THEORETICAL PREDICTION OF THE KINETICS CURVES OFPEARLITIC TRANSFORMATION IN HYPO-PROEUTECTOID STRUCTURAL STEELS

Supposing carbon contents of ferrite phases in pearlite precipitating from austenite in multicomponent steel at temperature T and in Fe-C ystem at T' are the same the pearlite formation temperature diference, can be calculated from the FeX phase diagrams and the equilibrium temperature Al. Using Tp and Fe-C binary thermodynamic model, the driving forces for phase transformation from austenite to pearlite in multicomponent steels have been successfully calculated. Through the combination of simplified Zener and Hillert's model for pearlite growth with Johnson-Mehl equation, using data from known TTT diagrams, the interfacial energy parameter and activation energy for pearlite formation can be determined and expressed as functions of chemical composition in steels by regression analysis. The calculated starting curves of pearlitic transformation in some commercial steels agree well with the experimental data.

BCKLUND TRANSFORMATIONS FOR THE EQUATION~2u/x^1x^1+~2u/x^2x^2=f(u)

Backlund transformations for the equation is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition is sufficient for the existence of Backlund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt[1,2]

Complex Maxwell's equations

A unified complex model of Maxwell＇s equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell＇s equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac＇s quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell＇s equations to include longitudinal waves.A formal analogy between this formulation and Dirac＇s equation is also discussed.

Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)

In this paper, we first introduce a Lie algebra of the special orthogonal group, g = so(4, C), whose elements are 4 × 4trace-free, skew-symmetric complex matrices. As its application, we obtain a new soliton hierarchy which is reduced to AKNS hierarchy and present its bi-Hamiltonian structure and Liouville integrability. Furthermore, for one of the equations in the resulting hierarchy, we construct a Darboux matrix T depending on the spectral parameter λ.

LOCAL ORTHOGONAL TRANSFORMATION FOR ACOUSTIC WAVEGUIDE

In this paper, a local orthogonal transformation is created to transform the Helmholtz waveguide with curved interface to the one with a flat interface within the two layer medium, and the Helmholtz equation u xx +u zz +κ 2(x,z)u=0 is transformed to V +αV +β V +γV=0 . Numerical results demonstrate that the transformation is more feasible. This transformation is particularly useful for the research on wave propagation in acoustic waveguide.

Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips

The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.

COHERENT STATES, INVERSE MAPPING FORMULA FOR WEYL TRANSFORMATIONS AND APPLICATION TO EQUATIONS OF KdV TYPE

In this paper, we consider the trace of generalized operators and inverse Weyl transformation.First of all we repeat the definition of test operators and generalized operators given in [18],denoting L~2(R) by H.

INTEGRABLE TYPES OF NONLINEAR ORDINARY DIFFERENTIAL EQUATION SETS OF HIGHER ORDERS

Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years Based on these papers and in virtue of Leibniz formula,and transformation set technique,this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders, moveover,its integrability is proven.The results obtained are the generalization of those in the references.

COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL

In this paper, the Poussinesq equations and mild-slope equation of wave transformation in near-shore shallow water were introduced and the characteristics of the two forms of equations were compared and analyzed. Meanwhile, a Boussinesq wave model which includes effects of bottom friction, wave breaking and subgrid turbulent mixing is established, slot technique dealing with moving boundary and damping layer dealing with absorbing boundary were estab lished. By adopting empirical nonlinear dispersion relation and including nonlinear term, the mild-slope equation model was modified to take nonlinear effects into account. The two types of models were validated with the experiment results given by Berkhoff and their accuracy was analysed and compared with that of correlated methods.

On the application of wavelet transform to the solution of integral equations for acoustic radiation and scattering

The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the previous methods in which Galerkin formulation or wavelet matrix transform approach is used. The boundary quantities are expended in terms of a basis of the periodic, orthogonal wavelets on the interval. Using wavelet transform leads a highly sparse matrix system. It can avoid an additional integration in Galerkin formulation, which may be very computationally expensive. The techniques of the singular integrals in two-dimensional and axisymmetric wavelet formulation are proposed. The new method can solve the boundary value problems with Dirichlet, Neumann and mixed conditions and treat axisymmetric bodies with arbitrary boundary conditions. It can be suitable for the solution at large wave numbers. A series of numerical examples are given. The comparisons of the results from new approach with those from boundary element method and analytical solutions demonstrate that the new techique has a fast convergence and high accuracy.

Simulation of Inviscid Compressible Flows Using PDE Transform

The solution of systems of hyperbolic conservation laws remains an interesting and challenging task due to the diversity of physical origins and complexity of the physical situations.The present work introduces the use of the partial differential equation(PDE)transform,paired with the Fourier pseudospectral method(FPM),as a new approach for hyperbolic conservation law problems.The PDE transform,based on the scheme of adaptive high order evolution PDEs,has recently been applied to decompose signals,images,surfaces and data to various target functional mode functions such as trend,edge,texture,feature,trait,noise,etc.Like wavelet transform,the PDE transform has controllable time-frequency localization and perfect reconstruction.A fast PDE transform implemented by the fast Fourier Transform(FFT)is introduced to avoid stability constraint of integrating high order PDEs.The parameters of the PDE transform are adaptively computed to optimize the weighted total variation during the time integration of conservation law equations.A variety of standard benchmark problems of hyperbolic conservation laws is employed to systematically validate the performance of the present PDE transform based FPM.The impact of two PDE transform parameters,i.e.,the highest order and the propagation time,is carefully studied to deliver the best effect of suppressing Gibbs’oscillations.The PDE orders of 2-6 are used for hyperbolic conservation laws of low oscillatory solutions,while the PDE orders of 8-12 are often required for problems involving highly oscillatory solutions,such as shock-entropy wave interactions.The present results are compared with those in the literature.It is found that the present approach not only works well for problems that favor low order shock capturing schemes,but also exhibits superb behavior for problems that require the use of high order shock capturing methods.