Regime-transition phenomenon

The above ratio is the so-called regime-transition phenomenon, evidenced by many experimental observations as well as molecular simulations. 

To understand properly the relationship between the glass transition phenomenon observed in computer-simulated systems and that observed in laboratory systems, it is necessary to be familiar with the temperature dependence of the relaxation time. The point to be made is that the transition, which is the thermodynamic manifestation of a failure to maintain equilibrium during cooling, occurs sharply in laboratory systems but diffusely in simulated systems, primarily because of a great difference in relaxation time temperature (or volume) dependence in the time-scale regimes in which the processes are observed in the two cases. 

Bubble dynamics and characteristics discussed above determine the hydrodynamic and heat and mass transfer behaviors in three-phase fluidization systems, which is important for better design and operation of three-phase fluidized beds. In this section, various hydrodynamic variables and transfer properties in three-phase systems are discussed. Specifically, areas discussed in the hydrodynamics section are minimum fluidization, bed contraction and moving packed bed phenomenon, flow regime transition, overall gas holdup and hydro-dynamic similarity, and bubble size distribution and the dominant role of larger bubbles. Later in this section, important topics covering transport phenomena will be discussed, which include heat and mass transfer and phase mixing. 

The transition from laminar to turbulent flow on a rotating sphere occurs approximately at Re = 1.5 4.0 x 104. Experimental work by Kohama and Kobayashi [39] revealed that at a suitable rotational speed, the laminar, transitional, and turbulent flow conditions can simultaneously exist on the spherical surface. The regime near the pole of rotation is laminar whereas that near the equator is turbulent. Between the laminar and turbulent flow regimes is a transition regime, where spiral vortices stationary relative to the surface have been observed. The direction of these spiral vortices is about 4 14° from the negative direction of the azimuthal angle,. The phenomenon is similar to the flow transition on a rotating disk [19]. 

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

Undoubtedly, the most promising modehng of the cardiac dynamics is associated with the study of the spatial evolution of the cardiac electrical activity. The cardiac tissue is considered to be an excitable medium whose the electrical activity is described both in time and space by reaction-diffusion partial differential equations [519]. This kind of system is able to produce spiral waves, which are the precursors of chaotic behavior. This consideration explains the transition from normal heart rate to tachycardia, which corresponds to the appearance of spiral waves, and the fohowing transition to fibrillation, which corresponds to the chaotic regime after the breaking up of the spiral waves, Figure 11.17. The transition from the spiral waves to chaos is often characterized as electrical turbulence due to its resemblance to the equivalent hydrodynamic phenomenon. 

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