PhiArg[a, b, c,d],1,opts] + OscInt[RectTransNeg[a,-b,-c,d,w,k], PhiArg[a,-b,-c,d],1,opts]) ) RectConst[w,k] ]; GaussTransTemp[fpos_, fneg_, x_, t_, w_, k_, n_, opts___Rule] := Module[{a,b,c,d,o1,o2, wp = Work<strong>in</strong>gP<strong>re</strong>cision/.{opts}/.Options[OscInt]}, a = -t; b = N[Pi k/Sqrt[w],wp+2]; c = x; d = N[-Pi k,wp+2]; o1 = QuadOffset[a, b+c,d]; o2 = QuadOffset[a,-b-c,d]; (OscInt[fpos[a, b, c,d,w,k,n], QuadZero[a, b +c,d,o1],1,FunctionType->ZeroList,opts] + OscInt[fneg[a,-b,-c,d,w,k,n], QuadZero[a,-b -c,d,o2],1,FunctionType->ZeroList,opts] ) GaussConst[w,k,n] ]; GaussTransTruncTemp[fpos_, fneg_, x_, t_, w_, k_, n_, opts___Rule] := Module[{wp = Work<strong>in</strong>gP<strong>re</strong>cision/.{opts}/.Options[OscInt], ag = AccuracyGoal/. {opts}/.Options[OscInt], pg = P<strong>re</strong>cisionGoal/. {opts}/.Options[OscInt], mi = M<strong>in</strong>Recursion/. {opts}/.Options[OscInt], ma = MaxRecursion/. {opts}/.Options[OscInt], limpos, limneg}, {limneg,limpos} = GaussTruncLims[w,k,n,wp]; (If[limpos DoubleExponential, Work<strong>in</strong>gP<strong>re</strong>cision->wp, AccuracyGoal->ag, P<strong>re</strong>cisionGoal->pg, M<strong>in</strong>Recursion->mi, MaxRecursion->ma]] + If[limneg >= -1, 0, NIntegrate[fneg[-t,-Pi k/Sqrt[w],-x,-Pi k,w,k,n][xi], {xi,1,-limneg}, Method->DoubleExponential, Work<strong>in</strong>gP<strong>re</strong>cision->wp, AccuracyGoal->ag, P<strong>re</strong>cisionGoal->pg, M<strong>in</strong>Recursion->mi, MaxRecursion->ma]] ) GaussConst[w,k,n] ]; GaussEvanTruncTemp[f_, w_, k_, n_, opts___Rule] := Module[{limpos,limneg, wp = Work<strong>in</strong>gP<strong>re</strong>cision/.{opts}/.Options[OscInt], ag = AccuracyGoal/. {opts}/.Options[OscInt], pg = P<strong>re</strong>cisionGoal/. {opts}/.Options[OscInt], mi = M<strong>in</strong>Recursion/. {opts}/.Options[OscInt], ma = MaxRecursion/. {opts}/.Options[OscInt]}, {limneg,limpos} = GaussTruncLims[w,k,n,wp]; limneg = Max[limneg,-1]; limpos = M<strong>in</strong>[limpos,1]; NIntegrate[f[xi],{xi,limneg,limpos}, Method->DoubleExponential, Work<strong>in</strong>gP<strong>re</strong>cision->wp, AccuracyGoal->ag, P<strong>re</strong>cisionGoal->pg, M<strong>in</strong>Recursion->mi, MaxRecursion->ma] GaussConst[w,k,n] ]; (*-- Driver functions for the computation of the wave <strong>in</strong>tegrals --*) PhiTrans[x_, t_, w_, k_, n_?Positive, opts___Rule] := Module[{sh = Shape/. {opts}/.Options[Phi], pt = PPo<strong>in</strong>ts/.{opts}/.Options[Phi]}, Switch[sh, Rect, Switch[pt, Approximate, RectTransTemp[RectTransPos,RectTransNeg,x,t,w,k,opts], Zeros, RectTransExact[x,t,w,k,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], Tria, Switch[pt, 226 A Mathematica packages
A.2 Solutions for the step potential ] ]; Approximate, TriaTransTemp[TriaTransPos,TriaTransNeg,x,t,w,k,opts], Zeros, TriaTransExactTemp[TriaTransPos,TriaTransNeg,x,t,w,k,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], Gauss, Switch[pt, Approximate, GaussTransTemp[GaussTransPos,GaussTransNeg,x,t,w,k,n,opts], Truncate, GaussTransTruncTemp[GaussTransPos,GaussTransNeg,x,t,w,k,n,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], _, Message[Phi::<strong>in</strong>validshape,sh] PhiTrans[x_, t_, w_, k_, opts___Rule] := If[(Shape/.{opts}/.Options[Phi]) === Gauss, Message[Phi::miss<strong>in</strong>gval], PhiTrans[x,t,w,k,1,opts]]; PhiGradTrans[x_, t_, w_, k_, n_?Positive, opts___Rule] := Module[{sh = Shape/. {opts}/.Options[Phi], pt = PPo<strong>in</strong>ts/.{opts}/.Options[Phi]}, Switch[sh, Tria, Switch[pt, Approximate, TriaTransTemp[TriaGradTransPos,TriaGradTransNeg,x,t,w,k,opts], Zeros, TriaTransExactTemp[TriaGradTransPos,TriaGradTransNeg,x,t,w,k,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], Gauss, Switch[pt, Approximate, GaussTransTemp[GaussGradTransPos,GaussGradTransNeg,x,t,w,k,n,opts], Truncate, GaussTransTruncTemp[GaussGradTransPos,GaussGradTransNeg,x,t,w,k,n,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], _, Message[Phi::<strong>in</strong>validshape,sh] ] ]; PhiGradTrans[x_, t_, w_, k_, opts___Rule] := If[(Shape/.{opts}/.Options[Phi]) === Gauss, Message[Phi::miss<strong>in</strong>gval], PhiGradTrans[x,t,w,k,1,opts]]; PhiEvan[x_, t_, w_, k_, n_?Positive, opts___Rule] := Module[{sh = Shape/. {opts}/.Options[Phi], pt = PPo<strong>in</strong>ts/.{opts}/.Options[Phi]}, Switch[sh, Rect, EvanTemp[RectEvan[-t,0,x,0,w,k],RectConst[w,k],opts], Tria, EvanTemp[TriaEvan[-t,0,x,0,w,k],TriaConst[w,k],opts], Gauss, Switch[pt, Approximate, EvanTemp[GaussEvan[-t,Pi k/Sqrt[w],x,-Pi k,w,k,n], GaussConst[w,k,n],opts], Truncate, GaussEvanTruncTemp[GaussEvan[-t,Pi k/Sqrt[w],x,-Pi k,w,k,n], w,k,n,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], _, Message[Phi::<strong>in</strong>validshape,sh] ] ]; PhiEvan[x_, t_, w_, k_, opts___Rule] := If[(Shape/.{opts}/.Options[Phi]) === Gauss, Message[PhiTransmit::miss<strong>in</strong>gval], PhiEvan[x,t,w,k,1,opts]]; PhiGradEvan[x_, t_, w_, k_, n_?Positive, opts___Rule] := Module[{sh = Shape/. {opts}/.Options[Phi], pt = PPo<strong>in</strong>ts/.{opts}/.Options[Phi]}, Switch[sh, Tria, EvanTemp[TriaGradEvan[-t,0,x,0,w,k],TriaConst[w,k],opts], Gauss, Switch[pt, Approximate, EvanTemp[GaussGradEvan[-t,Pi k/Sqrt[w],x,-Pi k,w,k,n], GaussConst[w,k,n],opts], Truncate, GaussEvanTruncTemp[GaussGradEvan[-t,Pi k/Sqrt[w],x,-Pi k,w,k,n], w,k,n,opts], _, Message[Phi::<strong>in</strong>validpart,pt]], _, Message[Phi::<strong>in</strong>validshape,sh] ] 227
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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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3.5 A dispersive system: the lossle
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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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3.7 Turn-on e ects in a lossless pl
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3.7 Turn-on e ects in a lossless pl
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3.7 Turn-on e ects in a lossless pl
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3.7 Turn-on e ects in a lossless pl
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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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4.3 Examples of scattering processe
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4.3 Examples of scattering processe
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4.3 Examples of scattering processe
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4.3 Examples of scattering processe
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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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4.6 Examples of tunnelling events 2
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4.6 Examples of tunnelling events -
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4.6 Examples of tunnelling events t
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4.6 Examples of tunnelling events P
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4.6 Examples of tunnelling events 8
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4.6 Examples of tunnelling events 8
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4.6 Examples of tunnelling events 7
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4.6 Examples of tunnelling events T
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Interlude Wave functions in graphic
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Wave functions in graphical represe
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Part II Numerical aspects of wave e
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5.1 Univariate numerical quadrature
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5.1 Univariate numerical quadrature
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5.2 Convergence acceleration one, t
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5.2 Convergence acceleration (1) ,1
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6.1 Partitioning the integration in
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6.1 Partitioning the integration in
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6.1 Partitioning the integration in
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6.2 Choosing the rst partition poin
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6.3 How to compute the rst integral
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6.3 How to compute the rst integral
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6.4 Asymptotic partition consuming
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6.4 Asymptotic partition of the int
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6.5 Considerations for a Mathematic
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6.5 Considerations for a Mathematic
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6.5 Considerations for a Mathematic
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6.6 Controlling the accuracy of the
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6.6 Controlling the accuracy of the
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6.6 Controlling the accuracy of the
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Chapter 7 Mathematica implementatio
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7.1 User interface of the function
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7.3 Implementation of OscInt and re
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7.3 Implementation of OscInt and re
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7.3 Implementation of OscInt and re
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7.3 Implementation of OscInt and re
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7.4 Auxiliary functions While[itera
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- Page 253 and 254: Bibliography Bibliography [1] James
- Page 255 and 256: Bibliography [29] Kurt Edmund Oughs
- Page 257 and 258: Bibliography [59] Ch. Spielmann, R.
- Page 259 and 260: Bibliography [91] C. R. Leavens and
- Page 261 and 262: Bibliography [123] T. O. Espelid an
- Page 263 and 264: Index Index absorption, 7, 9 accura
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- Page 267: Curriculum vitae Dipl.-Ing. Thilo S