Distribution of film orientations in free and strained foams

We show that the distribution of film orientations in a free (i.e., unstrained) foam cluster, though in general not uniform, has the same second moments as a uniform distribution. This is, however, in general not true of its other moments, which reflects the internal order of film orientations imposed by Plateau's laws. For a strained cluster, we relate the deviations of the second moments of the orientation distribution from their values for an unstrained cluster, to the stresses acting on the cluster. Our predictions are corroborated by experimental results for free and strained two-dimensional clusters, allowing us to find the force on a cluster bounded by two parallel walls.     

Optical signal quality metric based on statistical moments and Laguerre expansion

A new and straightforward optical signal quality metric, which is based on the approximation of the analytical probability density function by its Laguerre expansion, is proposed. This expansion uses statistical moments to approximate the true statistics, but, unlike the well-known Gaussian approximation, higher order moments can be used as well. The quality of the proposed metric is discussed and the metric is compared with the Gaussian approximation. It is shown that the new metric provides not only a good estimation of the bit error rate in the range of practical interest but, contrary to the Gaussian approximation, correctly estimates optimum decision threshold and accurately pictures the shape of the noise distribution.     

Moments of the Wigner distribution of rotationally symmetric partially coherent light

The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N, this number reduces to (1 + N/2)2 in the case of rotational symmetry. A way to measure the moments as intensity moments in the output planes of (generally anamorphic) fractional Fourier-transform systems is presented.     

Fractional calculus approach to the statistical characterization of random variables and vectors

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. Applications to the statistical characterization of raw data and in the representation of both random variables and vectors are provided, showing that the good numerical convergence makes the proposed approach a good and reliable tool also for practical data analysis.     

On the mechanics of rim instabilities in viscoelastic polymer thin films

We determine appropriate attractors for higher than third-order central moments for the relaxation process in three-dimensional lattice Boltzmann methods. It was previously assumed that the appropriate attractors for the relaxation of these moments were their equilibria values as derived from a Maxwell-Boltzmann distribution. However, when the attractor for fourth-order central moments is derived that way, the solution of three-dimensional lattice Boltzmann differs significantly from the analytical solution of the Navier-Stokes equation for simple test cases like Poiseuille flow. We show that the Navier-Stokes solution is recovered when we chose products of low order central moments as the attractors of the higher order central moments.     

400GeV/cpp碰撞中的多粒子关联、阶乘累积矩和关联积分

利用CERN NA27合作组提供的LEBC泡室照片,测量了400GeV/c pp碰撞产生的带电粒子赝快度分布.计算了标度阶乘累积矩K_q,与具有同样单粒子谱但是没有关联的蒙特卡罗事例得到的结果相比较,表明对于宽的混合多重数分布,K₂的一个显著部分是由于多重数涨落引起单粒子密度涨落造成的.利用星形关联积分法计算得到的阶乘累积矩,显著地降低了高阶阶乘累积矩的统计误差,但基本结论保持不变.     

High-order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.     

Dispersion-invariant features for classification

In dispersive propagation, waves from the same source will generally differ depending on how far they have traveled. Accordingly, it is desirable for classification in such environments to either account for propagation effects, or to obtain features that are invariant to such effects. The latter approach is taken in this paper, and features are derived that are unaffected by channel dispersion, per mode. A "local" view of pulse propagation in time-frequency phase space is considered. It is shown that the local duration of a wave, obtained from its time-frequency Wigner distribution, is invariant to dispersion. While higher moments of the Wigner distribution are not invariant to dispersion, the phase space considerations suggest an approach for defining "dispersion-invariant moments" (DIMs) of any order. This approach is also used to define a dispersion-invariant correlation coefficient that can be used for classification. The classification utility of the DIMs, and of the dispersion-invariant correlation coefficient, is evaluated via simulations of acoustic scattering from steel shells in a dispersive channel model (Pekeris waveguide). Receiver operating characteristic curves quantify the improved discriminability of the DIMs versus ordinary temporal moments, and of the dispersion-invariant correlation coefficient versus the ordinary correlation coefficient.     

Optimally discriminant moments for speckle detection in real B-scan images

The paper presents and evaluates a speckle detection method for B-scan images. This is a fully automatic method and does not require information about the sensor parameters, which is often missing in retrospective studies.The characterization and posterior detection of speckle noise in ultrasound (US) has been regarded as an important research topic in US imaging, for improving signal-to-noise ratio by removing speckle noise and for exploiting speckle correlation information. Most of the existing methods require either manual intervention, the need to know sensor parameters or are based on statistical models which often do not generalize well to B-scans of different imaging areas. The proposed method aims to overcome those limitations.The main novelty of this work is to show that speckle detection can be improved based on finding optimally discriminant low order speckle statistics. In addition, and in contrast with other approaches the presented method is fully automatic and can be efficiently implemented to B-scan images.The method detects speckle patches using an ellipsoid discriminant function which classifies patches based on features extracted from optimally discriminant low order moments of the uncompressed intensity B-scan information. In addition, if the uncompressed signal is not available, we propose and evaluate a method for the estimation of this factor.The computation of low order moments using an optimality criteria, the decompression factor estimation and other key aspects of the method are quantitatively evaluated using both simulated and real (phantom and in vivo) data. Speckle detection results are obtained using again phantom and in vivo studies which show the validity of our approach. In addition, speckle probability images (SPI) are presented which provide valuable information about the distribution of speckle and non-speckle areas in an image.The presented evaluation and results show the effectiveness of our approach. In particular, the need for using discriminant analysis to determine the optimal discriminant power of the statistical moments and that this optimal value strongly depends on the characteristics and imaged tissues in the B-scan data.     

An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.     

Non-classical effect of quantum non-demolition measurement in presence of parametric amplification

A full quantum treatment of the problem of quantum non-demolition measurements in non-linear optical media is considered. The system consists of four different coupling parameters in addition to different phase parameters. The solution of the Heisenberg equations of motion for the dynamical operators is obtained. The phenomenon of squeezing is examined for both normal and principal squeezing and it has been shown that it is more pronounced for the compound mode case. The intensity correlation function is also calculated and discussed where the observation of the antibunching can be reported. In addition to the higher-order moments we examined the quantum correlation functions, joint quasidistribution functions, as well as photon-number distribution and its factorial moments. It has shown that the non-classical properties is apparent of this system and more pronounced for the compound mode (1,3).     

Bohmian and quantum phase space distribution expansions and approximations

Dias and Patra derived an expansion of the Wigner distribution and related it to the de Broglie–Bohm model. We show that the coefficients of the expansion are related to the conditional central moments and cumulants of the Wigner distribution. The even order cumulants depend only on the amplitude of the wave function and the odd order cumulants depend only on the phase. In addition, we give a different expansion of the Wigner distribution from which their expansion can be derived as a special case. Our expansion allows for different approximations for higher order terms. We also give expansions for the momentum representation. We show how the results are applicable to pulse propagation in a dispersive medium.     

Analytical expressions for multiplicity distributions and deviations from KNO scaling

A simple method is presented for deducing multiplicity distributions from a few multiplicity moments. The essence of the method is the straightforward trick of converting a discrete distribution to a continuous distributions by interpolation. Interpolation changes the moments by calculable amounts, which depend only on the interpolation procedure and not on the multiplicity distribution. This device makes it possible to give a simple analytical expression for the multiplicity distribution, even at rather low energies, in terms of the measured moments. A quantitative discussion of KNO scaling, and deviations from scaling, is given, based on the measured moments.     

Existence and Regularity of a Solution of a Kac Equation Without Cutoff Using the Stochastic Calculus of Variations

We consider a generalized Kac equation without cutoff, with which we associate a non-standard nonlinear stochastic differential equation. We adapt the techniques in Bichteler and Jacod [2] to prove that the law of a solution of the stochastic differential equation has a density, which is a solution of the Kac equation. The initial law is very general: we only assume it has second order moments and is not the Dirac mass at 0. We thus generalize the analytical results of existence of a solution of this equation. If we furthermore assume existence of all moments for the initial law, we obtain as a corollary using the proof in Desvillettes [6] that the density is smooth. We prove a slightly better regularity result under more stringent assumptions using the stochastic calculus of variations, adapting the methods in [1]. Received: 15 July 1998 / Accepted: 4 March 1999     

正则长波方程的格子Boltzmann模型

提出了用于正则长波方程的5-Bit格子Boltzmann模型。应用Chapman-Enskog展开和多重尺度技术,通过选择平衡态分布函数的高阶矩,得到了时间尺度t₀上的守恒律,从而给出三阶精度的算法。模型中的参数通过稳定性分析给出。     

HfO2/SiO2高反射膜的缺陷及其激光损伤

用原子力、Normaski和扫描电子显微镜等分析仪器,对高损伤阈值薄膜常采用的HfO2光损伤所形成的孔洞,与镀制过程中形成的孔洞形貌相似,激光再损伤能力也相似。低能量密度的激光把节瘤缺陷变为孔洞缺陷是激光预处理提高薄膜损伤阈值的原因之一。     

Microscopically implicit–macroscopically explicit schemes for the BGK equation

In this work a new class of numerical methods for the BGK model of kinetic equations is introduced. The schemes proposed are implicit with respect to the distribution function, while the macroscopic moments are evolved explicitly. In this fashion, the stability condition on the time step coincides with a macroscopic CFL, evaluated using estimated values for the macroscopic velocity and sound speed. Thus the stability restriction does not depend on the relaxation time and it does not depend on the microscopic velocity of energetic particles either. With the technique proposed here, the updating of the distribution function requires the solution of a linear system of equations, even though the BGK model is highly non linear. Thus the proposed schemes are particularly effective for high or moderate Mach numbers, where the macroscopic CFL condition is comparable to accuracy requirements. We show results for schemes of order 1 and 2, and the generalization to higher order is sketched.     

Statistical properties in the chaotic regime of the Maxwell-Bloch equations

The statistical properties of the electric field solution of the Maxwell-Bloch equations describing a single mode, homogeneously broadened laser in the mean field limit are investigated in the strange attractor regime. The electric field distribution sis calculated and it is found that the low order intensity moments are somewhat higher than those for thermal-chaotic light whilst the higher order moments are substantially lower. The field and intensity correlation functions are also calculated and found to exhibit radically different behaviour. The results are interpreted in terms of iterative map which is dederived using multiple time-scale perturbation theory. It is shown that a simple random phasor model is compatible with the numerical data.