Oscillations spontaneous

If somewhere in the loop has a delay t, then the system may become absolutely unstable The decay constant p might become negative, and the system would oscillate spontaneously. This can be shown by considering the delay t as a perturbation to the system. Actually, by letting RC = 0 in the denominator of Eq. (11.35), the poles of F s) are determined by the following algebraic equation. 

For nonlinear motors operating at far from equilibrium, velocity reversal allows direction reversal without a change in the microscopic mechanism. Molecular motors are classified in two groups depending on whether they operate in groups or individually. Those that operate in groups are relevant to muscle contraction. In principle, muscle fibers can oscillate in appropriate conditions. Skeletal muscle myofibrils can oscillate spontaneously for example, spontaneous oscillations of asynchronous muscles are common in the wings of many insects. 

Today it comes as no surprise that chemical reactions can oscillate spontaneously—such reactions have become a standard demonstration in chemistry classes, and you may have seen one yourself. (For recipes, see Winfree (1980).) But in Belousov s day, his discovery was so radical that he couldn t get his work published. It was thought that all solutions of chemical reagents must go monoton-ically to equilibrium, because of the laws of thermodynamics. Belousov s paper was rejected by one journal after another. According to Winfree (1987b, p. 161), one editor even added a snide remark about Belousov s supposedly discovered discovery to the rejection letter. 

Monte Carlo simulations show that, during a simulation, due to stochastic fluctuations, synchronized kinetic oscillations spontaneously change into spatio-temporal patterns with steady state kinetic behavior, and vice versa. Also, rotating spirals can change into pulse generators and vice versa. 

An analogous explanation at the molecular level can be proposed for the spontaneous emergence of the cardiac rhythm at a precise stage of embryonic development. This appearance of one of the most remarkable biological rhythms results from the fact that in the course of development cells in nodal tissues of the heart acquire the capability to generate periodically, in an autonomous manner, the electrical signal that initiates cardiac contraction (Fukii, Hirota Kamino, 1981). As for the neurons, the variation of certain ionic conductances would endow these cells with the property of oscillating spontaneously, while other cardiac cells would only be excitable (DeHaan, 1980). 

Stanley R J and Boxer S G 1995 Oscillations in the spontaneous fluorescence from photosynthetic reaction centers J. Phys. Chem. 99 859-63... 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

The vast majority of single-molecule optical experiments employ one-photon excited spontaneous fluorescence as the spectroscopic observable because of its relative simplicity and inlierently high sensitivity. Many molecules fluoresce with quantum yields near unity, and spontaneous fluorescence lifetimes for chromophores with large oscillator strengths are a few nanoseconds, implying that with a sufficiently intense excitation source a single... 

In the Belousov-Zhabotinskii reaction, beautiful regular patterns form spontaneously as the result of the oscillating concentrations of reactants and products due to competing reactions. 

FIGURE 17.21 In spontaneous nuclear fission, the oscillations of the heavy nucleus (a) in cffccl tear the nucleus apart, thereby forming two or more smaller nuclei of similar mass (b). Here, two neutrons are released. 

Spontaneous nuclear fission takes place when the natural oscillations of a heavy nucleus cause it to break into two nuclei of similar mass (Fig. 17.21). We can think of the nucleus as distorting into a dumbbell shape and then breaking into two smaller nuclei. An example is the spontaneous disintegration of americium-244 into iodine and molybdenum ... 

CTx that has been purified from muscles of Gymnothorax javanicus stimulates the release of neurotransmitters such as 7-aminobutyric acid and dopamine from rat brain nerve terminals. It causes a membrane depolarization of mouse neuroblastoma cells and, under appropriate conditions, it creates spontaneous oscillations of... 

Switzer et al. found that CU/CU2O layered nanostructures are electrodeposited with spontaneous potential oscillations from alkaline Cu(II)-lactate solution in a self-... 

Saliba, R., Mingotaud, C., Argoul, F. and Ravaine, S. (2002) Spontaneous oscillations in gold electrodeposition. Electrochem. Commun., 4, 629-632. 

Eskhult, J., Herranen, M. and Nyholm, L. (2006) On the origin of the spontaneous potential oscillations observed during galvanostatic deposition oflayers of Cu and CU2O in alkaline citrate solutions. J. Electroanal. Chem., 594, 35-39. 

J. O. (2001) Spontaneous potential oscillations in the Cu(II)/tartrate and lactate systems, aspects of mechanisms and film deposition. J. Electrochem. Soc., 148, C513-C517. 

The oscillation at a liquid liquid interface or a liquid membrane is the most popular oscillation system. Nakache and Dupeyrat [12 15] found the spontaneous oscillation of the potential difference between an aqueous solution, W, containing cetyltrimethylammo-nium chloride, CTA+CK, and nitrobenzene, NB, containing picric acid, H" Pic . They explained that the oscillation was caused by the difference between the rate of transfer of CTA controlled by the interfacial adsorption and that of Pic controlled by the diffusion, taking into consideration the dissociation of H Pic in NB. Yoshikawa and Matsubara [16] realized sustained oscillation of the potential difference and pH in a system similar to that of Nakache and Dupeyrat. They emphasized the change of the surface potential due to the formation and destruction of the monolayer of CTA" Pic at the interface. It is... 

In this chapter, novel oscillations observed with liquid membrane systems by the present authors [22-25] will be introduced, and the mechanisms for the oscillation are clarified by using VITIES, taking into consideration ion transfer reactions and adsorptions at two aqueous-membrane interfaces. The mechanism of the spontaneous potential oscillation in a liquid membrane system proposed by Yoshikawa et al. is also discussed briefly. 

IV. SPONTANEOUS OSCILLATIONS OF MEMBRANE POTENTIAL WITHOUT APPLIED CURRENT... 

The oscillation of membrane potential with the membrane system as in Eq. (16) has been extensively investigated as a typical example of spontaneous oscillations. 

As mentioned in the introduction, it is difficult to explain the characteristics of the oscillation based on the mechanisms which have been proposed so far for the potential oscillations with systems similar to Eq. (16) [4,7,35-38]. A precise investigation on individual ion transfers and adsorptions at two interfaces is necessary for the elucidation of the oscillation mechanism, although the spontaneous oscillation might be realized by the combination of a much larger number of ion transfer reactions and adsorptions than those in the case of the oscillation under the applied potential or current. 

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