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Transient waves in nonstationary media : with applications to lightning and nonlinear media

Åberg, Ingegerd LU (1997)
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingen behandlar problem inom den tillämpade matematiken med speciell inriktning mot elektromagnetisk vågutbredning. Exempel på studerade elektromagnetiska vågor är radiovågor, mikrovågor och ljus. Det speciella som skiljer den här studien från andra liknande studier, är att det medium som vågen passerar genom är ickestationärt, vilket innebär att det ändras under den tid som vågen och dess efterdyningar kan observeras. De studerade fysikaliska tillämpningarna är antingen direkta eller inversa spridningsproblem. I det direkta spridningsproblemet är egenskaperna hos mediet kända. Man har även kunskap om den infallande vågen. Med hjälp härav försöker man beräkna hur vågen kommer att bete sig... (More)
Popular Abstract in Swedish

Avhandlingen behandlar problem inom den tillämpade matematiken med speciell inriktning mot elektromagnetisk vågutbredning. Exempel på studerade elektromagnetiska vågor är radiovågor, mikrovågor och ljus. Det speciella som skiljer den här studien från andra liknande studier, är att det medium som vågen passerar genom är ickestationärt, vilket innebär att det ändras under den tid som vågen och dess efterdyningar kan observeras. De studerade fysikaliska tillämpningarna är antingen direkta eller inversa spridningsproblem. I det direkta spridningsproblemet är egenskaperna hos mediet kända. Man har även kunskap om den infallande vågen. Med hjälp härav försöker man beräkna hur vågen kommer att bete sig vid passage genom mediet, samt hur det spridda vågfältet utanför mediet kommer att se ut. I det inversa problemet däremot, är både de infallande och spridda vågorna kända från mätningar, och man försöker med ledning härav lista ut vilka egenskaper som fanns hos det spridande mediet under den aktuella vågutbredningsperioden.



Avhandlingen omfattar en matematisk och en numerisk del. I båda är tiden en viktig parameter. Genom att studien utföres i tidsdomänen möjliggöres observation av snabbt föränderliga vågformer, s.k. transienter. Den föreslagna matematiska metoden bygger på våguppdelning. De studerade problemen förutsättes kunna modelleras med hjälp av hyperboliska partiella differentialekvationer med blandade initial- och randvillkor. Vågor från källor både inuti och utanför det spridande mediet behandlas. I den numeriska delen utvecklas algoritmer som bygger på den föreslagna matematiska metoden. Flera tillämpningar studeras, bl. a. utbredning av inducerade ström och spänningsvågor på en kraftledning i samband med åsknedslag i ledningens närhet. Den utvecklade metoden kan även användas för att studera vågutbredning i svagt olinjära medier. Två olika iterativa procedurer föreslås. De bygger på linearisering av de olinjära fenomenen. I ett numeriskt exempel studeras pulsgenerering för högfrekvens-switchar, i ett annat exempel studeras vågutbredning i ett Kerrmedium. Båda exemplen har anknytning till telekommunikation, speciellt till informationsöverföring på optiska fibrer. (Less)
Abstract
Propagation of transient waves in nonstationary, inhomogeneous, dispersive, stratified media is considered. Waves originating from sources exterior to the scatterer as well as from internal sources are treated. Algorithms are developed and illustrated by computations of wave phenomena in stationary, nonstationary and weakly nonlinear media. In the theoretical part, the underlying hyperbolic equation is a general, homogeneous, linear, first order 2x2 system of equations. The coefficients depend on one spatial coordinate and time. Memory effects are modeled by integral kernels, which are functions of two different time coordinates. The analysis builds on generalization of the wave splitting concept, originally developed for time-invariant... (More)
Propagation of transient waves in nonstationary, inhomogeneous, dispersive, stratified media is considered. Waves originating from sources exterior to the scatterer as well as from internal sources are treated. Algorithms are developed and illustrated by computations of wave phenomena in stationary, nonstationary and weakly nonlinear media. In the theoretical part, the underlying hyperbolic equation is a general, homogeneous, linear, first order 2x2 system of equations. The coefficients depend on one spatial coordinate and time. Memory effects are modeled by integral kernels, which are functions of two different time coordinates. The analysis builds on generalization of the wave splitting concept, originally developed for time-invariant media. Imbedding and Green functions (propagator kernels) equations are derived for the external source problem. The wave propagators of the internal source problem are based on generalized Green functions equations. Special attention is paid to characteristic curves and discontinuities. Particular solutions are obtained as integrals of fundamental waves from distributed point sources. Resolvent kernels and wave propagators are essential.



Direct and inverse computational algorithms are developed for the nonstationary, homogeneous semi-infinite medium. Generalized susceptibility kernels with one spatial and two time coordinates are used. A function depending on two time coordinates is reconstructed. Furthermore, direct scattering algorithms for internal sources are implemented. Waves in a Klein-Gordon slab are calculated and compared to alternative solutions obtained from analytical fundamental waves of an infinite Klein-Gordon medium. In a second example, the current and voltage waves, evoked on the power line after an imagined strike of lightning, are studied. The nonstationary properties are modeled by the shunt conductance, together with dispersion in the shunt capacitance. The nonstationary theory is used to study direct wave propagation phenomena in weakly nonlinear media by linearization. Two different iterative procedures to find the nonlinear solutions are discussed. One leads into a truly nonstationary, mixed initial boundary value problem with a linear equation characterized by time-dependent coefficients and source terms. This procedure is applied to a pulse generator for high-frequency switching. The alternative time-invariant procedure, which is a variation of the nonlinear Born approximation, is used to calculate wave propagation in Kerr media. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Professor Kreider, Kevin, Akron, Ohio, USA.
organization
publishing date
type
Thesis
publication status
published
subject
keywords
lightning, Klein-Gordon, nonlinear, characteristics, wave splitting, imbedding, sources, propagators, Green functions, direct and inverse scattering, Nonstationary, transient, high-frequency switching, Kerr., Technological sciences, Teknik
pages
200 pages
publisher
Department of Electromagnetic Theory, Lund Institute of Technology
defense location
Lund Institute of Technology, house E, auditorium E1406.
defense date
1997-02-11 10:15
external identifiers
  • Other:ISRN: LUTEDX/(TEAT-1009)/1-35/(1996)
language
English
LU publication?
yes
id
e41c20b0-dffe-46f0-872b-19d5a1d1217b (old id 28965)
date added to LUP
2007-06-14 11:29:45
date last changed
2016-09-19 08:45:07
@phdthesis{e41c20b0-dffe-46f0-872b-19d5a1d1217b,
  abstract     = {Propagation of transient waves in nonstationary, inhomogeneous, dispersive, stratified media is considered. Waves originating from sources exterior to the scatterer as well as from internal sources are treated. Algorithms are developed and illustrated by computations of wave phenomena in stationary, nonstationary and weakly nonlinear media. In the theoretical part, the underlying hyperbolic equation is a general, homogeneous, linear, first order 2x2 system of equations. The coefficients depend on one spatial coordinate and time. Memory effects are modeled by integral kernels, which are functions of two different time coordinates. The analysis builds on generalization of the wave splitting concept, originally developed for time-invariant media. Imbedding and Green functions (propagator kernels) equations are derived for the external source problem. The wave propagators of the internal source problem are based on generalized Green functions equations. Special attention is paid to characteristic curves and discontinuities. Particular solutions are obtained as integrals of fundamental waves from distributed point sources. Resolvent kernels and wave propagators are essential.<br/><br>
<br/><br>
Direct and inverse computational algorithms are developed for the nonstationary, homogeneous semi-infinite medium. Generalized susceptibility kernels with one spatial and two time coordinates are used. A function depending on two time coordinates is reconstructed. Furthermore, direct scattering algorithms for internal sources are implemented. Waves in a Klein-Gordon slab are calculated and compared to alternative solutions obtained from analytical fundamental waves of an infinite Klein-Gordon medium. In a second example, the current and voltage waves, evoked on the power line after an imagined strike of lightning, are studied. The nonstationary properties are modeled by the shunt conductance, together with dispersion in the shunt capacitance. The nonstationary theory is used to study direct wave propagation phenomena in weakly nonlinear media by linearization. Two different iterative procedures to find the nonlinear solutions are discussed. One leads into a truly nonstationary, mixed initial boundary value problem with a linear equation characterized by time-dependent coefficients and source terms. This procedure is applied to a pulse generator for high-frequency switching. The alternative time-invariant procedure, which is a variation of the nonlinear Born approximation, is used to calculate wave propagation in Kerr media.},
  author       = {Åberg, Ingegerd},
  keyword      = {lightning,Klein-Gordon,nonlinear,characteristics,wave splitting,imbedding,sources,propagators,Green functions,direct and inverse scattering,Nonstationary,transient,high-frequency switching,Kerr.,Technological sciences,Teknik},
  language     = {eng},
  pages        = {200},
  publisher    = {Department of Electromagnetic Theory, Lund Institute of Technology},
  school       = {Lund University},
  title        = {Transient waves in nonstationary media : with applications to lightning and nonlinear media},
  year         = {1997},
}