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Geometric Flows On Planar Lattices
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Book Synopsis Geometric Flows on Planar Lattices by : Andrea Braides
Download or read book Geometric Flows on Planar Lattices written by Andrea Braides and published by Springer Nature. This book was released on 2021-03-23 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Discrete Variational Problems with Interfaces by : Roberto Alicandro
Download or read book Discrete Variational Problems with Interfaces written by Roberto Alicandro and published by Cambridge University Press. This book was released on 2023-12-31 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Variational Theory of Convolution-Type Functionals by : Roberto Alicandro
Download or read book A Variational Theory of Convolution-Type Functionals written by Roberto Alicandro and published by Springer Nature. This book was released on 2023-05-02 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Flows written by Huai-Dong Cao and published by . This book was released on 2008 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Practical Asymptotics by : H.K. Kuiken
Download or read book Practical Asymptotics written by H.K. Kuiken and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Extrinsic Geometric Flows by : Bennett Chow
Download or read book Extrinsic Geometric Flows written by Bennett Chow and published by American Mathematical Soc.. This book was released on 2020-05-14 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gauß curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.
Book Synopsis Flow of Gas Through Turbine Lattices by : Mikhail Efimovich Deĭch
Download or read book Flow of Gas Through Turbine Lattices written by Mikhail Efimovich Deĭch and published by . This book was released on 1956 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Tomography by : Richard J. Gardner
Download or read book Geometric Tomography written by Richard J. Gardner and published by Cambridge University Press. This book was released on 2006-06-19 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: seventy-two unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. This comprehensive work will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
Book Synopsis Planar Graphs by : William T. Trotter
Download or read book Planar Graphs written by William T. Trotter and published by American Mathematical Soc.. This book was released on with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains research articles and extended abstracts submitted by participants in the Planar Graphs Workshop held at DIMACS in November 1991, one of four workshops held during the DIMACS Special Year on Graph Theory and Algorithms. With more than seventy participants, the workshop drew many of the top experts in this area. The book covers a wide range of topics, including enumeration, characterization problems, algorithms, extremal problems, and network flows and geometry.
Book Synopsis Advances in Theory and Practice of Computational Mechanics by : Lakhmi C. Jain
Download or read book Advances in Theory and Practice of Computational Mechanics written by Lakhmi C. Jain and published by Springer Nature. This book was released on 2020-03-31 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses physical and mathematical models, numerical methods, computational algorithms and software complexes, which allow high-precision mathematical modeling in fluid, gas, and plasma mechanics; general mechanics; deformable solid mechanics; and strength, destruction and safety of structures. These proceedings focus on smart technologies and software systems that provide effective solutions to real-world problems in applied mechanics at various multi-scale levels. Highlighting the training of specialists for the aviation and space industry, it is a valuable resource for experts in the field of applied mathematics and mechanics, mathematical modeling and information technologies, as well as developers of smart applied software systems.
Book Synopsis The Basics of Crystallography and Diffraction by : Christopher Hammond
Download or read book The Basics of Crystallography and Diffraction written by Christopher Hammond and published by OUP Oxford. This book was released on 2009-05-07 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear introduction to topics which are essential to students in a wide range of scientific disciplines but which are otherwise only covered in specialised and mathematically detailed texts. It shows how crystal structures may be built up from simple ideas of atomic packing and co-ordination, it develops the concepts of crystal symmetry, point and space groups by way of two dimensional examples of patterns and tilings, it explains the concept of the reciprocal lattice in simple terms and shows its importance in an understanding of light, X-ray and electron diffraction. Practical examples of the applications of these techniques are described and also the importance of diffraction in the performance of optical instruments. The book is also of value to the general reader since it shows, by biographical and historical references, how the subject has developed and thereby indicates some of the excitement of scientific discovery.
Book Synopsis Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry by : Renwei Mei
Download or read book Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry written by Renwei Mei and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis of Geometric Flows, with Applications to Optimal Homogeneous Geometries by : Michael Bradford Williams
Download or read book Analysis of Geometric Flows, with Applications to Optimal Homogeneous Geometries written by Michael Bradford Williams and published by . This book was released on 2011 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers several problems related to Ricci flow, including the existence and behavior of solutions. The first goal is to obtain explicit, coordinate-based descriptions of Ricci flow solutions--especially those corresponding to Ricci solitons--on two classes of nilpotent Lie groups. On the odd-dimensional classical Heisenberg groups, we determine the asymptotics of Ricci flow starting at any metric, and use Lott's blowdown method to demonstrate convergence to soliton metrics. On the groups of real unitriangular matrices, which are more complicated, we describe the solitons and corresponding solutions using a suitable ansatz. Next, we consider solsolitons involving the nilsolitons in the Heisenberg case above. This uses work of Lauret, which characterizes solsolitons as certain extensions of nilsolitons, and work of Will, which demonstrates that the space of solsolitons extensions of a given nilsoliton is parametrized by the quotient of a Grassmannian by a finite group. We determine these spaces of solsoliton extensions of Heisenberg nilsolitons, and we also explicitly describe many-parameter families of these solsolitons in dimensions greater than three. Finally, we explore Ricci flow coupled with harmonic map flow, both as it arises naturally in certain bundle constructions related to Ricci flow and as a geometric flow in its own right. In the first case, we generalize a theorem of Knopf that demonstrates convergence and stability of certain locally R[superscript N]-invariant Ricci flow solutions. In the second case, we prove a version of Hamilton's compactness theorem for the coupled flow, and then generalize it to the category of etale Riemannian groupoids. We also provide a detailed example of solutions to the flow on the three-dimensional Heisenberg group.
Book Synopsis Discrete Integrable Geometry and Physics by : Alexander I. Bobenko
Download or read book Discrete Integrable Geometry and Physics written by Alexander I. Bobenko and published by Clarendon Press. This book was released on 1999 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discreteanalogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team ofauthors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts areput into the context of classical and quantum dynamics.
Book Synopsis High Performance Computing Systems and Applications by : Douglas J. K. Mewhort
Download or read book High Performance Computing Systems and Applications written by Douglas J. K. Mewhort and published by Springer. This book was released on 2010-04-20 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 23rd International Symposium on High Performance Computing Systems and Applications, HPCS 2009, held in Kingston, Canada, in June 2009. The 29 revised full papers presented - fully revised to incorporate reviewers' comments and discussions at the symposium - were carefully selected for inclusion in the book. The papers are organized in topical sections on turbulence, materials and life sciences, bringing HPC to industry, computing science, mathematics, and statistics, as well as HPC systems and methods.
Book Synopsis Geometry, Analysis and Probability by : Jean-Benoît Bost
Download or read book Geometry, Analysis and Probability written by Jean-Benoît Bost and published by Birkhäuser. This book was released on 2017-04-26 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Book Synopsis Aeronautical Engineering Review by :
Download or read book Aeronautical Engineering Review written by and published by . This book was released on 1956 with total page 2126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
