Deceleration Curves

Dremin Shvedov (Ref 52 performed a series of expts with liq expls, granular expls (pressed and cast) and granular expls with inert liq and gas fillers, in which they monitored the barrier/exp interface velocity as a function of input pressure of rectangular shocks. According to the authors the shock-driven interface is decelerated by decompn products if there is reaction. Thus the data in F ° 2 fan4 in Pw 27 helnwt are interface deceleration curves. The data in Fig 26a are for liq TNT those in Fig 26b are for cast TNT ,numbers in the curves are input pressures in kbars... 

Deceleration curves for low density expl compacts (Taken from Ref 43a) are shown in Fig 27. Downward curvature of these plots indicates accelerating decompn. Note that the curves show the expected sensitivity order of PETN)... 

Figure 3 Theoretical braking deceleration curve of a train (from NN,1985)...

Figure 6 Original measurements of the electronic camera include the theoretical braking deceleration curve...

If we copy the time scale of the theoretical braking deceleration curve onto the figure which shows the measured abutment movements, we can also see, that the character of the movements is identical to the theoretical curve. Model and reality are corresponding. The maximum amplitude of the movement is about 0.5 mm during stopping the train. The accuracy is represented by the noise of the measurements and has a value of 0.1mm. This is the result if we use only an electronic camera as measuring instrument. All other brake tests show much the same results. So our example is representative for the selected test bridge. 

Fig. 1. Deceleration and penetration curves from dynamic impact tester. Time vs distance penetrated (A) and deceleration (B). Distance between vertical...

The great majority of experimental data (see Section III.A) indicate that the hydrogen-deuterium exchange reaction belongs to the class of acceptor reactions (i.e., reactions that are accelerated by electrons and decelerated by holes). This means that the experimenter, as a rule, remains on the acceptor branch of the thick curve in Fig. 8a, on which the chemisorbed hydrogen and deuterium atoms act as donors. Here a donor impurity must enhance the catalytic activity, while an acceptor impurity must decrease it. This is what actually occurs, as we have already seen (see Section III.A). 

The spreading behavior of droplets on a non-flat surface is not only dependent on inertia and viscous effects, but also significantly influenced by an additional normal stress introduced by the curved surface. This stress leads to the acceleration-deceleration effect, or the hindering effect depending on the dimensionless roughness spacing, and causes the breakup and ejection of liquid. Increasing impact velocity, droplet diameter, liquid density, and/or... 

The same form of rate equation and Mayo equation can also be obtained, though with different constants, on the assumption, made by Biddulph and Plesch when first discussing this work [77], that the chain breaking agent is the stannic chloride hydrate itself. Since this reaction too would be subject to deceleration by increasing viscosity, it is also compatible with the curves of Figure 9. 

Assign the accelerating, exponential growth, and decelerating phases of the growth curve in part 1. 

Usually the electrode reaction is considered to occur when the reactant reaches the OHP thus, the rate of electrode reaction is influenced by the value of ( ohp- s) For a reduction, Ox2 + ne - Red2 n, the experimental standard rate constant, ksexp, deviates from the standard rate constant expected for ( ohp s) = 0 [curve (b)]. If the latter rate constant is expressed by ks,cori there is a relation ks,exp=ks,con-exp[(an-z)( oHp- s)F/RT], where a is the transfer coefficient. If z=+l, n = 1, a 0.5, and ( ohp- s)<0, then (a-z)( Ohp s)>0 and kSjexp>kSjCon, showing that the electrode reduction of a univalent cation is accelerated by the double-layer effect. On the other hand, if z=0, n= 1, a 0.5, and ( ohp s) <0, ks,expneutral molecule is decelerated by the double-layer effect. In the study of electrode kinetics, it is usual to get kSiCon. by correcting for the double layer effect (see Table 8.6 for an example). 

Fig. 6.1 Typical growth curve of unicellular organisms (A) lag phase (B) accelerated growth phase (C) exponential growth phase (D) decelerated growth phase ...

Figure 2.9. Increase in temperature during polyurethane synthesis. Initial temperature. To = 90°C (curves 1 and 2) and 72°C (curves 3 and 4). Solid lines are according to a self-deceleration equation. Dotted lines correspond to the second-order kinetic equation. Points - experimental data.

The experimental curves in Fig. 2.9 are compared with the curves calculated according to the second-order kinetic equation for two different initial temperatures. The divergence between the pairs of curves at the final stages of the process reaches 15 %, while the experimental is less than 3 %. This proves that the equation is inadequate. On the other hand, a kinetic equation that takes into account the effect of self-deceleration fits the experimental data along the whole curve. Therefore, we can predict that the reaction in the system under discussion will be incomplete. 

Close to the vitrification curve and particularly after its interception, the reaction rate becomes diffusionally controlled. It decelerates with an autoretardation effect and eventually becomes negligible for practical pur-... 

The sigmoid form can be analyzed by splitting the curve into four regions (see Figure 3.2) the first region is the induction period, which ends at t = x. Afterward, there occurs an acceleration of the transformation, which ends approximately at t = tl/2. Thereafter, a deceleration period starts, which runs in the range 0.5 transformation completion when/= 1. 

It is quite different in the case of radical decay in polystyrene and polymethylmetacrylate. At high temperatures and concentrations everything is satisfactory the curves correspond to the second order kinetics. But at lower concentrations strong deviations from bimolecular kinetics are observed — the process of decay is greatly decelerated. 

At the initial moment of exponential growth experimental size of population and calculated one by equation (7) are often significantly differed. The difference may be equal to several orders by value. Although during the period of growth deceleration theoretical curve corresponds to experimental data. 

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