非平行导线型边界下Maxwell-Chern-Simons场的Casimir效应

在路径积分量子化框架下，利用复变函数论中的保角变换与Plana求和公式，计算了（2＋1）维空间中两个非平行导线型边界下Maxwell-Chern-Simons场的Casimir效应.不引入任何截断参数，而得出有限的解析表达式. 关键词： Casimir效应 路径积分 保角变换 Plana求和公式     

Time-Correlat ion Function for Periodically-Forced Nonlinear Stochastic System

The equilibrium time-correlation function for a general cosine-forced stochastic system are calculated respectively by the perturbation theory and the linear response theory. The results obtained by the two theories are basically identical. By calculation we find that it has two terms. One is the original time-correlation function (in the case when the external signal does not exist). The other is caused by the perturbing external signal. The two terms have the same relaxation time, and the latter has oscillator behavior.     

Dynamics and control of oscillations in a complex crystalline lattice

A highly nonlinear system of acoustic and optical oscillations in a complex crystalline lattice consisting of two sublattices is analyzed. The system is obtained as a generalization of the linear Carman–Born–Kun Huang theory. Large displacements of atoms up to structure stability loss and restructuring are admitted. It is shown that the system has nontrivial solutions describing movements of fronts, emergence of periodic structures and defects. Strong interaction of acoustic and optical modes of oscillation for media without center of symmetry is demonstrated. A possibility of energy-excitation of the optical mode by means of controlling torque applied to the ends of the lattice is examined. Control algorithm based on speed-gradient method is proposed and analyzed numerically. Simulation results demonstrate that application of control may eliminate or reduce influence of initial conditions. An easily realizable nonfeedback version of control algorithm is proposed possessing similar properties.     

A model system for strong interaction between internal solitary waves

A mathematical theory is mounted for a complex system of equations derived by Gear and Grimshaw that models the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring pycnoclines in a stratified fluid. For the model in question, the Cauchy problem is of interest, and is shown to be globally well-posed in suitably strong function spaces. Our results make use of Kato's theory for abstract evolution equations together with somewhat delicate estimates obtained using techniques from harmonic analysis. In weak function classes, a local existence theory is developed. The system is shown to be susceptible to the dispersive blow-up phenomenon investigated recently by Bona and Saut for Korteweg-de Vries-type equations.     

Dynamical process of complex systems and fractional differential equations

Behavior of dynamical process of complex systems is investigated. Specifically we analyse two types of ideal complex systems. For analysing the ideal complex systems, we define the response functions describing the internal states to an external force. The internal states are obtained as a relaxation process showing a “power law” distribution, such as scale free behaviors observed in actual measurements. By introducing a hybrid system, the logarithmic time, and double logarithmic time, we show how the “slow relaxation” (SR) process and “super slow relaxation” (SSR) process occur. Regarding the irregular variations of the internal states as an activation process, we calculate the response function to the external force. The behaviors are classified into “power”, “exponential”, and “stretched exponential” type. Finally we construct a fractional differential equation (FDE) describing the time evolution of these complex systems. In our theory, the exponent of the FDE or that of the power law distribution is expressed in terms of the parameters characterizing the structure of the system.     

爱因斯坦引力场Arnowitt-Deser-Misner约束方程的两种推导方法

给出两种不同方法,分别导出爱因斯坦引力理论中著名的Arnowitt-Deser-Misner(ADM)约束方程.其一是在具有洛伦兹号差的时空中,构造一个单参数引力场作用量,由此导出单参数ADM约束方程.该参数取某特定值时对应的就是熟知的ADM约束方程.其二是将二重复函数理论运用于爱因斯坦引力场的哈密顿形式表述中,得到引力场ADM约束的二重化形式,从而也能将通常的ADM约束作为其特殊情况包含其中.此外,这两种方法还能统一地表述具有不同时空号差(洛伦兹号差和欧几里得号差)的洛伦兹引力理论和欧几里得引力理论 关键词： Arnowitt-Deser-Misner约束方程 哈密顿表述 时空号差 引力场作用量     

Induced moment antiferromagnet in an external magnetic field—II: Green's function theory

A two level two sublattice antiferromagnetic induced moment system is examined in the Green's function theory in the random phase approximation. Attentions are drawn to the effects of an externally applied magnetic field. It is shown that a “soft mode” behavior occurs at the transition field similar to that observed at the transition temperature in the absence of a field. The transition becomes first order in the RPA. The sublattice magnetizations and the transition field are significantly lowered compared to the molecular field theory results.     

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein--Maxwell theory with $p$ Abelian gauge fields (EM-$p$ theory, for short). Two EHC structural Riemann--Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-$p$ theory. This symmetry group is verified to have the structure of semidirect product of Kac--Moody group $\widehat{SU(p+1,1)}$ and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.     

Cu、Zn掺杂对AlSb电子结构和光学性质影响

运用密度泛函平面波赝势方法和广义梯度近似,对替代式掺杂Cu和Zn的闪锌矿AlSb的超晶胞晶体结构、电子结构和光学性质进行了计算。分析了其电子态分布和结构的关系,给出了掺杂前后AlSb体系的复介电常数和复折射函数。结果表明,掺有Cu和Zn的AlSb晶体空穴密度增大,会明显提高材料的电导率;两种掺杂体系光学带隙均变窄;通过分析掺杂前后AlSb晶体的复介电常数和复折射函数,解释了体系的发光机制。     

射线平板探测器成像系统的数理模型

非晶硅X射线数字平板探测器是目前唯一可取代胶片照相的新型技术,对其成像特性的研究已成为高像质的DR和三维CT检测技术的基础。目前X射线成像系统均是以线性时不变理论作为分析基础的。基于X射线平板探测器成像系统、成像机理和几何参数建立了成像系统的点扩展函数(PSF)。用圆柱体等效二维PSF模型,使成像系统退化为比例系统,从而把复杂的反卷积运算转化成用代数方程来求解,能够快速实现通过探测器输出图像来估计透照工件的二维输入图像。此模型的建立为在实际检测中利用输出的图像通过线性变换得到输入估计。在DR系统中,基于上述数理模型建立了灵敏度模型,利用输出场强可以很好的再现输入场强。     

Invariant resolutions for several Fueter operators

A proper generalization of complex function theory to higher dimension is Clifford analysis and an analogue of holomorphic functions of several complex variables were recently described as the space of solutions of several Dirac equations. The four-dimensional case has special features and is closely connected to functions of quaternionic variables. In this paper we present an approach to the Dolbeault sequence for several quaternionic variables based on symmetries and representation theory. In particular we prove that the resolution of the Cauchy–Fueter system obtained algebraically, via Gröbner bases techniques, is equivalent to the one obtained by R.J. Baston (J. Geom. Phys. 1992).     

The properties of conformal blocks,the AGT hypothesis,and knot polynomials

Various properties of correlators of the two-dimensional conformal field theory are discussed. Specifically, their relation to the partition function of the four-dimensional supersymmetric theory is analyzed. In addition to being of interest in its own right, this relation is of practical importance. For example, it is much easier to calculate the known expressions for the partition function of supersymmetric theory than to calculate directly the expressions for correlators in conformal theory. The examined representation of conformal theory correlators as a matrix model serves the same purpose. The integral form of these correlators allows one to generalize the obtained results for the Virasoro algebra to more complicated cases of the W algebra or the quantum Virasoro algebra. This provides an opportunity to examine more complex configurations in conformal field theory. The three-dimensional Chern–Simons theory is discussed in the second part of the present review. The current interest in this theory stems largely from its relation to the mathematical knot theory (a rather well-developed area of mathematics known since the 17th century). The primary objective of this theory is to develop an algorithm that allows one to distinguish different knots (closed loops in three-dimensional space). The basic way to do this is by constructing the so-called knot invariants.     

A discontinuous Galerkin method for the Vlasov–Poisson system

A discontinuous Galerkin method for approximating the Vlasov–Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates of the approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov–Poisson system.     

The adaptive synchronization of fractional-order Liu chaotic system with unknown parameters

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule and a proper Lyapunov candidate function, the unknown coefficients of the system are estimated and the stabilization of the synchronizer system is demonstrated. Finally, the numerical simulation illustrates the efficiency of the proposed method in synchronizing two chaotic systems.     

Fermionization of two distinguishable fermions

We study a system of two distinguishable fermions in a 1D harmonic potential. This system has the exceptional property that there is an analytic solution for arbitrary values of the interparticle interaction. We tune the interaction strength and compare the measured properties of the system to the theoretical prediction. For diverging interaction strength, the energy and square modulus of the wave function for two distinguishable particles are the same as for a system of two noninteracting identical fermions. This is referred to as fermionization. We have observed this phenomenon by directly comparing two distinguishable fermions with diverging interaction strength with two identical fermions in the same potential. We observe good agreement between experiment and theory. By adding more particles our system can be used as a quantum simulator for more complex systems where no theoretical solution is available.     

Al，Mg掺杂GaN电子结构及光学性质的第一性原理研究

基于密度泛函理论,采用广义梯度近似方法,计算了Al,Mg掺杂的闪锌矿型GaN的电子结构和光学性质,分析了其电子态分布与结构的关系,给出了掺杂前后GaN体系的介电函数和复折射率函数.计算结果表明掺有Mg的GaN晶体空穴浓度增大,会明显提高材料的电导率,而Al掺杂GaN晶体的载流子浓度不变,只是光学带隙变宽;通过分析掺杂前后GaN晶体的介电函数和复折射率函数,解释了体系的发光机理,为GaN材料光电性能的进一步开发与应用提供了理论依据.通过比较可知,所得出的计算结果与现有文献符合得很好. 关键词： GaN晶体 电子结构 光学性质 掺杂     

Ultrarelativistic black-hole encounters

A method is given for investigating the ultrarelativistic encounter of two black holes which complements the usual low-speed approximation. It depends on the fact that the ultrarelativistic limit of a moving Schwarzschild black hole is a certain plane-fronted impulsive gravitational wave. This enables linearized theory on a curved background to be used. The solution is obtained, with the help of generalized function techniques, to the first order in the background energy, and the radiation pattern at conformal null infinity is examined. The whole approach has a strong connection with the theory of twistors.     

Role of spectrally varying mount properties in influencing coupling between powertrain motions under torque excitation

The influence of spectrally varying mount properties (including stiffness and damping) on the dynamics of powertrain motions is analytically examined. To overcome the deficiency of the direct inversion method (limited to only the frequency domain analysis), two methods are developed that describe the mount elements via a transfer function (in Laplace domain) or analogous mechanical model. New analytical formulations are verified by comparing the frequency responses with numerical results obtained by the direct inversion method (based on Voigt type mount model). Eigensolutions and transient responses of a spectrally varying mounting system are also predicted from new models. Based on complex eigenstructure, new coupling indices, including modal kinetic energy fractions, are defined for each method. Complex eigenvalue problem formulation with spectrally varying properties provides a closer match with measured natural frequencies than the real eigensolution with frequency-independent mounts. Given spectral variance in the mount properties, a simple roll mode decoupling scheme is suggested for the powertrain isolation system. Finally, an axiom for torque roll axis decoupling is provided by employing direct and adjoint eigenvalue problems.     

Exact solutions to the angular Teukolsky equation with s ≠ 0

We first convert the angular Teukolsky equation under the special condition of τ ≠ 0, s ≠ 0, m=0 into a confluent Heun differential equation (CHDE) by taking different function transformation and variable substitution. And then according to the characteristics of both CHDE and its analytical solution expressed by a confluent Heun function (CHF), we find two linearly dependent solutions corresponding to the same eigenstate, from which we obtain a precise energy spectrum equation by constructing a Wronskian determinant. After that, we are able to localize the positions of the eigenvalues on the real axis or on the complex plane when τ is a real number, a pure imaginary number, and a complex number, respectively and we notice that the relation between the quantum number l and the spin weight quantum number s satisfies the relation l=∣s∣+ n, n=0, 1, 2···. The exact eigenvalues and the corresponding normalized eigenfunctions given by the CHF are obtained with the aid of Maple. The features of the angular probability distribution (APD) and the linearly dependent characteristics of two eigenfunctions corresponding to the same eigenstate are discussed. We find that for a real number τ, the eigenvalue is a real number and the eigenfunction is a real function, and the eigenfunction system is an orthogonal complete system, and the APD is asymmetric in the northern and southern hemispheres. For a pure imaginary number τ, the eigenvalue is still a real number and the eigenfunction is a complex function, but the APD is symmetric in the northern and southern hemispheres. When τ is a complex number, the eigenvalue is a complex number, the eigenfunction is still a complex function, and the APD in the northern and southern hemispheres is also asymmetric. Finally, an approximate expression of complex eigenvalues is obtained when n is greater than ∣s∣.