Download or read book Numerical Methods of Reactor Analysis written by Melville Jr. Clark and published by Elsevier. This book was released on 2012-12-02 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nuclear Science and Technology, Volume 3: Numerical Methods of Reactor Analysis presents the numerical analysis frequently used in the nuclear reactor field. This book discusses the numerical approximation for the multigroup diffusion method, which results in simple algebraic equations. Organized into six chapters, this volume starts with an overview of the simplified formulation of linear algebra by defining the matrices and operations with matrices. This text then discusses the properties of special matrices and reviews the elementary properties of finite difference equations. Other chapters consider a variety of methods of obtaining numerical solutions to the approximating equations. The final chapter deals with Monte Carlo method, which is a statistical method for solving statistical or deterministic problems. This book is a valuable resource for nuclear engineers. Students at the graduate level who had an introductory course in reactor physics and a basic course in differential equations will also find this book useful.

Download or read book Deterministic Solvers for the Boltzmann Transport Equation written by Sung-Min Hong and published by Springer Science & Business Media. This book was released on 2011-07-31 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers all aspects from the expansion of the Boltzmann transport equation with harmonic functions to application to devices, where transport in the bulk and in inversion layers is considered. The important aspects of stabilization and band structure mapping are discussed in detail. This is done not only for the full band structure of the 3D k-space, but also for the warped band structure of the quasi 2D hole gas. Efficient methods for building the Schrödinger equation for arbitrary surface or strain directions, gridding of the 2D k-space and solving it together with the other two equations are presented.

Download or read book Numerical Solution of Time Dependent Advection Diffusion Reaction Equations written by Willem Hundsdorfer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique book on Reaction-Advection-Diffusion problems

Download or read book Lattice Gas Cellular Automata and Lattice Boltzmann Models written by Dieter A. Wolf-Gladrow and published by Springer. This book was released on 2004-10-19 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Download or read book NBS Special Publication written by and published by . This book was released on 1965 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Megavoltage X Ray Dose Computation Algorithms written by Jerry Battista and published by CRC Press. This book was released on 2019-01-04 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Read an exclusive interview with Dr. Jerry Battista here. A critical element of radiation treatment planning for cancer is the accurate prediction and delivery of a tailored radiation dose distribution inside the patient. Megavoltage x-ray beams are aimed at the tumour, while collateral damage to nearby healthy tissue and organs is minimized. The key to optimal treatment therefore lies in adopting a trustworthy three-dimensional (3D) dose computation algorithm, which simulates the passage of both primary and secondary radiation throughout the exposed tissue. Edited by an award-winning university educator and pioneer in the field of voxel-based radiation dose computation, this book explores the physics and mathematics that underlie algorithms encountered in contemporary radiation oncology. It is an invaluable reference for clinical physicists who commission, develop, or test treatment planning software. This book also covers a core topic in the syllabus for educating graduate students and residents entering the field of clinical physics. This book starts with a historical perspective gradually building up to the three most important algorithms used for today’s clinical applications. These algorithms can solve the same general radiation transport problem from three vantages: firstly, applying convolution-superposition principles (i.e. Green’s method); secondly, the stochastic simulation of radiation particle interactions with tissue atoms (i.e. the Monte Carlo method); and thirdly, the deterministic solution of the fundamental equations for radiation fields of x-rays and their secondary particles (i.e. the Boltzmann method). It contains clear, original illustrations of key concepts and quantities thoughout, supplemented by metaphors and analogies to facilitate comprehension and retention of knowledge. Features: Edited by an authority in the field, enhanced with chapter contributions from physicists with clinical experience in the fields of computational dosimetry and dose optimization Contains examples of test phantom results and clinical cases, illustrating pitfalls to avoid in clinical applications to radiation oncology Introduces four-dimensional (4D) dose computation, on-line dose reconstruction, and dose accumulation that accounts for tissue displacements and motion throughout a course of radiation therapy

Download or read book The Lattice Boltzmann Equation For Complex States of Flowing Matter written by Sauro Succi and published by Oxford University Press. This book was released on 2018-04-13 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task. The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines. Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.

Download or read book A Student s Guide to Numerical Methods written by Ian H. Hutchinson and published by Cambridge University Press. This book was released on 2015-04-30 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plain language style, worked examples and exercises in this book help students to understand the foundations of computational physics and engineering.

Download or read book Fractional Differential Equations Numerical Methods for Applications written by Matthew Harker and published by Springer. This book was released on 2020-01-25 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive set of practical tools for exploring and discovering the world of fractional calculus and its applications, and thereby a means of bridging the theory of fractional differential equations (FDE) with real-world facts. These tools seamlessly blend centuries old numerical methods such as Gaussian quadrature that have stood the test of time with pioneering concepts such as hypermatrix equations to harness the emerging capabilities of modern scientific computing environments. This unique fusion of old and new leads to a unified approach that intuitively parallels the classic theory of differential equations, and results in methods that are unprecedented in computational speed and numerical accuracy. The opening chapter is an introduction to fractional calculus that is geared towards scientists and engineers. The following chapter introduces the reader to the key concepts of approximation theory with an emphasis on the tools of numerical linear algebra. The third chapter provides the keystone for the remainder of the book with a comprehensive set of methods for the approximation of fractional order integrals and derivatives. The fourth chapter describes the numerical solution of initial and boundary value problems for FDE of a single variable, both linear and nonlinear. Moving to two, three, and four dimensions, the ensuing chapter is devoted to a novel approach to the numerical solution of partial FDE that leverages the little-known one-to-one relation between partial differential equations and matrix and hypermatrix equations. The emphasis on applications culminates in the final chapter by addressing inverse problems for ordinary and partial FDE, such as smoothing for data analytics, and the all-important system identification problem. Over a century ago, scientists such as Ludwig Boltzmann and Vito Volterra formulated mathematical models of real materials that -- based on physical evidence -- integrated the history of the system. The present book will be invaluable to students and researchers in fields where analogous phenomena arise, such as viscoelasticity, rheology, polymer dynamics, non-Newtonian fluids, bioengineering, electrochemistry, non-conservative mechanics, groundwater hydrology, NMR and computed tomography, mathematical economics, thermomechanics, anomalous diffusion and transport, control theory, supercapacitors, and genetic algorithms, to name but a few. These investigators will be well-equipped with reproducible numerical methods to explore and discover their particular field of application of FDE.

Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.

Download or read book Numerical Methods and Applications written by Ivan Dimov and published by Springer Science & Business Media. This book was released on 2011-01-14 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.

Download or read book Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows written by V.V. Aristov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

Download or read book National Bureau of Standards Miscellaneous Publication written by and published by . This book was released on 1965 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations

Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 1256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Lattice Boltzmann Method written by Timm Krüger and published by Springer. This book was released on 2016-11-07 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.