Wave Propagation in Linear Media | re-examined

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0 -5 -10 -15 0 20 ne 40 0 6Towards a quadrature routine Figure 6.7: Negative number of correct digits, log e S (k) n , S , for varying n (ns) and k (ne), computed with the -algorithm (WynnDegree->2). -5 -10 -15 10 20 30 ne 40 50 Figure 6.8: Negative number of correct digits, log e S (k) n , S , for varying n (ns) and k (ne), computed with the -algorithm (WynnDegree->Infinity). 154 0 20 20 40 ns 40 ns 60 60
6.6 Controlling the accuracy of the extrapolation result 60 50 40 30 20 10 0 10 20 30 40 50 60 Figure 6.9: Contour plot of g. 6.8, abscissa: ne, ordinate: ns. 6.6 Controlling the accuracy of the extrapolation result As we have seen in the last sections, we can improve the result of the extrapolation under most circumstances by increasing the number of sequence elements being subject to the extrapolation. The severe problem that still remains is that this is only a qualitative nding and that we have no guideline whatsoever as to how this parameter is to be chosen. From a user's point of view, the exact number of sequence members necessary to achieve a certain accuray is entirely irrelevant, provided that the goal is reached. On the contrary, it is much more convenient to let the user specify only the desired accuracy and to leave the choice of the other parameters to the algorithm, which then has to be somehow adaptive. If we want to adapt only the parameters of a basic numerical algorithm, then we in turn need a meta algorithm that starts from a given parameter set, calls the basic algorithm, judges the results and changes the parameters. This procedure must be repeated iteratively until either the outcome meets the requirements or a maximum number of iterations is reached | just to prevent the algorithm from being lost in an in nite loop or wasting precious computing time. From the previous sections, we can easily conclude what the three major elements of such a meta algorithm must look like: 1. The basic algorithm consists of the computation of the sequence of partial sums for a given integrand together with the extrapolation. It returns an estimate of the integral. 2. The parameters that can be in uenced directly by the meta algorithm are the number 155
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DISSERTATION Wave Propagation in Li
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Kurzfassung Seit der Entdeckung des
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Nullum est iam dictum, quod non sit
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Preface Our popular writers and rep
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the quest for superluminality and t
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Contents Part I Wave propagation ph
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7.3.4 PartitionPoints . . . . . . .
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Part I Wave propagation phenomena S
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1.1 Phase and group velocity 1.1 Ph
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1.1 Phase and group velocity ! !c v
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1.2 A few notes on dispersion He co
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1.2 A few notes on dispersion v/c 6
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1.3 Signal velocity dipoles with a
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1.3 Signal velocity The arbitrarine
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1.4 Energy velocity For electromagn
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1.5 Other velocity de nitions For n
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1.5 Other velocity de nitions evide
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2.1 Superluminal wave propagation 2
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2.1 Superluminal wave propagation a
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2.1 Superluminal wave propagation t
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2.2 Quantum mechanical tunnelling e
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2.2 Quantum mechanical tunnelling R
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Chapter 3 Wave propagation in elect
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3.1 Model of a transmission line th
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3.2 Excursion: a delay line section
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3.3 Re ection due to termination mi
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3.4 A simple thought experiment I0
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3.5 A dispersive system: the lossle
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3.6 Inhomogeneous transmission line
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3.7 Turn-on e ects in a lossless pl
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3.8 Turn-on e ects in a wave guide
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3.8 Turn-on e ects in a wave guide
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3.9 A Gaussian pulse in plasma Like
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3.9 A Gaussian pulse in plasma 250
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3.9 A Gaussian pulse in plasma 250
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3.9 A Gaussian pulse in plasma Note
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4.1 The potential step 4.1 The pote
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4.1 The potential step Inside the b
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4.2 Initial wave forms -60 -50 -40
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4.2 Initial wave forms -60 -50 -40
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4.3 Examples of scattering processe
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4.4 The square barrier they have va
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4.4 The square barrier 1 0.8 0.6 0.
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4.5 Tunnelling time de nitions for
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4.5 Tunnelling time de nitions for
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4.6 Examples of tunnelling events P
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Page 135 and 136: Interlude Wave functions in graphic
Page 137 and 138: Wave functions in graphical represe
Page 139 and 140: Part II Numerical aspects of wave e
Page 141 and 142: 5.1 Univariate numerical quadrature
Page 143 and 144: 5.1 Univariate numerical quadrature
Page 145 and 146: 5.2 Convergence acceleration one, t
Page 147 and 148: 5.2 Convergence acceleration (1) ,1
Page 149 and 150: 6.1 Partitioning the integration in
Page 155 and 156: 6.2 Choosing the rst partition poin
Page 157 and 158: 6.3 How to compute the rst integral
Page 159 and 160: 6.3 How to compute the rst integral
Page 161 and 162: 6.4 Asymptotic partition consuming
Page 163 and 164: 6.4 Asymptotic partition of the int
Page 165 and 166: 6.5 Considerations for a Mathematic
Page 167 and 168: 6.5 Considerations for a Mathematic
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Page 173 and 174: 6.6 Controlling the accuracy of the
Page 175 and 176: 6.6 Controlling the accuracy of the
Page 177 and 178: Chapter 7 Mathematica implementatio
Page 179 and 180: 7.1 User interface of the function
Page 181 and 182: 7.3 Implementation of OscInt and re
Page 189 and 190: 7.4 Auxiliary functions While[itera
Page 191 and 192: 7.4 Auxiliary functions Linear appr
Page 193 and 194: 7.4 Auxiliary functions For the sak
Page 195 and 196: 7.4 Auxiliary functions Out[8]= 3 f
Page 197 and 198: 7.5 Test of the quadrature routine
Page 207 and 208: 8.1 Preparation of the wave integra
Page 213 and 214: 8.2 Outline of the program structur
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Page 217 and 218: 8.3 Implementation of the quadratur
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8.4 Test of the package 8.4 Test of
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8.4 Test of the package -200 -150 -
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8.4 Test of the package 0.4 0.2 -0.
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8.4 Test of the package 8.4.2 Forma
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8.4 Test of the package Out[24]= 0
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A.1 Numerical quadrature Asymptotic
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A.1 Numerical quadrature WynnDegree
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A.1 Numerical quadrature Which[ft =
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A.2 Solutions for the step potentia
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A.3 Solutions for the square barrie
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A.3 Solutions for the square barrie
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A.4 Electromagnetic waves function
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A.5 Utilities for displaying points
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Bibliography Bibliography [1] James
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Bibliography [29] Kurt Edmund Oughs
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Bibliography [59] Ch. Spielmann, R.
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Bibliography [91] C. R. Leavens and
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Bibliography [123] T. O. Espelid an
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Index Index absorption, 7, 9 accura
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Index saddle point integration, 11,
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Curriculum vitae Dipl.-Ing. Thilo S
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