Fundamentals Of Dimensional Analysis
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| Author | : Alberto N. Conejo |
| Publisher | : Springer Nature |
| Total Pages | : 384 |
| Release | : 2021-05-31 |
| Genre | : Technology & Engineering |
| ISBN | : 9811616027 |
This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowledge on each problem it has serious consequences: the usefulness of dimensional analysis is not appreciated, is not possible to understand the real challenges of this subject and the result, which is a general relationship with dimensionless groups is useless. This book closes the hole in previous books because in addition to describe step by step how to reach the general relationship with dimensionless groups, which creates solid basis of different metallurgical problems to understand the role of the relevant variables. It provides a full description on how to obtain the experimental data and applies the experimental data to transform the general relationship in a particular solution. Once the reader learns how to design the experimental work and uses that information to define the particular solution, it is possible to asses if the selection of variables was adequate or not. The book is useful for both undergraduate and graduate students.
| Author | : Don S. Lemons |
| Publisher | : Cambridge University Press |
| Total Pages | : 115 |
| Release | : 2017-03-16 |
| Genre | : Mathematics |
| ISBN | : 1107161150 |
This introduction to dimensional analysis covers the methods, history and formalisation of the field. Utilising topics including mechanics, hydro- and electrodynamics, and thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis, making it perfect for students on introductory courses in physics, engineering and mathematics.
| Author | : Volker Simon |
| Publisher | : Springer |
| Total Pages | : 144 |
| Release | : 2017-02-09 |
| Genre | : Technology & Engineering |
| ISBN | : 3319520288 |
This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.
| Author | : Lothar Birk |
| Publisher | : John Wiley & Sons |
| Total Pages | : 876 |
| Release | : 2019-04-25 |
| Genre | : Technology & Engineering |
| ISBN | : 1118855515 |
Fundamentals of Ship Hydrodynamics: Fluid Mechanics, Ship Resistance and Propulsion Lothar Birk, University of New Orleans, USA Bridging the information gap between fluid mechanics and ship hydrodynamics Fundamentals of Ship Hydrodynamics is designed as a textbook for undergraduate education in ship resistance and propulsion. The book provides connections between basic training in calculus and fluid mechanics and the application of hydrodynamics in daily ship design practice. Based on a foundation in fluid mechanics, the origin, use, and limitations of experimental and computational procedures for resistance and propulsion estimates are explained. The book is subdivided into sixty chapters, providing background material for individual lectures. The unabridged treatment of equations and the extensive use of figures and examples enable students to study details at their own pace. Key features: • Covers the range from basic fluid mechanics to applied ship hydrodynamics. • Subdivided into 60 succinct chapters. • In-depth coverage of material enables self-study. • Around 250 figures and tables. Fundamentals of Ship Hydrodynamics is essential reading for students and staff of naval architecture, ocean engineering, and applied physics. The book is also useful for practicing naval architects and engineers who wish to brush up on the basics, prepare for a licensing exam, or expand their knowledge.
| Author | : Ioannis Koutromanos |
| Publisher | : John Wiley & Sons |
| Total Pages | : 724 |
| Release | : 2018-02-12 |
| Genre | : Technology & Engineering |
| ISBN | : 1119260086 |
An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis.
| Author | : Sandro G. Longo |
| Publisher | : Springer Nature |
| Total Pages | : 447 |
| Release | : 2022-02-04 |
| Genre | : Mathematics |
| ISBN | : 303079217X |
The book provides a summary of the historical evolution of dimensional analysis, and frames the problem of dimensions, systems of units and similarity in a vision dominated by the conventions that formalise even the exact sciences. The first four chapters address the definitions, with few dimensional analysis theorems and similarity criteria. There is also the analysis of self-similarity, both of first and second kind, with a couple of completely solved problems, framed within the group theory. From chapter 5 onward, the focus is on applications in some of the engineering sectors. The number of topics is necessarily limited, but, almost always, there are details, calculations and treatment of assumptions. The book contains descriptions of some of the experimental apparatuses currently used for the realisation of physical models, such as the wind tunnel, the shaking table, the centrifuge, and with the exclusion of many others, which can be found in specialist monographies. Measurement techniques and instrumentation and statistical data processing is also available in other books. Some more specific notions, required by the context, are reported in the appendix, where appears also the description of numerous dimensionless groups, all of engineering interest, but with the exclusion of many others related to physical processes of electrical nature or physics of particles. A glossary lists the meaning of some specific terms typical of dimensional analysis and used in the book.
| Author | : Johannes Lederer |
| Publisher | : Springer Nature |
| Total Pages | : 355 |
| Release | : 2021-11-16 |
| Genre | : Mathematics |
| ISBN | : 3030737926 |
This textbook provides a step-by-step introduction to the tools and principles of high-dimensional statistics. Each chapter is complemented by numerous exercises, many of them with detailed solutions, and computer labs in R that convey valuable practical insights. The book covers the theory and practice of high-dimensional linear regression, graphical models, and inference, ensuring readers have a smooth start in the field. It also offers suggestions for further reading. Given its scope, the textbook is intended for beginning graduate and advanced undergraduate students in statistics, biostatistics, and bioinformatics, though it will be equally useful to a broader audience.
| Author | : Christophe Giraud |
| Publisher | : CRC Press |
| Total Pages | : 410 |
| Release | : 2021-08-25 |
| Genre | : Computers |
| ISBN | : 1000408353 |
Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
| Author | : O. C. Zienkiewicz |
| Publisher | : Elsevier |
| Total Pages | : 1863 |
| Release | : 2005-11-25 |
| Genre | : Technology & Engineering |
| ISBN | : 0080531679 |
The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics.* This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference
| Author | : Avrim Blum |
| Publisher | : Cambridge University Press |
| Total Pages | : 433 |
| Release | : 2020-01-23 |
| Genre | : Computers |
| ISBN | : 1108617360 |
This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.
