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A facile one-step method for the synthesis of a water-soluble selenium/polypyrrole (Se/PPy) nanocomposite was developed. In the aqueous synthesis process, the pyrrole acted as a reductant for the reduction of H2SeO3, and then the elemental Se formed in situ acted as a catalyst for the polymerization of pyrrole. The characterization results show that the as-obtained composite (Se/PPy) is a spherical (Φ80 nm) product that is made up of amorphous Se particles coated by PPy layers. The formation mechanism and influence factors of the products were discussed, based on a series of experiments. It is proposed that remainder H2SeO3 adsorbed on the PPy chains increased the water-solubility and conductivity of the Se/PPy nanocomposite. Significantly, relying on the synergistic effect of photo-conductive Se nanoparticles and electric-conductive PPy molecules, the Se/PPy nanocomposite possesses a large two-photon absorption (2PA) cross-section and good optical limiting properties, which were demonstrated by the Z-scan technique using a femtosecond laser. We believe that this work should be an interesting strategy for developing polymer composites with excellent optoelectrical properties.

While high frequency approximation methods are widely used to solve flaw scattering in ultrasonic nondestructive evaluation, full wave approaches based on integral equations have great potentials due to their high accuracy. In this work, boundary integral equations for acoustic wave scattering are solved using high order Nystrom method. Compared with boundary elements method, it features the coincidence of the samples for interpolation basis and quadrature, which makes the far-field interaction free from numerical integration. The singular integral is dealt with using the Duffy transformation, while efficient singularity subtraction techniques are employed to evaluate the near singular integrals. This approach has the ease to go high order so highly accurate results can be obtained with fewer unknowns and faster convergence, and it is also amenable to incorporate fast algorithms like the multi-level fast multi-pole algorithm. The convergence of the approach for different orders of elements and interpolation basis functions is investigated. Numerical results are shown to validate this approach.While high frequency approximation methods are widely used to solve flaw scattering in ultrasonic nondestructive evaluation, full wave approaches based on integral equations have great potentials due to their high accuracy. In this work, boundary integral equations for acoustic wave scattering are solved using high order Nystrom method. Compared with boundary elements method, it features the coincidence of the samples for interpolation basis and quadrature, which makes the far-field interaction free from numerical integration. The singular integral is dealt with using the Duffy transformation, while efficient singularity subtraction techniques are employed to evaluate the near singular integrals. This approach has the ease to go high order so highly accurate results can be obtained with fewer unknowns and faster convergence, and it is also amenable to incorporate fast algorithms like the multi-level fast multi-pole algorithm. The convergence of the approach for different orders of elements and interpolati...

Grounding grid is a kind of critical infrastructure to ensure safe and stable operation of the grid and the personal safety. Buried in the ground and limited by the surface buildings, the ground grid is inconvenient to be detected and maintained. In this paper, in order to overcome the difficulties in detecting the ground grid of the high-voltage transmission and substation, we studied a detection system based on ground penetrating radar (GPR), which can present intuitive visual images of the grid, makes accurate diagnosis to the ground grid, without power failure and dug. The design, installation and maintenance of norms detection of grounding grid used in high voltage transmission lines and substations is the foundation to ensure the safe operation of circuits and systems, grounding grid has the characters of large-scale, complex structure and laying deep. In practical engineering, the means for measuring the grounding grid are primitive, traditional methods for measurement are indirect measurement or excavation, with blindness, and large workload, low efficiency and inadequate measurement accuracy. Meanwhile, the high-voltage transmission lines and substations is bearing the heavy responsibility of national production and people's lives, whose maintenance without power will inevitably bring many economic losses that makes the actual operation difficult. In this paper, to solve the current difficulties in the detection of ground grid used in high-voltage transmission lines and substation, we present a detection system based on ground penetrating radar (GPR), designing and forming a kind of device to the corresponding test(1-2). Meeting the electricity systems limitation of simple, accurate, free on-site operating conditions, the system for the grounding grid achieves diagnosis and practical detection for the grounding grid without power failure and dug (3-5)..

In this paper, the wave propagation in a grounded dielectric slab with double negative (DNG) metamaterials is studied. Dramatically different evanescent surface modes (electromagnetic fields exponentially decay both in air and inside the slab) are observed. They are highly dependent on medium parameters. An infinite number of complex surface modes are found to be existing which have proper field distribution in the air region. The investigations on the Poynting vectors show that they do not carry away energy in both transverse and longitudinal directions.

This paper studies the dispersion characteristics of open multilayer microstrip lines with a thin highly-conductive metallic substrate using the spectral domain approach. From the numerical results, it is found that, in both lossy (metal-insulator-silicon structure such as Si-SiO2) and lossless configurations (thin metal between lossless dielectric microstrip line), at the low frequency range, this thin metallic substrate can excite slow waves. And accordingly the frequency dependent transmission-line characteristics of interconnects, such as propagation constant, attenuation and the characteristic impedance, can change remarkably with the existence of the thin metallic substrate.

The properties of a grounded dielectric slab with double negative (DNG) metamaterials are investigated in this paper. Dramatically different dispersion curves of evanescent surface modes (electromagnetic fields exponentially decay both in air and inside the slab) are observed. They are highly dependent on the medium parameters. As the counterpart of the improper complex leaky modes in a double positive (DPS) medium, the complex modes in a DNG medium are proved to be exclusively proper. They have exponentially decaying fields in the air region and are termed complex surface modes. It is found that there are an infinite number of complex surface modes and they cannot be suppressed. The Poynting vectors of complex surface modes are studied and it is proved that their integrals along the transverse direction are simply zero. The complete mode spectrum of the dielectric slab for both DPS and DNG media are tabled and compared. Surface wave suppression is discussed and its necessary and sufficient conditions are presented.

Several surface integral formulations for electromagnetic interactions with homogeneous material bodies are studied numerically. Included are the well-known Muller and Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) formulations and two other formulations. One of the two formulations introduced gives a simple form of the Neumann series for low-contrast material bodies. The integral formulations are discretized into the matrix equations using the method of moments (MoM). The condition numbers of the matrices are evaluated using three definitions of norms and are shown as functions of combination constants. Numerical results also show the regions of the combination constants producing accurate results.

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling k/spl circ/ directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling k/spl circ/ directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single k/spl circ/ is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.

Three parameters are needed to model symmetrical adapters, but not enough equations can be found to solve them. The proposed two-impedance model with one shunt and one series impedance gives consistent results when applied to three different lengths of embedded microstrip transmission lines. This model can be used with more complicated structures than the single-impedance model. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 50–54, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20204

A multilevel algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error is presented. The algorithm termed "sparse data fast Fourier transform" (SDFFT) is particularly useful for signal processing applications where only part of the k-space is to be computed - regardless of whether it is a regular region like an angular section of the Ewald sphere or it consists of completely arbitrary points scattered in the k-space. In addition, like the various nonuniform fast Fourier transforms, the O(NlogN) algorithm can deal with a sparse, nonuniform spatial domain. In this paper, the parabolic reflector antenna problem is studied as an example to demonstrate its use in the computation of far-field patterns due to arbitrary aperture antennas and antenna arrays. The algorithm is also promising for various applications such as backprojection tomography, diffraction tomography, and synthetic aperture radar imaging.

This paper reviews the recent progress of fast integral equation solvers at the Center for Computational Electromagnetics and Electromagnetics laboratory, University of Illinois at Urbana-Champaign. We will demonstrate the ability to solve a variety of electromagnetic problems for complex structures and low-frequency structures as well as large scale scattering problems with over 10 million unknowns.

At the Center for Computational Electromagnetics at the University of Illinois, we recently solved a very-large-scale electromagnetic scattering problem. We computed the bistatic radar cross-section of a full-size aircraft at 8 GHz, involving the solution of a dense matrix equation with nearly 10.2 million unknowns. We regarded this as the "ultimate test" of a massively parallel implementation of the multilevel fast multipole algorithm (MLFMA), called ScaleME. In this paper, we narrate the technical difficulties faced and the experience gained from a very informal point of view. We describe the various methods developed for surmounting each of the obstacles.

8-Hydroxyquinoline cadmium (Cdq 2 ) nanobelts with width of 100–200 nm and lengths of 0.5–2 μm have been successfully synthesized through a facile solvothermal method at 120 °C for 24 h. The composition, morphology and structure of the as-prepared products were confirmed by X-ray powder diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Experiment results indicated that the concentration of ethanol played an important effect in the morphology of the final products. Moreover, the electrogenerated chemiluminescence (ECL) properties of the Cdq 2 sample with different morphologies were investigated. The ECL spectra show that the Cdq 2 nanobelts exhibited excellent electrogenerated chemiluminescence (ECL) behavior.

Based on the multilevel fast multipole algorithm (MLFMA), an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation, where the fast far-field approximation (FAFFA) is combined with MLFMA. The translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many k/spl circ/ directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single k/spl circ/ direction is involved in the translator. The condition for using FAFFA and the way to efficiently incorporate FAFFA with MLFMA are discussed. Complexity analysis illustrates that the computational cost in FAFFA-MLFMA can be asymptotically cut by half compared to the conventional MLFMA. Numerical results are given to verify the efficiency of the algorithm.

Rational assembly of carbon nanostructures into large-area films is a key step to realize their applications in ubiquitous electronics and energy devices. Here, a self-assembly methodology is devised to organize diverse carbon nanostructures (nanotubes, dots, microspheres, etc.) into homogeneous films with potentially infinite lateral dimensions. On the basis of studies of the redox reactions in the systems and the structures of films, the spontaneous deposition of carbon nanostructures onto the surface of the copper substrate is found to be driven by the electrical double layer between copper and solution. As a notable example, the as-assembled multiwalled carbon nanotube (MWCNT) films display exceptional properties. They are a promising material for flexible electronics with superior electrical and mechanical compliance characteristics. Finally, two kinds of all-solid-state supercapacitors based on the self-assembled MWCNT films are fabricated. The supercapacitor using carbon cloth as the current collector delivers an energy density of 3.5 Wh kg−1 and a power density of 28.1 kW kg−1, which are comparable with the state-of-the-art supercapacitors fabricated by the costly single-walled carbon nanotubes and arrays. The supercapacitor free of foreign current collector is ultrathin and shows impressive volumetric energy density (0.58 mWh cm−3) and power density (0.39 W cm−3) too.

Special functions with multiple values in solving the possible modes (guided and leaky) of the circular dielectric rod are analyzed in detail in this paper. By taking consideration of the physical meaning of these modes, the possible solutions are well defined and classified based on different types of special functions and Riemann sheets. Characteristic equations can be used to solve different types of modes are exhibited completely.

A novel approach to evaluate the doubly periodic Greens function for layered medium in matrix-friendly formulation is proposed, which takes advantages of factorization of the spectral Green's function, approximates a smooth part of it accurately, and then exploits high order asymptotic extraction techniques. The approach is fast and accurate for all ranges of distances between the source and observation points, and also allows fast frequency sweep for calculating Brillouin diagram in eigenvalue problem and for normal incidence in scattering problem. Numerical examples are presented to show the efficiency of the approach.

Graphene-like cobalt–nickel double hydroxide nanocomposites have been successfully prepared by a mild hydrolysis process at the room temperature. The samples were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, and thermal gravimetric analysis. The results reveal that the as-prepared samples are composed of α-Co(OH)2 and α-Ni(OH)2, and contain numerous thin flakes with wrinkle structure, and the thickness of the flakes is ca. 1 nm. Magnetic measurements indicate that the as-prepared nanocomposites have a weak ferromagnetic behavior at the room temperature, which is due to a small content of metallic Co. The as-synthesized products emerge large specific surface area (260.1 m2 g−1) from the measurement of Brunauer–Emmett–Teller. Interestingly, compared to single components, the obtained nanocomposites have exhibited superiorly and enhanced catalytic activity to the hydrogenation of p-nitrophenol in the presence of excess sodium borohydride at room temperature. In addition, the adsorption property of the nanocomposites for methyl blue has also been examined.

The boundary integral equations (BIE) method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations. It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics. The eddy current problem is formulated by the BIE and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The three dimensional arbitrarily shaped objects are described by a number of triangular patches. The Stratton-Chu formulation is specialized for the conductive medium. The equivalent electric and magnetic surface currents are expanded in terms of Rao-Wilton-Glisson (RWG) vector basis function while the normal component of magnetic field is expanded in terms of the pulse basis function. Also, a low frequency approximation is applied in the external medium. Additionally, we introduce Auld’s impedance formulas to calculate impedance variati...

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme.

A set of novel, grid-robust, higher order vector basis functions is proposed for the method-of-moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. These basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the Lagrange interpolation polynomials. The highlight of these basis functions is that the Lagrange interpolation points are chosen to be the same as the nodes of the well-developed Gaussian quadratures. As a result, the evaluation of the integrals in the MoM is greatly simplified. Additionally, the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch, which is a very stringent requirement for traditional vector basis functions. The proposed basis functions are implemented with point matching for the MoM solution of the electric-field integral equation, the magnetic-field integral equation, and the combined-field integral equation. Numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions.

A method is presented for solving the surface integral equation using the method of moments (MoM) at very low frequencies, which finds applications in geoscience. The nature of the Helmholtz decomposition leads the authors to choose loop-tree basis functions to represent the surface current. Careful analysis of the frequency scaling property of each operator allows them to introduce a frequency normalization scheme to reduce the condition number of the MoM matrix. After frequency normalization, the MoM matrix can be solved using LU decomposition. The poor spectral properties of the matrix, however, makes it ill-suited for an iterative solver. A basis rearrangement is used to improve this property of the MoM matrix. The basis function rearrangement (BFR), which involves inverting the connection matrix, can be viewed as a pre-conditioner. The complexity of BFR is reduced to O(N), allowing this method to be combined with iterative solvers. Both rectilinear and curvilinear patches have been used in the simulations. The use of curvilinear patches reduces the number of unknowns significantly, thereby making the algorithm more efficient. This method is capable of solving Maxwell's equations from quasistatic to electrodynamic frequency range. This capability is of great importance in geophysical applications because the sizes of the simulated objects can range from a small fraction of a wavelength to several wavelengths.

The translation matrix for the multilevel fast multipole algorithm (MLFMA) in an FISC (fast Illinois solver code) is calculated directly, and the complexity is O(N3/2), where N is the number of unknowns. For a problem with a small electrical size, the CPU time for calculating the translation matrix can be negligible. But for large problems, the calculation time increases significantly. In this paper, we use interpolation to calculate the translation matrix, and the complexity is reduced to O(N). Different interpolation techniques are tested, and it is found that the Lagrange polynomial interpolation with high sampling rates is the best. The saving factor is 10 for the VFY218 at 4 GHz. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 109–114, 2001.

Compared to the TM case, the inverse scattering problem for the TE incident field is more complicated due to its stronger nonlinearity. This work provides an effective method for the reconstruction of two-dimensional (2-D) inhomogeneous dielectric objects from TE scattering data. The algorithm applies the distorted Born iterative method to the integral equation of strong permittivity fluctuation to reconstruct scatterers with high-permittivity contrast. Numerical simulations are performed and the results show that the distorted Born iterative method (DBIM) for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrasts in comparison with ordinary DBIM. A frequency hopping technique is also applied to further increase the contrast.

A new approach is proposed to reduce the memory requirements of the multilevel fast multipole algorithm (MLFMA) when applied to the higher order Galerkin's method. This approach represents higher order basis functions by a set of point sources such that a matrix-vector multiply is equivalent to calculating the fields at a number of points from given current sources at these points. The MLFMA is then applied to calculate the point-to-point interactions. This permits the use of more levels in MLFMA than applying MLFMA to basis-to-basis interactions directly and, thus, reduces the memory requirements significantly.

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate---but fast---methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in a multilevel implementation is also investigated numerically.

This letter studies the influence of embedded thin-film metallization layers, normally designed as ground planes, upon the dispersive characteristics of multilayer microstrip lines. The spectral domain approach is used to analyze the effects of the metallization thickness as a design parameter in two structures: the thin-film microstrip line and metal-insulator-metal-insulator line. Numerical results indicate that the thin metallization layer can excite the slow-wave mode and change significantly the dispersive characteristics. Moreover, at low frequencies a local minimal attenuation can be achieved with certain metallization thickness. Thus, it is necessary to take into account this thin-film metal ground to achieve reliable numerical simulation from dc to millimeter-wave frequencies

The adaptive integral method (AIM) is applied to the solution of the combined field integral equation (CFIE) of scattering by a three-dimensional (3-D) perfect electric conductor (PEC). The employment of CFIE eliminates the interior resonance problem suffered by both the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE). Furthermore, it significantly improves the efficiency of AIM by reducing the number of iterations for convergence. It is shown that the memory requirement and computational complexity per iteration of the AIM solution of CFIE are O(N1.5) and O(N1.5log N), respectively, for 3-D PEC surface scattering problems. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 321–328, 1998.

FISC (Fast Illinois solver code), co-developed by the Center for Computational Electromagnetics, University of Illinois, and DEMACO, is designed to compute the RCS of a target described by a triangular-facet file. The problem is formulated using the method of moments (MoM), where the Rao, Wilton, and Glisson (1982) basis functions are used. The resultant matrix equation is solved iteratively by the conjugate gradient (CG) method. The multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiplication in the CG method. The complexities for both the CPU time per iteration and the memory requirements are of O(Nlog N), where N is the number of unknowns. A 2.4-million unknown problem is solved in a few hours on the SGI GRAY origin 2000 at NCSA of the University of Illinois at Urbana-Champaign.

An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the full-wave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures. In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch may be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions. TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method. TSM-FMA reduces the central processing unit (CPU) time per iteration to O(N log N) for sparse structures and to O(N) for dense structures, from O(N/sup 3/) for the Gaussian elimination method and O(N/sup 2/) per iteration for the CG method. The memory requirement for TSM-FMA also scales as O(N log N) for sparse structures and as O(N) for dense structures. Therefore, this approach is suitable for solving large-scale problems on a small computer.

This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method.

Neisseria meningitidis PorB class 3 porins obtained either from native membranes (wild-type) or recovered from inclusion bodies following expression in Escherichia coli (recombinant), have been reconstituted into solvent-free planar phospholipid membranes. The wild-type and recombinant porins exhibited the same single-trimer conductance (1–1.3 nS in 200 mM NaCl), tri-level closure pattern, characteristic of functional channel trimers, and pattern of insertion into planar membranes. Both proteins were open at low voltages and displayed two voltage-dependent closure processes, one at positive and the other at negative potentials. Both showed asymmetric voltage dependence such that one gating process occurred at lower voltages (Vo=15 mV) than the other (Vo=25 mV). The sign of the potential that resulted in closure at low voltages varied from membrane to membrane indicating that they may have the property of auto-directed insertion (in analogy to the mitochondrial channel, VDAC). In the case of the recombinant porin, the steepness of the voltage dependence of one gating process was slightly less (n=1.3) than that observed for the other process or for the wild-type channel (n=1.5–1.7). Both channels have a high (40%) probability of closure even at 0 mV. While both channels show a slight selectivity for Cl− over Na+, the selectivity of the recombinant porin is a bit higher (permeability ratio of 2.8 vs. 1.6) as measured using a 2-fold salt gradient. Thus, the method employed to refold the recombinant porin was successful in not only restoring wild-type structure [H.L. Qi, J.Y. Tai, M.S. Blake, Expression of large amounts of Neisserial porin proteins in Escherichia coli and refolding of the proteins into native trimers, Infect. Immun. 62 (1994) 2432–2439; C.A.S.A. Minetti, J.Y. Tai, M.S. Blake, J.K. Pullen, S.M. Liang, D.P. Remeta, Structural and functional characterization of a recombinant PorB class 2 protein from Neisseria meningitidis. Conformational stability and porin activity, J. Biol. Chem. 272 (1997) 10710–10720] but also the overall electrophysiological function.

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

To solve large scale computing and scattering problems and to expand knowledge about iterative solvers, the authors developed the Fast Illinois Solver Code, which uses the multilevel fast multipole algorithm (MLFMA). They discuss FISC's memory requirements and CPU time and give some empirically derived formulas and charts. The authors also plot examples they used to obtain these conclusions.

Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either solved directly or iteratively. A review of various differential equation solvers, their complexities, and memory requirements is given. The issues of grid dispersion and hybridization with integral equation solvers are discussed. Several fast integral equation solvers for surface and volume scatterers are presented. These solvers have reduced computational complexities and memory requirements.

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory.

A rapid chemical method has been developed for the synthesis of the CdTe nanoribbons with cubic crystalline phase. The method is based on the template-engaged synthesis in which the Te nanowires were used as template reagents. On the basis of a series of experiments and characterizations, the electrochemical property of CdTe nanoribbons was determined by the voltammetric technique. Furthermore, electrochemiluminescence property of CdTe nanoribbons was investigated. The results show that CdTe nanoribbons are helpful to obtain stable electrochemiluminescence emission for 1200 seconds.

This paper explores the effective permittivity and permeability of the structure which has periodic lossy dielectric objects embedded in a matrix. The asymptotic expressions for both high conductivity and quasi-static are derived and discussed. Numerical results both from the MG formula and an integral equation approach are provided to verify all the asymptotic expressions and related conclusions.

By employing the equivalence principle and connection scheme (EPACS), an efficient integral equation (IE) approach is used to model multilayer structure with metal inclusion is presented. The numerical results show a good agreement between EPACS and HFSS. Effective media theory is adopted to simplify the multilayer structure. Numerical results and computational costs show the advantages of EPACS and the effective media model.

This paper applies a novel integral equation approach to model the multilayer substrate with periodic metal inclusion. The approach combines the equivalence principle with connection scheme to avoid the sophisticated multilayered periodic Green's function. Effective media theory is adopted to extract the effective dielectric constant. Good agreement has been achieved between our approach and analytical result. A printed circuit board was designed, fabricated and tested to validate our model.

This paper investigates the optical bound states in the continuum (BIC) supported by a slotted high-contrast grating (sHCG) structure. The sHCG structure consists of a periodic array of silicon ridges with a slot in each ridge. Given that the BICs are perfectly confined, their spectral locations are identified using a finite-element method formulated from a generalized eigenvalue problem. The real eigenvalues represent the wavelengths of BIC modes and the associated eigenvectors correspond to the electric field distributions. In the spectral and angular vicinity of the BICs, we studied the leaky waveguide modes using the rigorous coupled-wave analysis. The combination of the full-wave eigenvalue solver and the coupled-wave analysis provides an ideal setting to investigate the optical BICs of periodic structures for various applications. The simulation results show, for example, that the sHCG structures can support symmetry-protected bound states with a zero in-plane wave vector as well as high-quality-factor (high-Q) resonances for both TE and TM polarizations. By adjusting the slot, we can turn the BIC mode into high-Q modes and determine the linewidth of the mode by the degree of asymmetry.

The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N2) to O(N1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592-unknown problem can be solved within 24 h on a SUN Sparc 10. © 1995 John Wiley & Sons, Inc.

A technique for computing the electromagnetic (EM) radiation and scattering from three-dimensional (3D) conducting bodies of general shape is presented. The arbitrary surface is described by dividing it into a number of connected patches which are mathematically described as parametric quadratic surfaces. The electric field integral equation (EFIE) is discretized by the standard method of moments (MOM) with specially designed basis functions for subdomains which now contain surface curvature. The use of the basis functions on curvilinear patch reduces the number of unknowns used in MOM.

P-nitrophenol (4-NP) and hydrazine hydrate are considered to be highly toxic pollutants in wastewater, and it is of great importance to remove them. Herein, TiO2-loaded Co0.85Se thin films with heterostructure were successfully synthesized by a hydrothermal route. The as-synthesized samples were characterized by x-ray diffraction, x-ray photoelectron spectroscopy, transmission electron microscopy and selective-area electron diffraction. The results demonstrate that TiO2 nanoparticles with a size of about 10 nm are easily loaded on the surface of graphene-like Co0.85Se nanofilms, and the NH3 · H2O plays an important role in the generation and crystallization of TiO2 nanoparticles. Brunauer-Emmett-Teller measurement shows that the obtained nanocomposites have a larger specific surface area (199.3 m(2) g(-1)) than that of Co0.85Se nanofilms (55.17 m(2) g(-1)) and TiO2 nanoparticles (19.49 m(2) g(-1)). The catalytic tests indicate Co0.85Se-TiO2 nanofilms have the highest activity for 4-NP reduction and hydrazine hydrate decomposition within 10 min and 8 min, respectively, compared with the corresponding precursor Co0.85Se nanofilms and TiO2 nanoparticles. The enhanced catalytic performance can be attributed to the larger specific surface area and higher rate of interfacial charge transfer in the heterojunction than that of the single components. In addition, recycling tests show that the as-synthesized sample presents stable conversion efficiency for 4-NP reduction.

In this paper, a facile and efficient method combined sol–gel method with hydrothermal process was employed for preparing titanium dioxide (TiO[Formula: see text]/reduced graphene oxide (rGO) nanocomposites without using any reductants or surfactants. This approach leads to the reduction of graphene oxide (GO) and the growth of TiO2 nanorods simultaneously. The results reveal that the TiO2 short nanorods with average size of 15[Formula: see text]nm in length and 10[Formula: see text]nm in diameter were uniformly grown on the rGO sheets with high dispersion. Compared with the pure TiO2 nanoparticles, the TiO2/rGO composites exhibit strong absorption in the visible light range. The photocurrent density of nanocomposites reached 0.826[Formula: see text]mA/cm2 under the simulated sunlight illumination, which is 3.5 times than that of pure TiO2. An enhancement of photocatalytic hydrogen formation rate for the water splitting was observed over the TiO2/rGO composite photocatalysts, the fastest formation rate can reach 889.28[Formula: see text][Formula: see text]mol[Formula: see text]g[Formula: see text]h[Formula: see text] when TiO2 coupling with 1wt.% rGO. Also the hydrogen production rate is about 3.27 times larger than pure TiO2 and 2.23 times than P25 due to the excellent electron trapping and transportation properties of rGO and the synergistic effect between TiO2 and rGO.

A novel volume integral equation for the current distribution over interconnects with arbitrary cross-sectional geometry is presented based on the free space Green's function without approximation. For very low frequency, it can be reduced to the widely-used quasi-static approximation. The quasi-static volume integral equation is not accurate enough for the calculation of current distribution. A comparison is made with the different methods known in literature to calculate the per unit length internal impedance. Detailed discussion is given for the different current distributions and the definitions with their effects to the internal impedance, either for a high frequency range or a low frequency range.