73 research outputs found
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
Proceedings of the Workshop on Applications of Distributed System Theory to the Control of Large Space Structures
Two general themes in the control of large space structures are addressed: control theory for distributed parameter systems and distributed control for systems requiring spatially-distributed multipoint sensing and actuation. Topics include modeling and control, stabilization, and estimation and identification
Solitons in low-dimensional sigma models
The aim of this thesis is to study topological soliton solutions in classical field theories, called sigma models, on a three-dimensional space. In chapter 1 we review the general field-theoretical framework of classical soliton solutions and exemplify it on the main features of the 0(3) σ-model and the Abehan Higgs model in (2+1) dimensions. In chapter 2 a U(l)-gauged 0(3) σ-model is discussed, where the behaviour of the gauge field is determined by a Chern-Simons term in the action. We find numerical solutions for radially symmetric fields and discuss those of degree one and two. They carry a non-vanishing angular momentum and can be interpreted as classical anyons. A similar model is studied in chapter 3. Here the potential is of Higgs-type and chosen to produce a Bogomol'nyi model where the energy is bounded from below by a linear combination of the topological degree of the matter fields and the local U(l)-charge. Depending on internal parameters, the solutions are solitons or vortices. We study them numerically and prove for a certain range of the matter field's vacuum value that there cannot be a 1-soliton.In chapter 4 we discuss a modified 0(3) σ-model in (3+0) dimensions. The topological stability of the solitons is here imphed by the degree of the map S(^3) → S(^2), which provides a lower boundon the potential energy of the configuration. Numerical solutions are obtained for configurations of azimuthal symmetry and the spectrum of slowly rotating solitons is approximated. Chapter 5 deals with a theory where the fields are maps IR(^2+1) → CP(^2). The Lagrangian includes a potential and a fourth-order term in the field-gradient. We find a family of static analytic solutions of degree one and study the 2-soIiton configuration numerically by using a gradient-flow equation on the moduli space of solutions. We conclude this thesis with a brief summary and give an outlook to open questions
Lattice Gas Automata for Reactive Systems
Reactive lattice gas automata provide a microscopic approachto the dynamics
of spatially-distributed reacting systems. After introducing the subject within
the wider framework of lattice gas automata (LGA) as a microscopic approach to
the phenomenology of macroscopic systems, we describe the reactive LGA in terms
of a simple physical picture to show how an automaton can be constructed to
capture the essentials of a reactive molecular dynamics scheme. The statistical
mechanical theory of the automaton is then developed for diffusive transport
and for reactive processes, and a general algorithm is presented for reactive
LGA. The method is illustrated by considering applications to bistable and
excitable media, oscillatory behavior in reactive systems, chemical chaos and
pattern formation triggered by Turing bifurcations. The reactive lattice gas
scheme is contrasted with related cellular automaton methods and the paper
concludes with a discussion of future perspectives.Comment: to appear in PHYSICS REPORTS, 81 revtex pages; uuencoded gziped
postscript file; figures available from [email protected] or
[email protected]
Simulation of hot carriers in semiconductor devices
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 109-113).by Khalid Rahmat.Ph.D
Simulation of hot carriers in semiconductor devices
Includes bibliographical references (p. 109-113).Supported by the U.S. Navy. N00174-93-C-0035Khalid Rahmat
Finite elements software and applications
The contents of this thesis are a detailed study of the software
for the finite element method. In the text, the finite element method
is introduced from both the engineering and mathematical points of view.
The computer implementation of the method is explained with samples of
mainframe, mini- and micro-computer implementations. A solution is
presented for the problem of limited stack size for both mini- and
micro-computers which possess stack architecture.
Several finite element programs are presented. Special purpose
programs to solve problems in structural analysis and groundwater flow
are discussed. However, an efficient easy-to-use finite element program
for general two-dimensional problems is presented. Several problems in
groundwater flow are considered that include steady, unsteady flows in
different types of aquifers. Different cases of sinks and sources in
the flow domain are also considered. The performance of finite element
methods is studied for the chosen problems by comparing the numerical
solutions of test problems with analytical solutions (if they exist) or
with solutions obtained by other numerical methods. The polynomial
refinement of the finite elements is studied for the presented problems
in order to offer some evidence as to which finite element simulation
is best to use under a variety of circumstances
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