Surface Integral Method Research Articles

A comparative study of classical approaches to surface plasmon resonance of colloidal gold nanorods

We report the errors in the evaluation of the surface plasmon resonance of gold nanorods by three classical approaches: the Gans model, the Discrete Dipole Approximation and the Surface Integral method. Using these methods, which are based on the propagation of an electromagnetic wave through a composite medium with different refractive indices, might result in an inaccurate prediction of absorption maxima. For test samples of nanorods prepared by a seed-mediated method, whose homogeneity and quality were also fully demonstrated in this study, the mismatches in the wavelengths of absorption maxima $$ \left| {\varDelta {\lambda_{\max }}} \right| $$ between experimental and theoretical data were observed to be greater than 50 nm. In general, the observed surface plasmon resonances exhibit two distinctive bands corresponding to the transverse and longitudinal modes. The weak transverse mode was located in the region from 510 to 518 nm and varied slightly with the aspect ratio of the rods. In contrast, the longitudinal mode showed a strong dependence on aspect ratio and ranged from 658 to 768 nm. We demonstrated that the mismatches may be sufficiently reduced if the interdependence between these two modes is taken into account.

Computations of Electromagnetic Wave Scattering From Penetrable Composite Targets Using a Surface Integral Equation Method With Multiple Traces

We present a surface integral equation domain decomposition method (SIE-DDM) for time harmonic electromagnetic wave scattering from bounded composite targets. The proposed SIE-DDM starts by partitioning the composite object into homogeneous sub-regions with constant material properties. Each of the sub-regions is comprised of two sub-domains (the interior of the penetrable object, and the exterior free space), separated on the material interface. The interior and the exterior boundary value problems are coupled to each other through the Robin transmission conditions, which are prescribed on the material/domain interface. A generalized combined field integral equation is employed for both the interior and the exterior sub-domains. Convergence studies of the proposed SIE-DDM are included for both single homogeneous objects and composite penetrable objects. Furthermore, a complex large-scale simulation is conducted to demonstrate the capability of the proposed method to model multi-scale electrically large targets.

The virtual-casing principle for 3D toroidal systems**This paper has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the US Department of Energy. The publisher, by accepting the paper for publication acknowledges, that the United States Government retains a non-exclusive,paid-up, irrevocable, worldwide license to publish or reproduce the published form of this paper, or allow others to do so,

The capability to calculate the magnetic field due to the plasma currents in a toroidally confined magnetic fusion equilibrium is of manifest relevance to equilibrium reconstruction and stellarator divertor design. Two methodologies arise for calculating such quantities. The first being a volume integral over the plasma current density for a given equilibrium. Such an integral is computationally expensive. The second is a surface integral over a surface current on the equilibrium boundary. This method is computationally desirable as the calculation does not grow as the radial resolution of the volume integral. This surface integral method has come to be known as the ‘virtual-casing principle’. In this paper, a full derivation of this method is presented along with a discussion regarding its optimal application.

Rapid 1D/3D inversion of shallow resistivity multipole data: Examples in archaeological prospection

Fifteen years ago, the introduction of mobile multipole arrays led to substantial improvements in shallow electric prospection because it allowed information related to the vertical distribution of ground resistivity, in complement to the horizontal pattern of the detected features, to be extracted. However, to make full use of this wealth of information, further progress is needed to extend the qualitative interpretation of data to a more quantitative evaluation of the explored terrain. To that intent, we developed a two-step process: In the first step, a 1D electric model is fitted to the data over the full explored area, and in the second step, using the moment method, localized 3D interpretation is applied to limited areas, for which the characteristics of a given feature require closer scrutiny. After a first test with synthetic data generated using the surface integral 3D modeling method, this process was applied to three different archaeological sites and one test site, for both handheld pole-pole array systems and a multipole continuous electric profiling mechanically pulled system. At the test site, the characteristics of a known wall were accurately recovered. At the Duntzenheim site, the thickness and width of the archaeological remains determined by 3D interpretation corresponded to the features observed through excavation. At the other two sites, 3D interpretation made it possible to establish that the conductive features extend across the full extent of the superficial resistive second layers.

Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model

Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding to two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.

Numerical Simulation of Single-Stream Jets from a Serrated Nozzle

Hybrid large-eddy type simulations for cold jet flows from a serrated nozzle are performed at an acoustic Mach number Ma ac = 0.9 and Re = 1.03×106. Since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES) or implicit LES (ILES) reminiscent procedure. To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended to the LES making a hybrid RANS-ILES. The geometric complexity of the serrated nozzle is fully considered without simplification or emulation. An improved but still modest hexahedral multi-block grid with circa 20 million grid points (with respect to 12.5 million in Xia et al., Int J Heat Fluid Flow 30:1067–1079, 2009) is used. Despite the modest grid size, encouraging and improved results are obtained. Directly resolved mean and second-order fluctuating quantities along the jet centerline and in the jet shear layer compare favorably with measurements. The radiated far-field sound predicted using the Ffowcs Williams and Hawkings (FW-H) surface integral method shows good agreement with the measurements in directivity and sound spectra.

Large-Eddy-Simulations of over-expanded supersonic jet noise for launcher applications

During the lift-off phase of a space launcher, powerful rocket motors generate harsh acoustic environment on the launch pad. Following the blast waves created at ignition, jet noise is a major contributor to the acoustic loads received by the launcher and its payload. This paper describes recent simulations performed at ONERA to compute the noise emitted by solid rocket motors at lift-off conditions. Far-field noise prediction is achieved by associating a LES solution of the jet flow with an acoustics surface integral method. The computations are carried out with in-house codes CEDRE for the LES solution and KIM for Ffowcs Williams and Hawkings porous surface integration method. This work has been conducted in the framework of the cooperation on launcher acoustics between CNES (French National Space Agency) and JAXA (Japan Aerospace Exploration Agency) involving the French AEID research group. The test case is that of a reduced scale solid rocket motor, fired vertically and has been provided by JAXA. Comp...

Asymptotic Exchange Energy of Heteronuclear Dimers

A simple expression for the asymptotic exchange energy of heteronuclear dimers is derived from the surface integral method. A five-dimensional hypersurface, consisting of all spherical surfaces centered at the nucleus of the atom with higher ionization energy, more appropriate for the case where the two atoms have different ionization energies, is used in the surface integral. All integrals are carried out analytically. Compared with the exchange energy of Smirnov and Chibisov, which is also obtained from the surface integral method with a hypersurface consisting of all infinite planes perpendicular to the internuclear axis, the present result is much simpler. The exchange energies of alkali hydrides are computed as an illustration. It is shown that the present method and the method of Smirnov and Chibisov are complementary to each other.

Theory of Piezoelectric Fields in InGaAs Site-Controlled Quantum Dots

We present a surface integral method to calculate the piezoelectric polarisation potential due to a strained quantum dot (QD) grown on a (111)-oriented substrate. We show that the potential is reduced in a QD compared to a strained quantum well of the same height, but that there still remains a significant polarisation field across (111)-oriented InGaAs/GaAs QD structures. We use the 8-band k.p method to show that these piezoelectric fields must be included to explain the measured interband transition energies in a series of site-controlled QDs with increasing height and In composition.

Theory of reduced built-in polarization field in nitride-based quantum dots

We use a surface integral method to show that the polarization potential in an InGaN/GaN quantum dot (QD) grown along the [0001] direction is strongly reduced compared to that in a quantum well (QW) of the same height. We use simple analytic expressions and different dot geometries to show that the reduction originates from two effects (i) the reduction in the QD [0001] surface area and (ii) strain redistributions in the QD system. The In composition can therefore be increased in a QD compared to a QW, enabling efficient recombination to longer wavelengths in InGaN QD structures.

Universal scaling of local plasmons in chains of metal spheres

The position, width, extinction, and electric field of localized plasmon modes in closely-coupled linear chains of small spheres are investigated. A dipole-like model is presented that separates the universal geometric factors from the specific metal permittivity. An electrostatic surface integral method is used to deduce universal parameters that are confirmed against results for different metals (bulk experimental Ag, Au, Al, K) calculated using retarded vector spherical harmonics and finite elements. The mode permittivity change decays to an asymptote with the number of particles in the chain, and changes dramatically from 1/f(3) to 1/f(1/2) as the gap fraction (ratio of gap between spheres to their diameter), f, gets smaller. Scattering increases significantly with closer coupling. The mode sharpness, strength and electric field for weakly retarded calculations are consistent with electrostatic predictions once the effect of radiative damping is accounted for.

Diffraction and external reflection by dielectric faceted particles

The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM.

The surface integral method in the theory of exchange interaction of a polar molecule with a highly charged ion

The surface integral method in the theory of exchange interaction of a polar molecule with a highly charged ion

Built‐in fields in non‐polar InxGa1–xN quantum dots

AbstractWe present a detailed analysis of the internal built‐in potential in polar and non‐polar Inx Ga1–x N quantum dots (QDs). The applied model is based on a surface integral method to calculate the three‐dimensional electrostatic built‐in potential in semiconductor QDs of arbitrary shape. This technique allows for a detailed and systematic analysis of the different contributions to the total built‐in field. Here, we also investigate the impact of the QD geometry on the built‐in potential in structures grown along non‐polar directions of the crystal.Since there is uncertainty in the literature as to the sign of the piezoelectric constant e15 associated with the shear strain, we study the influence of this constant in detail. While recent results on non‐polar GaN/AlN QDs indicate that only a negative e15 leads to significant reduction in the built‐in field, we show that for InN/GaN QDs there should still be a significant field present, independent of the sign of the piezoelectric constant e15. However, this field is strongly reduced with increasing Ga concentration in the nanostructure. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kriging for Eddy-Current Testing Problems

Accurate numerical simulation of Eddy-Current Testing (ECT) experiments usually requires large computational efforts. So, a natural idea is to build a cheap approximation of the expensive-to-run simulator. This paper presents an approximation method based on functional kriging. Kriging is widely used in other domains, but is still unused in the ECT community. Its main idea is to build a random process model of the simulator. The extension of kriging to the case of functional output data (which is the typical case in ECT) is a recent development of mathematics. The paper introduces functional kriging and illustrates its performance via numerical examples using an ECT simulator based on a surface integral method. A comparison with other classical data interpolation methods is also carried out.

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10 6. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10 6 cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.

Polarization fields in nitride-based quantum dots grown on nonpolar substrates

We use a surface-integral method to determine the polarization potential in nitride-based quantum dots (QDs) grown on a nonpolar substrate. There is uncertainty in the literature regarding the sign of the piezoelectric constant ${e}_{15}$. We find that only a negative ${e}_{15}$ can give the reduced electrostatic built-in field found experimentally in nonpolar GaN/AlN QDs. Our analysis of nonpolar InN/GaN QDs indicates that a significant built-in field remains in these structures. We calculate that despite the reduced polarization potential, ground-state electrons and holes can remain spatially separated in GaN/AlN QDs.

The application of computed piezomagnetic models to volcanic phenomena

Piezomagnetic models, suitable for volcanological applications, can be readily calculated by numerical surface integral methods, providing both savings in computational time and an ability to deal with arbitrarily shaped magnetoelastic media. Studies of piezomagnetic changes have traditionally used models based on the Mogi model in which a spherical underground pressure source is included to represent a magma chamber. We extended the Mogi model to include inclined column sources, as in the Walsh and Decker model, and evaluated piezomagnetic changes for vertical, horizontal, and inclined columns. Our analysis method considers any dependency of magnetic changes on the angle of column inclination. This numerical approach allows for construction of piezomagnetic models that closely resemble actual volcanic phenomena.

Surface Integral Methods in Jet Aeroacoustics: Refraction Corrections

One of the major challenges in computational jet aeroacousties is the accurate modeling and prediction of acoustic fields to reduce and control the jet noise. Surface integral methods (e.g., the Kirchhoff method and Ffowcs Williams-Hawkings method) can be used in computational aeroacoustics to extend the near-field computational fluid dynamics results to far field. The surface integral methods can efficiently and accurately predict aerodynamically generated noise provided the control surface surrounds the entire source region. However, for jet noise prediction, shear mean flow exists outside the control surface that causes refraction. Mean flow refraction corrections for the surface integral methods have been done in the past using simple geometric acoustics. A more rigorous method based on Lilley's equation is investigated here due to its more realistic assumption of the acoustic propagation. Jet noise computational results based on large-eddy simulation for the near field of an isothermal jet at Reynolds number 400,000 are used for the evaluation of the solution on the Ffowcs Williams-Hawkings control surface. The proposed methodology for prediction of far-field sound pressure level shows that the acoustic field within the zone of silence is consistent with the measured data.

Surface integral methods for high‐frequency electromagnetic scattering

AbstractSurface integral equation based methods are advantageous for simulation of electromagnetic waves scattered by three dimensional obstacles, because they efficiently reduce the dimension of the problem and are robust for high‐frequency problems. However, the cost of setting up the associated discretized dense linear systems is prohibitive due to evaluation of highly oscillatory magnetic and electric dipole surface integral operators using standard cubatures. The computational complexity of evaluating such integrals depends on the incident wave frequency, and the size and shape of the obstacles. In this work we discuss a surface integral reformulation of the scattering problem that involves evaluation of surface integrals with a highly oscillatory physical density, and discuss methods for efficient evaluation of such integrals for a class of smooth three dimensional scatterers whose diameter is a large multiple of the incident wavelength. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)