Two-body and three-body abrasion: A critical discussion

It is argued that the common classification of abrasive wear into 'two-body abrasion' and 'three-body abrasion' is seriously flawed. No definitions have been agreed upon for these terms, and indeed there are two quite different interpretations, the implications of which are mutually inconsistent. In the dominant interpretation, the primary thrust of the two-body/three-body concept is to describe whether the abrasive particles are constrained (two-body) or free to roll (three-body). In this view, two-body abrasion is generally much more severe than three-body. The alternative interpretation emphasises the presence (three-body) or absence (two-body) of a rigid counterface backing the abrasive. In this view, three-body abrasion is equated to high-stress (or grinding) abrasion and is generally more severe than two-body (low-stress) abrasion. This paper recommends that the 'two-body/three-body' terminology be abandoned, to be replaced by an alternative classification scheme based directly upon the manifest severity of wear. (C) 1998 Elsevier Science S.A.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.

Effect of hardness on three very different forms of wear

Different abrasive wear tests have been applied to materials with hardnesses ranging from 80 HV (aluminium) to 1700 HV (tungsten carbide). The tests were: dry sand rubber wheel (DSRbrW); a similar test using a steel wheel (DSStlW); a new combined impact-abrasion test (FIA). The DSRbrW results were as expected, giving generally decreasing wear with increasing hardness. White cast irons and tool steels containing coarse, hard carbide particles performed better than more homogeneous materials of comparable hardness. When normalized to load and distance, the DSStlW results for the homogeneous materials were similar to the DSRbrW results. The multi-phase materials performed poorly in the DSStlW test, with volume loss for high-speed steel (880 HV) higher than that of aluminium. Within this group, wear increased with increasing hardness. These unexpected results are explained in terms of (a) differential friction coefficients of wheel and specimen, (b) increased fracture of sand, and (c) introduction of microfracture wear mechanisms. The FIA combined impact-abrasion results lacked clear correlations with hardness. The span of relative wear rates was similar to that reported for materials in ball mills. White cast irons at maximum hardness performed fairly poorly and showed evidence of microfracture. (C) 1997 Elsevier Science S.A.

Many-body quantum dynamics of polarization squeezing in optical fibers

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fiber, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibers. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Estimation of total body water from bioelectrical impedance analysis in patients with pancreatic cancer - agreement between three methods of prediction

Introduction Bioelectrical impedance analysis (BIA) is a useful field measure to estimate total body water (TBW). No prediction formulae have been developed or validated against a reference method in patients with pancreatic cancer. The aim of this study was to assess the agreement between three prediction equations for the estimation of TBW in cachectic patients with pancreatic cancer. Methods Resistance was measured at frequencies of 50 and 200 kHz in 18 outpatients (10 males and eight females, age 70.2 +/- 11.8 years) with pancreatic cancer from two tertiary Australian hospitals. Three published prediction formulae were used to calculate TBW - TBWs developed in surgical patients, TBWca-uw and TBWca-nw developed in underweight and normal weight patients with end-stage cancer. Results There was no significant difference in the TBW estimated by the three prediction equations - TBWs 32.9 +/- 8.3 L, TBWca-nw 36.3 +/- 7.4 L, TBWca-uw 34.6 +/- 7.6 L. At a population level, there is agreement between prediction of TBW in patients with pancreatic cancer estimated from the three equations. The best combination of low bias and narrow limits of agreement was observed when TBW was estimated from the equation developed in the underweight cancer patients relative to the normal weight cancer patients. When no established BIA prediction equation exists, practitioners should utilize an equation developed in a population with similar critical characteristics such as diagnosis, weight loss, body mass index and/or age. Conclusions Further research is required to determine the accuracy of the BIA prediction technique against a reference method in patients with pancreatic cancer.

Body proportions in three Nigerian tribes

Prediction equations of body composition based on measurements of whole-body bioelectrical impedance analysis (BIA) have been found to be population-specific. It was hypothesised that this may be, in part, due to differences in proportional limb lengths between ethnic or racial groups. As a preliminary to a survey of body composition in urban Nigerians using BIA, the relative limb lengths of the three major tribal groups (Hausa, Yoruba and Ibo) were determined. We found small (5-9%) but significantly longer limb lengths in Nigerians compared to a Caucasian population, but no significant differences between tribes. This implies that BIA prediction equations generated in a Caucasian population are inappropriate for use in a Nigerian population.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

New techniques in nutritional assessment: body composition methods

New techniques in air-displacement plethysmography seem to have overcome many of the previous problems of poor reproducibility and validity. These have made body-density measurements available to a larger range of individuals, including children, elderly and sick patients who often have difficulties in being submerged underwater in hydrodensitometry systems. The BOD POD air-displacement system (BOD POD body composition system; Life Measurement Instruments, Concord, CA, USA) is more precise than hydrodensitometry, is simple and rapid to operate (approximately 1 min measurements) and the results agree closely with those of hydrodensitometry (e.g. +/-3.4% for estimation of body fat). Body line scanners employing the principles of three-dimensional photography are potentially able to measure the surface area and volume of the body and its segments even more rapidly (approximately 10 s), but the validity of the measurements needs to be established. Advances in i.r. spectroscopy and mathematical modelling for calculating the area under the curve have improved precision for measuring enrichment of (H2O)-H-2 in studies of water dilution (CV 0.1-0.9% within the range of 400-1000 mu l/l) in saliva, plasma and urine. The technique is rapid and compares closely with mass spectrometry (bias 1 (SD 2) %). Advances in bedside bioelectrical-impedance techniques are making possible potential measurements of skinfold thicknesses and limb muscle mass electronically. Preliminary results suggest that the electronic method is more reproducible (intra-and inter-individual reproducibility for measuring skinfold thicknesses) and associated with less bias (+ 12%), than anthropometry (+ 40%). In addition to these selected examples, the 'mobility' or transfer of reference methods between centres has made the distinction between reference and bedside or field techniques less distinct than in the past.

Three dimensional preparatory trunk motion precedes asymmetrical upper limb movement

Three-dimensional trunk motion. trunk muscle electromyography and intra-abdominal pressure were evaluated to investigate the preparatory control of the trunk associated with voluntary unilateral upper limb movement. The directions of angular motion produced by moments reactive to limb movement in each direction were predicted using a three-dimensional model of the body. Preparatory motion of the trunk occurred in three dimensions in the directions opposite to the reactive moments. Electromyographic recordings from the superficial trunk muscles were consistent with preparatory trunk motion. However, activation of transversus abdominis was inconsistent with control of direction-specific moments acting on the trunk. The results provide evidence that anticipatory postural adjustments result in movements and not simple rigidification of the trunk. (C) 2000 Elsevier Science B.V. All rights reserved.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Expression, purification, crystallization, and NMR studies of the helicase interaction domain of Escherichia coli DnaG primase

in Escherichia coli, the DnaG primase is the RNA polymerase that synthesizes RNA primers at replication forks. It is composed of three domains, a small N-terminal zinc-binding domain, a larger central domain responsible for RNA synthesis, and a C-terminal domain comprising residues 434-581 [DnaG(434-581)] that interact with the hexameric DnaB helicase. Presumably because of this interaction, it had not been possible previously to express the C-terminal domain in a stably transformed E coli strain. This problem was overcome by expression of DnaG(434-581) under control of tandem bacteriophage gimel-promoters, and the protein was purified in yields of 4-6 mg/L of culture and studied by NMR. A TOCSY spectrum of a 2 mM solution of the protein at pH 7.0, indicated that its structured core comprises residues 444-579. This was consistent with sequence conservation among most-closely related primases. Linewidths in a NOESY spectrum of a 0.5 mM sample in 10 mM phosphate, pH 6.05, 0.1 M NaCl, recorded at 36 degreesC, indicated the protein to be monomeric. Crystals of selenomethionine-substituted DnaG(434-581) obtained by the hanging-drop vapor-diffusion method were body-centered tetragonal, space group I4(1)22, with unit cell parameters a = b 142.2 Angstrom, c = 192.1 Angstrom, and diffracted beyond 2.7 Angstrom resolution with synchrotron radiation. (C) 2003 Elsevier Inc. All rights reserved.