Moments Of Increments Research Articles

Turbulent flows and intermittency in laboratory experiments

In turbulent flows, the transfer of energy from large to small scales is strongly intermittent, in contradiction with Kolmogorov's (Dokl. Akad. Nauk. SSSR 30 (1941) 299; hereafter K41) assumptions. The statistical properties associated with these energy transfer fluctuations at a given scale r have been widely studied theoretically, experimentally and numerically over the last 30 years or so. Such fluctuations are also encountered in various Planetary and Space Science domains. The present paper presents a review of laboratory experiments which clearly display the fractal nature of the (spatial or temporal) energy distribution at scale r, the departures from the K41 predictions being generally quantified through high-order moments of velocity increments.

Morphologic changes in the lumbar intervertebral foramen due to flexion-extension, lateral bending, and axial rotation: an in vitro anatomic and biomechanical study.

A biomechanical and anatomic study with human cadaveric lumbar spine. The purpose of this study is to examine the morphologic changes in the intervertebral foramen during flexion, extension, lateral bending, and axial rotation of the lumbar spine and to correlate these changes with the flexibility of the spinal motion segments. Previous studies showed morphologic changes in the intervertebral foramen during flexion and extension; however, those changes during lateral bending and axial rotation were not well known. There were 81 motion segments obtained from 39 human cadaveric lumbar spines (mean age 69 years). The motion segments were imaged with CT scanner with 1-mm thick consecutive sections. For biomechanical testing each motion segment was applied with incremental pure moments of flexion, extension, lateral bending, and axial rotation. Rotational movements of the motion segment were measured using VICON cameras. After application of the last load, the specimens were frozen under load, and then CT was performed with the same technique described above. Six parameters of the intervertebral foramen were measured, including foraminal width (maximum and minimum), foraminal height, disc bulging, thickness of ligamentum flavum, and cross-sectional area of the foramen. Flexion increased the foraminal width (maximum and minimum), height, and area significantly while significantly decreasing the disc bulging and thickness of ligamentum flavum (P < 0.05). However, extension decreased the foraminal width (maximum and minimum), height, and area significantly. Lateral bending significantly decreased the foraminal width (maximum and minimum), height, and area at the bending side, whereas lateral bending significantly increased the foraminal width (minimum), height, and area at the opposite side of bending. Likewise, axial rotation decreased the foraminal width (minimum) and area at the rotation side significantly while significantly increasing the foraminal height and foraminal area at the opposite side. The percent change in the foraminal area was found significantly correlated with the amount of segmental spinal motion except for the extension motion. This study showed that the intervertebral foramen of the lumbar spine changed significantly not only on flexion-extension but also on lateral bending and axial rotation. The percent change in cross-sectional foraminal area was correlated with the amount of segmental motion except for extension motions. Further studies are needed to assess the morphologic changes in the intervertebral foramen in vivo and to correlate clinically.

The temporal variation of the spherical and Cartesian multipoles of the gravity field: the generalized MacCullagh representation

The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation law allows a representation of the incremental mass density by the respective excitation function. A representation of an arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely: (1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of inertia.

Numerical study of grid turbulence in two dimensions and comparison with experiments on turbulent soap films.

Numerical simulations of two dimensional channel flow behind an array of cylinders are carried out for high Reynolds numbers. Results for the energy density and enstrophy spectra, as well as for velocity and vorticity differences, are presented. The results compare favorably with recent experiments carried out with turbulent soap films. Some marked deviations from expected behavior are found for the enstrophy spectrum and for moments of vorticity increments.

Wavelet packet transform initialization for piecewise polynomial and bandlimited inputs

This paper considers the problem of initializing the wavelet packet transform when the analog input x(t) is either bandlimited or else is piecewise polynomial on the dyadic intervals. This is accomplished by the construction of certain prefilter sequences that are applied to the samples {x/sub k/|x/sub k/=x(kT)} (T is the sampling period). In the piecewise polynomial case, the prefilter sequences are computed with the aid of the interpolatory graphical display algorithm (IGDA), which is used to compute the so-called incremental moment functions of the scaling function /spl phi/(t) on the dyadic points. The moments of /spl phi/(t) are also employed.

Second- and third-order longitudinal velocity structure functions in a fully developed turbulent channel flow

Second- and third-order moments of temporal increments of the longitudinal velocity fluctuation have been measured using hot wires in a fully developed turbulent channel flow and analyzed using values of the mean energy dissipation rate inferred from direct numerical simulation data for the same flow and Reynolds numbers. The results indicate that dissipative range scales approach isotropy relatively rapidly when the mean shear is negligible. For larger inertial range type scales, the approach is slower. The rate at which isotropy is approached seems slower for third-order than second-order structure functions. This rate depends more on the mean shear than on the turbulent Reynolds number. Two-point laser Doppler anemometry measurements provide reasonable support for the use of Taylor’s hypothesis, at least outside the buffer region.

Member Stiffness with Offset Hinges

In the most simple case of plastic collapse, it is said that a hinge forms in a member when the moment capacity is reached. In the more complex case of plastic collapse, when the effect of axial load on the moment capacity is considered, it is argued here that an “offset hinge” is formed since as you move along an interaction or limit surface, the incremental moment is proportional to the incremental axial load. In this note the stiffness of a plane, elastic, straight member with offset hinges at either or both ends is derived. An example of plastic collapse taken from the European literature is included.

Does it matter who authorises the discourse?: Michel de Certeau'sHeterologiesand black and white Australian literary criticism

Abstract This paper examines the relevance of the ‘particularity of the place where discourse is produced’ in two literary histories to discover if de Certeau's distinction, in Heterologies, between historiography and psychoanalysis, helps to determine if and how a work written by a white writer who writes about Aboriginal literature differs from the work of a black writer who does the same thing. It concludes that the status of the author is not a matter of indifference, neither is it simply a matter of personal experience. It ushers in the need to differentiate subject positions in relation to incremental moments of the past and in relation to constructs of the ‘other’.

Rolling maneuver load alleviation using active controls

Rolling maneuver load alleviation using active controls

Some checks of Taylor's hypothesis in a slightly heated turbulent circular jet

Taylor's hypothesis has been examined by comparing temporal variations of the temperature fluctuation θ with the corresponding spatial variations. The comparison is made on the axis of a circular jet in the self-preserving region of the flow for streamwise separations extending to about 10 Kolmogorov microscales. The use of the hypothesis yields reliable estimates of streamwise temperature correlations and also of second- and third-order moments of streamwise temperature increments. Fourth-order moments of these increments are estimated less accurately. Departures from the hypothesis are smaller than in the plane jet; consistently, local isotropy appears to be more closely satisfied in the circular jet.

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient‐related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, “roughness” and “sparseness”, respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from ≈60 m to ≈60 km. Finally, we define the “mean multifractal plane” and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Dynamic analysis of elasto-plastic flexural plates by the D/BEM

A direct domain/boundary element method is developed for the dynamic response analysis of thin elasto-plastic flexural plates of arbitrary geometry and boundary conditions subjected to any lateral loading history. The method employs the elastostatic fundamental solution of thin flexural plates in a time domain integral formulation. Thus, the plasticity effect, the inertial load and the external lateral load appear in domain integrals in the boundary integral formulation of the problem. This requires a boundary as well as an interior discretization of the plate. Quadratic isoparameteric boundary and interior elements are employed for increased accuracy. The solution is obtained by an explicit time integration scheme employed on the incremental form of the matrix equations of motion. The incremental plastic moments needed to evaluate the plasticity effect are calculated by a finite element methodology to avoid the evaluation of highly singular terms. Numerical examples are presented to illustrate the proposed method and compare it with the finite element method.

Progressive Collapse Analysis of a Ship's Hull under Longitudinal Bending

It is very important to estimate the load carrying capacity of a ship's hull as a whole from the viewpoints of safety and economy. For this purpose, a simple method was proposed to simulate the progressive collapse behaviour of a ship's hull girder subjected to longitudinal bending. In this method, the cross section of a hull girder is divided into small elements composed of a stiffener and attatched plating. For each stiffener element, the average stress-strain relationship under axial load is derived based on the equilibrium conditions of forces and moments. The buckling and yielding in both stiffener and plate are taken into account. Then, a step-by-step increase of vertical curvature is applied to the hull girder assuming that the plane cross section remains plane. At each incremental step, the tangential flexural rigidity of the cross section is evaluated using the tangential slope of the average stress-strain curves of the elements as well as the incremental bending moment due to the curvature increment.Performing sample calculations on existing girder models tested under pure bending, the rationality of the proposed method was examined. Then, the analysis was performed on an existing bulk carrier, and the progressive collapse behaviour of the cross section under bending load was discussed. It was found that the full plastic bending moment can not be attained due to buckling of the deck plates under sagging condition and that of the bottom and inner bottom plates under hogging condition. It was also found that the maximum bending moment carried by the cross section under sagging condition is 20% lower than that under hogging condition.

Packing Method for Resource Leveling (Pack)

A new heuristic for resource leveling based upon the critical path method is developed. The minimum moment of the resource histogram is used to measure the level of resources. The heuristic assigns project activities to specific days so that the final resource histogram approaches a rectangle and its moment approaches a minimum value. Activities are listed in a priority order and all possible assignments for each are determined. Incremental moments contributed by the activity's resource rate and penalties that recognize network interactions are calculated. Each activity is positioned in the time span where the sum of these quantities is a minimum. The histogram is thereby built step‐by‐step until all activities have been positioned within the constraints of a CPM or PERT network. The resulting leveled histogram is the same as, or very close to, that produced by other optimization or heuristic methods. The method is clear, logical, and computationally efficient whether the leveling is done manually or by c...

Elasto-plastic plate bending analysis by a boundary element method with initial plastic moments

The analysis of elasto-plastic plate bending using a boundary integral equation formulation is described. The integral equations are solved using standard boundary element techniques. The plasticity, as well as the external lateral load, appears in a domain integral. The solution is obtained by an incremental loading procedure with the initial incremental plastic moments calculated by an iterative method. Several study cases are examined and good agreement is shown with published results obtained by the finite element method.

The effects of chemonucleolysis on the mechanical properties of the canine lumbar disc.

One hundred and twenty-two lumbar intervertebral discs from 43 mongrel dogs were used to study the effect of chemonucleolysis on the flexion, torsion, and lateral bending flexibilities of the disc. The dogs were killed 2, 4, 12, 26, and 52 weeks following injection with 0.1-0.15 ml of either crude collagenase, semipurified collagenase, or chymopapain. Controls consisted of saline-injected and uninjected discs. The bending and torsional properties of each disc were determined by applying incremental moments up to 0.8 Nm and measuring the resultant rotations 60 seconds after each load increment was applied. The discs were then sectioned for morphologic evaluation. Increases in disc flexibilities ranging from 1.4 to 5.8-fold were found 2 weeks after injection with all three enzymes. The largest increase was noted in flexion in discs injected with chymopapain. By 3 months, all lateral bending flexibilities had returned to control values. In general, however, flexion and torsion flexibilities did not return to control values 6 months following chemonucleolysis. The extent of the gross morphologic changes produced by each of the three enzyme preparations did not correlate with the acute increases in disc flexibilities. Chymopapain and semipurified collagenase had similar morphologic and mechanical effects. The temporary increases in flexibility appeared to be due to decreases in the overall compression, tensile and shear stiffness of the annulus caused by the enzymes.

Thrust reverser effects on fighter aircraft aerodynamics

Wind tunnel studies were conducted using a 0.025 scale model of an F-18 type of configuration with thrust reversers in the Northrop 21X 30 in. low-speed wind tunnel at conditions representative of the aircraft on approach. A feature of these tests was a systematic buildup of reverser jets and tail surface components in order to identify and understand the major aerodynamic forces that the reversers generate on the tail surfaces. It is shown that the upper jets produce a blockage between the twin vertical tails and that this plays a key role in the reverserinduced effects. In sideslip or with the rudders deflected, this blockage is asymmetric and results in increases in directional stability and rudder effectiveness. In pitch, the blockage produces a download on the vertical tails but the resulting upwash on the horizontals greatly reduces the incremental pitching moment on the aircraft. The reverser jets induce a strong entrainment flow on the horizontal tails, which amplifies the tail load, resulting in either a pitch-up or a pitch-down, depending on the tail setting.

Lift-Cruise Fan V/STOL Configuration Characteristics near a Small Deck

Two V/STOL model configurations utilizing lift-cruise fans for the propulsion system have been tested in the presence of a small landing platform with finite deck edge positions. Results and analysis of these tests are presented. The model was tested at both static (zero velocity) and forward speed conditions with several heights and deck edge positions. Configurations utilizing three and four fans were investigated. Incremental forces and moments induced by the various deck edge positions are analyzed as relating to the model height above the ground and the thrust velocity relationships. The test and analysis show the induced forces to be relatively unaffected by deck edge. The magnitude of forces over the partial deck are approximately the same as over the full deck.

Stiffness and Force-Moment Interaction for Plates with Plastic Flow∗

Abstract The stress distribution in a homogeneous plate is approximated in the normal direction by stress functions satisfying the yield condition. Using the conjugate energy theorem the plate stiffnesses are derived for incremental internal forces and moments. In the limit state the interaction surface represents combinations of internal forces and moments.

Factors affecting the stability of T-tail transports.

A wind-tunnel research program has been undertaken by NASA to study the aerodynamic characteristics of T-tail aircraft at high angles of attack. The program was designed to show the effect on longitudinal sLability and control of several configuration variables encompassing horizontal-tail size, vertical position, planfbrm, and incidences; nacelle size, location, and pylon effects; wing section, stall-control devices, flaps, aspect ratio, and sweep; fuselage cross-sectional size, cross-sectional shape, and forebody length. .Results of this program are presented and analyzed to serve as a guide to preliminary design. Nomenclature b = wing span C L = lift coefficient (Cm)oA()r. = pitching-moment coefficient about ().4()c AG\4, = incremental moment due to horizontal tail c = wing mean aerodynamic chord //, = tail incidence A/* = change in tail incidence lt = tail arm M = Mach number S = wing reference area Si = tail area z = tail height a = angle of attack oxtail = angle of attack at wing stall at = angle of attack of horizontal tail