Geometric Flows on Planar Lattices - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Flows on Planar Lattices write by Andrea Braides. This book was released on 2021-03-23. Geometric Flows on Planar Lattices available in PDF, EPUB and Kindle. This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
Discrete Variational Problems with Interfaces
Discrete Variational Problems with Interfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Variational Problems with Interfaces write by Roberto Alicandro. This book was released on 2023-12-31. Discrete Variational Problems with Interfaces available in PDF, EPUB and Kindle. Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
A Variational Theory of Convolution-Type Functionals
A Variational Theory of Convolution-Type Functionals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Variational Theory of Convolution-Type Functionals write by Roberto Alicandro. This book was released on 2023-05-02. A Variational Theory of Convolution-Type Functionals available in PDF, EPUB and Kindle. This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.
Practical Asymptotics
Practical Asymptotics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Practical Asymptotics write by H.K. Kuiken. This book was released on 2012-12-06. Practical Asymptotics available in PDF, EPUB and Kindle. Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced. In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few. A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.
Flow of Gas Through Turbine Lattices
Flow of Gas Through Turbine Lattices - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Flow of Gas Through Turbine Lattices write by Mikhail Efimovich Deĭch. This book was released on 1956. Flow of Gas Through Turbine Lattices available in PDF, EPUB and Kindle. Abstract: This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.
