Data-driven Modelling and Scientific Machine Learning in Continuum Physics
Author: Krishna Garikipati
Publisher: Springer Nature
Published:
Total Pages: 233
ISBN-13: 3031620291
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Tensor Voting
Author: Philippos Mordohai
Publisher: Springer Nature
Published: 2022-06-01
Total Pages: 126
ISBN-13: 3031022424
DOWNLOAD EBOOKThis lecture presents research on a general framework for perceptual organization that was conducted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organization methodology applicable in situations that may seem heterogeneous initially. We show how several problems can be posed as the organization of the inputs into salient perceptual structures, which are inferred via tensor voting. The work presented here extends the original tensor voting framework with the addition of boundary inference capabilities; a novel re-formulation of the framework applicable to high-dimensional spaces and the development of algorithms for computer vision and machine learning problems. We show complete analysis for some problems, while we briefly outline our approach for other applications and provide pointers to relevant sources.
Mathematical Modelling
Author: Seppo Pohjolainen
Publisher: Springer
Published: 2016-07-14
Total Pages: 247
ISBN-13: 3319278363
DOWNLOAD EBOOKThis book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Mathematical Modelling
Author: Seyed M. Moghadas
Publisher: John Wiley & Sons
Published: 2018-07-24
Total Pages: 238
ISBN-13: 1119483999
DOWNLOAD EBOOKAn important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.
Nonequilibrium Statistical Mechanics
Author: Robert Zwanzig
Publisher: Oxford University Press, USA
Published: 2001-05-17
Total Pages: 233
ISBN-13: 0195140184
DOWNLOAD EBOOKThis is a presentation of the main ideas and methods of modern nonequilibrium statistical mechanics. It is the perfect introduction for anyone in chemistry or physics who needs an update or background in this time-dependent field. Topics covered include fluctuation-dissipation theorem; linear response theory; time correlation functions, and projection operators. Theoretical models are illustrated by real-world examples and numerous applications such as chemical reaction rates and spectral line shapes are covered. The mathematical treatments are detailed and easily understandable and the appendices include useful mathematical methods like the Laplace transforms, Gaussian random variables and phenomenological transport equations.
Data-Driven Modeling & Scientific Computation
Author: Jose Nathan Kutz
Publisher:
Published: 2013-08-08
Total Pages: 657
ISBN-13: 0199660336
DOWNLOAD EBOOKCombining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.
Mechanics 4
Author: John Hebborn
Publisher: Heinemann
Published: 2001
Total Pages: 150
ISBN-13: 9780435510770
DOWNLOAD EBOOKA syllabus-specific textbook providing worked examples, exam-level questions and many practice exercises, in accordance to the new Edexcel AS and Advanced GCE specification.
Mathematics Applied to Continuum Mechanics
Author: Lee A. Segel
Publisher: SIAM
Published: 2007-07-12
Total Pages: 598
ISBN-13: 0898716209
DOWNLOAD EBOOKThis classic work gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text for both classroom use and independent study.
Effective Lagrangians for the Standard Model
Author: Antonio Dobado
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 322
ISBN-13: 3642591914
DOWNLOAD EBOOKThis book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of parti cle physics. All together they are known as the effective or phenomenological Lagrangian formalism. Motivated by the enormous amount of work carried out in this field during the last years, our purpose when writing this book has been to give a modern and pedagogical exposition of the most relevant as pects of the topic. We hope that our efforts will be useful, both for graduated students in the search for a solid theoretical background in modern phe nomenology and for more experimented particle physicists willing to learn about this field or to start working on it. Even though we have tried to keep the book as self-contained as possible, it has been written assuming that the reader is familiar, at least, with the most basic concepts and techniques of QFT, gauge theories, the standard model (SM) and differential geometry, at the level of graduate studies. It is therefore possible that senior high-energy physicists may find the book too detailed and so they could probably omit several sections. The book is divided into two main parts and the appendices. In the first part we introduce the fundamentals of the effective Lagrangian formalism and other basic topics such as Ward identities, non-linear sigma models (NLSM), spontaneous symmetry breaking (SSB), anomalies, the SM symmetries, etc.
Handbook of Materials Modeling
Author: Sidney Yip
Publisher: Springer Science & Business Media
Published: 2007-11-17
Total Pages: 2903
ISBN-13: 1402032862
DOWNLOAD EBOOKThe first reference of its kind in the rapidly emerging field of computational approachs to materials research, this is a compendium of perspective-providing and topical articles written to inform students and non-specialists of the current status and capabilities of modelling and simulation. From the standpoint of methodology, the development follows a multiscale approach with emphasis on electronic-structure, atomistic, and mesoscale methods, as well as mathematical analysis and rate processes. Basic models are treated across traditional disciplines, not only in the discussion of methods but also in chapters on crystal defects, microstructure, fluids, polymers and soft matter. Written by authors who are actively participating in the current development, this collection of 150 articles has the breadth and depth to be a major contributor toward defining the field of computational materials. In addition, there are 40 commentaries by highly respected researchers, presenting various views that should interest the future generations of the community. Subject Editors: Martin Bazant, MIT; Bruce Boghosian, Tufts University; Richard Catlow, Royal Institution; Long-Qing Chen, Pennsylvania State University; William Curtin, Brown University; Tomas Diaz de la Rubia, Lawrence Livermore National Laboratory; Nicolas Hadjiconstantinou, MIT; Mark F. Horstemeyer, Mississippi State University; Efthimios Kaxiras, Harvard University; L. Mahadevan, Harvard University; Dimitrios Maroudas, University of Massachusetts; Nicola Marzari, MIT; Horia Metiu, University of California Santa Barbara; Gregory C. Rutledge, MIT; David J. Srolovitz, Princeton University; Bernhardt L. Trout, MIT; Dieter Wolf, Argonne National Laboratory.
