Oscillation irregular

The instantaneous velocity oscillates irregularly. We define the time-smoothed velocity by taking a time average of over a time interval to, which is large with respect to the time of turbulent oscillation but small with respect to the overall time... 

General conditions for transition to irregular behaviour in an oscillator under wave action... 

General conditions for transition to irregular and chaotic behaviour in an oscillator under wave action have been derived using the notion about the Melnikov distance ... 

Under the condition D(ta, t0) = 0 and taking into account that sin(z/f0 + 0 < I and that 6d. > 0, the general condition for transmission to irregular (chaotic) behaviour in nonlinear oscillator under the wave action takes the form 25dsh( v w) < ttu2 Fg ev. ... 

Damgov, V. N. Quantized Oscillations and Irregular Behaviour of a Class of Kick-Excited Self-Adaptive Dynamical Systems. Progress of Theoretical Physics Suppl, Kyoto, Japan, No. 139, P. 344 (2000)... 

Damgov, V.N. Quantized Oscillations and Irregular Behaviour of Inhomoge-neously Driven, Damped Pendulum. Dynamical Systems and Chaos. World Scientific, London, Vol. 2, P. 558 (1995)... 

To summarize this subsection one can state that i) The role of second-order shell-effect terms can be determined by investigating the discrepancies between the discrete second derivatives of the functions 8E (Z) and 8 Ehfr(Z,Y(,). ii) For the second row of elements these terms determine the whole pattern of the oscillating part of the energy iii) They also play an important role in critical regions of shell filling (i.e., around shells fully, half, or irregularly filled). 

In practice, this model is oversimplified since the exciting wake shedding is by no means harmonic and is itself coupled with the shape oscillations and since Eq. (7-30) is strictly valid only for small oscillations and stationary fluid particles. However, this simple model provides a conceptual basis to explain certain features of the oscillatory motion. For example, the period of oscillation, after an initial transient (El), becomes quite regular while the amplitude is highly irregular (E3, S4, S5). Beats have also been observed in drop oscillations (D4). If /w and are of equal magnitude, one would expect resonance to occur, and this is one proposed mechanism for breakage of drops and bubbles (Chapter 12). 

The variation of scattered light intensity with 0 as typified by Fig. 9.19 clearly becomes more complex as the particle size increases, with sharp oscillations seen at a 10. However, recall that this is for a spherical homogeneous particle of a fixed size and for monochromatic light (e.g., a laser) when the particle is irregular in shape, these oscillations are far less prominent. This is also true for a group of particles of various sizes, that is, a polydisperse aerosol, where the overall scattering observed is the sum of many different contributions from particles of various sizes. Finally, nonmonochro-matic light and fluctuations in polarization also help to smooth out the oscillations. 

---