A Deterministic Particle Method Solving The Linearized Boltzmann Equation
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Author | : Randolph Bank |
Publisher | : Birkhäuser |
Total Pages | : 314 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034885288 |
Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation. Discussions on experiences with standard software packages and improvements of such packages are included. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. In this connection, mention is made, for example, of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations.
Author | : Randolph E. Bank |
Publisher | : American Mathematical Soc. |
Total Pages | : 206 |
Release | : 1990-02-15 |
Genre | : Technology & Engineering |
ISBN | : 9780821896938 |
Numerical simulation is rapidly becoming an important part of the VLSI design process, allowing the engineer to test, evaluate, and optimize various aspects of chip design without resorting to the costly and time-consuming process of fabricating prototypes. This procedure not only accelerates the design process, but also improves the end product, since it is economically feasible to numerically simulate many more options than might otherwise be considered. With the enhanced computing power of today's computers, more sophisticated models are now being developed. This volume contains the proceedings of the AMS-SIAM Summer Seminar on Computational Aspects of VLSI Design, held at the Institute for Mathematics and Its Applications at the University of Minnesota, in the spring of 1987. The seminar featured presentations by some of the top experts working in this area. Their contributions to this volume form an excellent overview of the mathematical and computational problems arising in this area.
Author | : V.V. Aristov |
Publisher | : Springer Science & Business Media |
Total Pages | : 305 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401008663 |
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.
Author | : Jack Venselaar |
Publisher | : CRC Press |
Total Pages | : 539 |
Release | : 2012-11-08 |
Genre | : Science |
ISBN | : 1439844984 |
Modern brachytherapy is one of the most important oncological treatment modalities requiring an integrated approach that utilizes new technologies, advanced clinical imaging facilities, and a thorough understanding of the radiobiological effects on different tissues, the principles of physics, dosimetry techniques and protocols, and clinical expertise. A complete overview of the field, Comprehensive Brachytherapy: Physical and Clinical Aspects is a landmark publication, presenting a detailed account of the underlying physics, design, and implementation of the techniques, along with practical guidance for practitioners. Bridging the gap between research and application, this single source brings together the technological basis, radiation dosimetry, quality assurance, and fundamentals of brachytherapy. In addition, it presents discussion of the most recent clinical practice in brachytherapy including prostate, gynecology, breast, and other clinical treatment sites. Along with exploring new clinical protocols, it discusses major advances in imaging, robotics, dosimetry, Monte Carlo-based dose calculation, and optimization.
Author | : Society for Industrial and Applied Mathematics |
Publisher | : |
Total Pages | : 644 |
Release | : 1990 |
Genre | : Mathematical analysis |
ISBN | : |
Author | : Gary C. Cohen |
Publisher | : SIAM |
Total Pages | : 830 |
Release | : 1995-01-01 |
Genre | : Science |
ISBN | : 9780898713503 |
This volume contains the papers presented at the title conference. Speakers from 13 different countries were represented at the meeting. A broad range of topics in theoretical and applied wave propagation is covered.
Author | : Andrzej Lasota |
Publisher | : Cambridge University Press |
Total Pages | : 376 |
Release | : 2008-11-27 |
Genre | : Mathematics |
ISBN | : 9780521090964 |
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Author | : Jerry Battista |
Publisher | : CRC Press |
Total Pages | : 418 |
Release | : 2019-01-04 |
Genre | : Science |
ISBN | : 1351676148 |
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
Author | : Bernie D. Shizgal |
Publisher | : AIAA |
Total Pages | : 580 |
Release | : 1994 |
Genre | : Rarefied gas dynamics |
ISBN | : 9781600864131 |
Author | : Martin Galler |
Publisher | : World Scientific |
Total Pages | : 247 |
Release | : 2005 |
Genre | : Philosophy |
ISBN | : 9812563555 |
Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail.This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.