Exponential Time Differencing Method for a Reaction-Diffusion System with Free Boundary

For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.

DYNAMIC CHARACTERISTIC ANALYSIS OF FUZZY-STOCHASTIC TRUSS STRUCTURES BASED ON FUZZY FACTOR METHOD AND RANDOM FACTOR METHOD

A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh＇s quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable＇s moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.

ANALYSIS OF THE LARGE DEFLECTION DYNAMIC PLASTIC RESPONSE OF SIMPLY-SUPPORTED CIRCULAR PLATES BY THE“MEMBRANE FACTOR METHOD”

Based on energy equilibrium,a new procedure called the Membrane Factor Method is devel- oped to analyze the dynamic plastic response of plates with deflections in the range where both bending mo- ments and membrane forces are important.The final deflection of a simply -supported circular rigid-plastic plate loaded by a uniformly distributed impulse is obtained.In comparison with other approximate solutions, the present results are found to be simpler and in better agreement with the corresponding experimental values reoorded by Florence.

The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrdinger Equations

This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of （A＊ A） ^1/4 and G which maps more general incident fields than plane waves into the scattering amplitude coincide.As an application we characterize the support of the potential using only the spectral data of the operator A.

Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.

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.

Source Apportionment of Ambient PM_(10) in the Urban Area of Longyan City,China:a Comparative Study Based on Chemical Mass Balance Model and Factor Analysis Method

In order to identify the day and night pollution sources of PM10 in ambient air in Longyan City,the authors analyzed the elemental composition of respirable particulate matters in the day and night ambient air samples and various pollution sources which were collected in January 2010 in Longyan with inductivity coupled plasma-mass spectrometry（ICP-MS）.Then chemical mass balance（CMB） model and factor analysis（FA） method were applied to comparatively study the inorganic components in the sources and receptor samples.The results of factor analysis show that the major sources were road dust,waste incineration and mixed sources which contained automobile exhaust,soil dust/secondary dust and coal dust during the daytime in Longyan City,China.There are two major sources of pollution which are soil dust and mixture sources of automobile exhaust and secondary dust during the night in Longyan.The results of CMB show that the major sources are secondary dust,automobile exhaust and road dust during the daytime in Longyan.The major sources are secondary dust,soil dust and automobile exhaust during the night in Longyan.The results of the two methods are similar to each other and the results will guide us to plan to control the PM10 pollution sources in Longyan.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties: Factorization method

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrrdinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU（1, 1） dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.

Compact implicit integration factor methods for some complex-valued nonlinear equations

The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.

Comprehensive Evaluation on the Regional Economy of Commodity Grain Base in Heilongjiang Province Based on Factor Analysis Method

Taking a total of 13 areas in Heilongjiang commodity grain base as the research objects,9 indices are selected,which are regional GDP(X1),per capita GDP(X2),total value of tertiary industry(X3),financial revenue(X4),urban fixed assets investment(X5),average salary(X6),gross industrial output value(X7),total output value of farming,forestry,husbandry and fishing(X8),and retail sales of social consumer goods(X9).Based on this,evaluation index system of regional economy is established.According to the 2006-2008 Heilongjiang Statistical Yearbook,average values within 3 years are used as analytical data.Factor Analysis Method is adopted to establish regression model and to carry out comprehensive analysis.Result shows that Heilongjiang commodity grain base has extremely uneven regional economic development in different areas.According to the score order and actual situation,the 13 areas are divided into 4 types.The first and second types are Harbin and Daqing,respectively.The third type is Qiqihaer,Suihua,Mudanjiang and Jiamusi.And the forth type is Jixi,Shuangyashan,Heihe,Yichun,Qitaihe,Hegang and Daxinganling.Suggestions for the development of these areas are put forward.

A Research on Competitiveness of Guangxi City——Based on System Clustering Method and Principal Component Analysis Method

A total of 10 indices of regional economic development in Guangxi are selected.According to the relevant economic data,regional economic development in Guangxi is analyzed by using System Clustering Method and Principal Component Analysis Method.Result shows that System Clustering Method and Principal Component Analysis Method have revealed similar results analysis of economic development level.Overall economic strength of Guangxi is weak and Nanning has relatively high scores of factors due to its advantage of the political,economic and cultural center.Comprehensive scores of other regions are all lower than 1,which has big gap with the development of Nanning.Overall development strategy points out that Guangxi should accelerate the construction of the Ring Northern Bay Economic Zone,create a strong logistics system having strategic significance to national development,use the unique location advantage and rely on the modern transportation system to establish a logistics center and business center connecting the hinterland and the Asean Market.Based on the problems of unbalanced regional economic development in Guangxi,we should speed up the development of service industry in Nanning,construct the circular economy system of industrial city,and accelerate the industrialization process of tourism city in order to realize balanced development of regional economy in Guangxi,China.

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

Method of Calculating the Safety Factor Profile on the HT-7 Tokamak

A method of calculating the safety profile on the HT-7 tokamak has been described in this paper. It is derived from Maxwell's equations, among which we-mainly use .two of them: one is the magnetic field diffusion equation, and the other is Ampere's Law. This method can be also used to evaluate the safety factor on other devices with a circular cross sections. It is helpful to the study of the plasma MHD behavior on the HT-7 tokamak.

Relativistic Schrodinger Wave Equation for Hydrogen Atom Using Factorization Method

In this investigation a simple method developed by introducing spin to Schrodinger equation to study the relativistic hydrogen atom. By separating Schrodinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound state Energy levels and wave functions of relativistic Schrodinger equation for Hydrogen atom have been obtained. Calculated results well matched to the results of Dirac’s relativistic theory. Finally the factorization method and supersymmetry approaches in quantum mechanics, give us some first order raising and lowering operators, which help us to obtain all quantum states and energy levels for different values of the quantum numbers n and m.

INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS

This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.

Evaluation, prediction, and protection of water quality in Danjiangkou Reservoir, China

The water quality in the Danjiangkou Reservoir has attracted considerable attention from the Chinese public and government since the announcement of the Middle Route of the South to North Water Diversion Project （SNWDP）, which commenced transferring water in 2014. Integrated research on the evaluation, prediction, and protection of water quality in the Danjiangkou Reservoir was carried out in this study in order to improve environmental management. Based on 120 water samples, wherein 17 water quality indices were measured at 20 monitoring sites, a single factor evaluation method was used to evaluate the current status of water quality. The results show that the main indices influencing the water quality in the Danjiangkou Reservoir are total phosphorus （TP）, permanganate index （CODM,）, dissolved oxygen （DO）, and five-day biochemical oxygen demand （BODs）, and the concentrations of TP, BODs, ammonia nitrogen （NH3--N）, CODM,, DO, and anionic surfactant （Surfa） do not reach the specified standard levels in the tributaries. Seasonal Mann--Kendall tests indicated that the CODMn concentration shows a highly significant increasing trend, and the TP concentration shows a significant increasing trend in the Danjiangkou Reservoir. The distribution of the main water quality indices in the Danjiangkou Reservoir was predicted using a two-dimensional water quality numerical model, and showed that the sphere of influence from the tributaries can spread across half of the Han Reservoir if the pollutants are not controlled. Cluster analysis （CA） results suggest that the Shending River is heavily polluted, that the Jianghe, Sihe, and Jianhe rivers are moderately polluted, and that they should be the focus of environmental remediation.

Mobility of toxic metals in sediments: Assessing methods and controlling factors

Metals and metalloids（termed as metals in this article）are important constituent elements of the earth＇s crust.A number of metals,if present in excess,are toxic to organisms and therefore they are usually defined as toxic metals.

Exact solutions of the Klein-Gordon equation with Makarov potential and a recurrence relation

In this paper, the Klein-Gordon equation with equal scalar and vector Makaxov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number l is established and some special cases of Makarov potential axe discussed.

Analytical analysis for vibration of longitudinally moving plate submerged in infinite liquid domain

The vibration of a longitudinally moving rectangular plate submersed in an infinite liquid domain is studied analytically with the Rayleigh-Ritz method. The liquid is assumed to be incompressible, inviscid, and irrotational, and the velocity potential is used to describe the fluid velocity in the whole liquid field. The classical thin plate theory is used to derive mechanical energies of the traveling plate. As derivative of transverse displacement with respect to time in the compatibility condition equation exists, an exponential function is introduced to depict the dynamic deformation of the moving plate. It is shown that this exponential function works well with the Rayleigh- Ritz method. A convergence study shows a quick convergence speed for the immersed moving plate. Furthermore, the parametric study is carried out to demonstrate the effect of system parameters including the moving speed, the plate location, the liquid depth, the plate-liquid ratio, and the boundary condition. Results show that the above system parameters have significant influence on the vibration characteristics of the immersed moving plate. To extend the study, the method of added virtual mass incremental （AVMI） factor is used. The results show good agreement with those from the Rayleigh-Ritz method.