Envelope oscillator

Note that the amplitude of the oscillator is controlled by an envelope, which in this case is implemented by means of another oscillator unit. The lookup table for the envelope oscillator holds the shape of the envelope and is read only once per note. In this case, the frequency of the envelope oscillator must be set to the inverse of the duration of the note ifreq = 1/duration). 

Nuclear motion drags along the electronic cloud, so that as temperature rises, molecular envelopes oscillate more and more. If the intermolecular potential were perfectly harmonic, the overall volume effect would be nil, because the compressions and expansions would average out but the potential is much steeper on the compression side (Fig. 4.4), so expansion is hindered less than contraction and molecules effectively occupy more and more space as mobility increases. So thermal expansion is very strictly dependent on the shape of the potential curve, that is on the strength and anisotropy of the intermolecular potential, in a typical structure-property relationship. The simple equation that defines the isobaric thermal expansion coefficient a is... 

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

The second part of the cancellation puzzle concerns the full state-to-state DCS and ICS (i.e., including all the impact parameters). In this case, the GP effects do not cancel in the DCS [26, 27, 29], as is shown in Fig. 10. Instead, they shift the phase of the fine oscillations that are superimposed on the main DCS envelope. Following the above, this indicates that the 1-TS and 2-TS paths scatter into overlapping regions of space, so that the GP produces an effect by changing the sign of the interference between(0) and (0). This is confirmed by Fig. 10b, which shows that the 1-TS and 2-TS DCS do indeed overlap. 

To obtain a clear understanding of electrodynamic bonding, start with the field of a static electric dipole. Then, let the dipole oscillate so it emits electromagnetic waves (photons). Consider what happens when the emitted field envelopes another dipole (London, 1937). Finally, determine the factors that convert neutral molecules into dipoles (that is, their polarizabilities). 

ESE envelope modulation. In the context of the present paper the nuclear modulation effect in ESE is of particular interest110, mi. Rowan et al.1 1) have shown that the amplitude of the two- and three-pulse echoes1081 does not always decay smoothly as a function of the pulse time interval r. Instead, an oscillation in the envelope of the echo associated with the hf frequencies of nuclei near the unpaired electron is observed. In systems with a large number of interacting nuclei the analysis of this modulated envelope by computer simulation has proved to be difficult in the time domain. However, it has been shown by Mims1121 that the Fourier transform of the modulation data of a three-pulse echo into the frequency domain yields a spectrum similar to that of an ENDOR spectrum. Merks and de Beer1131 have demonstrated that the display in the frequency domain has many advantages over the parameter estimation procedure in the time domain. 

Figure 6.7. Temperature dependence of a hypothetical laser diode. Several modes are shown oscillating within the 2-nm bandwidth envelope of this laser the mode spacing and position change somewhat with temperature as well. Note that some longer-wave-length lasers exhibit significant increases in the bandwidth with temperature.

Even though the bifurcation behavior exhibits a Z-shaped curve, it is more complicated due to the existence of the HB. For example, upon ignition, the system is expected to oscillate because no locally stable stationary solutions are found (an oscillatory ignition). Time-dependent simulations confirm the existence of self-sustained oscillations [7, 12]. The envelope of the oscillations (amplitude of H2 mole fraction) is shown in circles (a so-called continuation in periodic orbits). 

The Debye-Waller factor, Eq. 4, describes how the uncertainty in real space (u) determines the range of S(Q) in Q space. Now the exact converse happens with respect to the resolution of the measurement in Q space. If the Q resolution of the instrument is AQ, the PDF will have an envelope exp(- r ( AQ) ), and the oscillations in the PDF decay. Therefore in order to determine the PDF up to large distances it is important to use an instrument with high Q resolution. Since the PDF method was initially applied to glasses and liquids in which atomic correlation decays quickly with distance, this point was not... 

The modification of the electronic potentials due to the interaction with the electric field of the laser pulse has another important aspect pertaining to molecules as the nuclear motion can be significantly altered in light-induced potentials. Experimental examples for modifying the course of reactions of neutral molecules after an initial excitation via altering the potential surfaces can be found in Refs 56, 57, where the amount of initial excitation on the molecular potential can be set via Rabi-type oscillations [58]. Nonresonant interaction with an excited vibrational wavepacket can in addition change the population of the vibrational states [59]. Note that this nonresonant Stark control acts on the timescale of the intensity envelope of an ultrashort laser pulse [60]. 

The pulse has a real-valued envelope t) and oscillates with the carrier frequency Q. Because ultrafast laser pulses are too short to be shaped directly in the time domain, the pulse is manipulated in the frequency domain. To this end, a linear spectral transfer function M co) is applied to the pulse spectrum (m), with... 

It is interesting that envelope functions can also behave as multiperiod oscillations. This takes place if we take into account small damping. By way of an example, for the damping constant yj = y2 = 0.1, the envelope function has a feature of two period doubling oscillations. 

Some typical oscillatory records are shown in Fig. 4.6. For conditions close to the Hopf bifurcation points the excursions are almost sinusoidal, but this simple shape becomes distorted as the oscillations grow. For all cases shown in Fig. 4.6, the oscillations will last indefinitely as we have ignored the effects of reactant consumption by holding /i constant. We can use these computations to construct the full envelope of the limit cycle in /r-a-0 phase space, which will have a similar form to that shown in Fig. 2.7 for the previous autocatalytic model. As in that chapter, we can think of the time-dependent... 

The harmonic oscillator model does not take into account the real nature of chemical bonds, which are not perfect springs. The force constant k decreases if the atoms are pulled apart and increases significantly if they are pushed close together. The vibrational levels, instead of being represented by a parabolic function as in equation (10.3), are contained in an envelope. This envelope can be described by the Morse equation (Fig. 10.5) ... 

Fig. 3. Time dependent field of the 3.9fs pulse reconstructed from the FROG trace. The solid curve is the field and the dotted curve is the envelope of the field. The central wavelength is 595nm corresponding to the oscillation period of 2 fs. The carrier envelope cannot be determined and arbitrary phase is used for the description.

In fact, a breather may be thought of as a result of the attractive interaction between soliton and antisoliton. Inside the breather envelope, the soliton and antisoliton oscillate with respect to each other with period 2tt/ojb. Because creating a breather requires an arbitrarily small energy, excitations of this type should persist at low temperature and should dominate the dynamics of the rotor chain. 

---