Movchan, A. B. (Alexander B.)
        Asymptotic models of fields in dilute and densely packed composites / A.B. Movchan, N.V. Movchan, C.G. Poulton. - London : Imperial College Press, 2002. - xi, 190 pages : illustrations ; 24 cm.
        Includes bibliographical references and index

        Tóm tắt: This book is about asymptotic models for problems of elasticity, electrostatics and electromagnetism describing physical phenomena in heterogeneous composite structures. Particular attention is paid to analysis of structures containing inclusions or voids which are either of small relative volume (dilute composites) or are placed close to each other (densely packed composites). The methods described in this text are analytical, and the range of our interests covers two areas: (a) the method of compound asymptotic expansions applied to singularly perturbed boundary value problems and (b) the multipole method which proves to be efficient in analysis of fields for domains containing arrays of inclusions of circular or spherical shapes. The book came as a result of our recent work on mathematical modelling of defects in electromagnetism and elasticity. One simple and efficient method for the study of small defects is via evaluation of their dipole tensors and the corresponding energy change associated with the perturbation field. However, when inclusions are finite in size and interact with each other one needs the high-order multipole approximations of solutions. A particular feature of singularly perturbed problems is the presence of so-called boundary layer fields concentrated in the high-gradient regions. Boundary layers are usually described by solutions of model problems posed in unbounded domains. In some cases one can obtain these solutions explicitly or evaluate their asymptotics at infinity. In this text we study models of solids containing small inclusions or voids, and the boundary layers describe perturbations of elastic fields associated with these inclusions

        ISBN
        
1. Differential equations, Partial -- Asymptotic theory.2. Phương trình vi phân -- Lý thuyết tiệm cận.
I. Movchan, N. V. (Nataliya V. II. Poulton, C. G. (Chris G.). III. Nhan đề

Số định danh : 515.353 M435

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NV18001838

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