Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Experimental Studies on Mass Distribution of Impinging Jets

Noting that practical impinging injectors are likely to have skewness, an experimental study has been made to understand the behavior of such jets using water as the simulant. In perfectly impinging jets, a high aspect ratio ellipse-like mass distribution pattern is obtained with major axis normal to the plane of two jets whereas in skewed jets the major axis turns from its normal position. A simple analysis shows that this angle of turn is a function of skewness fraction and impingement angle only and is independent of injection velocity. Experimental data from both mass distribution and photographic technique validate this prediction.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

Potential and electric field distribution in a ceramic disc insulator string with faulty insulators

Ceramic/Porcelain suspension disc insulators are widely used in power systems to provide electrical insulation and mechanically support for high-voltage transmission lines. These insulators are subjected to a variety of stresses, including mechanical, electrical and environmental. These stresses act in unison. The exact nature and magnitude of these stresses vary significantly and depends on insulator design, application and its location. Due to various reasons the insulator disc can lose its electrical insulation properties without any noticeable mechanical failure. Such a condition while difficult to recognize, can enhance the stress on remaining healthy insulator discs in the string further may lead to a flashover. To understand the stress enhancement due to faulty discs in a string, attempt has been made to simulate the potential and electric field profiles for various disc insulators presently used in the country. The results of potential and electric filed stress obtained for normal and strings with faulty insulator discs are presented.

A Model for the Temperature Distribution in Resin Impregnated Paper Bushings

Resin impregnated paper (RIP) is a relatively new insulation system recommended for the use in transformer bushings. In the recent past, RIP has acquired prominence as insulation in bushings, over conventional oil impregnated paper (OIP), in view of its overwhelming advantages the more important among them being low dielectric loss and possibility for positioning the bushing at any desired angle over the transformer. In addition, the fact that such systems do not pose problems of fire hazard is counted as a very important consideration. The disadvantage of RIP compared to OIP, however, is its much higher cost and involved manufacturing process. The temperature rise in RIP bushings under normal operating conditions is seen to be a difficult parameter to control in view of the limited options for effective cooling. It is therefore essential to take serious note of this aspect, to arrest rapid deterioration of bushing. The degradation of dry-type insulation such as RIP is often due to thermal stress. The long time performance thereof, depends strongly, on the maximum operating temperature. With this in view, the Authors have developed a theoretical model and computational method to study the temperature distribution in the body of insulation. The Authors consider that the basis for the model as being the temperature and electric stress aided AC conductivity. The ensuing heat balance (continuity) equations in 2-D cylindrical geometry are treated as a Dirichelet-Neumann boundary value problem.

Role of interface curvature on stress distribution under indentation for ZrN/Zr multilayer coating

Contact damage in curved interface nano-layeredmetal/nitride (150 (ZrN)/10 (Zr) nm) multilayer is investigated in order to understand the role of interface morphology on contact damage under indentation. A finite element method (FEM) model was formulated with different wavelengths of 1000 nm, 500 nm, 250 nm and common height of 50 nm, which gives insight on the effect of different curvature on stress field generated under indentation. Elastic-plastic properties were assigned to the metal layer and substrate while the nitride layer was assigned perfectly elastic properties. Curved interface multilayers show delamination along the metal/nitride interface and vertical cracks emanating from the ends of the delamination. FEM revealed the presence of tensile stress normal to the interface even under the contact, along with tensile radial stresses, both present at the valley part of the curve, which leads to vertical cracks associated with interfacial delamination. Stress enhancement was seen to be relatively insensitive to curvature. (C) 2014 Elsevier B.V. All rights reserved.

Reconstructing The Vertical Distribution Of The Aeolian Saltation Mass Flux Based On The Probability Distribution Of Lift-Off Velocity

The probability distribution of lift-off velocity of the saltating grains is a bridge to linking microscopic and macroscopic research of aeolian sand transport. The lift-off parameters of saltating grains (i.e., the horizontal and vertical lift-off velocities, resultant lift-off velocity, and lift-off angle) in a wind tunnel are measured by using a Phase Doppler Particle Analyzer (PDPA). The experimental results show that the probability distribution of horizontal lift-off velocity of saltating particles on a bed surface is a normal function, and that of vertical lift-off velocity is an exponential function. The probability distribution of resultant lift-off velocity of saltating grains can be expressed as a log-normal function, and that of lift-off angle complies with an exponential function. A numerical model for the vertical distribution of aeolian mass flux based on the probability distribution of lift-off velocity is established. The simulation gives a sand mass flux distribution which is consistent with the field data of Namikas (Namikas, S.L., 2003. Field measurement and numerical modelling of acolian mass flux distributions on a sandy beach, Sedimentology 50, 303-326). Therefore, these findings are helpful to further understand the probability characteristics of lift-off grains in aeolian sand transport. (c) 2007 Elsevier B.V. All rights reserved.

Interface Layer Effect On The Stress Distribution Of A Wafer-Bonded Bilayer Structure

The interface layer plays an important role in stress transfer in composite structures. However, many interface layer properties such as the modulus, thickness, and uniformity are difficult to determine. The model developed in this article links the influence of the interface layer on the normal stress distribution along the layer thickness with the layer surface morphology before bonding. By doing so, a new method of determining the interfacial parameter(s) is suggested. The effects of the layer thickness and the surface roughness before bonding on the normal stress distribution and its depth profile are also discussed. For ideal interface case with no interfacial shear stress, the normal stress distribution pattern can only be monotonically decreased from the interface. Due to the presence of interfacial shear stress, the normal stress distribution is much more complex, and varies dramatically with changes in the properties of the interface layer, or the dimensions of the bonding layers. The consequence of this dramatic stress field change, such as the shift of the maximum stress from the interface is also addressed. The size-dependent stress distribution in the thickness direction due to the interface layer effect is presented. When the interfacial shear stress is reduced to zero, the model presented in this article is also demonstrated to have the same normal stress distribution as obtained by the previous model, which does not consider the interface layer effect.

Angular distribution and conversion of multi-keV L-shell X-ray sources produced from nanosecond laser irradiated thick-foil targets

An experimental study on the angular distribution and conversion of multi-keV X-ray sources produced from 2 ns-duration 527nm laser irradiated thick-foil targets on Shenguang II laser facility (SG-II) is reported. The angular distributions measured in front of the targets can be fitted with the function of f(theta) = alpha+ (1- alpha)cos(beta) theta (theta is the viewing angle relative to the target normal), where alpha = 0.41 +/- 0.014, beta = 0.77 +/- 0.04 for Ti K-shell X-ray Sources (similar to 4.75 keV for Ti K-shell), and alpha = 0.085 +/- 0.06, beta = 0.59 +/- 0.07 for Ag/Pd/Mo L-shell X-ray Sources (2-2.8 keV for Mo L-shell, 2.8-3.5 keV for Pd L-shell, and 3-3.8 keV for Ag L-shell). The isotropy of the angular-distribution of L-shell emission is worse than that of the K-shell emission at larger viewing angle (>70 degrees), due to its larger optical depth (stronger self-absorption) in the cold plasma side lobe Surrounding the central emission region, and in the central hot plasma region (emission region). There is no observable difference in the angular distributions of the L-shell X-ray emission among Ag, Pd, and Mo. The conversion efficiency of Ag/Pd/Mo L-shell X-ray sources is higher than that of the Ti K-shell X-ray sources, but the gain relative to the K-shell emission is not as high as that by using short pulse lasers. The conversion efficiency of the L-shell X-ray sources decrease, with increasing atomic numbers (or X-ray photon energy), similar to the behavior of the K-shell X-ray Source.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

The distribution of Corixidae in relation to the water quality of British lakes: A monitoring model

This article is an attempt to devise a method of using certain species of Corixidae as a basis for the assessment of general water quality in lakes. An empirical graphical representation of the distribution of populations or communities of Corixidae in relation to conductivity, based mainly on English and Welsh lakes, is used as a predictive monitoring model to establish the "expected" normal community at a given conductivity, representing the total ionic concentration of the water body. A test sample from another lake of known conductivity is then compared with "expected" community. The "goodness of fit" is examined visually or by calculation of indices of similarity based on the relative proportions of the constituent species of each community. A computer programme has been devised for this purpose.

Modelagem numérica de ligações viga-coluna em aço sob momento fletor e força normal.

As ligações desempenham um papel fundamental no comportamento global das estruturas de aço. Inúmeros trabalhos de pesquisa têm sido desenvolvidos para entender o comportamento real de uma ligação e sua influência na resistência global dos pórticos. Atualmente, a Norma Brasileira de estruturas de aço de edificações, NBR 8800, considera o comportamento das ligações entre duas situações extremas: rígidas, onde não ocorre nenhuma rotação entre os membros conectados, transferindo momento fletor, força cortante e força normal; ou flexíveis, caracterizadas pela liberdade de rotação entre os membros conectados, impedindo a transmissão de momento fletor. Outras normas de projeto de estruturas de aço, consideram que as ligações apresentam um comportamento intermediário, ou seja, semi-rigídas, que podem estar submetidas a uma combinação de momento fletor e esforço normal. Porém, mesmo com a combinação, estas normas não consideram a presença de esforço normal (tração e/ou compressão). Uma limitação empírica de 5% da resistência plástica da viga é a única condição imposta no Eurocode 3. Para o estudo da ligação semi-rigída será utilizada a filosofia do Método das Componentes, que verifica a resistência da ligação e sua classificação quanto à rigidez rotacional, desenvolvida através de modelos mecânicos (modelos de molas). O objetivo deste trabalho é descrever alguns resultados de caracterização de ligações viga-coluna com placa de extremidade ajustada à altura da viga obtidos através de um modelo de elementos finitos. Para tal, será realizada uma análise não-linear geométrica e de material. Esta análise possibilitará avaliar os principais parâmetros que influenciam no comportamento deste componente no que diz respeito a sua avaliação em termos de distribuição de tensões e deformações no modelo de forma global.

Localization and distribution of tissue type and urokinase type plasminogen activators and their inhibitors type 1 and 2 in human and rhesus monkey fetal membranes

Fetal membranes consist of 10 distinct layers including components of amnion, chorion and decidua, the latter being of maternal origin. They form mechanically integrated sheets capable of retaining amniotic fluid and play an essential role in protecting fetal growth and development in the pregnant uterus. The extracellular matrix, substrate for plasminogen activators (PAs), is an important supportive framework of the fetal membranes. :Fetal membranes from women with preterm premature rupture of membranes may differ in their protease activity compared with normal membranes. To identify the presence of PAs and their inhibitors (PAI) and their possible role in the process of fetal membrane rupture, this study in investigated the distribution and localization of both protein and mRNA for tissue (t) and urokinase (u) PA and their inhibitors type 1 (PAI-1) and type 2 (PAI-2) in amniochorion of human and rhesus monkey using conventional and. confocal immunofluorescence microscopy. In situ hybridization analysis showed that the distribution and localization of mRNAs for tPA, uPA, PAI-I and PAI-2 were similar in the fetal membranes of human and rhesus monkey; no obvious species difference was observed. Evidence of tPA mRNA was detected in amniotic epithelium, trophoblast cells and nearly all cells of the decidual layer. Strong expression of uPA mRNA was noted in the decidual cells which increased in intensity as the abscission point was approached. Weak staining in chorion laeve trophoblast was also detected. In situ hybridization experiments showed PAI-1 mRNA to be concentrated mainly in the decidual cells, some of which were interposed into the maternal-facing edge of the chorion laeve. Maximal labelling of the decidua occurred towards the zone of abscission. Weak expression of PAI-1 mRNA nas also noted in some cells of the chorion laeve. The distribution of PAI-2 mRNA in amniochorion was also concentrated in the cells of the decidual layer, maximum expression of the mRNA was in the level of abscission. No detectable amount of mRNAs for tPA, uPA, PAI-1 and PAI-2 was found in the fibroblast, reticular and spongy layers. Distribution of the proteins of tPA, uPA and PAI-1 in the fetal membranes of these two species was consistent with the distribution of their mRNA. Anti-PAI-2 immunofluorescence was found to be strongly concentrated in the amniotic epithelium, but PAI-2 mRNA was negative in this layer, suggesting that the epithelium-associated PAI-2 is not of epithelial origin. These findings suggest that a local fibrinolysis in fetal membranes generated by precisely balanced expression of PAs and their inhibitors via paracrine or autocrine mechanisms may play an essential role in fetal membrane development, maturation and in membrane rupture. Following an analysis of the distribution and synthesis of activators and inhibitors it was found that they may play a role in abscission during the third stage of labour. (C) 1998 W. B. Saunders Company Ltd.

C1q-like inhibits p53-mediated apoptosis and controls normal hernatopoiesis during zebrafish embryogenesis

Except for the complement C1q, the immunological functions of other C1q family members have remained unclear. Here we describe zebrafish C1q-like, whose transcription and translation display a uniform distribution in early embryos, and are restricted to mid-hind brain and eye in later embryos. In vitro studies showed that C1q-like could inhibit the apoptosis induced by ActD and CHX in EPC cells, through repressing caspase 3/9 activities. Moreover, its physiological roles were studied by morpholino-mediated knockdown in zebrafish embryogenesis. In comparison with control embryos, the C1q-like knockdown embryos display obvious defects in the head and cramofacial development mediated through p53-induced apoptosis, which was confirmed by the in vitro transcribed C1q-like mRNA or p53 MO co-injection. TUNEL assays revealed extensive cell death, and caspase 3/9 activity measurement also revealed about two folds increase in C1q-like morphant embryos, which was inhibited by p53 MO co-injection. Real-time quantitative PCR showed the up-regulation expression of several apoptosis regulators such as p53, mdm2, p21, Box and caspase 3, and down-regulation expression of hbae1 in the C1q-like morphant embryos. Knockdown of C1q-like in zebrafish embryos decreased hemoglobin production and impaired the organization of mesencephalic vein and other brain blood vessels. Interestingly, exposure of zebrafish embryos to UV resulted in an increase in mRNA expression of C1q-like, whereas over-expression of C1q-like was not enough resist to the damage. Furthermore, C1q-like transcription was up-regulated in response to pathogen Aeromonas hydrophila, and embryo survival significantly decreased in the C1q-like morphants after exposure to the bacteria. The data suggested that C1q-like might play an antiapoptotic and protective role in inhibiting p53-dependent and caspase 3/9-mediated apoptosis during embryogenesis, especially in the brain development, and C1q-like should be a novel regulator of cell survival during zebrafish embryogenesis. (c) 2008 Elsevier Inc. All rights reserved.