Oscillations, Waves, and Interactions - GWDG

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354 R. Pottel, J. Haller and U. Kaatze Figure 19. Zinc(II)chloride complexation scheme in water (w). the characteristics of zinc chloride aqueous solutions. The formation of mono-, bi-, tri-, and tetrachloro complexes is well established now. All these species seem to exist not only as contact ion complexes but also as solvent separated outer-sphere species [89–92]. Following the above lines of reasoning (sect. 4.1) the extrapolated solvent contribution ɛ1 to the static permittivity can be evaluated in terms of the concentration C0 of completely dissociated zinc ions. According to our arguments zinc chloride ion complexes unlikely induce dielectric saturation effects. Let us assume the number Z + of apparently irrotationally bound water molecules around the completely dissociated Zn 2+ ion to agree with that around the Mg 2+ ion. The cation-water distances (Zn 2+ : 2.08 ˚A; Mg 2+ : 2.11 ˚A [93]) and the apparent molar volumes at infinite dilution (Zn 2+ : -32.4 cm 3 mol −1 ; Mg 2+ : -32.0 cm 3 mol −1 [94]) almost agree with one another. The experimental ɛ1 data can thus be evaluated in terms of the Zn 2+ concentration. The relative Zn 2+ content C0/C following thereby is displayed in Fig. 20 where also predictions from a reasonable set of of equilibrium constants Ki, i = 1, 2, 3, 4 [95] for the association scheme of zinc ions and chloride ions are shown. In deriving this set of Ki values no distinction was made between inner sphere complexes and their water-containing analoga. The transition between these species and their outer-sphere analoga was assumed to be fast as compared to the transition between the complexes with different number of chloride ions. The agreement between our data from the ɛ1 values and the predictions from the equilibrium constants of the multistep reaction scheme is striking. According to our expectations the relative content of completely dissociated Zn 2+ ions decreases substantially with C. Most species in the zinc chloride complexation scheme (Fig. 19) are nondipolar or only weakly dipolar. In the dichloro complex with linearly arranged chloride, zinc, and chloride ions, in the planar trichloro complex, as well as in the tetrahedrally structured tetrachloro complex the individual dipole moments largely compensate
Multistep association of cations and anions 355 Figure 20. Concentration ratios C0/C(•) and C1/C(◦) of completely dissociated Zn 2+ ions and of (Zn(H2O)Cl) + complexes, respectively, as following from dielectric spectra of aqueous solutions of ZnCl2 with salt concentration C [23]. The lines show the predictions from a set of equilibrium constants [95] for the zinc chloride association scheme. each other. Therefore, the solute contribution ɛ(0) − ɛ1 (Fig. 18) to the static permittivity of zinc chloride solutions appears to be mainly due to monochloro complexes. We used the relation C1 = (ɛ(0) − ɛ1) ɛ0 N � �2 2 3kBT 3 µ 2 to derive the concentration C1 of monochloro complexes from the relaxation amplitude ɛ(0) − ɛ1 and the dipole moment µ of the ion pairs [23]. Here N is Avogadro’s number and kB is the Boltzmann constant. Using the simple relation (18) µ = e · l (19) for the dipole moment in solution, where e denotes the elementary charge and l the cation-anion distance, perfect agreement of the C1 values with those from the set of equilibrium constants Ki, i = 1, ..., 4 is observed (Fig. 20), if l = 4.2 ˚Ais assumed. This is the cation-anion distance in an outer-sphere complex. Hence, obviously, the monochloro complex exists predominantly as solvent-separated species. The ultrasonic absorption spectra of zinc chloride solutions extend over a broader frequency band than a single Debye type relaxation term, thus indicating a distribution of relaxation times [30]. A relaxation time distribution had been already inferred from previous ultrasonic measurements, in a reduced frequency range, of zinc(II)halide aqueous solutions [96] and also from a combined ultrasonic and Bril-
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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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404 U. Kaatze and R. Behrends Copyr
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406 U. Parlitz here chaos control m
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408 U. Parlitz Figure 2. Amplitude
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410 U. Parlitz 4 10 5 5 (a) (b) (c)
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412 U. Parlitz two-parameter studie
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414 U. Parlitz GN differential opti
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416 U. Parlitz P 1 P 2 P 3 S P 1 P
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418 U. Parlitz Figure 9. Correlatio
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420 U. Parlitz series” where for
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422 U. Parlitz current state future
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424 U. Parlitz tion [69] of two uni
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426 U. Parlitz LD1 LD2 M BS1 BS2 OD
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428 U. Parlitz with a clear tendenc
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430 U. Parlitz (a) y (c) y 40 20 È
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432 U. Parlitz [29] P. Grassberger,
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434 U. Parlitz [76] H. D. I. Abarba
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436 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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