Global oscillations

Strykowski, P. J., and R. K. Wilcoxon. 1993. Mixing enhancement due to global oscillations in jet with annular counterflow. AIAA J. 31 3. 

But what does the Sun provide us with in the way of measurable quantities How can we guarantee the veracity of our model stars The key quantities all concern the surface intrinsic brightness, radius and effective temperature, that is, the temperature of the equivalent blackbody. But new constraints have now been added to this visible data, this time directly affecting the depths of our great star. These are the neutrino flux and global oscillations of the Sun s great body. 

Helioseismic waves are detected by measuring the Doppler shift of lines in the solar spectrum due to vertical motion of the Sun s surface along the line of sight. With appropriate data-reduction techniques, the frequencies for global oscillations can be determined to an accuracy of 5 ppm. This extreme accuracy requires long-term, continuous observations that are best done by spacecraft such as the joint ESA/NASA SOHO spacecraft, which observes the Sun from the Lagrangian point where the Earth gravity balances that of the Sun. 

Figure 8 Low-frequency spectta of MbCO, deoxyMb, and photolyzed MbCO (Mb ). Shoulders on the recoilless absorption line are attributed to translational motion of the heme in response to global oscillations of the surrounding protein matrix, and become more prominent with increasing temperature. Filled circles overlaid on the photolyzed MbCO spectrum represent the spectrum of imphotolyzed MbCO. Subtraction of the latter two spectra reveals no measurable influence of ligand binding on these vibrations...

H. Hempel, L. Schimansky-Geier, and J. Garcia-Ojalvo. Noise-sustained pulsating patterns and global oscillations in subexcitable media. Phys. Rev. Lett,... 

Figure 6 Family of cluster patterns observed in experiments for variable strength g of the global negative feedback. Snapshots of cluster patterns are separated in time by one period of global oscillation.

Theoretical studies of defect-mediated turbulence in two-dimensional systems have generally followed two approaches. One starts with local oscillators that couple through a diffusion process [36] another starts from a stationary patterned state [49] (see also the discussion of [10]). Both approaches lead to a turbulent state. However, our data do not distinguish in an obvious way between these two approaches. We do not observe any hint of global oscillations in the neighborhood of the transition from hexagons or stripes to turbulence, as would be expected in the first hypothesis. Nor do we observe any indication of a spatially biperiodic pattern, as would be expected in the second hypothesis. More experiments and analyses are needed to characterize and understand the mechanism of chemical turbulence. 

Ropelewski, C. F. and Halpert, M. S. (1987). Global and regional scale precipitation patterns associated with the El Nino/Southem Oscillation. Mon. Wea. Rev. 115,1606-1626. 

Straile D, Adrian R (2000) The North Atlantic Oscillation and plankton dynamics in two European lakes - two variations on a general theme. Global Change Biol 6 663-670... 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

Let us now consider the velocity autocorrelation function (VACF) obtained from the MCYL potential, (namely, with the inclusion of vibrations). Figure 3 shows the velocity autocorrelation function for the oxygen and hydrogen atoms calculated for a temperature of about 300 K. The global shape of the VACF for the oxygen is very similar to what was previously determined for the MCY model. Very notable are the fast oscillations for the hydrogens relative to the oxygen. 

One can see that the coupling between the two oscillators is proportional to qiq2, and that the global minimum of Eq. (7.55) occurs when qt = l. The potential function (7.55) can be rewritten in a variety of ways by making appro-... 

---