Search

It is time-consuming to simulate the unmanned aerial vehicle (UAV) swarm by the Multi-Level Fast Multipole Algorithm (MLFMA). This paper proposes a method to accelerate the simulation by neglecting...

Silicon has been utilized in metasurfaces to produce structural color filters due to its compatibility with mature and cost-effective methods for complementary metal oxide semiconductor devices. In this work, we propose and demonstrate efficiency- and scattering-enhanced structural color filters using all-dielectric metasurfaces made up of engineered hydrogenated amorphous silicon (a-Si:H) nanoblocks. Wavelength-dependent filtering is achieved by Mie scattering as each structure individually supports the electric dipole (ED) and magnetic dipole (MD) resonances. The ED and MD resonances are identified by observing the field profiles of the resonance calculated by finite element method (FEM) simulations. To enhance the efficiency and scattering response of the all-dielectric metasurfaces, the proposed structural color filters are designed with consideration of the lattice resonances and scattering directivity. The spectral positions of the transmission dips and peaks are rigorously analyzed in accordance with the Mie theory and multipole expansion. The transmission spectra exhibit 100% transmission where Kerker's first condition is satisfied, while the lattice resonances amplify the ED and MD scattering responses throughout the entire visible regime. Various colors are generated by varying the resonance peak, which is controlled by varying the geometric parameters of a-Si:H nanoblocks. The proposed structural color printing devices are expected to have applications in dynamic color displays, imaging devices, and photorealistic color printing.

The subject of this paper is to build a physical model describing shape and size correlations of galaxies due to weak gravitational lensing and due to direct tidal interaction of elliptical galaxies with gravitational fields sourced by the cosmic large-scale structure. Setting up a linear intrinsic alignment model for elliptical galaxies which parameterises the reaction of the galaxy to an external tidal shear field is controlled by the velocity dispersion, we predict intrinsic correlations and cross-correlations with weak lensing for both shapes and sizes, juxtaposing both types of spectra with lensing. We quantify the observability of the intrinsic shape and size correlations and estimate with the Fisher-formalism how well the alignment parameter can be determined from the Euclid weak lensing survey. Specifically, we find a contamination of the weak lensing convergence spectra with an intrinsic size correlation amounting to up to 10% over a wide multipole range $\ell=100\ldots300$, with a corresponding cross-correlation exhibiting a sign change, similar to the cross-correlation between weak lensing shear and intrinsic shapes. A determination of the alignment parameter yields a precision of a few percent forecasted for Euclid, and we show that all shape and many size correlations should be measurable with Euclid., Comment: 16 pages, 6 figures

The formulations of problems of analysis and synthesis in multipolar communication networks with variable flow rates on the arcs of the network are considered. In contrast to traditional formulations, the concepts of flow density, flow rate, and flow intensity are introduced, and the temporal characteristics of the movement of the given volumes through the network are analyzed. Similar problems arise in various spheres of human activity, for example, when studying traffic flows in models of evacuation of large cities or in problems of planning and managing transportation in problems of urban logistics. Mathematical formulations and algorithms for solving problems of transportation in a multipole network with variable flow rates are presented, which, under certain conditions, make it possible to avoid solving complex nonlinear problems of mathematical programming of large dimensions.

An iterative hybrid method is proposed for analyzing the electromagnetic (EM) scattering from complex target above rough surface. First, the electric/magnetic current-combined field integral equation (JMCFIE) is formulated to calculate the EM scattering from the complex target combining conductor and multiple dielectric objects. Then, the single integral equation (SIE) method for multiple dielectric objects in the complex target (MSIE) is applied to reduce one-half of the unknowns in dielectric regions, and the hybrid JMCFIE-MSIE method is formulated. Afterward, physical optics (PO) approximation is employed for computing the EM scattering on the rough surface, and the iterative hybrid based on the combination of JMCFIE-MSIE and PO is derived for composite scattering from complex target above rough surface. Furthermore, the multilevel fast multipole algorithm is utilized to accelerate the matrix-vector multiplications in the computation process. The equivalent edge currents method is applied to meliorate the result. Finally, the validation and applicability of the proposed iterative solution are demonstrated by several numerical examples.

In this study, a modified multilevel fast multipole algorithm is constructed for investigating large-scale particle systems. The algorithm expands the number of levels of the modified dual-level fast multipole algorithm from dual-level grids to multipole levels by a layer-by-layer correction and recursive calculation. The linear equations on coarse grid are recursively solved by a two-level grid. The single sparse matrix having higher filling rate is decomposed into a set of sparse matrices with much lower filling rate. Subsequent theoretical analysis and examples demonstrate that the total storage space of sparse matrices is significantly reduced, yet efficiency of the algorithm is almost unaffected. The fast multipole method is applied to expedite the matrix–vector multiplications. Complexity analysis demonstrates the algorithm has O(N) operation efficiency and storage complexity for three-dimensional potential model. A potential example with 10 million degrees of freedom is accurately computed via a single laptop with 16GB RAM. Finally, the development process of the modified multilevel fast multipole algorithm is briefly overviewed.

A novel fast multipole boundary element method (FM-BEM) is proposed to analyze 2-D potential problems by using linear and three-node quadratic elements. In FM-BEM, fast multipole expansions are used for the integrals on elements which are far away from the source point, whereas direct evaluations are used for the integrals on elements which are close to the source point. The use of higher-order elements results in more complex forms of the integrands, which increases the burden in direct evaluations, especially for singular and nearly singular integrals. Herein, the complex notation is introduced to simplify the computational formulations in boundary integral equations for 2-D potential problems. The singular and nearly singular integrals on linear elements are calculated by the analytic formulas, and those on three-node quadratic elements are evaluated by a robust semi-analytical algorithm. Numerical examples show that the proposed FM-BEM possesses higher accuracy than the conventional FM-BEM. Besides, the present method can analyze thin structures and evaluate accurately the physical quantities at interior points much closer to the boundary.

Conservation of magnetic flux is associated with regions of the powerful magnetic fields (B ∽ 1013 G) near neutron stars' surface. The vector potential generated by moving electric charge Q is uniformly distributed within a Neutron star's surface (radius R). The evolution of the magnetic field of isolated neutron stars is studied and based on magnetic flux conservation; the multipolar magnetic fields for (l = 1; l = 2; l = 3; l = 4) have calculated. We developed the field line equations and simulated the magnetic field line geometry for the interaction between neutron stars’ dipole–multipolar magnetic fields using the MATLAB software program.

Objective: Electromagnetic recordings are useful for non-invasive measurement of human brain activity. They typically sample electric potentials on the scalp or the magnetic field outside the head using electroencephalography (EEG) or magnetoencephalography (MEG), respectively. EEG and MEG are not, however, symmetric counterparts: EEG samples a scalar field via a line integral over the electric field between two points, while MEG samples projections of a vector-valued field by small sensors. Here we present a unified mathematical formalism for electromagnetic measurements, leading to useful interpretations and signal processing methods for EEG and MEG. Methods: We represent electric and magnetic fields as solutions of Laplace's equation under the quasi-static approximation, each field representable as an expansion of the same vector spherical harmonics (VSH) but differently weighted by electro- and magnetostatic multipole moments, respectively. Results: We observe that the electric and the magnetic fields are mathematically symmetric but couple to the underlying electric source distribution in distinct ways via their corresponding multipole moments, which have concise mathematical forms. The VSH model also allows us to construct linear bases for MEG and EEG for signal processing and analysis, including interference suppression methods and system calibration. Conclusion: The VSH model is a powerful and simple approach for modeling quasi-static electromagnetic fields. Significance: Our formalism provides a unified framework for interpreting resolution questions, and paves the way for new processing and analysis methods.

—A two-dimensional problem of the diffraction of a plane electromagnetic wave of the TM type by a cylindrical nanostructure made of silver or gold, the cross-sectional contour of which is a circle or an ellipse with a different ratio of the semiaxes, is considered. In the wavelength range $$300\,\,{\text{nm}} < \lambda < 900\,\,{\text{nm}}$$ the spectra of the scattering diameter and scattering diagrams were calculated by a rigorous numerical method. The influence of the losses of the medium, the geometric dimensions of the structure, and the angle of incidence of a plane wave on the scattering diameter and the scattering diagram are investigated. It is shown that the position of the dipole resonance and the number of multipole resonances for the silver (gold) nanostructure depend on the thickness of the structure, its length, and the angle of incidence of the plane wave. In this case, real losses of silver (gold) make it impossible for the existence of higher multipole resonances.

The accuracy problem of the classically Rao-Wilton-Glisson (RWG) discretized magnetic field and combined field integral equations originates from the strong singularity of the identity operator. With a novel basis transformation scheme, i.e. two subsequent weak-form rotations of the RWG basis functions, the accuracy of the identity operator discretization is improved. The presented discretization scheme is immediately compatible with fast algorithms and is combined with the multilevel fast multipole algorithm. The good accuracy and the good conditioning behavior of the formulation are verified in several numerical simulations, also including electrically large problems.

We are investigating the free components of an electromagnetic current, which we describe as a De Rham current over an arbitrary worldline on an arbitrary spacetime MST . These calculations are an extension of a previous research done on dipoles and quadrupoles, in which they are described in a metric-free manner. In this thesis, we consider an adapted coordinate system to define the free components of an electromagnetic distribution over an arbitrary worldline and extend the previous work done by going up to the octupole order of the electromagnetic current expansion. Using the symmetries of the components found in the calculations, we derive a generalized expression for the number of free components of any 2^k-tupole current, which satisfies the equation which leads to conservation of charge, dJ = 0.

Cu/TiO2 is a well-known photocatalyst for the photocatalytic transformation of CO2 into methane. The formation of C2+ products such as ethane and ethanol rather than methane is more interesting due...

The Unsteady Vortex Lattice Method (UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most time-consuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O N 2 , we present an O N Dipole Panel Fast Multipole Method (DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P . Two methods (the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments (with three harmonics), DPFMM is approximately two times faster for N ∈ [ 10 3 , 10 6 ] . The simulation time of a multirotor ( N ∼ 10 4 ) is reduced from 100 min (with unaccelerated direct solver) to 2 min (with DPFMM).

This article introduces an efficient method to determine the dielectric model parameters of a thin film substrate from microstrip line measurements and electromagnetic analysis. The proposed method avoids using optimization algorithms which normally require extensive computation time. The complex permittivity is extracted through only one full-wave simulation. The multipole Debye model was employed to fit the extracted complex permittivity. The parameters of the best-fitting model obtained through this procedure are considered as the final results, which also ensure physically consistent characteristics. Polyimide was selected to validate the methodology. The best-fitting model generated by the proposed method has shown excellent agreement to the polyimide data sheet values at 1 MHz. Moreover, simulations using the parameters of the best-fitting model exhibit good agreement with the experimental propagation constant data of microstrip lines up to 60 GHz.

Recently, a novel type of a multiscale simulation, called Relative Resolution (RelRes), was introduced. In a single system, molecules switch their resolution in terms of their relative separation, with near neighbors interacting via fine-grained potentials yet far neighbors interacting via coarse-grained potentials; notably, these two potentials are analytically parameterized by a multipole approximation. This multiscale approach is consequently able to correctly retrieve across state space, the structural and thermal, as well as static and dynamic, behavior of various nonpolar mixtures. Our current work focuses on the practical implementation of RelRes in LAMMPS, specifically for the commonly used Lennard-Jones potential. By examining various correlations and properties of several alkane liquids, including complex solutions of alternate cooligomers and block copolymers, we confirm the validity of this automated LAMMPS algorithm. Most importantly, we demonstrate that this RelRes implementation gains almost an order of magnitude in computational efficiency, as compared with conventional simulations. We thus recommend this novel LAMMPS algorithm for anyone studying systems governed by Lennard-Jones interactions., 38 pages, 10 figures, 4 tables

Split theta-shaped nanocavities composed of an elliptical disk embedded in a nonconcentric split ring are theoretically investigated by the finite-difference time-domain method. Symmetric and antisymmetric mode-based Fano resonances are both formed, due to the interference between the bright mode of the cavity and two types of multipole modes of the split ring, and experience different changes through adjusting the degree of symmetry breaking via an asymmetry of the ring width and displacement of the disk. As the cavity remains symmetrical with respect to the axis of the split ring, only the symmetric Fano resonances are observed. Further breaking the cavity symmetry, the antisymmetric Fano resonances appear and increase, while symmetric ones decrease. When the overall degree of symmetry breaking becomes larger due to an increasing offset of the disk relative to the asymmetric ring, this change trend becomes more complicated, and some Fano resonances are suppressed or enhanced again. Our work demonstrates that the proposed cavities with tunable Fano line shape could be used as platforms for multiwavelength biochemical sensors and enhanced spectroscopies.

The Independent Atom Model (IAM) of electron density is used in routine X-ray data analysis. However, this model does not give a quantitative description of the electron-density distribution. A better model that allows for modelling of aspherical charge density deformations is introduced by the Hansen–Coppens variant of the multipole model of electron density. However, the application of this model requires crystals of excellent quality and high-resolution XRD data which are quite often difficult criteria to fulfil. Therefore, Mo Kα and Cu Kα data of three model compounds (tricyclic imide, xylitol and methyluracil) were refined using IAM and new methods which enabled the refinement and reconstruction of charge density based on the Cu Kα data. These methods were the Bond-Oriented Deformation Density (BODD) model, Hirshfeld Atom Refinement (HAR) and the Transferable Aspherical Atom Model (TAAM). The final results were compared to the model obtained from neutron diffraction experiments. Our results demonstrated not only that Cu Kα data may be refined using BODD, HAR and TAAM methods, but also revealed systematic errors arising from the use of Cu Kα data. These errors were a result of the limited information in the low-resolution data set that manifested as higher values for the anisotropic displacement parameters (ADPs) and smaller maxima and minima of the residual electron density for the Cu Kα data compared to the Mo Kα data. Notably, these systematic errors were much less significant than those found for the IAM. Therefore, the application of BODD, HAR and TAAM on Cu Kα data has a more significant influence on the final results of refinement than for the Mo Kα data.

We assess the performance of the multipole expansion formalism in the case of single-dish HI intensity mapping, including instrumental and foreground removal effects. This formalism is used to provide MCMC forecasts for a range of HI and cosmological parameters, including redshift space distortions and the Alcock-Paczynski effect. We first determine the range of validity of our power spectrum modelling by fitting to simulation data, concentrating on the monopole, quadrupole, and hexadecapole contributions. We then show that foreground subtraction effects can lead to severe biases in the determination of cosmological parameters, in particular the parameters relating to the transverse BAO rescaling, the growth rate and the HI bias ($\alpha_\perp$, $\overline{T}_\text{HI} f\sigma_8$, and $\overline{T}_\text{HI} b_\text{HI} \sigma_8$, respectively). We attempt to account for these biases by constructing a 2-parameter foreground modelling prescription, and find that our prescription leads to unbiased parameter estimation at the expense of increasing the estimated uncertainties on cosmological parameters. In addition, we confirm that instrumental and foreground removal effects significantly impact the theoretical covariance matrix, and cause the covariance between different multipoles to become non-negligible. Finally, we show the effect of including higher-order multipoles in our analysis, and how these can be used to investigate the presence of instrumental and systematic effects in HI intensity mapping data., Comment: 18 pages, 12 figures, 5 tables, main concepts in figures 2 and 3, main results in figures 5 and 10

Based on an X-ray diffraction experiment at high resolution and a multipole refinement, the experimental electron density for R,R-tartaric acid (1) was determined. The consistent description of the different hydrogen bonds in 1 confirmed the quality of the diffraction data. The multipole-derived anisotropic displacement parameters (ADPs) for the non-hydrogen atoms were used as benchmarks for ADPs calculated from density-functional theory. For this theoretical approach, the structure was minimized with a dispersion-corrected exchange-correlation functional, and the phonon calculations were performed according to the harmonic and also the computationally more demanding quasiharmonic approximation. ADPs from experiment and quasiharmonic theory match very well with respect to amplitudes and directions of displacement. Numerical and graphical tests for the agreement between experimental and calculated ADPs for all non-hydrogen atoms indicate only small discrepancies. ADPs for hydrogen atoms were validated indirectly by their modest but positive effect on the quality indicators of the diffraction experiment.

In the article "A Rational QZ Method"" by D. Camps, K. Meerbergen, and R. Vandebril [SIAM J. Matrix Anal. Appl., 40 (2019), pp. 943-972], we introduced rational QZ (RQZ) methods. Our theoretical examinations revealed that the convergence of the RQZ method is governed by rational subspace iteration, thereby generalizing the classical QZ method, whose convergence relies on polynomial subspace iteration. Moreover the RQZ method operates on a pencil more general than Hessenberg-upper triangular, namely, a Hessenberg pencil, which is a pencil consisting of two Hessenberg matrices. However, the RQZ method can only be made competitive to advanced QZ implementations by using crucial add-ons such as small bulge multishift sweeps, aggressive early deflation, and optimal packing. In this paper we develop these techniques for the RQZ method. In the numerical experiments we compare the results with state-of-the-art routines for the generalized eigenvalue problem and show that the presented method is competitive in terms of speed and accuracy.

A novel fast algorithm is proposed to analyze the EM scattering from electrically large conducting targets with varying geometrical shapes. Firstly, the target surface can be constructed with several control points by using the non-uniform rational B-spline surface modeling method. More specifically, the surface integral equation can be rewritten in terms of these control points, which contains the geometrical coordinate information. Moreover, it should be noted that the derivatives of both the L and K operates are needed to describe the perturbation of electric currents. Therefore, a perturbed multilevel fast multipole algorithm (P-MLFMA) is proposed to accelerate the matrix vector multiplication. At last, numerical results are given to verify the accuracy and efficiency of the proposed P-MLFMA. It can be seen that higher computational efficiency can be obtained when compared with both the traditional Monte Carlo method and the Perturbation Approach for MoM.

An acoustic field scattered by an object can be presented as a multipole series. The set of values of every coefficient in this series is limited for objects with cylindrical symmetry when there are no internal sources of energy. Relations are presented for the phases and amplitudes of these coefficients, and between the powers of the absorbed and scattered fields.

The energy-momentum tensor (EMT) for a spin-3/2 baryon is related to \emph{seven} mechanical quantities. In this work, we provide the general form of the gravitational form factors (GFFs) for a spin-3/2 baryon by using the multipole expansion and interesting relations between the EMT densities and the GFFs. To verify those general relations, we study the nucleon and the $\Delta$ GFFs within the SU(2) Skyrme model based on the large $N_{c}$ limit., Comment: 20 pages, 7 figures

The creation of single photon sources on a chip is a mid-term milestone on the road to chip-scale quantum computing. An in-depth understanding of the extended multipole decomposition of non-isolated sources of electromagnetic radiation is not only relevant for a microscopic description of fundamental phenomena, such as light propagation in a medium, but also for emerging applications such as single-photon sources. To design single photon emitters on a chip, we consider a ridge dielectric waveguide perturbed with a cylindrical inclusion. For this, we expanded classical multipole decomposition that allows simplifying and interpreting complex optical interactions in an intuitive manner to make it suitable for analyzing light-matter interactions with non-isolated objects that are parts of a larger network, e.g. individual components such as a single photon source of an optical chip. It is shown that our formalism can be used to design single photon sources on a chip.

A hybrid scheme that combines the pre-corrected fast Fourier transform (p-FFT) and iterative Kirchhoff approximation (IKA) is developed to solve the electromagnetic scattering from multiple complex targets above a three-dimensional (3D) rough surface. Based on the domain distribution method (DDM), multiple targets are divided into an FFT region, and the rough surface is divided into an IKA region. Scattering on the FFT region and IKA region is calculated by p-FFT and IKA, respectively. In addition, iterative strategies are considered in both solving interaction between facets in the IKA region and interactions between FFT region and IKA region. However, interactions between FFT region and IKA region are the most time-consuming in the entire computational process. To overcome this computational bottleneck, the combined multilevel fast multipole algorithm (MLFMA), ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) are incorporated into interactions between FFT region and IKA region. They accelerate the matrix vector multiplication by “interpolation –translation –anterpolation”, while their translators are different, which result in their different computation efficiencies and application conditions. To effectively combine these three algorithms, the IKA region is divided into MLFMA area, RPFMA area and FAFFA area according to the distance, where interactions between these areas and the targets are accelerated by MLFMA, RPFMA and FAFFA, and the surface outside these areas is discarded. Compared with MLFMA, the accuracy and efficiency of this hybrid method are verified.

We present a novel approach to accelerate the electromagnetic simulations by the multilevel fast multipole algorithm (MLFMA). The strategy is based on a progressive elimination of the electromagnetic interactions, resulting in trimmed tree structures, during iterative solutions. To perform such eliminations systematically, artificial neural network (ANN) models are constructed and trained to estimate the errors in the updated surface current coefficients. These column eliminations are supported by straightforward row eliminations, leading to increasingly sparse tree structures and matrix equations as iterations continue. We show that the proposed implementation, namely, trimmed MLFMA (T-MLFMA), leads to significantly accelerated electromagnetic simulations of the large-scale objects, while the accuracy is still much better than the high-frequency techniques. T-MLFMA can be seen as an exemplar of the implementations, where machine learning is successfully integrated into an electromagnetic solver for enhanced simulations.

Piezoelectric responsive molecular ferroelectrics have become a research hotspot due to their advantages of simple fabrication, environmental friendliness, light weight and good mechanical flexibility. Here we proposed a new kind of multipole rare earth molecular ferroelectric, ((nBu)4N)3[Ce(NO3)4(SCN)2]((CH3CH2CH2CH2)4N = tetrabutylammonium) (1). Compound 1 undergoes a high temperature ferroelectric phase transition at 408 K. It is worth noting that compound 1 has a narrow band gap of 2.61 eV, flexible switchable SHG effect, moderate spontaneous polarization Ps = 3.6 μC cm−2, and piezoelectric constant = 3 pC N−1. The results show that these findings provide ideas for exploring multifunctional rare earth molecular ferroelectrics with a piezoelectric effect.

In this paper, an improved hybrid scheme combining the method of moment (MoM) and physical optic (PO) is proposed to analyze composite scattering from multiple 3D conductingobjects above a 2D random rough dielectric surface. In the calculation scheme, rough surface scattering is calculated using the PO method and target scattering is calculated by the MoM. The coupling interactions between the multiple targets are considered using the domain distribution method (DDM), where the matrix equations are constructed upon each individual target and are then presented and solved as a whole. The contribution from rough surface scattering, which is calculated by the PO method, is coupled with the impedance matrix, and the unknowns must be considered only in the MoM region. Most of the composite scattering problems are computing interactions between objects and rough surface, and solving the complex impedance matrix equation in the MoM part. To solve these two problems, first, the combined multilevel fast multipole algorithm (MLFMA) and the fast far field approximation (FaFFA) are introduced to accelerate interactions between objects and rough surface, where the near area on the rough surface is computed by MLFMA, while the far area is computed by FaFFA. In addition, to further improve the efficiency, the adaptive integral method (AIM) is employed to solve the impedance matrix equation of the MoM part in the scheme. The results are compared to those obtained with the traditional MoM-PO method, showing that the hybrid method proposed in this paper can maintain a high accuracy with a much smaller computational time and fewer resource requirements. The numerical results obtained under several different conditions are presented and discussed in this paper.