A unified study on the output probability distribution of arbitrary linear vibratory systems with arbitrary random excitation

New theoretical expressions of probability density and cumulative distribution functions for the output response are exactly derived without any simplification of the problem and any approximation of analysis in the case when a general random signal with arbitrary probability distribution and correlation functions is passed through an arbitrary linear vibratory system with finite order. The result is given as an explicit solution of expansion series in a functional form of input statistics and vibratory system parameters, and not given as a mere numerical solution by use of a recurrence algorithm. An effect of random input and system characteristics is concretely reflected in the expansion coefficients. The experimental results obtained by digital simulation are in good agreement with the theory. Thus, the above theory is experimentally confirmed for some typical examples by the method of digital simulation.     

Nuclear magnetic resonance chemical shift in an arbitrary electronic spin state

We present a general and systematic electronic structure theory of the nuclear magnetic resonance shielding tensor and the associated chemical shift for paramagnetic atoms, molecules, and nonmetallic solids. The approach is for the first time rigorous for an arbitrary spin state as well as arbitrary spatial symmetry and is formulated without reference to spin susceptibility. The leading-order magnetic-field dependence of shielding is derived. The theory is demonstrated by first principles calculations of organometallic molecules.     

Local quantum statistics in arbitrary curved space-time

A local quantum statistics based on a finite temperature field theory in an arbitrary Riemann space-time is considered. The expressions have been derived for the partition functions, the grand thermodynamic potential and the particle distributions 〈n _k〉 of massive scalar gas and fermion gas in arbitrary space-time. It is shown that the chemical potential depends on the geometry of manifold.     

Gaseous ion mobility and diffusion in electric fields of arbitrary strength

In a previous paper we presented the first kinetic theory of gaseous ion mobility which is valid for electric fields of arbitrary strength and for arbitrary ion-neutral interaction potentials and mass ratios. In this paper we extend this theory to gaseous ion diffusion and systematize it so as to greatly decrease the effort involved in computing high approximations to the transport coefficients. Analytical results in low approximation are discussed, as are scaling rules for ion mobilities and diffusion coefficients. An extensive study of the convergence of the successive approximations of this theory is given for model systems, from which it is concluded that the theory is accurate, particularly in third and higher approximation, when applied to ion mobility and mean kinetic energy. When applied to diffusion, the theory is less successful in some circumstances, but it is still the best general theory currently available.     

QED in arbitrary linear media: Amplifying media

Recently, we have developed a unified approach to QED in arbitrary linearly responding media in equilibrium—media that give rise to absorption [Phys. Rev. A 75, 053813 (2007)]. In the present paper we show that, under appropriate conditions, the theory can be quite naturally generalized to amplifying media the effect of which is described within the framework of linear response theory. We discuss the limits of validity of the generalized theory and make contact with earlier quantization schemes suggested for the case of linearly and locally responding amplifying dielectric-type media. To illustrate the theory, we present the electromagnetic-field correlation functions that determine the Casimir force in the presence of amplifying media.     

Axial anomaly in lattice abelian gauge theory in arbitrary dimensions

The axial anomaly of lattice abelian gauge theory on a hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.     

Quantum Langevin equation and input-output fields for arbitrary linear response

A retarded quantum Langevin equation is derived for a small subsystem coupled to an arbitrary number of large reservoirs by treating the small back-action on the reservoir within linear response theory. Interpreting the coupling to the reservoirs as input to the small subsyste, and using the advanced quantum Langevin equation to define the corresponding output emitted into the reservoirs, causally connected input and output variables are constructed which are used to set up anS-matrix formalism relating input and output variables in a unitary and causal way. An application to squeezing by subharmonic generation with arbitrary linear response is given.     

Algebraic classification of Weyl anomalies in arbitrary dimensions

Conformally invariant systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to the Weyl invariance of classical massless field systems in interaction with gravity. In the quantum theory, the latter symmetry no longer survives: A Weyl anomaly appears. Anomalies are a cornerstone of quantum field theory, and, for the first time, a general, purely algebraic understanding of the universal structure of the Weyl anomalies is obtained, in arbitrary dimensions and independently of any regularization scheme.     

Electron transport and permittivity in a plasma with an arbitrary ionic charge

Based on the solution of a linearized kinetic equation for electrons with a Landau collision integral, we develop a theory of electron transport for small perturbations in a completely ionized plasma with an arbitrary ionic charge that is free from any constraints on the characteristic perturbation time and length scales. We calculate the potential and vortex electron fluxes for an arbitrary electron collision frequency that allow the spatial and temporal nonlocal transport to be described. We also derive expressions for the longitudinal and transverse electron permittivities of a collisional plasma with an arbitrary ionic charge that are suitable for describing the plasma response to small perturbations with an arbitrary frequency and wave vector. Using the transverse permittivity, which allows the absorption of an electromagnetic wave to be described in the entire range of plasma parameters (from the strongly collisional to the collisionless one), as an example, we provide a detailed comparison with previously known models.     

任意分集方式多输入多输出无线通信系统的统计信道建模

针对极化分集多输入多输出系统的传统统计模型存 在着对不同极化方向上的功率变化设置不合理的问题, 提出一种功率矩阵对其进行纠正; 对采用不同分集方式的多输入多输出系统信道建模的原理进行分析, 提出对功率矩阵和相关矩阵进行复合计算的方法, 建立了一种适用于任意分集方式多输入多输出系统的统计信道模型, 该模型能够确切反映出同时受到距离分集和极化分集影响的多输入多输出系统之统计特征.     

Variational solution of the superconducting proximity effect for arbitrary mean free path

We have developed an improved variational calculation of superconducting transition temperatures for non-homogeneous systems with arbitrary electron mean free path. This form of the variational theory is at least as accurate as the diffusion theory. Calculations have been carried out for both planar and spherical geometries: we obtain an approximate scaling law involving a characteristic length which is essentially the generalized coherence length of Silvert and Cooper.     

均质多边形薄板绕任一对角线转动的转动惯量

运用均质三角形薄板对任一边、对过顶点且与对边平行的轴的转动惯量公式,得到了用薄板的质量、边长及对角线长表示的均质多边形薄板对任一对角线的转动惯量.     

Generalized thermal radiation from arbitrary fractional dimension

Properties of the thermal radiation from arbitrary fractional dimension are investigated. Generalized blackbody radiation for arbitrary dimension can be obtained and the energy density is shown as a function of arbitrary dimension as well as temperature. Maximum frequency factor representing the relation between most probable photon energy and thermal energy is shown as a function of arbitrary fractional dimension. It is also shown how to measure the arbitrary fractional dimension of the body with thermal radiation.     

Generic Bell inequalities for multipartite arbitrary dimensional systems

We present generic Bell inequalities for multipartite arbitrary dimensional systems. The inequalities that any local realistic theory must obey are violated by quantum mechanics for even dimensional systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities that are violated for all the systems including odd dimensional systems.     

Expansion on free-space modes for fast and accurate evaluation of vectorial modes of arbitrary waveguides

A novel method of expansion of the mode of an arbitrary waveguide on the modes of free space based on coupled-mode theory is presented. We propose a detailed algorithm based on this expansion to solve efficiently waveguide problems. We call this method Vectorial Free-Space Mode Expansion Method (VFSMEM). It is shown to have the potential to deliver precise fields and effective indices of arbitrary waveguides in a short computation time. Several possible improvements on our current implementation are also presented.     

Zitterbewegung of particles with arbitrary spin

The existence of zitterbewegung of particles with higher spins (s≥1) is proved. The investigation is based on the idea of Curie, Jordan, and Sudarshan that there are two aspects of relativistic invariance and also on the determination of the dynamical variables that describe systems with arbitrary spin obtained by Jordan and Mukunda. A number of new paradoxical properties of zitterbewegung unknown in Dirac theory is revealed. For example, particles with high spins (s≥1) can have a velocity greater than light. It is shown in a general form that elimination of zitterbewegung in all directions of space, or even only in a plane, is impossible. There can be only partial liquidation of zitterbewegung, in one of the directions of space, and then only at the price of violation of relativistic invariance of the theory. Finally, it is suggested that the paradoxical properties of zitterbewegung can be understood by redefining the momentum and mass operators. In this way, a connection between zitterbewgung and tachyons is established.     

轴对称渐变型类周期慢波结构的色散特性

 运用场匹配法和傅里叶级数理论,提出一种原则上可数值求解任意轴对称渐变型类周期慢波结构色散特性的方法。采用该方法编制了计算渐变型波纹波导和渐变型盘荷波导色散曲线的Matlab程序,详细分析并讨论了这两类典型渐变型类周期慢波结构的色散特性。数值计算结果与多维全电磁模拟软件模拟结果的数据吻合度较高,验证了该数值算法的可靠性。另外,该方法具有较强的普适性和扩展性,也可退化到任意轴对称周期慢波结构色散特性的求解,为慢波结构的设计提供一种简单有效的途径。     

Growth rate of condensed particles with arbitrary Knudsen numbers

A theory is developed for the growth of spherical particles in their own vapor in the case of arbitrary Knudsen numbers. Use is made of a gas-kinetic analysis based on solution, by the Lees method, of the kinetic Boltzmann equation with the collision integral in Boltzmann form. A numerical analysis is made of the effect of different parameters on growth rate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 48–51, August, 1985.     

Vibration of doubly curved shallow shells with arbitrary boundaries

The first comprehensive study of shallow shell vibrations subjected to as many as 21 possible boundary conditions is presented. Thin shallow shell theory is used. Relatively accurate results for natural frequencies of doubly-curved shallow shells have been obtained. These can be used for benchmarking by researchers as well as reference data for practicing engineers. The Ritz method is used to solve for natural vibrations of these shells with arbitrary boundary conditions. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.