Time-progressing

Khundkar L R and Zewail A H 1990 Ultrafast molecular reaction dynamics in real-time progress over a decade Annu. Rev. Phys. Chem. 41 15-60... 

As time progresses, charge is generated by photon currents, semiconductor dark currents, diffusion, depletion, surface, avalanche, and tunneling. The time required to fill the well by dark currents is the storage time, given by the following. 

As time progresses, the two homopolyamides in the melt form a block and eventually a random copolymer as a result of amide interchange (Fig. 

Molecular transport concerns the mass motion of molecules in condensed and gaseous phases. The mass motions are driven primarily by temperature. As time progresses, the initial mass motion results in concentration gradients. In the condensed phase, dow along concentration gradients is described by Fick s law. 

Stress Relaxation. Another important consequence of the viscoelastic nature of plastics is that if they are subjected to a particular strain and this strain is held constant it is found that as time progresses, the stress necessary to maintain this strain decreases. This is termed stress relaxation and is of vital importance in the design of gaskets, seals, springs and snap-fit assemblies. This subject will also be considered in greater detail in the next chapter. 

Figures 8.8-a through 8.8-d show a few snapshots illustrating intermittent behavior. We have used the logistic-equation driven CML (equation 8.34) and set D = 0.25 and a = 3.83. Each figure shows 16 times overlapped after a certain number of iterations have elapsed (100 iterations in figure 8.7-a, 200 in figure 8,7-b, 300 in 8.7-c, and 500 in 8.8-d). Notice how, depending on the time of the snapshot, some regions are periodic and others are turbulent. Islands cf order tend to come and go as time progresses i.e. the local order is intermittent.

In bulb B we approached equilibrium from a higher temperature (which favors NOj) then redaction (5) predominated at first. Using the same sort of argument we applied to bulb A, we see jthat as time progresses, reaction (4) becomes more and more rapid (as N204 is produced) and reaction (5) becomes slower (as N02 is used up). Finally, when the rates become equal, equilibrium is reached and the equilibrium expression (6) is applicable in bulb B. 

When a polymer sheet of thickness L is immersed in the gas at a constant pressure, the surface concentration increases instantaneously, to a steady value which is then spread by diffusion throughout the whole bulk of the polymer sheet to finally give a uniform concentration. During the sorption the concentration gradients in the polymer decrease as the time progresses reducing the sorption... 

Both of these effects cause a reduction in Q values compared with low-pressure measurements as time progresses, this reduction can increase. 

Figure 4.5 The trajectory of water molecules during an ab initio simulation of the electrode/ electrolyte interface. The disentanglement and then reorganization of water molecules into bilayers can be clearly seen as time progresses [Taylor, 2009b].

Equation (1.28) relates the wave packet at time t to the wave packet at time t = 0 if the k-dependence of the angular frequency includes terms up to k. The profile of the wave packet y(x, /) changes as time progresses because of... 

Once a wave funetion (jc, i) has been normalized, it remains normalized as time progresses. To prove this assertion, we consider the integral... 

If the wave function for the system is initially symmetric (antisymmetric), then it remains symmetric (antisymmetric) as time progresses. This property follows from the time-dependent Schrodinger equation... 

The negative sign is introduced because the concentration is falling as time progresses. 

As time progresses, the term associated with x2 (or a2) will decay away faster. We consider the term with the larger time constant X as the dominant pole. 1... 

As time progresses, the exponential term decays away, and the temperature approaches the new value MKp. Also illustrated in the figure is the much used property that at t = ip. the normalized response is 63.2%. 

On the plus side, the integration of the error allows us to detect and eliminate very small errors. To make a simple explanation of why integral control can eliminate offsets, refer back to our intuitive explanation of offset with only a proportional controller. If we desire e = 0 at steady state, and to shift controller output p away from the previous bias ps, we must have a nonzero term. Here, it is provided by the integral in Eq. (5-5). That is, as time progresses, the integral term takes on a final nonzero value, thus permitting the steady state error to stay at zero. 

One of the major trends to be anticipated is greater availability of instrumentation that can be used to perform multidimensional separations at ultrahigh pressures. Some instrument makers have recently introduced LC pumps capable of operating at pressures up to 15,000 psi. As time progresses, ultrahigh pressure separations are likely to become more routine and the pressure limit of commercial instruments is likely to increase... 

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