On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids

The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.

Simplified quantitative analysis method and its application in the insitu synthesized copper-based azide chips

Copper-based azide(Cu(N_(3))2 or CuN_(3),CA)chips synthesized by in-situ azide reaction and utilized in miniaturized explosive systems has become a hot research topic in recent years.However,the advantages of in-situ synthesis method,including small size and low dosage,bring about difficulties in quantitative analysis and differences in ignition capabilities of CA chips.The aim of present work is to develop a simplified quantitative analysis method for accurate and safe analysis of components in CA chips to evaluate and investigate the corresponding ignition ability.In this work,Cu(N_(3))2 and CuN_(3)components in CA chips were separated through dissolution and distillation by utilizing the difference in solubility and corresponding content was obtained by measuring N_(3)-concentration through spectrophotometry.The spectrophotometry method was optimized by studying influencing factors and the recovery rate of different separation methods was studied,ensuring the accuracy and reproducibility of test results.The optimized method is linear in range from 1.0-25.0 mg/L,with a correlation coefficient R^(2)=0.9998,which meets the requirements of CA chips with a milligram-level content test.Compared with the existing ICP method,component analysis results of CA chips obtained by spectrophotometry are closer to real component content in samples and have satisfactory accuracy.Moreover,as its application in miniaturized explosive systems,the ignition ability of CA chips with different component contents for direct ink writing CL-20 and the corresponding mechanism was studied.This study provided a basis and idea for the design and performance evaluation of CA chips in miniaturized explosive systems.

Direct sound field separation method on holography surface

In order to simplify the process which aims at separating the coherent sources located at different sides of holography surface, a direct sound field separation method which only depends on the data of holography surface is proposed. Assume that the reconstruction surface is holography surface, according to the equivalent sources located at the spherical surface, there exists a relationship between the measured sound pressure and the calculated value based on equivalent source method. Then, the coherent sources are separated. Nmnerical simulation an- alyzes the separation results when the interference sources are pulsating ball source and simply supported steel sheet with forced oscillation, respectively. The separation method is validated by experiment with two loudspeakers. The results show that the proposed method has high accuracy to the two kinds of interference sources and high tolerate deviation.

Separation Method of Bi-directional Reflected Waves and Oblique Incident Regular Waves

Wave reflection is one of the key problems affecting wave simulation quality in ocean engineering basin. The deep ocean engineering basin is equipped with two-sided segmented wavemakers and two wave absorbing beaches, which are located opposite to wave generators to reduce wave reflection effects. When an oblique longcrested wave is made by two-sided segmented wavemakers in a wave basin, two bi-directional reflected waves with the same azimuth but opposite propagation directions are generated. According to this feature, based on the two-point approach developed by Goda, a method to separate an incident regular wave from two bi-directional reflected waves using three wave gauges is proposed. The validity of this method is proved by numerical composite waves. The results indicate that the method can separate incident wave from reflected waves effectively. The method can be used to determine the reflection coefficient and verify the capacity of wave absorbing beaches in deep ocean engineering basin.

A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM

By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.

A Novel Method for Separation of Tungsten and Molybdenum

Research on the separation of tungstenand molybdenum is of importance as it is a ba-sic problem in the metallurgy and industry oftungsten.Traditional methods for the separa-tion include precipitation with sulfides andsolvent extraction.There are,however,certaindisadvantages for these methods.A novelmethod was developed based on another

A new method for separating complex touching equiaxed and lamellar alpha phases in microstructure of titanium alloy

A new method for separating complex touching equiaxed and lamellar alpha phases in the optical micrograph of titanium alloy was proposed for quantitative characterization. This new method involves three steps. First, concave points of the microstructural feature are identified with a threshold of the concaveness of the comer points which are extracted from the binarized image. Secondly, concave points pairs are selected from the concave points group established by means of marker circle or distance. Third, whether a candidate separation line which connects two concave points within a pair can be accepted or not is determined by the proposed four rules. The obtained results show that this method is effective on separating complex touching microstructural features.

New Families of Rational Form Variable Separation Solutions to(2+1)-Dimensional Dispersive Long Wave Equations

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.

Analyses on normal background characteristics about deformation observation data on the basis of wavelet transform method

Wavelet transform method is applied to measure time-frequency distribution characteristics of digital deformation data and noise. Based on the characteristics of primary modulus and stochastic white noise discrimination factor of wavelet decomposition, we analyze the variation rule of normal background and noise data from Shandong digital deformation observation data. The research results indicate that: a) 1/4 daily wave, semi-diurnal tide wave, daily wave and half lunar wave and so on quasi-periodic signal exist in the detail decomposing signal of wavelet when scale are equal to 2, 3 and 4; b) The amplitude of detail decomposing signal is the biggest when scale is equal to 3; c) The detail decomposing signal contains mainly noise corresponding to scale 1 and 5, respectively; d) We may trace the abnormal precursory which is related to earthquake by analyzing non-earthquake wavelet decomposing signal whose scale is specified from digital deformation observation data.

Solving mKdV-sinh-Gordon equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV-sinh-Gordon equation by this approach.

Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ordinary differential equation method is presented for solving the （2 ＋ 1）-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the （2 ＋ 1）-dimensional sine-Poisson equation are derived in a simple manner by this technique.

Research on Design Method of the Full Form Ship with Minimum Thrust Deduction Factor

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique（SUMT） interior point method of Nonlinear Programming（NLP） was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

Improved delayed detached-eddy simulation of massive separation around triple cylinders

The massively separated flow past triple cylin- ders （TriC） in tandem arrangement is simulated using the improved delayed detached-eddy simulation （IDDES） method based on the shear stress transport （SST） model, coupled with the high order adaptive dissipation scheme. The spacing between adjacent cylinders is sub-critical （1.435D）. IDDES prediction of two cylinders （TC） with the same spacing is compared to experimental data for validation, and the numerical results agree well with the available measurements, except for the asymmetry in the gap region. The flow past TriC is investigated using the same method. Generally, the mean flow quantities past TriC, such as the velocity, pressure, and vorticity, are similar to the corresponding components of TC. However, the pressure fluctuations on the TriC surface are uniformly larger than those on TC. Meanwhile, the instantaneous flows past TriC are much more complex. The periodical blockage in the first gap region is found in the TriC case and leads to the up-and-down movement of shear layer in the second gap region.

Some discussions about method for solving the variable separating nonlinear models

Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of these equations come from the nonzero seed solution. However, these nonzero seed solutions is likely to result in the divergent phenomena for the other field component of the same equation. The convergence and the signification of all field components should be discussed when someone solves the nonlinear equation using the variable separating method.

Spatial charge and compensation method in a whirler

Based on particle-in-cell simulation, we studied the motions of ions and electrons. The results have shown that electrons are bounded by a magnetic field and only a small number of electrons can pass through the whirler channel. The plasma becomes non-neutral when it is emitted from the whirler, and the spatial charge leads to a beam divergence, which is unfavorable for mass separation. In order to compensate the spatial charge, a cathode is designed to transmit electrons and the quasi-neutral plasma beam. Experiment results have demonstrated that the auxiliary cathode can obviously improve the compensation degree of the spatial charge.

Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method

The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique.

Periodical characteristics of baseflow in the source region of the Yangtze River

Baseflow, which represents the drainage of groundwater aquifers, is an essential component of runoff in hydrological basins. In the source region of the Yangtze River, the change of baseflow typically reflects the in- teractions between groundwater system and climatic factors in cold and arid areas. With modified Kalinen separa- tion method, annual baseflow between 1957 and 2009 in this region was estimated and calculated. In comparison with the inner-annual variations of total streamflow, baseflow showed a weaker fluctuation. Before the 1980s, it was in a steady state; and after then, it demonstrated dramatic variations and large amplitudes. Based on the calculation results of baseflow, the real Morlet wavelet method was applied to reveal the periodical characteristics of baseflow as well as the precipitation and air temperature in the study area. It was found that annual baseflow has a 43-year trend as well as a 21-year period and a 7-year period. The 21-year period is most significant, with its wavelet coef- ficient having the largest fluctuation and amplitude. Summation of wavelet coefficients on these periods exhibits a similar change pattern with respect to that of annual baseflow. The summation curve takes a ＂W＂ shape, which means that the baseflow follows a four-stage sequence of descending-ascending-descending-ascending. As analyzed, the relationship among baseflow, precipitation and temperature is implied in the correlation between their normalized wavelet coefficients at different temporal scales. By the significant positive linear correlations both be- tween precipitation and baseflow （correlation coefficient is 0.98） and between temperature and baseflow （correla- tion coefficient is 0.90） for the 43-year wavelet coefficients, it is suggested that the long-term increasing trends of precipitation and air temperature will lead to an increasing trend of baseflow. For wavelet coefficients of 21-year and 7-year periods, the positive linear correlation between precipitation and baseflow is significant. However, the cor- relation between air temperature and baseflow is not so evident, especially for the 21-year period. As a conclusion, correlation analysis with normalized wavelet coefficients showed that the change of annual baseflow was contrib- uted mostly by the change of precipitation and secondly by the change of temperature.

Wave Radiation and Diffraction by A Two-Dimensional Floating Body with An Opening Near A Side Wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.

Influence of central buckle on suspension bridge dynamic characteristics and driving comfort

The central buckle, which is often used in a suspension bridge, can improve bridges' performance in the actual operation condition. The influence of the central buckle on natural vibration characteristics and bridge-deck driving comfort of a long-span suspension bridge is studied by using a case study of Siduhe Suspension Bridge in China. Based on the finite element software ANSYS and independently complied program, the influence of the central buckle on the structure force-applied characteristics of a long-span suspension bridge has been explored. The results show that the huge increases of natural frequencies can result in the presence of central buckles because of the increases of bending and torsional rigidities. The central buckle basically makes the stiffening girders and cables within the triangular area covered as a relatively approximate rigid area. Hence, the central buckle can reduce the torsional displacement of the main girder. However, the increases of bending and torsional rigidities have little influence on the impact factor, which is obtained by using vehicle-bridge coupled vibration analysis. This means that the central buckle has little effect on the comfort indices. In addition, it is found that the central buckle can enhance the bridge deck's driving stability due to the decrease of the torsional displacements of the main girder.

Analysis of steady heat conduction for 3D axisymmetric functionally graded circular plate

The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation （ODE） in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.