Coupled oscillator concept

A number of theoretical models of VOA can be considered as generalizations of the coupled oscillator concept to more than two oscillators. For VCD, these models have the form... 

By resonance transfer, we mean two radiators which are radiating at the same frequency. This is quite different from the example given above for radiative exchange. Note that we are not speaking of lattice vibrational frequencies but of radiation frequencies. We thus speak of two "coupled" oscillators. To further illustrate this concept, suppose we take two dipoles, there wUl be an electric moment, E 6), which is a vector product whose strength is a function of the angle, 6, between the vector moments of the dipoles ... 

The concept of coupled oscillators is important from the viewpoint of understanding oscillatory phenomena in biochemical systems where the basic question relates to the type of dynamic behaviour when two are more such systems are coupled together. The concept of coupling is quite relevant in the context of spatial dissipative structures in cases where chemical oscillators are coupled through diffusion. 

Synchronization or entrainment is a key concept to the understanding of selforganization phenomena occurring in the fields of coupled oscillators of the dissipative type. We may even say that Part II is devoted to the consideration of this single mode of motion in various physical situations. Specifically, Chap. 6 is concerned with wave phenomena and pattern formation, which may be viewed as typical synchronization phenomena in distributed systems. In contrast, we shall study in Chap. 7 turbulence in reaction-diffusion systems, which is caused by desynchronization among local oscillators. Chapter 5 deals with self-synchronization phenomena in the discrete populations of oscillators where the way they are distributed in physical space is not important (for reasons stated later). We shall introduce some kind of randonmess by assuming that the oscillators are either different in nature from each other or at best statistically identical. One may then expect phase-transition-like phenomena, characterized by the appearance or disappearance of collective oscillations in the oscillator communities. In describing such a new class of phase transitions. Method I turns out to be very useful. 

The concept of resonance was introduced into quantum mechanics by Heisenberg16 in connection with the discussion of the quantum states of the helium atom. He pointed out that a quantum-mechanical treatment somewhat analogous to the classical treatment of a system of resonating coupled harmonic oscillators can be applied to many systems. The resonance phenomenon of classical mechanics is observed, for example, for a system of two tuning forks with the same characteristic frequency of oscillation and attached to a common base, hich... 

The examples presented in this chapter [308 320] are illustrations of the concepts presented in the previous chapters. They correspond to recent numerical analysis of burners which are typical of most modern high-power combustion chambers, especially of gas turbines the flame is stabilized by strongly swirled flows, the Reynolds numbers are large, the flow field sensitivity to boundary conditions is high, intense acoustic/combustion coupling can lead to self-sustained oscillations. Flames are stabilized by swirl. Swirl also creates specific flow patterns (a Central Toroidal Recirculation Zone called CTRZ) and instabilities (the Precessing Vortex Core called PVC). 

Next, we discuss the concept of phonon-assisted reactions. In relation to thermal reactions, they can be assisted by phonon-mode softening leading to large-amplitude overdamped oscillations. In the case of a photochemical reaction, a strong electron-phonon coupling can assist in polymerization. Then some non-linear spectroscopic studies are discussed which illuminate on the dynamics of photopolymerization process. Then follows a discussion of results on reaction in a different kind of molecular assembly, the Langmuir-Blodgett films. Finally, some gas-solid interface reactions which produce polymers in a doped state are discussed. 

Especially valuable to the engineer with no math lieyond elementary calculus. Emphasizing intuitive rather than formal aspects of concepts, the author covers an extensive territory. Partial contents Law of causality, energy theorem, damped oscillations, coupling by friction, cylindrical and spherical coordinates, heat source, etc. Index. 48 figures. 160pp. 5% x 8. Paperbound 1.35... 

Chaotic systems. Here the mere notion of synchrony is non-trivial, and several concepts have been developed. The effect of phase synchronization is a direct extension of the classical theory to the case of a subclass of self-sustained continuous time chaotic oscillators which admit a description in terms of phase. Synchronization of these systems can be described as a phase and frequency locking, in analogy to the theory of synchronization of noisy systems. An alternative approach considers a synchronization of arbitrary chaotic systems as a coincidence of their state variables (complete synchronization) or as an onset of a functional relationship between state variables of two unidirection-ally coupled systems (generalized synchronization). Although physical mechanisms behind the two latter phenomena essentially differ from the mechanisms of phase and frequency locking, all these effects constitute the field of application of the modern synchronization theory. 

The origin of these multiple temperature effects lies in the dependence of the kinetic rate constants on only the translational (or more generally the bath ) temperature. For vibrational states, these results were first derived for diatomic anharmonic oscillators and used to explain laser action in CO via anharmonic pumping. Multiple vibrational temperature concepts were later applied to the polyatomic molecule SF to explain discrepancies between relaxation rates measured by ultrasonic and laser techniques. The close correspondence between the temperature picture for vibrational levels weakly coupled to a thermal bath and that for nuclear or electron spin levels also weakly coupled to a thermal bath will be immediately obvious to those familiar with spin temperature concepts. ... 

The concept of intramolecular vibrational energy redistribution (IVR) can be formulated from both time-dependent and time-independent viewpoints (Li et al., 1992 Sibert et al., 1984a). IVR is often viewed as an explicitly time-dependent phenomenon, in which a nonstationary superposition state, as described above, is initially prepared and evolves in time. Energy flows out of the initially excited zero-order mode, which may be localized in one part of the molecule, to other zero-order modes and, consequently, other parts of the molecule. However, delocalized zero-order modes are also possible. The nonstationary state initially prepared is often referred to as the bright state, as it carries oscillator strength for the spectroscopic transition of interest, and IVR results in the flow of amplitude into the manifold of so-called dark states that are not excited directly. It is of interest to understand what physical interactions couple different zero-order modes, allowing energy to flow between them. A particular type of superposition state that has received considerable study are A/-H local modes (overtones), where M is a heavy atom (Child and Halonen, 1984 Hayward and Henry, 1975 Watson et al., 1981). 

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