Oscillation parameters

To obtain expressions for the principal dielectric functions we need only write three equations similar to (9.20) with three different sets of oscillator parameters appropriate to , c2, e3. Each set of parameters corresponds to one... 

Table 9.1 Oscillator Parameters Used to Fit the Reflectance Data Shown in Fig. 9.9 (From Spitzer and Kleinman, 1961)...

We used the dielectric function e of bulk MgO calculated from oscillator parameters determined by Jasperse et al. (1966), together with the dielectric function em of the KBr matrix given by Stephens et al. (1953) (corrected by June, 1972), to calculate the absorption spectrum (12.37) of a dilute suspension of randomly oriented MgO cubes. These theoretical calculations are compared with measurements on well-dispersed MgO smoke in Fig. 12.16c. Superimposed on a more or less uniform background between about 400 and 700 cm-1, similar to the CDE spectrum, are two peaks near 500 and 530 cm- , the frequencies of the two strongest cube modes. It appears that for the first time these two modes have been resolved experimentally. If this is indeed so we conclude that the widths of individual cube modes are not much greater than the width of the dominant bulk absorption band. Genzel and Martin (1972)... 

Allen, G.J., Chu, S.P., Harrington, C.L., Schumacher, K., Hoffmann, T., Tang, Y.Y., Grill, E. and Schroeder, J.I., 2001, A defined range of guard cell calcium oscillation parameters encodes stomatal movements. Nature 411 1053-1057. 

Artifacts can also be generated by inappropriately selected operational parameters including the feedback-loop control, oscillation parameters of the AFM cantilever and scan speed. Setting appropriate parameters for operation relies primarily on an operator s experience however,... 

Fig. 12. More accurate determination of the oscillation parameters with time (taken...

In summary, in this work, the application of OBT to biological systems is explored. An electronic (non-linear) feedback loop is used to convert the cell-electrode system into an oscillator whose oscillating parameter values (frequency, amplitude and phase) are strongly related to the cell-culture area. In this first approach, we use a simple second order band-pass filter followed by the bio-impedance and a simple comparator to estabhsh the oscillations. The oscillating conditions are analysed using the Describing-Function (DF) method and validated through simulation with Simulink. Preliminary experimental results obtained from a discrete components prototype are also presented. 

For the example, using the values of Fig. 2 (for a 50 x 50 qm electrode size), there exists an oscillatory solution for each fill factor (ff) value. As a consequence, the main oscillation parameters are function of the occupied cell-culture area, as it is shown by theoretical predictions in Fig. 5, for the frequency and amplitude of the oscillations. 

Figure 5. Theoretically expected oscillation parameters obtained from cell-to-electrode area overlap defined hyff= A A in the range of [0,0.9], The approximated sensitivities are 0.16 Hz/pm and...

With the aim to vahdate the results obtained from the above-mentioned mathematical procedure, we implemented the oscillators in Simulinlc. A comparison between theoretical predictions and simulation results let us determine that both are very similar. It can be seen that the adopted methods predict the oscillation parameters with enough precision for the intended apphcations. The obtained results are summarized at Table 1 foTff= 0.1, 0.5 and 0.9. The obtained frequency spectrum is shown in Fig. 6 for the case ff= 0.9. 

Figure 6. Simulated frequency spectrum for and usingjfT =0.9. The oscillation parameters are...

Another way of regulating fluid flow for noncontact component manipulation was created by mechanical oscillation. Within a fluid environment, a tool capable of oscillating its tip at high frequencies would then create local streamlined flow. Tool oscillation parameters could be adjusted to define whether the local flow would repel, attract, or rotate components. For this technique, there was no contact between the tool and the manipulated component. This concept is attractive for manipulating cells and live organisms [5]. 

Table 3.2. Oscillator parameters of Maxwell-Helmholtz-Drude dispersion formula (1.46) for a-Fe203...

Figure 3.34. Simulated p-polarized IRRAS of layer 1 nm thick with optical properties specified by oscillator parameters vq = 1090 cm, y = y/vo = 0.05, Soo = 2.5, S = (1)0.8, (2) 0.6, (3) 0.4, (4) 0.2 ns = 3.42, (pi = 71°. Reprinted, by permission, from V. P. Tolstoy, Methods of UV-Vis and IR Spectroscopy of Nanolayers, St. Petersburg Univ. Press, St. Petersburg, 1998, p. 179, Fig. 1.15. Copyright 1998 St. Petersburg University Press.

Figure3.35. Variation in ratio IAAloI/IAAtoI in p-polarized IRRAS spectra of hypothetical strongly absorbing 1-nm layer with optical properties described by oscillator parameters VO = 1064 cm, Boo = 2.5, (1) S = 0.6 at different y = y/vo, (2) y = y/vo = 0.06 at different S (p = 71°, ri3 = 3.42. Reprinted, by permission, from V. P. Tolstoy and S. N. Gruzinov, Opt. Spectrosc. 71, 77 (1991), p. 79, Fig. 4. Copyright 1991 Optical Society of America.

KJ/mol and a gauche-trms energy difference of 2.5 kJ/mol). The constants D, and y [see Eq. (2)] represent the usual Morse oscillator parameters. The nonbonded terms e and a [Eq. (3a)] represent the Lennard-Jones parameters, b and C [Eq. 3b)] are related to the overlap and dispersion of the atoms i and j, and A is a parameter related to the position and well-depth of the interaction. The bending force constant is, and 6o [Eq. (4)] indicates the equilibrium value of the angle formed by the three atoms of interest. The above potential energy functions [Eqs. (2-5)] have been demonstrated to yield good spectroscopic, thermodynamic, and kinetic data, as well as to provide the atomistic details of temperature-dependent phase transitions for crystalline polymers. 

Equivalent Circuit of a Quartz Resonator Experimental Determination of the Crystal Oscillator Parameters... 

Method A uses bulk ATR spectra of thick polycrystalline samples of PEG with a random orientation of helical coils Using the SpectraRay 2 software package (SENTECH Instruments GmbH, Berlin, Germany), Drude-Lorentz oscillator parameters [15] were determined by spectral line fits to selected vibrational bands of an ATR spectrum, taken from... 

The table presents oscillator parameters of five selected CH2 vibrations between 1200 and 1400 cm used to fit the Drude-Lorentz spectrum calculation to an experimental spectrum of random polycrystalline PEG. See ref. [15] for the meaning of Qq. Gp, and Q. Lor the high-frequency dielectric constant 00 = 2.10 was used, see text... 

Basically, in WPD, for fixed values of / and fe, analyses the fluctuations of the signal roughly around the position 2 fe, at scale 2 and oscillation parameter n. WPA operates by approximating a signal with scaled and translated wavelet packet functions,... 

The results shown in table 4.1 correspond to different prescriptions for the variational parameter K, namely different levels of expansion N at which it is adjusted. As pointed out by Moshinsky [49], minimizing the ground state at the N =2 order does not provide any improvement with respect to N = 0. Otherwise, the value of the harmonic-oscillator parameter K depends rather sensitively on which level and to which order the minimization is performed. However, the accuracy of the eventual energies depends less on the prescription adopted for K than on the number of quanta N introduced in the expansion. 

Symmetric and scalar states ([56,0 ]) for quark masses m, = 1 and linear confinement V= i E r, using a harmonic-oscillator expansion up to N quanta. The oscillator parameter K is adjusted by minimizing either the first or second level with an expansion limited to N quanta (the minimized energy is underlined). The exact values are very close to = 3.8631, ,(, = 5.3207, and 20 = 6.595 3. ... 

For the numerical illustration, let us consider again a linear potential T, r j and the sets of constituent masses (1,1,5) and (1,1,0.2) which are relevant for qqc and ccq charmed baryons, respectively. We display in table 4.3 the behaviour of the ground state energy as a function of the maximal number of quanta, N, introduced in the expansion. Also shown is the order N to which the oscillator parameter K has been optimized. Some remarks are in order. 

The energy halfway between the bottom of the Morse oscillator well and the dissociation limit is —U, /2, or Djl when measured from the bottom of the well. Call the difference between minimum and maximum classically allowed R values at this energy 8R (by classically allowed we mean that timneUng is neglected). At the same energy from the bottom of the well, D, /2, a harmonic oscillator with the same force constant k, wiU predict a different value for 8R, where the Morse oscillator parameter... 

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