Internal resonance

The foundation and machine body/structure must prevent internal resonance, which is possible by slightly altering their designs. 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

For both H.F. modes a choice can be made from a few possibilities of measurement, viz., the observance of voltage and current in the ac circuit at a frequency imposed externally, or the establishment of internal resonance conditions where... 

Antioxidants act so as to interrupt this chain reaction. Primary antioxidants, such as hindered phenol type antioxidants, function by reacting with free radical sites on the polymer chain. The free radical source is reduced because the reactive chain radical is eliminated and the antioxidant radical produced is stabilised by internal resonance. Secondary antioxidants decompose the hydroperoxide into harmless non-radical products. Where acidic decomposition products can themselves promote degradation, acid scavengers function by deactivating them. 

Fig. 13 shows an example where data for an irregular struetured multilayer thin-film-filter (TFF) are imported into a waveguide design. A FDTD-simulation earned out in order to check the influence of the internal resonator-like strueture of the TFF onto the waveguide deviee shows a signifieant transversal shift for oblique incidence. This hinders symmetrical multi-port designs, but may be used for specific WDM functionality. ... 

Quinoline is a base since, as for pyridine, the lone pair of electrons on the nitrogen atom is not utilized in its internal resonance. Although it is an aromatic compound, the valence bond description of quinoline shows two of the neutral contributors, A and C (see Scheme 3.1), to the resonance hybrid as quinonoid in character, whereas in B either the carbo-cycle or the heterocycle must exist in the form of a 1,3-diene. The presence of the pyridine nucleus is reflected by the inclusion of doubly charged canonical forms. 

Resonance within the unsaturated lactone unit of coumarin gives a strong hint as to its likely reactivity. Thus, the oxygen atom of the carbonyl group receives electron density both via the enone chromophore and from the internal resonance of the lactone group (Scheme 5.2). 

Pyrrole and its simple derivatives do not react easily as dienes. Pyrrole itself only combines with dimethyl acetylenedicarboxylate (DMAD, dimethyl but-2-ynedicarboxylate) under high pressure and then it is by C-2 substitution. However, A-acylpyrroles, such as A-acetyl- and N- tert-butoxycarbonyl)pyrrole, do undergo Diels-AIder addition reactions. Here, internal resonance within the acyl group reduces the availability of the lone-pair electrons, formally on nitrogen, to delocalize into the ring, thus making the carbon unit more diene-like (Scheme 6.12). 

R. A. Marcus Prof. Schinke has certainly described an array of exciting results. In the case where your wave functions showed a complicated pattern, it would be useful (for the case of an isolated internal resonance) to seek out the relevant vibrational periodic trajectories to sort out the series of such states and relate (directly or indirectly) to Kellman s algebraic analysis of bound states. 

R. A. Marcus Perhaps the following remark relates to Stuart Rice s question regarding invertibility and quantum chaos . One might regard quantum chaos as corresponding to the overlapping of a number of internal resonances. In that case, if your method doesn t apply when several resonances overlap, it wouldn t, of course apply and probably wasn t intended to apply, to quantum chaos . 

In chapter 8, we discussed the sensitivity of carbon production to various physical parameters. Carbon is made inside stars and is the basis of life on Earth. The difficulty is to get two helium nuclei in the Sun to stick together until they are struck by a third.13 It turns out that this is accomplished only because of internal resonances of carbon and oxygen nuclei. If the carbon resonance level were only 4 percent lower, carbon atoms wouldn t form. If the oxygen resonance level were only half a percent higher, almost all the carbon would disappear as it combined with helium to form oxygen.14 This means that human existence depends on the fine-tuning of these two nuclear resonances. Of these resonances, the famous astronomer Sir Fred Hoyle said that his atheism was shaken by these facts ... 

The charge transfer complex resulting from the one-electron transfer from the electron donor monomer to the electron acceptor monomer has a stability which varies as a function of the internal resonance stabilization. The degree of stabilization apparently determines the ease with which the diradical complex opens, and consequently the stability of the complex determines whether the copolymerization occurs spontaneously or under the influence of heat, light, or free radical attack. 

A. J. Szeri and L. G. Leal, The onset of chaotic oscillations and rapid growth of a gas bubble at subcritical conditions in an incompressible liquid, Phys. Fluids A3, 551-5 (1991) Z. C. Feng and L. G. Leal, Bifurcation and chaos in shape and volume oscillations of a periodically driven bubble with two-to-one internal resonance, J. Fluid Mech. 266, 209-42 (1994) L. G. Leal and Z. C. Feng, Nonlinear bubble dynamics, Annu. Rev. Fluid Mech. 29, 201-42 (1997). 

You respond with an internal resonance You know Truth when you hear it. 

The first detailed discussion of the various dissipation processes occurring in an acoustic cavity was given by Kamm in 1976 These losses can be divided into surface effects and volumetric effects. The surface effects are due to the interaction of the standing wave with the internal resonator surface and may be subdivided into the following dissipation processes. 

The stability of charge-transfer complexes depends upon internal resonance stabilization. This degree of stabilization determines how easily the diradical opens up. Consequently, this stability also determines how the copolymerization occurs. It can occur spontaneously, or under the influence of light or heat, or because of an attack by an initiating free radical. 

Estimate the optimum transmission of the laser output mirror if the unsaturated gain is 2 and the internal resonator losses are 10. 

The occurrence of internal resonance between the dominant frequency of the incoming open-ocean waves and the fundamental harbor mode frequency. 

A classical microcanonical ensemble for an intrinsie non-RRKM molecule consists of chaotic, vague tori and quasiperiodic trajeetories. Such a complex non-ergodie phase spaee strueture leads to a non-exponential P i). As an applieation of the KAM theorem, Oxtoby and Riee have shown that the intrinsic non-RRKM dynamics that Bunker found for model triatomic Hamiltonians results from insufficient internal resonances to yield ergodic dynamics. 

Among the aliphatic species the best evidence for a monomeric radical cation exists for r-Bu2S which derives its particular stability from internal resonance. It exhibits a distinct UV absorption band which in aqueous solution peaks at 310 nm[129]. 

---