Error in measuring one-dimensignal probability distribution functions of random processes

Conclusions The relative error of the above method for measuring a one-dimensional integral probability distribution function is determined from (6) and it depends on the type of the measured function. It was shown, as an example of a normal distribution law, that the above error decreases with an increasing distribution function argument.The relative error in measuring the values of a probability distribution function does not depend on the type of the function and is detemined from (8). An effective means for raising the measurement precision consists of setting appropriately the pulse counter triggering threshold. The measurement error tends to its minimum value when x_t=1/2x_s.Translated from Izmeritel'naya Tekhnika, No. 7, pp. 20–23, July, 1969.     

The potential integral for a linear distribution over a triangular domain

In this paper an exact expression is derived for the potential at an arbitrary point due to a linear distribution of source over a triangular domain. The integral which gives the potential is evaluated by means of an extension of an analytical procedure previously evolved for a constant distribution. Numerical values of the potential are obtained for several field points by evaluating the above analytical expression, and are compared with those calculated by using triangle quadratures.     

Calculating particle velocities and concentrations in the space above a pseudofluidized bed

We offer a statistical model to calculate the dynamic characteristics of the disperse phase in the space above the bed. We have derived expressions which determine the distribution functions for particles on the basis of velocities and height in the space above the bed, the average values for velocity, flow, and particle concentration as functions of the height to which these particles are ejected at a given initial-velocity distribution. It is demonstrated that the concentration, flow, and mean velocity of the particles at any given height in the space above the bed depends only slightly on the form of the initial distribution, provided that its dispersion is maintained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 2, pp. 238–243, August, 1990.     

Strength distributions of warm frozen clay and its stochastic damage constitutive model

There are many defects, such as fissures and cavities, in warm frozen clay and in warm ice-rich frozen clay. These defects are distributed randomly, which make some mechanical properties of these clays exhibit great uncertainty. Thus it is unreasonable to take some deterministic values as the mechanics parameters of these frozen clays. Furthermore, warm frozen clay and warm ice-rich frozen clay are less stable than clays at colder temperatures. Therefore, it is necessary to determine the strength and constitutive relationship of these clays using probabilistic methods. In this paper, based on the characteristics of the random distribution of defects in the warm frozen clay and warm ice-rich frozen clay, the strength distribution laws for both clays are investigated at − 0.5 °C, − 1.0 °C and − 2.0 °C through a series of experimental data, respectively. The investigated results show that the Weibull distribution can more closely reflect the strength distribution law than other probability distributions. Based on the results mentioned above, a stochastic damage model for the warm frozen clay and warm ice-rich frozen clay was developed using the continuous damage theory and probability, as well as statistic theory. Comparing theoretical results of the model with experimental data at these three temperatures, respectively, it is found that the stress-strain relationships of the two kinds of frozen clays, especially their deformation characteristics after failures, could be described by the model very well. Since the range of strength variation for both kinds of frozen clays is very large, it is unsafe and unreasonable for engineering design to use the average strengths of frozen clay soils. The reliability of the strength of these two clays was investigated and discussed on the basis of the fact that the strength of warm frozen clay and warm ice-rich frozen clay satisfy the Weibull distribution.     

Determination of residual stresses in components of complex shape – correction of measurements using finite element method

Abstract

A method by which measured values of residual stresses in a component of complex shape may be corrected using the finite element is presented. The surface of the component is removed layer by layer and the residual stresses after removal of each layer are measured using X-ray diffraction; the correction factors are calculated using the finite element method, thereby obtaining the distribution of internal stresses in the complex component. In addition, methods of verifying the final values of the internal stresses are suggested. As examples, the distributions of the residual stresses, within several cross-sections of two types of heat treated shaft are calculated using the above method. Finally, the reliability of the results is discussed.

MST/16     

Study of Size Distribution in Nanostructured Se<Subscript>58</Subscript>Ge<Subscript>39</Subscript>Pb<Subscript>3</Subscript> Glass Using Various Characterization Methods

The present paper aims at the study of size distribution of particles in nanostructured Se₅₈Ge₃₉Pb₃ glass using X-ray diffraction (XRD), Transmission electron microscopy (TEM) and UV–visible spectrophotometer. The thin film sample has been prepared using melt quenching technique and inert gas consolidation method. The particle size distribution obtained from XRD and UV–Vis spectrophotometer shows more uncertainty than the results obtained from TEM measurements. The absorption spectra recorded on UV–Vis spectrophotometer is employed to get band gap values corresponding to different size distribution in sample. Further, it is concluded that TEM is the best measurement technique for size distribution as it has less uncertainty in the obtained results.     

Fluid-bed coater modifications and study of their influence on the coating process of pellets

Objective: In this study, different modifications of bottom spray fluid-bed coater with draft tube inserted were characterized and evaluated. Materials and methods: After coating the neutral pellets with polymeric solution comprising coloring agent pellet batches were characterized for coating variation, yield and degree of agglomeration. Results: Funnel-shaped distribution plate was found to improve process yield and decrease the degree of agglomeration at selected values of process parameters, whereas coating uniformity was worse in all cases when compared to conventional Wurster chamber. Results of the coating chamber with the swirl airflow generator indicate more uniform deposition of the coating material and in some cases an improved process yield and decreased formation of agglomerates when compared to conventional Wurster chamber. In series of experiments using Wurster chamber, having tangentially oriented air intake slots, which enabled introduction of air above the distribution plate, coating layer was more uniformly deposited on the pellet cores and formation of agglomerates was lower compared to the results obtained in a conventional Wurster coating chamber. Conclusion: Modifications of Wurster coating process by introducing swirling air motion within the draft tube or by introduction of air above the distribution plate have at selected values of process parameters resulted in reduced per-particle coating variation, degree of agglomeration and improved process yield.     

Measurement of activation energy values for sintering of active urania powder compacts

Abstract

Wide variations in sintering behaviour have been observed for uranium dioxide powder compacts prepared from ammonium diuranate (ADU) powder precursor and calcined at various temperatures. In general, it is observed using X-ray diffraction that powders calcined below 800°C are non-crystalline and they are also highly sinterable (active), whereas powders calcined above 800°C have poor sinterability and are designated inactive. A model has been proposed for measurement of the activation energy values for sintering of compacts of urania powder based upon a modification derived from Frenkel's sintering model as applicable to non-crystalline powders, from which the shrinkage rate at zero time (t → 0) can be obtained. Moreover, the associated effect on sintering due to the non-crystalline to crystalline transition with progressive thermal treatment is eliminated using this model. The activation energy values for sintering of the non-crystalline powders at various calcination temperatures are in good agreement and, below 800°C, values of ~167·5 kJ mol^?1 are obtained. For powders calcined above 800#x00B0;C, values of ~314·1 kJ mol^?1 are obtained.

MST/812     

Reliability study of ceramic matrix composites based on clinker portland doped with alumina and silica

A study was made of the Weibull modulus of white clinker portland reinforced with alumina and silica. The Weibull distribution was introduced as a way of measuring the reliability of materials through the slope or shape parameter, known as Weibull modulus, and it is used as a reference and estimation of the probability of failure. The manufacturing process of composite materials (3, 6 and 9% Al₂O₃ and SiO₂ by weight) includes mixing in a ball mill, cold isostatic pressing in wet bag at 180 MPa and sintering at 1400°C in air. Bending strength was used as the key property for measuring the Weibull modulus using more than 20 tests in all cases. The correlation coefficients obtained in all the estimations for the studied materials are above 95%. These ceramic matrix composite (CMCs) materials present a high Weibull modulus (in some materials about 26) and better behaviour than plain white clinker portland. Most results are above typical values of the conventional and advanced ceramics (between 5 and 15). Microstructural analysis was carried out to explain the reliable behaviour of these materials, a behaviour that could make them very interesting for structural applications.     

A Computer Simulation of Latent Image Formation in Photographic Emulsion by a Monte Carlo Method

A digital computer analysis has been made of photon absorption, chemical sensitization and latent image distribution in a silver halide photographic emulsion, using the Bayer Hamilton model but with a different approach in treating the positive holes.

In discussing the effect of sulphur sensitization it has been assumed that silver sulphide molecules can play a dual role in latent image formation, undergoing partial thermal dissociation to increase both the number of electron traps by providing more interstitial silver ions and that of positive hole traps by forming AgS^-. The increased interstitial silver ion concentration has also been supposed to lead to an increase in the stability of single silver atoms. As to gold sensitization, it has been assumed that the main effect of gold is to enhance the developahility of latent image centres.

Parameter values for simulation under various conditions of chemical sensitization have been calculated, based upon the above assumptions. The results have, as expected, reproduced in many respects those shown by experiments. Finally, a relation between the concentration of interstitial silver ions and the sulphur content in the emulsion grain has been derived.     

A two-dimensional analysis of multiple matrix cracking in a laminated composite close to its characteristic damage state

The proposed approach incorporates all the stress components of interest in each layer of a cracked cross-ply laminate. Its starting point is a very general distribution of the shearing stress in both types of layer, represented by a series, each term of which is the product of a trigonometric function in the axial coordinate, a hyperbolic function in the thickness coordinate and an undetermined coefficient a_q; all the other stress components in each layer are deduced from the above by using the equilibrium equations, interface continuity conditions and traction boundary conditions. Minimizing the complementary energy of the whole laminate yields an algebraic system whose unknowns (a_q) are the above coefficients. The validity of the proposed model is assessed by comparing the stress values it gives with those estimated through other semi-analytical models or a finite element method. Moreover, the series convergence is all the faster since the crack density is large, thus enabling careful investigation of the stress field when transverse cracking attains its saturation spacing.     

Zur Statistik in der Betriebsfestigkeit

About statistics in fatigue strength Material strength values can be distributed over a wide range. The lower limit of this range (e.g. minimum strength) is always well above zero. It is the reference point for design purposes. Formulas to describe the strength distribution F must be apt to explicitly fix this point. Formulas assuming negative or zero minimum values, as Normal or Weibull's two parametric distribution formula, are unsuited. The standard deviation is dependent of size (e.g. volume) of the specimens and therefore can not serve as a characteristic of a material or of a type of machine element. And therefore estimating minimum values via mean value and standard deviation is quite unreliable. This is especially critical with notched specimens where the volume at risk is extremely small. To evaluate reliable minimum values it is necessary to have a number of test specimens as high as possible and to extrapolate the distribution curve to the failure free time (or strength). The number of specimens can hardly be reduced. On the other hand the fatigue test time can be reduced by abstaining from searching the standard deviation. Usually an engineering object has to be designed absolutely failure free in the s‐n‐diagram. The allowable design reference point has to be situated below or left of the failure‐free curve F = 0. Small remaining risks resulting from non‐material influences in field application can by no means be quantified out of laboratory material tests.     

Study the Performance of the AC/DC Resistors During Their DC and AC Measurements

Some of traceability chains for the AC resistance measurements are based on AC/DC resistors. In this paper, performance of two types of them with different values has been investigated for their optimum utilization. Tinsley and Cambridge AC/DC resistors have been measured as DC resistors using different measurement methods and as AC resistors at various frequencies. DC direct method using digital reference multimeter is more accurate for the resistance values 1, 10, 100 Ω, and 1 kΩ. For the values 10 and 100 kΩ; measurement results are very near by using the DC direct and ratio methods. At 100 kΩ; representation of the resistance as an equivalent series resistance is not suitable at frequencies above 10 kHz, while for 100 mΩ and 1 Ω; the equivalent parallel representation is not suitable above the same frequency. The uncertainty analysis is also studied for all the obtained results.     

Are Iranian scientists recognized as their productivity enhances? A comparison of Iran’s impact to global norms in different subfields of Science Citation Index during 2002–2005

Witnessing a substantial growth rate in its scientific production, Iran is considered as one of the recently rising stars in scientific contribution scene. However, its impact in science progress is widely unknown, especially at global level. Studying Iran’s scholarly publications and recognition in SCI, the present communication tries to clarify the country’s science system performance using regression analyses and then to compare its performance to that of the world, using Relative Citation Rate (RCR) and Relative Subfield Citedness (RW). The results of the regression analyses reveal that although Iran displays considerable weaknesses in its performance, it is increasingly recognized as its outputs grow. According to the RCR values, Iran performed at/above the global level in 21 subfields. However, the RW values show that the country’s performance is above the global level in only two subfields. Although Iran is very far from an ideal situation; these evidences can be considered as heralds of a successful movement towards a wealthy scientific future.     

Spatially varied orientation selective epitaxial growth of CeO2(100) and (110) regions on Si(100) substrates by reactive magnetron sputtering utilizing electron beam irradiation

Spatially varied epitaxial growth of CeO₂(100) and CeO₂(110) regions on Si(100) substrates is attained using electron beam induced orientation selective epitaxial (OSE) growth by reactive magnetron sputtering. The spatially controlled OSE grown samples are made on Si(100) substrates with various electric resistivity values. By X-ray diffraction measurements, we obtain the lateral orientation mapping within the epitaxial layer surfaces and reveal existence of the transition regions in between the above mentioned two orientation areas. The width of the transition regions is clarified to decrease proportionally with the logarithm of underlying Si substrate resistivity. A surface potential distribution model is proposed to explain the results.     

Evaluation of the stability of gas hydrates in Northern Alaska

The factors which control the distribution of in situ gas hydrate deposits in colder regions such as Northern Alaska include; mean annual surface temperatures (MAST), geothermal gradients above and below the base of permafrost, subsurface pressures, gas composition, pore-fluid salinity and the soil condition. Currently existing data on the above parameters for the forty-six wells located in Northern Alaska were critically examined and used in calculations of depths and thicknesses of gas hydrate stability zones. To illustrate the effect of gas hydrate stability zones, calculations were done for a variable gas composition using the thermodynamic model of Holder and John (1982). The hydrostatic pressure gradient of 9.84 kPa/m (0.435 lbf/in²ft), the salinity of 10 parts per thousand (ppt) and the coarse-grained soil conditions were assumed. An error analysis was performed for the above parameters and the effect of these parameters on hydrate stability zone calculations were determined.After projecting the hydrate stability zones for the forty-six wells, well logs were used to identify and to obtain values for the depth and thickness of hydrate zones. Of the forty-six wells, only ten wells showed definite evidence of the presence of gas hydrates.     

Diffusion and electrical conductivity studies in some heterophase glasses containing bismuth

Self-diffusion coefficients of sodium in the temperature range 300 to 375° C have been measured for glasses in the system Na₂O-B₂O₃-Bi₂O₃-SiO₂, by using a radioactive tracer technique. All these glasses have a two-phase structure. The d.c. resistivities of these glasses were also measured over the temperature range 30 to 375° C. The correlation factors,f, of all the samples have been calculated by using the diffusion coefficients and d.c. resistivity values for temperatures above 300° C. The anomalously largef values in the case of Bi₂O₃-containing glasses are thought to be due to a distribution of sodium ions in the dispersed as well as the continuous phases in these systems.     

Sensitivity analysis of entropy-constrained designs of water distribution systems

A study of the relationship between the statistical entropy and hydraulic reliability of water distribution systems (WDS) was carried out by assessing the effects of layout, flow direction, and pipe costs. Because of an invariance property of the entropy function, different WDS layouts can have identical maximum entropy values. The properties of designs that have identical maximum entropy values were also compared. The results reinforce previous observations that entropy is a potential surrogate measure for hydraulic reliability and suggest that any influences due to the design factors mentioned above are negligible. Maximum entropy designs are shown to be more reliable than other designs, while designs with different layouts but equal maximum entropy values have very similar levels of reliability. The head-dependent analysis method was used and revealed the correlation between entropy and reliability more clearly than hitherto achieved using demand-driven analysis.     

Sur quelques facteurs intervenant dans le bombardement de couches pulvérisées

The voltage distributions of the discharges employed in sputtering are reviewed. In bias sputtering the voltage difference between the substrates and the discharge plasma is used to obtain film bombardment by charged particles during growth. This voltage difference, which is the effective bias, is related to the externally applied bias and to the voltage distribution for the discharge in various sputtering systems. It is shown that the effective bias is generally different from the external bias and may even exist without it; this makes the externally applied bias illusory as a process controlling parameter. Both positive and negative biasing is discussed. Due to the inconvenience of using positive values of the effective bias in film deposition, only negative values of the effective bias are dealt with when discussing the measurement of the effective bias and the energy distribution of ions bombarding the films.     

A new type of extreme value distributions

The three classical pairs of extreme value distributions correspond to random variables with ranges of values unbounded from either one or both sides. Some applications of statistics of extremes, however, deal with variables, which are bounded on both sides (local values of specific fracture energy in crack diffusion theory is one such example). In this paper, we derive a fourth pair of extreme value distributions, which are supported on a finite segment (one for maxima and one for minima). First, we propose a derivation of the three known maximal value distributions, which lends itself to a generalization (everything is done for maxima, since transition to minima is standard). The derivation is then extended to a slightly more general setting, and the fourth distribution is obtained. It is explained that certain fact concerning groups of transformations of the real line prevents any further generalization, i.e. the extended list of extreme value distributions is complete. The three classical maximal value distributions can be obtained as limits of the new one. A possible criterion of when one may expect the new distribution to be more adequate than the Weibull distribution is offered. An illustrative numerical example is considered, in which the scatter of sample minima is modeled by both Weibull and the new distribution. Another example shows that when the modeling of data requires very high values of the shape parameter of the Weibull distribution, the new distribution may be expected to have much smaller “shape parameter” values. The modeling of experimentally observed scatter of crack arrest length, using the Weibull distribution, is compared to that using the new distribution.