试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式，再利用三阶多项式的完 全判别系统求解，由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解 关键词： 试探方程法 非线性发展方程 孤波解 Jacobi椭圆函数 周期解     

二维椭圆量子台球中的谱分析

研究了二维椭圆台球中的量子谱和经典轨道之间的对应关系.为尝试求解没有解析波函数和本征能量又不能分离变量的体系，采用了定态展开方法(expansion method for stationary states，简称EMSS)得到尽可能精确的数值解，这是闭合轨道理论被推广到计算开轨道的情况.比较了傅里叶变换谱和经典轨道，发现量子谱的峰位置与经典轨道的长度在可分辨的范围内符合得很好，这是半经典理论为经典与量子力学的联系提供桥梁作用的又一个例子. 关键词： 椭圆量子台球 定态展开方法 闭合轨道理论 量子谱     

On the boundary slip of fluid flow

For hundreds of years, in all the textbooks of classical fluid mechanics and lubrica- tion mechanics it is assumed that there was no wall slip (boundary slip) at a liquid-solid interface, i.e. no relative motion between liquid and solid at the interface. This is the no-slip boundary condition. It has been widely applied to engineering and experiments and to almost all the rheology or viscosity measurements of fluids. Rheology is one of the most important bases for fluid mechanics and lubricati…     

Direct numerical simulation methods of hypersonic flat-plate boundary layer in thermally perfect gas

High-temperature effects alter the physical and transport properties of air such as vibrational excitation in a thermally perfect gas,and this factor should be considered in order to compute the flow field correctly.Herein,for the thermally perfect gas,a simple method of direct numerical simulation on flat-plat boundary layer is put forward,using the equivalent specific heat ratio instead of constant specific heat ratio in the N-S equations and flux splitting form of a calorically perfect gas.The results calculated by the new method are consistent with that by solving the N-S equations of a thermally perfect gas directly.The mean flow has the similarity,and consistent to the corresponding Blasius solution,which confirms that satisfactory results can be obtained basing on the Blasius solution as the mean flow directly in stability analysis.The amplitude growth curve of small disturbance is introduced at the inlet by using direct numerical simulation,which is consistent with that obtained by linear stability theory.It verified that the equation established and the simulation method is correct.     

A microfluidic pumping mechanism driven by non-equilibrium osmotic effects

A mechanism is presented which drives a fluid flow using two chemically reacting molecular species and osmotic effects. For concreteness the mechanism is discussed in the context of a tube which at each end has a capping membrane which is permeable to the fluid but impermeable to the two molecular species. The chemical reactions occur at sites embedded in the capping membrane. Labeling the two chemical species A and B, at one end the reactions split each molecule of species B into two molecules of species A. On the other end two molecules of species A are fused together to form a single molecule of species B. A mathematical model of the solute diffusion, fluid flow, and osmotic effects is presented and used to describe the non-equilibrium steady-state flow rate generated. Theoretical and computational results are given for how the flow rate depends on the relative diffusivities of the solute species and the geometry of the system. An interesting feature of the pump is that for the same fixed chemical reactions at the tube ends, fluid flows can be driven in either direction through the tube, with the direction depending on the relative diffusivities of the solute species. The theoretical results are compared with three-dimensional numerical simulations of the pump.     

Evolution of the ring-like vortices and spike structure in transitional boundary layers

At the late stage of transitional boundary layers, the nonlinear evolution of the ring-like vortices and spike structures and their effects on the surrounding flow were studied by means of direct numerical simulation with high order accuracy. A spatial transition of the flat-plate boundary layers in the compressible flow was conducted. Detailed numerical results with high resolution clearly represented the typical vortex structures, such as ring-like vortices and so on, and induced ejection and sweep events...     

(n+1)维双Sine-Gordon方程的新精确解

给出包含第一种椭圆方程的三角函数型辅助方程及其解的叠加公式.在一般函数变换下,借助符号计算系统Mathematica,构造了(n+1)维双sine-Gordon方程新的Jacobi椭圆函数精确解.这些解包括了行波变换下的Jacobi椭圆函数精确解、精确孤立波解和三角函数解.     

Forward and inverse problem for cardiac magnetic field and electric potential using two boundary element methods

This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials.A torso-heart model established by boundary element method(BEM) is used for studying the distributions of cardiac magnetic fields and electric potentials.Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions,their properties and influences are compared.Then based on constructed torso-heart model and supposed current source functional model-current dipole array,the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time.Through figure and reconstructing parameter comparison,though the magnetic current dipole array imaging possesses better reconstructing effect,however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.     

Computational study of plasma-surface interaction in plasma-assisted technologies

The influence of the unevenness of substrates immersed into plasma important for plasma-based treatment of materials were studied by computer experiment. The role of both substrate properties and plasma parameters was investigated. For this analysis the combination of multidimensional fluid modelling and particle simulation was used. The fluid part of our model consisted of continuity equations for all charged species, energy balance equation for electrons and Poisson equation. The basic scattering processes were also included. The particle simulation technique was used both for the calculation of electron energy distribution function and for the derivation of quantities characterising plasma-surface interaction. This approach enabled us to study in detail the structure of the sheath and presheath near metal substrates with realistic geometries and finite dimensions. The main attention was devoted to the influence of substrate geometry in both macroscopic and microscopic spatial scales on the local electric fields in plasma.     

Physisorption kinetics of electrons at plasma boundaries

Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions leading to the formation of a quasi-stationary electron film at the boundaries. We propose to interpret the build-up of surface charges at inert plasma boundaries, where other surface modifications, for instance, implantation of particles and reconstruction or destruction of the surface due to impact of high energy particles can be neglected, as a physisorption process in front of the wall. The electron sticking coefficient s_e and the electron desorption time τ_e, which play an important role in determining the quasi-stationary surface charge, and about which little is empirically and theoretically known, can then be calculated from microscopic models for the electron-wall interaction. Irrespective of the sophistication of the models, the static part of the electron-wall interaction determines the binding energy of the electron, whereas inelastic processes at the wall determine s_e and τ_e. As an illustration, we calculate s_e and τ_e for a metal, using the simplest model in which the static part of the electron-metal interaction is approximated by the classical image potential. Assuming electrons from the plasma to loose (gain) energy at the surface by creating (annihilating) electron-hole pairs in the metal, which is treated as a jellium half-space with an infinitely high workfunction, we obtain s_e≈10^-4 and τ_e≈10^-2 s. The product s_eτ_e≈10^-6 s has the order of magnitude expected from our earlier results for the charge of dust particles in a plasma but individually s_e is unexpectedly small and τ_e is somewhat large. The former is a consequence of the small matrix elements occurring in the simple model while the latter is due to the large binding energy of the electron. More sophisticated theoretical investigations, but also experimental support, are clearly needed because if s_e is indeed as small as our exploratory calculation suggests, it would have severe consequences for the understanding of the formation of surface charges at plasma boundaries. To identify what we believe are key issues of the electronic microphysics at inert plasma boundaries and to inspire other groups to join us on our journey is the purpose of this colloquial presentation.