Seventh Order Research Articles

Enhancement of higher-order plasmonic modes in a dense array of split-ring resonators.

It is demonstrated that higher-order plasmonic modes in the split-ring resonators (SRRs) are strongly enhanced when SRRs are arranged in a densely spaced two-dimensional array. The mode enhancement results from the near-field electrical coupling between the adjacent resonators. The effect is most pronounced in narrow gap SRRs which allows to observe experimentally plasmon modes up to the seventh order. In the array of narrow gap SRRs, the fifth-order resonance demonstrates high Q-factor, high resonance strength and wide tunability which opens up attractive features for practical applications of planar SRR structures.

New seventh and eighth order derivative free methods for solving nonlinear equations

The purpose of this work is to develop two new iterative methods for solving nonlinear equations which does not require any derivative evaluations. These composed formulae have seventh and eighth order convergence and desire only four function evaluations per iteration which support the Kung-Traub conjecture on optimal order for without memory schemes. Finally, numerical comparison is provided to show its effectiveness and performances over other similar iterative algorithms in high precision computation.

Comparison of Septic and Octic Recursive B-spline Collocation Solutions for Seventh Order Differential Equation

Comparison of Septic and Octic Recursive B-spline Collocation Solutions for Seventh Order Differential Equation

An improved non-linear weights for seventh-order weighted essentially non-oscillatory scheme

In this article, the construction and implementation of a seventh order weighted essentially non-oscillatory scheme is reported for solving hyperbolic conservation laws. Local smoothness indicators are constructed based on L1-norm, where a higher order interpolation polynomial is used with each derivative being approximated to the fourth order of accuracy with respect to the evaluation point. The global smoothness indicator so constructed ensures the scheme achieves the desired order of accuracy. The scheme is reviewed in the presence of critical points and verified the numerical accuracy, convergence with the help of linear scalar test cases. Further, the scheme is implemented to non-linear scalar and system of equations in one and two dimensions. As the formulation is based on method of lines, to move forward in time linear strong-stability-preserving Runge–Kutta scheme (lSSPRK) for the linear problems and the fourth order nonlinear version of five stage strong stability preserving Runge–Kutta scheme (SSPRK(5, 4)) for nonlinear problems is used.

Analysis of structure function equations up to the seventh order

ABSTRACTWe examine balances of structure function equations up to the seventh order N = 7 for longitudinal, mixed and transverse components. Similarly, we examine the traces of the structure function equations, which are of interest because they contain invariant scaling parameters. The trace equations are found to be qualitatively similar to the individual component's equations. In the even-order equations, the source terms proportional to the correlation between velocity increments and the pseudo-dissipation tensor are significant, while for odd N, source terms proportional to the correlation of velocity increments and pressure gradients are dominant. Regarding the component equations, one finds under the inertial range assumptions as many equations as unknown structure functions for even N, i.e. can solve for them as function of the source terms. On the other hand, there are more structure functions than equations for odd N under the inertial range assumptions. Similarly, there are not enough linearly independent equations in the viscous range r → 0 for orders N > 3.

Analysis of space–time profiles of the concentrations of contaminants in soil during electrokinetic remediation

A new semiempirical method for the mathematical description of the space–time concentration profiles of contaminants in soil during its electrokinetic remediation is proposed. The method is based on approximating the experimental data on the spatiotemporal behavior of the concentration, C = C(D a , t). The experimental and theoretical C = C(D a , t) dependences reported in the literature and obtained in our studies were approximated by seventh order polynomials. For example, the space–time concentration profiles of chlorinated hydrocarbon contaminants in unsaturated soils, such as tetrachloroethylene, trichloroethylene and carbon tetrachloride, have been successfully described by a polynomial function with determination coefficients of R 2 = 0.9941, 0.9988, and 0.9972, respectively. A pilot test setup for studying the electrokinetic remediation of soils contaminated with mercury compounds, with ten sampling sections and replaceable cartridges with ionites, was designed and built. This setup allowed measuring the space–time concentration profile of mercury in soil samples during electrokinetic remediation. This profile obtained was approximated by a seventh order polynomials with a determination coefficient of R 2 = 0.9929. It is shown that the polynomial approximation of the space–time concentration profiles of contaminants in soil describes the experimental C = C(D a , t) dependences no worse (sometimes better) than the Poisson–Nernst–Planck model for ionic flow.

High-Gain and Wide-Bandwidth Filtering Planar Antenna Array-Based Solely on Resonators

This paper presents a new approach for the design of high-gain and wide-bandwidth planar antenna arrays. It is based on the coupling matrix theory which allows the design of the arrays using all-resonator structures. The parameters of the matrix offer the flexibility of achieving a controllable bandwidth. They also introduce a frequency filtering functionality into the arrays which can remove the need to place a bandpass filter after the arrays at the very front end of a communication system. The new approach has been applied to using novel topologies to form two wideband $4 \times 4$ planar antenna arrays utilizing rectangular waveguide cavity resonators operated at X-band frequencies. The first topology is seventh order and based on 39 resonators configured in two waveguide-layers; that is one layer for the feed resonators and one layer for the radiating resonators. The second topology is fourth order based on 25 resonators configured only in a single waveguide-layer. Fabrication and measurements have been performed, showing very good agreement with the simulations.

NEW TYPE OF NEARLY MONOTONIC PASSBAND FILTERS WITH SHARP CUTOFF

New type of nearly monotonic rational function with one pair of zeros on imaginary axis has been proposed. By using these new functions with zeros as a parameter, it is possible to make tradeoff between minimum stopband attenuation and selectivity of the amplitude characteristic. In order to present efficiency of the proposed filter, comparison with allpole filter monotonic in the passband and inverse Chebyshev filter is presented. Also, design example for the seventh order new type lowpass filter is given.

Comparison Of Cascaded H-bridge Inverters for Harmonic Mitigation Considering Various Loads

This paper compares the reduction of harmonics in various level cascaded H-bridge inverters. The switching angles for the cascaded H-bridge inverter were calculated by evolutionary optimization technique. Fourier analysis is used to determine the switching angles for the desired electrical parameters. Lower order harmonics such as third, fifth, seventh, ninth and eleventh order harmonics were taken into consideration to reduce the total harmonic distortion. Simulation was done for thirteen, fifteen and seventeen level cascaded H-bridge inverters using Matlab. Total harmonic distortion of voltage and current for R, RL and Motor load were analyzed.

Dark spatial solitary waves in a cubic-quintic-septimal nonlinear medium

We consider the evolution of light beams in nonlinear media exhibiting nonlinearities up to the seventh order wherein the beam propagation is governed by the cubic-quintic-septimal nonlinear Schr\odinger equation. An exact analytic solution that describes dark solitary wave propagation is obtained, based on a special ansatz. Unlike the well-known $\text{tanh}$-profile dark soliton in Kerr media, the present one has a functional form given in terms of ``${\text{sech}}^{2/3}$''. The requirements concerning the optical material parameters for the existence of this localized structure are discussed. This propagating solitary wave exists due to a balance among diffraction, cubic, quintic, and septimal nonlinearities. We also investigate its stability under initial pertubations by employing numerical simulations. The modulational stability of the continuous-wave background, which supports the dark soliton, is also studied analytically. Collisions between stable dark solitons are finally investigated.

First principle and series expansions calculations of electronic and magnetic properties of Co(Ni)Cr2O4 spinels

Self-consistent ab initio calculations, based on Density Functional Theory approach and using full potential Linear Augmented Plane Wave method, are performed to investigate both electronic and magnetic properties of the CoCr2O4 and NiCr2O4. Magnetic moment considered to lie along (010) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions calculations to compute other magnetic parameters. The high temperature series expansions of the magnetic susceptibility are given up to seventh order series in (x=JMn-Mn/kBT) of CoCr2O4 and NiCr2O4. The Néel temperature TN(K) and critical exponent γ associated with the magnetic susceptibility are obtained as well for both compounds.

Improved Chebyshev–Halley family of methods with seventh and eighth order of convergence for simple roots

The principle aim of this manuscript is to introduce a new highly efficient improved modification of Chebyshev–Halley family with increasing order of convergence. The idea is based on the schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). The proposed scheme has at least seventh-order of convergence and also posses an optimal eighth-order of convergence for a particular value of the disposable parameter. Each member of the proposed scheme is free from second-order derivative and requires only four functional evaluations (viz. three evaluations of function f and one of first-order derivative $$f'$$ ) per full iteration. A variety of concrete numerical examples demonstrates that our proposed scheme performs better than the existing schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). Dynamical study of our methods also confirms the above conclusions to a great extent. Moreover, the local convergence of these methods is given using hypotheses only on the first derivative and Lipschitz constants.

PERFORMANCE IMPROVEMENT OF INDOOR DS-UWB COMMUNICATION USING PSD ESTIMATION AND PULSE SHAPE OPTIMIZATION

Ultra-wideband system offers a great substitution for short-range, high-speed Personal Wireless Area Network, as well as for detection and ranging applications. IR-UWB technology can also be used in the military for radar and image sensing as well as localization of objects. In spite of this tremendous usefulness of UWB, some bandwidth interfering issues with the coexisting narrowband system can also be arises due to the huge bandwidth of UWB (> 500 MHz). This spectrum interference makes a huge pressure and lot of regulations to restrict the use of UWB in different environment. Consequently, the trait of UWB is not fully utilized. In this paper, we proposed the modified seventh order derivative of Gaussian monocycle and presented the performance analysis of pulse in an indoor environment with AWGN and the Rayleigh noise distributions. The aim of pulse shape optimization is for detection and ranging application of UWB to spectral interference. We recommended that higher order derivative of the Gaussian monocycle pulse offers an excellent reliability for the detection and ranging purpose in an indoor environment with co-existing narrowband communication. The pulse is windowed with a rectangular window function in the time domain to bind the pulse into the finite time interval. The pulse is analyzed for the interference with co-existing narrowband communication by fulfilling the power spectral density (PSD) masks provided by regulatory bodies of different countries.

Growth Characteristics of Methanomassiliicoccus luminyensis and Expression of Methyltransferase Encoding Genes.

DNA sequence analysis of the human gut revealed the presence a seventh order of methanogens referred to as Methanomassiliicoccales. Methanomassiliicoccus luminyensis is the only member of this order that grows in pure culture. Here, we show that the organism has a doubling time of 1.8 d with methanol + H2 and a growth yield of 2.4 g dry weight/mol CH4. M. luminyensis also uses methylamines + H2 (monomethylamine, dimethylamine, and trimethylamine) with doubling times of 2.1–2.3 d. Similar cell yields were obtained with equimolar concentrations of methanol and methylamines with respect to their methyl group contents. The transcript levels of genes encoding proteins involved in substrate utilization indicated increased amounts of mRNA from the mtaBC2 gene cluster in methanol-grown cells. When methylamines were used as substrates, mRNA of the mtb/mtt operon and of the mtmBC1 cluster were found in high abundance. The transcript level of mtaC2 was almost identical in methanol- and methylamine-grown cells, indicating that genes for methanol utilization were constitutively expressed in high amounts. The same observation was made with resting cells where methanol always yielded the highest CH4 production rate independently from the growth substrate. Hence, M. luminyensis is adapted to habitats that provide methanol + H2 as substrates.

An efficient class of WENO schemes with adaptive order

Finite difference WENO schemes have established themselves as very worthy performers for entire classes of applications that involve hyperbolic conservation laws. In this paper we report on two major advances that make finite difference WENO schemes more efficient.The first advance consists of realizing that WENO schemes require us to carry out stencil operations very efficiently. In this paper we show that the reconstructed polynomials for any one-dimensional stencil can be expressed most efficiently and economically in Legendre polynomials. By using Legendre basis, we show that the reconstruction polynomials and their corresponding smoothness indicators can be written very compactly. The smoothness indicators are written as a sum of perfect squares. Since this is a computationally expensive step, the efficiency of finite difference WENO schemes is enhanced by the innovation which is reported here.The second advance consists of realizing that one can make a non-linear hybridization between a large, centered, very high accuracy stencil and a lower order WENO scheme that is nevertheless very stable and capable of capturing physically meaningful extrema. This yields a class of adaptive order WENO schemes, which we call WENO-AO (for adaptive order). Thus we arrive at a WENO-AO(5,3) scheme that is at best fifth order accurate by virtue of its centered stencil with five zones and at worst third order accurate by virtue of being non-linearly hybridized with an r=3 CWENO scheme. The process can be extended to arrive at a WENO-AO(7,3) scheme that is at best seventh order accurate by virtue of its centered stencil with seven zones and at worst third order accurate. We then recursively combine the above two schemes to arrive at a WENO-AO(7,5,3) scheme which can achieve seventh order accuracy when that is possible; graciously drop down to fifth order accuracy when that is the best one can do; and also operate stably with an r=3 CWENO scheme when that is the only thing that one can do. Schemes with ninth order of accuracy are also presented.Several accuracy tests and several stringent test problems are presented to demonstrate that the method works very well.

Collocation Method for Seventh Order Boundary Value Problems by Using Sextic B-splines

A finite element method involving collocation method with sextic B-splines as basis functions has been developed to solve seventh order boundary value problems. The seventh and six order derivatives for the dependent variable is approximated by the central differences. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on three linear and two non-linear boundary value problems. The solution to a nonlinear problem has been obtained as the limit of a sequence of solutions of linear problems generated by the quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literature

Two-dimensional Legendre wavelet method for travelling wave solutions of time-fractional generalized seventh order KdV equation

In this paper, a new method based on the Legendre wavelets expansion together with operational matrices of fractional integration and derivative of these basis functions is proposed to solve time-fractional seventh order KdV (sKdV) equation. Two-dimensional Legendre wavelet method is applied to compute the numerical solution of nonlinear time-fractional sKdV equation. The approximate solutions of nonlinear time fractional sKdV equation thus obtained by Legendre wavelet method are compared with the exact solutions as well as homotopy analysis method (HAM). The present scheme is very simple, effective and convenient for obtaining numerical solution of the sKdV equation.

Virial and high-density expansions for the Lee-Yang lattice gas.

On the basis of the recently established "hole-particle" symmetry of the lattice-gas Hamiltonian, the high-density equation of state has been derived in a form of pressure and density expansions in powers of activity. This equation is proposed as an alternative and complementary to the previously obtained pressure expansion in powers of density. For the well-known Lee-Yang lattice-gas model (a two-dimensional square lattice with a square-well interaction potential), the power coefficients (i.e., cluster and irreducible cluster integrals) up to the seventh order have been evaluated as accurate functions of temperature. The convergence of the expansions in powers of both density and activity to the exact Lee-Yang solution is investigated.

Modelling and characterization of the roof tile-shaped modes of AlN-based cantilever resonators in liquid media

In this work, roof tile-shaped modes of MEMS (micro electro-mechanical systems) cantilever resonators with various geometries and mode orders are analysed. These modes can be efficiently excited by a thin piezoelectric film and a properly designed top electrode. The electrical and optical characterization of the resonators are performed in liquid media and the device performance is evaluated in terms of quality factor, resonant frequency and motional conductance. A quality factor as high as 165 was measured in isopropanol for a cantilever oscillating in the seventh order roof tile-shaped mode at 2 MHz. To support the results of the experimental characterization, a 2D finite element method simulation model is presented and studied. An analytical model for the estimation of the motional conductance was also developed and validated with the experimental measurements.

Haar Wavelet Approach for the Solution of Seventh Order Ordinary Differential Equations

Haar Wavelet Approach for the Solution of Seventh Order Ordinary Differential Equations