Approximate Homotopy Direct Reduction Method: Infinite Series Reductions to Perturbed mKdV Equations

An approximate homotopy direct reduction method is proposed and applied to two perturbed modified Korteweg- de Vries （mKdV） equations with fourth-order dispersion and second-order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solutions but also for the Painlevd Ⅱ waves and periodic waves expressed by Jacobi elliptic functions for both fourth-order dispersion and second-order dissipation. The method is also valid for strong perturbations.     

Experimental research for direction of arrival estimation based on signal phase matching principle

In order to test the validity of signal phase matching principle (SPMP) applied to direction of arrival (DOA) estimation, experiments are carried out at a reservoir using 16 sensors array. Two kinds of method, Least Square Method for Signal Matching principle (LSMSPM) and singular value decomposition method for signal matching principle (SVDSPM), are used for DOA estimation. Their performances were analyzed and compared with MUSIC and conventional beam-forming (CBF) method. The results show that the 3 dB beam width obtained by SPMP is 1/4 to 1/7 as much as that obtained by CBF and 1/2 to 1/3 by MUSIC method. In addition, LSMSPM and SVDSPM are available for multi-sources DOA estimation and high resolution DOA estimation, which demonstrates that DOA estimation by SPMP method is better than that by MUSIC and CBF method.     

A meshless Galerkin method with moving least square approximations for infinite elastic solids

Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.     

A Novel Method to Measure Acoustic Power of Focusing Transducer with Spherical Surface Based on Self-Reciprocity Theorem

A novel method to measure acoustic power of focusing transducer based on the self-reciprocity theorem of convergent spherical acoustic wave is proposed. The performance of this reciprocity method is compared with that of the radiation force balance (RFB) method and the admittance circle method. The average deviations of the reciprocity method from RFB in measurements of the acoustic power and the radiation conductance for a focusing transducer of 1.525 MHz are 7.5% and 3.6% respectively, and for another focusing transducer of 5.27 MHz,they are 1.7% and 1.1%. The measured radiation conductance deviation by the reciprocity method from the admittance circle method for the focusing transducer of 1.525 MHz is 7.9%. It presents encouraging results even in measuring low acoustic power level. The overall uncertainty of acoustic power measurement using the method is evaluated below 10%, and it has many advantages such as high signal-to-noise ratio, good stability and less interference of bubbles and environment.     

A novel image fusion method using WBCT and PCA

A novel image fusion algorithm based on wavelet-based contourlet transform(WBCT)and principal com- ponent analysis(PCA)is proposed.The PCA method is adopted for the low-frequency components.Using the proposed algorithm to choose the greater of the active measures,the region consistency test is per- formed for the high-frequency components.Experiments show that the proposed method works better in preserving the edge and texture information than wavelet transform method and Laplacian pyramid(LP) method do in image fusion.Four indicators for the fusion image are given to compare the proposed method with other methods.     

A novel image fusion method using WBCT and PCA

A novel image fusion algorithm based on wavelet-based contourlet transform （WBCT） and principal component analysis （PCA） is proposed. The PCA method is adopted for the low-frequency components. Using the proposed algorithm to choose the greater of the active measures, the region consistency test is performed for the high-frequency components. Experiments show that the proposed method works better in preserving the edge and texture information than wavelet transform method and Laplacian pyramid （LP） method do in image fusion. Four indicators for the fusion image are given to compare the proposed method with other methods.     

Track Reconstruction in the High Rate Environment of the HERA—B Spectrometer

In this paper a method of track reconstruction developed for the HERA-B main tracking system is discussed.The method based on a track following algorithm is used for track finding in the field-free area and for the track propagation through the inhomogeneous magnetic field.The performance of program for simulated and real data is shown.     

Extraction of resonance parameters from meson production reaction

We have developed an analytic continuation method for extracting parameters of nucleon resonances within a Hamiltonian formulation of meson-nucleon reactions. The method was tested for simple solvable models and then applied for our recent coupled channels model （πN, ηN, π△, ρN, and σN ） of the π＊N and γ＊N reactions. The resonance pole positions and their properties are studied for P11and P11 channels.     

Various Methods for Constructing Auto-Baicklund Transformations for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified.     

Comparison of calculation methods for the tunnel splitting at excited states of biaxial spin models

We present the calculation and comparison of tunnel splitting at excited levels of biaxial spin models by various methods, including the generalized instanton method, the generalized path integral method for coherent spin states, the perturbation method, and the exact method by numerical diagonalization of the Hamiltonian. It is found that, for integer spin with spin number around 10, tunnel splitting predicted by the generalized path integral for coherent spin states is about 10^{-n} times of the exact numerical result for the nth excited level, while the ratio of the results of the perturbation method and the exact numerical method diverges in the large spin limit. We thus conclude that the generalized instanton method is the best approximate way for calculating tunnel splitting in spin models.     

A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics

We present a numerical method to solve the linear stability of impulsively accelerated density interfaces in two dimensions such as those arising in the Richtmyer–Meshkov instability. The method uses an Eulerian approach, and is based on an upwind method to compute the temporally evolving base state and a flux vector splitting method for the perturbations. The method is applicable to either gas dynamics or magnetohydrodynamics. Numerical examples are presented for cases in which a hydrodynamic shock interacts with a single or double density interface, and a doubly shocked single density interface. Convergence tests show that the method is spatially second-order accurate for smooth flows, and between first and second-order accurate for flows with shocks.     

Analytic continuation of harmonic sums

We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a harmonic sum to be calculated as an expansion valid for large values of its argument. A program for implementing this method is also provided.     

The two-level element free Galerkin method for MHD flow at high Hartmann numbers

In this Letter, a new element free Galerkin method, namely the two-level element free Galerkin method, is presented for solving the governing equations of steady magnetohydrodynamic duct flow. Because this element free Galerkin method makes use of the nodal point configurations which do not require a mesh, therefore it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. Another distinguished feature of the proposed method is the resolving capability of high gradients near the layer regions without local or adaptive refinements. Numerical results indicate that no matter how large the Hartmann number is, this method has the ability to produce the satisfactory results for the velocity and the magnetic field simultaneously. That is to say, the presented method has some excellent properties, such as better stability and accuracy.     

The transfer-matrix and max-plus algebra method for global combinatorial optimization: Application to cyclic and polyhedral water clusters

A new method for the combinatorial optimization of quasi-one-dimensional systems is presented. This method is in close analogy with the well-known transfer-matrix method. The method allows for the calculation of the lowest energy levels of the system. However, when finding the ground and some low-lying states of large complex systems, this method is more economical when compared to the standard transfer-matrix method. The method presented here is based on max-plus algebra, which has maximization and addition as its basic arithmetic operations. For the explanation of this method we use cyclic water clusters as simple examples. The efficiency of the max-plus-algebraic method is demonstrated in the course of global combinatorial optimization of hydrogen bond arrangements in large polyhedral water clusters with fixed positions of the oxygen atoms. The energy of the clusters is estimated using approximate discrete models for the intermolecular interactions.     

Phase transitions in Edwards-Anderson model by means of information theory

A numeric method to characterize phase transitions is presented, explained and applied to a two-dimensional disordered system that can be thought of as a diluted ferromagnet or an Edwards-Anderson model near the ferromagnetic limit. A computer simulation is implemented to define a time series for order parameters; a file stores the time evolution of each parameter for different dilution concentrations and for a series of temperatures. These files are compressed and they reach a maximum size for temperatures in agreement with critical temperatures for the ferromagnetic/paramagnetic transition obtained by other methods. Site order parameter gives optimum results for this method based on data compression. Data compression procedures are invoked to give a qualitative explanation of this phenomenon. The advantages of this method are discussed by comparing results and procedures with two established methods: the crossing of Binder cumulants and the crossing of time autocorrelation functions. Other possible applications and extensions of this method are also mentioned.     

Approximated Vector Diffraction Theory for Readout Signal of Multi-Level Run-Length-Limited Discs

Multi-level run-length-limited read-only optical storage is a kind of high density storage method. The width and height of recording marks are varied with different levels, which is the key technology for the optical storage. Then the readout signal of these discs with complex recording marks is computed by vector analysis method, it is very hard and time-consuming. Approximated vector computation combines the convenience of scalar method and precision of vector method, which is effective for multi-level run-length-limited read-only optical storage.     

Solution of singular two-point boundary value problems using differential transformation method

In this Letter, we implemented relatively new, exact series method of solution known as the differential transform method for solving singular two-point boundary value problems. Several illustrative examples are given to demonstrate the effectiveness of the present method.     

An evolutional approach to the numerical construction of polycrystalline structures using the Voronoi tessellation

We developed a method to numerically construct a polycrystalline structure with a specified grain-size distribution by utilizing the genetic algorithm, which is suitable for global optimization of complex parametric space, and the Voronoi tessellation. The computational merits of our new method compared with the conventional optimization method are: (a) it is able to escape more easily from local minima of the penalty function; and (b) it is suitable for parallel processing. The method efficiently creates input data for numerical simulations of microstructural evolution such as recrystallization, grain growth, deformation, and fracture.     

Numerical solution of 3D Green's function for the dynamic system of anisotropic elasticity

In this Letter, we used homotopy perturbation method to obtain numerical solution of the 3D Green's function for the dynamic system of anisotropic elasticity. Application of homotopy perturbation method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results obtained from convolution of Green's function and data of the Cauchy problem are compared with the exact solution for cubic media. The results reveal that the proposed method is very effective and simple.     

A Novel Method for Enhancing Goos-Hänchen Shift in Total Internal Reflection

Due to the tiny shift in order of optical wavelength for Goos-Hǎnchen （GH） shift, it is very difficult to directly measure and apply the GH shift. We develop a new method for enhancing GH shift of both TE and TM polarized waves. The method is based on a total reflection prism made of BK9 glass combined with a precise measurement of the resulting spatial displacement with a one-dimensional charge coupled device （CCD）. Measurements are performed to examine the validity of the method. Experimental and theoretical results indicate the feasibility of the method with an enhancement in optical wavelenghth shift at millimetre scale. The method is advantageous to application the GH shift in the optical domain, and is also meaningful for measuring even smaller changes in the refractive index of a liquid.