Modeling of bistatic scattering from an underwater non-penetrable target using a Kirchhoff approximation method

A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.

Electromagnetic scattering from two-layer rough interfaces in the Kirchhoff approximation

Electromagnetic wave scattering from multilayers consisting of two two-layer Caussian rough surfaces with lossless media is investigated in the Kirchhoff approximation （KA）, with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment （MOM） over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square （RMS） height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.

Stationary phase approximation in the ambient noise method revisited

The method of extracting Green＇s function between stations from cross correlation has proven to be effective theoretically and experimentally. It has been widely applied to surface wave tomography of the crust and upmost mantle. However, there are still controversies about why this method works. Snieder employed stationary phase approximation in evaluating contribution to cross correlation function from scatterers in the whole space, and concluded that it is the constructive interference of waves emitted by the scatterers near the receiver line that leads to the emergence of Green＇s function. His derivation demonstrates that cross correlation function is just the convolution of noise power spectrum and the Green＇s function. However, his derivation ignores influence from the two stationary points at infinities, therefore it may fail when attenuation is absent. In order to obtain accurate noise-correlation function due to scatters over the whole space, we compute the total contribution with numerical integration in polar coordinates. Our numerical computation of cross correlation function indicates that the incomplete stationary phase approximation introduces remarkable errors to the cross correlation function, in both amplitude and phase, when the frequency is low with reasonable quality factor Q. Our results argue that the dis- tance between stations has to be beyond several wavelengths in order to reduce the influence of this inaccuracy on the applications of ambient noise method, and only the station pairs whose distances are above several （〉5） wavelengths can be used.

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.

Approximate Inertial Manifold for a Class of the Kirchhoff Wave Equations with Nonlinear Strongly Damped Terms

This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.

Stochastic Approximation Method for Fixed Point Problems

We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.

On M–Term Approximations of the Nikol'skii–Besov Class in the Lorentz Spaces

In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.

Controllable precision of the projective truncation approximation for Green's functions

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.

Magnetic Properties of One-Dimensional Ferromagnetic Mixed-Spin Model within Tyablikov Decoupling Approximation

In this paper, we apply the two-time Green's function method, and provide a simple way to study themagnetic properties of one-dimensional spin-(S, s) Heisenberg ferromagnets.The magnetic susceptibility and correlationfunctions are obtained by using the Tyablikov decoupling approximation.Our results show that the magnetic susceptibilityand correlation length are a monotonically decreasing function of temperature regardless of the mixed spins.It isfound that in the case of S = s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropicferromagnetic Heisenberg chain in the whole temperature region.Our results for the susceptibility are in agreement withthose obtained by other theoretical approaches.

On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm

In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.

An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data

There exist many iterative methods for computing the maximum likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the likelihood equations in a neighborhood of the constrained maximum likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure.

ON CONSERVATIVE APPROXIMATION BY LINEAR POLYNOMIAL OPERATORS AN EXTENSION OF THE BERNSTEIN'S OPERATOR

In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.

H2 and H∞-Feedback Control Design for Nonlinear Gene Networks via Successive Galerkin’s Approximation

This paper presents a design method of H2 and H∞-feedback control loop for nonlinear smooth gene networks that are in control affine form. Formulaic solution methodology for solving the nonlinear partial differential equations, namely the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations through successive Galerkin’s approximation is implemented and the results are compared. Throughout the implementation, there were several caveats that need to be further resolved for practical applications in general cases. Such issues and the clarification of causes are mathematically established and reviewed.

基于Fresnel-Kirchhoff理论的无限大声屏障绕射声衰减

从实际工业噪声控制中大面积有壁障噪声源的噪声控制问题出发,应用Fresnel-Kirchhoff理论和Babinet原理,建立计算无限大声屏障绕射声衰减的理论模型。通过数值求解,分析了声源、接收点位置,声波频率和地面反射等对声屏障绕射声衰减的影响。

The quantum Kirchhoff equation and quantum current and energy spectrum of a homogeneous mesoscopic dissipation transmission line

On the basis of quantization of charge, the loop equations of quantum circuits are investigated by using the Helsenberg motion equation for a mesoscopic dissipation transmission line. On the supposition that the system has a symmetry under translation in charge space, the quantum current and the quantum energy spectrum in the mesoscopic transmission llne are given by solving their eigenvalue equations. Results show that the quantum current and the quantum energy spectrum are not only related to the parameters of the transmission llne, but also dependent on the quantized character of the charge obviously.

Approximate expression of Young's equation and molecular dynamics simulation for its applicability

In 1805, Thomas Young was the first to propose an equation(Young's equation) to predict the value of the equilibrium contact angle of a liquid on a solid. On the basis of our predecessors, we further clarify that the contact angle in Young's equation refers to the super-nano contact angle. Whether the equation is applicable to nanoscale systems remains an open question. Zhu et al. [College Phys. 4 7(1985)] obtained the most simple and convenient approximate formula, known as the Zhu–Qian approximate formula of Young's equation. Here, using molecular dynamics simulation, we test its applicability for nanodrops. Molecular dynamics simulations are performed on argon liquid cylinders placed on a solid surface under a temperature of 90 K, using Lennard–Jones potentials for the interaction between liquid molecules and between a liquid molecule and a solid molecule with the variable coefficient of strength a. Eight values of a between 0.650 and 0.825 are used. By comparison of the super-nano contact angles obtained from molecular dynamics simulation and the Zhu–Qian approximate formula of Young's equation, we find that it is qualitatively applicable for nanoscale systems.

Von Misses Pure Shear in Kirchhoff’s Plate Buckling

The pure shear strength for the all-simply supported plate has not yet been found;what is described as pure shear in that plate, is, in fact, a pure-shear solution for another plate clamped on the “Y-Y” and simply supported on the long side, X-X. A new solution for the simply supported case is presented here and is found to be only 60-percent of the currently believed results. Comparative results are presented for the all-clamped plate which exhibits great accuracy. The von Misses yield relation is adopted and through incremental deflection-rating the effective shear curvature is targeted in aspect-ratios. For a set of boundary conditions the Kirchhoff’s plate capacity is finite and invariant for bending, buckling in axial and pure-shear and in vibration.

Approximate aggregate nearest neighbor search on moving objects trajectories

Aggregate nearest neighbor(ANN) search retrieves for two spatial datasets T and Q, segment(s) of one or more trajectories from the set T having minimum aggregate distance to points in Q. When interacting with large amounts of trajectories, this process would be very time-consuming due to consecutive page loads. An approximate method for finding segments with minimum aggregate distance is proposed which can improve the response time. In order to index large volumes of trajectories, scalable and efficient trajectory index(SETI) structure is used. But some refinements are provided to temporal index of SETI to improve the performance of proposed method. The experiments were performed with different number of query points and percentages of dataset. It is shown that proposed method besides having an acceptable precision, can reduce the computation time significantly. It is also shown that the main fraction of search time among load time, ANN and computing convex and centroid, is related to ANN.

Approximate Private Quantum Channels on Fermionic Gaussian Systems

The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (ε-PQC) on fermionic Gaussian systems (i.e., ε-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for ε-FPQC on the fermionic Gaussian systems with respect to the Schatten p-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the ε-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.

基于 Kirchhoff 指标的极值多边形链

令 G 是一个简单连通图。 图 G 的 Kirchhoff 指标是图 G 中所有顶点对之间的电阻距离之和。 图 G 的电阻距离等效于将图 G 中的每条边替换为一个单位电阻后得到的电网络 N 中任意节点对之间的 有效电阻。 一个包含 n + 2 个多边形和 n + 1 个四边形的链,使得其中每个四边形的两条平行边各 与一个多边形有一条公共边,这样的链被称为多边形链。 本文利用电网络的标准技术和 S, T -同分 异构体的 Kirchhoff 指标的比较结果,刻画了 Kirchhoff 指标达到最大的极值多边形链为线性多 边形链 Ln, Kirchhoff 指标达到最小的极值多边形链为螺旋多边形链 Dn。 此结果推广了杨玉军 等人以及张雷雷刻画的基于 Kirchhoff 指标的极值亚苯基链的结果。