Space Time Methods

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Space-Time Methods

Ulrich Langer,Olaf Steinbach
Space Time Methods Book PDF

Author : Ulrich Langer,Olaf Steinbach
Publisher : Walter de Gruyter GmbH & Co KG
Page : 261 pages
File Size : 51,7 Mb
Release : 2019-09-23
Category : Mathematics
ISBN : 9783110548488

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Space-Time Methods by Ulrich Langer,Olaf Steinbach Pdf

This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.

Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry

Roger Penrose,Wolfgang Rindler
Spinors and Space Time Volume 2 Spinor and Twistor Methods in Space Time Geometry Book PDF

Author : Roger Penrose,Wolfgang Rindler
Publisher : Cambridge University Press
Page : 516 pages
File Size : 48,8 Mb
Release : 1984
Category : Mathematics
ISBN : 0521347866

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Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry by Roger Penrose,Wolfgang Rindler Pdf

In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.

The Analysis of Space-Time Singularities

C. J. S. Clarke
The Analysis of Space Time Singularities Book PDF

Author : C. J. S. Clarke
Publisher : Cambridge University Press
Page : 196 pages
File Size : 48,9 Mb
Release : 1993
Category : Science
ISBN : 0521437962

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The Analysis of Space-Time Singularities by C. J. S. Clarke Pdf

The different possible singularities are defined and the mathematical methods needed to extend the space-time are described in detail in this book. Results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor.

The Large Scale Structure of Space-Time

S. W. Hawking,G. F. R. Ellis
The Large Scale Structure of Space Time Book PDF

Author : S. W. Hawking,G. F. R. Ellis
Publisher : Cambridge University Press
Page : 406 pages
File Size : 43,9 Mb
Release : 1975-02-27
Category : Science
ISBN : 9781139810951

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The Large Scale Structure of Space-Time by S. W. Hawking,G. F. R. Ellis Pdf

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

Languages in Space and Time: Models and Methods from Complex Systems Theory

Marco Patriarca,Els Heinsalu,Jean Leó Leonard
Languages in Space and Time Models and Methods from Complex Systems Theory Book PDF

Author : Marco Patriarca,Els Heinsalu,Jean Leó Leonard
Publisher : Cambridge University Press
Page : 223 pages
File Size : 50,9 Mb
Release : 2020-10-29
Category : Computers
ISBN : 9781108480659

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Languages in Space and Time: Models and Methods from Complex Systems Theory by Marco Patriarca,Els Heinsalu,Jean Leó Leonard Pdf

Demonstrates how complexity theory and statistical mechanics help define the language groups and model the language dynamics.

Modelling Longitudinal and Spatially Correlated Data

Timothy G. Gregoire,David R. Brillinger,Peter Diggle,Estelle Russek-Cohen,William G. Warren,Russell D. Wolfinger
Modelling Longitudinal and Spatially Correlated Data Book PDF

Author : Timothy G. Gregoire,David R. Brillinger,Peter Diggle,Estelle Russek-Cohen,William G. Warren,Russell D. Wolfinger
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206996

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Modelling Longitudinal and Spatially Correlated Data by Timothy G. Gregoire,David R. Brillinger,Peter Diggle,Estelle Russek-Cohen,William G. Warren,Russell D. Wolfinger Pdf

Correlated data arise in numerous contexts across a wide spectrum of subject-matter disciplines. Modeling such data present special challenges and opportunities that have received increasing scrutiny by the statistical community in recent years. In October 1996 a group of 210 statisticians and other scientists assembled on the small island of Nantucket, U. S. A. , to present and discuss new developments relating to Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Direc tions. Its purpose was to provide a cross-disciplinary forum to explore the commonalities and meaningful differences in the source and treatment of such data. This volume is a compilation of some of the important invited and volunteered presentations made during that conference. The three days and evenings of oral and displayed presentations were arranged into six broad thematic areas. The session themes, the invited speakers and the topics they addressed were as follows: • Generalized Linear Models: Peter McCullagh-"Residual Likelihood in Linear and Generalized Linear Models" • Longitudinal Data Analysis: Nan Laird-"Using the General Linear Mixed Model to Analyze Unbalanced Repeated Measures and Longi tudinal Data" • Spatio---Temporal Processes: David R. Brillinger-"Statistical Analy sis of the Tracks of Moving Particles" • Spatial Data Analysis: Noel A. Cressie-"Statistical Models for Lat tice Data" • Modelling Messy Data: Raymond J. Carroll-"Some Results on Gen eralized Linear Mixed Models with Measurement Error in Covariates" • Future Directions: Peter J.

Displaying Time Series, Spatial, and Space-Time Data with R

Oscar Perpinan Lamigueiro
Displaying Time Series Spatial and Space Time Data with R Book PDF

Author : Oscar Perpinan Lamigueiro
Publisher : CRC Press
Page : 228 pages
File Size : 44,6 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781351611350

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Displaying Time Series, Spatial, and Space-Time Data with R by Oscar Perpinan Lamigueiro Pdf

Focusing on the exploration of data with visual methods, this book presents methods and R code for producing high-quality static graphics, interactive visualizations, and animations of time series, spatial, and space-time data. Practical examples using real-world datasets help you understand how to apply the methods and code. Each of the three parts of the book is devoted to different types of data. In each part, the chapters are grouped according to the various visualization methods or data characteristics. Recent developments in the "htmlwidgets" family of packages are covered in this second edition with many new interactive graphics.

Experimental Methods in Kinetic Studies

Bohdan Wojciechowski,Norman Rice
Experimental Methods in Kinetic Studies Book PDF

Author : Bohdan Wojciechowski,Norman Rice
Publisher : Elsevier
Page : 322 pages
File Size : 53,8 Mb
Release : 2003-02-20
Category : Science
ISBN : 0080531369

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Experimental Methods in Kinetic Studies by Bohdan Wojciechowski,Norman Rice Pdf

This book is a guide to kinetic studies of reaction mechanisms. It reviews conventional reactor types and data collection methods, and introduces a new methodology for data collection using Temperature Scanning Reactors (TSR). It provides a theoretical and practical approach to temperature scanning (TS) methodology and supports a revival of kinetic studies as a useful approach to the fundamental understanding of chemical reaction mechanisms and the consequential reaction kinetics. · Describes a new patented technology · Of interest to industrial and academic researchers in the fields of kinetics and catalysis · No existing competitor for this title

Periodic Differential Equations in the Plane

Rafael Ortega
Periodic Differential Equations in the Plane Book PDF

Author : Rafael Ortega
Publisher : de Gruyter
Page : 195 pages
File Size : 43,8 Mb
Release : 2019-05-06
Category : Mathematics
ISBN : 3110550407

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Periodic Differential Equations in the Plane by Rafael Ortega Pdf

Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Space-Time Coding

Hamid Jafarkhani
Space Time Coding Book PDF

Author : Hamid Jafarkhani
Publisher : Cambridge University Press
Page : 328 pages
File Size : 48,6 Mb
Release : 2005-09-22
Category : Science
ISBN : 0521842913

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Space-Time Coding by Hamid Jafarkhani Pdf

This book covers the fundamental principles of space-time coding for wireless communications over multiple-input multiple-output (MIMO) channels, and sets out practical coding methods for achieving the performance improvements predicted by the theory. Starting with background material on wireless communications and the capacity of MIMO channels, the book then reviews design criteria for space-time codes. A detailed treatment of the theory behind space-time block codes then leads on to an in-depth discussion of space-time trellis codes. The book continues with discussion of differential space-time modulation, BLAST and some other space-time processing methods and the final chapter addresses additional topics in space-time coding. The theory and practice sections can be used independently of each other. Written by one of the inventors of space-time block coding, this book is ideal for a graduate student familiar with the basics of digital communications, and for engineers implementing the theory in real systems.

Numerical Methods for Unsteady Compressible Flow Problems

Philipp Birken
Numerical Methods for Unsteady Compressible Flow Problems Book PDF

Author : Philipp Birken
Publisher : CRC Press
Page : 246 pages
File Size : 48,7 Mb
Release : 2021-07-04
Category : Mathematics
ISBN : 9781000403527

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Numerical Methods for Unsteady Compressible Flow Problems by Philipp Birken Pdf

Numerical Methods for Unsteady Compressible Flow Problems is written to give both mathematicians and engineers an overview of the state of the art in the field, as well as of new developments. The focus is on methods for the compressible Navier-Stokes equations, the solutions of which can exhibit shocks, boundary layers and turbulence. The idea of the text is to explain the important ideas to the reader, while giving enough detail and pointers to literature to facilitate implementation of methods and application of concepts. The book covers high order methods in space, such as Discontinuous Galerkin methods, and high order methods in time, in particular implicit ones. A large part of the text is reserved to discuss iterative methods for the arising large nonlinear and linear equation systems. Ample space is given to both state-of-the-art multigrid and preconditioned Newton-Krylov schemes. Features Applications to aerospace, high-speed vehicles, heat transfer, and more besides Suitable as a textbook for graduate-level courses in CFD, or as a reference for practitioners in the field

Galerkin Finite Element Methods for Parabolic Problems

Vidar Thomee
Galerkin Finite Element Methods for Parabolic Problems Book PDF

Author : Vidar Thomee
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 40,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662033593

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Galerkin Finite Element Methods for Parabolic Problems by Vidar Thomee Pdf

My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.

Causality, Measurement Theory and the Differentiable Structure of Space-Time

R. N. Sen
Causality Measurement Theory and the Differentiable Structure of Space Time Book PDF

Author : R. N. Sen
Publisher : Cambridge University Press
Page : 413 pages
File Size : 53,8 Mb
Release : 2010-02-11
Category : Science
ISBN : 9781139485371

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Causality, Measurement Theory and the Differentiable Structure of Space-Time by R. N. Sen Pdf

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

Least-Squares Finite Element Methods

Pavel B. Bochev,Max D. Gunzburger
Least Squares Finite Element Methods Book PDF

Author : Pavel B. Bochev,Max D. Gunzburger
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 40,6 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387689227

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Least-Squares Finite Element Methods by Pavel B. Bochev,Max D. Gunzburger Pdf

Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Model Reduction of Parametrized Systems

Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban
Model Reduction of Parametrized Systems Book PDF

Author : Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban
Publisher : Springer
Page : 504 pages
File Size : 51,8 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9783319587868

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Model Reduction of Parametrized Systems by Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban Pdf

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).