Oscillation large-amplitude

Figure 10-14. Time evolution of the nonadiabatic surface hopping parameter, P10 (Eq. 10-10), for a transition from the 5 excited state to the. V0 ground state for representative 7Me-keto (fast oscillating, small amplitude dark grey curve) and 9Me-keto (fast oscillating, large amplitude light grey curve) G trajectories. The steep increase of P10 at / 10 fs in the case of 9Me-keto coincides with the transition from a quasi-planar to an out-of-plane distorted structure. At / 40 fs the amino group starts rotating...

MMOs have been observed in many experiments. Typically, a MMO consists of one or more large amplitude oscillations followed by several small amplitude oscillations. The size of tire small oscillations may grow slowly. Suppose L large oscillations are followed by s small oscillations, where L and s are integers, tlien tliis MMO can be... 

Rapid eye movement sleep. Sleep stage characterized by rapid movements of the eyes and asynchronous EEG activity in the theta-frequency (5-10Hz) range. Counterpart is slow wave sleep, characterized by other electrophysiological (synchronized low frequency l-2Hz, large amplitude EEG and neuronal sharp wave-ripple oscillations) and endocrine (growth hormone surge) activities. 

This step is important in that it prevents the large-amplitude oscillations (typically present at low k) from dominating over the smaller ones (typically at high k). This is critical since the determination of interatomic distances depends on the frequency and not the amplitude of the oscillations. Other approaches having the same effect have also been employed.37,47... 

Analytical approaches applicable for small and large amplitudes (for weak and strong nonlinearity) of the oscillations in a nonlinear dynamic system subjected to the influence of a wave has been developed (Damgov, 2004 Damgov, Trenchev and Sheiretsky, 2003). 

Rotation of the oxygen around the Fe-O bond involves a small energy barrier ( 2 kcal mol ), suggesting that several rotational conformations could be available at room temperature. Indeed, our molecular dynamics simulations show that the 02 ligand undergoes large-amplitude oscillations within one porphyrin quadrant, jumping to another quadrant on the picosecond timescale. The dynamics of the FeCO unit are characterized by rapid mo-... 

The tendency of premixed flames to detach from the flame holder to stabilize further downstream has also been reported close to the flammability limit in a two-dimensional sudden expansion flow [27]. The change in flame position in the present annular flow arrangement was a consequence of flow oscillations associated with rough combustion, and the flame can be particularly susceptible to detachment and possible extinction, especially at values of equivalence ratio close to the lean flammability limit. Measurements of extinction in opposed jet flames subject to pressure oscillations [28] show that a number of cycles of local flame extinction and relight were required before the flame finally blew off. The number of cycles over which the extinction process occurred depended on the frequency and amplitude of the oscillated input and the equivalence ratios in the opposed jets. Thus the onset of large amplitudes of oscillations in the lean combustor is not likely to lead to instantaneous blow-off, and the availability of a control mechanism to respond to the naturally occurring oscillations at their onset can slow down the progress towards total extinction and restore a stable flame. 

Near the point of drop release, transfer coefficients can be much different from those predicted, due to large amplitude oscillation and internal circulation induced by departure from the nozzle or tip (Al, G4, Y3). 

Other complex oscillatory waveforms include bursting , in which large-amplitude oscillations are interspersed with periods of non-oscillatory evolution, or by small oscillations (Fig. 1.19). 

V-shaped regions, but in general close up again at sufficiently large amplitude. The number marked in each of the tongues indicates how many forcing periods are required for one full oscillation or, equivalently, how many points appear in the stroboscopic map. 

Notice that the partial oxygen pressure remains constant and that in both situations large amplitude oscillations in NADH and some amino acid concentrations are observed. 

In closed system studies of the BZ reaction, three principal modes of homogeneous oscillations have been identified (1) low-frequency, large amplitude, highly nonlinear (i.e., nonharmonic) relaxation oscillations... 

This is equivalent to the harmonic oscillator potential, eqn 3.13, if x represents the distance from the equilibrium separation and if the zero of energy is taken as the minimum potential Vt. The approximation is not accurate for vibrations of large amplitude, but is good enough for the lowest allowed energy levels, three of which are shown in Fig. 3.8. 

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