Confidence intervals in Cavalieri sampling

The aim of this study is to derive a formula that allows the prediction, from a Cavalieri data sample, of an appropriate confidence interval for a parameter Q. Two different approaches are used to address the problem. The first approach is to investigate whether the asymptotic distribution of the Cavalieri estimator exists when the sampling period T tends to zero. In particular, the distribution of the standardized version of the Cavalieri estimator z_T is analysed for a measurement function f whose smoothness constant is an integer number m. The analysis reveals that when the first noncontinuous derivative of f, f^(m), exhibits a unique discontinuity, the asymptotic distribution of z_T exists and it has a bounded support. An analytical expression of the distribution is derived for the cases m = 0 and 1. However, when f^(m) has two or more discontinuities, the asymptotic distribution of z_T does not exist and its support may be unbounded. In the second approach, a generalized version of the refined Euler Mac‐Laurin summation formula, valid for measurement functions with a fractional, rather than just an integer, smoothness constant, is applied to the Cavalieri estimator. As a result, a formula that predicts a lower and upper bound for the true parameter is derived for small T. This bound prediction formula is applied to Cavalieri data samples of human cerebral cortex. In particular, for sample sizes n = 8, 12 and 16, the true volume of cerebral cortex is bounded by relative distances 8%, 4% and 2% of the Cavalieri estimate, respectively.     

New variance expressions for systematic sampling: the filtering approach

We present a collection of variance models for estimators obtained by geometric systematic sampling with test points, quadrats, and n‐boxes in general, on a bounded domain in n‐dimensional Euclidean space ?ⁿ, n = 1, 2, ... , and for systematic rays and sectors on the circle. The approach adopted ? termed the filtering approach ? is new and different from the current transitive approach. This report is only preliminary, however, because it includes only variance models in terms of the covariogram of the measurement function. The estimation step is in preparation.     

Structural analyses of Nd-doped CeO2 thin films deposited by pulsed laser deposition

CeO₂ thin films doped with neodymium oxides for application to gas sensors have been elaborated by the pulsed laser deposition technique. The films were deposited on orientated Si (100) substrates with variable deposition times (t = 90, 180 and 360 s) and molar fractions of Nd₂O₃ (0, 6.5, 15, 21.5 and 27 at.%). The resulting Nd–CeO₂ thin films were characterized by means of X‐ray diffraction analysis, scanning electron microscopy and transmission electron microscopy equipped with EDS (Energy Dispersive Spectrometer) microanalysis. From X‐ray diffraction analyses, it is clearly established that the texture is modified by Nd additions. The preferred (111) orientations of the CeO₂ crystals change into the (200) orientation. The morphology of the CeO₂ grains changes from triangles, for pure CeO₂ thin films, to spherical grains for Nd‐doped films. In addition, cell parameter analyses from X‐ray diffraction data show that a partial chemical substitution of Ce by Nd should occur in the face‐centred cubic lattice of ceria: this should give rise to Ce_1‐xNd_xO_2?z phases with oxygen non‐stoichiometry.     

An extrapolation method for the determination of Cliff-Lorimer kAB factors at zero foil thickness

An extrapolation method is proposed to be useful for the determination of the Cliff-Lorimer k_AB factor at zero foil thickness. The method consists of measuring k_AB factors as a function of the measured foil thickness, t_M, and extrapolating the relationship toward t_M=0. The intersection between the extrapolated line and the ordinate of t_M=0 gives (k_AB)₀ which is free from the effect of absorption. The straight line extrapolation that can be achieved by a linear-least squares method is particularly developed to eliminate arbitrariness introduced in the extrapolation process. The extrapolation method is applied to data available in the literature. It is shown that the method yields the (k_AB)₀ factors compatible with those predicted from the theoretical calculation. It is also shown that this method can circumvent several problems which make it complex and difficult to determine accurate values of the absorption-free k_AB factors. Using the straight line extrapolatioin, it is possible to estimate the degree of the thickness overestimation which arises when the foil thickness is measured by the contamination spot separation (CSS) method. Validity of the straight line extrapolation is further discussed.     

Dissociation of basal dislocations in hexagonal barium titanate

Dislocation substructure in hot-pressed hexagonal BaTiO₃ ceramics was analysed by transmission electron microscopy. Two dislocation networks each consisting of dissociated half-partials were determined for the Burgers vectors ( b ) using the g · b  = 0 effective invisibility criteria, and the true directions ( u ) by trace analysis. Each of the networks contains three partial nodes that are in the form: 1/3[010]+1/3[100]+1/3[100]+1/3[100] = 0, where four partials meet at a point and the Burgers vectors are conserved, as analysed by the weak-beam dark field technique. Basal dislocation with b _b = 1/3<110> is dissociated into two prism plane half-partials with b _hp = 1/3<100> by: 1/3<110> → 1/3<010> + 1/3<100>. Dissociation of basal dislocation by a glide mechanism creates a stacking fault when shear occurs along <100> in the c-layer of (000l), where l = 1, 3, 4 and 6, of the (chc)₁(chc)₂ (or (CBC)(ABA)) stacking sequence. The slip system of 1/3<110>(0001) in hexagonal BaTiO₃ has been activated at 1300 °C by hot-pressing under ∼25.8 MPa. Plastic flow contributing to the densification of hexagonal BaTiO₃ ceramics occurs through glide of half-partials in the basal plane by a glide-controlled dislocation glide mechanism. Dislocation motion governed by the Peierls mechanism, where velocity is determined by both correlated and uncorrelated double-kink nucleation on two half-partials, is discussed.     

Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses

Exact solutions are presented for the free vibration and buckling of rectangular plates having two opposite edges (x=0 and a) simply supported and the other two (y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress σ_x=−N₀[1−α(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement (w) to vary as sin(mπx/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients, for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and b yields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters α=0,0.5,1,1.5,2, for which α=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for α=0,1,2 obtained by the method of integration of the differential equation (α=0) or the method of energy (α=1,2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b=0.5,1,2 subjected to three types of loadings (α=0,1,2), with load intensities N₀/N_cr=0,0.5,0.8,0.95,1, where N_cr is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes are also shown.     

Temperature measurement in orthogonal metal cutting

Orthogonal cutting experiments were carried out on steel at different feedrates and cutting speeds. During these experiments the chip temperatures were measured using an infrared camera. The applied technique allows us to determine the chip temperature distribution at the free side of the chip. From this distribution the shear plane temperature at the top of the chip as well as the uniform chip temperature can be found. A finite-difference model was developed to compute the interfacial temperature between chip and tool, using the temperature distribution measured at the top of the chip.Nomenclature contact length with sticking friction behaviour [m] - c specific heat [J kg^–1 K^–1] - contact length with sliding friction behaviour [m] - F _P feed force [N] - F _V main cutting force [N] - h undeformed chip thickness [m] - h _c deformed chip thickness [m] - i,j denote nodal position - k thermal conductivity [W m^–2 K^–1] - L chip-tool contact length [m] - p defines time—space grid, Eq. (11) [s m^–2] - Q _C heat rate entering chip per unit width due to friction at the rake face [W m^–1] - Q _T total heat rate due to friction at the rake face [W m^–1] - Q _% percentage of the friction energy that enters the chip - q ₀ peak value ofq(x) [W m^–2] - q _e heat rate by radiation [W] - q(x) heat flux entering chip [W m^–2] - t time [s] - T temperature [K] - T _C uniform chip temperature [°C] - T _max maximum chip—tool temperature [°C] - T _mean mean chip—tool temperature [°C] - T _S measured shear plane temperature [°C] - x,y Cartesian coordinates [m] - V cutting speed [m s^–1] - V _C chip speed [m/s] - rake angle - ,, control volume lumped thermal diffusivity [m² s^–1] - emmittance for radiation - exponent, Eq. (3) - density [kg m^–3] - Stefan-Boltzmann constant [W m^–2 K⁴] - (x) shear stress distribution [N m^–2] - shear angle     

About the role of the various types of secondary electrons (SE1; SE2; SE3) on the performance of LVSEM

The relative weight, δ_Β, of the yield of secondary electrons, SE₂, induced by the backscattered electrons, BSE, with respect to that, δ_P, of secondary electrons, SE₁, induced by the primary electrons, PE, is deduced from simple theoretical considerations. At primary energies E₀ larger than E_M (where the total SE yield δ = δ_P + δ_B is maximum), the dominant role of the backscattering events is established. It is illustrated in SEM by a direct comparison of the contrast between SE images and BSE images obtained at E₀ ～ 5 keV and E₀ ～ 15 keV on a stratified specimen. At energies E₀ less than E_M, the dominant role of SE₁ electrons with respect to SE₂ (and SE₃) is established. It is illustrated by the better practical resolution of diamond images obtained with an in‐lens detection in low voltage SEM E₀ ～ 0.2–1 keV range compared with that obtained with a lateral detector. The present contribution illustrates the improved performance of LVSEM in terms of contrast and of practical resolution as well as the importance of variable voltage methods for subsurface imaging. The common opinion that the practical lateral resolution is given by the incident spot diameter is also reconsidered in LVSEM.     

Method of retrospective prediction as applied to predicting the trend of a steady random process

An effective algorithm of predicting the trend (deterministic basis) m(t) of a steady (in a wide sense) random process X(t) is proposed. The initial information about the random process X(t) is limited to the assumption that its mean value (mathematical expectation) is equal to zero. The interval [0, T] of observation of the trend sum m(t) and the sample x(t) of the random process X(t) is assumed to be finite. Construction of a prediction estimate μ(T +τ), where τ is the prediction interval, ensures automatic allowance for statistical characteristics of the random process X(t).     

Surface roughness measurement in turning carbon steel AISI 1045 using wiper inserts

Surface roughness of the workpiece is an important parameter in machining technology. Wiper inserts have emerged as a significantly class of cutting tools, which are increasingly being utilized in last years. This study considers the influence of the wiper inserts when compared with conventional inserts on the surface roughness obtained in turning. Experimental studies were carried out for the carbon steel AISI 1045 because of its great application in manufacturing industry. Surface roughness is represented by different amplitude parameters (R_a, R_zD, R_3z, R_q, R_t, R_a/R_q, R_q/R_t, R_a/R_t). With wiper inserts and high feed rate it is possible to obtain machined surfaces with R_a < 0.8 μm (micron). Consequently it is possible to get surface quality in workpiece of mechanics precision without cylindrical grinding operations.     

Influence of nozzle exit tip thickness on the performance and flow field of jet pump

The influence of exit tip thickness of nozzle δ _e on the flow field and performance of a jet pump was studied numerically in this paper. It is found that δ _e has influence on the distribution of turbulence kinetic energy k. If δ _e is ignored, k takes the highest value but dissipates rapidly than that of nozzle with a certain tip thickness. δ _e also affect apparently the development of tip vortex, which will occur near the exit tip of nozzle. The bigger the δ _e is, the larger the vortex is. The tip vortex develops with the increase of flow rate ratio q. When q=1 and δ _e =0.6∼0.8mm, a small vortex will be found downstream the tip vortex. And a concomitant vortex happens down the tip vortex in the case of q=1 and δ _e =0.8mm. As q increases to 2, the downstream small vortex disappears and the concomitant vortex becomes bigger. It is also found that the tip vortex might interact with the possible backflow that formed in the throat tube and parts of suction chamber. The center of backflow was affect evidently by δ _e . With the increase of δ _e , the center of backflow under the same q will go downstream. When δ _e =0.4mm, the center of backflow goes farthest. Then, as the further increase of δ _e , the center of backflow will go back some distance. Although, δ _e has relatively great influence on the flow field within the jet pump, it exerts only a little impact on the performance of jet pump. When δ _e =0.2∼0.6mm, the jet pump possess better performance. In most case, it is reasonable to ignore the nozzle exit tip thickness in performance prediction for the purpose of simplicity. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

Quasi-static axial compression of thin-walled circular aluminium tubes

This paper presents further experimental investigations into axial compression of thin-walled circular tubes, a classical problem studied for several decades. A total of 70 quasi-static tests were conducted on circular 6060 aluminium tubes in the T5, as-received condition. The range of D/t considered was expanded over previous studies to D/t=10–450. Collapse modes were observed for L/D10 and a mode classification chart developed. The average crush force, F_AV, was non-dimensionalised and an empirical formula established as F_AV/M_P=72.3(D/t)^0.32. It was found that test results for both axi-symmetric and non-symmetric modes lie on a single curve. Comprehensive comparisons have been made between existing theories and our test results for F_AV. This has revealed some shortcomings, suggesting that further theoretical work may be required. It was found that the ratio of F_MAX/F_AV increased substantially with an increase in the D/t ratio. The effect of filling aluminium tubes with different density polyurethane foam was also briefly examined.     

Baseline correction of AFM force curves in the force–time representation

This note reports on the proper correction of force data acquired with an atomic force microscope (AFM). The force–time representation is hereby used to obtain the correction factors for the overall offset and slope for a single force–time curve, as the initial force, F₀ = F(t₀), and the rate of change in the force per unit of time, dF/dt, respectively. The report shows that a complete set of force data, including the approach, delay and retraction regions, can be simultaneously corrected in the force–time representation by subtracting the line CL_t = F₀ + dF/dt·t to the experimental data. The method described here outperforms the one commonly employed in the correction of AFM force curves and highlights the convenience of using the force–time representation for force data processing wherein the artifactual behavior can be expressed as a single, differentiable function of time.     

Modelling of Tool Wear Based on Component Forces

Polynomial and exponential wear models of the joint effect of different combinations of component forces or ratios were fitted to determine the wear model that would give the best approximation of actual tool wear rates. Statistical analysis revealed the combination of force ratios: F ₁=F _f/F _t, F ₂=F _r/F _t and F ₄ = to have the highest statistical significance with tool wear rate based on F _cal and r ² statistics for both polynomial and exponential models, with the latter giving the best approximation of the actual tool wear rates. A wear map was established using the exponential wear model of the force ratios for the machining of a nimonic C-263 nickel-base alloy with PVD TiN/TiCN/TiN-coated carbide insert grade.     

An electron microscopy study of the phase Al3Fe

The phase Al₃Fe (monoclinic C2/m, a = 1·549 nm, b = 0·808 nm, c = 1·248 nm, β = 107·8°) has been studied by transmission electron microscopy (TEM) and high resolution electron microscopy (HREM). Crystals were obtained from a direct chill-cast ingot of an Al-0·25 wt% Fe-0·13 wt% Si alloy. Extracted crystals were prepared by dissolving the aluminium phase in butanol and filtering off the particles. The extracted Al₃Fe crystals were mainly (100) platelets. The monclinic lattice was confirmed by tilt experiments and the mirror plane was confirmed by convergent beam electron diffraction. Experimental HREM images from the [100] and [110] projection agreed with images calculated by the multislice method. The interpretation of images in terms of a projected crystal structure is discussed. Common defects in Al₃Fe crystals were: twins on (100) and faults on (001). The (001) faults could be described by a displacement 1/2·[100] on a fault plane at z = 0·5 in the unit cell. A model for (001) faults, based on multiple twinning, is proposed.     

Estimation of the number of stellate cells in a liver with the smooth fractionator

To better evaluate the activation and proliferative response of hepatic stellate cells (HSC) in hepatic fibrosis, it is essential to have sound quantitative data in non‐pathological conditions. Our aim was to obtain the first precise and unbiased estimate of the total number of HSC in the adult rat, by combining the optical fractionator, in a smooth sampling design, with immunocytochemistry against glial fibrillary acidic protein. Moreover, we wanted to verify whether there was sufficiently relevant specimen inhomogeneity that could jeopardize the high expected estimate precision when using the smooth fractionator design for HSC. Finally, we wanted to address the question of what sampling scheme would be advisable a priori for future studies. Microscopical observations and quantitative data provided no evidence for inhomogeneity of tissue distribution of HSC. Under this scenario, we implemented a baseline sampling strategy estimating the number (N?) of HSC as 207E⁰⁶ (CV = 0.17). The coefficient of error [CE(N?)] was 0.04, as calculated by two formerly proposed approaches. The biological difference among animals contributed ? 95% to the observed variability, whereas methodological variance comprised the remaining 5%. We then carried out a half reduction of sampling effort, at the level of both sections and fields. In either occasion, the CE(N?) values were low (? 0.05) and the biological variance continued to be far more important than methodological variance. We concluded that our baseline sampling (counting 650–1000 cells/rat) would be appropriate to assess the lobular distribution and the N? of HSC. However, if the latter is the only parameter to be estimated, around half of our baseline sampling (counting 250–600 cells/rat) would still generate precise estimates [CE(N?) < 0.1], being in this case more efficient to reduce the number of sections than to reduce the sampled fields.     

Grease Lubrication of Rolling Bearings in Spacecraft (I)

A test rig for measuring the rate of evaporation of lubricant from an operating bearing into an evacuated space through a seal was built and data for two different seal designs were obtained. The evaporation data is found to fil a probabilistic function m =m₀[1 ? e^?(1/a)^β] where m = mass lubricant lost in time l. If vapor pressure data are available, one may then run accelerated tests at elevated temperatures, convert the data to a desired operating temperature and use the above function for predictive purposes.     

Third-order aberration theory of Wien filters for monochromators and aberration correctors

Third-order aberrations at the first and the second focus planes of double focus Wien filters are derived in terms of the following electric and magnetic field components – dipole: E₁, B₁; quadrupole: E₂, B₂; hexapole: E₃, B₃ and octupole: E₄, B₄. The aberration coefficients are expressed under the second-order geometrical aberration free conditions of E₂ = −(m + 2)E₁/8R, B₂ = −mB₁/8R and E₃R²/E₁ − B₃R²/B₁ = m/16, where m is an arbitrary value common to all equations. Aberration figures under the conditions of zero x- and y-axes values show very small probe size and similar patterns to those obtained using a previous numerical simulation [G. Martínez & K. Tsuno (2004) Ultramicroscopy, 100 , 105–114]. Round beam conditions are obtained when B₃ = 5m²B₁/144R² and (E₄/E₁ − B₄/B₁)R³ = −29m²/1152. In this special case, aberration figures contain only chromatic and aperture aberrations at the second focus. The chromatic aberrations become zero when m = 2 and aperture aberrations become zero when m = 1.101 and 10.899 at the second focus. Negative chromatic aberrations are obtained when m < 2 and negative aperture aberrations for m < 1.101. The Wien filter functions not only as a monochromator but also as a corrector of both chromatic and aperture aberrations. There are two advantages in using a Wien filter aberration corrector. First, there is the simplicity that derives from it being a single component aberration correction system. Secondly, the aberration in the off-axis region varies very little from the on-axis figures. These characteristics make the corrector very easy to operate.     

Pecularities of nanocrystal formation in rapidly quenched (FeCo)MoCuB amorphous alloys

The effect of the substitution of Fe by Co on the enhancement of glass‐forming ability limits and subsequent nanocrystallization was studied in a rapidly quenched amorphous system (Fe_xCo_y)₇₉Mo₈Cu₁B₁₂ for y/x ranging from 0 to 1. The effect of Cu on nanocrystallization was investigated by comparison with Cu‐free amorphous Fe₈₀Mo₈B₁₂. Systems partially crystallized at the surface layer were prepared for y/x = 0 using different quenching conditions. The effect of heat treatment of master alloys used for ribbon casting was also assessed. The microstructure and surface/bulk crystallization effects were analysed using transmission electron microscopy and electron and X‐ray diffraction in relation to the expected enhancement of high‐temperature soft magnetic properties, drastically reduced grain sizes (～5 nm) and Co content. Unusual surface phenomena were observed, indicating the origin of possible nucleation sites for preferential crystallization in samples with low Co content.     

Computer-aided selection of optimum machining parameters in multipass turning

In this paper a model and the interactive program system MECCANO2 for multiple criteria selection of optimal machining conditions in multipass turning is presented. Optimisation is done for the most important machining conditions: cutting speed, feed and depth of cut, with respect to combinations of the criteria, minimum unit production cost, minimum unit production time and minimum number of passes. The user can specify values of model parameters, criterion weights and desired tool life. MECCANO2 provides graphical presentation of results which makes it very suitable for application in an educational environment.Nomenclature a _min,a _max minimum and maximum depth of cut for chipbreaking [mm] - a _w maximum stock to be machined [mm] - C _a, _a, _a coefficient and exponents in the axial cutting force equation - C _r, _r, _r coefficient and exponents in the radial cutting force equation - C _T, , , coefficient and exponents in the tool life equation - C _v, _v, _v coefficient and exponents in the tangential cutting force equation - D _w maximum permissible radial deflection of workpiece [mm] - F _a axial cutting force [N] - F _b design load on bearings [N] - F _c clamping force [N] - F _k ^/* minimum value of criterionk, k=1, ...,n, when considered separately - f _m rotational flexibility of the workpiece at the point where the cutting force is applied [mm Nm^–1] - f _r radial flexibility of the workpiece at the point where the cutting force is applied [mm N^–1] - F _r radial cutting force [N] - F _tmax maximum allowed tangential force to prevent tool breakage [N] - F _v tangential cutting force [N] - k slope angle of the line defining the minimum feed as a function of depth of cut [mm] - l length of workpiece in the chuck [mm] - L length of workpiece from the chuck [mm] - L _c insert cutting edge length [mm] - M _g cost of jigs, fixtures, etc. [$] - M _o cost of labour and overheads [$/min] - M _u tool cost per cutting edge [$] - n number of criteria considered simultaneously - N _q, N_p minimum and maximum spindle speed [rev/min] - N _s batch size - N _z spindle speed for maximum power [rev/min] - P _a maximum power at the point where the power-speed characteristic curve changes (constant power range) [kW] - R tool nose radius [mm] - r workpiece radius at the cutting point [mm] - r _c workpiece radius in the chuck [mm] - s _min,s _max minimum and maximum feed for chipbreaking [mm] - T tool life [min] - T _a process adjusting time [min] - T _b loading and unloading time [min] - T _d tool change time [min] - T _des desired tool life [min] - T _h total set-up time [min] - T _t machining time [min] - V _rt speed of rapid traverse [m/min] - W volume of material to be removed [mm³] - W _k weight of criterionk, k=1, ...,n - x=[x ₁,x ₂,x ₃ ] ^T vector of decision variables - x ₁ cutting speed [m/min] - x ₂ feed [mm/rev] - x ₃ depth of cut [mm] - approach angle [rad] - _a coefficient of friction in axial direction between workpiece and chuck - _c coefficient of friction in circumferential direction between workpiece and chuck