Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

The generalized moment method is applied to average the Ginzburg-Landau equation with quintic nonlinearity in the neighborhood of a soliton solution to the nonlinear Schrödinger equation. A qualitative analysis of the resulting dynamical system is presented. New soliton solutions bifurcating from a known exact soliton solution are obtained. The results of the qualitative analysis are compared with those obtained by direct numerical solution of the Ginzburg-Landau equation.     

Exact solution for temerature field due to non-equilibrium heating of solid substrate

Non-equilibrium energy transfer between electron and lattice sub-systems due to short-pulse heating is formulated and the closed form solution for electron and lattice site temperatures is presented. The electron kinetic theory approach is incorporated to formulate non-equilibrium energy transfer in the electron and lattice sub-systems. The method of Lie point symmetries is used in the exact solution of governing energy equation. In the analysis, the volumetric heat source, representing the laser heating pulse, and surface heat source, corresponding to short thermal contact of the surface, are incorporated and the analytical solutions for each heating source are presented. Electron temperature distribution obtained from the closed form solution is compared with its counterpart predicted from the numerical simulation. It is found that the results obtained from the closed form agree well with electron temperature predictions obtained from numerical simulation.     

A note on transverse vibrations of a rectangular plate with a free,rectangular, corner cut-out

An approximate solution to the title problem is presented, obtained by using the Rayleigh-Ritz method. The analysis is presented for the case of simply supported and clamped plates. For the case of a rigidly clamped plate results are presented of numerical experiments on minimizing the calculated value of the fundamental frequency coefficient by using Schmidt's approach. An experimental investigation is described on a clamped square plate with a free square, corner cut-out, which has led to the conclusion that the fundamental frequency coeficient remains practically invariant with respect to size when compared with the frequency coefficient of the fully clamped plate. A similar conclusion is arrived at by means of the mathematical model. The problem under consideration is important from a practical viewpoint since cut-outs of the type considered here are quite common in engineering practice.     

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.     

等离子体平衡逆问题的一种数值解法

本文借助离散化算子,把滤波方法推广到非圆截面,对具有非圆截面的等离子体平衡逆问题建立了一个稳定的显式逆推滤波算法;给出了部分非圆截面的计算结果;对圆截面情形的数值解与解析解作了比较。     

二维二相不规则网格的油藏数值模拟

本文采用不规则网格的差分方法,对平面油水模型进行了数值模拟,并用IMPES方法计算了两个实例。例1的计算结果与精确解吻合良好,比Pedrosa的局部加密网格法使用的网格数少而且计算更简便。例2为矩形网格难以计算的问题,应用本文方法也得出了较好的结果。这表明本文的不规则网格差分方法是可靠而简便的,它可以有效地应用于复杂外边界和复杂地层结构的油藏模拟问题。     

On the use of two classical series expansion methods to determine the vibration of harmonically excited pure cubic oscillators

An analytical approach to determine the steady-state response of a damped and undamped harmonically excited oscillator with no linear term and with cubic non-linearity is presented. The governing equation is transformed into a form suitable for the application of a classical series expansion technique. The Linstedt–Poincaré method and the method of multiple scales are then used to determine the amplitude-frequency response and approximate solution for the response at the excitation frequency. The results obtained are compared with numerical solutions and analytical solutions found in the literature for the case when there is strong non-linearity.     

Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

A novel explicit analytical solution is reported for the transmission and recovery of information signals using a simple communication scheme. Analytical solutions are obtained for the normalized state equations of coupled second-order chaotic transmitter and receiver systems embedding the information signal. The analytical solution of the difference system obtained from the state equations of the transmitter and receiver systems has been identified as a measure of the recovered information signal which is transmitted securely by chaotic masking. The analytical solutions are used to reveal the nature of synchronization and the enhancement of the amplitude of recovered information signal. The difference signal of the coupled state variables indicating the recovered information signal obtained through numerical simulations is presented to validate the analytical results. The electronic circuit experimental results are presented to confirm the analytical and numerical results of the communication scheme discussed.     

On the numerical solution of the evolution equation in QCD

We discuss in some detail the algorithm for the numerical solution of QCD evolution equations in the next-to-leading order. Relative merits and shortcomings of this method are presented and compared with those of other available approaches. Effective control of the accuracy of obtained results is stressed.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

Theoretical and numerical calculation of the acoustic radiation force acting on a circular rigid cylinder near a flat wall in a standing wave excitation in an ideal fluid

The acoustic radiation force acting on a cylinder near a flat wall in a standing wave is calculated by analytical methods and numerical simulations. An exact theoretical solution is presented as well as an approximate solution. The approximate solution is in algebraic form and quite easy to compute. The numerical simulation is based on FVM (Finite Volume Method) on unstructured triangular meshes. The exact theoretical, approximate and numerical solutions are compared with each other and good agreements are obtained. Furthermore, the effects of the flat wall are investigated in detail by the three methods.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

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.     

FREE VIBRATION ANALYSIS OF COMPOSITE RECTANGULAR MEMBRANES WITH AN OBLIQUE INTERFACE

The natural frequencies and mode shapes of a composite rectangular membrane with no exact solutions are found by using an analytical method appropriate for the geometric feature of the title problem membrane presented here. The method has a key feature in which the theoretical development is very simple and only a small amount of numerical calculation is required. Example studies show that the natural frequencies and their associated modes obtained from the method are found to be very accurate compared with the results by the FEM (SYSNOISE) or exact solutions. Furthermore, the natural frequencies converge rapidly and accurately to the exact values or the numerical results obtained from the finite element model using meshes sufficient to yield already converging natural frequencies, even when a small number of series functions are used in the proposed method.     

快速计算阵列波导光栅波导耦合系数的修正重叠积分方法

提出了一种修正的重叠积分方法用以计算阵列波导光栅(AWG)波分复用器件中光从自由传输区域到阵列波导的耦合系数,并和光束传播法(BPM)数值方法计算得到的结果做了比较通过比较分析,得出结论:当波导中心距不是太小时,用修正重叠积分这一快速方法是合适的.     

Scattering of a Gaussian beam by an anisotropically coated circular cylinder

A solution to the problem of Gaussian beam scattering by an anisotropically coated circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with a Tayor’s series. The transmitted field in the anisotropically coated region is expressed as a infinite summation of eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting the similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.     

多排叶片内部流动以及叶片排与排气系统相互作用研究

本文采用高分辨率格式和多块多网格方法求解雷诺平均Navier-Stokes方程,数值模拟多排叶片内的三维粘性流动;使用数值激盘模拟叶片排的存在,研究叶片排与非轴对称排气部件之间的相互作用以及复杂的内部流动。文中描述了数值方法,给出了NASA透平导叶和单级透平内部流场的数值结果及其与相应实验结果的对比,也给出了多级透平内部流场的数值结果,以及透平与排气部件之间的耦合流场的结果。     

Analysis of the evolution of perturbations in a magnetized collisionless plasma with an integral-equation technique

Summary A technique recently proposed to study the classical problem of the evolution of small perturbations in a collisionless unmagnetized plasma is extended to a magnetized plasma. A time-convolutive integral equation for the plasma density is obtained from the Vlasov equation for a homogeneous plasma in a uniform, stationary magnetic field. The equation can be solved by means of simple numerical algorithms and, in some cases, analytical solutions can be obtained. The procedure proves to be analytically simpler than the classical one and is more convenient from a numerical point of view. Techniques of solution are presented and analytical and numerical results for electrostatic perturbations are discussed.     

Kinetic modeling of a slow flow CW CO2 laser

A kinetic model for analysis of the slow-flow CW-discharge CO₂ laser with diffusion cooling has been developed in which the gas temperature is obtained from energy balance equations. The method is based on the numerical solution of a set of nonlinear differential equations for vibrational kinetics. The numerical predictions from the model are compared with some experimental results and a good agreement is obtained.     

Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications

Shallow water flows are found in a variety of engineering problems always dominated by the presence of bed friction and irregular bathymetry. These source terms determine completely the possible evolution of the flooded area in time. It is well known that appropriate numerical schemes for this type of flows must be well-balanced. Well-balanced numerical schemes are based on the preservation of cases of quiescent equilibrium over variable bed elevation. Commonly they are formulated as an adaptation of numerical solvers defined for cases without source terms. This procedure is insufficient when applied to real situations. Then, it is possible to argue that appropriate numerical schemes cannot arise directly from those derived from the simplest homogeneous case without source terms. New solutions are presented in this work by defining weak solutions that include the presence of source terms. To do that, the solvers presented in this work extend the number of waves in the well known HLL and HLLC solvers involving a stationary jump in the solution. This is done without modifying the original solution vector of conserved quantities. The resulting approximate Riemann solvers include variable bed level surface and friction. Solvers are systematically assessed via a series of test problems with exact solutions for one and two dimensions, including steady and unsteady flow configurations, variation of the flooded area in time and comparisons with experimental data. The obtained results point out that the new method is able to predict faithfully the overall behavior of the solution and of any type of waves.