New Insights Into Numerical Solutions of the Even-parity Transport Equation in Two-dimensional X-Y Geometry PDF Download

Author: Taewan Noh
Publisher:
ISBN:
Category :
Languages : en
Pages : 244

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Author: John C Souders (Jr)
Publisher:
ISBN:
Category :
Languages : en
Pages : 137

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The purpose of this research was to determine the feasibility of extending the use of the even-parity form of the Boltzmann Equation (EPFBE) to complex linear transport problems. Previous applications had been limited to problems involving simple geometry and low order scatter approximations. The air-over-ground problem was selected for this more complex extension since it required two-dimensional cylindrical geometry, anisotropic scatter, and a multigroup solution. To eliminate the ray effect in this problem, both the finite element and synthesis method were used. With these methods the Galerkin and collocation numerical techniques were applied. The Galerkin method proved infeasible because the integrals that resulted could not be efficiently evaluated either numerically or analytically. The collocation method allowed the analytic evaluation of all derivative and integral operations, but forced a fixed anisotropy on the solution. The multigroup method applied to the EPFBE produced a nested integral problem that increased proportionately with the number of energy groups. This research demonstrated that the finite element method can not be cost effectively used in solving the EPFBE for transport problems requiring complex geometries, anisotropic scatter, and a multigroup method. Criteria developed during this research for pursuing future work with the EPFBE is presented. (Author).

Author: Richard S. Varga
Publisher:
ISBN:
Category : Geometry, Modern
Languages : en
Pages : 40

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Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467

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Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 6

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Considerable effort has been expended in recent years in finding improved spatial differencing schemes for the neutron and radiation transport equations. Standard criteria used to select a candidate scheme are its order of spatial convergence for small mesh size and its positivity in the sense that positive solutions emerge from positive input data. More recently, it has become clear that truly robust schemes must behave well in diffusing regions and must be compatible with an effective iteration acceleration method. Recently, Morel and Larsen reported their work on a promising new method called the multiple balance method that has virtually all the desirable characteristics. Here we study a different approach to the problem by considering discrete-ordinates approximations to the even-parity transport equations. We analyze three spatial difference approaches: diamond differencing, cell-edge differencing, and cell-center differencing. For the case of isotropic scattering and sources, the latter two approaches are shown to be strictly positive, to be second-order accurate, to be compatible with derived diffusion synthetic acceleration methods, and to possess the necessary diffusion limits. Unlike previous work with the even-parity equation, we do not use finite elements or variational principles. 5 refs., 1 tab.

Author: Joseph K. Blitzstein
Publisher: CRC Press
ISBN: 1466575573
Category : Mathematics
Languages : en
Pages : 599

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Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595

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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author: George B. Rybicki
Publisher: John Wiley & Sons
ISBN: 352761818X
Category : Science
Languages : en
Pages : 402

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Radiative Processes in Astrophysics: This clear, straightforward, and fundamental introduction is designed to present-from a physicist's point of view-radiation processes and their applications to astrophysical phenomena and space science. It covers such topics as radiative transfer theory, relativistic covariance and kinematics, bremsstrahlung radiation, synchrotron radiation, Compton scattering, some plasma effects, and radiative transitions in atoms. Discussion begins with first principles, physically motivating and deriving all results rather than merely presenting finished formulae. However, a reasonably good physics background (introductory quantum mechanics, intermediate electromagnetic theory, special relativity, and some statistical mechanics) is required. Much of this prerequisite material is provided by brief reviews, making the book a self-contained reference for workers in the field as well as the ideal text for senior or first-year graduate students of astronomy, astrophysics, and related physics courses. Radiative Processes in Astrophysics also contains about 75 problems, with solutions, illustrating applications of the material and methods for calculating results. This important and integral section emphasizes physical intuition by presenting important results that are used throughout the main text; it is here that most of the practical astrophysical applications become apparent.

Author: Sandro Salsa
Publisher: Springer
ISBN: 3319150936
Category : Mathematics
Languages : en
Pages : 714

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The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Author: Serguei Popov
Publisher: Cambridge University Press
ISBN: 1108472451
Category : Mathematics
Languages : en
Pages : 224

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A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.