Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

Study of the temperature rise induced by a focusing transducer with a wide aperture angle on biological tissue containing ribs

We used the spheroidal beam equation to calculate the sound field created by focusing a transducer with a wide aperture angle to obtain the heat deposition, and then we used the Pennes bioheat equation to calculate the temperature field in biological tissue with ribs and to ascertain the effects of rib parameters on the temperature field. The results show that the location and the gap width between the ribs have a great influence on the axial and radial temperature rise of multilayer biological tissue. With a decreasing gap width, the location of the maximum temperature rise moves forward; as the ribs are closer to the transducer surface, the sound energy that passes through the gap between the ribs at the focus decreases,the maximum temperature rise decreases, and the location of the maximum temperature rise moves forward with the ribs.     

Refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation

The expressions of the refractive indices corresponding wave vector k(θ,) are given by using coordinate transformations for the refractive indices ellipsoid equation of biaxial crystals. The refractive index expression of the wave, whose velocity is slower, is given by

and that of the wave, whose velocity is faster, is given by

     

两个非平行波导间的能量转换

提出一种分析非平行波导间耦合的简明方法-耦合系数推广法.利用这种方法,导出一种新的非平行双波导的耦合方程,由此得到一组非平行波导耦合的完美的分析解,依据这些分析解可以优化非平行波导的传输距离、输入／输出端口波导间距和夹角.     

Reduction and New Explicit Solutions of (2+1)-Dimensional Breaking Soliton Equation

By applying the Lie group method, the (2+1)-dimensional breaking soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.     

Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations

In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.     

Volume Effect of Bound States in Quark-Gluon Plasma

Bound states, such as qq and q(q), may exist in quark-gluon plasma. As the system is at high density,the volume of the bound states may evoke a reduction in the phase space. We introduce an extended bag model to investigate qualitatively the volume effect on the properties of the system. We find a limit temperature where the bound states start to be completely melted.     

Band Theory in the Context of the Hamilton-Jacobi Formulation

In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band structure for the energy spectrum in the Krönig-Penney model.     

The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.     

Dark Multi-Soliton Solution of the Nonlinear Schrödinger Equation with Non-Vanishing Boundary

The inverse scattering transform for the nonlinear Schrödinger equation in normal dispersion with non-vanishing boundary values is re-examined using an affine parameter to avoid double-valued functions. An operable algebraic procedure is developed to evaluate dark multi-soliton solutions. The dark two-soliton solution is given explicitly as an example, and is verified by direct substitution. The additional motion of the soliton center is given by its asymptotic behavior.