurations of SWCNTs and various lengths, we investigated the length scale and chiral configuration where perturbative intertube interactions can suppress phonon transports. We found that thermal resistance attributed to intertube interactions manifests in the low-temperature ballistic regime and quasi-ballistic regime for DWCNT lengths greater than 1 μm. Revisiting the influence of the intertube interactions helps comprehend the intrinsic origin of the reduced thermal conductivity of MWCNTs. In addition, the reported findings are beneficial for the thermal engineering of SWCNT-assembled materials, including emerging one-dimensional vdW heterostructures. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the thermal spin transport properties of hydrogen-saturated graphene-like nanoribbons substituted for doped nonmetallic B by using density functional theory combined with non-equilibrium Green's function approach. We find that A C 2 N NR-H(B) is a distinctly narrow bandgap semiconductor material and exhibits significant spin Seebeck effect, temperature switching effect, and giant magnetoresistance. Surprisingly, the spin Seebeck coefficients can reach 1.16 mV/K and the magnetoresistance value not only reaches 10 8 % at low temperature, but also 10 4 % near room temperature. These unique transport properties can be explained using spin-dependent transmission spectra combined with energy band structure. The current work further extends the theoretical study of graphene-like derivatives and provides new ideas for the construction of spintronic devices. • AC 2 NNR-H doped with B (AC 2 NNR-H(B)) is a narrow band gap semiconductor material. • The A C 2 N NR-H(B) homojunction device exhibits multiple thermal spin transport performances by applying only a temperature gradient. • The A C 2 N NR-H(B) homojunction device has significant spin-Seebeck effect, the temperature switching effect and giant magnetoresistance. • AC 2 NNR-H(B) would be a promising candidate for thermal-based spin valve, the spin-Seebeck energy-saving device etc. [ABSTRACT FROM AUTHOR]

We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable – the geodesic distance. But now this dependence can be somewhat non-trivial. We demonstrate that, like in the flat case, the coordinate differential equations for powers of Green functions can still be expressed as determinants of certain operators. Therefore, not-surprisingly, the coordinate equations remain straightforward – while their reformulation in terms of momentum integrals and Picard-Fuchs equations can seem problematic. However we show that the Feynman parameter representation can also be generalized, at least for banana diagrams in simple harmonic spaces, so that the Picard-Fuchs equations retain their Euclidean form with just a minor modification. A separate story is the transfer to the case when the Green function essentially depends on several rather than a single argument. In this case, we provide just one example, that the equations are still there, but conceptual issues in the more general case will be discussed elsewhere. [ABSTRACT FROM AUTHOR]

Aiming to attain porous carbon nitride photocatalysts with high specific surface area, abundant active sites, broad absorption range and effective electron-hole separation, we remove carbon rings from graphene and replace all the edge carbon atoms of the cavity with nitrogen atoms. The accurate electronic structures and exciton properties of the proposed materials are revealed by the ab initio many-body Green's function theory. Computational results show that the absorption of the designed materials can cover both the visible and the near-infrared light region. The exciton binding energies of the materials are one order of magnitude lower than those of the typical two-dimensional photocatalyst graphitic carbon nitride. Due to the formation of hydrogen bonds between pyridinic nitrogen atoms and water molecules during water splitting, the key excited-state proton-coupled electron transfer reactions are barrierless. These findings could serve as guidelines for the realization of high-performance metal-free two-dimensional photocatalysts. Graphene with suitable-size nitrogen-doped cavity can photocatalyze water-splitting reaction barrierlessly even without the metal co-catalyst. [Display omitted] • Graphene with suitable-size N-doped cavity can photocatalyze water-splitting reaction directly without metal co-catalyst. • New metal-free two-dimensional porous graphitic carbon nitrides with semiconducting features are designed. • The key excited-state proton-coupled electron transfer reactions on the new photocatalyst are barrierless. • The exciton binding energies of the new two-dimensional photocatalyst are rather low. • The new photocatalyst can utilize sun light efficiently with a large region of visible and near-infrared light absorbed. [ABSTRACT FROM AUTHOR]

• The mechano-chemical degradation was modeled theoretically based on diffusion-reaction. • SCG behavior of main crack after multiple initiations in polyethylene pipe was simulated. • Green's function for crack evolution considering multiple initial cracks was constructed. • A new lifetime prediction methodology of the crack growth from multiple cracks was proposed and validated. In a chemically aggressive environment, polyethylene pipes are affected by oxidation-induced brittle fracture as follows: (i) multiple crack initiation through a thin degradation layer, (ii) mechano-chemical discontinuous slow crack growth of a main crack, and (iii) eventual fast fracture. A new analytical model for the second stage is proposed based on a modified crack layer theory. The mechano-chemical degradation of the process-zone medium was modeled theoretically by diffusion-reaction equation. Interactions between cracks immediately follow multiple crack initiations based on Green's function. Also, the parametric study involved several model parameters to provide a physical explanation. Further, this study proposed a theoretical method to estimate the crack lifetime by simulating crack initiation and slow crack growth periods, providing a new framework for predicting the durability of polyethylene pipes under aggressive chemicals. [Display omitted] [ABSTRACT FROM AUTHOR]

In this work, we investigate the complexities (coupling range and magnetic ordering) of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction on the (001) surface of SnTe which is a topological crystalline insulator. We aim to enable the transition between ferromagnetic and antiferromagnetic couplings, as well as between collinear and noncollinear magnetic spins by manipulating doping and the gap structure. The gap is achieved through electron–phonon coupling and gate voltage. The spin susceptibility is calculated by Green's functions in real space. The modulation of RKKY interactions via doping occurs specifically over short (large) impurity separations, with the influence of electron–phonon coupling (gate) only manifesting when the doped Fermi level lies outside the gap. Additionally, electron–phonon coupling leads to weaker adjustments in magnetic orderings, attributed to the renormalized Fermi velocities, while gate voltage induces stronger modifications. This inquiry is of considerable interest due to the potential applications in the realm of spintronics. • Coupling range and magnetic ordering of the RKKY interaction on the (001) surface of SnTe are investigated. • The modulation of RKKY interactions occurs specifically over short impurity separations. • Electron–phonon coupling leads to weaker adjustments in magnetic orderings, attributed to the renormalized Fermi velocities while gate voltage induces stronger modifications. • The results are of considerable interest due to the potential applications in the realm of spintronics. [ABSTRACT FROM AUTHOR]

The particle size effect on the overall thermoelastic behavior of a composite containing many identical spherical particles reduces with the specimen-particle size ratio (SPR). When SPR is large enough, the effective stiffness converges, and the homogenized properties can represent the composite. This paper addresses two challenging questions: How large of an SPR is enough to reach the convergent results for different loading conditions, and whether is the critical SPR obtained from a uniform loading condition applicable to a nonuniform loading condition? When a uniform load is applied to a composite beam, the elastic moduli and thermal expansion coefficients can be calculated from the material's response. When the beam is subjected to pure or thermal bending, the deflection can be predicted by the heterogeneous or homogenized beams. The inclusion-based boundary element method (iBEM) is developed for high-fidelity simulation of many-particle systems. Given a volume fraction of particles, particle and beam size, and beam geometry, the local fields and the effective deformation are calculated for uniform and nonuniform loading conditions. The comparative study between a homogenized beam by the micromechanical approach and the numerical simulation of the heterogeneous particle system shows that a much larger SPR is required for thermal bending to reach a convergent result between the heterogeneous and homogenized beam. When the SPR is moderate, a cross-scale modeling method shall replace the micromechanical modeling to achieve accurate results. • Green's functions are provided for volume integral with polynomial source fields. • Dual equivalent inclusion method (DEIM) is provided for thermoelastic analysis. • Virtual experiments of particulate composites are conducted by iBEM. • Cross-scale modeling is recommended when the SPR is moderate or small. • Convergent results are obtained at different SPRs for different loading conditions. [ABSTRACT FROM AUTHOR]

The engineering design of metamaterials with selected acoustic properties necessitates adequate prediction of the elastic wave propagation across various domains and specific frequency ranges. This study proposes a systematic approach centered on the finite element characterization of the three-dimensional Green's function for a representative volume element. The inherent characteristics of broadband waves and singular impulses contribute to notable challenges related to accuracy and high-frequency oscillations, and thus the emphasis is set on providing an exhaustive analysis for this numerical characterization scheme. The study focuses on the broadband wave dispersion and requisite considerations for numerical damping, and evaluates the impact of dissipation and space–time discretization schemes for optimal performance. In contrast to conventional methods that employ a plane wave, the proposed approach does not need extra assumptions on the enforcement of boundary conditions and can effectively consider the influences of length scale from the material configurations. A quasi-equiaxed polycrystalline ice microstructure is utilized as an application example for homogenizing heterogeneous materials, in line with advancements in cryo-ultrasonic testing techniques. • The approach combines FE and Green's function analysis to predict wave propagation. • Homogenization uses 3D assumption-free numerical Green functions over complex RVEs. • Key dissipation and discretization parameters for accuracy are reported. • The methodology is tested on polycrystalline ice microstructure. [ABSTRACT FROM AUTHOR]

The multi-barrier system of a nuclear waste repository consists of engineered barriers and natural barriers. The uneven surface caused by mechanical excavation at the rock wall leads to incomplete contact between bentonite and surrounding rock. The incomplete contact contributes to the decay heat conduction at the rock wall being subject to resistance, which is known as the thermal resistance effect. The mathematical model for heat conduction, in which the thermal resistance is considered, is established according to the design concept of the Swedish repository. With the Green's function method, the explicit analytical solutions to the model, which can straightforwardly represent the temperature at any spatial point and time, are derived. The rationality is verified by comparing the results of present solutions with existing solutions and numerical simulations. Based on the present solutions, the influence mechanism of thermal resistance on thermal responses within the multi-barrier system are systematically investigated. The findings indicate that the effect of thermal resistance in the bentonite is more significant than that in the rock. This effect increases during the initial stage of disposal and then decreases with the passage of time. The impact of thermal resistance on the temperature field is minimally influenced by variations in the thermal conductivities of the bentonite and rock. Furthermore, the impact of thermal resistance on the temperature distribution attenuates as the buffer layer thickness increases. [ABSTRACT FROM AUTHOR]

We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering. Higher-order corrections are addressed through numerical calculations or approximations. The RTE solution corresponds to Monte Carlo sampling of photon trajectories with fixed start and end points. Validated against traditional Monte Carlo simulations, featuring random end points, our solution demonstrates enhanced efficiency for both anisotropic and isotropic scattering functions, significantly reducing computational time and resources. The advantage of our method over Monte Carlo simulations varies with the position of interest and the asymmetry of light scattering, but it is typically orders of magnitude faster while achieving the same level of accuracy. The exploitation of hidden symmetries further accelerates our numerical calculations, enhancing the method's overall efficiency. In addition, we extend our analysis to the first and second moments of the photon's flux, elucidating the transition between transport and diffusive regimes. • Innovative method for RTE in anisotropic media via infinite series expansion. • Series terms represent light scatterings; analytical solutions for zero/single scatter. • Conceptually linked to Monte Carlo by interpreting terms as photon trajectories. • Enhanced performance over explicit Monte Carlo, confirmed by comparative analysis. • Green's function series aids fast simulations for neutrino telescopes and beyond. [ABSTRACT FROM AUTHOR]