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This topical volume on ""Recent Developments of Diffusion Processes and their Applications: Fluid, Heat and Mass"" addresses diffusion in a wider sense with a special focus on technical applications. Diffusion phenomena play an important role in the development of modern engineering materials and related fields. Understanding these different transport phenomena at many levels, from atomistic to macro, has therefore long attracted the attention of many researchers in materials science and engineering and related disciplines. The present topical volume captures a representative cross-section of

Diffusion. --- Diffusion processes. --- Markov processes --- Gases --- Liquids --- Physics --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Diffusion --- Properties

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This book gives an overview of atomic diffusion, a fundamental physical process, as applied to all types of stars, from the main sequence to neutron stars. The superficial abundances of stars as well as their evolution can be significantly affected. The authors show where atomic diffusion plays an essential role and how it can be implemented in modelling.  In Part I, the authors describe the tools that are required to include atomic diffusion in models of stellar interiors and atmospheres. An important role is played by the gradient of partial radiative pressure, or radiative acceleration, which is usually neglected in stellar evolution. In Part II, the authors systematically review the contribution of atomic diffusion to each evolutionary step. The dominant effects of atomic diffusion are accompanied by more subtle effects on a large number of structural properties throughout evolution. One of the goals of this book is to provide the means for the astrophysicist or graduate student to evaluate the importance of atomic diffusion in a given star.

Astrophysics --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Astrophysics. --- Nuclear physics. --- Diffusion. --- Gases --- Liquids --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Astronomical physics --- Diffusion --- Physics. --- Cosmology. --- Astrophysics and Astroparticles. --- Particle and Nuclear Physics. --- Physics --- Astronomy --- Cosmic physics --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Properties --- Deism --- Metaphysics

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This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.

Mathematics. --- Functional Analysis. --- Partial Differential Equations. --- Mathematical Applications in the Physical Sciences. --- Mathematical Physics. --- Functional analysis. --- Differential equations, partial. --- Mathématiques --- Analyse fonctionnelle --- Differential equations, Partial --- Differential equations, Elliptic --- Boundary value problems --- Geometry, Differential --- Functions --- Diffusion --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Numerical solutions --- Gases --- Liquids --- Analysis (Mathematics) --- Differential geometry --- Boundary conditions (Differential equations) --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Partial differential equations --- Partial differential equations. --- Mathematical physics. --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Boundary value problems. --- Differential equations, Elliptic. --- Differential equations, Partial. --- Diffusion. --- Geometry, Differential. --- Functions. --- Numerical solutions. --- Numerical analysis --- Differential equations --- Mathematical analysis --- Numbers, Complex --- Set theory --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Differential equations, Linear --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Properties