Neumann Boundary Conditions Inhibiting SSB in Coleman-Weinberg Mechanism

In this work we show that homogeneous Neumann boundary conditionsinhibit the Coleman-Weinberg mechanism for spontaneous symmetry breakingin the scalar electrodynamics if the length of the finite region is small enough (a = e²M^-1_φ, where M_φ is the mass of the scalar field generated by the Coleman-Weinberg mechanism).     

Random Motions at Finite Speed in Higher Dimensions

We present a general method of studying the transport process , t≥0, in the Euclidean space ℝ ^m , m≥2, based on the analysis of the integral transforms of its distributions. We show that the joint characteristic functions of are connected with each other by a convolution-type recurrent relation. This enables us to prove that the characteristic function (Fourier transform) of in any dimension m≥2 satisfies a convolution-type Volterra integral equation of second kind. We give its solution and obtain the characteristic function of in terms of the multiple convolutions of the kernel of the equation with itself. An explicit form of the Laplace transform of the characteristic function in any dimension is given. The complete solution of the problem of finding the initial conditions for the governing partial differential equations, is given. We also show that, under the standard Kac condition on the speed of the motion and on the intensity of the switching Poisson process, the transition density of the isotropic transport process converges to the transition density of the m-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension m. We give the conditional characteristic functions of the isotropic transport process in terms of the inverse Laplace transform of the powers of the Gauss hypergeometric function. Some important models of the isotropic transport processes in lower dimensions are considered and some known results are derived as the particular cases of our general model by means of the method developed.     

Inflow conditions for spatial direct numerical simulation of turbulent boundary layers

The inflow conditions for spatial direct numerical simulation (SDNS) of turbulent boundary layers should reflect the characteristics of upstream turbulence, which is a puzzle. In this paper a new method is suggested, in which the flow field obtained by using temporal direct numerical simulation (TDNS) for fully developed turbulent flow (only flow field for a single moment is sufficient) can be used as the inflow of SDNS with a proper transformation. The calculation results confirm that this method is feasible and effective. It is also found that, under a proper time-space transformation, all statistics of the fully developed turbulence obtained by both temporal mode and spatial mode DNS are in excellent agreement with each other, not only qualitatively, but also quantitatively. The normal-wise distributions of mean flow profile, turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses of the fully developed turbulence obtained by using SDNS, bear similarity in nature. Supported by the National Natural Science Foundation of China (Grant No. 90205021), the China Postdoctoral Science Foundation (Grant No. 20060400707), and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200328), and partially supported by Liu-Hui Center of Applied Mathematics, Nankai University and Tianjin University     

Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

Bounded holomorphic functions and maps with some boundary behavior

Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions.     

近自由面细长体的振荡问题

本文引进细长体的假定,把三维的流体运动问题化成了二维的非定常问题。前面剖面对后面剖面的干扰作用用积分表示,对物体作了适当近似以后,改善了切片理论。根据物面条件把整个问题的求解分解为兴波问题和振荡问题,而振荡问题可由兴波问题的适当组合表示出来。这样,大大简化了问题的求解。作为例子,本文数值计算了细长体的水动力导数,给出了结果。     

Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is Mp+1×Tq which has q dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature regardless of the boundary conditions assumed on the compact torus. The asymptotic limits of the Casimir force in the small plate separation limit are also obtained.     

Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers

We present a modelling approach for photonic crystal structures and vertical-cavity surface-emitting lasers (VCSELs). This method is based on vectorial eigenmode expansion combined with perfectly matched layer (PML) boundary conditions. Compared to other methods, a relatively small computational effort is required, while at the same time accurate results are obtained, even in the presence of strong scattering and diffraction losses.     

Uniform theory of the boundary diffraction wave

A uniform version of the potential function of the Maggi-Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.     

伏安法测电阻时安培表采用内、外接法的判定条件

导出了在物理实验中用伏安法测电阻时安培表采用内、外接法的判定条件,并在实验上给予了验证．