Third-order Moments Research Articles

A model for two-dimensional bursty turbulence in magnetized plasmas

The nonlinear dynamics of two-dimensional electrostatic interchange modes in a magnetized plasma is investigated through a simple model that replaces the instability mechanism due to magnetic field curvature by an external source of vorticity and mass. Simulations in a cylindrical domain, with a spatially localized and randomized source at the center of the domain, reveal the eruption of mushroom-shaped bursts that propagate radially and are absorbed by the boundaries. Burst sizes and the interburst waiting times exhibit power-law statistics, which indicates long-range interburst correlations, similar to what has been found in sandpile models for avalanching systems. It is shown from the simulations that the dynamics can be characterized by a Yaglom relation for the third-order mixed moment involving the particle number density as a passive scalar and the E×B drift velocity, and hence that the burst phenomenology can be described within the framework of turbulence theory. Statistical features are qualitatively in agreement with experiments of intermittent transport at the edge of plasma devices, and suggest that essential features such as transport can be described by this simple model of bursty turbulence.

On statistics of the free-troposphere synoptic component: an evaluation of skewnesses and mixed third-order moments contribution to the synoptic-scale dynamics and fluxes of heat and humidity

On statistics of the free-troposphere synoptic component: an evaluation of skewnesses and mixed third-order moments contribution to the synoptic-scale dynamics and fluxes of heat and humidity

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

Output Power PDF of a Saturated Semiconductor Optical Amplifier: Second-Order Noise Contributions by Path Integral Method

We have developed a second-order small-signal model for describing the nonlinear redistribution of noise in a saturated semiconductor optical amplifier. In this paper, the details of the model are presented. A numerical example is used to compare the model to statistical simulations. We show that the proper inclusion of second-order noise terms is required for describing the change in the skewness (third-order moment) of the noise distributions. The calculated probability density functions are described far out in the tails and can hence describe signals with very low bit error rate (BER). The work is relevant for describing the noise distribution and BER in, for example, optical regeneration.

Blind identification of sparse Volterra systems

AbstractThis paper is concerned with blind identification for single‐input single‐output Volterra systems with finite order and memory with the second‐order and the third‐order statistics. For the full‐sized Volterra system (i.e. all its kernels are nonzero) excited by unknown independently and identically distributed stationary random sequences, it is shown that blind identifiability does not hold in the second‐order moment (SOM) and the third‐order moment (TOM) domain. However, under some sufficient conditions, a class of truncated sparse Volterra systems, where some kernels are restricted to being zero, can be identified blindly and more Volterra parameters can be estimated in TOM than in SOM. Numerical examples illustrate the effectiveness of the proposed methods. Copyright © 2007 John Wiley & Sons, Ltd.

DOA estimation in multipath based on third-order cyclic moment

A new direction of arrival (DOA) estimation algorithm in multipath based on third-order cyclic moment is proposed in this paper. The algorithm can highly solute every DOA in multipath, and the use of third-order cyclic moment suppresses all stationary measurement noises. The simulation shows the advantages of this algorithm.

Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence

Laws governing the behavior of statistical third-order moments in the inertial range are among the few rigorous results in the theory of statistically homogeneous incompressible magnetohydrodynamic turbulence. These fundamental laws apply to both isotropic and anisotropic turbulence. Assuming that the turbulence is stationary in time and statistically axisymmetric under proper rotations about the direction of the mean magnetic field, it is shown that the general mathematical form of the tensor quantities appearing in these laws is constrained by symmetry to have a particular form. Using these forms, the general solutions of the law for the vector and pseudovector third-order moments F and FC are obtained in the limit of large kinetic Reynolds number and large magnetic Reynolds number. The physical meaning of the different terms in F and FC are investigated and a method for obtaining the cascade rates of energy ϵ and cross-helicity ϵC from experimental data is described. The results show that the measurement of the cascade rates goes hand-in-hand with the measurement of the spatial anisotropy of the third-order moments F and FC. The theory developed here can be applied to measure the turbulent cascade rates of energy and cross-helicity in laboratory plasma experiments, numerical simulations, and the solar wind.

Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall

The effects of surface roughness on a spatially developing turbulent boundary layer (TBL) are investigated by performing direct numerical simulations of TBLs over rough and smooth walls. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300 ∼ 1400. The roughness elements were periodically arranged two-dimensional spanwise rods, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.045 ∼ 0.125, δ being the boundary layer thickness. To avoid generating a rough-wall inflow, which is prohibitively difficult, a step change from smooth to rough was placed 80θin downstream from the inlet. The spatially developing characteristics of the rough-wall TBL were examined. Along the streamwise direction, the friction velocity approached a constant value, and self-preserving forms of the turbulent Reynolds stress tensors were obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer but also in the outer layer. Despite the roughness-induced increase of the turbulent Reynolds stress tensors in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations.

Biomechanics of Torque from Twisted Rectangular Archwires

To evaluate the magnitudes of initial and subsequent sequential deactivational third-order moments generated in rectangular twisted archwires (either when the archwires are actually twisted before insertion in the standard edgewise bracket slots or when they are indirectly twisted in the preadjusted slots of the modern edgewise brackets) in order to judge their biologic acceptability. A finite element study was carried out with the MSC Patran/Nastran interface. Three-dimensional models were constructed with 170 nodes of upper 0.017- x 0.025-inch and 0.019- x 0.025-inch archwire segments extending bilaterally from the maxillary central incisors to the first premolars. Required twists were applied at the appropriate locations to derive the applied and reactionary moments both initially and during the time needed for complete deactivation. The results indicated that a round-tripping possibility does exist in certain clinical procedures. Furthermore, the moments produced could be quite high, thereby enhancing the possibility of root resorption. Twists in rectangular archwires may be used only when reciprocal torque is needed on adjacent teeth. In other situations, alternative torquing methods should be considered.

Measurements of higher-order turbulent statistics in a turbulent boundary layer subjected to a short roughness strip

Hot-wire measurements have been undertaken in a turbulent boundary layer which is subjected to an impulse in form of a short roughness strip with the aim of determining its effect on turbulence structure. The quantifications were made through the measurements of higher-order turbulent statistics. The changes observed in the distributions of correlation coefficient, third-order moments, skew ness and flatness factor relative to the smooth wall suggests that the turbulence structure is modified downstream of the short roughness strip. Relative to the undisturbed smooth wall, the third-order moments were increased in the region between the two internal layers. This increased extends to significant portion of the outer region of the boundary layer. While a gain in turbulent kinetic energy by diffusion occurs throughout the boundary layer for a flow over the short roughness strip, those of the smooth wall occur near the wall.

Higher-Order Moments of Velocity Fluctuations in an Open-Channel Flow with Large Bottom Roughness

The present study was undertaken to examine the effect of surface roughness on the higher-order velocity moments in a turbulent open-channel flow. The wall roughness is large and the ratio of the roughness size to the depth of flow ranges from 0.1 to 0.15. Flow over two types of roughness conditions (ribs and dunes) are examined and compared with that over a smooth open channel. In the case of the rib roughness, three different spacings are used: p∕k=4.5, 9, and 18; here, p=distance between the leading edges of two consecutive ribs and k=height of a rib with square cross section. The shape of the smooth wall dunes was geometrically similar to that commonly used in previous studies. In an effort to understand the influence of local wall roughness, rough-wall dunes are also used in the present study. The variables of interest include higher-order moments, conditional statistics based on a quadrant analysis, relationship of higher-order moments to the Reynolds stress and energy production. Although there are some similarities between open-channel flows and turbulent boundary layers, there are important differences as indicated by the third-order moments. The triple products and the second quadrant events are sensitive to the wall condition. Ejection events are found to be prevalent throughout the depth. It is also clear from the study that one needs to explicitly account for the surface condition in any model development to be able to predict transport characteristics.

A comparison of the shear-peel and third-order bond strengths of orthodontic brackets with 2 etch techniques and the role of bracket asymmetry

Innovations in orthodontic bonding are inevitably followed by a flurry of studies to ascertain efficacy. Unfortunately, the published reports are often contradictory or highly variable. The primary purpose of this study was to analyze protocols that measure orthodontic bracket bond strength. The effects of loading mode and the role of bracket asymmetry were examined. The secondary goal was to test a self-etch enamel preparation system. Flattened stainless steel orthodontic brackets (.022-in Victory Series, 3M Unitek, Monrovia, Calif) were bonded to a total of 192 flattened bovine incisors with a resin composite bonding agent (Transbond XT, 3M Unitek.) The enamel was prepared with traditional, two-step (TS) acid (37% phosphoric acid gel) etching and priming (Transbond XT Primer, 3M Unitek) or with a single step (SS) self-etch (Transbond Plus, 3M Unitek) material. Cement thickness was held constant and bonding was done under controlled temperature and humidity. The brackets were debonded in the occlusogingival and in the gingivocclusal directions (ie, the 2 senses of shear-peel) and using a new technique in the buccal-root and in the lingual-root directions (ie, the 2 senses of a third-order moment.) Data showed no significant differences between TS and SS regardless of load modality. However, significant differences were revealed between the senses of debonding, indicating bracket asymmetry effects. The wide clinical use of these newer self-etching primers has been supported by these limited findings. A new third-order debonding protocol has been demonstrated to be a useful tool. Bracket asymmetry affects some bond strength values, and there is a need for standardization of testing protocols.

Nonlocal Treatment of the Buoyancy-Shear-Driven Boundary Layer

Abstract A successful description of a convective boundary layer requires that the model employed takes into account the nonlocal nature of turbulent convection. In this paper new third-order moments (TOMs) are presented and tested. Numerical solutions are obtained using mean flow components and second-order moments as input. The problem of the turbulent damping of the TOMs is considered. The terms in the dynamic equations responsible for the unphysical growth of the TOMs are parameterized, taking into account their dependence on the integral length scale vertical profile. The calculated profiles are presented and tested against large-eddy simulation data and aircraft measurements. In both cases the results compare favorably.

Columnar modelling of nucleation burst evolution in the convective boundary layer – first results from a feasibility study Part II: Meteorological characterisation

Abstract. While in Paper I of four papers a revised columnar high-order modelling approach to investigate gas-aerosol-turbulence interactions in the convective boundary layer (CBL) was deduced, in the present Paper II the model capability to predict the evolution of meteorological CBL parameters is demonstrated. Based on a model setup to simulate typical CBL conditions, predicted first-, second- and third-order moments were shown to agree very well with those obtained from in situ and remote sensing turbulence measurements such as aircraft, SODAR and LIDAR measurements as well as with those derived from ensemble-averaged large eddy simulations and wind tunnel experiments. The results show, that the model is able to predict the meteorological CBL parameters, required to verify or falsify, respectively, previous hypothesis on the interaction between CBL turbulence and new particle formation.

Columnar modelling of nucleation burst evolution in the convective boundary layer – first results from a feasibility study Part III: Preliminary results on physicochemical model performance using two "clean air mass" reference scenarios

Abstract. In Paper I of four papers, a revised columnar high-order model to investigate gas-aerosol-turbulence interactions in the convective boundary layer (CBL) was proposed. In Paper II, the model capability to predict first-, second- and third-order moments of meteorological variables in the CBL was demonstrated using available observational data. In the present Paper III, the high-order modelling concept is extended to sulphur and ammonia chemistry as well as to aerosol dynamics. Based on the previous CBL simulation, a feasibility study is performed using two "clean air mass" scenarios with an emission source at the ground but low aerosol background concentration. Such scenarios synoptically correspond to the advection of fresh post-frontal air in an anthropogenically influenced region. The aim is to evaluate the time-height evolution of ultrafine condensation nuclei (UCNs) and to elucidate the interactions between meteorological and physicochemical variables in a CBL column. The scenarios differ in the treatment of new particle formation (NPF), whereas homogeneous nucleation according to the classical nucleation theory (CNT) is considered. The first scenario considers nucleation of a binary system consisting of water vapour and sulphuric acid (H2SO4) vapour, the second one nucleation of a ternary system additionally involving ammonia (NH3). Here, the two synthetic scenarios are discussed in detail, whereas special attention is payed to the role of turbulence in the formation of the typical UCN burst behaviour, that can often be observed in the surface layer. The intercomparison of the two scenarios reveals large differences in the evolution of the UCN number concentration in the surface layer as well as in the time-height cross-sections of first-order moments and double correlation terms. Although in both cases the occurrence of NPF bursts could be simulated, the burst characteristics and genesis of the bursts are completely different. It is demonstrated, that observations from the surface layer alone are not conclusive to elucidate the origin of newly formed particles. This is also true with respect to the interpretation of box modelling studies. The binary and ternary NPF bursts observed in the surface layer differ with respect to burst amplitude and phase. New particles simulated in the binary scenario are formed in the forenoon in the upper part of the growing CBL, followed by turbulence-induced top-down transport. Hence, with respect to the burst observation site in the surface layer, new particles are formed ex situ. In opposite to this, the ternary case reveals a much more complex pattern. Here, NPF is initiated in the early morning hours in the surface layer, when temperature (T) is low and relative humidity (RH), sulphur dioxide (SO2) and NH3 concentrations are high, hence new particles are formed in situ. Shortly after that, ex situ NPF in the free troposphere sets in, followed by entrainment and top-down diffusion of newly formed particles into the surface layer. Altogether, these processes mainly contribute to the formation of a strong burst in the morning hours in the ternary scenario. While the time-height cross-section of the binary nucleation rate resembles a "blob"-like evolution pattern, the ternary one resembles a "sucking tube"-like pattern. The time-height cross-sections of the flux pattern and double correlations could be plausibly interpreted in terms of CBL turbulence and entrainment/detrainment processes both in the binary and in the ternary case. Although the present approach is a pure conceptual one, it shows the feasibility to simulate gas-aerosol-turbulence interactions in the CBL. Prior to a dedicated verification/validation study, further attempts are necessary to consider a more advanced description of the formation and activation of thermodynamically stable clusters according to modern concepts proposed by Kulmala et al. (2000), Kulmala (2003) and Kulmala et al. (2004a).

Non-local ocean mixing model and a new plume model for deep convection

Turbulent fluxes can be represented by a diffusivity tensor, the symmetric part of which describes “ turbulent diffusion” while the anti-symmetric part describes “ advection”. Diffusion is a local process in the sense that it depends only on the local gradients of the mean fields while advection is non-local for it is represented by an integral over all length scales (all eddies) that can “fit” from say the bottom of the physical domain to the z where the fluxes are computed. In the ocean, there are two main regimes where non-local transport is important. One regime is where storms release a sudden burst of mechanical energy to the ocean surface that is then transported downward by energetic eddies that deepen the mixed layer. Even relatively simple non-local models yield results considerably more realistic than those of local models. The second regime is deep convection (DC) caused by loss of surface buoyancy, the description of which is required for a reliable assessment of water masses formation. At present, there is no reliable model for either of these non-local regimes individually or much less a formalism capable of accounting for both regimes simultaneously. The goal of this paper is to present a formalism that provides the expressions for the non-local fluxes for momentum, heat and salinity encompassing both cases. Since the resulting number of dynamic equations involves is however large, we work out two sub-models, one when only shear must be treated non-locally (e.g., when storms release mechanical energy) and one when only buoyancy is to be treated non-locally (the DC case). We employ the Reynolds Stress formalism in which non-locality is represented by the third-order moments which in turn depend on the fourth-order moments for which we employ a new model that has been tested against LES data, aircraft data and a full PBL simulation. For the DC case, we rewrite the non-local model in terms of Plumes since thus far the only non-local model used to treat oceanic DC has been the “plume model” of Morton, Taylor and Turner (MTT model). We show that the MTT model has two key limitations, (1) an important physical process such as the rate of entrainment cannot be determined by the model and remains an adjustable parameter and (2) MTT is purely advective and thus only applicable to the initial stages of DC but not to the whole process which is both advective and diffusive. The model we derive bypasses these limitations, is a generalization of the MTT model and is applicable to the entire development of deep convection.

Blind image deconvolution using the zero-lag slice of higher-order statistics

A novel algorithm for blind image deconvolution using the zero-lag slice (ZLS) of higher-order statistics only is presented. This method first estimates the point-spread function (PSF) using the ZLS of its third-order moment (TOM) and then uses it with one of the known classical image deconvolution methods. The proposed method has simple computations for PSF estimation because it solves a nonlinear problem by using an iterative method with fast convergence. In each iteration, one need only calculate the ZLS of the TOM and estimate the PSF using simple two-dimensional operations. Furthermore, the method presented achieves good results, since the ZLS estimate obtained from the degraded image exhibits high reliability. The good performance of the proposed algorithm is demonstrated by applying it to synthetic and real data sets.

A Parameterization of Third-order Moments for the Dry Convective Boundary Layer

We describe one-dimensional (1D) simulations of the countergradient zone of mean potential temperature \(\overline{\theta}\) observed in the convective boundary layer (CBL). The method takes into account the third-order moments (TOMs) in a turbulent scheme of relatively low order, using the turbulent kinetic energy equation but without prognostic equations for other second-order moments. The countergradient term is formally linked to the third-order moments \(\overline{w^{\prime 2}\theta'}\) and \(\overline{w'\theta^{\prime 2}}\), and a simple parameterization of these TOMs is proposed. It is validated for several cases of a dry CBL, using large-eddy simulations that have been realized from the MESO-NH model. The analysis of the simulations shows that TOMs are responsible for the inversion of the sign of \(\partial \overline{\theta}\,/\,\partial z\) in the higher part of the CBL, and budget analysis shows that the main terms responsible for turbulent fluxes and variances are now well reproduced.

Compression of surface EMG signals with algebraic code excited linear prediction

Despite the interest in long timescale recordings of surface electromyographic (EMG) signals, only a few studies have focused on EMG compression. In this paper we investigate a lossy coding technique for surface EMG signals that is based on the algebraic code excited linear prediction (ACELP) paradigm, widely used for speech signal coding. The algorithm was adapted to the EMG characteristics and tested on both simulated and experimental signals. The coding parameters selected led to a compression ratio of 87.3%. For simulated signals, the mean square error in signal reconstruction and the percentage error in average rectified value after compression were 11.2% and 4.90%, respectively. For experimental signals, they were 6.74% and 3.11%. The mean power spectral frequency and third-order power spectral moment were estimated with relative errors smaller than 1.23% and 8.50% for simulated signals, and 3.74% and 5.95% for experimental signals. It was concluded that the proposed coding scheme could be effectively used for high rate and low distortion compression of surface EMG signals. Moreover, the method is characterized by moderate complexity (approximately 20 million instructions/s) and an algorithmic delay smaller than 160 samples (∼160 ms).

Statistics of Absolute and Relative Dispersion in the Atmospheric Convective Boundary Layer: A Large-Eddy Simulation Study

Abstract The influence of the different scales of turbulent motion on plume dispersion in the atmospheric convective boundary layer (CBL) is studied by means of a large-eddy simulation (LES). In particular, the large-scale (meandering) and small-scale (relative diffusion) contributions are separated by analyzing dispersion in two reference systems: the absolute (fixed) coordinate system and the coordinate system relative to the plume’s instantaneous center of mass. In the relative coordinate system, the (vertically) inhomogeneous meandering motion is removed, and only the small-scale, homogeneous turbulent motion contributes to the dispersion process. First, mean plume position, dispersion parameters (variance), and skewness of the plume position are discussed. The analysis of the third-order moments shows how the structure and the symmetry of scalar distribution are affected with respect to the turbulent characteristics of the CBL (inhomogeneity of the large-scale vertical motion) and the presence of the boundary conditions (surface and top of the CBL). In fact, the reflection of the plume by the CBL boundaries generates the presence of nonlinear cross-correlation terms in the balance equation for the third-order moments of the plume position. As a result, the third-order moment of the absolute position is not balanced by the sum of the third-order moments of the meandering and relative plume position. Second, mean concentration and concentration fluctuations are calculated and discussed in both coordinate systems. The intensity of relative concentration fluctuation icr, which quantifies the internal (in plume) mixing, is explicitly calculated. Based on these results, a parameterization for the probability distribution function (PDF) of the relative concentration is proposed, showing very good agreement with the LES results. Finally, the validity of Gifford’s formula, which relates the absolute concentration’s high-order moments to the relative concentration and the PDF of the plume centerline, is studied. It is found that due to the presence of the CBL boundaries, Gifford’s formula is not able to reproduce correctly the value of the absolute mean concentration near the ground. This result is analyzed by showing that, when the plume is reflected by the CBL boundaries, the instantaneous relative plume width z′2r(t) departs from its mean value σ2r. By introducing the skewness of the relative plume position into a parameterization for the relative mean concentration, the results for the calculated mean concentration are improved.