Mode Oscillations

Otwinowski Z, Minor W. Processing of X-ray diffraction data collected in oscillation mode. Methods Enzymol 1997 276 307-26. 

Potential differences between the nitrobenzene and aqueous phases at the interfaces in the presence [Fig. 2(B)] and absence of surfactant (C) were measured simultaneously. KCl salt bridges were inserted into the octanol phase to monitor potential. Oscillation measurement data across the nitrobenzene membrane are given in Fig. 2(A) for comparison. The oscillation mode in Fig. 2(C) is virtually the same as that in (A) with respect to oscillatory period and amplitude but quite different with that in (B). Although the potential across the nitrobenzene membrane (A) was not recorded simultaneously with that between nitrobenzene-water phases (B) and (C) but successively, it was noted that the algebraic sum of (B) and (C) should be essentially the same as (A). This is an indication that potential oscillation across the nitrobenzene membrane is likely generated at the interface between the nitrobenzene phase and aqueous phase initially containing no surfactant. 

It follows from the above that the mechanism for electrical potential oscillation across the octanol membrane in the presence of SDS would most likely be as follows dodecyl sulfate ions diffuse into the octanol phase (State I). Ethanol in phase w2 must be available for the transfer energy of DS ions from phase w2 to phase o to decrease and thus, facilitates the transfer of DS ions across this interface. DS ions reach interface o/wl (State II) and are adsorbed on it. When surfactant concentration at the interface reaches a critical value, a surfactant layer is formed at the interface (State III), whereupon, potential at interface o/wl suddenly shifts to more negative values, corresponding to the lower potential of oscillation. With change in interfacial tension of the interface, the transfer and adsorption of surfactant ions is facilitated, with consequent fluctuation in interface o/ wl and convection of phases o and wl (State IV). Surfactant concentration at this interface consequently decreased. Potential at interface o/wl thus takes on more positive values, corresponding to the upper potential of oscillation. Potential oscillation is induced by the repetitive formation and destruction of the DS ion layer adsorbed on interface o/wl (States III and IV). This mechanism should also be applicable to oscillation with CTAB. Potential oscillation across the octanol membrane with CTAB is induced by the repetitive formation and destruction of the cetyltrimethylammonium ion layer adsorbed on interface o/wl. Potential oscillation is induced at interface o/wl and thus drugs were previously added to phase wl so as to cause changes in oscillation mode in the present study. 

In this study, potential oscillation was measured in the presence of lOOmM sodium salts of barbital, allobarbital, phenobarbital, and amobarbital in phase wl [19]. Their chemical structures are shown in Fig. 15. Amplitude and the oscillatory and induction periods were noted to depend on the particular hypnotic used. Amplitude decreased in the order, barbital > allobarbital > phenobarbital > amobarbital. The oscillatory period increased in the order, barbital < allobarbital < phenobarbital < amobarbital. Induction period increased in the order, barbital < allobarbital < phenobarbital < amobarbital. These parameters changed depending on drug concentration. Hypnotics at less than 5 mM had virtually no effect on the oscillation mode. 

Antibiotics may be classified by chemical structure. Erythromycin, chloramphenicol, ampicillin, cefpodoxime proxetil, and doxycycline hydrochloride are antibiotics whose primary structures differ from each other (Fig. 19). Figure 20 shows potential oscillation across the octanol membrane in the presence of erythromycin at various concentrations [23]. Due to the low solubility of antibiotics in water, 1% ethanol was added to phase wl in all cases. Antibiotics were noted to shift iiB,sDS lo more positive values. Other potentials were virtually unaffected by the antibiotics. On oscillatory and induction periods, there were antibiotic effects but reproducibility was poor. Detailed study was then made of iiB,sDS- Figure 21 (a)-(d) shows potential oscillation in the presence of chloramphenicol, ampicillin, cefpodoxime proxetil, and doxycycline hydrochloride [21,23]. Fb.sds differed according to the antibiotic in phase wl and shifted to more positive values with concentration. No clear relationship between activity and oscillation mode due to complexity of the antibacterium mechanism could be discovered but at least it was shown possible to recognize or determine antibiotics based on potential oscillation measurement. 

The artificial sweeteners erythritol, sodium saccharin, and aspartame (Fig. 25) were also studied. Figure 26 shows potential oscillation in the presence of these artificial sweeteners [22]. The oscillation modes of these substances differed considerably. For erythritol above 10 mM, Fa.sds slightly shifted to more negative potentials. and Fb.sds were essentially unaffected by this sweetener. Erythritol thus induces change in the oscillation mode in much the same way as sugars. At 1 mM-1 M sodium saccharin, E and Fa.sds shifted to more negative values with increase in its concentration. For aspartame at less than 10 mM, there was no change in potential. 

Figure 27 shows potential oscillation in the presence of quinine hydrochloride and sucrose as a mixture [21]. The mean value of low potentials of the initial five pulses was taken as b,sds- In the presence of ImM quinine hydrochloride without sucrose, in contrast to oscillation without any substance in phase wl, iiB,sDS was more positive by 56 mV and E and a,sds> slightly more negative. This change was due only to quinine hydrochloride. With sucrose in addition to quinine hydrochloride, iiB,sDS shifted to more negative values. With 1 mM quinine hydrochloride and 500 mM sucrose, the oscillation mode was basically the same as with only 500 mM sucrose. 

Stenning, A. H., and T. N. Veziroglu, 1965, Flow Oscillations Modes in Forced Convection Boiling, Proc. 1965 Heat Transfer and Fluid Mechanics Inst., pp. 301-316, Stanford University Press, Palo Alto, CA. (6)... 

In Eqs. (II. 1)—(II.4) we have assumed that there is only one system oscillator. In the case where there exists more than one oscillator mode, in addition to the processes of vibrational relaxation directly into the heat bath, there are the so-called cascade processes in which the highest-frequency system mode relaxes into the lower-frequency system modes with the excess energy relaxed into the heat bath. These cascade processes can often be very fast. The master equations of these complicated vibrational relaxation processes can be derived in a straightforward manner. 

In addition to the deformation modes described above, there are some other modes of practical interest, for example, the cyclic spreading, recoiling, and oscillation mode typical of solder jetting process.[5°1 This mode leads to a final splat shape of multiple surface ripples at low substrate temperatures and hemispherical shape without surface ripples at high substrate temperatures. 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

Equations (4) and (8) can be used to simulate the reactor at point P3 of Figure 5 in [1]. Remember that point P2 is unstable, so if the initial conditions are those corresponding to this point, it is easy to show [16], [28], the reactor evolves to points P or P3. Then, two forcing actions on the reactor are considered 1) when the coolant flow rate and the inlet stream temperature are varied as sine waves, and 2) reactor being in self-oscillating mode, an external disturbance in the coolant flow rate can drive it to chaotic behavior. 

The single-mode laser naturally gives less output power than a multimode laser with the same active volume since its induced emission is concentrated into a smaller frequency range. This loss in intensity, however, is much less than one would expect from the ratio of linewidths or from the reduction in oscillating mode number 3i. 32,41) jbis is due to the fact, that not only atoms with the exact transition frequency can contribute to the induced emission, but also those inside the homogeneous linewidth which is determined by collision processes in the case of gas lasers or by crystal line broadening in solid lasers... 

The last method has been pushed to an impressive sensitivity by putting the probe inside the cavity of a cw dye laser oscillating on several modes close above threshold. The sensitivity of such a broad-band dye laser to selective intracavity absorption on a single mode is proportional to the number of oscillating modes due to... 

When combustion instability occurs for an internal burning grain of a rocket motor, the burning rate of the grain varies with time and so does the pressure in the rocket motor. The pressure versus time curve shows oscillations of a certain frequency. When the propellant burning mode is not in harmony with the pressure oscillation mode, the combustion instabiUty tends to decay. However, when the burning mode is in harmony with the oscillation mode, the pressure oscillation is amplified. 

Otwinowski, Z. and Minor, W. (1997). Processing of X-ray Diffraction Data Collected in the Oscillation Mode. Method Enzymol. 276A, 307-326. 

Avery sharp electromechanical resonance occurs at certain discrete frequencies of the voltage applied. If mass is added to the surface of the quartz crystal oscillating in resonance, this resonance frequency is diminished. This frequency shift is very reproducible and is now understood precisely for various oscillation modes of quartz. Today this phenomenon, which is easy to understand in heuristic terms, is an indispensable measuring and process control fool, with which a coating increase of less than one atomic layer can be detected. 

We shall call the frequency at which t = —2em and t" — 0 the Frohlich frequency coF the corresponding normal mode—the mode of uniform polarization—is sometimes called the Frohlich mode. In his excellent book on dielectrics, Frohlich (1949) obtained an expression for the frequency of polarization oscillation due to lattice vibrations in small dielectric crystals. His expression, based on a one-oscillator Lorentz model, is similar to (12.20). The frequency that Frohlich derived occurs where t = —2tm. Although he did not explicitly point out this condition, the frequency at which (12.6) is satisfied has generally become known as the Frohlich frequency. The oscillation mode associated with it, which is in fact the lowest-order surface mode, has likewise become known as the Frohlich mode. Whether or not Frohlich s name should be attached to these quantities could be debated we shall not do so, however. It is sufficient for us to have convenient labels without worrying about completely justifying them. 

A one-level system e) that can exchange its population with the bath states [/) represents the case of autoionization or photoionization. However, the above Hamiltonian describes also a qubit, which can undergo transitions between the excited and ground states e) and g), respectively, due to its off-diagonal coupling to the bath. The bath may consist of quantum oscillators (modes) or two-level systems (spins) with different eigenfrequencies. Typical examples are spontaneous emission into photon or phonon continua. In the RWA, which is alleviated in Section 4.4, the present formalism applies to a relaxing qubit, under the substitutions... 

Apparently, in field depositing reduces also slightly the coercivity (from 6 mT to 4 mT). High-amplitude flexural and torsional-oscillation modes were observed for these films. 

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