Antiphase oscillations

In [53], oscillatory wave patterns observed during electrochemical dissolution of a nickel wire in acidic media was reported. It was shown that space-averaged potential or current oscillations are associated with the creation of an inhomogeneous current distribution, and that the selection of a specific spatial current pattern depends on the current control mode of the electrochemical cell. In the almost potentiostatic (fixed potential) mode of operation, a train of traveling pulses prevails, whereas antiphase oscillations occur in the galvanostatic (constant average current) mode. 

Fig. 64. Local current distribution of antiphase oscillations during the dissolution of Ni under galvano-static control. (Reproduced with permission from O. Lev, M. Sheintuch, L. M. Pismen, and C. Yarnitzky, Nature 336, 488, 1988, (1988) Macmillan Magazines Limited.)...

During galvanostatic oscillations, the current in one part of the electrode was always found to be shifted by 180° relative to the other part of the electrode. This behavior was maintained down to the smallest electrodes tested, which had a length of 1 cm. An example of these antiphase oscillations, also referred to as standing waves, is shown in Fig. 66. 

When the electrodes are covered with only a thin layer of solution, a potential gradient along the working electrode can arise, which leads to chaotic potential oscillations under galvanostatic conditions. In this chaotic regime, the current distribution still exhibited the general features of the antiphase oscillations, hut the maximum local amplitude as well as the period of the oscillations varied from one oscillation cycle to the next. 

When an external resistor was incorporated between the working and reference electrodes, and the system was operated under potentiostatic conditions, the antiphase oscillations became transformed into traveling pulses with velocities of about 4.5 m s. ... 

The discussion of the experimental results in Section in.2 shows that a fundamental understanding of pattern formation in electrochemical systems has been achieved. However, it also demonstrates that the present state represents just a first step toward a complete picture of possible dynamic behaviors. There are many observations that cannot yet be explained, for example, the spatiotemporal period-doubling bifurcation detected during the electrodissolution of iron, the occurrence of antiphase oscillations during Ni electrodissolution, or the emergence of modulated waves during the electrodissolution of Co. Nevertheless, these phenomena seem to be understandable through an extension of the models introduced in Section III.l. 

Localized clusters arise if the initial reagent concentrations are close to the parameter space boundary between the oscillatory and the reduced steady state regions. Domains of antiphase oscillations in localized clusters occupy only part of the area, while no pattern can be seen in the remaining part of the system. Figure 9 shows two snapshots separated by half a period of oscillations. There are two adjacent large domains of antiphase oscillations separated by a nodal line. The two small domains at the ri t boundary of the st frame and one small domain near the left boundary are transients that subsequently die off. 

Subsequent studies revealed that the transcription of Rev-erba, is regulated by essentially the same mechanisms as those of Per and Cry genes it is activated by BMALl and CLOCK and repressed by PER and CRY. Therefore, REV-ERBa directly connects two antiphasic feedback loops within the positive and negative limbs of the oscillator (Fig. 1). 

Hastings I am not a geneticist, but it is safe to say that penetrance isn t complete. Some of the animals are completely arrhythmic, but most of them aren t. This is a phenotype we have seen in several different animal facilities. These mice are interesting at a number of levels. For example, they can be useful as a model to study the liver devoid of SCN control. As for the origin of the antiphasic behaviour, it is a systems neuroscience question. Recent work from Mike Menaker s lab (Abe et al 2002) has shown the existence of weak extra-SCN oscillators in the brain which may or not be involved in the antiphasic behaviour of Vpacl knockout mice under dark—dark conditions (DD). 

Darlington et al 1998, Emery et al 1998). However, these oscillations are antiphase to those of per and tim, suggesting that they are indirect targets of the... 

Figure 6.5 Dynamics of a classical electric dipole induced and driven on resonance by a sequence of two phase-locked ultrashort laser pulses, The driving laser field is shown as gray solid lines in all frames, In addition, the top frames show the induced dipole oscillation as a black dashed line. The instantaneous interaction energy V(t) of the induced dipole in the external driving field is shown in the bottom frames as a black dotted line. Bold black lines display the time average of the interaction energy In Figure 6,5a, the phase relation between both pulses is designed such that the second pulse couples in antiphase to...

In order to switch the system into the upper target state 5) merely the sine-phase 0 has to be varied by half an optical cycle, that is, by A(p = n. In this case, the main pulse is phase-shifted by Af = -l- r/2 with respect to the pre-pulse and couples in antiphase to the induced charge oscillation. Hence, the interaction energy is maximized and the upper dressed state u) is populated selectively. Due to the energy increase, the system rapidly approaches the upper target state 5). The ensuing nonadiabatic transitions between the dressed states u) and 1 5) result in a complete population transfer from the resonant subsystem to the upper target state, which is selectively excited by the end of the pulse. 

This shows that the eigenstate interferograms oscillates in antiphase between the neighboring levels. These features are clearly seen in Figure 7.10. 

The cell cycle automaton model permits us to clarify the reason why circadian delivery of 5-FU is least or most toxic when it peaks at 4 a.m. or 4 p.m., respectively. Indeed, the model allows us to determine the position of the peak in S-phase cells relative to that of the peak in 5-FU. As shown in Fig. 10.5, 5-FU is least cytotoxic when the fraction of S-phase cells oscillates in antiphase with 5-FU (when 5-FU peaks at 4 a.m.) and most toxic when both oscillate in phase (when 5-FU peaks at 4 p.m). Intermediate cytotoxicity is observed for other circadian patterns of 5-FU (when the drug peaks at 10 a.m. or 10 p.m.), for which the peak of 5-FU partially overlaps with the peak of S-phase cells. For the continuous infusion of 5-FU, the peak in S-phase cells necessarily occurs in the presence of a constant amount of 5-FU. Hence, the constant delivery pattern is nearly as toxic as the circadian pattern peaking at 4 p.m. 

To some extent the idea of resonance is also present in the case of circadian 5-FU delivery. Indeed, the circadian patterns of 5-FU which peak at 4 a.m. or 4 p.m. correspond to oscillations that are, respectively, in antiphase or in corresponding phase with the circadian variation of the fraction of cells in S phase. This effect can be seen even for cell cycle durations that differ from 24 h, because of the entrainment of the cell cycle by the circadian clock. 

At some point in this oscillation, we execute the simultaneous 90° pulses and transfer this magnetization to antiphase 13C coherence (28 1 ), which oscillates at the frequency in the 13C spectrum of the 13C (Cb) that is bonded to Ha This oscillation is recorded in the... 

The challenging task of high frequency resonators arises from inharmonic modes, often called spurious modes or spurs. These are characterized by movement of particles in several regions of the quartz disc in antiphase. If the frequency separation between the harmonic and inharmonic modes is not sufficiently large, modes can efficiently be coupled. Frequency jumps of quartz oscillators are an unwanted effect that impedes a reliable frequency measurement. Spurious modes, especially those which lie close to the resonance frequency, enhance the challenges of oscillator design. 

From measurements of the temporal variations of chemical species, comparison is made of the phases of as many essential oscillating species as possible. The phases of the species are assigned as in phase (I), antiphase (A), advanced (+), or delayed (-) with respect to the oscillations of a reference species. This results in a sign-symbolic phase shift matrix. The sign-symbolic shift matrix Athsymb for the prototype of each category is given in table 11.2. 

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