Mode of access: World Wide Web.

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 91-97) and index.

1. Introduction -- 1.1 Background -- 1.2 Ferromagnetic nanoparticles -- 1.3 Outline of the book --

2. Numerical and analytical methods on boundary value problems -- 2.1 A two-point boundary value problem -- 2.2 Numerical approaches -- 2.2.1 Shooting methods -- 2.2.2 Finite difference methods -- 2.2.3 Finite element methods -- 2.3 Analytical approaches -- 2.3.1 Images method -- 2.3.2 Green's function method -- 2.3.3 Separation of variables method -- 2.3.4 Expansions in orthogonal functions method -- 2.4 Chapter remarks --

3. Governing equations -- 3.1 Scalar magnetic potential -- 3.2 Spherical coordinates system -- 3.3 Bispherical coordinates system -- 3.4 Solution to the Laplace equation in bispherical coordinates -- 3.5 Boundary conditions -- 3.5.1 Magnetic flux density -- 3.5.2 Magnetic potential -- 3.5.3 Normal component of the magnetic flux density -- 3.6 The basic model -- 3.7 Chapter remarks --

4. Mathematical model -- 4.1 Scalar magnetic components outside -- 4.1.1 Field along the x axis -- 4.1.2 H0 along the y axis -- 4.1.3 Field along the common axis -- 4.2 Scalar magnetic components inside -- 4.2.1 H0 along the x axis -- 4.2.2 Field along the y axis -- 4.2.3 H0 along the z axis -- 4.3 The potential at the poles -- 4.4 Chapter remarks --

5. Results and numerical analysis -- 5.1 Particles of same size R1 = R2 -- 5.2 Particles of different sizes R1 [is not] = R2 -- 5.3 Chapter remarks --

6. Conclusions --

7. Solutions -- 7.1 Exercise 3.2 -- 7.2 Exercise 3.3 -- 7.3 Exercise 4.1 -- Bibliography -- Author's biography -- Index.

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The investigation of the behavior of ferromagnetic particles in an external magnetic field is important for use in a wide range of applications in magnetostatics problems, from biomedicine to engineering. To the best of the author's knowledge, the systematic analysis for this kind of investigation is not available in the current literature. Therefore, this book contributes a complete solution for investigating the behavior of two ferromagnetic spherical particles, immersed in a uniform magnetic field, by obtaining exact mathematical models on a boundary value problem. While there are a vast number of common numerical and analytical methods for solving boundary value problems in the literature, the rapidly growing complexity of these solutions causes increase usage of the computer tools in practical cases. We analytically solve the boundary value problem by using a special technique called a bispherical coordinates system and the numerical computations were obtained by a computer tool. In addition to these details, we will present step-by-step instructions with simple explanations throughout the book, in an effort to act as inspiration in the reader's own modeling for relevant applications in science and engineering. On the other hand, the resulting analytical expressions will constitute benchmark solutions for specified geometric arrangements, which are beneficial for determining the validity of other relevant numerical techniques. The generated results are analyzed quantitatively as well as qualitatively in various approaches. Moreover, the methodology of this book can be adopted for real-world applications in the fields of ferrohydrodynamics, applied electromagnetics, fluid dynamics, electrical engineering, and so forth. Higher-level university students, academics, engineers, scientists, and researchers involved in the aforementioned fields are the intended audience for this book.

Also available in print.

Title from PDF title page (viewed on February 24, 2018).