Wave Propagation in Linear Media | re-examined

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]; N[zerof[0]] < max, Ceiling[i/.FindRoot[zerof[i] == max,{i,0,1}]], True, Message[ZerosInBetween::outside];0] HypOffset[a_,b_,c_,d_] := Which[ (Abs[b] > Abs[a]) && (c >= 0) && (a+b) > 0, Ceiling[((a+b) (-Sign[a b] Sqrt[a^2 c/(b^2-a^2)]) + d)/Pi], (Abs[b] > Abs[a]) && (c >= 0) && (a+b) < 0, Floor[((a+b) (-Sign[a b] Sqrt[a^2 c/(b^2-a^2)]) + d)/Pi], (a+b) > 0, Ceiling[d/Pi], (a+b) < 0, Floor[d/Pi], True, 0]; HypZero[a_,b_,c_,d_,o_][k_] := Which[ (a+b) > 0, (( k + o) Pi - d)/(a + b), (a+b) < 0, ((-k + o) Pi - d)/(a + b), True, Infinity]; HypOffsetExact[a_,b_,c_,d_] := Which[ (Abs[b] > Abs[a]) && (c >= 0) && (a+b) > 0, Ceiling[((a x + b Sqrt[x^2+c] + d)/Pi)/. x->(-Sign[a b] Sqrt[a^2 c/(b^2-a^2)])], (Abs[b] > Abs[a]) && (c >= 0) && (a+b) < 0, Floor[((a x + b Sqrt[x^2+c] + d)/Pi)/. x->(-Sign[a b] Sqrt[a^2 c/(b^2-a^2)])], (a+b) > 0, Ceiling[(b Sqrt[c] + d)/Pi], (a+b) < 0, Floor[(b Sqrt[c] + d)/Pi], True, 0]; HypZeroExact[a_,b_,c_,d_,o_][k_] := Which[ (a+b) > 0 && (Abs[b] > Abs[a]), (a (( k+o) Pi-d) - Sqrt[b^2 ((a^2-b^2) c + (( k+o) Pi-d)^2)])/(a^2-b^2), (a+b) < 0 && (Abs[b] > Abs[a]), (a ((-k+o) Pi-d) - Sqrt[b^2 ((a^2-b^2) c + ((-k+o) Pi-d)^2)])/(a^2-b^2), (a+b) < 0 && (Abs[b] < Abs[a]), (a ((-k+o) Pi-d) - Sign[a b] Sqrt[b^2 ((a^2-b^2) c + ((-k+o) Pi-d)^2)])/(a^2-b^2), (a+b) > 0 && (Abs[b] < Abs[a]), (a (( k+o) Pi-d) - Sign[a b] Sqrt[b^2 ((a^2-b^2) c + (( k+o) Pi-d)^2)])/(a^2-b^2), a == b && N[(2 a ((k+o) Pi - d))] != 0, (((k+o) Pi - d)^2 - a^2 c)/(2 a ((k+o) Pi - d)), True, Infinity]; PartInt[f_, zerotab_List, a_, opts___Rule] := Module[{zeros = zerotab, seqtab, wp = WorkingPrecision/.{opts}/.Options[OscInt], ag = AccuracyGoal/. {opts}/.Options[OscInt], pg = PrecisionGoal/. {opts}/.Options[OscInt], mi = MinRecursion/. {opts}/.Options[OscInt], ma = MaxRecursion/. {opts}/.Options[OscInt], nt = NSumTerms/. {opts}/.Options[OscInt], ne = NSumExtraTerms/. {opts}/.Options[OscInt], wd = WynnDegree/. {opts}/.Options[OscInt]}, If[N[zeros[[1]]] < N[a], zeros = Select[zeros,(N[#] >= a)&]; Message[OscInt::lowfirst,Length[zeros]]]; If[N[zeros[[1]]] == N[a], 0, NIntegrate[f[x],{x,a,zeros[[1]]}, Method->DoubleExponential, WorkingPrecision->wp, AccuracyGoal->ag, PrecisionGoal->pg, MinRecursion->mi, MaxRecursion->ma]] + If[N[zeros[[1]]] == Infinity, 0, seqtab = Table[NIntegrate[f[x],{x,zeros[[i]],zeros[[i+1]]}, Method->GaussKronrod, WorkingPrecision->wp, AccuracyGoal->ag, PrecisionGoal->pg, MinRecursion->mi, MaxRecursion->ma], {i,1,Length[zeros]-1}]; SequenceLimit[Take[FoldList[Plus,0,seqtab],{nt+1,nt+ne}], WynnDegree->wd]] ]; PartitionTable[zerof_, a_, n_, opts___Rule] := Module[{ofs=0,x,xoffs,koffs,extrema,cfoffs=0, wp = WorkingPrecision/.{opts}/.Options[PartitionTable], ag = AccuracyGoal/. {opts}/.Options[PartitionTable], ma = MaxRecursion/. {opts}/.Options[PartitionTable], ft = FunctionType/. {opts}/.Options[PartitionTable]}, 218 A Mathematica packages
A.1 Numerical quadrature Which[ft === ZeroList, If[N[zerof[0]] < N[a], ofs = Ceiling[x/.FindRoot[zerof[x] == a,{x,0,1}, WorkingPrecision->wp, AccuracyGoal->ag, MaxIterations->ma]]]; Table[zerof[x],{x,ofs,ofs+n-1}], ft === SinArgument || ft === CosArgument, If[ft === CosArgument, cfoffs=1/2]; extrema = Select[NSolve[zerof'[x] == 0,x,WorkingPrecision->wp], (Im[x/.#] == 0)&]; xoffs = If[Length[extrema] == 0, a, Max[x/.Last[extrema],a]]; Which[NumberQ[Limit[zerof[x],x->Infinity]], Table[Infinity,{k,0,n-1}], N[zerof'[xoffs+1]] > 0, koffs = N[Ceiling[zerof[xoffs]/Pi],2 wp]; Re[Table[x/.FindRoot[zerof[x] == (k+koffs+cfoffs) Pi, {x,xoffs,xoffs+1}, WorkingPrecision->wp, AccuracyGoal->ag, MaxIterations->ma], {k,0,n-1}]], True, koffs = N[Floor[zerof[xoffs]/Pi],2 wp]; Re[Table[x/.FindRoot[zerof[x] == (-k+koffs-cfoffs) Pi, {x,xoffs,xoffs+1}, WorkingPrecision->wp, AccuracyGoal->ag, MaxIterations->ma], {k,0,n-1}]] ], True, Message[PartitionTable::badparam,ft]] ]; PartitionOffs[zerof_, a_, opts___Rule] := Module[{x,extrema,cfoffs=0, wp = WorkingPrecision/.{opts}/.Options[PartitionTable], ag = AccuracyGoal/. {opts}/.Options[PartitionTable], ma = MaxRecursion/. {opts}/.Options[PartitionTable], ft = FunctionType/. {opts}/.Options[PartitionTable]}, Which[ft === ZeroList, If[N[zerof[0]] < N[a], Ceiling[x/.FindRoot[zerof[x] == a,{x,0,1}, WorkingPrecision->wp, AccuracyGoal->ag, MaxIterations->ma]], 0], ft === SinArgument || ft === CosArgument, If[ft === CosArgument, cfoffs=1/2]; extrema = Select[NSolve[zerof'[x] == 0,x,WorkingPrecision->wp], (Im[x/.#] == 0)&]; If[Length[extrema] == 0, a, Max[x/.Last[extrema],a]], True, Message[PartitionTable::badparam,ft]] ]; PartitionPoints[zerof_, a_, n_, offs_, irel_, opts___Rule] := Module[{x,koffs,cfoffs=0, wp = WorkingPrecision/.{opts}/.Options[PartitionTable], ag = AccuracyGoal/. {opts}/.Options[PartitionTable], ma = MaxRecursion/. {opts}/.Options[PartitionTable], ft = FunctionType/. {opts}/.Options[PartitionTable]}, Which[ft === ZeroList, Table[zerof[x],{x,offs+irel,offs+irel+n-1}], ft === SinArgument || ft === CosArgument, If[ft === CosArgument, cfoffs=1/2]; Which[NumberQ[Limit[zerof[x],x->Infinity]], Table[Infinity,{k,0,n-1}], N[zerof'[offs+1]] > 0, koffs = N[Ceiling[zerof[offs]/Pi],2 wp]; Re[Table[x/.FindRoot[zerof[x] == (k+koffs+cfoffs) Pi, {x,offs,offs+1}, WorkingPrecision->wp, AccuracyGoal->ag, MaxIterations->ma], {k,irel,irel+n-1}]], True, koffs = N[Floor[zerof[offs]/Pi],2 wp]; Re[Table[x/.FindRoot[zerof[x] == (-k+koffs-cfoffs) Pi, {x,offs,offs+1}, WorkingPrecision->wp, 219
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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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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 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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6.2 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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6.6 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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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
Page 215 and 216: 8.2 Outline of the program structur
Page 217 and 218: 8.3 Implementation of the quadratur
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Page 221 and 222: 8.4 Test of the package 8.4 Test of
Page 223 and 224: 8.4 Test of the package -200 -150 -
Page 225 and 226: 8.4 Test of the package 0.4 0.2 -0.
Page 227 and 228: 8.4 Test of the package 8.4.2 Forma
Page 229 and 230: 8.4 Test of the package Out[24]= 0
Page 231 and 232: A.1 Numerical quadrature Asymptotic
Page 233: A.1 Numerical quadrature WynnDegree
Page 237 and 238: A.2 Solutions for the step potentia
Page 245 and 246: A.3 Solutions for the square barrie
Page 247 and 248: A.3 Solutions for the square barrie
Page 249 and 250: A.4 Electromagnetic waves function
Page 251 and 252: A.5 Utilities for displaying points
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
Page 265 and 266: Index saddle point integration, 11,
Page 267: Curriculum vitae Dipl.-Ing. Thilo S
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