Prescribing a multistage analytical method to a prey-predator dynamical system

This article discusses the effectiveness of a fresh analytical method in solving a prey-predator problem, which is described as a system of two nonlinear ordinary differential equations. The method of interest is the multistage variational iteration method (MVIM), which provides a slight modification of the classical variational iteration method (VIM). We shall compare solutions of the classical VIM along with MVIM and match them against the conventional numerical method, Runge-Kutta (RK4) (fourth-order).     

A short remark on fractional variational iteration method

This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed.     

Variational approximations in a path integral description of potential scattering

Using a recent path integral representation for the T -matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables --over which one has to integrate functionally-- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading). We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.     

Design of quantum VQ iteration and quantum VQ encoding algorithm taking O（√N） steps for data compression

Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take $O(N)$ steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes $O(\sqrt N )$ steps are presented in this paper. The unitary operation of distance computing can be performed on a number of vectors simultaneously because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal.     

Quantum Multi-Image Encryption Based on Iteration Arnold Transform with Parameters and Image Correlation Decomposition

A novel quantum multi-image encryption algorithm based on iteration Arnold transform with parameters and image correlation decomposition is proposed, and a quantum realization of the iteration Arnold transform with parameters is designed. The corresponding low frequency images are obtained by performing 2-D discrete wavelet transform on each image respectively, and then the corresponding low frequency images are spliced randomly to one image. The new image is scrambled by the iteration Arnold transform with parameters, and the gray-level information of the scrambled image is encoded by quantum image correlation decomposition. For the encryption algorithm, the keys are iterative times, added parameters, classical binary and orthonormal basis states. The key space, the security and the computational complexity are analyzed, and all of the analyses show that the proposed encryption algorithm could encrypt multiple images simultaneously with lower computational complexity compared with its classical counterparts.     

Steepest descent inversion of plasma spectral intensities

An iterative inversion of the spectral intensities emitted by an asymmetric and absorbing plasma is considered. The iteration procedure is the method of steepest descent in two forms: steplengths for largest residual reduction in each iteration, and steplengths independent of iteration, and related to the largest eigenvalue of the matrix operator for the normal equations. The effects of both constrained and unconstrained optimization, as well as of two different initial conditions, are reported. Inversions are shown of reversed and nonreversed line profiles.     

Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms

An advanced random phase-shifting algorithm to extract phase distributions from randomly phase-shifted interferograms is proposed. The algorithm is based on a least-squares iterative procedure, but it copes with the limitation of the existing iterative algorithms by separating a frame-to-frame iteration from a pixel-to-pixel iteration. The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. The algorithm is simple, fast, and fully automatic. A computer simulation is conducted to prove the concept.     

Two-body solution of the Newman-Penrose asymptotic equations

The Newman-Penrose nonlinear asymptotic field equations are separated in terms of spin weight spherical harmonics (s.w.s.h.). As an example, the results are used to study the radiation effects on a two-body system. The presence of radiation is manifest through the nonlinear terms in the asymptotic equations. If these terms are assumed to be small, the asymptotic equations can be formally solved by an iteration procedure. For the above example the first step of the iteration procedure is implemented to an accuracy that includes the effects of radiation up to octopole order. The results illustrate the usual internal decay of the orbit as well as an acceleration of the system's center of mass. In favorable cases, the two-body source can reach significant velocities due to the radiation reaction.     

Solutions of nonlinear oscillators with fractional powers by an iteration procedure

A modified iteration procedure is applied to nonlinear oscillations with fractional powers. With the procedure, the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained.     

Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.     

基于琼斯矩阵的FIR晶体光滤波器设计方法

FIR晶体光滤波器由夹在两个偏振片之间的N个厚度相同的晶片构成,设计过程中需要根据要求的频率响应求出各个晶体波片的光轴方向和输出端偏振片的通光方向.提出了一种基于琼斯矩阵的反向递推设计方法.FIR晶体光滤波器的琼斯矩阵是各个晶片以及偏振片琼斯矩阵的乘积,利用这一关系可以建立简单的反向递推关系,并计算出与输出偏振分量对应的正交偏振分量,通过迭代运算确定所有元件的角度参数.实例设计的结果与使用其它方法得到的结果一致,设计过程简单.     

三维空腔辐射场计算的一种简化数值方法

给出三维空腔辐射场计算的一种简化数值方法。在一些物理假定条件下,把问题简化为解反照边界条件的 Boltzmann方程。对方法作了详细描述,讨论了迭代过程的收敛性,最后给出了数值例子。     

The imaginary time step method for Thomas-Fermi equations

The imaginary time step iteration procedure is extended to the solution of the Thomas-Fermi equations and their modifications. The convergence of the procedure is discussed and illustrated by a numerical example. The generalization to the finite temperature calculations is indicated.     

Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schro^edinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

Theory of non-adiabatic cranking and nuclear collective motion

The cranking model is extended to the case of a general non-adiabatic motion. The time-dependent many-body Schrödinger equation is solved, where the time dependence of the collective motion is determined by the classical Lagrange equations of motion. The Lagrangian is obtained from the expectation value of the energy. In the case of one collective degree of freedom the condition that the expectation value of the energy is constant in time is sufficient to determine the collective motion. An iteration procedure is applied, of which the zeroth order is shown to be the common cranking formula. In an alternative approach the energy conservation is expressed in differential form. This leads in the case of one collective degree of freedom to a set of coupled, non-linear first-order differential equations in time for the expansion coefficients of the many-body wave function and for the collective variable. As an illustrative example we solve the case of two coupled linear harmonic oscillators.     

用SIP和SSIP方法求解三维反应堆中子扩散方程

本文首先简要介绍三维区域中的中子扩散方程及其差分方程的建立及求解的内、外迭代过程。然后导出内迭代过程中求解差分方程的SIP和SSIP公式,以及内、外迭代的加速方法和迭代参数的选取。最后给出一些数值结果。     

Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schrodinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part I. First post-Newtonian equations

The iteration procedure of Anderson and DeCanio (1975) for obtaining hydrodynamic equations in the slow-motion approximation to general relativity is modified at each iteration step. These improvements keep all expressions needed for the 2 1/2 post-Newtonian approximation (PNA) manifestly finite, but fail to prevent some divergent terms in the third and higher PNAs. In this Part I, the improvements to the iteration scheme are outlined, and the calculation is completed through the second iteration, yielding Newtonian-like hydrodynamic equations in the first PNA. Paper II will complete the calculation through the 2 1/2 PNA, allowing the calculation of the gravitational radiation reaction force, and making explicit the source of the divergences which occur in the higher PNAs.     

Comparing two iteration algorithms of Broyden electron density mixing through an atomic electronic structure computation

By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known VASP code.The other was given by Eyert. We solve the Kohn-Sham equation by using a conventional outward/inward integration of the differential equation and then connect two parts of solutions at the classical turning points, which is different from the method of the matrix eigenvalue solution as used in the VASP code. Compared to Johnson's algorithm, the one proposed by Eyert needs fewer total iteration numbers.