Logarithmic Conformal Field Theories Near a Boundary

We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two-dimensional magnetohydrodynamics is discussed.     

高斯波束对界面附近离轴球形粒子的轴向声辐射力

从声波的散射理论出发,利用级数展开法得到高斯波束的波束因子,推导其对阻抗边界下离轴球形粒子声辐射力.针对刚性球与液体球两种球形粒子进行数值模拟,与自由空间的情况进行比较.讨论边界反射系数、粒子与边界距离、束腰半径以及离轴角度与距离等对声辐射力的影响.仿真结果表明：边界反射系数的增大会引起声辐射力的增加,但不改变峰值的位置;在合适的频率处,可以产生负向声辐射力;声辐射力随粒子与边界距离呈周期性变化;束腰半径的影响主要体现在中高频;随着粒子偏离传播轴的距离和角度增大,声辐射力明显衰减.该研究为利用高斯波束实现对粒子的操纵提供理论基础.     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

Photodetachment Spectrum of Hydrogen Negative Ion Near a Partially Reflecting Spherical Surface

Photodetachment of negative ions near surfaces is of great interest in view of its fundamental significance and technological applications. We reinvestigate the dynamics of photoelectrons in H^? photodetachment near a partially reflecting spherical surface by the semiclassical closed-orbit theory. Reflection parameter R and curvature K is used to observe inelastic and spherical effects of the surface, respectively. The classical action is evaluated from the photodetached electron trajectories incident normally at the surface, arising simultaneously from the source and its image. The derived analytical formula of photodetachment cross section correctly recovers the results of reflective spherical surface published recently based on theoretical imaging method.     

Radiation Rate of a Two-Level Atom in a Spacetime with a Reflecting Boundary

We study a two-level atom in interaction with a real massless scalar quantum field in a spacetime with a reflecting boundary. We calculate the rate of change of the atomic energy for the atom. The presence of the boundary modifies the quantum fluctuations of the scalar field, which in turn modifies the rate of change of the atomic energy. It is found that the modifications induced by the presence of a boundary make the spontaneous radiation rate of an excited atom to oscillate near the boundary and this oscillatory behaviour may offer a possible opportunity for experimental tests for geometrical （boundary） effects in flat spacetime.     

Heat Kernel Asymptotics of Zaremba Boundary Value Problem

The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat Trace Asymptotics Defined by Transfer Boundary Conditions

We compute the first five terms in the short-time heat trace asymptotics expansion for an operator of the Laplace type with transfer boundary conditions using the functorial properties of these invariants.     

Oscillator Algebra With Reflecting Boundary and Generalized Statistics

The oscillator algebra with reflecting boundary is constructed together with its Fock space,and is generalized to the cases with generalized statistics and multicomponent.Such oscillators depend manifestly on the reflection factor and the statistical(exchange)factor.By construction,the Fock space of such oscillator algebras can be obtained by certain projection operation.from that of the usual bosonic oscillator without reflection condition.     

Boundary Fractal Dimensions from Sections of a Particle Profile

The fractal dimension of particles is commonly evaluated from complete particle boundaries. In this work, a study has been made of the self-similar nature of complete and incomplete boundary profiles of a range of morphologically different copper powders. Boundary images were captured from SEM micrographs of particle boundaries at a range of magnifications up to nearly 14000X. An algorithm was developed to compute the fractal dimension of boundary segments. This algorithm was tested against the Koch Island fractal, and was found to give excellent estimates of the fractal dimension. For the particle system studied, the boundary fractal was found to be sensitive to magnification with appreciable drops in value at high magnification. This demonstrates that the particles studied did not have true fractal boundaries and the use of fractal theory to study particle surface roughness must be used with caution.     

Spontaneous Emission of an Inertial Multi-Level Atom in a Spacetime with a Reflecting Plane Boundary

We calculate the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy for a multi-level hydrogen atom in the multipolar coupling scheme in a spacetime with a reflecting boundary. Our results show that, due to the presence of the boundary, the polarizations of the atom in the parallel direction and in the normal direction are weighted differently in terms of their contributions to the spontaneous emission rate, which is an oscillating function of the atom distance from the boundary. The possible experimental implications of our result are briefly discussed.     

近场接收时颗粒的消光特性

讨论了在近场接收条件下颗粒的消光特性。计算表明：在近场接收时，颗粒的实际消光将性与远场接收相比，存在很大的区别－－实际消光纱数不但同颗粒的性质和大小有关，而且与颗烊在光束中的位置相联系。对于大颗粒，近场间的消光系数在数值上也有很大差异，如果采用近场接收来测量颗粒的大小，必须考虑这些因素的影响，否则将极大增加测量误差。还论述了近场接收时消光法测量颗粒时测量区定义中的问题，论证了如何能恰当定义测量区，     

Small Mass Asymptotics for a Charged Particle in a Magnetic Field and Long-Time Influence of Small Perturbations

We consider small mass asymptotics of the motion of a charged particle in a potential combined with a magnetic field. After an appropriate regularization, a Smoluchowski-Kramers type approximation is established. This approximation allows to study long-time influence on the motion of various perturbations, deterministic and stochastic. In particular, even in the case of pure deterministic perturbations, the long-time evolution of the perturbed system can be stochastic.     

固壁面附近激光产生空泡脉动过程的实验研究

采用自行研制的光纤传感器研究了激光等离子体空泡在固壁面附近的脉动特性。实验获得了激光空泡三次膨胀到最大位置对应的波形图;并据此判定了激光空泡在脉动过程中对应的最大泡半径和溃灭周期;在此基础上结合空泡溃灭理论,计算了激光泡溃灭周期的延长因子κ。结果表明:随着脉动次数的增加,最大泡半径依次减小;随着作用激光能量的增大,最大泡半径,空泡溃灭周期的延长因子κ均增大;而无量纲参量的增大将导致延长因子的减小。所得到的延长因子同样可用于无限域流场。     

Heat Content Asymptotics for Operators of Laplace Type with Spectral Boundary Conditions

Let P be an operator of Dirac type and let D=P ² be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for D.     

Radiative Energy Shifts of an Atom Coupled to the Derivative of a Scalar Field near a Reflecting Boundary

We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom＇s distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z^4 when the atom＇s distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z^3 when z is very small     

Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.     

General Asymptotics of the Density of a Restricted Coalescing Random Walk System

These results explore the asymptotic behavior of the density of a system of coalescing random walks where particles begin from only a subspace of the integer lattice and are allowed to walk anywhere on the lattice. They generalize results by Bramson and Griffeath from 1980.⁽¹⁾ Since the probability that a given site is occupied depends on how far that site is from the originating subspace, the density of the system at a given time must be re-defined. However, the general idea is still that if the density is larger than we expect at a given time, more coalescing events will occur, and the density will correct itself over time.     

The CWKB Method of Particle Production Near the Chronology Horizon

In this paper we investigate the phenomenon of particle production of massles scalar field, in a model of spacetime where the chronology horizon could be formed, using the method of complex time WKB approximation (CWKB). For the purpose, we take two examples in a model of spacetime, one already discussed by Sushkov, to show that the mode of particle production near chronology horizon possesses the similar characteristic features as are found while discussing particle production in time dependent curved background. We get identical results as that obtained by Sushkov in this direction. We find, in both the examples studied, that the total number of particles remain finite at the moment of the formation of the chronology horizon.