Bursting dynamics

Finally, Section 2.4 analyses a simplified model of a bursting pancreatic /3-cell [12]. The purpose of this section is to underline the importance of complex nonlinear dynamic phenomena in biomedical systems. Living systems operate under far-from-equilibrium conditions. This implies that, contrary to the conventional assumption of homeostasis, many regulatory mechanisms are actually unstable and produce self-sustained oscillatory dynamics. The electrophysiological processes of the pancreatic /3-cell display (at least) two interacting oscillatory processes A fast process associated with the K+ dynamics and a much slower process associated with the Ca2+ dynamics. Together these two processes can explain the characteristic bursting dynamics in the membrane potential. 

The bursting dynamics ends in a different type of process, referred to as a global (or homoclinic) bifurcation. In the interval of coexisting stable solutions, the stable manifold of (or the inset to) the saddle point defines the boundary of the basins of attraction for the stable node and limit cycle solutions. (The basin of attraction for a stable solution represents the set of initial conditions from which trajectories asymptotically approach the solution. The stable manifold to the saddle point is the set of points from which the trajectories go to the saddle point). When the limit cycle for increasing values of S hits its basin of attraction, it ceases to exist, and... 

Calculations of mutual locations of poles and zeros for these TF models allow to trace dynamics of moving of the parameters (poles and zeros) under increasing loads. Their location regarding to the unit circle could be used for prediction of stability of the system (material behavior) or the process stationary state (absence of AE burst ) [7]. 

Intennittency, in tire context of chaotic dynamical systems, is characterized by long periods of nearly periodic or Taminar motion interspersed by chaotic bursts of random duration [28]. Witliin tliis broad phenomenological... 

Static The fan total pressure minus the dynamic pressure corresponding to the mean air velocity at the fan outlet. The fan static pressure is the bursting or collapsing pressure on the enclosure,... 

The solid lines in Figure 4.5 represent extrapolations of experimental data to full-scale vessel bursts on the basis of dimensional arguments. Attendant overpressures were computed by the similarity solution for the gas dynamics generated by steady flames according to Kuhl et al. (1973). Overpressure effects in the environment were determined assuming acoustic decay. The dimensional arguments used to scale up the turbulent flame speed, based on an expression by Damkohler (1940), are, however, questionable. 

Wiederman, A. H. 1986a. Air-blast and fragment environments produced by the bursting of vessels filled with very high pressure gases. In Advances in Impact, Blast Ballistics, and Dynamic Analysis of Structures. ASME PVP. 106. New York ASME. 

This chapter discusses the apphcation of femtosecond lasers to the study of the dynamics of molecular motion, and attempts to portray how a synergic combination of theory and experiment enables the interaction of matter with extremely short bursts of light, and the ultrafast processes that subsequently occur, to be understood in terms of fundamental quantum theory. This is illustrated through consideration of a hierarchy of laser-induced events in molecules in the gas phase and in clusters. A speculative conclusion forecasts developments in new laser techniques, highlighting how the exploitation of ever shorter laser pulses would permit the study and possible manipulation of the nuclear and electronic dynamics in molecules. 

The situation changes when there is a concentration imbalance. Figure 12-15 shows red blood cells immersed in solutions of different concentrations. When the fluid outside the cell has a higher solute concentration, the result is slower movement of water through the membrane into the cell. The net result is that water leaves the cell, causing it to shrink. When the fluid outside the cell has a lower concentration, movement of water into the cell increases. The extra water in the cell causes an increase in internal pressure. Eventually, the internal pressure of the cell matches the osmotic pressure, and water transport reaches dynamic equilibrium. Unfortunately, osmotic pressures are so large that cells can burst under the increased pressure before they reach equilibrium. 

The pulse mode experiments were conducted by placing the sample between the quartz plates and exposing it to 30 second bursts of UV radiation. Dynamic rheological tests were then applied to the sample and this process was repeated until the sample had passed its gel point and became highly cross-linked. 

More specific results are beyond the scope of our limited presentation for plumes. However, we will examine some gross features of transient plumes namely (a) the rise of a starting plume and (b) the dynamics of a fire ball due to the sudden release of a finite burst of gaseous fuel. Again, our philosophy here is not to develop exact solutions, but to represent the relevant physics through approximate analyses. In this way, experimental correlations for the phenomena can be better appreciated. 

The loads from external near-surface burst explosions are based on hemispherical surface burst relationships. Peak pressure (P psi) and scaled. impulse Ci/W psi/lb ) are plotted vs. scaled distance (R/W ft/lb ). Roof and sidewall elements, side-on to the shock wave, see side-on loads (P and i ). The front wall, perpendicular to the shock wave, sees the much higher reflected shock wave loads (P and i ). An approximate triangular pressure-time relationship is shown in Figure 5a. The duration, T, is determined from the peak pressure and impulse by assuming a triangular load. Complete load calculations include dynamic loads on side-on elements, the effect of clearing times on reflected pressure durations, and load variations on structural elements due to their size and varying distance from the explosive source. 

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