ON PROPER ORTHOGONAL CO-ORDINATES AS INDICATORS OF MODAL ACTIVITY

Proper orthogonal decomposition (POD) is applied for examining modal activity. The extraction of proper orthogonal modal co-ordinates (POCs) is outlined. The proper orthogonal values (POVs) are the mean squared values of the POCs. The number of POVs above the noise floor provides a bound on the number of significant modes based on POVs above the noise floor. The ideas are illustrated on a linear cantilevered beam experiment. The displacement ensembles are obtained by processing six strain measurements. Coherent proper orthogonal modes (POMs) and POVs above the noise floor together confirm that six active modes are detected in the system. The distribution of modal components in POCs is discussed. The characteristics of the POMs, POVs and POCs are then examined in the presence of added noise.     

Projection-free proper orthogonal decomposition method for a cantilever plate in supersonic flow

This paper explores the use of the proper orthogonal decomposition (POD) method for supersonic nonlinear flutter of a cantilever plate or wing. The aeroelastic equations are constructed using von Karman plate theory and first-order piston theory. The two-dimensional POD modes (POMs) in xy plane are determined from the chaotic results given by the traditional Rayleigh–Ritz (RR) approach. For a specific structure, the POMs need to be calculated once and then can be used for various parameters of interest. The derivatives of the POMs are calculated numerically to avoid the complex projection from the POMs to the Rayleigh–Ritz modes (RRMs). Numerical examples demonstrate that the POD method using 4 POMs can obtain accurate limit cycle oscillation (LCO) results with substantial computational cost savings, compared with 12 RRMs by the Rayleigh–Ritz method. The POD method is employed for the analysis of the chaotic oscillations. It is also demonstrated that the POD modes are robust over a range of flight parameters.     

A new distribution scheme of decryption keys used in optical verification system with multiple-wavelength information

A new distribution scheme of decryption keys used in optical verification systems is proposed. The encryption procedure is digitally implemented with the use of an iteration algorithm in computer. Three target images corresponding to three wavelengths are encoded into three sets of phase-only masks （POMs） by a special distributing method. These three sets of POMs are assigned to three authorized users as the personal identification. A lensless optical system is used as the verification system. In the verification procedure, every two of the three authorized users can pass the verification procedure cooperatively, but only one user cannot do. Numerical simulation shows that the proposed distribution scheme of decryption keys not only can improve the security level of verification system, but also can bring convenience and flexibility for authorized users.     

Optical image encryption with silhouette removal based on interference and phase blend processing

To completely eliminate the silhouette problem that inherently exists in the earlier interference-based encryption scheme with two phase-only masks (POMs), we propose a simple new encryption method based on optical interference of one random POM and two analytically obtained POMs. Different from the previous methods which require time-consuming iterative computation or postprocessing of the POMs for silhouette removal, our method can resolve the problem during the production of the POMs based on interference principle. Information associated with the original image is smoothed away by modulation of the random POM. Illegal deciphers cannot retrieve the primitive image using only one or two of the POMs. Incorporated with the linear phase blend operation, our method can provide higher robustness against brute force attacks. Simulation results are presented to support the validity and feasibility of our method.     

Correlation dimension: A pivotal statistic for non-constrained realizations of composite hypotheses in surrogate data analysis

Currently surrogate data analysis can be used to determine if data is consistent with various linear systems, or something else (a nonlinear system). In this paper we propose an extension of these methods in an attempt to make more specific classifications within the class of nonlinear systems.

In the method of surrogate data one estimates the probability distribution of values of a test statistic for a set of experimental data under the assumption that the data is consistent with a given hypothesis. If the probability distribution of the test statistic is different for different dynamical systems consistent with the hypothesis, one must ensure that the surrogate generation technique generates surrogate data that are a good approximation to the data. This is often achieved with a careful choice of surrogate generation method and for noise driven linear surrogates such methods are commonly used.

This paper argues that, in many cases (particularly for nonlinear hypotheses), it is easier to select a test statistic for which the probability distribution of test statistic values is the same for all systems consistent with the hypothesis. For most linear hypotheses one can use a reliable estimator of a dynamic invariant of the underlying class of processes. For more complex, nonlinear hypothesis it requires suitable restatement (or cautious statement) of the hypothesis. Using such statistics one can build nonlinear models of the data and apply the methods of surrogate data to determine if the data is consistent with a simulation from a broad class of models. These ideas are illustrated with estimates of probability distribution functions for correlation dimension estimates of experimental and artificial data, and linear and nonlinear hypotheses.     

Controlled spin pattern formation in multistable cavity–polariton systems

Theoretical studies are performed of planar cavity–polariton systems under resonant optical excitation. We show that if the cavity is spatially anisotropic, the polariton spin is highly sensitive to the pump polarization direction, which can be used to modulate the circular polarization of the output light. In particular, when the right- and left-circular components of the incident wave have equal intensities and mutually opposite angular momenta, the pump has strictly linear yet angle-dependent polarization and as such brings about a periodic angular variation of the polariton spin. Free motion of polaritons is the other factor determining the shape of the cavity-field distribution. Such externally driven and highly tunable spin patterns represent a counterpart of spin shaping in nonresonantly excited Bose–Einstein condensates of cavity polaritons.     

Shear Viscosity and Temperature Inequalities for Multi-Species Plasmas

The first coefficients in the orthogonal expansions of the velocity distribution functions with respect to Grad's tensorial (three-dimensional) Hermite polynomials are shown to be proportional to ther-modynamic fluxes, if the weight functions are local Maxwellians centered at the mean mass velocity and widened with a mean temperature. Balance equations for the stress tensors are established and reduced to linear algebraic systems under certain restrictions. Explicit solutions for the traces and the tracefree parts of the stress tensors are given.     

Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion

In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the “classical” Fick-Jacobs approximate reduction to an exact subdynamics.     

On the transformation of mass and momentum densities in special relativity

By considering the mass and momentum densities of a point mass moving at uniform velocity, the known transformation of these densities from a representation in one inertial system to another is easily derived. The transformation is not linear in mass and momentum density, but the introduction of a dyadic stress density tensor gives a linear relation. The transformation is shown to hold for a general continuous mass distribution in which mass and momentum are conserved, provided a specific choice is made for the stress density tensor. This result contrasts with the particle viewpoint of matter in which only the divergence of the stress density tensor need be fixed so far as the transformation is concerned. A change of functions is made which greatly simplifies the transformations. The new functions are shown to represent a conserved fluid.Research supported in part by a grant from the California State University, Long Beach Foundation.     

C.w. optical parametric oscillators: single mode or multimode?

This paper details the conditions for which a c.w. OPO pumped by a single mode field is working in a single or multimode regime. It shows that c.w. OPOs are intrinsically single mode systems in the steady state regime, both for the longitudinal and transverse modes, unless special conditions of mode degeneracy or mode coupling are met. Complex optical patterns may appear in such cicumstances, that we have recently observed. Furthermore, if one adds a linear coupling between the signal and idler modes, these two modes can phase-lock on each other: one then obtains a perfect degenerate single mode operation for the c.w. OPO.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.     

Low- and high-frequency noise from coherent two-level systems

Recent experiments indicate a connection between the low- and high-frequency noises affecting superconducting quantum systems. We explore the possibilities that both noises can be produced by one ensemble of microscopic modes, made up, e.g., by sufficiently coherent two-level systems (TLS's). This implies a relation between the noise power in different frequency domains, which depends on the distribution of the parameters of the TLS's. We show that a distribution, natural for tunneling TLS's, with a log-uniform distribution in the tunnel splitting and linear distribution in the bias, accounts for experimental observations.     

多金属氧酸盐TBA3[VW5O19]及TBA4[PVW11O40]的固体核磁共振研究

多金属氧酸盐（简称多酸,Polyoxometalates,POMs)是由处于d⁰电子构型的前过渡金属元素通过共边或共角缩聚而成的金属-氧簇类化合物．由于其具有丰富的分子结构和独特的物理化学性质,已经被广泛应用于功能材料、催化化学和药物化学等领域．其中钒取代的多酸阴离子具有很好的催化活性,特别是对烃类的氧化,它的活性主要受钒取代的数目和钒中心的阴离子环境这两个因素影响．该文利用固体核磁技术分析了一取代钒的两类典型结构中⁵¹V的局域结构和化学环境,以及有机阳离子对多酸阴离子结构的影响,特别是对⁵¹V的化学环境的影响,为研究多酸的催化活性和催化机理提供基本的结构信息．     

Normal vibration frequencies of two- and three-dimensional arrays of alternating point masses

Normal vibration frequencies are calculated for alternating point-masses of mass M and m in two-dimensional rectangular and a three-dimensional parallelepiped arrays. The method of intermediate co-ordinate transformation is used in the analysis. In applying this method, the vibrating systems consisting of alternating masses are treated as the basic systems of linear chains of identical point-masses of mass m (the zero-order system) that are coupled together to form the two- and three-dimensional systems and then further modified by inclusion of an additional mass ?m at alternating sites, where M = (1 + ?)m. The zero-order solution for the linear array of identical particles of mass m is well known. The present calculation shows the advantage of the process of intermediate co-ordinate transformation in simplifying problems which are otherwise complicated and also illustrates how such a process can be applied in more than one successive step.     

Single-molecule single crystals of poly(ethylene oxide)

Single-molecule single crystals were prepared from two fractions of poly(ethylene oxide) (PEO) with narrow molar mass distribution and an equimolar mixture of the two fractions. It was proven that the molar mass distribution of the single-molecule single crystals from the mixed sample corresponds to an addition of those of the pure fractions. Well-shaped crystals were obtained after isothermal crystallization or on annealing. A variety of morphologies typical for multimolecule single crystals of PEO were found and are described on the basis of the various known modes of twinning. The results are in agreement with the known unit cell of PEO.     

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied.     

On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.     

Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential

The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo’s linear response theory.     

Representations of Canonical Commutation Relations Describing Infinite Coherent States

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.