Ferrotoroidic moment as a quantum geometric phase

We present a geometric characterization of the ferrotoroidic moment tau in terms of a set of Abelian Berry phases. We also introduce a fundamental complex quantity z munu, which provides an alternative way to calculate tau and its moments and is derived from the tensor T munu=2 under summation operator jrj muSj nu. This geometric framework defines a natural computational approach for density functional and many-body theories.     

Linear-spline estimation of the correlation function of a stationary random process

Estimation of the correlation function of a stationary random process in measurements made at random times is discussed. The estimate is taken in the form of a first-order spline with uniform node distribution. Analytic formulas are derived for the rms error of estimation of the correlation function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 23–29, April, 1996.     

底混响空间相关函数方法估计载体姿态

在海底是起伏不大的非均匀薄层的假设条件下,建立了底混响空间相关函数模型。当混噪比较高时,模型中空间相关函数相位等于基元间垂向矢量与波数的乘积。对于平面阵而言,基元间垂向矢量是由于基阵载体姿态引起的。因此,可以给出底混响空间相关函数相位与载体横摇角和纵摇角之间的关系式。如果接收阵存在3个接收基元,它们对应平行四边形面积与对角线之比不小于半波长,那么可以通过解方程组的方法得到横摇角和纵摇角的确定解或优化解。由于相位模糊的存在,解的范围是有限的。通过Fisher信息矩阵得到了这种方法姿态估计的Cramer-Rao下限。仿真实验和海试结果表明这种方法是可行的。     

Method for vessel attitude estimation by spatial correlation function for bottom reverberation

Under the assumption that the sea bottom is an almost-flat and randomly rough thin layer, a spatial correlation model for bottom reverberation is constructed. At high signal noise ratio, the phase of the spatial correlation function is the product of sound wave number and the vertical vector between two hydrophones. In a nominally horizontal plane, roll and pitch bring on the vertical vector between the hydrophones. Then an equation including roll, pitch and the phase of the spatial correlation function is found. If a parallelogram can be constructed by 3 hydrophones and the rat ios of its acreage to diagonals are not smaller than half of the wavelength, roll and pitch can be obtained analytically or by optimal method. However, the ranges of roll and pitch are restricted because of the phase ambiguity. Using Fisher information matrix, the Cramer-Rao lower bound is obtained. Results from computer simulation and sea test data prove the feasibility of the method.     

A geometric wave function for a few interacting bosons in a harmonic trap

We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a one-dimensional trap. By means of a combination of the exact wave function solution for contact interactions and the asymptotic behavior of the harmonic potential solution we obtain the ground state energy, probability density and profiles of a few boson system in a harmonic trap. We are able to access all regimes, ranging from the strongly attractive to the strongly repulsive one with an original and simple formulation.     

Triple correlation in a plasma and the collision integral for the dual correlation function

A solution is derived to the equation for the triple correlation function of a system of charged particles, allowing for the effects of dynamic polarization and yielding an equation for dual correlation analogous to the kinetic equation for the simple distribution function.     

The sixth frequency moment of the relaxation-shape function for a Heisenberg paramagnet

A correction to the hitherto published expression for the sixth frequency moment of the relaxation-shape function of a Heisenberg paramagnet at elevated temperatures is presented. The results are in accord with a computer calculation for a face-centred cubic lattice with nearest- neighbour exchange interactions.     

A vectorized algorithm for correlation dimension estimation

We present an algorithm for the efficient and reliable computation of the Grassberger-Procaccia correlation dimension in cases where the correlation integral is constructed using all pairs of points. This algorithm is explicitly designed for modern super-scalar processors.     

Strain field estimation based on digital image correlation and radial basis function

Two methods based on digital image correlation (DIC) and radial basis function (RBF) were proposed to obtain the accurate strain field in this paper. One is a combined method. RBF was applied to remove the noisy discrete displacement data first. After that, the strain was computed by a local least-squares algorithm. The other is a partial derivative of RBF (PD-RBF) based strain estimation method which integrated denoising with differential process. The effectiveness and accuracy of the proposed methods were verified through two numerical simulation experiments. A practical application on the normal strain measurement of an aluminum alloy beam under symmetric four-point bending via an outer loading frame was also presented. The measurement results are in good accordance with the data obtained by strain gauges. Furthermore, a shape parameter selection method based on rate of convergence was suggested. The new method simplifies the choice of the good shape parameter.     

The correlation function for a quantum oscillator in a low-temperature heat bath

The momentum autocorrelation function c(t) for a quantum oscillator coupled with harmonic forces to a heat bath of oscillators is calculated at low temperatures. It is found that c(t) contains two distinct terms: one, the zero-point contribution c₀(t), is temperature independent, and the other, c₁(t), does depend on temperature. We concentrate our attention on the low-temperature case. An expression for c₁(t) is obtained, which is valid for arbitrary strenghts of the coupling and for arbitrary times. It is shown that c₁(t) is governed by the low-frequency behaviour of F(λ) = A²(λ)ϱ(λ), where ϱ(λ) is the density of normal modes and A(λ) is the central-oscillator component of the λth normal mode; other details of the problem are irrelevant. It is found that c₁(t) decays in time as an inverse-power law, with a relaxation time t_q ≈ ħ/kT.     

Exact time correlation function for a nonlinearly coupled vibrational system

The time correlation function (t)=Re<[c(t), c (0)]>, which is related to the dipole spectrum and is the main focus of quantum molecular time scale generalized Langevin equation theory, is calculated for the Hamiltonian system in which a single oscillator is coupled by a nonlinear Davydov term to a chain of oscillators comprising a phonon heat bath. An exact expression for (t) is obtained. At long times we find that the time correlation function decays as a small power law atT=0K, but switches to exponential decay at higher temperature. This is a new result and bears on the long-standing issue of the existence of long-time tails.     

Ergodic theorems arising in correlation dimension estimation

The Grassberger-Procaccia (GP) empirical spatial correlation integral, which plays an important role in dimension estimation, is the proportion of pairs of points in a segment of an orbit of lengthn, of a dynamical system defined on a metric space, which are no more than a distancer apart. It is used as an estimator of the GP spatial correlation integral, which is the probability that two points sampled independently from an invariant measure of the system are no more than a distancer apart. It has recently been proven, for the case of an ergodic dynamical system defined on a separable metric spaceythat the GP empirical correlation integral converges a.s. to the GP correlation integral at continuity points of the latter asn. It is shown here that for ergodic systems defined on ^d with the max metric the convergence is uniform inr. Further, a simplified proof based on weak convergence arguments of the result in separable spaces is given. Finally, the Glivenko-Cantelli theorem is used to obtain ergodic theorems for both the moment estimators and least square estimators of correlation dimension.     

Structure function in lieu of correlation function

Using experimental data subject to noise and drift, we find the structure function can be computed to higher accuracy, yet using less data, than the correlation function. While this tendency is in line with theoretical reasoning, we seem to be the first to report on quantitative aspects. Taking wall pressure data from a transsonic wind tunnel, our structure functions are obtained with one to two orders less of data points than correlation functions of comparable information content. These advantages apply to auto- and cross-structure functions alike when compared to auto- and cross-correlation functions, respectively. Some comments are added on the possibility of designing digital “structurators” similar to existing digital correlators, either as software products using the FFT and recursive algorithms, or as hardware products in the form of fast special purpose paralled processors.     

Resolving statistical uncertainty in correlation dimension estimation

In this paper we propose a novel method for obtaining standard errors and confidence intervals for the correlation dimension estimated on an observed chaotic time series. This method is based on the U-Statistics theory and an ingenious combination of the moving block and parametric bootstrap procedures. We test the method on the basis of computer simulations for both clean and noisy series. We show that the distribution of the correlation dimension estimate obtained by our method agrees very well with the "true" distribution obtained by the Monte Carlo simulation. One of the main advantage of our method is the ability to estimate the distribution (and hence, the standard error) of the correlation dimension estimate using only one observed time series.     

Pair correlation function near a convective instability

The pair correlation function immediately below and above the first hydrodynamic instability in a Bénard cell is computed. In both cases a modified Ornstein-Zernike-type behavior is found that couldbe detected by microwave experiments.     

Assessment of a Wiener filter synthetic discriminant function for optical correlation

The Wiener filter (WF), which has been used extensively for image restoration and signal processing, is employed for robust optical pattern recognition and classification. The WF is formulated to incorporate the in-class image (to be detected) and the out-of-class noise image (to be rejected) into a single step filter construction. It is compared with the classical matched filter (CMF) and phase-only filter (POF), demonstrating a superior discriminatory capability. The WF is incorporated into a synthetic discriminant function (SDF); correlation results show that it is tolerant to image distortion. With a 30 ° out of plane rotation between training set images, the WF SDF achieves a 100% success rate in discriminating one class of images from another. The CMF SDF and POF SDF fail to achieve 100% discrimination even at rotation increments of 15 °.     

Optimized dithering technique in frequency domain for high-quality three-dimensional depth data acquisition

On the basis of the objective functions, dithering optimization techniques can be divided into the intensity-based optimization technique and the phase-based optimization technique. However, both types of techniques are spatial-domain optimization techniques, while their measurement performances are essentially determined by the harmonic components in the frequency domain. In this paper, a novel genetic optimization technique in the frequency domain is proposed for highquality fringe generation. In addition, to handle the time-consuming difficulty of genetic algorithm(GA), we first optimize a binary patch, then join the optimal binary patches together according to periodicity and symmetry so as to generate a full-size pattern. It is verified that the proposed technique can significantly enhance the measured performance and ensure the robustness to various amounts of defocusing.