Harmonic impulse

Here 4 and p are the vectors of dimensionless coordinates and impulses, respectively, o>.is the frequency of the harmonic vibrations active in the Jahn-Teller effect a is the vibronic constant related to the usual F (Ber-... 

These are physically the correct equations of motion, only the momentum degree of freedom is spreading diffusively. This is expected classically from the medium giving the system minute impulse kicks changing its momentum only. If we have a harmonic oscillator,... 

Determination of the sensor transfer function, unperturbed by the interface electronics, is a major advantage of impulse excitation. Other forms of excitation have been proven to overcome limitations when applied to liquid analytes. Access to harmonic analysis of the resonator is an inherent feature of this method. 

To qualitatively understand the mechanism of impulsive Raman excitation, we apply the above-mentioned cycle average condition to the harmonic oscillator model for a Raman active mode I of which the reduced mass and vibrational frequency are ft/ and an, respectively. The applied pulse is assumed to be rectangular, and the duration is Tp./(f) is constant, that is,/(f) = / for the pulse duration. From Eqs. (7.7) and (7.8), we can derive the classical equation of motion for Qi. The field-induced... 

Periodic impulse train has equal-amplitude harmonic spectrum... 

The impulse response and spectrum of the filter shown in Figure 9.4 is shown in Figure 9.5. As would be expected, the impulse response is an exponentially decaying train of pulses spaced T = P/SRATE seconds apart, and the spectrum is a set of harmonics spaced = 1/PHz apart. This type of... 

Some systems can be decomposed into a harmonic (quadratic) part Ho(q,p) = p M p/2 + q Aq/2 and an anharmonic part H q,p) = U q). Then a splitting method can be formulated based on exact solution of the linear system together with kicks representing impulses defined by the anharmonic part. For a simple system consisting of a harmonic oscillator Ho q,p) = -I- such a method can... 

This technique successfully reverses the MFCC coding operation. The main weakness is that because we threw away the harmonic information in the filter bank step, we have to resort to a classical LP style technique of using an impulse to drive the LP filter. A number of improvements have been made to this, with the motivation of generating a more natural source, while still keeping a model systems where the parameters are largely statistically independent. For example in the technique of Yoshimura et al [510] a munber of excitation parameters are used that allow mixing of noise and impulse, and allow a degree of aperiodicity in the positions of the impulses. 

The harmonic functions are symmetrical functions with respect to time, conhrming the insensitivity of the oscillator behavior on a time reversal t - -t. Naturally, all the state variables also follow a harmonic function, cosine (an even function) for capacitive state variables, effort e, and basic quantity q, and sine (an odd function) for inductive state variables (impulse p, and flow In Figure 9.10 are plotted the variations of these four state variables assuming scalar constitutive properties (linear case). 

Fig. 15. Impulsive time- and frequency resolved fluorescence spectra as obtained for the 25-mode model of rhodopsin coupled to a harmonic bath.

An earlier suggestion of Fixman of how to mimic flexibility has been discussed with respect to a system with two degrees of freedom. Harmonic stretching and bending of the bonds of butane in liquid CCI4 has subsequently been allowed transition state theory does not exactly apply as many barrier crossings are reflected by solvent collisions. In a modified molecular dynamics examination of conformational isomerizations in butane the effect of solvent was expressed with a stochastic model in which the Newtonian trajectory was modified by random impulses. The frequency of these impulses, which have a frictional effect upon the trajectory, reduced the value of the transmission coefficient by inducing oscillatory motion at the col. At the inner bonds of decane isomerization rates are less than in butane. 

The analysis of the transmission of electrical impulses through amplifiers rests on the finding by Fourier, that a periodic impulse function can be thought of as being composed of an infinite series of harmonic functions. Let f(t) be a function which repeats itself after time T, then f(t) can be expressed as... 

The impulsive noise of a helicopter leads to several effects with pulsing characteristic and high amphtudes at discrete frequencies. Again, we are concerned with the higher harmonics of the blade passage frequency. These types of noise occur in different flight situations and are recognized by the human ear... 

V = applied voltage r = tip or rod radius L = liquid gap). The hypothesis of a constant streamer initiation field does not hold in most cases, since with the measured streamer initiation voltages, the harmonic field values obtained via the above approximations are much higher with sharp tips (> 10 MV/cm, for r < 3 ym < 1 MV/cm, for r > 100 ym). This has been observed for both impulse (Rzad et al., 1979 Chadband, 1980 ... 

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