Dynamic instability

B14. Becker, K. M., Jahnberg, S., Haga, I., Hansson, P. T. and Mathisen, R. P., Hydro-dynamic instability and dynamic burn-out in natural circulation two-phase flow. An experimental and theoretical study, Nukleonik 6, 224 (1964). 

Kakac S, Bon B (2008) A review of two-phase flow dynamic instabilities in tube boiling systems. Int. J. Heat Mass Transfer 51 399 33... 

Newport-. The way that spindles and microtubules are normally reoriented is by the stabilization of dynamic instability at the plus-end of the microtubule. So if microtubules were to embed in this apically localized complex, they would effectively be capped and this would reorient the spindle. One would expect that this would happen to the centriole prior to mitosis, so that the interphase microtubules would be stabilized at that location as well. Are you saying this doesn t happen If it doesn t happen, perhaps Cdc2 is necessary to activate this apical region for stabilizing plus ends, and this would explain why it rocks about. Are any of these molecules potential candidates for capping microtubules at the plus-end, for instance ... 

In Chapter 3 the steady-state hydrodynamic aspects of two-phase flow were discussed and reference was made to their potential for instabilities. The instability of a system may be either static or dynamic. A flow is subject to a static instability if, when the flow conditions change by a small step from the original steady-state ones, another steady state is not possible in the vicinity of the original state. The cause of the phenomenon lies in the steady-state laws hence, the threshold of the instability can be predicted only by using steady-state laws. A static instability can lead either to a different steady-state condition or to a periodic behavior (Boure et al., 1973). A flow is subject to a dynamic instability when the inertia and other feedback effects have an essential part in the process. The system behaves like a servomechanism, and knowledge of the steady-state laws is not sufficient even for the threshold prediction. The steady-state may be a solution of the equations of the system, but is not the only solution. The above-mentioned fluctuations in a steady flow may be sufficient to start the instability. Three conditions are required for a system to possess a potential for oscillating instabilities ... 

Simple dynamic instability. Single dynamic instability involves the propagation of disturbances, which in two phase flow is itself a very complicated phenomenon. Disturbances are transported by two kinds of waves pressure (or acoustic) waves, and void (or density) waves. In any real system, both kinds of waves are present and interact but their velocities differ in general by one or two orders of... 

Compound dynamic instabilities as secondary phenomena. Pressure-drop oscillations are triggered by a static instability phenomenon. They occur in systems that have a compressible volume upsteam of, or within, the heated section. Maul-betsch and Griffith (1965, 1967), in their study of instabilities in subcooled boiling water, found that the instability was associated with operation on the negative-sloping portion of the pressure drop-versus-flow curve. Pressure drop oscillations were predicted by an analysis (discussed in the next section), but because of the... 

To analyze dynamic instabilities, the above equations have been programmed as computer codes such as STABLE (Jones and Dight, 1961-1964), DYNAM (Efferding, 1968), HYDNA (Currin et al., 1961), RAMONA (Solverg and Bak-stad, 1967), and FLASH (Margolis and Redfield, 1965). 

Computer codes Because of the computer s ability to handle the complicated mathematics, most of the compounded and feedback effects are built into computer codes for analyzing dynamic instabilities. Most of these codes can analyze one or more of the following instabilities density wave instability, compound dynamic instabilities such as BWR instability and parallel-channel instability, and pressure drop oscillations. 

The connection between anomalous conductivity and anomalous diffusion has been also established(Li and Wang, 2003 Li et al, 2005), which implies in particular that a subdiffusive system is an insulator in the thermodynamic limit and a ballistic system is a perfect thermal conductor, the Fourier law being therefore valid only when phonons undergo a normal diffusive motion. More profoundly, it has been clarified that exponential dynamical instability is a sufRcient(Casati et al, 2005 Alonso et al, 2005) but not a necessary condition for the validity of Fourier law (Li et al, 2005 Alonso et al, 2002 Li et al, 2003 Li et al, 2004). These basic studies not only enrich our knowledge of the fundamental transport laws in statistical mechanics, but also open the way for applications such as designing novel thermal materials and/or... 

Chandrasekhar, S. (1964). The dynamical instability of gaseous masses approaching the Schwarz-schild limit in general relativity. Astrophys. J., 140 417—433. 

Since the concern here is with the destruction of a contiguous laminar flame in a turbulent field, consideration must also be given to certain inherent instabilities in laminar flames themselves. There is a fundamental hydro-dynamic instability as well as an instability arising from the fact that mass and heat can diffuse at different rates that is, the Lewis number (Le) is nonunity. In the latter mechanism, a flame instability can occur when the Le number (oJD) is less than 1. 

Figure 13. Diagram showing how dynamical instability characterized by the sum of positive Lyapunov exponents > o contributes to dynamical randomness characterized by the Kolmogorov-Sinai entropy per unit time h s and to the escape y due to transport according to the chaos-transport formula (95).

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