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The paper reports a mathematical model governing unsteady coupled moisture and heat energy transport through a green roof, e.g. the canopy (leaf cover), the soil and the structural support. The mathematical model that governs the transport phenomena in the canopy is represented by a system of nonlinear ordinary differential equations (ODEs) for the unknown temperature of the plants, and the unknown temperature and moisture content of the canopy air. A set of nonlinear partial differential equations (PDEs) describe the heat and moisture transport through the soil and structural support. Continuous field functions such as temperature and relative humidity, are considered as the driving potentials. A finite difference numerical model is used to solve the ODEs and the boundary element numerical model is used to discretize the PDEs.

The present paper reports the simulation of unsteady coupled moisture and heat transport through a multi-layer porous solid. The governing partial-differential transport equations are written and solved simultaneously for the continuous driving potentials, i.e. relative humidity and temperature. The coupled equations are solved numerically using a singular boundary integral representation of the governing equations. The multi-layer porous solid building elements under study are submitted to convective heat and mass exchange with the surrounding environment and exposed to solar heat flux. The integral equations are discretized using mixed-boundary elements and a multidomain method also known as the macro-elements technique (Brebbia, 1984 [1], Popov et al., 2007 [2]). The numerical model uses quadratic approximation over space and linear approximation over time for all field functions, which provides highly accurate numerical results.

The Boundary Element Method (BEM) has now become a well established numerical technique with a number of computer programmes to its credit oriented towards industrial applications. They are reliable and robust tools which stress its unique features versus finite elements, ie reduced dimensionality which makes it easier to interface it to CAD codes; better accuracy, the elegant way in which moving boundaries are dealt with and the possibility of taking into consideration infinite domains without the need of introducing artificial boundaries. An excellent paper on the early work that led to the development of boundary elements has been given by A&D Cheng [1] and from which many of the illustrations depicting famous scientists were taken. The present contribution aims to explain further how the methodology developed and consolidated towards the end of the 1970s, beginning of the 1980s.

In this paper, the domain integrals due to uniform load or self-weight that appear in the boundary element method (BEM) formulation for thick plates resting on elastic foundations are transformed to boundary integrals. The Reissner plate bending model is used to model the plate behavior, and the two-parameter Pasternak model is used to model the behavior of the foundation. The necessary particular solutions are derived, and the explict forms for the new boundary kernels are given. Two different collocation procedures are considered—external and boundary collocations. In the case of the boundary collocation and internal collocation (for computing internal functions) procedures, an additional free term is obtained, due to the discontinuity of the transformed kernels. The new boundary integrals are hypersingular integrals. However, it will be shown that these hypersingular terms vanish when integrated around a closed contour. Three numerical examples are presented with several parametric studies to demonstra...

Compactly supported radial basis functions have been used to interpolate the forcing term in the DRM. The resulting DRM matrix is sparse and our approach is very accurate and efficient. Our proposed method is especially attractive for large scale problems. Copyright © 1999 John Wiley & Sons, Ltd.

In this work, the hypersingular boundary element formulation for plate bending analysis based on Reissner theory is presented. First order Taylor expansion are used to deal with the strong singularity O(1/r), whereas, rigid body considerations together with the Taylor expansion are used to compute the hypersingular kernels O(l/r2). The plate boundary is discretised into quadratic isoparametric discontinuous boundary elements to satisfy the continuity requirements for the boundary unknowns. Several examples are tested, including thin and thick plates. The results show a good agreement with both the analytical solutions and the corresponding results for the standard displacement boundary element formulation. © 1998 Elsevier Science Ltd. All rights reserved

This paper deals with the evaluation of the boundary and internal stresses in the boundary element method (BEM) for plate-bending analysis. The Reissner plate theory is employed as the general plate-bending theory for modelling both thin and thick plates. Two methods are discussed for the evaluation of boundary stresses. The first is based on the local boundary tractions and strains, and the other is based on the direct evaluation of the stress tensor using the stress integral equation. The proposed methods can be used as postprocessing procedures for the BEM solution. The evaluation of three-dimensional (3-D) internal stresses through the plate thickness is also discussed and compared with the 3-D boundary element solutions. Numerical examples are presented to demonstrate the accuracy of the proposed methods.

The higher order fundamental solutions to the two-dimensional (2-D) modified Helmholtz equation have been derived. The Lth order fundamental solution has the form φ i ∗(L) = A L (kr) L K L (kr) , which satisfies the equation ∂ 2 ∂r 2 + 1 r ∂ ∂r − k 2 φ ∗(L) i +φ ∗(L−1) i =0 and the relationship of the coefficients AL is given as A L = A L−1 (2Lk 2 ) with A 0 = 1 (2π) . These solutions can be used for applying the multiple reciprocity boundary element method to the 2-D modified Helmholtz problems. The derivation procedure shown in the present paper can also be applied to obtaining higher order fundamental solutions to other engineering equations.

The multiple reciprocity method has been applied to one-group fission neutron source iteration problems. The domain integral related to the fission neutron source in the m th source iteration stage is transformed into a series of m − 1 boudary integrals. These integrals require the zero order to the m − 1 order fundamental solutions and the boundary neutron fluxes and currents calculated in the previous m − 1 source iterations. Results obtained in a simple test calculation indicate that the source iteration based on the present technique converges rapidly to the desired eigenvalue as long as a certain condition is satisfied.

In this paper, axisymmetric heat conduction and thermal stress problems with three types of boundary conditions are analysed by the boundary element method. The temperature and thermal stress fields for the piston of a diesel engine are calculated using triangular finite elements and constant boundary elements, respectively, and the two results agree. However, BEM needs fewer data, less computer time (about one-sixth that of FEM) and storage volume. The advantages of BEM are sufficiently demonstrated.

The assessment of current distribution induced along complex grounding systems has been undertaken using the corresponding antenna model and the set of Pocklington integro-differential equations for curved wires. The set of Pocklington equations is numerically handled via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM) featuring the isoparametric elements. Some illustrative numerical results for the current distribution are presented in the paper.

This paper describes a selective numerical integration scheme to compute the integrals present in a 2-D elastostatic boundary element formulation including those due to body forces. The selective integration ensures that the program runs efficiently while producing accurate results. The integrals are solved numerically using the third order polynomial transformation 9 which increases the accuracy of the classical Gaussian quadrature schemes.

A round-off error accumulation is observed in a multiple reciprocity computation for a fission neutron source iteration problem when a certain convergence condition is not satisfied. The present paper presents a reformulation of the multiple reciprocity method to remove the numerical problem. The neutron diffusion equation (NDE) is arranged using Wielandt's spectral shift technique in such a way that the convergence condition is always satisfied through source iterations. The boundary integral equation in this case requires the fundamental solution to the standard Helmholtz equation, while the fundamental solution corresponding to the correspoding to the original NDE was one to the modified Helmholtz equation. Except for this, the new multiple reciprocity formulation is identical to the original one for the fission source iteration problems. Some test calculation results indicate that a rapid and stable convergence can be realized using the new method and no round-off error accumulation is observed any more.

This paper deals with the numerical solution of contact problems between elastic bodies by using a boundary element flexibility approach formulation. As a first step, a flexibility matrix involving only the nodes which are expected to come into contact is computed by boundary elements. This produces a small system of equations which results in a procedure which is computationally very efficient. The relevant theory is described in this paper and validated by solving contact problems and comparing results with analytical or other numerical solutions. The examples comprise contact problems between elastic and rigid bodies with and without friction. The results are in good agreement with previous solutions.

This paper presents fundamentals of the multiple reciprocity method as well as its application to linear potential problems with body forces. Results of some numerical tests and comparisons with analytical solutions are presented.

Time-domain analysis of the transient current distribution along parallel wires located at different heights above a real ground is presented. The numerical solution is carried out via time-domain variant of the Galerkin–Bubnov indirect boundary element method (GB-IBEM) of solution extended to handle the case of arbitrary array of parallel wires located in a homogenous lossless medium, above a perfectly conducting (PEC) ground, or above a dielectric half-space. The mathematical formulation is based on the set of coupled space-time integral equations of the Hallen type. Some illustrative numerical results being compared to the results obtained via other methods wherever possible are presented.

This paper discusses the validity and accuracy of the results obtained using the boundary element flexibility approach for solving elastic contact problems. The method is such that the size of the flexibility matrices, which represent the relationship between tractions and displacements at the contact nodes depends only on the actual number of nodes in contact. Therefore, the approach is computationally very efficient. Moreover the contact analysis and the formation of the boundary element matrices can be carried out separately. Thus it is easy to implement the flexibility contact approach into any standard boundary element code. This paper presents a new contact criterion for the solution and carries out a series of comparisons with results obtained using other techniques. Although constant elements were employed in all cases, it is possible to extend the same approach to higher order elements if required. The flexibility approach is validated against Hertzian and non-Hertzian contact problems, including numerical solutions. The results are shown to be in agreement and the accuracy of the solution is investigated.

The present paper describes a general way of transforming domain integrals into equivalent boundary ones in boundary element formulations of fission neutron source problems. The critical eigenvalue, which is defined originally by the ratio of two different domain integrals has been transformed into a ratio involving only boundary integrals. The domain integral of fission source multiplied by the fundamental solution is converted into an equivalent boundary integral by the use of a particular solution technique, in which the source distribution is expanded into a Fourier series. The coefficients required in the expansion are determined using a boundary-only integral which has a recurrence form and is updated throughout the neutron source iteration scheme.

This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations.

This work extends the formulation developed in part I to include multiple knots and non-uniform blending functions. In this way, it is possible to lower the degree of continuity of the main variable at points of geometric discontinuity. Applications are presented for problems with corners, including the flow through an earth dam for which B-splines are specially suitable since they are able to maintain continuity of the slope between the free surface and the seepage face.

The paper presents a new boundary element model based on a generalized functional which involves three types of independent variables, i.e. potentials and fluxes on the boundary and potentials inside the domain. The formulation therefore may be classified as a hybrid potential boundary element method. The approach uses classical fundamental solutions which interpolate the potentials inside the domain and permits one to transform the domain integrals into integrals on the boundary. Hence the final equations are written in terms of only boundary unknowns. Furthermore, the model produces symmetric matrices.

The dual reciprocity method (DRM) is a general technique for taking domain integrals to the boundary in BEM analysis. In this paper it is applied to the eigenvalue analysis of Helmholtz problems. A solution procedure is presented which avoids the complex eigenvalues usually associated with the non-symmetric BEM matrices and which is at the same time easy to implement. Characteristics numerical examples are used to illustrate the proposed method.

Experiments conducted at Clarence Colliery into the potential for co-disposal of the two rejects from Clarence Colliery and Kable’s Transport Sand Mine suggested that the co-disposal option was beneficial and mutually beneficial to the two companies. Column experiments were undertaken to simulate field conditions consisting of creating the required co-disposal arrangement and structure in containers, infiltrating water through each container and measuring the rates of infiltration and overflow and measuring the chemical properties of the leachate water. Geotechnical tests of co-disposal pile stability were undertaken using a specially constructed shear box. Layering the coal reject with clay tailings creates a semi-permeable barrier, which acts to restrict water percolation through the reject as well as reacting with the leachate to increase the leachate pH and adsorb metals.

This work develops a new element formulation for boundary element analysis using uniform cubic B-splines. These functions can be employed to provide higher degrees of continuity along the geometric boundary of the region, and also as interpolation functions for the problem variables. Applications are presented related to potential problems governed by Laplace's equation but there are no restrictions in the formulation regarding its extension to other physical problems.

Transient response of a multiple wire configuration in the presence of a two-media configuration excited by a voltage source (antenna mode) or illuminated by an incident field is analysed using the boundary element method (BEM). The analysis is based on the solution of the corresponding set of the coupled space-time Hallen integral equation and it is carried out directly in the time domain. The influence of a two media configuration is taken into account via the space time reflection coefficient. The corresponding integral equation set is handled via the time domain variant of the Galerkin–Bubnov indirect boundary element method (GB-IBEM). Some illustrative numerical results for both antenna and scattering mode are presented in the paper.

The paper presents an accurate and efficient boundary element procedure for the analysis of radiation from base station antennas. The base station antenna system is represented by the vertical antenna array in front of perfectly conducting (PEC) ground plane reflector. The formulation of the problem is based on a set of coupled Pocklington integro-differential equations for vertical antenna array. This set of coupled equations has been numerically treated by the indirect Galerkin–Bubnov boundary element method (GB-IBEM). The numerical results for the currents induced along the wires obtained via GB-IBEM are compared to the results computed via numerical electromagnetic code (NEC). Knowing the current distribution along the antenna array the corresponding radiated field is calculated. Some illustrative numerical results are presented in the paper.

Electromagnetic– thermal analysis of human exposure to base station antennas radiation is presented in this article. The formulation is based on a simplified cylindrical representation of the human body. Electromagnetic analysis involves incident and internal field dosimetry, while the thermal model deals with the bio-heat transfer phenomena in the body. The electric field induced in the body is determined from the axial current distribution inside the body. This current distribution is obtained along the body obtained by solving the Pocklington integral equation via the Galerkin– Bubnov Boundary Element Method. Once the internal electric field and related total absorbed power in the human body is obtained, a related temperature rise in the body due to the Global system Mobile exposure is calculated. This temperature rise is determined by solving the bio-heat transfer equation via the dual reciprocity boundary element method, and is found to be rather negligible.

The evaluation of boundary element influence integrals often involve numerical complexities due to the inherent singular nature of the integrals. A common practice to avoid some of the difficulties in treating these singularities is based on a simple technique commonly known as RowSum) '2 This technique takes advantage of certain relationships between influence terms that must hold in order to satisfy conditions of constant potential, rigid body displacement, (Brebbia l) or rigid body rotations (Niku & Brebbia 2) which are based on the physical interpretation of the problem. The RowSum technique is simple to implement and produces accurate results, provided of course that the regular influence terms are evaluated accurately. However, their application is limited to problems for which the conditions of constant potential or rigid body displacement exist and also those which produce a single singular term. In this paper a technique based on particular solutions is presented. The technique is simple and versatile, it can be applied to any problem and be used to evaluate as many influence terms as required.

A solution of steady-state Darcy’s flow in heterogeneous porous media is developed by means of the Dual Reciprocity Boundary Element Method (DRBEM). The governing equation is reduced to a Poisson-type equation involving a nonlinear non-homogeneous term. The Dual Reciprocity Method (DRM) is used for converting the resulting domain integral into equivalent boundary integrals. The present formulation is general as it allows the solution of Darcy’s flow with any hydraulic conductivity variation. Numerical examples are provided to demonstrate the validity of the procedure.

Up to now, all applications of the Dual Reciprocity Method considered is this book were related to the Laplace operator. This means that the governing partial differential equations were initially recast as some kind of Poisson’s equation and the fundamental solution of Laplace’s equation employed to obtain an equivalent integral formulation. The resulting domain integral was then approximated in a DRM fashion, and a boundary integral equation obtained and solved without resorting to internal discretization or integration.

Preface. Solving heat transfer problems by the dual reciprocity BEM. Transient problems using time-dependent fundamental solutions. Solving linear heat conduction problems by the multiple reciprocity method. Solving nonlinear heat transfer problems using the boundary element method. Coupled conduction-convection problems. Solving coupled problems involving conduction, convection and thermal radiation. Advanced thermoelastic analysis. Integral equation analyses of natural convection problems in fluid flow. Improperly posed problems in heat transfer. Acknowledgments. References.

In the previous chapter the boundary element Dual Reciprocity Method was developed and applied to problems governed by a Poisson-type equation in which the right-hand side is a known function of position, i.e. $${\nabla^2}u=b\left({x,y}\right)$$ (4.1) for which the basic DRM matrix expression was established in the form $$ Hu - Gq = (H\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}\to {U} - \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}\to {G} )\alpha = d$$ (4.2) In such analyses, as is usual in BEM, the solution is divided into two parts: (a) A boundary solution, and (b) An internal solution.

It is generally agreed that the modern definition of Boundary Elements dates from 1978 when the notation used nowadays was accepted, partly due to the publication of the Proceedings of the first international conference on Boundary Elements [1] and partly as a result of the first book on the topic by the Computational Mechanics research group at Southampton [2]. Other books by the Southampton group have been published since, all of them using the same notation [3,4,5] which, with minor changes, will be that used in the present book.

The impressive success of the Boundary Element Method [1],[2] in the last decade has been mainly due to the fact that the technique became applicable to a wide range of engineering problems e.g. [3–8]. The boundary value problems of heat transfer are among those which can be effectively solved by BEM. For many practical cases, e.g. linear and non-linear steady-state heat conduction, some problems of thermal radiation and many others, BEM can result in a simple and elegant formulation. However, some heat transfer problems lead to an integral equation with domain integrals. The presence of these integrals diminishes the efficiency of the method and makes the data preparation needed for the computer codes much more difficult.

Since its origin in 1978, the International Conference on Boundary Element Methods has provided the recognized and established forum for innovations in boundary element research. Practically all new ideas on boundary ele ments have been presented at these conferences and the resulting papers can be found in the published books. The conference brings together the most renowned scientists and engineers working on boundary element research throughout the world. A unique feature of these meetings is that the participation of younger researchers is actively encouraged by the organizers in an effort to .bring forward to the attention of the international community an ever expanding range of new ideas. This book contains the edited version of the papers presented at the XIIIth BEM Conference held in Tulsa, Oklahoma in August of 1991. The meeting attracted a large number of participants and many excellent contributions which have been divided into nineteen different sections, i.e. Potential Prob lems; Diffusion and Convection Problems; Fluid Mechanics; Fluid Flow; Wave Propagation; Groundwater Flow; Heat Transfer; Electrical Problems; Geomechanics; Plates and Shells; Inelastic Problems; Damage Tolerance; Contact Mechanics; Industrial Applications; Design Sensitivity and Opti mization; Inverse Problems; Special Techniques; Numerical Aspects and Computational Aspects."

Advanced Architecture and Technology of Supercomputing Systems.- Parallel and Supercomputer Architecture in Japan.- FACOM VP2000 Series.- Expert Systems Based on Object Model - An Approach to Deep Knowledge Systems.- Trends in Expert Systems in Japan.- Computer Graphics and its Expansion to Image Industry.- Neurocomputers in Japan.- Advanced Communication Technology and OSI Oriented Academic Network TAINS.

Section 1: Theoretical Reliability Analysis.- On Excursions of Non-Homogeneous Vector-Valued Gaussian Random Fields.- Fitting-Adaptive Importance Sampling in Reliability Analysis.- Exceedance Probabilities Under Various Combinations of Rare Events.- Skewness and Kurtosis of Safety Margin.- A Curve-Fitting Method of Combined Distribution in Probabilistic Modeling of Random Variables.- On Procedures to Calculate the Reliability of Structural Systems under Stochastic Loading.- The Sensitivity Analysis of Stochastic Hysteretic Dynamic Systems.- Solution of Random Eigenvalue Problem by Crossing Theory and Perturbation.- SORM Analysis Using Quasi-Newton Optimization.- Method of Stochastic Linearization Revised and Improved.- Maximal Lyapunov Exponent for a Stochastically Perturbed Co-Dimension Two Bifurcation.- Updating of a Model and its Uncertainties Utilizing Dynamic Test Data.- Section 2: Damage Analysis.- Identification of Structural Dynamic Systems by Sequential Prediction Error Method.- Computer and Test Aided Modelling and its Application to Identify Structural Damage.- The Effect of Model Uncertainty on the Accuracy of Global Nondestructive Damage Detection in Structures.- Evaluation of Maxium Softening as a Damage Indicator for Reinforced Concrete Under Seismic Excitation.- Section 3: Applied Reliability Analysis.- Empirical Formulae to Presume the Resistance Performance of High Speed Craft Models.- Computational Experience with Damage-Tolerant Optimization of Structural Systems.- On the Effect of Stochastic Imperfections on the Buckling Strength of Certain Structures.- Chaos, Stochasticity and Stability of a Nonlinear Oscillator with Control Part I: Analysis.- Chaos, Stochasticity, and Stability of a Nonlinear Oscillator with Control Part II: Simulation.- Section 4: Theoretical Random Vibrations.- Stochastic Response of Nonlinear Multi-Degrees-of-Freedom Structures Subjected to Combined Random Loads.- Moment Equations Approach to Nonstationary Responses of a Nonlinear System Subjected to Nonwhite Random Excitation.- The Path Integral Solution Technique Applied to the Random Vibration of Hysteretic Systems.- Non-Stationary Probabilistic Response of Linear Systems Under Non-Gaussian Input.- Stochastic Linearization for the Response of MDOF Systems Subjected to External and Parametric Gaussian Excitations.- Equivalent Linearization of a Newly Introduced General Hysteretic Model.- A Method for Solving the Diffusion Equation with Random Coefficients.- Response Statistics of Nonlinear Systems Under Variations of Excitation Bandwidth.- Stochastic Equivalent Linearization of Nonlinear Complex Structures.- Numerical Solution of the Fokker-Planck Equation for First Passage Probabilities.- Approximate Analysis of Nonstationary Random Vibrations of MDOF Systems.- Section 5: Stochastic Finite Element Concept.- First Order Reliability Analysis Using Stochastic Finite Element Methods.- Analysis of Two-Dimensional Stochastic Systems by the Weighted Integral Method.- Non Conservatively Loaded Stochastic Columns.- Section 6: Fatigue/Fracture.- Inspection Strategy for Deteriorating Structures Based on Cost Minimization Approach.- Probabilistic Approach to Cumulative Damage of Car Components.- Stochastic Two-Dimensional Fatigue Crack Growth Analysis Including the Effect of Crack Coalescence.- Stochastic Fatigue Damage in Welded Cruciforms.- Statistical Evaluation of the Distribution of Crack Propagation Fatigue Life by Simulating the Crack Growth Process.- Filter Technique for Stochastic Crack Growth.- Section 7: Monte Carlo Simulations.- Probabilistic Seismic Response Analysis of a Steel Frame Structure Using Monte Carlo Simulation.- Galerkin Method to Analyze Systems with Stochastic Flexural Rigidity.- Monte Carlo Simulation of Beams on Winkler Foundation.- Simulation of Multi-Variate Stationary and Nonstationary Random Processes: A Recent Development.- Optimality in the Estimation of a MA System from a Long AR Model.- Random Fields. Digital Simulation and Applications in Structural Mechanics.- Section 8: Earthquake Engineering Applications.- Stochastic Estimation of Orientation Error in Buried Seismometers.- Strains in Long Dams due to Spatially Correlated Random Ground Motions.- Seismic Reliability Assessment of Redundant Structural Systems.- Seismic Ground Strain Simulations for Pipeline Response Analysis.- Parametric Study of the Stochastic Seismic Response of Simple Nonlinear Structures.- Applications of Stochastic-Adaptive Filters in Earthquake Engineering.- Study of the Propagation and Amplification of Seismic Waves in Caracas Valley with Reference to the July 29, 1967 Earthquake Response.- Seismic Response of Stochastic Ground.- An Efficient Treatment of Model Uncertainties for the Dynamic Response of Structures.- Evaluation of Response Statistics of Moment Resisting Steel Frames under Seismic Excitation.- Section 9: Materials.- On Wavefront Propagation in Random Nonlinear Media.- A Stochastic Approach to the Rheology of Fibrous Systems.- Stability of Composite Structures with Random Material Imperfections.- Section 10: Applied Random Vibrations.- Thermally Forced Random Vibrations of Thick Plates.- Random Vibration of the Rigid Block.- Response of Non-linear Trusses with Spatial Variability under Random Excitations.- Nonlinear Effects on TLP Springing Response and Reliability.- Disordered Periodic Structures.- Response Statistics of a Nonlinear Coupled Oscillator Under Parametric Excitation.- Random Field Interpolation Between Point by Point Measured Properties.- Application of Dynamic Response Analysis in Calculation of Natural Frequencies.- Section 11: Applied Stochastic Finite Element Analysis.- Stochastic Eigenvalue Analysis by SFEM Code "SAINT".- A Probabilistic Postbuckling Analysis of Composite Shells.- An Efficient SFEM Algorithm for Nonlinear Structures.- Stochastic Methods for Systems with Uncertain Properties under Plane Stress/Strain.- Section 12: Flow Related Applications and Chaotic Dynamics.- Nonlinear Response and Sonic Fatigue of High Speed Aircraft.- Necessary Condition for Homoclinic Chaos Induced by Additive Noise.- Authors' Index.

Industrial and domestic pollution agricultural pollution lakes, rivers and channels pollution of estuaries, coastal seas and open seas sewage outfalls saltwater intrusion methods for pollution studies remote sensing hydrodynamic and water quality modelling algae growth wastewater treatment sanitary quality of beaches and bathing waters.