Oscillatory media

In the rest of the discussion, we shall focus on the behavior of our model at 490 K, unless stated otherwise. When diffusion is absent, the system behaves as an excitable medium. When diffusion is included, the system behaves as an excitable or an oscillatory medium, depending on the relative gas phase pressures. In an excitable medium, the system is in a stable state and will return to that state when perturbations are applied. Upon small perturbations, the system returns to its stable state, whereby it makes only a small excursion in phase space. Often, it will turn directly back to the stable state. When the perturbation has a sufficiently large amplitude, the system will show a strong dynamic response. It will make a large excur-... 

Consider the continuum description of an oscillatory medium subject to advection and diffusion... 

In the previous oscillatory systems, the local dynamics was assumed to be the same everywhere in space and the synchronization of identical oscillatory regions was studied. In many cases the oscillatory medium is not uniform. In real chemical or biological systems this can be a consequence of non-uniform external conditions, like variation of temperature, or of illumination in a photosensitive reaction,... 

Our attention is focused on the properties of periodic trains formed by kinks or traveling Bloch walls. Our analysis reveals that, depending on the parameters of the oscillatory medium and the spatial period of a train, it can undergo a reversal of its propagation direction [19]. We show how this phenomenon can be used to design traps for traveling kinks and Bloch walls. Furthermore, we find that a new kind of patterns - twisted rotated spiral waves - exist in oscillatory media under the conditions of front propagation reversal. 

In conclusion, the study of models for Ca signalling indicates that the phenomena of Ca oscillations and waves are closely intertwined. The spatiotemporal patterns correspond to the propagation of a Ca front in a biochemically excitable or oscillatory medium, at a rate much higher than that associated with simple diffusion. Such a property could also underlie a possible role of Ca waves in intercellular communication (Charles et al., 1991). The results presented in figs. 9.30 and 9.31 show that a unique mechanism, based on CICR, can account for the... 

Bouzat, S., Wio, H.S. Pattern formation in inhomogeneous active media a localized bistable domain immersed in an oscillatory medium. Phys. Lett. A 268(4-6), 323-329 (2000). http //dx.doi.org/10.1016/S0375-9601(00)00181-X... 

The bottom line of Table IV gives the calculated recurrence times for critical fluctuations in Br. The smallest recurrence time seen in Table IV is the amount of time necessary to wait for [Br ] to fluctuate to the critical bromide concentration within at least one small sphere of radius 0.5 /rm anywhere within the total volume of the excitable system studied. This minimum recurrence time of 10 seconds, or one billion years, is in fact the smallest recurrence time obtained from all our calculations considering fluctuations in any species for either the excitable or oscillatory medium. Clearly, such critical perturbations predicted by the deterministic equations necessary for the initiation of a chemical wave have vanishingly small probabilities of occurring spontaneously in solution. 

In a similar vain, the period of the waves in an oscillatory medium we consider in our calculations is identical to the period the bulk medium. Experimentally, spontaneous waves in oscillatory media generally have a period smaller than the bulk period. Again, the initial perturbation necessary to induce waves of a shorter period would be laiger than the perturbation to initiate waves of equal period of the bulk as the more frequent waves would... 

We first consider an apparently simple situation a trigger wave in an oscillatory medium. The period-1 limit cycle that exists for small K2 values to the left of the period doubling cascade shown in Figure 2 takes on a relaxation character as 2 is increased towards period-2. If the temporal profile of such an oscillation is transcribed into the spatial domain a trigger wave is formed as is shown in the top panel of Figure 7. To obtain the results in this panel... 

Budroni, M.A., Rossi, F. A novel mechanism for in situ nucleation of spirals controlled by the interplay between phase fronts and reaction diffusion waves in an oscillatory medium. J. Phys. Chem. C 119(17), 9411-9417 (2015) Carballido-Landeira, J., Trevelyan, P.M.J., Almarcha, C., De Wit, A. Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes. Phys. Fluids 25(2), 024107 (2013)... 

Budroni, M.A., Rossi, F. A novel mechanism for in situ nucleation of spirals controlled by the interplay between phase fronts and reaction diffusion waves in an oscillatory medium. J. Phys. Chem. C 119(17), 9411-9417 (2015)... 

Busch B W and Gustafsson T 1998 Oscillatory relaxation of Al(110) reinvestigated by using medium-energy ion scattering Surf. Set 415 LI 074... 

The local dynamics of tire systems considered tluis far has been eitlier steady or oscillatory. However, we may consider reaction-diffusion media where tire local reaction rates give rise to chaotic temporal behaviour of tire sort discussed earlier. Diffusional coupling of such local chaotic elements can lead to new types of spatio-temporal periodic and chaotic states. It is possible to find phase-synchronized states in such systems where tire amplitude varies chaotically from site to site in tire medium whilst a suitably defined phase is synclironized tliroughout tire medium 51. Such phase synclironization may play a role in layered neural networks and perceptive processes in mammals. Somewhat suriDrisingly, even when tire local dynamics is chaotic, tire system may support spiral waves... 

Effective medium theory, 37 154 Eggshell catalysts, 39 231 EH method, 37 153 EHT, see Extended Hiickel treatment Eigenberger model, oscillatory reactions, 39 80-81, 83... 

Combustion of a propellant in a rocket motor accompanied by high-frequency pressure oscillation is one of the most harmful phenomena in rocket motor operation. There have been numerous theoretical and experimental studies on the acoustic mode of oscillation, concerning both the medium-frequency range of 100 Hz-1 kHz and the high-frequency range of 1 kHz-30 kHz. The nature of oscillatory combustion instability is dependent on various physicochemical parameters, such... 

Low-Viscosity Media. The time is measured that is required to produce a homogeneous suspension of particles in the dispersion medium using an oscillatory shaking... 

Cavitation is the formation of gaseous cavities in a medium upon ultrasound exposure. The primary cause of cavitation is ultrasound-induced pressure variation in the medium. Cavitation involves either the rapid growth and collapse of a bubble (inertial cavitation) or the slow oscillatory motion of a bubble in an ultrasound field (stable cavitation). Collapse of cavitation bubbles releases a shock wave that can cause structural alteration in the surrounding tissue [13]. Tissues contain air pockets trapped in the fibrous structures that act as nuclei for cavitation upon ultrasound exposure. The cavitational effects vary inversely with ultrasound frequency and directly with ultrasound intensity. Cavitation might be important when low-frequency ultrasound is used, when gassy fluids are exposed, or when small gas-filled spaces are exposed. 

The model was solved by a numerical method based on BAND and orthogonal collocation.21 This method was suitable for solving this model, but in the case of the highest applied potential exhibited oscillatory, fluctuating behavior. Figure 21 shows the typical potential and concentration distributions under medium potential conditions for 2-D model. 

The average lifetime of a coagulated pair (doublet) of small particles can be calculated by examining the relative Brownian motion of the particle pair in the interaction potential well- If the energy imparted by the collisions of the molecules of the medium is smaller than the depth of the interaction potential well, the particle pair will exhibit an oscillatory motion within the potential well. It will be shown later that, for sufficiently small particles, the time scale of these oscillations is much smaller than... 

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