Truncation Parameter Research Articles

二元相位菲涅尔波带片近场俘获高低折射率粒子

A method of near-field trapping high and low refractive index Rayleigh particles was proposed using a binary phase Subwavelength Fresnel Zone Plate(SFZP)illuminated by the double-ring-shaped vortex beam.Based on the angular spectrum representation,the distribution of SFZP′s diffraction field was calculated.Bright and dark spots can be generated in the near field of the SFZP by changing the truncation parameter(β)and the vortex angle(δ)of the incident beam.Numerical results show that the SFZP can generate a subwavelength three-dimensional(3D)bright spot in the near-field region whenβ=1.09andδ=0.The tiny bright spot can be used to stably trap agold particle with radius 19 nm,whose refractive index is higher than that of the ambient medium.The axial and transverse trap distances are respective 0.4921λand 0.2844λ.Whenβ=1.45andδ=0.414π,a 3Ddark spot surrounded by a light shell can be formed in the near-field region.An air bubble with radius 30 nm is stably trapped at the center of this subwavelength dark spot.The refractive index of the air bubble is lower than the ambient medium.The axial and transverse trap distances are 0.62λand 0.3081λ.The trap distance obtained under two conditions is less than that in the conventional far-field trap system.The single trap system can be used to accurately trap two types of Rayleigh particles with different refractive indices.

Let’s fix it: Fixed-[formula omitted] asymptotics versus small-[formula omitted] asymptotics in heteroskedasticity and autocorrelation robust inference

In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the small-b asymptotics and the fixed-b asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixed-b asymptotic approximation provides a higher order refinement to the first order small-b asymptotics. This result provides a theoretical justification on the use of the fixed-b asymptotics in empirical applications. On the basis of the fixed-b asymptotics and higher order small-b asymptotics, the paper introduces a new and easy-to-use asymptotic F test that employs a finite sample corrected Wald statistic and uses an F-distribution as the reference distribution. Finally, the paper develops a bandwidth selection rule that is testing-optimal in that the bandwidth minimizes the type II error of the asymptotic F test while controlling for its type I error. Monte Carlo simulations show that the asymptotic F test with the testing-optimal bandwidth works very well in finite samples.

Novel Iterative Truncated Total Least Squares Algorithm for Image Restoration

Image restoration is a typical ill-posed inverse problem, which can be solved by a successful total least squares (TLS) method when not only the observation but the system matrix is also contaminated by addition noise. Considering the image restoration is a large-scale problem in general, project the TLS problem onto a subspace defined by a Lanczos bidiagonalization algorithm, and then the Truncated TLS method is applied on the subspace. Therefore, a novel iterative TTLS method, involving appropriate the choice of truncation parameter, is proposed. Finally, an Image reconstruction example is given to illustrate the effectiveness and robustness of proposed algorithm.

Experimental study of the fractional Fourier transform for a hollow Gaussian beam

Abstract Hollow Gaussian beam (HGB) was introduced in [Cai et al., Optics Letters 2003;28:1084–1086 [12] ] and the fractional Fourier transform (FRT) for a HGB was studied theoretically in [Zheng, Physics Letters A 2006;355:156–161 [53] ] . In this paper, we derive the analytical formula for the truncated FRT for a HGB, and we report experimental observation of the FRT and the truncated FRT for a HGB. The influences of the fractional order and the truncation parameter on the intensity distribution of the HGB in the FRT plane have been studied in detail both theoretically and experimentally. It is found that the FRT optical system provides an efficient way for modulating the beam profile of a HGB. Our experimental results agree well with the theoretical predictions.

Electromagnetic surface waves at a metal 2D photonic crystal interface

The conditions to observe and excite electromagnetic surface modes at the interface between a two-dimensional (2D) photonic crystal (PC) and bulk metal are studied. It is shown that these modes can exist in the region where bandgaps of the PC overlap with the region below the plasma frequency of a metal in the dispersion diagram in both polarizations. The dispersion relation of these electromagnetic surface modes is determined numerically by considering a system of a thin metallic layer in contact with a finite PC of some periods. The reflectance is computed by using the finite-difference time-domain (FDTD) method. With this method, it is shown that these modes can be excited and observed even under normal incidence from a vacuum. For the studied system, the cell in contact with the metallic layer must be truncated in order to observe the interface mode. It is shown that we can select the frequency of the mode inside the bandgaps by properly choosing the truncation parameter.

Packing and self-assembly of truncated triangular bipyramids

Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic packings with small unit cells that were obtained via numerical and analytical optimization. The maximal packing fraction φ(max) changes continuously with the truncation parameter t. Eight distinct packings are identified based on discontinuities in the first and second derivatives of φ(max)(t). These packings differ in the number of particles in the fundamental domain (unit cell) and the type of contacts between the particles. In particular, we report two packings with four particles in the unit cell for which both φ(max)(t) and φ(max)'(t) are continuous and the discontinuity occurs in the second derivative only. In the self-assembly simulations that we perform for larger boxes with 2048 particles, only one out of eight packings is found to assemble. In addition, the degenerate quasicrystal reported previously for triangular bipyramids without truncation [Haji-Akbari et al., Phys. Rev. Lett. 107, 215702 (2011)] assembles for truncations as high as 0.45. The self-assembly propensities for the structures formed in the thermodynamic limit are explained using the isoperimetric quotient of the particles and the coordination number in the disordered fluid and in the assembled structure.

Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z=500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ɛ in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ɛ in far-field. At receiving plane z=500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.

Existence of a solution for a thermoelectric model with several phase changes and a Carathéodory thermal conductivity

We present an existence result for the time domain eddy current model for electromagnetic field, coupled with a Stefan problem for temperature. We have extended the existence result proved by Bermúdez et al. (2005) [40] to the case of materials with several phase changes and thermal conductivity depending on both position and temperature.The new proof starts from a totally implicit time discretization of a truncated system. The thermal part can be rewritten as a variational inequality of the second kind. Then, a priori estimates independent of the truncation parameter are obtained for the solution of the truncated problem, using a technique that adapts the method of Boccardo and Gallouët (1989) [28] to the case of materials with several phase changes.

Active elastodynamic cloaking

An active elastodynamic cloak destructively interferes with an incident time harmonic in-plane (coupled compressional/shear) elastic wave to produce zero total elastic field over a finite spatial region. A method is described which explicitly predicts the source amplitudes of the active field. For a given number of sources and their positions in two dimensions it is shown that the multipole amplitudes can be expressed as infinite sums of the coefficients of the incident wave decomposed into regular Bessel functions. Importantly, the active field generated by the sources vanishes in the far-field. In practice the infinite summations are clearly required to be truncated and the accuracy of cloaking is studied when the truncation parameter is modified.

Analysis of a Cartesian PML approximation to acoustic scattering problems in [formula omitted] and [formula omitted

We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift (“stretching”) and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem).This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior.

An efficient and near linear scaling pair natural orbital based local coupled cluster method

In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) [F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)]. The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large molecules, the number of amplitudes to be determined is reduced by a factor of 10(5)-10(6) relative to a canonical CCSD calculation on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a number of fifth order scaling steps that eventually rendered the method computationally expensive for large molecules (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on average. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no additional truncation parameters have been introduced. Any additional truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy estimate based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calculations reported here featured >8800 basis functions and >450 atoms. In all larger test calculations done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calculation, provided no approximations have been introduced in the latter. Thus, based on the present development reliable CCSD calculations on large molecules with unprecedented efficiency and accuracy are realized.

Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties

Heterogeneous media consisting of segregated flow regions are fractional-order systems, where the regional-scale anomalous diffusion can be described by the fractional derivative model (FDM). The standard FDM, however, first, cannot characterize the Darcy-scale dispersion through repacked sand columns, and second, the link between medium properties and model parameters remains unknown. To fill these two knowledge gaps, this study applies a tempered fractional derivative model (TFDM) to capture bromide transport through laboratory repacked sand. Column transport experiments are conducted first, where glass beads and silica sand with different diameters are repacked individually. Late-time tails are observed in the breakthrough curves (BTC) of bromide even in relatively homogeneous glass beads. The TFDM can capture the observed subdiffusion, especially the late-time BTC with a transient declining rate. Results also show that both the size distribution of repacked sand and the magnitude of fluid velocity can affect subdiffusion. In particular, a wider sand size distribution or a smaller flow rate can enhance the subdiffusion, leading to a smaller time index and a higher truncation parameter in the TFDM. Therefore, the Darcy-scale dispersion follows the tempered stable law, and the model parameters might be related to the soil size and flow conditions.

Transformation of a hollow Gaussian beam into a ring-shaped beam using a phase aperture

Propagation of a hollow Gaussian beam diffracted by a circular phase aperture is studied without making the paraxial approximation. The analytical expression of the intensity of the apertured hollow Gaussian beam is presented in the far field. The influences of the truncation parameter and the order of hollow Gaussian beam on the intensity distributions are discussed. It is shown that a circular Ͽ-phase aperture can be used to transform a hollow Gaussian beam into a ring-shaped beam in the far field with the appropriate parameters.

Convergence properties ofab initiocalculations of light nuclei in a harmonic oscillator basis

We study recently proposed ultraviolet and infrared momentum regulators of the model spaces formed by construction of a variational trial wave function which uses a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. These model spaces are defined by a truncation of the expansion characterized by a counting number ($\mathcal{N}$) and by the intrinsic scale ($\ensuremath{\hbar}\ensuremath{\omega}$) of the HO basis---in short by the ordered pair ($\mathcal{N},\ensuremath{\hbar}\ensuremath{\omega}$). In this study we choose for $\mathcal{N}$ the truncation parameter ${N}_{\mathrm{max}}$ related to the maximum number of oscillator quanta, above the minimum configuration, kept in the model space. The uv momentum cutoff of the continuum is readily mapped onto a defined uv cutoff in this finite model space, but there are two proposed definitions of the ir momentum cutoff inherent in a finite-dimensional HO basis. One definition is based upon the lowest momentum difference given by $\ensuremath{\hbar}\ensuremath{\omega}$ itself and the other upon the infrared momentum which corresponds to the maximal radial extent used to encompass the many-body system in coordinate space. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. We calculate the ground-state energy of light nuclei with ``bare'' and ``soft'' nucleon-nucleon ($NN$) interactions. By doing so, we investigate the behaviors of the uv and ir regulators of model spaces used to describe ${}^{2}$H, ${}^{3}$H, ${}^{4}$He, and ${}^{6}$He with $NN$ potentials Idaho N${}^{3}$LO and JISP16. We establish practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces characterized by ($\mathcal{N},\ensuremath{\hbar}\ensuremath{\omega}$).

Propagation of radially polarized beams diffracted at a circular aperture in turbulent atmosphere

Based on the extended Huygens–Fresnel integral and the beam coherence–polarization matrix, the analytical formulae for the average intensity and the degree of polarization of the radially polarized beams diffracted at a circular aperture in turbulent atmosphere are derived, which provide a convenient approach to study the propagation and polarization properties of the apertured radially polarized beams in turbulent atmosphere. The unapertured and free-space cases can be viewed as the special cases of our general result. The analyses indicate that the average intensity and the degree of polarization are closely related to the propagation distance, the structure constant of the atmospheric turbulence, and the truncation parameter. The existence of the circular aperture weakens the influence of the atmospheric turbulence on the evolution properties of the radially polarized beams.

Hidden truncation circular normal distribution

Many circular distributions are known to be not only asymmetric but also bimodal. Hidden truncation method of generating asymmetric distribution is applied to a bivariate circular distribution to generate an asymmetric circular distribution. While many other existing asymmetric circular distributions can only model an asymmetric data, this new circular model has great flexibility in terms of asymmetry and bi-modality. Some properties of the new model, such as the trigonometric moment generating function, and asymptotic inference about the truncation parameter are presented. Simulation and real data examples are provided at the end to demonstrate the utility of the novel distribution.

Object recognition using Gabor co-occurrence similarity

We present an object recognition approach using co-occurrence similarities of Gabor magnitude textures in this paper. A novel image descriptor, multichannel Gabor magnitude co-occurrence matrices (MGMCMs), is designed to characterize Gabor textures for object representation and similarity matching. The descriptor is a generalization of multichannel color co-occurrence matrices (MCMs), which focus on using robust and discriminative magnitude textures in filtered images. Our approach starts from Gabor wavelet transformation of each object image. An exploratory learning algorithm is proposed for learning channel-adaptive magnitude truncation parameters and level parameters. This allows us to design the magnitude quantization that can reduce overall biased and peaked levels of resulting feature distributions in each channel, to avoid over-sparse co-occurrence distributions on average. The direction-based grouping is adopted for computational complexity reduction of MGMCMs extraction under a specific neighborhood mode on the grouped rescaled magnitude images of per object image. When each MGMCM is treated as a probability distribution lying on a multinomial manifold, we represent per object image as a point on a product multinomial manifold. Using multinomial geometry and metric extension technique, we construct the p-order Minkowski co-occurrence information distance for similarity matching between the albums of Gabor magnitude textures. The feasibility and effectiveness of the approach is validated by the experimental results on the Yale and FERET face databases, PolyU palmprint database, COIL-20 object database and Zurich buildings database.

Analytical study of wave diffraction and radiation by a submerged sphere in infinite water depth

The wave diffraction and radiation of a submerged sphere in deep water are studied using the multipole method within the frame of linear wave theory. By expressing the velocity potential in spherical harmonics and formulating the problems into truncating and solving M sets of linear equation systems, simple analytical expressions are derived for the hydrodynamic characteristics. A novel analytical expression for the multipoles coefficient is derived to accelerate the numerical implementation. A similar procedure of Wu et al. (1994) and Rahman (2001) is used to condense the expression for the total wave potentials at the sphere surface in the diffraction problem. Results obtained by present model precisely coincide with other numerical schemes, and converge very rapidly with the increase of the truncation parameter that generally the number of series terms N=4 and M=0,1 are sufficient to an accuracy of 3 decimals. A further analysis shows that for large submergences, the surge and the heave exciting forces approach equal. In the mean time, there exists an exact relationship a11−0.5=(a00−0.5)/2 between the surge and the heave added mass, and b11=b00/2 between the surge and the heave damping, where j=0 and j=1 correspond to the heave and surge motion, respectively. Extensive numerical results involving convergence of the multipole method, exciting forces and hydrodynamic coefficients for various parameters are also presented.

Scintillation properties of a truncated flat-topped beam in a weakly turbulent atmosphere

We derive an explicit expression for the scintillation index of a truncated flat-topped (FT) beam in a weakly turbulent atmosphere. Under suitable conditions, the derived formula reduces to the expression for the scintillation index of a FT beam or Gaussian beam without truncation. The scintillation properties of a truncated FT beam in a weakly turbulent atmosphere are illustrated numerically. It is found that the truncation parameter has strong influence on the scintillation properties, and the advantage of a FT beam over a Gaussian beam for reducing the negative influence of turbulence disappears gradually as the truncation parameter decreases.

Two-machine flowshop scheduling with a truncated learning function to minimize the makespan

Abstract Scheduling with learning effects has continued to attract the attention of scheduling researchers. However, the majority of the research on this topic has been focused on the single-machine setting. Moreover, under the commonly adopted learning model in scheduling, the actual processing time of a job drops to zero precipitously as the number of jobs increases, which is at odds with reality. To address these issues, we study a two-machine flowshop scheduling problem with a truncated learning function in which the actual processing time of a job is a function of the job's position in a schedule and the learning truncation parameter. The objective is to minimize the makespan. We propose a branch-and-bound and three crossover-based genetic algorithms (GAs) to find the optimal and approximate solutions, respectively, for the problem. We perform extensive computational experiments to evaluate the performance of all the proposed algorithms under different experimental conditions. The results show that the GAs perform quite well in terms of both efficiency and solution quality.