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The fast multipole method (FMM) is an efficient method in the iterative solution of the matrix equation that is associated with the integral equation of wave scattering. The key idea of the FMM is to divide the interactions between groups of scatterers into near-field interactions and non-near-field interactions, and perform the non-near-field interactions efficiently with the aid of the multipole expansion of the fields. The far-field approximation is introduced in FMM to calculate the wave interactions between groups that are separated by a very large distance. The advantage of this approach is that it automatically switches back to the original FMM for small problems. Under the far-field approximation, the translation operator is much simpler than that used in the FMM. Numerical results show speed up of the modified FMM over the original FMM for problems as small as several thousands.

The method of moments (MoM) remains one of the most popular methods to analyze antennas, or indeed, any perfect-electric-conductor (PEC) scattering problem. Since many antennas can be modeled as infinitely thin PEC surfaces, the electric field integral equation (EFIE) formulation has been used. Initially, the current basis function introduced by Rao, Wilton, and Glisson (1982) for PEC surfaces meshed with triangular patches was used. However it was noticed that for structures with both very small and very large features, the condition number of the resulting matrix was very large. This is unfortunate because many antennas fall into this category and because a large condition number may lead to problems in solving the linear system of equations. If a direct method is used to solve the matrix equation, a large condition number will lead to a large relative error between the exact solution and the calculated one. If an iterative method is used, a large condition number may mean that the iterative method will converge only very slowly. Nevertheless, in an effort to reduce the condition number, the RWG basis function was augmented with a loop basis function to form an alternative basis set. The effect of patch size and choice of basis set on the condition number are examined for a simple plate. The RWG basis function may also be augmented with a solenoidal basis function to create a higher order basis set. The effect of this higher order basis set on the convergence of the input impedance for a blade dipole is also examined.

We have implemented a numerical algorithm for solving the integral equations of electromagnetic scattering from conducting objects using the method of moments. This code is implemented and developed for the computation of near-field interactions in the multilevel fast multipole algorithm (MLFMA). The implementation utilized the flat-triangular patch for the surface description and the Rao-Wilton-Glisson (1982) basis as the current expansion function. The triangular patch basis was introduced by Rao et. al. for solving the electrical field integral equation (EFIE). Our implementation is focused on the consideration of reducing the condition number of the impedance matrix. Hence, the implementation includes the electrical field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE). In the computation of the matrix elements associated with the nearby elements, the near-singular integrals are treated properly with the aid of the formulas given previously. This allows the code to deal with objects that contain very thin structures. Moreover, we added a partial diagonal preconditioner in the code in case the iterative solver does not provide any preconditioners. This is very important in the Galerkin's method. We have tested the code for various ill-conditioning problems to validate the performance of the implementation.

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) have been applied for solving integral equations of electromagnetic scattering iteratively. FMM reduces the complexity of a matrix-vector multiply from O(N/sup 2/) to O(N

The performance of an impulse radar in a sea-surface environment is strongly influenced by the ability to minimize the sea clutter. Two methods of determining the transient scattering from a sea-surface interface are investigated. One method utilizes the Rayleigh approximation, and therefore is valid only for certain parameter regimes, while the other method uses magnetic field integral equations (MFIE) and yields correct results for all regimes. The advantage of the Rayleigh approximated analysis is in the computation time involved. In both methods, frequency-domain results are obtained. A large frequency bandwidth is needed to properly reconstruct the time-domain transient response; this implies a large number iterations is needed to implement such a bandwidth. The knowledge gained from this analysis will allow for a minimization of the sea clutter, thus improving the impulse radar detection in a sea environment. The TM polarization is of the greatest interest, because of the Brewster angle phenomenon, therefore only the TM case is discussed in detail.

Practical electromagnetic problems are often three-dimensional (3-D) and involve arbitrary geometry. In the case when an object of curvature is of interest, the use of flat facets creates unnecessary artificial discretization in the solution. Recently, many researchers have been investigating the use of curved patches. This paper presents the method of moments (MoM) technique for computing the electromagnetic radiation and scattering from 3-D conducting bodies of general shape. The arbitrary surface is described by dividing it into a number of connected patches which are mathematically described as parametric quadric surfaces. The electric field integral equation (EFIE) is solved by standard MoM technique with specifically designed basic functions for subdomains which now contain surface curvature. Numerical results agree very well with those of existing studies.

This paper reviews the state of the art in fast integral equation techniques for solving large scale electromagnetic radiation and compatibility problems. The fast multipole method (FMM) and its frequency and time domain derivatives are discussed. These techniques permit the rapid evaluation of fields due to known sources and hence accelerate the solution of boundary value problems arising in the analysis of a wide variety of electromagnetic phenomena. Specifically, the application of the steepest descent fast multipole method (SDFMM) and the thin stratified medium fast multipole algorithm (TSM-FMA) to the frequency domain analysis of radiation from microstrip structures residing on finite and infinite substrates and ground planes, respectively, is described. In addition, the extension of the FMM concept to plane wave time domain (PWTD) algorithms that permit the analysis of transient phenomena is outlined.

The Fast Illinois Solver Code (FISC) is a code to tackle large scale computing and scattering problems using multi-level fast multipole algorithms. FISC requirements for memory and CPU time are discussed. Some empirically derived formulas and charts are given. The examples used to get these conclusions are also plotted. FISC is designed to compute the RCS of a target described by a triangular facet file. Both complexities for the CPU time per iteration and memory requirements are of O(NlogN), where N is the number of unknowns.

We present a frequency extrapolation scheme to speed up the signature prediction procedure using FISC by avoiding exhaustive computations. We adopt a model-based approach to the frequency extrapolation problem. The key in the success of an extrapolation algorithm is a good model of the physical observable to be extrapolated. We propose a scheme that parameterizes the current on the target, which is available in the FISC solution, based on a multipath excitation model. We first run FISC for the scattering problem at several frequency points, then apply the ESPRIT superresolution algorithm directly to the induced current output at these frequency points to extract the time-of-arrival and amplitude parameters. Once these parameters are obtained, the frequency dependent model of the induced current on each facet of the target can be constructed. Thus the induced currents over the whole frequency band can be extrapolated and the multifrequency far field can be calculated. The range profiles of a low-Q missile model are calculated as an example to demonstrate the performance of the algorithm.

The matrix vector multiplication encountered in the iterative solution of scattering problems can be performed in O(N) operations by using a multilevel fast multipole algorithm (MLFMA). This paper presents estimates for the errors introduced by MLFMA. The details of the algorithm are described in Koc and Chew (1997). An analysis of the errors in the FMM algorithm for the monopole and dipole terms is given in Song et al. (1997). The analysis is extended to higher order multipole terms, and integration and interpolation errors are also included.

In this paper, we have presented the major features and some preliminary results from the parallel fast multipole library, ScaleME (scalable multipole engine). We have briefly outlined the major features of the library and its applications.

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 2D inhomogeneous dielectric objects from TE scattering data. The algorithm is the combination of the distorted Born iterative method and strong permittivity fluctuation theory. Numerical simulations are performed and the results show that the distorted Born iterative method for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrast in comparison with the ordinary distorted Born iterative method (DBIM). A frequency hopping technique is also applied to further increase the contrast.

It is found that the fast multipole algorithm (FMA), used to compute interactions between M bodies, can be used effectively in computing the electrostatic potential due to M bodies. This paper describes some of the few combinations of a parallel fast multipole algorithm and a capacitance solver. Another group has also combined the parallel FMA with a capacitance solver (Wang et al. 1996). The main difference between this and previous implementations of the fast multipole algorithm is the way parallelization was implemented. The current implementation performs well when compared to previous implementations. Other advances include precomputation, multiprocessor scalability, and a focus on data memory layout techniques. Many of these concepts that have been utilized in this implementation can be used in developing distributed memory implementations.

Summary form only given. Recently there has been renewed interest in solving integral equations due to the advent of fast multilevel techniques. These fast solvers exploit the special structure of the matrices that arise from the numerical approximation of the integral equation. The kernel of the integral equation is usually related to the Green's function which is translationally invariant. This property manifests itself in the numerical approximations of the Green's operator: the matrix has an inherent Toeplitz-like structure, or the matrix can be factored by translational matrices. As a result, an otherwise dense matrix vector multiplication can be performed in O(NlogN) operations. The authors review these methods.

For the analysis of large-scale electromagnetic scattering problems, high-frequency asymptotic methods are fast but approximate, whereas low-frequency numerical methods are accurate but slow. Neither can produce an efficient and accurate solution to scattering by large bodies containing small structures. A promising approach is to combine the best features of both types of methods to produce a hybrid technique that is sufficiently fast, reasonably accurate, and applicable to a class of unsolvable problems such as the scatterers mentioned above. There are two extremes for this type of hybridization. One is simply to superimpose solutions from asymptotic and numerical methods. The other extreme is to combine an asymptotic and a numerical method in an exact manner. A more practical approach is to develop a technique that can include all significant interactions and neglect all trivial interactions. The resulting hybrid technique can produce sufficient accuracy and can be implemented in a general-purpose computer code. In this paper, we develop a technique that combines the shooting-and-bouncing-ray (SBR) method and the method of moments (MoM) to solve for the scattering by large conducting bodies with small structures mounted on their surfaces. The radar cross-section of a VFY 218 airplane is used as an example.

The hybrid finite-element and boundary-integral (FE-BI) method is a powerful numerical technique for computing scattering by inhomogeneous objects. Although the application of edge-based finite elements and the combined field integral equation (CFIE) in the FE-BI method has successfully removed the difficulties of the treatment of dielectric interfaces, sharp conducting edges and corners, spurious solutions, and interior resonance problems inherited in the original FE-BI method using node-based elements and the electric-field integral equation (EFIE) or magnetic field integral equation (MFIE), the FE-BI method still has a bottleneck which is the dense matrix generated by the boundary integral equation (BIE). Our renewed interest in the FE-BI method originated from the recent development of the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA). Our objective is to apply MLFMA to BIE to completely remove the aforementioned bottleneck for general 3D problems. During the course of pursuing this goal, we have encountered several problems associated with the efficiency and accuracy of the FE-BI method implemented using the edge-based elements and CFIE. This paper reports our study of these problems and the implementation of MLFMA in the FE-BI method.

In this paper, we describe several fast methods for solving electromagnetic scattering problems. Notably, we discuss iterative surface integral equation solvers such as the 3D fast multipole method, multilevel fast multipole method, rough surface scattering using steepest descent path fast multipole method, and the thin-stratified media fast multipole method.

The fast multipole method is an effective way to expedite iterative solutions of integral equations for electrodynamic and elastodynamic problems. Iterative solvers, such as the conjugate gradient method, require matrix vector multiplies, and for dense matrices, these matrix-vector multiplies constitute the predominant computational cost as well as requiring a large memory. The fast multipole method is based on the translation of multipoles from one coordinate system to another, which is achieved by using translation matrices. However, the mere use of translation matrices does not reduce the computational cost nor the memory requirement for dynamic problems involving surface scatterers. For such problems, the crucial step in the fast multipole method is the diagonalization of the translation operators. The translation matrix for the three dimensional Helmholtz wave equation has been successfully diagonalized using an alternative and succinct method. The method reveals the relationship between the translation matrices and their representation of the translation group. A diagonalization is expected under a plane-wave basis for the representation since a plane-wave basis forms an irreducible representation for the translation group. Hence, the diagonalization of the translation matrices from the spherical harmonic representation can be viewed as a series of similarity transforms. The result can be used in the fast multipole method and the multilevel fast multipole method where multiple scattering involves interaction between multipoles.

Because the multilevel fast multipole algorithm (MLFMA) expedites matrix-vector multiplication, it can be used to speed up iterative solutions of scattering problems. We have combined MLFMA with the conjugate gradient and the biconjugate gradient methods to arrive at efficient solvers for matrix equations arising from the integral equation of scattering. The computational and memory-requirement complexities are both O(NlogN) for surface scatterers. The total CPU time is hence proportional to N/sub iter/NlogN. Compared to traditional matrix solvers requiring O(N/sup 2/) memory, and N/sub iter/N/sup 2/ CPU time for iterative solvers, and O(N/sup 3/) CPU time for LUD, this is a vast improvement, especially for large problems. Therefore, large problems that previously require the resources of a supercomputer to solve, can now be solved on a workstation-size computer.

Wilkes and Cha (1991) extended the flat triangular patch moment method solution developed by Rao, Wilton and Glisson (1982) to the curved triangular patch. Song and Chew (1995) divided an arbitrary surface into a number of parametric quadratic surfaces with fourth order polynomials. In this paper, we solve the electric field integral equation (EFIE), magnetic field integral equation (MFIE), and combined field integral equation (CFIE) by using curvilinear triangular patches with line matching. We define a basis function with no line charge accumulation on each point of the common edge of adjacent cells. We extract the self-term and near-neighbor-term singularities of EFIE, MFIE, and CFIE, and evaluate them in closed forms so that the matrix elements can be obtained by standard numerical integration methods. The current distribution and the scattered fields of an arbitrary 3-D surface can also be obtained. Numerical results are given.

The fast multipole method (FMM) speeds up the matrix-vector multiplication in the conjugate gradient (CG) method when it is used to solve the matrix equation iteratively. The FMM is applied to solve the problem of electromagnetic scattering from three dimensional arbitrary shape conducting bodies. The electric field integral equation (EFIE), magnetic field integral equation (MFIE), and the combined field integral equation (CFIE) are considered. The FMM formula for the CFIE has been derived, which reduces the complexity of the matrix-vector multiplication from O(N/sup 2/) to O(N/sup 1/.5), where N is the number of unknowns. With a nonnested method, using the ray-propagation fast multipole algorithm (RPFMA), the cost of the FMM matrix-vector multiplication is reduced to O(N/sup 4/3/). We have implemented a multilevel fast multipole algorithm (MLFMA), whose complexity is further reduced to O(NlogN). The FMM also requires less memory, and hence, can solve a larger problem on a small computer.

An algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error is presented. Unlike the ordinary nonuniform fast Fourier transform (NUFFT), which becomes O(N/sup 2/) for sparse r-space and sparse k-space data, the sparse data fast Fourier transform (SDFFT) presented herein decreases the cost to O(N log N) while preserving the O(N log N) memory complexity. The algorithm can be readily employed in general 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's sphere or it consists completely of arbitrary points. Among its applications in electromagnetics are back-projection tomography, diffraction tomography, synthetic aperture radar imaging, and the computation of far field patterns due to general aperture antennas and antenna arrays.

In general, three parameters are needed to model symmetrical adapters, but not enough equations can be found to solve them. The measurement of through adapters gives two conditions only, but neither open nor short adapter gives any useful condition. The results from lines with length L and length 2L can be used to derive the result for through adapters. This paper proposes one approach with a 2-impedance model, which has one shunt impedance and one series impedance. This model can be used with more complicated structures than the single impedance model.

The multilevel fast multipole algorithm has been applied for solving volume integral equations. Tetrahedron volume cells are used to discretize the material objects, providing a flexible representation for complex object shapes. Due to the reduction of the computational complexity, the method can be applied to solve electromagnetic scattering problems with electrically large dielectrics.

FISC (Fast Illinois Solver Code) is designed to compute the RCS of complex three-dimensional targets. The problem is formulated by the method of moments, where the RWG 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 accelerate the matrix-vector multiply in CG. Both complexities for the CPU time per iteration and memory requirements are of O(NlogN), where N is the number of unknowns. Some computations other than the matrix-vector multiply in FISC may have higher complexity than O(NlogN). When the translation matrix in MLFMA is calculated directly, the complexity is O(N/sup 3/2/). For calculating the bistatic RCS or radiation pattern on a one-plane cut, the number of observation angles (M) is proportional to the frequency for a surface scatterer. So the complexity of calculating bistatic RCS or radiation pattern is O(NM) or O(N/sup 1.5/). In this paper, we use interpolation to calculate the translation matrix and the complexity is reduced to O(N). MLFMA has been implemented to calculate the bistatic RCS or radiation pattern reducing its complexity to O(M)+O(NlogN). With these improvements, we have solved the problem of scattering from a 120/spl lambda/ sphere with 9,633,792 unknowns and VFY218 at 8 GHz with 9,990,918 unknowns. MLFMA has also been implemented for targets with a perfect electric conductor (PEC) ground plane.

This paper proposes a set of novel, grid-robust, higher-order vector basis functions for the MoM solution of integral equations for three-dimensional (3D) electromagnetic 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 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.

The nonuniform fast Fourier transform (FFT) on a line has been of interest to a number of scientists for its practical applications. However, not much has been written on Fourier transforming sparse spatial data where the Fourier transform is needed at only sparse data points in the Fourier space in 2D or 3D. It finds applications in remote sensing, inverse problems, and synthetic aperture radar where the scattered field is related to the Fourier transform of the scatterers. We outline an algorithm to perform this transform in NlogN operations, where N is the number of spatial data available, and we assume that the number of Fourier data desired is also of O(N). The algorithm described here is motivated by the multilevel fast multipole algorithm (MLFMA), but is different from that described by Brandt (1991). In MLFMA, an embedded fast Fourier transform algorithm is inherent, where the spatial data is arbitrarily distributed, but the Fourier data is required on the Ewald sphere. In the present algorithm, the restriction of the Fourier data to an Ewald sphere is lifted so that it can be arbitrarily distributed as well. The present algorithm can be easily generalized to 3D.

We propose to implement the multilevel fast multipole algorithm (MLFMA) based on point-to-point interactions, instead of the traditional basis-to-basis interactions. When we calculate the matrix elements for which the testing and source bases are not close to each other, we can apply Gaussian quadrature to evaluate the integrals. This process can be interpreted as replacing a continuous source distribution with discrete sources. Thus, one matrix-vector multiply is similar to the calculation of the electromagnetic fields for a given distribution of N source bases and then testing them with these bases. In this implementation, we first find Q equivalent point sources from these N source bases, then calculate electromagnetic fields at these Q points, and finally test them with each testing basis. The value of Q depends on the number of patches and the quadrature rule used for each patch. The MLFMA is used to calculate electromagnetic fields at Q points generated by Q point sources. By doing so, the number of levels used is not limited by the size of basis functions, making MLFMA more efficient.

In this paper, we present a higher-order multilevel fast multipole algorithm (MLFMA) for solving integral equations of electromagnetic wave scattering by three-dimensional conducting objects. We first employ higher-order parametric elements to provide an accurate modeling of the scatterer's geometry and then higher-order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. The resultant numerical system of equations is then solved using the MLFMA with a reduced computational complexity. Appropriate preconditioning techniques are employed to speedup the MLFMA solution.

We study the solution of integral equation using the method of moments such that it is stable all the way from static to some moderately low frequencies. As the frequency decreases, the electric and magnetic fields became decoupled. The unknown current consists of two components, a curl-free part and a divergence-free part. To maintain a physically finite charge as the frequency approaches zero, it is necessary that the divergence of the curl-free part scales as O(w) as the frequency approaches zero. No such frequency scaling is needed for the divergence-free part. The different frequency dependence of the current causes the so-called low frequency breakdown. Many researchers have investigated this problem. One way to overcome this difficulty is to use the loop-tree or loop-star basis function which can separate the contribution from the divergence-free current and the curl-free current. To improve the convergence property, a basis rearrangement is used. We also implement the method on the curvilinear-patches to reduce the number of unknowns.

The multilevel fast multipole algorithm (MLFMA) has been shown to provide substantial improvement over traditional method of moments (MOM) in the analysis of interconnections of linear surfaces and wires. In order to reduce the number of unknowns involved in modeling surface and wire structures with a high degree of curvature, the curvilinear RWG basis and the curvilinear wire basis are applied to expand the current distribution on curved surfaces and wires. The techniques for singularity extraction proposed by Champagne, Williams and Wilton (1992) are extended for the curvilinear RWG basis. In the present work, the original MLFMA code is modified to be an application-independent library similar to ScaleME. The aim is to hide the details of MLFMA implementation and let users exploit the power of MLFMA through a simple interface. For users who have a general MOM code with arbitrary basis functions, they only have to write support functions for computing the impedance matrix elements and radiation and receiving patterns of each basis function. Then, they can call the functions in the MLFMA library to setup MLFMA-related parameters and to accelerate the matrix-vector multiplication with the freedom of using any iterative matrix solver.

In this work, Fe3O4@Ag2Se/Ag nanocomposites were fabricated on a self-cleaning and recyclable surface-enhanced Raman scattering (SERS) substrate via a simple and ingenious precipitation shift reaction. The superparamagnetic property of Fe3O4 facilitates the efficient purification of products with the assistance of an external magnetic field. The as-prepared substrates have excellent stability and show no significant loss after six recycles for the photodegradation of rhodamine B (RhB). The unique Raman enhancement effect of Fe3O4@Ag2Se/Ag substrates indicates that RhB can be detected at a concentration as low as 1 × 10−8 M. Furthermore, the experimental results also suggest that these nanocomposites may be promising multifunctional SERS substrate candidates for environmental monitoring, cleaning and so on.

Shuttle-like AgBr–ZnO nanocomposites were successfully synthesized via a facile chemical precipitation method using CTAB as both an cationic surfactant and Br− source. The structure, composition and morphology of the as-synthesized products were characterized by means of powder X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), field-emission scanning electron microscopy (SEM), transmission electron microscopy (TEM), diffuse reflectance spectroscopy (DRS), photoluminescence spectroscopy (PL) and the Brunauer–Emmett–Teller (BET) surface area measurements. The results revealed that the as-synthesized samples were single crystalline nanostructures with a shuttle-like morphology. The reaction temperature played an important role in the composition and morphology of the products. When the temperature was increased from 40 °C to 80 °C, the components of corresponding products changed from binary Ag–ZnO to ternary Ag–AgBr–ZnO, then to binary AgBr–ZnO, and the morphology underwent a change from aggregated nanoparticles to regular shuttle-like shaped crystals with diameters of ca. 200 nm and lengths of ca. 600 nm. Significantly, the as-prepared AgBr–ZnO nanocomposites showed enhanced photocatalytic properties for the degradation of Rhodamine B in aqueous solution under UV irradiation with a filter (λ = 365 nm) in comparison to the pure ZnO nanomaterials.

In this work, novel CeCO3OH@C nanocomposites were prepared via a one-pot approach by hydrothermal carbonization of a solution of glucose as a carbon precursor in the presence of Ce(NO3)3·6H2O and urea. It was found that glucose not only facilitates the formation of CeCO3OH nanoparticles, but also leads to a uniform, glucose-derived, carbon-rich polysaccharide (GCP) overlayer on the CeCO3OH nanocomposites. By adjusting the concentrations of glucose, the morphology of the samples was transformed from spindle nanoparticles to uniform spherical particles. CeO2@C with a core–shell structure was fabricated after calcining the CeCO3OH@C nanospheres under an N2 atmosphere. The obtained products were characterized by SEM, TEM, XRD, TG-DSC, FT-IR and charge–discharge test. The electrochemical performance test showed that these CeO2@C core–shell spheres as an anode material for lithium ion batteries exhibited an initial discharge specific capacity of 863.0 mA h g−1 in the potential range of 3.0–0.0 V. After 50 cycles, the capacity of the CeO2@C core–shell spheres was stabilized reversibly at about 355.0 mA h g−1. The improved cycling performance was attributed to the carbon shells, which can enhance the conductivity of the CeO2 core and suppress the aggregation of active particles during cycling. These CeO2@C core–shell spheres are promising anode materials for lithium ion batteries.

Zn(PAN)2 nanobelts with widths of 100–200 nm and lengths of 1–2 μm have been successfully synthesized through a facile solvothermal method at 140 °C for 24 h. The composition, morphology and size of the as-prepared products were confirmed by elemental analysis (EA), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The effects of Zn/PAN molar ratio, reaction solvent and reaction time on the morphology of Zn(PAN)2 nanostructures have been studied systematically. A possible growth process of the Zn(PAN)2 nanobelts has been proposed. Moreover, the nonlinear optical property of the Zn(PAN)2 sample was investigated for the first time, indicating that these nanomaterials have potential future application in nonlinear optics.

Novel bracelet-like Cu@cross-linked poly(vinyl alcohol) (PVA) microrings have been prepared through a PVA-assisted hydrothermal process. Bracelet-like microrings are composed of inner copper nanorings and outer cross-linked PVA beads. The formation of bracelet-like microrings consists of two steps, i.e. the growth and self-coiling of PVA-wrapped copper nanowires and corresponding adhering of cross-linked PVA to form bracelet-like structures. Copper nanowires are formed by reduction from a mixed copper source consisting of CuCl2 and CuBr in the presence of NaBr by PVA. When an appropriate amount of NaBr was added, a product with a high yield of microrings can be obtained. A further investigation on ultra-thin section TEM images indicates that addition of the appropriate amount of NaBr leads to thinner copper nanowires within the crosss-linked PVA coatings. We proposed that thinner copper nanowires have less elastic resistance during bending processes, so PVA wrapped copper nanowires are more easily bent arbitrarily during vigorous Brownian motion at 210 °C. When two ends of one single nanowire join, the formation of van der Waals bonds and diminishing of the interfacial area through overlapping compensate the elastic resistance to get stable ring-like structures.

Hexagonal Co0.85Se with Ni0.85Se-type structure has been successfully synthesized without any surfactants by a solvothermal reduction route. SEM observation indicated that the obtained Co0.85Se nanostructures were of graphene-like morphology with a thickness less than 10 nm. The influence of the reaction temperature and the molar ratios of reactants has been studied in detail, and the results reveal the two reaction conditions play a crucial role in determining the final morphologies of the samples. The as-prepared product is determined to be ferromagnetic at room temperature from magnetic measurements. And the product with high specific surface area could be used as an adsorbent in wastewater treatment, which may be very useful for the environment.

In this paper, we used a coarse-grained model at the residue level to calculate the binding free energies of three protein-protein complexes. General formulations to calculate the electrostatic binding free energy and the van der Waals free energy are presented by solving linearized Poisson-Boltzmann equations using the boundary element method in combination with the fast multipole method. The residue level model with the fast multipole method allows us to efficiently investigate how the mutations on the active site of the protein-protein interface affect the changes in binding affinities of protein complexes. Good correlations between the calculated results and the experimental ones indicate that our model can capture the dominant contributions to the protein-protein interactions. At the same time, additional effects on protein binding due to atomic details are also discussed in the context of the limitations of such a coarse-grained model.

A simple solvothermal route was explored to prepare hierarchical, nanostructured flower-like bismuth oxychlorides (BiOCl) by employing pyridine as the solvent. The volume ratios of distilled water to pyridine play an important role in the assembly of the BiOCl nanostructure from nanoplates to nanoflowers. The as-prepared BiOCl nanoflowers were characterized by X-ray powder diffraction, scanning electron microscopy, transmission electron microscopy, high-resolution transmission electron microscopy, and nitrogen sorption. The resulting BiOCl nanoflowers with high specific surface area were phase-pure and self-assembled from thin nanoplates during the reaction process. In addition, the photocatalytic properties of the as-prepared samples were further investigated by photocatalytic decomposition of methyl orange (MO) dye, and it was found that the BiOCl nanoflowers showed a higher photocatalytic activity than that of TiO2 (Degussa, P25) under modeling sunlight.

Large area arrays of patterned carbonate nanofibers have been constructed viapolymer controlled mineralization. Micropatterned octadecyltrichlorosilane (OTS)-coated domains on the smooth substrate were found to preferentially deposit mineral films, which could act as a secondary template for growth of nanofibers after their solidification or crystalization.