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This book discusses the extension of classical continuum models. To the first class addressed belong various thermodynamic models of multicomponent systems, and to the second class belong primarily microstructures created by phase transformations.
The interest in the problem of surface diffusion has been steadily growing over the last fifteen years. This is clearly evident from the increase in the number of papers dealing with the problem, the development of new experimental techniques, and the specialized sessions focusing on diffusion in national and international meetings. Part of the driving force behind this increasing activity is our recently acquired ability to observe and possibly control atomic scale phenomena. It is now possible to look selectively at individual atomistic processes and to determine their relative importance during growth and reactions at surfaces. The number of researchers interested in this problem also has...
Let $\mathcal{M}$ denote the space of probability measures on $\mathbb{R}^D$ endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare. In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. In particular they prove an analogue of Green's theorem for 1-forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes. For $D=2d$ the authors then define a symplectic distribution on $\mathcal{M}$ in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced by Ambrosio and Gangbo. Throughout the paper the authors emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of $\mathbb{R}^D$.
The invited talks include applications from the fields of solid state physics, plasma physics, hydrodynamics, high-energy physics, thermodymanics, atomic and molecular physics, chemistry, statistical physics, earth sciences, neural networks, meteorology, astrophysics, and presentations on cellular automata and quantum Monte Carlo methods. The emphasis is on methods of software development and engineering, graphic tools, and storage of physical data.
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