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In this paper, dynamic anti-plane problem in graded non-homogeneous magnetic-electric-elastic material with a conductive cylindrical rigid inclusion is studied. Cracks are generated from the inclusion edge under the action of SH guided waves. By applying a pair of reversed shear stresses to the crack surface, the mechanical model of the crack is achieved, and Green's function method is used in this process. The scattering fields of displacement, electric potential and magnetic potential are constructed by the wave function expansion method. Numerical results clarified the factors that affect the dynamic stress intensity factor of the crack tips, including material parameters, inclusion parameters, wave number and incident angle. It is expected that the investigation of magnetic-electric-elastic material with inclusion-initiated crack defects can provide some references for the project designing, manufacture and application of non-homogeneous multi-fields coupling materials. [ABSTRACT FROM AUTHOR]

This work aims to develop an effective method for evaluating the stress concentration at the tip of permeable interfacial cracks near a circular hole in functionally graded piezoelectric bi-materials. The structure is loaded by anti-plane incident SH-wave and all material parameters are assumed to obey exponential variations. Fracture analysis is performed by the Green function method, which is used to solve the boundary conditions problem. The mechanical model of the cracks is constructed by crack-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack tips can be derived. The validity of the present method is verified by comparison with references. Numerical cases reveal parametric dependence of DSIFs on the geometry of circular holes and cracks, the characteristics of the incident waves and the inhomogeneity of materials. The method proposed in this paper can circumvent the limitations of using dual integral equations to deal with asymmetric defects and opens up a new way for the research on fracture problems in functionally graded piezoelectric materials with more complex defects. [ABSTRACT FROM AUTHOR]

Thermal responses of the metal materials subjected to intense laser irradiation are complicated due to the phase change in the melting process. In order to simplify this problem, previous studies usually ignored the liquid phase or took the usage of finite element method, which limited the achievement of theoretical breakthroughs. In the present study, a one-dimensional heat transfer model with consideration of phase change was established to describe the melting process of the metal materials caused by a constant intense laser beam. The governing equations with three domains were constructed in the piecewise form: the liquid phase region (melted already), the solid phase region (unmelted yet) and the melting region. The limited discretization method was employed to describe the moving of the soli-liquid interface and the energy exchange. The piecewise governing equations in liquid and solid region were solved separately and analytically by means of the Green's function method, and the calculation result was verified by the finite element simulation. The results of the analytical model were in good agreement with those of the finite element simulation, and the maximal prediction errors of the temperature field prediction between the theoretical model and FE simulation is limited to 2.8 %. In addition, the influences of heat source intensity, material heat conductivity, latent heat on the melting process were discussed in detail. The analytical and simulation results reveal that the semi-analytical solution in piecewise for 1-D laser melting process can be successfully used to reflect the dynamic temperature response of the metal materials and the movement of the solid-liquid interface. This work is of guiding significance for the analytical solution of the multi-dimensional melting process of the metal materials under the fixed and continuous laser beams.

The analytical solution of two magnetic-electro-elastic materials with hole-initiated cracks are investigated under anti-plane shearing. The modeling of the cracks is achieved by applying a pair of negative shear stresses in the region where the cracks occur. During this investigation, the fundamental solution of the displacement field is expressed by Green's function method. The expressions of the magneto-electric-elastic wave fields around the interface can be obtained by using the wave function expansion method and Sommerfeld radiation conditions. Then, combined with permeable electromagnetic boundary conditions, the crack problem is reduced to a system of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tip is obtained. Finally, various examples are provided to illustrate the effects of the geometrical parameters, material properties, wave number, and incident angle on the DSIF. Compared with previous traditional numerical and analytical methods, the methods proposed in this article are more applicable in practical engineering and theoretical analysis. [ABSTRACT FROM AUTHOR]

Novel zinc-blende (zb) group-IV binary XC and ternary XxY1−xC alloys (X, Y ≡ Si, Ge, and Sn) have recently gained scientific and technological interest as promising alternatives to silicon for high-temperature, high-power optoelectronics, gas sensing and photovoltaic applications. Despite numerous efforts made to simulate the structural, electronic, and dynamical properties of binary materials, no vibrational and/or thermodynamic studies exist for the ternary alloys. By adopting a realistic rigid-ion-model (RIM), we have reported methodical calculations to comprehend the lattice dynamics and thermodynamic traits of both binary and ternary compounds. With appropriate interatomic force constants (IFCs) of XC at ambient pressure, the study of phonon dispersions ω j q → offered positive values of acoustic modes in the entire Brillouin zone (BZ)—implying their structural stability. For XxY1−xC, we have used Green's function (GF) theory in the virtual crystal approximation to calculate composition x, dependent ω j q → and one phonon density of states g ω . With no additional IFCs, the RIM GF approach has provided complete ω j q → in the crystallographic directions for both optical and acoustical phonon branches. In quasi-harmonic approximation, the theory predicted thermodynamic characteristics (e.g., Debye temperature ΘD(T) and specific heat Cv(T)) for XxY1−xC alloys. Unlike SiC, the GeC, SnC and GexSn1−xC materials have exhibited weak IFCs with low [high] values of ΘD(T) [Cv(T)]. We feel that the latter materials may not be suitable as fuel-cladding layers in nuclear reactors and high-temperature applications. However, the XC and XxY1−xC can still be used to design multi-quantum well or superlattice-based micro-/nano devices for different strategic and civilian application needs. [ABSTRACT FROM AUTHOR]

As a continuation of our previous work on the conservation and breaking of the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847, 138320 (2023)], in this work, the PSS in nuclear single-particle bound and resonant states are investigated uniformly within a relativistic framework by exploring the poles of the Green's function in spherical Woods-Saxon potentials. As the potential depths increase from zero to finite depths, the PS partners evolve from resonant states to bound states. In this progress, the PSS is broken gradually with energy, width, and density splittings. Specially, the energy and width splittings for the resonant and bound states are directly determined by the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious threshold effect is observed for the energy splitting at a critical potential depth, with which one PS partner has become a quasi-bound state inside the centrifugal barrier while the other one is still a high-energy resonant state outside the centrifugal barrier. The differences in the density distributions of the lower component between the PS partners are manifested in the phase shift for the resonant states and amplitudes for bound states.

In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green's function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering. [ABSTRACT FROM AUTHOR]

In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green's function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity–moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green's function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green's function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described. [ABSTRACT FROM AUTHOR]

In this study, a variable cross-sectional flexible pin of a megawatt wind turbine gearbox is taken as the research object, and the deflection curve equation of the variable cross-sectional flexible pin considering the influence of shear deformation is established. The deflection equation and slope-deflection equation of the variable cross-sectional flexible pin are obtained by using the Green's function method. The effectiveness of this method is verified by comparing with the calculation results of the engineering algorithm and the finite element method. The simulation model of the wind power gearbox is established using Romax software, and it is verified that the deformation characteristics of the variable cross-sectional flexible pin can improve the load distribution and load sharing coefficient. The influence of the supporting stiffness of the pin and gear mesh misalignment on the load sharing performance is investigated. The research results provide a theoretical basis for improving the load sharing performance of the wind turbine gearbox and the design optimization of the variable cross-sectional flexible pin.

Pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the lower component of the Dirac spinor. Here, we investigate the conservation and breaking of PSS in the single-nucleon resonant states, as an example, using Green's function method that provides a novel way to precisely describe not only the resonant energies and widths but also the spacial density distributions for both narrow and wide resonances. The PSS conservation and breaking are perfectly displayed in the evolution of resonant parameters and density distributions with the potential depth: In the PSS limit, i.e., when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign, PSS is exactly conserved with strictly the same energy and width between the PS partners as well as identical density distributions of the lower components. As the potential depth increases, the PSS is broken gradually with energy and width splittings and a phase shift in the density distributions.

In this article, the issue of the unique solvability of a problem with shift in an unbounded domain is investigated; the elliptical part of the domain is a horizontal strip. The uniqueness of the theorem is proven by the method of energy integrals under constraints of unequal type on known functions and different orders of fractional differentiation operators in the boundary condition. Problem in the elliptical part of the mixed domain, which is a horizontal strip, is solved by the Green's function method. By reduction to the Fredholm equation of the second kind, the existence of a solution to the problem is proved; the unconditional solvability to the problem follows from the uniqueness of the solution to the problem. [ABSTRACT FROM AUTHOR]

The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been developed accordingly to optimize their computation cost. In particular, recursive techniques have been efficiently applied within the Green's function calculation approach. Recently, with the discovery of Moiré materials, several attractive superlattices have been explored using these recursive Green's function techniques. However, numerical difficulty issues were reported as most of these superlattices have relatively large supercells, and consequently a huge number of atoms to be considered. In this article, improvements to solve these issues are proposed in order to keep optimizing the recursive Green's function calculations. These improvements make the electronic structure calculations feasible and efficient in modelling large superlattice-based devices. As an illustrative example, twisted bilayer graphene superlattices are computed and presented to demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Novel zinc-blende (zb) group-IV binary XC and ternary XxY1−xC alloys (X, Y ≡ Si, Ge, and Sn) have recently gained scientific and technological interest as promising alternatives to silicon for high-temperature, high-power optoelectronics, gas sensing and photovoltaic applications. Despite numerous efforts made to simulate the structural, electronic, and dynamical properties of binary materials, no vibrational and/or thermodynamic studies exist for the ternary alloys. By adopting a realistic rigid-ion-model (RIM), we have reported methodical calculations to comprehend the lattice dynamics and thermodynamic traits of both binary and ternary compounds. With appropriate interatomic force constants (IFCs) of XC at ambient pressure, the study of phonon dispersions ωjq→ offered positive values of acoustic modes in the entire Brillouin zone (BZ)—implying their structural stability. For XxY1−xC, we have used Green’s function (GF) theory in the virtual crystal approximation to calculate composition x, dependent ωjq→ and one phonon density of states gω. With no additional IFCs, the RIM GF approach has provided complete ωjq→ in the crystallographic directions for both optical and acoustical phonon branches. In quasi-harmonic approximation, the theory predicted thermodynamic characteristics (e.g., Debye temperature ΘD(T) and specific heat Cv(T)) for XxY1−xC alloys. Unlike SiC, the GeC, SnC and GexSn1−xC materials have exhibited weak IFCs with low [high] values of ΘD(T) [Cv(T)]. We feel that the latter materials may not be suitable as fuel-cladding layers in nuclear reactors and high-temperature applications. However, the XC and XxY1−xC can still be used to design multi-quantum well or superlattice-based micro-/nano devices for different strategic and civilian application needs.

This paper aims to develop an effective theoretical method for analyzing the interaction of interfacial crack and complex defect in functionally graded magnetic-electro-elastic bi-materials with exponential variation under the action of anti-plane incident SH-wave. The boundary value problem of interest is solved by Green's function method. The mechanical model of the cracks is constructed through interface conjunction and crack deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips of the left crack are expressed. The validity of the present method is verified by comparing with a single crack model in previous work. Through the analyses of numerical cases, it can be concluded that the DSIF is related with 3 factors：the geometry of complex defect and crack, the characteristics of incident wave and the inhomogeneity of materials. Comparing with dual integral equations in dealing with asymmetric defects, the method in this paper is relatively more flexible and applicable, also it comes up with a new way to study fracture problems in functionally graded magnetic-electro-elastic materials with more complex defects. [ABSTRACT FROM AUTHOR]

In this paper, the electron transport through a zigzag single-walled carbon nanotube (SWCNT) junction consisting of zigzag SWCNT (central region) sandwiched between two semi-infinite metallic zigzag SWCNT leads to the presence of an applied uniaxial strain is numerically investigated. This study is based on a nearest-neighbor tight-binding approximation within the framework of a generalized Green’s function technique and relies on the Landauer-B¨utikker formalism. The results show that the electron transport properties of the system can be well controlled by modifying the uniaxial strain strength and length of the SWCNT junction. Besides, applying compressive strain is more effective than tensile strain in opening a band gap in the system. Furthermore, the current amplitude for the tensile strain is bigger than the compressive strain with the same absolute values of uniaxial strain strength. As the length of the intermediate region increases, the density of states in Fermi energy decreases, and the magnitude of the electron emission function in Fermi energy decreases to zero, leading to the transition of the metal to the semiconductor.

This paper deals with dynamic analysis of functionally graded beams on elastic foundation considering damping effect. It is assumed that the mechanical properties of the material vary along the beam thickness. The fourth-order differential equation is analytically solved by means Green's function method, and exact answer is achieved. Damping effect, which is an intrinsic property of structures with great influence on the forced vibration of mechanical systems is included in the analysis. However, due to difficulty involved, it is usually neglected in the analysis of structures. Furthermore, the effect of rotary inertia is considered in the problem formulations. Green's function method is a straightforward way to model physical problems subjected to arbitrary loads and affected by various parameters, such as, elastic foundation, damping, geometry and mechanical properties. It could be a unique solution to gain the exact answers via the superposition manner. To demonstrate the accuracy and efficiency of the presented solution, dynamic response of the beam under different harmonic loads is obtained and compared to available results in some cases. [ABSTRACT FROM AUTHOR]

In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green’s function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity–moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green’s function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green’s function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

This paper is concerned with coupled vibration of rotating composite laminated beams under hygrothermal environment. The governing equations of the coupled vibration of the beams considering hygrothermal effects and rotating motion are derived on the base of d'Alembert principle. Green's function method is adopted to obtain the flapwise-edgewise coupled vibration characteristics of the beams. Then, a comprehensive parametric study on natural frequencies of flapwise and edgewise bending vibrations is numerically performed. Results indicate that the flapwise-edgewise coupling factors are essential for the vibration analysis of the high-speed rotating structures. Temperature variation, moisture concentration, rotating speed, and design parameters have a significant influence on the coupled vibration characters of the beams, and thermal expansion deformation is nonnegligible in the coupled vibration analysis. [ABSTRACT FROM AUTHOR]

Modeling three-dimensional contaminant transport released from arbitrary shape source geometries is useful in hydrological and environmental sciences. This article produces several analytical solutions for three-dimensional contaminant transport in a homogeneous and isotropic aquifer by using Green's function with the groundwater flow which is assumed to be in three directions. The solutions are obtained for both finite depth aquifer and semi-infinite depth aquifer. Various types of sources are discussed: point, line, plane, or cuboid sources. The continuous and instantaneous sources are also investigated. A MATLAB coding is developed to calculate the numerical integrals which occur at the solutions. Some solutions are verified with the solutions obtained in the literature. This study confirms the effect of groundwater velocities in all directions on the degree and the directions of contaminant spreading. Additionally, the results highlight the significant effect of the geometrical shape of the contaminant sources on contaminant concentrations for instantaneous and continuous sources. In particular, the cuboid source and the horizontal rectangular source provide the highest concentrations. The analytical solutions developed in this article can be applied for a wide range of contaminant transport. [ABSTRACT FROM AUTHOR]

The Green's function method is a powerful technique to investigate the existence and uniqueness of the solution for two-point boundary value problems. The main task of this paper is to establish the maximal order of convergence of the Green's function method applied in the approximation of the solution for third- and fourth-order two-point boundary value problems with deviating argument. The developed iterative method uses a complete cubic spline interpolation procedure being able to provide both discrete and continuous approximation of the solution. Some numerical examples confirm the obtained theoretical results and illustrate the accuracy of the algorithm. [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]

The purpose of this work is to investigate the convergence properties of Green's function method applied to boundary value problems for functional differential equations. Recently, involving Picard and Mann iterations, a Green's function technique was developed (in Int. J. Computer Math. 95, no. 10 (2018) 1937-1949) for third order functional differential equations, but without specifying the order of convergence of the proposed method. In order to improve this aspect, here we establish the maximal order of convergence of Green's function method applied to two-point boundary value problems associated to second and third order functional differential equations. In this context, by using suitable quadrature rule and appropriate spline interpolation procedure, the Picard iterations are approximated by a sequence of cubic splines on uniform mesh. Some numerical experiments are presented in order to test the theoretical results and to illustrate the accuracy of the method. [ABSTRACT FROM AUTHOR]

The antiplane deformation of a wedge made of a functionally graded material (FGM) with finite radius has been investigated analytically in the present article. In relation to the boundary conditions imposed on the arc portion of the wedge, displacement or traction, two problems have been studied. In each of the problems three various kinds of boundary conditions (tractiondisplacement, displacement-displacement and traction-traction) have been applied to the radial edges of the wedge. The governing differential equations have been solved by employing finite Fourier transforms and Green's function method. The closed form solutions for stress and displacement distribution have been achieved for the whole domain. Explicit relations have been extracted for the order of stress singularity in all cases. These relations indicated the dependence of the order of stress singularity on the boundary conditions, material property and wedge angle. In fact, despite of an isotropic wedge, for which the order of stress singularity depends only the geometry of the wedge, in an FG wedge the order of stress singularity depends both the geometry as well as the material property. [ABSTRACT FROM AUTHOR]

Polythiophene is a highly conductive molecule which possesses thermal and chemical stability showing great performance in electrical devices. Polythiophene also shows an uncommon highly demanding electrical property named negative differential resistance which is a decrease of electron current with increase of applied voltage. To address this issue, in this work we study theoretically electron transport properties of a polythiophene molecular bridge sandwiched between two metal leads in the presence of Nitrogen atom as a substitute for one or two of the Carbon atoms in the molecule. The results based on Green’s function formalism show that the presence of Nitrogen reduces the electron transmission coefficient. On the other hand, Nitrogen can lead to amplification of negative differential resistance. Strength of the resistance is affected by the positions and number of Nitrogen atoms in the system. Therefore, choosing right positions for locating impurities is very important. We found that by substituting a Carbon atom with Nitrogen in some positions the system shows notable negative differential resistance. Besides, when two Carbon atoms are replaced by Nitrogen atoms there are some special locations that not only the system shows negative deferential resistance but also it works as an electronic molecular switch which is highly demanding in electronic industry.

This work introduces Green Networks (GreenNets), a novel class of neural network architectures designed to address a wide spectrum of boundary problems in partial differential equations (PDEs). Demonstrated versatility includes solving the Poisson equation, convection-diffusion equation, and unsteady incompressible Navier-Stokes equations. GreenNets comprises two specialized variants: Boundary Transformation Green Network (BT-GreenNet), focusing on transforming Dirichlet boundary conditions into source terms, and Boundary Integral Green Network (BI-GreenNet), considering boundary integral terms with shared weights between the boundary and source integrals. Comparisons with existing deep learning and traditional numerical methods underscore their accuracy and efficiency. BT-GreenNet excels in efficiency, and BI-GreenNet offers enhanced flexibility. The research pinnacle, Boundary Unified Green Network (BU-GreenNet), merges BT-GreenNet and BI-GreenNet to address coupled PDEs, specifically unsteady incompressible Navier-Stokes equations. BU-GreenNet stands out by surpassing traditional numerical approaches, offering remarkable computational efficiency while faithfully capturing the intricate evolution of fluid dynamics phenomena. This research redefines the means of solution to boundary problems in PDEs through innovative neural network architectures, emphasizing practical utility and computational efficiency. • Propose Green Networks for solving boundary problems in PDEs. • Be suitable for nonlinear PDEs. • Achieve high efficiency and accuracy in Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

As a continuation of our previous work on the conservation and breaking of the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847 , 138320 (2023)], in this work, the PSS in nuclear single-particle bound and resonant states are investigated uniformly within a relativistic framework by exploring the poles of the Green's function in spherical Woods-Saxon potentials. As the potential depths increase from zero to finite depths, the PS partners evolve from resonant states to bound states. In this progress, the PSS is broken gradually with energy, width, and density splittings. Specially, the energy and width splittings for the resonant and bound states are directly determined by the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious threshold effect is observed for the energy splitting at a critical potential depth, with which one PS partner has become a quasi-bound state inside the centrifugal barrier while the other one is still a high-energy resonant state outside the centrifugal barrier. The differences in the density distributions of the lower component between the PS partners are manifested in the phase shift for the resonant states and amplitudes for bound states. [ABSTRACT FROM AUTHOR]

In this paper, and on the basis of the equivalent eigenstrain principle, a fundamental formulation for inhomogeneous inclusion problems is proposed, which is to transform the inhomogeneous inclusion problems into auxiliary equivalent homogenous inclusion problems. Then, the analysis, which is based on the equivalent homogenous inclusions, would significantly reduce the workload and would enable the analytical solutions that are possible for a series of inhomogeneous inclusion problems. It also provides a feasible way to evaluate the effective properties of composite materials in terms of their equivalent homogenous materials. This formulation allows for solving the problems: (i) With an arbitrarily connected and shaped inhomogeneous inclusion; (ii) Under an arbitrary internal load by means of the nonuniform eigenstrain distribution; and (iii) With any kind of external load, such as singularity, uniform far field, and so on. To demonstrate the implementation of the formulation, an oblate inclusion that interacts with a dilatational eigenstrain nucleus is analyzed, and an explicit solution is obtained. The fundamental formulation that is introduced here will find application in the mechanics of composites, inclusions, phase transformation, plasticity, fractures, etc. [ABSTRACT FROM AUTHOR]

Scouring can reduce the strength and rigidity of the pile–soil system and become one of the major causes for the failure of the structure of the partially-embedded single pile. The stratification of the soil fields has a significant influence on the internal force and deformation of laterally-loaded piles. A dynamic model of the laterally-loaded single pile in layered soil is established employing Hamilton's principle based on the modified Vlasov foundation model. Then, the finite difference method is used to obtain the numerical matrix containing the control equations of the single pile to achieve accurate modeling of the soil–structure interaction (SSI) system affected by scouring, so as to solve the natural frequencies of the single pile. Green's function method obtains the analytical solution of the forced vibration of the single pile. The effects of scouring and the layered soil on the dynamic response of the single pile are studied by numerical calculation and parameter analysis. It is shown that the dynamic model of the partially-embedded single pile in layered soil based on the modified Vlasov foundation model can accurately predict the dynamic characteristics of pile foundation affected by scouring. As the scouring degree intensifies, the first-order natural frequencies of the single pile in layered soil decrease significantly. The subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. The first-order natural frequencies of the single pile at each scour level increase with the increase in the thickness of the underlying soil. When the elastic modulus of the first layer of soil is increased by one time, the first-order natural frequencies of the single pile are increased by about 20%. [ABSTRACT FROM AUTHOR]

Objectives：Continuous and dense global navigation satellite system (GNSS) surface deformation data provide an effective tool to invert refined regional surface mass variations. However, the factors influencing the reliability of GNSS inversion results need to be further studied, such as regularization (including the construction of regularization matrix and determination of optimal regularization parameter), observation noise and distribution of GNSS stations. Methods: First, we proposed an improved regularized Laplacian constraint matrix and discussed the adaptability of the generalized cross⁃validation (GCV) method in selecting the regularization parameter of ill⁃posed equations for inversion of regional surface mass variations based on the loading Green's function theory. Second, we compared the effects of different constraint matrices and constraint methods on the GNSS inversion results. Third, we further investigated the influences of different noise levels of GNSS vertical displacement, the number and distribution of GNSS stations on the inversion results. Results: (1) The regularized Laplacian matrix in this paper can better suppress the edge effects than the traditional Laplacian matrix. (2) The GCV method can effectively determine the optimal regularization parameter, and the inversion results are in good agreement with those solved by the root mean square error (RMSE) criterion. (3) If there are enough GNSS stations and the observation accuracy is high enough in the studied area, the inversion results will be more reliable. Meanwhile, the accuracy of inversion results for uniformly distributed stations is comparable to that of randomly distributed stations when the number of stations is large enough. Conclusions: The improved regularized Laplacian matrix and the GCV method can improve the reliability of GNSS inversion results, which can guide the inversion of surface mass variations using measured GNSS data. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green's function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability. [ABSTRACT FROM AUTHOR]

This paper presents a model for the mathematical description of the diffusion process, as well as an attempt to use Green’s function approach to solve the one-dimensional diffusion equation within the necessary bounds. By studying the initial condition for, we will be able to obtain the appropriate solution to this diffusion equation. With a constant diffusion coefficient, this equation represents the rate of change of concentrations of substances in their own lattice or in separate substances. Finally, numerical answers will be obtained via a computational approach. Because we consider t = 0 throughout the equation, the result can also be applied to an isothermal diffusion. [ABSTRACT FROM AUTHOR]

Abstract This article concerns the Cauchy problem for the fractional semilinear pseudo-parabolic equation. Through the Green’s function method, we prove the pointwise convergence rate of the solution. Furthermore, using this precise pointwise structure, we introduce a Sobolev space condition with negative index on the initial data and give the nonlinear critical index for blowing up.

We present a new simulation method for predicting the data retention time distribution including random dopant fluctuation (RDF). It is a critical problem that a long simulation time is required to predict a wide range of retention time distributions, but our model has extremely fast computation speed compared with the Monte–Carlo method and machine learning method. The proposed model is applied to the dynamic random access memory cell transistor of the 20 nm technology node. The simulation results show that RDF degrades data retention time, particularly in tail cells, and this can be effectively improved by reducing the interface trap density and the drain doping density. [ABSTRACT FROM AUTHOR]

This paper describes some numerical experiments for stress modeling in the zone around a reservoir in a sedimentary basin, where oil and gas exploration is real or potential. We aim to map mainly low- and high-pressure zones, under the principle that they act as push-and-pull natural pumps for fluid accumulation. The necessary data for practical work is based on seismic data, as a post-migration process with the knowledge of velocities of the P and S waves, and the density information. The computation is designed for simple geometries to represent a reservoir geology, and it is addressed as a boundary value problem (BVP) involving the Beltrami-Michell's partial differential equation with Dirichlet conditions. The method employed was the Green's function expressed by Fourier series for the solution of the BVP, where the boundary conditions are given by the stress components along the boundary of the target volume. The first stress invariant controls the elastic mechanical behavior of the subsoil; therefore, once the distribution of rock pressure is obtained, and the boundary conditions are defined, solving the BVP allows the calculation of the stress components distribution (normal and tangential) within a separate target volume for details. The relationship between rock pressure and stress components is established by the Beltrami-Michell problem, which takes the form of a Poisson's equation. The proposed method was applied in a more complex target zone present in the Marmousi model, which contains reservoirs within regions of interest, expanding to more realistic complex problems. [Display omitted] • The low- and high-pressure zones act as natural pumps for fluid accumulation. • The first stress tensor invariant rules the subsoil elastic mechanical behavior. • The Beltrami-Michell equation relates rock pressure and stress tensor components. • The Beltrami-Michell solution is closely related to stress boundary conditions. • The Poisson's ratio values can cause deviations in the expected solution. [ABSTRACT FROM AUTHOR]

Abstract This article deals with the novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method, shortly called SGHPM. The SGHPM is a method which combines the homotopy perturbation method with Green’s function method. The convergence analysis for the SGHPM is shown. Furthermore, some examples are presented to illustrate the validity of the proposed method and to ensure that SGHPM is a technique which is powerful and efficient for finding approximate analytic solutions of IBVPs.

It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous one-dimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑ k = 1 ∞ sin k x sin k y / ( k 2 - α 2 ) is found in the process.

The magnetic properties of the 2D anisotropic antiferromagnetic spin‐1/2 Heisenberg model with Dzyaloshinskii–Moriya interaction and in‐plane frustration are studied. The method of spin Green's functions within the framework of Tyablikov's random‐phase‐approximation decoupling scheme is used to derive expressions for the spin‐wave spectrum, sublattice magnetization, and transition temperature. Based on these expressions, a detailed analysis of the influence of varying values of model parameters on their magnetic properties is conducted. The model is also applied to the high‐Tc superconducting parent compound La2CuO4 and the results compared with available experimental data. [ABSTRACT FROM AUTHOR]

The magnetic properties of the 2D anisotropic antiferromagnetic spin‐1/2 Heisenberg model with Dzyaloshinskii–Moriya interaction and in‐plane frustration are studied. The method of spin Green's functions within the framework of Tyablikov's random‐phase‐approximation decoupling scheme is used to derive expressions for the spin‐wave spectrum, sublattice magnetization, and transition temperature. Based on these expressions, a detailed analysis of the influence of varying values of model parameters on their magnetic properties is conducted. The model is also applied to the high‐Tc superconducting parent compound La2CuO4 and the results compared with available experimental data. [ABSTRACT FROM AUTHOR]

This paper presents a Green’s function method for the modal analysis of structures with interval parameters. By introducing first order approximations, the governing equations of modal displacements for interval analysis are decomposed into two sets of governing equations for the midpoints and deviations of modal responses, respectively. Utilizing the similarity between these equations and the governing equations for deterministic static analysis, Green’s functions for the linear static problem are directly used in the modal analysis process. Different from the traditional finite element method which needs the element refinement to improve solution accuracy, the proposed Green’s function method needs just one element for each beam member to achieve accurate results. Numerical examples presented demonstrate the applicability of the proposed method, and reveal some regular patterns of the effects of interval parameters in structural modal analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the long time behavior of the solution for the nonlinear wave equation with frictional and visco-elastic damping terms in Rn+. It is shown that for the long time, the frictional damped effect is dominated. The Green's functions for the linear initial boundary value problem can be described in terms of the fundamental solutions for the full space problem and reflected fundamental solutions coupled with the boundary operator. Using the Duhamel's principle, we get the pointwise long time behavior of the solution ∂xαu for |α| ≤ 1. [ABSTRACT FROM AUTHOR]

In this paper, and on the basis of the equivalent eigenstrain principle, a fundamental formulation for inhomogeneous inclusion problems is proposed, which is to transform the inhomogeneous inclusion problems into auxiliary equivalent homogenous inclusion problems. Then, the analysis, which is based on the equivalent homogenous inclusions, would significantly reduce the workload and would enable the analytical solutions that are possible for a series of inhomogeneous inclusion problems. It also provides a feasible way to evaluate the effective properties of composite materials in terms of their equivalent homogenous materials. This formulation allows for solving the problems: (i) With an arbitrarily connected and shaped inhomogeneous inclusion; (ii) Under an arbitrary internal load by means of the nonuniform eigenstrain distribution; and (iii) With any kind of external load, such as singularity, uniform far field, and so on. To demonstrate the implementation of the formulation, an oblate inclusion that interacts with a dilatational eigenstrain nucleus is analyzed, and an explicit solution is obtained. The fundamental formulation that is introduced here will find application in the mechanics of composites, inclusions, phase transformation, plasticity, fractures, etc.

The reflection and transmission of surface waves propagating over an irregular surface located on a flexible base in an ice-covered fluid are analyzed within the context of linearized water wave theory. The ice-floe and flexible bed surface are assumed as narrow elastic sheets with different compositions. Under such circumstances, there are two types of proliferating waves that exist for any specific frequency. The proliferating waves having smaller wavenumber spread at just beneath the ice-floe (ice cover mode) and the other spreads over the flexible bottom of the fluid (flexural base mode). An elementary perturbation theory is used for reforming the governing boundary value problem (bvp) to a first-order bvp which is solved by utilizing the Green's function technique. The first-order correction of the reflection and transmission coefficients are calculated in the form of integrals comprising of a function which represents the base deformation. A particular example of base deformation is taken to evaluate all these coefficients and the results are depicted graphically. The major strength of the recent study is that the results for the values of reflection and transmission coefficients for both the wavenumbers are established to meet the energy relation almost exactly. [ABSTRACT FROM AUTHOR]

Data retention time distribution of the dynamic random-access memory cell transistor of the 20-nm technology generation has been investigated using the physics-based statistical simulation. Traps cause high leakage current of the leaky cells; however, we found that the reduction of trap is not effective in improving the refresh cycle. Therefore, an effective method is needed to overcome the retention time degradation due to the traps. This study shows that the data retention time of the tail cells can be increased more than 50% by adopting the dual work function metal gate structure. [ABSTRACT FROM AUTHOR]

Scouring can reduce the strength and rigidity of the pile–soil system and become one of the major causes for the failure of the structure of the partially-embedded single pile. The stratification of the soil fields has a significant influence on the internal force and deformation of laterally-loaded piles. A dynamic model of the laterally-loaded single pile in layered soil is established employing Hamilton’s principle based on the modified Vlasov foundation model. Then, the finite difference method is used to obtain the numerical matrix containing the control equations of the single pile to achieve accurate modeling of the soil–structure interaction (SSI) system affected by scouring, so as to solve the natural frequencies of the single pile. Green’s function method obtains the analytical solution of the forced vibration of the single pile. The effects of scouring and the layered soil on the dynamic response of the single pile are studied by numerical calculation and parameter analysis. It is shown that the dynamic model of the partially-embedded single pile in layered soil based on the modified Vlasov foundation model can accurately predict the dynamic characteristics of pile foundation affected by scouring. As the scouring degree intensifies, the first-order natural frequencies of the single pile in layered soil decrease significantly. The subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. The first-order natural frequencies of the single pile at each scour level increase with the increase in the thickness of the underlying soil. When the elastic modulus of the first layer of soil is increased by one time, the first-order natural frequencies of the single pile are increased by about 20%.

The temperature, doping concentration, size, and magnetic field dependences of the real part of the dielectric function ϵ′ for Fe and Er ion‐doped BaTiO3bulk and nanoparticles—are calculated using microscopic models and the Green's function technique. The Fe ions substitute the Ti ions and cause a tensile strain. The maximum value of ϵ′ and the ferroelectric phase transition temperature TC decrease with increasing the Fe doping concentration. Moreover, ϵ′ decreases with decreasing particle size and increases with increasing an external magnetic field. The latter is an evidence for a strong magnetodielectric effect. By substituting the Ba with Er ions, there appears a strong compressive strain. It causes an increase in the maximum of ϵ′ and TC with increasing the Er ion concentration. [ABSTRACT FROM AUTHOR]