理性、有序地建设探究实验室

建设探究实验室是提高学生对学习、学科兴趣的重要举措.本文提出了一套探究实验室评价方案以期对实验室的建设和发展有所帮助.总体评价和导向性评价基于对一个个实验就一些指标进行评估以及其后的统计.我们还对一些深层次的要求和指标进行了探讨.     

The sound power of an individual mode of a clamped-free annular plate

The main aim of this study is an analysis of sound radiation of some clamped-free and free-clamped annular plates. The plates are embedded in some infinite perfectly rigid baffles and vibrate with the free-field condition satisfied. The Kirchhoff-Love linear theory of a perfectly elastic plate is used to solve the plates’ equations of motion. The sound pressure at the plates’ surfaces is expressed by its Hankel transform. The closed-path integral technique known from the literature and the stationary-phase method are used to find the standardized active and reactive sound power of an individual mode in the form of some high-frequency asymptotic formulae useful for some highly efficient engineering computations. Their non-oscillating and oscillating parts have been separated. It is assumed that the vibration and sound radiation are axisymmetric and time harmonic. Low fluid loading is also assumed. The complex sound power of an individual mode forms the basis for computing the total sound power of some excited and damped vibrations in the fluid. The total sound power is not discussed in this study.     

Microlocalization of Resonant States and Estimates of the Residue of the Scattering Amplitude

We obtain some microlocal estimates of the resonant states associated to a resonance z₀ of an h-differential operator. More precisely, we show that the normalized resonant states are outside the set of trapped trajectories and are in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove such a bound in some examples.     

Geometric Simultaneity and the Continuity of Special Relativity

In this note I briefly discuss some aspects of relative geometric simultaneity in special relativity. After saying a few words about the status and nature of Minkowski spacetime in special relativity, I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.     

Directed Transport of Brownian Particles in a Periodic Channel

The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears.     

Directed Transport of Brownian Particles in a Periodic Channel

The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears.     

Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.     

Modular values and weak values of quantum observables

The concept of a modular value of an observable of a pre- and postselected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an effective interaction when the coupling is weak, it describes a coupling of any strength but only to qubit meters. The generalization of the concept for a coupling of a composite system to a multiqubit meter provides an explanation of some current experiments.     

Solitons for a generalized variable-coefficient nonlinear Schrdinger equation

In this paper,we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear Schrdinger equation (NLS) with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions,one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results,some previous one-and two-soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one-and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.     

对冲击电流计测直螺线管磁场的两项改进措施

通过一些具体数据，对冲击电流计测直螺线管磁场的实验进行了分析，指出了两个重要误差来源，并介绍了改进措施。     

Relativistic Simultaneity and Causality

We analyzed two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer. These foliation structure allows us to incorporate the simultaneity submanifolds for studying some dynamical systems, for instance free elementary massless particles.     

Geometrically nonlinear flexural vibrations of plates: In-plane boundary conditions and some symmetry properties

This study is devoted to the derivation of some properties of the von Kármán equations for geometrically nonlinear models of plates, with a boundary of arbitrary shape, for applications to nonlinear vibration and buckling. An intrinsic formulation of the local partial differential equations in terms of the transverse displacement and an Airy stress function as unknowns is provided. Classical homogeneous boundary conditions—with vanishing prescribed forces and displacements—are derived in terms of the Airy stress function in the case of a boundary of arbitrary geometry. A special property of this operator, crucial for some energy-conserving numerical schemes and called “triple self-adjointness”, is derived in the case of an edge of arbitrary shape. It is shown that this property takes a simple form for some classical boundary conditions, so that the calculations in some practical cases are also simplified. The applications of this work are either semi-analytical methods of solution, using an expansion of the solution onto an eigenmode basis of the associated linear problem, or special energy-conserving numerical methods.     

Meromorphic continuation approach to noncommutative geometry

Following an idea of Nigel Higson, we develop a method for proving the existence of a meromorphic continuation for some spectral zeta functions. The method is based on algebras of generalized differential operators. The main theorem states, under some conditions, the existence of a meromorphic continuation, a localization of the poles in supports of arithmetic sequences and an upper bound of their order. We give an application in relation to a class of nilpotent Lie algebras.     

修改形式的机械补偿器

为便于产生和分析各种椭圆偏振光 ,需要有产生椭圆偏振光的光学元件 ,其中一个重要的光学元件就是补偿器。补偿器有多种类型 ,在机械补偿器中应用最广泛的是巴俾涅补偿器和索累补偿器 ,但它们各有其缺点。现设计出了一种新的补偿器件 ,它克服了这两种补偿器的不足 ,结构简单、操作方便。     

New aspects on current enhancement in Brownian motors driven by non-Gaussian noises

Recent studies on Brownian motors driven by colored non-Gaussian noises have shown that the departure of the noise distribution from Gaussian behavior induces an enhancement of its current and efficiency. Here, we discuss some new aspects of this phenomenon focusing on some analytical results based on an adiabatic approximation and in the analysis of the role of long probability distribution tails.     

δ-Function Operator Formulas of Photon Creation and Annihilation Operators

Using the technique of integration within an ordered product of operators we derive some &function operator formulas of photon creation and annihilation operators. Applications of these new formulas in simplifying some Louisell's operator theorems and in discussing the eigenket of creation operator are presented.     

The ’t Hooft vertex revisited

In 1976 ’t Hooft introduced an elegant approach towards understanding the physical consequences of the topological structures that appear in non-Abelian gauge theories. These effects are concisely summarized in terms of an effective multi-fermion interaction. These old arguments provide a link between a variety of recent and sometimes controversial ideas including discrete chiral symmetries appearing in some models for unification, ambiguities in the definition of quark masses, and flaws with some simulation algorithms in lattice gauge theory.     

Gravity from self-interaction redux

I correct some recent misunderstandings about, and amplify some details of, an old explicit non-geometrical derivation of GR.     

矩量法研究平面波导点缺陷引起的散射损耗

对平面波导工艺过程里出现的点缺陷,如气泡、灰尘颗粒等对平面波导内光场造成的散射提供了一种简单而又实用的计算方法。计算基于格林函数方法,并利用矩量法求解积分方程,采用分块矩阵优化算法,使得算法的计算时间直接与点缺陷大小相关,提高了效率。证明了一定大小的点缺陷在特定的波长处会产生很大的散射损耗,证明点缺陷的散射损耗依赖于缺陷大小和光学性质而与其在波导中的位置无直接关系。以二氧化硅平面波导为例,分析了对中心波长1．55μm的入射光场,分别存在气泡和灰尘颗粒两种点缺陷时,散射损耗随点缺陷大小的关系特性,指出工艺过程特别应该避免某些孔径的点缺陷。