First-principles study of repeated current switching in a bimolecular device

Using nonequilibrium Green’s functions in combination with the first-principles density-functional theory, we investigate electronic transport properties of a bimolecular device consisting of two parallel placed phenalenyl molecules. When the two molecules get close enough, the currents of this bimolecular device could switch repeatedly by the mechanical strain. The deeper analysis indicates that the overlapping region size sensibly alters the coupling and charge transfer between the two parallel π-conjugated molecules is a very important factor for this behavior.     

Deriving the time-dependent dyadic Green’s functions in conductive anisotropic media

A homogeneous anisotropic conductive medium, characterized by symmetric positive definite permeability and conductivity tensors, is considered in the paper. In this anisotropic medium, the electric and magnetic dyadic Green’s functions are defined as electric and magnetic fields arising from impulsive current dipoles and satisfying the time-dependent Maxwell’s equations in quasi-static approximation. A new method of deriving these dyadic Green’s functions is suggested in the paper. This method consists of several steps: equations for electric and magnetic dyadic Green’s functions are written in terms of the Fourier images; explicit formulae for the Fourier images of dyadic Green’s functions are derived using the matrix transformations and solutions of some ordinary differential equations depending on the Fourier parameters; the inverse Fourier transform is applied numerically to obtained formulae to find dyadic Green’s functions values. Using suggested method images of electric and magnetic dyadic Green’s function components are obtained in such conductive anisotropic medium as the white matter of a human brain.     

Elastostatic Green’s functions for an arbitrary internal load in a transversely isotropic bi-material full-space

The problem of a full-space which is composed of two half-spaces with different transversely isotropic materials with an internal load at an arbitrary distance from the interface is considered. By virtue of Hu-Nowacki-Lekhnitskii potentials, the equations of equilibrium are uncoupled and solved with the aid of Hankel transform and Fourier decompositions. With the use of the transformed displacement- and stress-potential relations, all responses of the bi-material medium are derived in the form of line integrals. By appropriate limit processes, the solution can be shown to encompass the cases of (i) a homogeneous transversely isotropic full-space, and (ii) a homogeneous transversely isotropic half-space under arbitrary surface load. As the integrals for the displacement- and stress-Green’s functions, for an arbitrary point load can be evaluated explicitly, illustrative results are presented for the fundamental solution under different material anisotropy and relative moduli of the half-spaces and compared with existing solutions.     

Stress-intensity-factor equations for compact specimen subjected to concentrated forces

A Green’s function (GF) for the standard compact C(T) specimen was developed that can be applied over a wide range in crack-configuration parameters and for any arbitrary residual-stress distribution along a symmetry-plane crack path from the front face to the back face. Finite-element and boundary-element analyses were conducted to obtain stress-intensity factors over a wide range in crack-length-to-width ratios (a/w) and in concentrated force locations along the crack surface. These results were compared with previous boundary-collocation results from the literature and were used to develop an improved GF equation. As a validation of the newly developed wide-range equation, stress-intensity factors were calculated on a C(T) specimen subjected to a stress distribution induced by the standard pin loading without a crack-starter notch or crack and were compared with well-known results from the literature. The accuracy of the GF equation is within about ±1.3% of the numerical analyses over a wide range in a/w ratios from 0.2 to 0.9.     

Green’s functions for non-self-adjoint problems in heat conduction with steady motion

Heat conduction in a rectangular parallelepiped that is in steady motion relative to a fluid is studied in this paper. The governing equation consists of the standard heat equation plus lower-order derivative terms with the space variables that represent the effects of the solid flow. The presence of the first-order-derivative terms with the space variables renders the spatial part of the governing differenial equation non-self-adjoint and care must be exercised in defining the new Green’s functions to be used in representing the solutions of initial- and boundary-value problems. It is illustrated how the Green’s functions may be constructed and how solutions of initial- and boundary-value problems may be obtained that lead to numerical results. Convergence properties of the solutions are also discussed.     

Magnetic-field calculation for a high-temperature superconducting cryogenic current comparator

The problem considered in this paper arises in the design of a high-temperature superconducting cryogenic current comparator (CCC). The CCC consists of two currents flowing in opposite directions inside a toroidal superconducting shield. The shield has a radial cut, necessary for the measurement of the current ratio, but causing an error in the obtained ratio. The problem of interest is the dependence of the error on the geometric parameters of the device: the major and minor radii of the shield, the cut width, the material thickness, and the location of the currents. In the first part of the paper, a toroidal shield with an infinitesimal cut is considered and analytic expressions are derived for the magnetic field and the surface-current distribution. In the second part, a cut of finite width is introduced. Since all the perturbing currents are present in the narrow region around the cut, a shield of cylindrical shape is assumed. Expressions are derived for the flux through the cut and the magnetic field around the cut. Analytical results are in good agreement with the numerical results obtained by a finite-element method. In the final part, the expression for the ratio error is derived, which shows that in order to minimize the error, currents should be concentrated around the shield axis, the major radius of the shield should be maximized and the bore radius minimized. The error depends logarithmically on the cut width.     

A time-marching scheme based on implicit Green’s functions for elastodynamic analysis with the domain boundary element method

The present work presents an alternative time-marching technique for boundary element formulations based on static fundamental solutions. The domain boundary element method (D-BEM) is adopted and the time-domain Green’s matrices of the elastodynamic problem are considered in order to generate a recursive relationship to evaluate displacements and velocities at each time-step. Taking into account the Newmark method, the Green’s matrices of the problem are numerically and implicitly evaluated, establishing the Green–Newmark method. At the end of the work, numerical examples are presented, verifying the accuracy and potentialities of the new methodology.     

Treatment of residual stress in failure assessment procedure

The effect of residual stress on component failure has been investigated using the distributions from current failure assessment procedures, and a residual stress profile simple to apply with less conservatism has been proposed for the weld geometries of T-plate and tubular T-joint. The stress intensity factors (SIFs) in the two weld geometries under various types of loads have been calculated using the Green’s function method. The Green’s functions were determined not only for the T-plate but also for the tubular T-joint with the built-in ends. The use of a linear (bending) stress profile, derived from an analysis of measured residual stress distributions in T-plate and tubular T-joints, has been examined. The profile was validated with experimentally measured residual stress distributions in two materials, a high strength and medium strength ferritic steel and two geometries, a T-plate joint and a tubular T-joint for crack lengths up to half the plate or pipe thickness. Whereas the recommended residual stress distributions are geometry and material specific, it is shown that a simplified linear bending profile provides a possible guideline, applicable to a range of materials and geometries, where detailed information on weld procedures or residual stress profiles are unavailable.     

Derivatives of Green’s functions in piezoelectric media and their application in dislocation dynamics

Three-dimensional extended Green’s functions and their high-order derivatives in general anisotropic piezoelectric materials are derived and expressed in integral forms. They can be evaluated directly by the Gaussian numerical integration method. The extended Green’s functions and their derivatives by the present method have accuracy and computational efficiency. Using the extended Green’s functions, the stress field induced by an arbitrary dislocation in an anisotropic piezoelectric medium, is obtained and expressed as a line integral around the dislocation.     

Axial soil-pile interaction in a transversely isotropic half-space

A rigorous integral equation formulation is presented for the axisymmetric load-transfer analysis of a thin-walled pile embedded in a transversely isotropic half-space under axial load. By virtue of a set of ring-load Green’s functions for the pile and one for the half-space, the problem is shown to be reducible to a pair of Fredholm integral equations. Through a mathematical analysis of an auxiliary pair of Cauchy integral equations, the inherent singularities of the contact stress distributions are rendered explicit. With a direct incorporation of the singular nature of the resultant load transfers, the numerical solution of the integral equations is shown to be possible by an interpolation of regular functions only. Typical results for various material and geometrical conditions are presented, including a comparison with past classical solutions, to illustrate the effects of transverse anisotropy on the load-transfer process.     

Urbach’s rule of Bi4Ge3O12 doped with 3d and 4d ions

In this work, the influence of 3d (Fe, Mn) and 4d (Ru) ions on the absorption coefficient of the doped Bi₄Ge₃O₁₂ (BGO) in the spectral range 3.6-4.05 eV has been determined. The validity of Urbach’s rule is verified in an illuminated and an annealed state of the samples. The dependence between the incorporation of the different dopants and the values of their Urbach’s parameters is established. The creation and the destruction of the excitons, associated with the ionized donors, are explained. The Urbach’s energy of all samples is determined.     

Multiple cracks on the arc-shaped interface in a semi-cylindrical magneto-electro-elastic composite with an orthotropic substrate

The present work investigates the problem of multiple cracks on the arc-shaped interface of a semi-cylindrical magneto-electro-elastic layer bonded onto an orthotropic substrate. Continuously distributed dislocation is used to simulate the anti-plane interfacial cracks. The problem is formulated as a Cauchy singular integral equation by integrating the Green’s function of an interfacial point dislocation. Both the theoretical derivation and numerical computation are verified in special cases. The effects of the interface end, crack space, layer thickness, stiffness ratio and material orthotropy are surveyed, among which the fracture behavior of the interface end deserves special attention in design.     

A point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material

We use the compact mono-harmonic general solutions of transversely isotropic electro-magneto-thermo-elastic material to construct the three-dimensional Green’s function for a steady point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material by five newly introduced mono-harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results are given graphically by contours.     

A note on the divergence problem arising in calculation of Green’s function for a 2D piezoelectric thin film strip with free boundaries and containing straight line defects: Fourier approach for bodies of cubic symmetry

Analytic formulas for the Green’s function and the coupled electro-elastic fields for a 2D piezoelectric strip with free boundaries and containing a distribution of straight line defects have already been found some years ago. These formulas exploit the well-known Stroh formalism and the Fourier approach, so the result is given as the Fourier integral and therefore its numerical implementation should pose no problem. However, in this note we show that for the case of cubic symmetry this form of the Green’s function contains strong divergences, excluding possibilities of direct application of well-known numerical schemes. It is also shown that these divergences translate to divergences of the corresponding electro-elastic fields of a single defect. By means of a rigorous analysis it is demonstrated that imposing physical conditions implied by the nature of the problem all of these divergences cancel and the final, physical result exhibits expected, regular behavior at infinity. Unfortunately, although the nature of this problem is purely mathematical, it leads to irremovable numerical ∞ − ∞ uncertainties which tend to spread over the whole Fourier domain and severely impede engineering applications of the Green’s function. This motivates us to compute the exact form of all divergent terms. These novel formulas will serve as a guide when establishing numerically stable algorithms for engineering computations involving the system in question.     

Green’s functions for transversely isotropic magnetoelectroelastic media

Based on the governing equations of transversely isotropic magnetoelectroelastic media, four general solutions on the cases of distinct eigenvalues and multiple eigenvalues are given and expressed in five mono-harmonic displacement functions. Then, based on these general solutions, employing the trial-and-error method, the three-dimensional Green’s functions of infinite, two-phase and semi-infinite magnetoelectroelastic media under point forces, point charge and magnetic monopole are all presented in terms of elementary functions for all cases of distinct eigenvalues and multiple eigenvalues. Numerical results are also presented.     

A note on the divergence problem arising in calculation of Green’s function for a 2D piezoelectric thin film strip containing straight line defects and free boundaries: Fourier approach for bodies of unrestricted anisotropy

In this paper we derive a set of novel formulas for computation of the Green’s function and the coupled electro-elastic fields in a 2D piezoelectric strip with free boundaries and containing a distribution of straight line defects. The strip is assumed to be of unrestricted anisotropy, but allowing piezoelectricity, and in this sense situation is more general than in the available literature where only cubic symmetry was investigated. We employ a set of already known analytic formulas for the Fourier amplitude of the Green’s function and the corresponding electro-elastic fields. The key novelty of this paper is solution for the divergence problem occurring during integration of the Fourier amplitude. This problem is caused by poles at k = 0 in various matrix components of the amplitude. From purely mathematical point of view such poles lead to quantities which do not tend to zero at infinity, and this situation is clearly unphysical. To resolve this issue it is demonstrated by means of rigorous analysis that when some additional physical conditions are imposed, physical fields exhibit regular behavior at infinity - the poles do not contribute. Nevertheless, they lead to irremovable numerical ∞ − ∞ uncertainties spreading over the whole domain of integration. This motivates us to compute exact formulas for all these poles to enable engineering calculations involving the system in question.     

基于HITEMP数据库的分子吸收光谱高精度快速建模方法

为解决高温环境下分子吸收光谱精确计算的时间复杂性,满足宽光谱测量领域对理论吸收光谱计算的需求,本研究利用Python语言以逐线计算为基础,结合线型函数的简化、线翼截止准则和谱线数据库的优化,建立了基于高温分子吸收参数数据库(High-Temperature molecular spectroscopic absorption parameters data-base,HITEMP)的分子吸收光谱精确快速计算模型。以Hartmann-Tran线型函数作为吸收光谱标准线型编写部分相关二次速度依赖硬碰撞函数(partially-Correlated quadratic-Speed-Dependent Hard-Collision Profile,p Cq SDHC),结合复概率函数(Complex Probability Function,CPF)简化模型实现了线型函数的精确快速计算,相较于理论计算模型计算速度提高了20倍。按照光谱计算残差在10^-5量级确定了固定波数截断结合谱线半宽等倍数截断的线翼截止准则。以阈值线强度10^-25 cm^-...     

Numerical studies on crack problems in three-layered elastic media using an image method

Two-dimensional crack problems in a three-layered material are analyzed numerically under the conditions of plane strain. An image method is adopted to obtain fundamental solutions for dislocation dipoles in trilayered media. The governing equations for equilibrium cracks can be constructed by distributed dislocation technique and their solutions are sought in terms of the displacement discontinuity method (DDM). Comparisons are made with available analytical or reference solutions for several examples at various contrasts of material constants, and good agreements are found. A crack within a brittle adhesive layer joining two semi-infinite blocks can propagate in a variety of ways. In particular, crack paths in the form of sigmoidal waves within the adhesive layer are revisited to reveal the sensitivities of cracking paths to initial crack locations and directions and residual stresses. In addition, Z-shape and H-shape cracks alternating from interface to interface are re-examined to highlight the transition of failure modes and the role of the interlayer thickness.     

T-stress of cracks loaded by near-tip tractions

T-stress solutions were derived for tractions acting on the crack-faces near a crack tip. Such solutions are of interest for the determination of the leading term of a weight function representation of T-stresses and the computation of an “intrinsic” T-stress for cracks growing in a material with a rising crack growth resistance. First, the type of the Green’s function for T-stresses is theoretically established. Then, results of finite element computations are reported for edge-cracked bars, DCB and CT specimens, which are suited for the determination of the first series term. As an application of the Green’s functions, the T-stresses caused by bridging interactions very close to the crack tip are computed.     

A new family of time integration methods for heat conduction problems using numerical green’s functions

This paper is concerned with the formulation and numerical implementation of a new class of time integration schemes applied to linear heat conduction problems. The temperature field at any time level is calculated in terms of the numerical Green’s function matrix of the model problem by considering an analytical time integral equation. After spatial discretization by the finite element method, the Green’s function matrix which transfers solution from t to t + Δt is explicitly computed in nodal coordinates using efficient implicit and explicit Runge-Kutta methods. It is shown that the stability and the accuracy of the proposed method are highly improved when a sub-step procedure is used to calculate recursively the Green’s function matrix at the end of the first time step. As a result, with a suitable choice of the number of sub-steps, large time steps can be used without degenerating the numerical solution. Finally, the effectiveness of the present methodology is demonstrated by analyzing two numerical examples.