Oscillations, Waves, and Interactions - GWDG

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410 U. Parlitz 4 10 5 5 (a) (b) (c) x 2 0 −2 dx/dt 0 −4 0 10 20 30 −5 −4 −2 0 2 4 10 0 1 2 3 4 5 6 t x 2 5 20 10 ν / ν 0 5 (d) (e) (f) x 0 dx/dt 10 0 −10 −5 0 10 20 30 −20 −5 0 5 10 0 1 2 3 4 5 6 t x 2 20 ν / ν 0 5 10 10 4 10 5 (g) (h) (i) x 0 dx/dt 0 −10 −5 0 10 20 30 −20 −5 0 5 10 0 1 2 3 4 5 6 t x 2 10 3 5 20 ν / ν 0 10 10 4 10 5 (j) (k) (l) x 0 dx/dt 0 −10 −5 0 10 20 30 −20 −5 0 5 10 0 1 2 3 4 5 6 t x 2 10 3 5 20 ν / ν 0 10 10 4 10 5 (m) (n) (o) x 0 −5 0 10 20 30 t dx/dt 0 −10 −20 −5 0 x 5 S(ν) S(ν) S(ν) S(ν) S(ν) 10 4 10 3 10 4 10 3 10 3 10 0 1 2 3 4 5 6 2 ν / ν 0 Figure 3. Time series, (stroboscopic) phase portraits, and power spectra of the Duffing oscillator Eq. (7) for d = 0.2, ω = 2 and (a-c) f = 10 (symmetric period-1), (d-f) f = 42 (asymmetric period-1), (g-i) f = 48 (period-2), (j-l) f = 54 (chaos), and (m-o) f = 56 (symmetric period-3). Red markers are plotted whenever a period T = 2π/ω = 1/ν0 of the drive elapsed. and bifurcations) in parameter space. Figure 5(a) shows such a bifurcation diagram where the driving frequency ω is varied and in Fig. 5(b) the driving force f is used as a control parameter. Although providing already a very detailed view of the bifurcation structure, bifurcation diagrams are limited to a single parameter axis. To get an even better overview
Complex dynamics of nonlinear systems 411 Figure 4. Poincaré section of a chaotic attractor of Duffing’s equation (7) (d = 0.2, ω = 2, f = 54) generated by stroboscopic sampling of z1(n) = x(nT ) and z2(n) = ˙x(nT ) with the driving period T = 2π/ω. (a) Poincaré section of the full attractor (see Fig. 3k) and (b) section (zoom in) showing the underlying self-similar fractal structure. Figure 5. Bifurcation diagrams of the Duffing oscillator (7) with control parameter (a) driving frequency ω (d = 0.2, f = 23) and (b) driving amplitude f (d = 0.2, ω = 2).
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Thomas Kurz, Ulrich Parlitz, and Ud
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erschienen im Universitätsverlag G
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Bibliographische Information der De
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iv Contents Laser speckle metrology
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Oscillations, Waves and Interaction
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Applied physics at the “Dritte”
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noise component [GNE] 5 4 3 2 1 can
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3.4 Transfer to running speech Spee
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3.4.2 Analysis of running speech Sp
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Speech research 33 Area [Pixels] 60
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Speech research 35 [13] D. Michaeli
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Specific signal types in hearing re
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74 D. Ronneberger et al. Mechel fou
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76 D. Ronneberger et al. (flow velo
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78 D. Ronneberger et al. |t + acous
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80 D. Ronneberger et al. Figure 6.
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82 D. Ronneberger et al. Figure 8.
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84 D. Ronneberger et al. (flow velo
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86 D. Ronneberger et al. R / L ⋅
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88 D. Ronneberger et al. e. g. temp
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90 D. Ronneberger et al. 3.2 Qualit
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92 D. Ronneberger et al. As usual t
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94 D. Ronneberger et al. (wavenumbe
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96 D. Ronneberger et al. powers of
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98 D. Ronneberger et al. an increas
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100 D. Ronneberger et al. The term
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102 D. Ronneberger et al. Neverthel
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104 D. Ronneberger et al. [4] J. Br
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106 D. Ronneberger et al. strömung
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108 D. Guicking synchronised tuning
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110 D. Guicking primary noise micro
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112 D. Guicking primary sensor desi
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114 D. Guicking by an antiphase sou
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116 D. Guicking R L C C + + 1 1−C
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118 D. Guicking More involved than
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120 D. Guicking In the 1980s, longi
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122 D. Guicking with electrodynamic
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124 D. Guicking 3.6 Noise reduction
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126 D. Guicking the turbulence of a
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128 D. Guicking References [1] Lord
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130 D. Guicking [44] Falcke, H.,
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132 D. Guicking [84] J. Melcher,
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134 D. Guicking [125] D. Heyland et
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136 D. Guicking [166] S. Zommer et
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138 D. Guicking [212] M. L. Post an
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140 W. Lauterborn et al. liquid κ
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142 W. Lauterborn et al. Figure 2.
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144 W. Lauterborn et al. nator, and
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146 W. Lauterborn et al. by types a
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148 W. Lauterborn et al. bubble rad
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154 W. Lauterborn et al. P koll [kb
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156 W. Lauterborn et al. Pulse widt
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158 W. Lauterborn et al. laser puls
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168 W. Lauterborn et al. R [µ m] 1
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170 W. Lauterborn et al. [17] M. P.
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172 R. Mettin (a) (b) Figure 1. Bub
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174 R. Mettin 0 ms 2 mm 1 ms 2 ms 3
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176 R. Mettin important quantity ch
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178 R. Mettin 100 kPa 200 kPa | | F
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180 R. Mettin Figure 7. Trapped sin
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182 R. Mettin concentration of spec
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184 R. Mettin which is called the p
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186 R. Mettin R 02 [µm] R 02 [µm]
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188 R. Mettin constant to M a = 2π
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190 R. Mettin (a) p a [Pa] 140 120
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192 R. Mettin z [mm] 5 4 3 2 1 0 -1
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194 R. Mettin Figure 17. Left: Expe
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196 R. Mettin - a hot microlaborato
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198 R. Mettin [52] R. Mettin, C.-D.
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200 W. Eisenmenger and U. Kaatze Th
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202 W. Eisenmenger and U. Kaatze Fi
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214 W. Eisenmenger and U. Kaatze 6
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216 W. Eisenmenger and U. Kaatze Pr
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218 A. Vogel, I. Apitz, V. Venugopa
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260 K. D. Hinsch Generally, any of
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262 K. D. Hinsch Figure 1. Monitori
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264 K. D. Hinsch Figure 3. ESPI stu
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266 K. D. Hinsch Figure 4. Deterior
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268 K. D. Hinsch Often, in-plane mo
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270 K. D. Hinsch Figure 7. Optical
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272 K. D. Hinsch Figure 9. Humidity
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274 K. D. Hinsch locations that tak
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276 K. D. Hinsch Figure 13. Map of
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278 K. D. Hinsch References [1] D.
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280 Schreiber not moving along with
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282 Schreiber These properties made
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284 Schreiber Figure 3. The G ring
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286 Schreiber Rotation Rate [rad/s]
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288 Schreiber and it is currently b
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290 Schreiber n1 D A B n Figure 8.
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292 Schreiber Beamwalk [µm] 80.0 7
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294 Schreiber ∆ Perimeter [*10e12
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296 Schreiber and the last term acc
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298 Schreiber Δf [µHz] 100 50 0 -
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300 Schreiber formation of a new wo
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302 Schreiber PSD [*10 16 (rad/s) 2
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304 Schreiber 7.2 The ring laser co
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306 Schreiber Demodulator Signal [V
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308 Schreiber Est. Phase Vel. (m/s)
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310 Schreiber [18] V. Frede and V.
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312 Martin Dressel tice is reduced
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314 Martin Dressel Metallic whisker
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316 Martin Dressel (a) (b) (c) CH 3
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318 Martin Dressel 3.1 Charge densi
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320 Martin Dressel Absorptivity σ
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322 Martin Dressel brought a confir
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324 Martin Dressel a charge disprop
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326 Martin Dressel Conductivity 70
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328 Martin Dressel Reflectivity Con
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330 Martin Dressel References [1] M
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332 Martin Dressel and L. Montgomer
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334 R. Pottel, J. Haller and U. Kaa
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460 S. Lakämper and C. F. Schmidt
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462 Index basin of attraction, 144
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464 Index cone bubble structure, 19
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466 Index turbulent, 111, 126 fluct
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468 Index LPC, 29 luminescence of b
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470 Index peak factor, 38, 43 Peier
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472 Index laser-induced bubble, 152
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474 Index ultraharmonic resonance,
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