一类特殊初值柯西问题的简易解法

通过对初始条件为平面波的三维波动方程柯西问题的研究,利用变量变换,将三维波动方程柯西问题转化为一维波动方程柯西问题,以利用达朗贝尔公式来求解,从而避开了使用复杂的泊松公式.     

Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin-Huxley neurons

Transition of spiral wave in the regular networks of Hodgkin-Huxley (H-H) neurons is simulated and discussed in detail when the effect of membrane temperature and forcing current is considered. Neurons are distributed in the sites of two-dimensional array, neurons are connected with complete nearest-neighbor connections, no-flux boundary conditions, appropriate initial values and physiological parameters are used to develop a stable rotating spiral wave. A statistic factor of synchronization is defined to discuss the transition and development of spiral wave in the two parameters space (membrane temperature T and forcing current I), and it is found that spiral wave keeps alive due to positive current forcing and the spiral wave can be removed completely when the temperature is increased to a threshold about T = 22.3 °C at a fixed current intensity. Periodical forcing current is imposed on the networks of neurons globally and locally, respectively. It is found that spiral wave could be suppressed by the new generated traveling wave or target wave when periodical forcing current is imposed on the border of networks of neurons, and the most effective frequency of the external forcing current is close to the intrinsic frequency of the spiral wave of the networks.     

Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method＊

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.     

高频引力波与现代宇宙学

文章简要综述了由典型现代宇宙学模型和膜振荡模型预期的微波频带的高频引力波的特性和可能的观测方案，以及研究这一课题的重要科学意义和所面临的挑战和机遇．     

正常金属d_(x~2-y~2)+id_(xy)混合波超导结中的隧道谱

在Blonder-Tinkham-Klapwijk散射理论框架下,通过求解Bogoliubov-deGennes方程,计算正常金属dx2-y2+idxy混合波超导结中的准粒子输运系数和隧道谱。研究表明:隧道谱中的电导峰位置强烈地依赖电子的入射角、超导的晶轴方位和dxy波分量的强度。     

Reverse scans in square wave voltammetry

Reverse scans in square wave voltammetry (SWV) leading to the regeneration of the substance initially present in solution are studied. Widths and peak potentials of waves in SWV performed with both negative and positive potential scans allow us to determine easily the kinetic parameters of a slow electrochemical reaction. The theoretical treatment is verified using the U(V)–U(VI) system in a carbonate medium, which has already been studied by Krulic, Fatouros and Chevalet [J. Electronal. Chem. 251 (1988) 151].     

Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface

The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg—de Vries equation.     

Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis

In this preliminary paper we introduce a mathematical model based on an autocatalytic reaction scheme with termination, and general reaction orders. Rigorous stability analysis and numerical solutions are presented which illustrate that the problem can for certain parameter values admit a stable stationary pattern in the concentration of the autocatalyst and reactant. This pattern forms at the rear of a permanent form travelling wave or pulse solution.     

Shock wave interaction with porous plates

Previous detailed studies of the interaction of a shock wave with a perforated sheet considered the impact of a shock wave on a plate with regularly spaced slits giving area blockages of 60 and 67%, at various angles of incidence, and resulting in both regular and Mach reflection. The current work extends this study to a much wider variety of plate geometries. Blockage ratios of 20, 25, 33, 50, and 67 and inclinations of 45, 60, 75, and 90° to the shock wave were tested. Four different thicknesses of plate were tested at the same frontal blockage in order to assess the effects of gap guidance. Tests were conducted at two shock Mach numbers of 1.36 and 1.51 (inverse pressure ratios of 0.4 and 0.5). It is found that secondary reflected and transmitted waves appear due to the complex interactions within the grid gaps, and that the vortex pattern which is generated under the plate is also complex due to these interactions. The angle of the reflected shock, measured relative to the plate, decreases with plate blockage and the angle of inflow to the plate reduces with increasing blockage. By analysing the flow on the underside of the plate the pseudo-steady flow assumption is found to be a reasonable approximation. Both the pressure difference and the stagnation pressure loss across the plate are evaluated. It is found that over the range tested the plate thickness has a minimal effect.