Download or read book Solution of an Initial value Problem in Linear Transport Theory written by Perry A. Newman and published by . This book was released on 1971 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of an initial-value problem in linear transport theory is obtained by using the normal-mode expansion technique of Case. The problem is that of monoenergetic neutrons migrating in a thin slab surrounded by infinitely thick reflectors and the scattering is taken to be isotropic. The results obtained indicate that the reflector may give rise to a branch-cut integral term typical of a semi-infinite medium whereas the central slab may contribute a summation over discrete residue terms. Exact expressions are obtained for these discrete time eigenvalues, and numerical results showing the behavior of real time eigenvalues as a function of the material properties of the slab and reflector are presented. These eigenvalues are finite in number and may disappear into the branch cut or continuum as the material properties are varied; such disappearing eigenvalues correspond to exponentially time-decaying modes. The two largest eigenvalues can be compared with critical dimensions of slabs and spheres, and the numerical values are shown to agree with the critically results of others. In the limit of purely absorbing reflectors or a bare slab, the present solution has the same properties as have been previously reported by others who used the approach of Lehner and Wing.
Download or read book NASA Technical Report written by and published by . This book was released on 1971 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Mathematical Methods in Transport Theory written by Greenberg and published by Birkhäuser. This book was released on 2013-11-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Eleventh International Transport Theory Conference and Symposium in honor of the sixty-fifth birthday of Kenneth Case and the sixtieth birthday of Paul Zweifel was held in Blacksburg, Virginia, during May 22-26, 1989, on the campus of Virginia Polytechnic Institute and State University (Virginia Tech). This volume consists of a selection of the invited papers delivered at the Conference, and represents a cross section of the research currently being carried out in the field of transport theory. The volume is divided into two sections. The Symposium lectures are intended each to summarize an important aspect of transport theory, as well as to present timely new results of the author's research interest. The Conference lectures are contributions of each author on his current research. As has been the custom in this series of conferences, each lecturer was invited to participate by the organizing committee of the Conference: W. Greenberg, Virginia Tech, chairman; V. Boffi, Universita di Firenze; N. Corngold, California Institute of Technology; B. Ganapol, University of Arizona; N. McCormick, University of Washington; P. Nelson, Texas Tech; G. Pomraning, University of California, Los Angeles. The Eleventh International Transport Theory Conference was funded by generous con tributions from Science Applications International Corporation, R. Beyster, president, and from Virginia Polytechnic Institute and State University. Conference participants, and, we believe, researchers in this and related areas, are indebted to these organizations. We would like to thank Lamberto Rondoni, in the graduate program at Virginia Tech, for proofreading manuscripts of all the Italian contributors.
Download or read book Partial Differential Equations written by Michael Shearer and published by Princeton University Press. This book was released on 2015-03-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors
Download or read book Boundary Value Problems in Abstract Kinetic Theory written by W. Greenberg and published by Birkhäuser. This book was released on 2013-12-14 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to be a reasonably self -contained and fairly complete exposition of rigorous results in abstract kinetic theory. Throughout, abstract kinetic equations refer to (an abstract formulation of) equations which describe transport of particles, momentum, energy, or, indeed, any transportable physical quantity. These include the equations of traditional (neutron) transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. The mathematical problems addressed within the monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The reader is assumed to have a certain familiarity with elementary aspects of functional analysis, especially basic semigroup theory, and an effort is made to outline any more specialized topics as they are introduced. Over the past several years there has been substantial progress in developing an abstract mathematical framework for treating linear transport problems. The benefits of such an abstract theory are twofold: (i) a mathematically rigorous basis has been established for a variety of problems which were traditionally treated by somewhat heuristic distribution theory methods; and (ii) the results obtained are applicable to a great variety of disparate kinetic processes. Thus, numerous different systems of integrodifferential equations which model a variety of kinetic processes are themselves modelled by an abstract operator equation on a Hilbert (or Banach) space.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1970 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: NSA is a comprehensive collection of international nuclear science and technology literature for the period 1948 through 1976, pre-dating the prestigious INIS database, which began in 1970. NSA existed as a printed product (Volumes 1-33) initially, created by DOE's predecessor, the U.S. Atomic Energy Commission (AEC). NSA includes citations to scientific and technical reports from the AEC, the U.S. Energy Research and Development Administration and its contractors, plus other agencies and international organizations, universities, and industrial and research organizations. References to books, conference proceedings, papers, patents, dissertations, engineering drawings, and journal articles from worldwide sources are also included. Abstracts and full text are provided if available.
Download or read book Applied and Industrial Mathematics written by Renato Spigler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Venice-1 symposium on applied and industrial mathematics, 1989
Download or read book Transport Theory written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1969 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The industrial and military applications of atomic energy have stimulated much mathematical research in neutron transport theory. The possibility of controlled thermonuclear processes has similarly focussed attention upon plasmas, sometimes called the "fourth state of matter". Independently, many classical aspects of kinetic theory and radiative transfer theory have been studied both because of their basic mathematical interest and of their physical applications to areas such as upper-atmosphere meteorology - introduction.
Download or read book Boundary Value Problems for Transport Equations written by Valeri Agoshkov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1993 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 1468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U S Government Research Reports written by and published by . This book was released on 1964 with total page 1118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computing Qualitatively Correct Approximations of Balance Laws written by Laurent Gosse and published by Springer Science & Business Media. This book was released on 2013-03-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics or linearized Boltzmann models. “Caseology” is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models.
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
