A hierarchy of rational Timoshenko dispersion relations

This paper shows that the conventional Timoshenko dispersion relation for bending waves is the (0,1) member of a two-parameter family (m,n) of approximations to the exact dispersion relation obtained from linear elasticity. Higher members of the family are shown to converge rapidly to the exact dispersion relation; in particular, any number of branches can be captured accurately over their entire length, i.e. up to arbitrarily high frequencies and wavenumbers. The theory admits a rigorous accuracy analysis, and demonstrates that the conventional Timoshenko dispersion relation is a completely rational approximation, thus answering some previous doubts about this matter. Lower members of the two-parameter family include the Euler-Bernoulli dispersion relation and a Rayleigh-type inertia correction. Especially useful is the Timoshenko (1,2) dispersion relation, which extends the conventional Timoshenko (0,1) dispersion relation by capturing the first four branches of the exact dispersion relation rather than merely the first two, and is accurate over a wide range. An inertia-corrected Timoshenko dispersion relation is also derived, and is shown to include many previous approximations as special cases.     

A comparative study of the full dispersion relation, Compton dispersion relation, and Raman dispersion relation of a free-electron laser in helical wiggler and guiding magnetic fields

The full dispersion relation obtained for a free-electron laser in the presence of circularly polarized, periodic, static wiggler and guiding magnetic fields by the kinetic approach incorporating the particle trajectories is reduced to Compton and Raman regime approximations in the case of a tenuous electron beam. The temporal growth rate has been compared between the full dispersion relation and the Compton dispersion relation, as well as between the full dispersion relation and the Raman dispersion relation in the microwave region. The results show the maxima of growths in the full dispersion relation and the Compton dispersion relation, as well as the full dispersion relation and the Raman dispersion relation, are at the same locations, but the growth rates in both regimes are enhanced with respect to the full dispersion relation for the same plasma frequency and cavity parameters.     

热敏电阻温度计的线性化设计

基于惠斯通非平衡电桥的热敏电阻温度计,其电压—温度的关系是非线性的。在此基础上利用运算放大电路,通过选择合适的电路参数可以使电压与温度的关系线性化。实验结果与利用计算程序软件得到电压—温度特性的理论值非常接近。     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

A rigorous uncertainty relation (Cauchy Inequality) for an electromagnetic field in quantum superpositions of coherent states and in a two-photon coherent state

It is shown that the Heisenberg uncertainty relation (or soft uncertainty relation) determined by the commutation properties of operators of electromagnetic field quadratures differs significantly from the Robertson–Schrödinger uncertainty relation (or rigorous uncertainty relation) determined by the quantum correlation properties of field quadratures. In the case of field quantum states, for which mutually noncommuting field operators are quantum-statistically independent or their quantum central correlation moment is zero, the rigorous uncertainty relation makes it possible to measure simultaneously and exactly the observables corresponding to both operators or measure exactly the observable of one of the operators at a finite measurement uncertainty for the other observable. The significant difference between the rigorous and soft uncertainty relations for quantum superpositions of coherent states and the two-photon coherent state of electromagnetic field (which is a state with minimum uncertainty, according to the rigorous uncertainty relation) is analyzed.     

光子晶体光纤非线性系数与其结构参量及光波长的关系

推导计算了全内反射型光子晶体光纤的非线性系数与其两个几何结构参量:包层空气孔半径和空气孔间距之间的关系,给出了输入光波长为1550 nm处,非线性系数与这两个结构参量之间的关系曲线并对其进行了分析.给出了全内反射型光子晶体光纤的非线性系数随输入光波长变化的曲线,分析了短波处高非线性系数产生的原因并指出这一特性的应用潜力.     

Mask相位法校准液晶空间光调制器的相位调制特性

提出Mask相位法校准出厂标定波长在532 nm的液晶空间光调制器(LC-SLM)在561 nm处的相位调制特性曲线.首先基于傅里叶光学模拟计算得出棋盘型二维相位光栅相位对比度与零级衍射光斑光强之间的对应关系,然后搭建实验光路测量计算机所发灰度图所对应的零级衍射光斑光强值.根据前面两组结果最后得到相位延迟量与计算机灰度...     

Transformation of recursion relations for generalized random walks

It is shown that recursion relation for the generalized random walks (GRW) or correlated random walks can be directly transformed into the recursion relation for the usual random walks. The recursion relation for the GRW is expressed by a non-linear difference equation. To transform the non-linear difference equation, the Hopf-Cole transformation is modified and expressed in a discrete form. Formal solution of the GRW is obtained in an integral representation.     

Causal groups of space-time

The present paper is concerned with a finite dimensional space, considered as a real ordered linear space, directed with respect to a partial ordering relation (causal relation) in which a given reflexion (called temporal inversion) is antiisotone and the positive cone is closed in the euclidean topology.A generalized Zeeman theorem [1] is obtained, which states that the causal group relative to the causal relation is a subgroup of the affine group ofM.     

Dispersion of laser generated surface waves in an epoxy-bonded layered medium

In this paper, the dispersion of laser generated surface wave in an epoxy bonded copper-aluminum layered specimen is studied. A laser ultrasonic experiment based on the point-source/point-receiver (PS/PR) technique was conducted to measure the surface wave signals in the layered specimen. The received wave signals were then processed in the frequency domain to obtain the dispersion relation of the fundamental surface wave mode. Theoretical calculations of the dispersion relations of the fundamental surface wave modes in two-layered and three-layered specimens were conducted to explore the influence of the bonding layer thickness on the dispersion relation. The experimental dispersion relation for the epoxy bonded copper-aluminum layered specimen is in good agreement with the calculated dispersion relation. The influence of the bonding layer thickness on the dispersion relation is studied and the potential application of the present results to the NDE of bonded layered media based on laser ultrasonics is also addressed.     

First-principles study of the thermal properties of half-metallic ferromagnetic systems

The origin of the half-metallicity is different in diluted magnetic semiconductors and Heusler alloys. I briefly review our earlier work on (GaMn)As and (GaMn)N focusing on the relation between the half-metallicity and the strength of the interatomic exchange interactions. This relation is governed by the properties of the valence-band holes. In Heusler alloys the factors determining the thermal behavior are distinct. Here the relation between half-metallicity and the longitudinal fluctuations of atomic moments is considered. The temperature dependence of the Ni magnetization in NiMnSb is studied.     

Bohr-Mottelson转动谱公式参数之间的新关系式

在利用Harris两参数公式研究Bohr-Mottelson转动谱公式参数之间的关系的基础上,改用Harris三参数公式,并由此提出了Bohr-Mottelson转动谱公式参数之间的新关系式,进而用I(I+1)四参数展开式计算了A～60,80,130,140,150,190区超形变偶偶核的基带和锕系和稀土区正常形变核基带,讨论了参数之间的关系,发现新关系式与实验较好地符合.     

X波段相对论速调管放大器同轴双间隙输出腔输出特性

 设计了工作在X波段的相对论速调管放大器同轴双间隙输出结构,并采用3维PIC程序对其进行了粒子模拟,分析了输出微波功率随直流渡越角、输出腔品质因数值等相关参数的变化,对输出腔体结构进行了优化设计。模拟结果表明：同轴双间隙输出结构可以降低束流的势能,增加束流与腔体的作用时间,提高速调管的微波提取效率。模拟中采用束压600 kV、束流5 kA、调制深度100%和峰值频率9.37 GHz的电子束以及1T的轴向引导磁场强度,得到了周期平均功率1.2 GW、峰值频率9.37 GHz、效率40%的微波输出。     

Extension of an empirical charged lepton mass relation to the neutrino sector

It is known that the charged lepton masses obey to high precision an interesting empirical relation (Koide relation). In turn, the light neutrino masses cannot obey such a relation. We note that if neutrinos acquire their mass via the seesaw mechanism, the empirical mass relation could hold for the masses in the Dirac and/or heavy Majorana mass matrix. Examples for the phenomenological consequences are provided. We furthermore modify the mass relation for light neutrino masses including their Majorana phases, and show that it can be fulfilled in this case as well, with interesting predictions for neutrinoless double beta decay.     

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials. The phonon dispersion relation, as well as the vibrational density of states, is also often used as an indicator of variation of lattice thermal conductivity with the external stress, defects, etc. In this study, a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package. The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present. The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell. Then, the phonon dispersions corresponding to several potentials or force fields, which are commonly used in the LAMMPS package to modeling the graphene, are obtained to compare with that from the DFT calculation. They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation. The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell, which predicts the phonon band gaps along the cross-plane direction. Since the phonon dispersion relation plays an important role in the physical properties of condensed matter, the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.     

Validity of the Einstein relation in disordered organic semiconductors

It is controversial whether energetic disorder in semiconductors is already sufficient to violate the classical Einstein relation, even in the case of thermal equilibrium. We demonstrate that the Einstein relation is violated only under nonequilibrium conditions due to deeply trapped carriers, as in diffusion-driven current measurements on organic single-carrier diodes. Removal of these deeply trapped carriers by recombination unambiguously proves the validity of the Einstein relation in disordered semiconductors in thermal (quasi)equilibrium.     

电子束电流对介质切伦科夫脉塞色散关系的影响

采用等离子体流体理论,从线性扰动方程出发,研究了电子束电流大小对介质切伦科夫脉塞中束波相互作用色散关系的影响,得到了当等离子体返回电流能有效中和与不能有效中和电子束电流两种情形下色散关系和波的增长率,并讨论了电子束电流对束波相互作用色散关系和波增长率的影响。研究表明,等离子体返回电流能有效中和与不能有效中和电子束电流两种情况下有着不同的色散关系和波的增长率。在波导参数和背景等离子体参数固定的情况下,电子束电流并不是越大越好,电子束电流过大不利于提高器件效率,它们之间存在最佳匹配关系。     

Scaling and universality in electrical failure of thin films

We describe the electrical failure of thin films as a percolation in two-dimensional random resistor networks. We show that the resistance evolution follows a scaling relation expressed as R approximately epsilon(-&mgr;) where epsilon = (1-t/tau), tau is the time of electrical failure of the film, and &mgr; is the same critical exponent appearing in the scaling relation between R and the defect concentration. For uniform degradation the value of &mgr; is universal. The validity of this scaling relation in the case of nonuniform degradation is proved by discussing the case in which the failure is due to a filamentary defect growth. The existence of this relation allows predictions of failure times from early time measurements of the resistance.     

Derivation of the pulse front tilt caused by angular dispersion

A simple and device-independent derivation of the relation between the angular dispersion and the pulse front tilt of short pulses is given. The obtained relation is also applicable when material dispersion is present.     

Kramers-Kronig type of dispersion relation in nonlinear optics

The applicability of Kramers-Kronig (K-K) relation under nearly sharp resonant transition regime in narrow-gap semiconductors has been established and consequently, a generalized dispersion relation for nonlinear optical susceptibility of a dielectric is derived. This relation can be employed in the study of nonlinear optical processes in solids as well as in plasmas over a wide frequency spectrum.