Numerical instabilities of the integral approach to the interior boundary-value problem for the two-dimensional Helmholtz equation

The integral equations arising from the Green's formula, applied to the two-dimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out. A complete study has been carried out for a circular domain and the conditions under which such instabilities can occur in a domain of arbitrary geometry have been investigated. In particular, it has been shown that in every case the use of a complex Green's function is able to avoid their presence.     

Ultralong-Range Energy Transport in a Disordered Organic Semiconductor at Room Temperature Via Coherent Exciton-Polariton Propagation

Amorphous molecular solids are inherently disordered, exhibiting strong exciton localization. Optical microcavities containing such disordered excitonic materials have been theoretically shown to support both propagating and localized exciton-polariton modes. Here, the ultrastrong coupling of a Bloch surface wave photon and molecular excitons in a disordered organic thin film at room temperature is demonstrated, where the major fraction of the polaritons are propagating states. The delocalized exciton-polariton has a group velocity as high as 3 × 10⁷ m s^–1 and a lifetime of 500 fs, leading to propagation distances of over 100 µm from the excitation source. The polariton intensity shows a halo-like pattern that is due to self-interference of the polariton mode, from which a coherence length of 20 µm is derived and is correlated with phase breaking by polariton scattering. The demonstration of ultralong-range exciton-polariton transport at room temperature promises new photonic and optoelectronic applications such as efficient energy transfer in disordered condensed matter systems.     

Elastoplastic BIE analysis of cracked plates and related problems. Part 1: Formulation

The boundary-integral equation formulation for two-dimensional, planar fracture mechanics based on the use of a special Green's function forms the basis of this analytical paper. The Green's function method is extended to problems of anelastic strain distributions (e.g. elastoplasticity, thermal gradients, residual strains) through a volume (area) integral. The role of the elastic Green's function for the crack problem on the distribution of elastoplastic strains is reviewed. Further, new analytical results for elastic stress intensity factor models for the residual strain and thermal gradient problems are presented. Part 2 of this paper outlines the numerical solution strategy and results for several test problems.     

Long-range surface plasmon polariton mode cutoff and radiation in slab waveguides

The normal-mode-analysis method is used to model the radiative spreading of long-range surface plasmon polariton modes injected into regions where the bound surface mode is cutoff or radiative. Mode cutoff is induced by an asymmetry between the index of refraction of the top cladding layer and that of the bottom. The analysis was performed at lambda(0)=1.55 microm for infinite-width (slab) metal waveguides where the metal was Au and the bounding dielectrics were SiO(2). Results show that a change in insertion loss of > 20 dB is possible for an appropriate waveguide geometry and dielectric asymmetry.     

An algorithm based on the boundary element method for problems in engineering mechanics

The solution to a two-dimensional problem using the boundary element method requires the evaluation of a line integral over the boundary. The integrand ot this line integral is a product of a known Green's function and an unknown function. A large number of Green's functions for two-dimensional problems can be represented by a linear combination of four singular functions. By approximating the unknown function by a linear combination of known polynomials, integrals are generated whose integrand is a product of the polynomiais and one of the four singular functions. To evaluate these integrals analytically, the boundary is approximated by a sum of straight-line segments. Recursive formulae are established which reduce the generality and the complexity of the integrands to simple expressions. Analytical forms for these simple expressions are found and are used for initiating the algorithm.     

Green's functions in orthotropic thermoelastic diffusion media

The aim of the present paper is to study the Green's function in orthotropic thermoelastic diffusion media. With this objective, firstly the two-dimensional general solution in orthotropic thermoelastic diffusion media is derived. On the basis of general solution, the Green's function for a steady point heat source in the interior of semi-infinite orthotropic thermoelastic diffusion material is constructed by four newly introduced harmonic functions. The components of displacement, stress, temperature distribution and mass concentration are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced, to depict the effect of diffusion on components of stress and temperature distribution.     

Design Considerations for Semiconductor Nanowire–Plasmonic Nanoparticle Coupled Systems for High Quantum Efficiency Nanowires

The optimal geometries for reducing the radiative recombination lifetime and thus enhancing the quantum efficiency of III–V semiconductor nanowires by coupling them to plasmonic nanoparticles are established. The quantum efficiency enhancement factor due to coupling to plasmonic nanoparticles reduces as the initial quality of the nanowire increases. Significant quantum efficiency enhancement is observed for semiconductors only within about 15 nm from the nanoparticle. It is also identified that the modes responsible for resonant enhancement in the quantum efficiency of an emitter in the nanowire are geometric resonances of surface plasmon polariton modes supported at the nanowire/nanoparticle interface.     

Radiative gas dynamics of large landing spacecraft

Problems of the radiative gas dynamics of new-generation landing spacecraft are discussed. Numerical and theoretical study of the aerodynamics of large-scale spacecraft of the Orion type entering the Earth’s atmosphere along the landing trajectory from the International Space Station is performed in the two-dimensional axially symmetric formulation. Distribution of convective and radiation heat flows along the spacecraft surface is obtained. It is shown that for the typical trajectory of a large spacecraft entering dense layers of the Earth’s atmosphere, the density of radiation heat flows is comparable to or exceeds the density of convective heat flows.     

Stress intensity factors for cracks of arbitrary shape near an interfacial boundary

Modes I, II and III stress intensity factors for a crack of arbitrary planar shape near a bimaterial interface are calculated. The solution utilizes the body-force method and requires Green's functions for perfectly bonded elastic half-spaces. The formulation leads to a system of two-dimensional singular integral equations whose solutions represent the three modes of crack opening displacement. Numerical examples of a semicircular or semielliptical crack terminating at the interface and circular or elliptical cracks contained in one material are given for both internal pressure and farfield tension.     

Position resolution in silicon sampling calorimeters

Due to the coupling between closely spaced detectors, the position resolution of a silicon sampling calorimeter can be degraded. In a capacitance coupling model, a Green's function is found which quantitatively describes signal spreading over two-dimensional detector arrays. The result provides some theoretical guidance in choosing calorimeter parameters to get the best performance.     

3-D and 2-D Dynamic Green's functions and time-domain BIEs for piezoelectric solids

Dynamic Green's functions for linear piezoelectric solids are derived by using Radon transform. Time-harmonic and Laplace transformed dynamic Green's functions are obtained subsequently by applying the Fourier and the Laplace transform to the time-domain Green's functions. Time-domain boundary integral equation formulations are presented for transient dynamic analysis of linear piezoelectric solids. In particular, hypersingular and non-hypersingular time-domain traction BIEs are derived by two different ways. Their potential application in transient dynamic crack analysis of three-dimensional and two-dimensional piezoelectric solids is discussed.     

A Green's function time‐domain boundary element method for the elastodynamic half‐plane

The transient Green's function of the 2‐D Lamb's problem for the general case where point source and receiver are situated beneath the traction‐free surface is derived. The derivations are based on Laplace‐transform methods, utilizing the Cagniard–de Hoop inversion. The Green's function is purely algebraic without any integrals and is presented in a numerically applicable form for the first time. It is used to develop a Green's function BEM in which surface discretizations on the traction‐free boundary can be saved. The time convolution is performed numerically in an abstract complex plane. Hence, the respective integrals are regularized and only a few evaluations of the Green's function are required. This fast procedure has been applied for the first time. The Green's function BEM developed proved to be very accurate and efficient in comparison with analogue BEMs that employ the fundamental solution. Copyright © 1999 John Wiley & Sons, Ltd.     

Efficient evaluation of three-dimensional Green's functions in anisotropic elastostatic multilayered composites

The three-dimensional Green's functions in anisotropic elastostatic multilayered composites (MLCs) obtained within the framework of generalized Stroh formalism are expressed as two-dimensional integrals of Fourier inverse transform over an infinite plane. Their numerical evaluations involve tremendous computational efforts in particular in the presence of various singularities and near-singularities due to the presence of material mismatches across interfaces. The present paper derives the complete set of the Green's functions including displacement, stress and their derivatives with respect to source coordinates using a novel and computationally efficient approach. It is proposed for the first time that the Green's functions in the MLCs are expressed as a sum of a special solution and a general-part solution, with the former consisting of the first few terms of the trimaterial expansion solution around a source load. Since the zero-order term contains the singularity corresponding to the homogeneous full-space solution and can be evaluated analytically, and the other higher-order terms contain most of the near-singular behaviors and can be reduced to a line integral over a finite interval, the general-part solution becomes regular and the Green's functions overall can be evaluated efficiently. As an example, the Green's functions in a five-layered orthortropic plate are evaluated to demonstrate the efficiency of the proposed approach. Also, the detailed characteristics of these Green's functions are examined in both the transform- and physical-domains. These Green's functions are essential in developing the boundary-integral-equation formulation and numerical boundary element method for composite laminate problems involving regular and cracked geometries.     

A numerical Green's function BEM formulation for crack growth simulation

This paper presents a crack growth prediction analysis based on the numerical Green's function (NGF) procedure and on the minimum strain energy density criterion for crack extension, also known as S-criterion. In the NGF procedure, the hypersingular boundary integral equation is used to numerically obtain the Green's function which automatically includes the crack into the fundamental infinite medium. When solving a linear elastic fracture mechanisms (LEFM) problem, once the NGF is obtained, the classical boundary element method can be used to determine the external boundary unknowns and, consequently, the stress intensity factors needed to predict the direction and increment of crack growth. With the change in crack geometry, another numerical analysis is carried out without need to rebuilding the entire element discretization, since only the crack built in the NGF needs update. Numerical examples, contemplating crack extensions for two-dimensional LEFM problems, are presented to illustrate the procedure.     

Approximate Green's functions in boundary integral analysis

It is well known that employing a Green's function which satisfies the prescribed conditions on a part of the boundary is advantageous for boundary integral calculations. In this paper, it is shown that an approximate Green's function, one in which the known data is nearly reproduced, can also be highly beneficial in implementations of the boundary-element method. This approximate Green's function approach is developed herein for solving the Laplace equation, and applied to the modeling of void dynamics under electromigration conditions in metallic thin-film interconnects used in integrated circuits.     

Finite element computation of Green's functions

Green's functions are important mathematical tools in mechanics and in other parts of physics. For instance, the boundary element method needs to know the Green's function of the problem to compute its numerical solution. However, Green's functions are only known in a limited number of cases, often under the form of complex analytical expressions. In this article, a new method is proposed to calculate Green's functions for any linear homogeneous medium from a simple finite element model. The method relies on the theory of wave propagation in periodic media and requires the knowledge of the finite element dynamic stiffness matrix of only one period. Several examples are given to check the accuracy and the efficiency of the proposed numerical Green's function.     

The 3‐D BEM implementation of a numerical Green's function for fracture mechanics applications

The use of Green's functions has been considered a powerful technique in the solution of fracture mechanics problems by the boundary element method (BEM). Closed‐form expressions for Green's function components, however, have only been available for few simple 2‐D crack geometry applications and require complex variable theory. The present authors have recently introduced an alternative numerical procedure to compute the Green's function components that produced BEM results for 2‐D general geometry multiple crack problems, including static and dynamic applications. This technique is not restricted to 2‐D problems and the computational aspects of the 3‐D implementation of the numerical Green's function approach are now discussed, including examples. Copyright © 2000 John Wiley & Sons, Ltd.     

Modulation of Cathodoluminescence by Surface Plasmons in Silver Nanowires

The waveguide modes in chemically-grown silver nanowires on silicon nitride substrates are observed using spectrally- and spatially-resolved cathodoluminescence (CL) excited by high-energy electrons in a scanning electron microscope. The presence of a long-range, travelling surface plasmon mode modulates the coupling efficiency of the incident electron energy into the nanowires, which is observed as oscillations in the measured CL with the point of excitation by the focused electron beam. The experimental data are modeled using the theory of surface plasmon polariton modes in cylindrical metal waveguides, enabling the complex mode wavenumbers and excitation strength of the long-range surface plasmon mode to be extracted. The experiments yield insight into the energy transfer mechanisms between fast electrons and coherent oscillations in surface charge density in metal nanowires and the relative amplitudes of the radiative processes excited in the wire by the electron.     

Nonlinear Green's function method for the Tzitzéica and related equations

In this short note we apply the nonlinear Green's function method for the solution of the Tzitzéica type equation hierarchies arising in nonlinear science. Using the travelling wave ansatz, we first transform the nonlinear partial differential equations to nonlinear ordinary differential equations. Then, we establish a general representation formula for nonlinear Green's function of these equations. Eventually, using Frasca's short time expansion, we obtain the exact solution to these equations. Numerical analysis shows that the obtained Green's function solution is sufficiently close to the numerical solution obtained by the well-known method of lines. Finally, we involve the inverse transform and study the full nature of the Tzitzéica equation.     

Comparison of boundary and finite element methods for moving-boundary problems governed by a potential

Three formulations of the boundary element method (BEM) and one of the Galerkin finite element method (FEM) are compared according to accuracy and efficiency for the spatial discretization of two-dimensional, moving-boundary problems based on Laplace's equation. The same Euler-predictor, trapezoid-corrector scheme for time integration is used for all four methods. The model problems are on either a bounded or a semi-infinite strip and are formulated so that closed-form solutions are known. Infinite elements are used with both the BEM and FEM techniques for the unbounded domain. For problems with the bounded region, the BEM using the free-space Green's function and piecewise quadratic interpolating functions (QBEM) is more accurate and efficient than the BEM with linear interpolation. However, the FEM with biquadratic basis functions is more efficient for a given accuracy requirement than the QBEM, except when very high accuracy is demanded. For the unbounded domain, the preferred method is the BEM based on a Green's function that satisfies the lateral symmetry conditions and which leads to discretization of the potential only along the moving surface. This last formulation is the only one that reliably satisfies the far-field boundary condition.