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In the open literature and recent publications, many explorations were done on the flow in axial two-dimensional tandem cascades whereby examining each cascade parameter separately it has been shown that the performance strongly depends on the interference effects of the front and aft blade profiles. Governed by the fact that very limited research is done and published on the influence and the effects of separate parameters in a radial tandem cascade for water turbines, this paper presents an initial research in that area. In order to achieve high efficiency for water turbines, the working medium has to be pre-conditioned for entering the runner of the turbine. Despite the role of the spiral casing of the turbine, the stay and guide vanes also play a huge role in these requirements. The flow in the zone of the stay and guide vanes of an existing Francis turbine has been numerically analyzed, emphasizing the effects of the relative angular position between the stay and guide vanes forming a tandem cascade. By varying the relative angular position as a parameter, the total loss, acting forces and the flow distribution of the configurations have been examined. The specialized grid generation software GAMBIT and the solver FLUENT by ANSYS, employing the finite volume method, are used to solve the governing equations for turbulent flows, and conclusions and insights are being made on the basis of the obtained results.

A heuristic scheme for predicting the overall properties of composite media has been proposed, explored and widely used in the last 25 years by Kanaun and Levin. The numerous results and technical details are collected in the impressive volume Kanaun and Levin (Petrozavodsk: Izdatel'stvo Petrozavodskogo Universiteta, 1993 (in Russian)). The method is based on a certain old, natural and appealing physical reasoning, which well explains its name effective field method (EFM). The predictions of the methods agree very well with many experimental data. However, no attempt has been made to justify the method, putting it into the frame of a more rigorous theory of heterogeneous media. The present study represents such an attempt. The main conclusion is that the EFM approach, at least in elasto-statics when the effective moduli of the composite are looked for, is in essence a variational procedure of Hashin–Shtrikman type. Hence Kanaun–Levin's results provide, for the microstructures treated by the authors, rigorous variational prescriptions. The latter represent bounds on the effective moduli of the composites, if the matrix is weaker or stiffer than the inclusions. Moreover, it is shown that in the special, though quite general case of a matrix containing several kinds of ellipsoidal inclusions, distributed with “ellipsoidal” symmetry, an obvious generalization of the EFM method yields results that coincide with the variational estimates, recently obtained by Ponte Castaneda and Willis (J. Mech. Phys. Solids 43 (1995) 1919).

The work considers two–phase (binary) random media. Its main objective is a detailed investigation of the recent inequalities of Markov and others (1996) between certain statistical parameters of such media. The parameters represent integrals of arbitrary kernels multiplied by the two– and three–point correlation functions. An inequality for a two–point parameter is first derived from the basic ones and its equivalence to the familiar positive–definiteness of the two–point correlation function γ 2 ( r ) is pointed out. A special but natural choice of a kernel function leads to the appearance of a statistical parameter, i 2 ( p ), proportional in 3–D to the Laplace transform of the function r γ 2 ( r ). Necessary conditions on this transform are then found as a consequence of the positive–definiteness of γ 2 ( r ). The three–point inequalities are recast in a form, fully similar to the positive–definiteness of the two–point correlation. As an essential application of these inequalities a new derivation of two–point estimates of Hashin–Shtrikman9type on the effective sink strength of binary media is given. The derivation can serve as a model when dealing with other classes of homogenization problems.

Random dispersions of spheres are useful and appropriate models for a wide class of particulate random materials. They can be described in two equivalent and alternative ways — either by the multipoint moments of the characteristic function of the region, occupied by the spheres, or by the probability densities of the spheres' centers. On the "two-point" level, a simple and convenient integral formula is derived which interconnects the radial distribution function of the spheres with the two-point correlation of the said characteristic function. As one of the possible applications of the formula, the behavior of the correlation function near the origin is studied in more detail and related to the behavior of the radial distribution function at the "touching" separation of the spheres.

The paper is concerned with the problem of predicting macroscopic properties of solids, containing randomly distributed penny-shaped microcracks. It is proposed to employ the formalism of marked sets of random points, treating the mark as orientation of the crack located at a given point. As a first and simplest application of this approach the so-called first-order cluster bound of Torquato (1986 J. Chem. Phys. 84, 6345‐6359) on the eective scalar conductivity is derived. It turns out that the bound does not depend on the two- and three-point statistics of the distribution of cracks, unlike the case of dispersions of spheres or spheroids. The “optimality” of the bound within a much wider class of “cluster type” trial fields is demonstrated. In the elastic case the cluster bounds are explicitly derived as well, and are again found to be independent of cracks’ statistics. In both scalar and elastic cases the bounds coincide with the so-called “approximation of non-interacting cracks” thus rigorously proving that for the assumed isotropic cracks’ statistics the interactions always decrease the conductivity and the elastic moduli of a microcracked solid.

This work concerns steady-state diffusion in a medium containing a random distribution of sinks. The internal structure of the medium is described in terms of geometrical correlation functions, for example, two- or three-point correlations. Variational principles of the classical type are developed, and configuration-dependent trial fields are substituted into them. Restrictions on certain integrals of the two- and three-point correlation functions then follow from the avoidance of mathematical contradictions. The consequences of the restrictions and the relationship between the classical variational principles and variational principles of the Hashin-Shtrikman type are discussed.

A general method of placing variational bounds on the effective scalar conductivity of random heterogeneous solids is proposed. The method utilizes the Hashin-Shtrikman variational principle and trial fields which are obtained upon truncating the functional series expansion for the polarization field in the medium. It is shown how the earlier variational procedures due to Hashin and Shtrikman, Milton and Phan-Thien and Willis find natural places in the proposed general scheme. The new results reported include, for example, the fact of nonexistence of certain Gaussian-like random media and, for dispersions of spheres with volume fraction c, an exact O(c2) relation for the effective conductivity which contains absolutely convergent integrals only.

The aim of the paper is to outline and discuss some ideas and preliminary results concerning microstructural modelling of brittle-like damage in solids. We argue that the basic premises of the simple microelastic theory (independent micro-dilatation of particles), developed by S. Cowin et al. and the author, are a natural starting point in developing certain continuum damage mechanics models. In the brittle-like case under study, with the assumption of isotropic deterioration, the damage rate is added to the arguments (strain, damage and damage gradient) of the elastic energy density. The additional field quantity of the theory—the damage parameter in our context—leads to the appearance of hyperstresses and a balance equation for them. It is shown that the latter can be conveniently identified with the well-known Kachanov's law of damage growth. Thus this law, traditionally introduced through purely phenomenological arguments, finds a natural place in the herein proposed damage model as an equation expressing hyperstress equilibrium.

A series of periphyton, sediment, and water samples has been collected from the Kolubara River and its tributaries at selected locations, characterized by heavy industrialization, and analysed for stable isotopes by X-ray-fluorescence spectrometry. The results of measurements for stable metals revealed that the anthropogenic contribution essentially overwhelms the natural system of the catchment. Thus, concentrations of heavy metals near points of industrial discharge were significantly higher than background concentrations. The existing primary and secondary waste water-treatment plants associated with heavy industry of the area must therefore be revived, and control should be instituted at the sources of pollution. The bioaccumulation factors (BF), and sediment distribution coefficients (K(D)), and concentration ratios (CR) for sixteen stable isotopes were calculated. It is shown that the concentration ratios of periphyton over sediment for Mn, Zn, As, Sb, I, Ba, and Pb exceeded unity. Furthermore, the recorded partition coefficients were indicative of the distribution and mobility of the stable metals in the Kolubara River environment.

We consider a random two-phase medium which represents a matrix containing an array of allowed to overlap spherical inclusions with random radii. A statistical theory of transport phenomena in the medium, on the example of heat propagation, is constructed by means of the functional (Volterra-Wiener) series approach. The functional series for the temperature is rendered virial in the sense that its truncation after the p-tuple term yields results for all multipoint correlation functions of the temperature field that are asymptotically correct to the order np, where n is the mean number of spheres per unit volume. The case p=2 is considered in detail and the needed kernels of the factorial series are found to the order n2. In this way not only the effective conductivity, but also the full statistical solution, i.e., all needed correlation functions, can be expressed in a closed form, correct to the said order.

Functional series with a pointwise random input (the density field of a random set of points ${\bf x}_j $) are considered. The series are rearranged so as the so-called factorial fields of the set ${\bf x}_j $ appear; the obtained series are called factorial. The basic result of the paper states that the factorial series possess virial property. This means that if a random field $u( {\bf x} )$ is expanded as a factorial series, the truncation $u^{( p )} ( {\bf x} )$ of the latter after the p-tuple term coincides, in the statistical sense, with $u( {\bf x} )$ to the order $n^p $, where n is the number density of the set ${\bf x}_j ,\, p = 1,2, \cdots $. The performance of the factorial series in random media problems is illustrated on the example of steady-state diffusion in a random dispersion of spheres whose sink strength differs from that of the matrix. The full statistical solution of this problem, correct to the order $c^2 $, is obtained; in particular, the effective sink-strength of the dispersion i...

The introductory and more elementary ideas and results of micromechanics of heterogeneous media are collected in the survey. The central problem under discussion is “homogenization.” It replaces such media by homogeneous ones, which behave macroscopically in the same way and possess certain gross effective properties. These properties are related in a complicated manner to the prescribed internal structure of the medium and their evaluation, in general, represents a profound challenge in any specific situation. A brief historical survey is given, underlying the reappearance of essentially the same “homogenization” quest in numerous guises and contexts over the last two centuries. Within the framework of the volume-averaging approach the basic notions are introduced and some of the central, now classical, results are then derived and discussed such as perturbation expansions, Hashin-Shtrikman’s bounds, variational estimates and Levin’s cross-property relation. A general “one-particle” scheme for approximate evaluation of the effective properties (in the static case) is detailed in its various implementations like selfconsistency, iterated limits and effective field. Illustrations concern conductivity, elasticity, and absorption phenomena in heterogeneous particulate media, as well as a simple self-consistent model for polycrystals’ homogenization.

A two-point statistical parameter which naturally appears in variational bounds in the absorption problem for random media is studied. For random dispersions of nonoverlapping sphere an analytic formula for the parameter is first given through the radial distribution function for the spheres. Analyzing the asymptotic behaviour of the parameter, two kinds of formulae are derived: i) Simple relations between the values of the two-point correlation function and its derivatives at r = 0 with the values of radial distribution function and its derivatives at the “touching distance” r = 2a. ii) Relations between the moments of the two-point correlation on (0,∞) and the moments of the radial distribution function. As a simple application, the failure of the well-stirred approximation for sphere fractions higher than 1/8 is finally demonstrated.

This paper is devoted to the steady-state problem of absorption of a diffusing species (say, irradiation defects) in a random dispersion of spheres. The defects are created at a constant rate throughout the medium and are absorbed afterward, with different sink strengths, by the matrix and by the inclusions. One is to find the random diffusing species field and, in particular, the effective sink strength of the dispersion, having assumed the statistics of the spheres known. The problem is modeled by a Helmhotz equation with a random coefficient (the randomly fluctuating sink strength of the dispersion). The statistical solution of the latter is explicitly constructed, in a simple form, by means of the so-called factorial functional series, recently introduced by one of the authors. In particular, analytical formulas, correct to the order “square of sphere fraction,” are obtained for the effective sink strength of the dispersion and for the two-point correlation function of the diffusing species field. An effective numerical procedure, allowing to specify these quantities, is described and numerical results are finally presented and discussed.

The paper is devoted to the steady-state problem of absorption of a diffusing species in a random heterogeneous medium. The variational principles of classic type, using ensemble averaging, are first discussed and then used for derivation of variational estimates on the effective absorption coefficient (sink strength) of the medium. The estimates are three-point, i.e. They employ statistical information, contained in the l- point correlation functions for the medium up to l = 3 , and could be viewed as counterparts of the well-known Beran's bounds in the scalar conductivity problem. Moreover, the bounds are third-order in the weakly-inhomogeneous case. Explicit results are obtained for Miller's cellular media which indicate that the bounds remain useful even when the absorption capabilities of the constituents differ 100 times.

Elementary Micromechanics of Heterogeneous Media.- 1.1 Introduction.- 1.2 The homogenization problem.- 1.3 Some basic results.- 1.4 The single inclusion problem.- 1.5 One-particle approximations.- 1.6 Elastic properties of polycrystals.- 1.7 References.- Diffusion-Absorption and Flow Processes in Disordered Porous Media.- 2.1 Introduction.- 2.2 Microstructure functions.- 2.3 Steady-state trapping problem.- 2.4 Time-dependent trapping problem.- 2.5 Steady-state fluid permeability problem.- 2.6 Time-dependent flow problem.- 2.7 Variational principles for trapping problem.- 2.8 Variational principles for flow problem.- 2.9 Bounds on trapping constant.- 2.10 Bounds on fluid permeability.- 2.11 Cross-property relations.- 2.12 References.- Self-Consistent Methods in the Problem of Wave Propagation through Heterogeneous Media.- 3.1 Introduction.- 3.2 The main hypotheses of the methods.- 3.3 Integral equation of the diffraction problem.- 3.4 General scheme of the effective field method.- 3.5 General scheme of versions I and II of the EMM for matrix composite materials.- 3.6 The solutions of the one-particle problems of version I of the EMM and of the EFM.- 3.7 Asymptotics of the solutions of the dispersion equations.- 3.8 Versions II and III of the EMM in the case of spherical inclusions.- 3.9 Version I of the EMM and the EFM in the case of isotropic random sets of inclusions.- 3.10 Versions I, II, and III of the EMM for matrix composite materials.- 3.11 An approximate solution of the one-particle problem.- 3.12 The EFM for composites with regular lattices of spherical inclusions.- 3.13 Versions I and IV for polycrystals and granular materials.- 3.14 Discussion.- 3.15 Conclusions.- 3.16 References.- Deformable Porous Media and Composites Manufacturing.- 4.1 Introduction.- 4.2 Ensemble average approach.- 4.3 Effective media approach.- 4.4 Deformable and saturated porous media models.- 4.5 Boundary conditions.- 4.6 One-dimensional infiltration.- 4.7 Simulations.- 4.8 Three-dimensional unsaturated isothermal model.- 4.9 Open problems.- 4.10 References.- Micromechanics of Poroelastic Rocks.- 5.1 Introduction.- 5.2 Hydrostatic poroelasticity.- 5.3 Undrained compression.- 5.4 Constitutive equations of linearized poroelasticity.- 5.5 Equations of stress equilibrium and fluid flow.- 5.6 Dependence of poroelastic parameters on pore structure.- 5.7 Conclusions and future directions.- 5.8 References.

It is shown that the CCSNo7 link availability depends on both the signalling load and signalling unit length if the signal unit error rate monitor (SUERM) algorithm is built according to current ITU-T recommendations. A rearrangement of the SUERM algorithm is suggested so that the link availability has the largest and most constant possible value for the prescribed BER.

A generalised model of the signal unit error rate monitor in CCSNo7 is described. It is shown that a desired link availability may be obtained by adjusting two parameters in the generalised model. The desired link availability may be, according to ITU-T recommendation Q.703, independent of load or equalised, and high and dependent on the signalling load and SU length.

A call collision reducing method for telephone networks using CCS no. 7 is suggested. The proposed method slightly increases the probability of blocking or waiting, but greatly reduces the probability of double seizure. Calculation of the collision and blocking probabilities for the new method is illustrated with an example.

An exact calculation of the minimum required power of a ringing signal generator in a telephone exchange is presented. The problem of power calculation is treated as a traffic problem. As can be seen, the required ringing power is a function of the traffic parameters of subscribers, the electrical characteristics of the telephone lines and sets, and the allowed overload time.

Two methods of mean CCSNo7 link alignment time calculation are suggested. One of these methods is also applicable for mean CCSNo7 link changeover time calculation. The results obtained are compared to results of known methods and simulation results.

The Volterra-Wiener functional expansion is employed to the analysis of statistic properties for random heterogeneous solids. For simplicity, the technique is displayed on an elastic suspension of spheres. The basis function in the expansion is chosen as that corresponding to the so-called “perfect disorder” of spheres (PDS), recently introduced by the authors. An infinite hierarchy of equations for the kernels in the expansion is derived whose truncating after the nth equation is shown to yield results for the averaged statistical characteristics which are valid to order c n f , where c f is the volume fraction of the spheres. The kernels for the first and the second approximations, n = 1, 2, are found and related to the displacement fields in an infinite elastic body containing, respectively, one and two spherical inhomogeneities. Within the frame of the so-called singular approximation the overall tensor of elastic moduli for a suspension of perfectly disordered spheres is shown to coincide to the order c 2 f with a formula, earlier obtained by means of the method of the effective field.

The random field created by a system of random points which are centers of perfectly disordered equi-sized spheres of a finite radius is introduced and named the PDS-field. The notion of Perfect Disorder is defined statistically correctly taking the cumulants instead of moments to be $\delta $-functions. The Volterra-Wiener functional expansion with the PDS-field as a basis function is considered and a system of orthogonal Wiener functionals is explicitly constructed. The expansion is employed to the problem of specifying the overall conductivity for a random medium containing an array of perfectly disordered spherical inclusions. An infinite hierarchy of coupled equations for the kernels of the Wiener functionals is derived. It is shown that the Wiener expansion with respect to the PDS-field is also a virial one, i.e. the nth order term contributes quantities of order $c^n $, where c is the volume fraction of the inclusions. This allows the full stochastic solution to the problem of heat conduction throu...

A general method of placing optimal bounds on the overall conductivity of random heterogeneous media is proposed. It utilizes truncated Volterra-Wiener functional series, generated by the random conductivity field K(x), as classes of trial functions for the classical variational principles. The method simplifies, unifies and/or generalizes the earlier proposed variational techniques of Beran (3), Dederichs and Zeller (10), Hori (15), Kr6ner (17) and Prager (25). The general procedure is displayed in detail in the simplest case of interest, the construction of the optimal third-order bounds, that requires knowledge of the two- and three-point correlation functions for K(x). The evaluation of these bounds is reduced to the solution of an integrodifferential equation whose coefficients and kernels are expressed through the said correlation functions. A perturbation solution to this equation is given. For Miller's cell materials the equation is explicitly solved and the obtained optimal bounds are shown to coincide with those of Beran-Miller.

In this paper a linear theory for a solid, for which the displacement and dilatation (volume change) fields are independent, is investigated in details. The theory is applied to describe the mechanical behaviour of an elastic solid containing a large number of microvoids and the material constants, entering the theory, are calculated for this case. In dieser Arbeit wird die lineare Theorie des Festkorpers, fur welche das Verschiebungsfeld und die Volumendilatation unabhangig sind, in Einzelheiten erforscht. Die Theorie ist fur eine Beschreibung des Elastizitatskorpers, der eine grose Zahl Mikroporen enthalt, angewandt. Fur diesen Fall wurden die in der Theorie vorkommenden Materialkonstanten berechnet.

In the analysis of response of anisotropic media there exists a general problem about the material symmetry restrictions imposed on the constitutive equations. Numerous studies on this question have been carried out (cf. the survey [18]). However, these studies have been based on the assumption that the tensor relations involved are polynomial (or that they could be approximated by polynomials). According to the apt remark of Pipkin and Wineman [8], this assumption ‘is a matter of mathematical convenience; it seems somewhat foreign to a discussion of material symmetry’.

On montre que la convexite de la surface de plasticite dans l'espace des contraintes n'entraine pas, en general, la convexite de la surface dans l'espace des invariants

In this paper we present an Agent-based Open Service Architecture (OSA) which integrates geographically distributed agents in the Web. Agents can be realized with traditional AI techniques, but they also provide a set of Web Services to the outside world which constitute their capabilities. The architecture extends the Web with a facilitator level providing agents' specific support. Moreover it provides primitives for Web Services invocation and inter-agent communication based on Agent Communication Languages. We present the design of the architecture and an implementation which extends a common Web Server based on Apache/Tomcat platform.