ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR REACTION DIFFUSION EQUATION

In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.

The (G'/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations

The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.

A NOTE ON UPPER AND LOWER SOLUTIONS METHOD FOR FOURTH-ORDER BOUNDARY VALUE PROBLEMS

In this paper,we deal with a class of boundary value problem.We give the existence of solution under the assumption that there exist lower and upper solutions to the problem.Our result extends and complements the relevant ones which were obtained by many authors previously.

DETERMINATION OF STABILITY CONSTANTS OF THE COORDINATION COMPOUNDS OF Au(Ⅲ)-2-MERCAPTOPYRIDINE-1-OXIDE AND METHYL DERIVATIVES——METHOD OF DUAL-WAVELENGTH CORRESPONDING SOLUTIONS

In this paper,we report the deductive formula used for the method of dual-wavelength corresponding solutions under condition of having ligand interference and the stability constants of three new coordination compounds [AuL_2]^+determined with this method.The stability of the three compounds,the necessity of controlling pH in experimental systems and the advantage of this method are discussed in detail.

ON THE METHOD OF RECIPROCAL THEOREM TO FIND SOLUTIONS OF THE PLANE PROBLEMS OF ELASTICITY

In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.

Verification of an Explicitly Coupled Thermal-Phase Field-Mechanical Electromagnetic (TPME) Framework by the Method of Manufactured Solutions

An explicitly coupled two-dimensional (2D) multiphysics finite element method (FEM) framework comprised of thermal, phase field, mechanical and electromagnetic (TPME) equations was developed to simulate the conversion of solid kerogen in oil shale to liquid oil through in-situ pyrolysis by radio frequency heating. Radio frequency heating as a method of in-situ pyrolysis represents a tenable enhanced oil recovery method, whereby an applied electrical potential difference across a target oil shale formation is converted to thermal energy, heating the oil shale and causing it to liquify to become liquid oil. A number of in-situ pyrolysis methods are reviewed but the focus of this work is on the verification of the TPME numerical framework to model radio frequency heating as a potential dielectric heating process for enhanced oil recovery. Very few studies exist which describe production from oil shale;furthermore, there are none that specifically address the verification of numerical models describing radio frequency heating. As a result, the Method of Manufactured Solutions (MMS) was used as an analytical verification method of the developed numerical code. Results show that the multiphysics finite element framework was adequately modeled enabling the simulation of kerogen conversion to oil as a part of the analysis of a TPME numerical model.

THE ANALYTICAL SOLUTIONS BASED ON THE CONCEPT OF FINITE ELEMENT METHODS

On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.

APPLICATION OF THE METHOD OF THE RECIPROCAL THEOREM TO FINDING DISPLACEMENT SOLUTIONS OF CUBES

In this paper the method of reciprocal theorem is extended to find solutions of three-D problems of elasticity.First we give the basic solution of the cube with six surfaces fixed as the basic system and then using the reciprocal theorem between the basic system acted on by unit concentrated loads and the actual system with prescribed surface displacements, we find displacement solution of the actual system.

A Multi-Symplectic Compact Method for the Two-Component Camassa-Holm Equation with Singular Solutions

The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, the proposed method is derived by the sixth-order compact finite difference method in spatial discretization and the symplectic implicit midpoint scheme in temporal discretization. Numerical experiments finely describe the velocity and density variables in the two-component integrable system and distinctly display the evolvement of the singular solutions. Moreover, the proposed method shows good conservative properties during long-time numerical simulation.

Preparation,Characterization and Photothermal Study of PVA/Ti_(2)O_(3) Composite Films

In this work,flexible photothermal PVA/Ti_(2)O_(3) composite films with different amount(0 wt%,5 wt%,10 wt%,15 wt%)of Ti_(2)O_(3) particles modified by steric acid were prepared by a simple solution casting method.The microstructures,XRD patterns,FTIR spectra,UV-Vis-NIR spectra thermo-conductivity,thermo-stability and photothermal effects of these composite films were all characterized.These results indicated that Ti_(2)O_(3) particles were well dispersed throughout the polyvinyl alcohol(PVA)matrix in the PVA/Ti_(2)O_(3) composite films.And Ti_(2)O_(3) particles could also effectively improve the photothermal properties of the composite films which exhibited high light absorption and generated a high temperature(about 57.4℃for film with 15 wt%Ti_(2)O_(3) amount)on the surface when it was irradiated by a simulated sunlight source(1 kW/m^(2)).

2-D Numerical Simulation of Natural Gas Hydrate Decomposition Through Depressurization by Fully Implicit Method

Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor injection. However, many issues have to be resolved before the commercial production. In the present study, a 2-D axisymmetric simulator for gas production from hydrate reservoirs is developed. The simulator includes equations of conductive and convective heat transfer, kinetic of hydrate decomposition, and multiphase flow. These equations are discretized based on the finite difference method and are solved with the fully implicit simultaneous solution method. The process of laboratory-scale hydrate decomposition by depressurization is simulated. For different surrounding temperatures and outlet pressures, time evolutions of gas and water generations during hydrate dissociation are evaluated, and variations of temperature, pressure, and multiphase fluid flow conditions are analyzed. The results suggest that the rate of heat transfer plays an important role in the process. Furthermore, high surrounding temperature and low outlet valve pressure may increase the rate of hydrate dissociation with insignificant impact on final cumulative gas volume.

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.

New exact solutions of nonlinear Klein-Gordon equation

New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.

COMPARISON OF TDOA LOCATION ALGORITHMS WITH DIRECT SOLUTION METHOD

For Time Difference Of Arrival(TDOA) location based on multi-ground stations scene,two direct solution methods are proposed to solve the target position in TDOA location.Therein,the solving methods are realized in the rectangular and polar coordinates.On the condition of rectangular coordinates,first of all,it solves the radial range between the target and reference station,then cal-culates the location of the target.In the case of polar coordinates,the azimuth between the target and reference station is solved first,then the radial range between the target and reference station is figured out,finally the location of the target is obtained.Simultaneously,the simulation and comparison analysis are given in detail,and show that the polar solving method has the better fuzzy performance than that of rectangular coordinate.

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD

The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.

Structural and Optical Properties of Cu2+ + Ce3+ Co-Doped ZnO by Solution Combustion Method

In this work, ZnO, Ce3+ doped ZnO (ZnO/Ce3+) and Cu2+ + Ce3+ co-doped ZnO (ZnO/Cu2+ + Ce3+ ) solid solutions powders were synthesized by a solution combustion method maintaining the Ce3+ ion concentration constant in 3%Wt while the Cu2+ ion concentration was varied in 1, 2, 3, 10 and 20%Wt. After its synthesis, all the samples were annealed at 900?C by 24 h. The ZnO, ZnO/Ce3+ and ZnO/Cu2+ + Ce3+ powders were structurally characterized using X-ray diffraction (XRD) technique, and the XRD patterns showed that for pure ZnO, Cu2+ undoped ZnO/Ce3+ and ZnO/Ce3+ doped with the Cu2+ ion, the three samples exhibited the hexagonal wurtzite ZnO crystalline structure. However, the morphology and particle size of both samples were observed by means of a scanning electron microscopy (SEM);from SEM image, it is observed that the crystallites of both samples are agglomerated forming bigger amorphous particles with an approximate average size of 1 μm. In addition, the photoluminescence of the ZnO, Ce3+ doped ZnO and Cu2+ + Ce3+ doped ZnO samples was measurement under an illumination of 209 nm wavelength (UV region): for the ZnO/Ce3+ sample, your emission spectrum is in the visible region from blue color until red color;the UV band of the ZnO is suppressed. The multicolor emission visible is attributed to the Ce3+ ion photoluminescence, while for the ZnO/Cu2+ + Ce3+, its emission PL spectrum is quenching by the Cu2+ ion, present in the ZnO crystalline.

Fundamental solution method for inverse source problem of plate equation

The elastic plate vibration model is studied under the external force. The size of the source term by the given mode of the source and some observations from the body of the plate is determined over a time interval, which is referred to be an inverse source problem of a plate equation. The uniqueness theorem for this problem is stated, and the fundamental solution to the plate equation is derived. In the case that the plate is driven by the harmonic load, the fundamental solution method （FSM） and the Tikhonov regularization technique axe used to calculate the source term. Numerical experiments of the Euler-Bernoulli beam and the Kirchhoff-Love plate show that the FSM can work well for practical use, no matter the source term is smooth or piecewise.

Preparation of Superhydrophobic ZnO Films on Zinc Substrate by Chemical Solution Method

Superhydrophobic surface was prepared on the zinc substrate by chemical solution method via immersing clean pure zinc substrate into a water solution of zinc nitrate hexahydrate[Zn（NO3）2.6H2O] and hexamethylenete- traamine（C6H12N4） at 95 ℃ in water bath for 1.5 h, then modified with 18 alkanethiol. The best resulting surface shows superhydrophobic properties with a water contact angle of about 158° and a low water roll-off angle of around 3°. The prepared samples were characterized by powder X-ray diffraction（XRD）, X-ray photoelectron spectroscopy （XPS）, energy-dispersive X-ray spectroscopy（EDX）, transmission electron microscopy（TEM）, and scanning electron microscopy（SEM）. SEM images of the films show that the resulting surface exhibits flower-shaped micro- and nano-structure. The surfaces of the prepared films were composed of ZnO nanorods which were wurtzite structure. The special flower-like micro- and nano-structure along with the low surface energy leads to the surface superhydro- phobicity.