"Computational Physics" is designed to provide direct experience in the computer modeling of physical systems. Its scope includes the essential numerical techniques needed to "do physics" on a computer. Each of these is developed heuristically in the text, with the aid of simple mathematical illustrations. However, the real value of the book is in the eight Examples and Projects, where the reader is guided in applying these techniques to substantial problems in classical, quantum, or statistical mechanics. These problems have been chosen to enrich the standard physics curriculum at the advanced undergraduate or beginning graduate level. The book will also be useful to physicists, engineers, and chemists interested in computer modeling and numerical techniques. Although the user-friendly and fully documented programs are written in FORTRAN, a casual familiarity with any other high-level language, such as BASIC, PASCAL, or C, is sufficient. The codes in BASIC and FORTRAN are available on the web at http: //www.computationalphysics.info (Please follow the link at the bottom of the page). They are available in zip format, which can be expanded on UNIX, Window, and Mac systems with the proper software. The codes are suitable for use (with minor changes) on any machine with a FORTRAN-77 compatible compiler or BASIC compiler. The FORTRAN graphics codes are available as well. However, as they were originally written to run on the VAX, major modifications must be made to make them run on other machines.

This book gathers papers presented at the Workshop on Computational Diffusion MRI, CDMRI 2020, held under the auspices of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), which took place virtually on October 8th, 2020, having originally been planned to take place in Lima, Peru.This book presents the latest developments in the highly active and rapidly growing field of diffusion MRI. While offering new perspectives on the most recent research challenges in the field, the selected articles also provide a valuable starting point for anyone interested in learning computational techniques for diffusion MRI. The book includes rigorous mathematical derivations, a large number of rich, full-colour visualizations, and clinically relevant results. As such, it is of interest to researchers and practitioners in the fields of computer science, MRI physics, and applied mathematics. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice.

Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.

A clear methodological and philosophical introduction to complexity theory as applied to urban and regional systems is given, together with a detailed series of modelling case studies compiled over the last couple of decades. Based on the new complex systems thinking, mathematical models are developed which attempt to simulate the evolution of towns, cities, and regions and the complicated co-evolutionary interaction there is both between and within them. The aim of these models is to help policy analysis and decision-making in urban and regional planning, energy policy, transport policy, and many other areas of service provision, infrastructure planning, and investment that are necessary for a successful society.

Introductory Mathematics for the Life Sciences offers a straightforward introduction to the mathematical principles needed for studies in the life sciences. Starting with the basics of numbers, fractions, ratios, and percentages, the author explains progressively more sophisticated concepts, from algebra, measurement, and scientific notation through the linear, power, exponential, and logarithmic functions to introductory statistics. Worked examples illustrate concepts, applications, and interpretations, and exercises at the end of each chapter help readers apply and practice the skills they develop. Answers to the exercises are posted at the end of the text.

The main objective of the book is to highlight the modeling of magnetic particles with different shapes and magnetic properties, to provide graduate students and young researchers information on the theoretical aspects and actual techniques for the treatment of magnetic particles in particle-based simulations. In simulation, we focus on the Monte Carlo, molecular dynamics, Brownian dynamics, lattice Boltzmann and stochastic rotation dynamics (multi-particle collision dynamics) methods. The latter two simulation methods can simulate both the particle motion and the ambient flow field simultaneously. In general, specialized knowledge can only be obtained in an effective manner under the supervision of an expert. The present book is written to play such a role for readers who wish to develop the skill of modeling magnetic particles and develop a computer simulation program using their own ability. This book is therefore a self-learning book for graduate students and young researchers. Armed with this knowledge, readers are expected to be able to sufficiently enhance their skill for tackling any challenging problems they may encounter in future.

Contents:
1. Basic Principles: The Operating Regime Approach 2. Modelling: Fuzzy Set Methods for Local Modelling Identification 3. Modelling of Electrically Stimulated Muscle 4. Process Modelling Using a Functional State Approach 5. Markov Mixtures of Experts 6. Active Learning With Mixture Models 7. Local Learning in Local Model Networks 8. Side Effects of Normalising Basic Functions 9. Control: Heterogeneous Control Laws 10. Local Laguerre Models 11. Multiple Model Adaptive Control 12. H Control Using Multiple Linear Models 13. Synthesis of Fuzzy Control Systems Based on Linear Takagi-Sugeno Fuzzy Models

Carefully separating the essential from the ornamental, Essentials of Control Techniques and Theory presents the nuts and bolts for designing a successful controller. It discusses the theory required to support the art of designing a working controller as well as the various aspects to convince a client, employer, or examiner of your expertise. A Compelling Account of the Basics of Control Theory Control solutions for practicing engineers Using the author's own Javascript On-Line Learning Interactive Environment for Simulation (Jollies), the text relies on computer-based graphical analysis methods, such as Nyquist, Nichols, root locus, and phase-plane, to illustrate how useful computer simulation can be for analyzing both linear and nonlinear systems. It explains step-by-step the design and modeling of various control systems, including discrete time systems and an inverted pendulum. Along with offering many web-based simulations, the book shows how mathematics, such as vectors, matrices, and the differential equations that govern state variables, can help us understand the concepts that underpin the controller's effects. From frequency domain analysis to time-domain state-space representation, this book covers many aspects of classical and modern control theory. It presents important methods for designing and analyzing linear systems and controllers.

This monograph provides a general background to the modelling of a special class of offshore structures known as compliant structures. External forcing is resisted by buoyancy and tension forces which increase when the structure is slightly offset from its equilibrium. The technical development given in this book is presented in such a way as to highlight the adaptability of the modelling, and the reader is shown how the techniques described can be applied to a variety of different offshore structures.

The development of constitutive relations for geotechnical materials, with the help of numerical models, have increased notably the ability to predict and to interpret mechanical behaviour of geotechnical works. These proceedings cover the applications of computational mechanics in this area.

Providing a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.

Offers information necessary for the development of mathematical models and numerical techniques to solve specific drying problems. The book addresses difficult issues involved with the drying equations of numerical analysis, including mesh generation, discretinization strategies, the nonlinear equation set and the linearized algebraic system, convergance criteria, time step control, experimental validation, optimum methods of visualization results, and more.

Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.

Large observational studies involving research questions that require the measurement of several features on each individual arise in many fields including the social and medical sciences. This book sets out both the general concepts and the more technical statistical issues involved in analysis and interpretation. Numerous illustrative examples are described in outline and four studies are discussed in some detail.

The use of graphical representations of dependencies and independencies among the features under study is stressed, both to incorporate available knowledge at the planning stage of an analysis and to summarize aspects important for interpretation after detailed statistical analysis is complete. This book is aimed at research workers using statistical methods as well as statisticians involved in empirical research.

Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry.
The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research.
Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.

Mathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined.
Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.

Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

A comprehensive mathematical and computational modeling of CO2 Geosequestration and Compressed Air Energy Storage Energy and environment are two interrelated issues of great concern to modern civilization. As the world population will soon reach eight billion, the demand for energy will dramatically increase, intensifying the use of fossil fuels. Utilization of fossil fuels is by far the largest anthropogenic source of CO2 emission into the earth's atmosphere. This unavoidable reality necessitates efforts to mitigate CO2 from indefi nitely being emitted in the atmosphere. CO2 geo-sequestration is currently considered to be a vital technology for this purpose. Meanwhile, and as fossil fuels will sooner or later be depleted, utilization of renewable energy resources is inevitable. Nowadays, wind and solar energy, being clean and sustainable, are gaining momentum. However, their availability is intermittent. This intermittent nature of solar and wind energy necessitates storing the produced energy at off-peak times for later use. Compressed air energy storage in subterranean caverns, aquifers and coal seams is currently considered to be a plausible technology for this purpose. CO2 geo-sequestration and compressed air energy storage are thus vital technologies for current and future energy strategy development. These technologies can be made safe and cost-effective by utilizing computational tools capable of simulating the involved multiphysical phenomena and processes. Computational modeling of such systems is challenging and resource-consuming. Meeting such a challenge constitutes the focal point of this book. This book addresses comprehensive theoretical and computational modeling aspects of CO2 geosequestration and compressed air energy storage. The book consists of 16 chapters authored by prominent researchers in these two fi elds. The authors of the book endeavoured to present years of innovative work, making it available for a wide range of readers, including geoscientists, poromechanists, applied mathematicians, computational geoscientists, geologists and reservoir engineers.

'A brilliant account of how models are so often abused and of how they should be used' John Kay How do mathematical models shape our world - and how can we harness their power for good? Models are at the centre of everything we do. Whether we use them or are simply affected by them, they act as metaphors that help us better understand the increasingly complex problems facing us in the modern world. Without models, we couldn't begin to tackle three of the major challenges facing modern society: regulation of the economy, climate change and the COVID-19 pandemic. Yet in recent years, the validity of the models we use has been hotly debated and there has been renewed awareness of the disastrous consequences when the makers and interpreters of models get things wrong. Drawing on contemporary examples from finance, climate and health policy, Erica Thompson explores what models are, why we need them, how they work and what happens when they go wrong. This is not a book that argues we should do away with models, but rather, that we need to properly understand how they are constructed - and how some of the assumptions that underlie the models we use can have significant unintended consequences. Unexpectedly humorous, thought-provoking and passionate, this is essential reading for everyone.

The use of mathematical modeling in engineering allows for a significant reduction of material costs associated with design, production, and operation of technical objects, but it is important for an engineer to use the available computational approaches in modeling correctly. Taking into account the level of modern computer technology, this new volume explains how an engineer should properly define the physical and mathematical problem statement, choose the computational approach, and solve the problem by proven reliable computational approach using computer and software applications during the solution of a particular problem. This work is the result of years of the authors' research and experience in the fields of power and rocket engineering where they put into practice the methods of mathematical modeling shown in this valuable volume. The examples in the book are based on two approaches. The first approach involves the use of the relatively simple mathematical system MathCad. The second one involves the solving of problems using Intel Visual Fortran compiler with IMSL Libraries. The use of other software packages (Maple, MathLab, Mathematica) or compilers ( , ++, Visual Basic) for code is equally acceptable in the solution of the problems given in the book. Intended for professors and instructors, scientific researchers, students, and industry professionals, the book will help readers to choose the most appropriate mathematical modeling method to solve engineering problems, and the authors also include methods that allow for the solving of nonmathematical problems as mathematical problems.

Nonlinear Dynamics of Reservoir Mixtures provides an overview of modeling techniques for solving nonlinear problems in hydrodynamics, with an emphasis on compositional flows in porous reservoirs. The volume focuses on nonlinear wave techniques for simulating and predicting fluid dynamic processes in petroleum reservoirs and discusses general applications of these models for other fluids.
Topics covered include inhomogeneous space structures in reservoir processes, gradient models for analyzing changes in thermodynamic and hydrodynamic fluid properties, phase transition dynamics in fluids and rock minerals, and wetting phenomena. The book also discusses the stages involved in developing compositional simulators for enhanced oil recovery and describes applications used in hydrocarbon fields in the former USSR.
Nonlinear Dynamics of Reservoir Mixtures provides excellent reference material for mathematicians, petroleum engineers, exploration geophysicists, and mechanical engineers. It is also a useful compositional modeling text for graduate students in the earth sciences and in petroleum and chemical engineering.

In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts.

The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus.

This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.

Computational Mathematics: Models, Methods, and Analysis with MATLAB (R) and MPI is a unique book covering the concepts and techniques at the core of computational science. The author delivers a hands-on introduction to nonlinear, 2D, and 3D models; nonrectangular domains; systems of partial differential equations; and large algebraic problems requiring high-performance computing. The book shows how to apply a model, select a numerical method, implement computer simulations, and assess the ensuing results. Providing a wealth of MATLAB, Fortran, and C++ code online for download, the Second Edition of this very popular text: Includes a new chapter with two sections on the finite element method, two sections on shallow water waves, and two sections on the driven cavity problem Introduces multiprocessor/multicore computers, parallel MATLAB, and message passing interface (MPI) in the chapter on high-performance computing Updates and adds code and documentation Computational Mathematics: Models, Methods, and Analysis with MATLAB (R) and MPI, Second Edition is an ideal textbook for an undergraduate course taught to mathematics, computer science, and engineering students. By using code in practical ways, students take their first steps toward more sophisticated numerical modeling.

The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject. This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB (R) supplement that gives basic codes and commands for solving differential equations. MATLAB (R) is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com.

Building Information Modelling (BIM) is a global phenomenon which is gaining significant momentum across the world. Currently there is little information on how to realise and monitor benefits from implementing BIM across the life-cycle of a built environment asset. This book provides a practical and strategic framework to realise value from implementing BIM by adapting Benefit Realisation Management theory. It presents an approach for practitioners aiming to implement BIM across the life-cycle of built environment assets, including both buildings and infrastructure. Additionally, the book features: wide-ranging information about BIM, the challenges of monitoring progress towards benefit goals and the greater context of implementation; a set of dictionaries that illustrate: how benefits can be achieved, what the benefit flows are and the enabling tools and processes that contribute to achieving and maximising them; a suite of measures that can serve to monitor progress with examples of how they have been used to measure benefits from BIM; real-world examples from across the world and life-cycle phases that show how these benefits can be achieved; and information on international maturity and competency measures to complement the value realisation framework. Including a blend of academic and industry input, this book has been developed in close collaborative consultation with industry, government and international research organisations and could be used for industry courses on BIM benefits and implementation for asset management or by universities that teach BIM-related courses.