Threshold behaviour region

The characteristic threshold behaviour of conductive composites is an unsatisfactory feature for many applications, both because the poor mechanical properties incurred at concentrations where conduction is obtained cannot be tolerated, and because the high level of conductivity above the threshold is not required or even not desirable. Thus a common requirement is for an antistatic material which has good plastics properties, sufficient conductivity to allow charges to leak away, and sufficient resistivity to prevent dangerous shocks to personnel who may become accidentally connected to mains electrical supplies through it. Unfortunately, the very steep slope of the conductivity versus filler concentration curve in the region of the threshold makes it very difficult to manufacture materials with reliable intermediate conductivities. 

More challenging is the behaviour of a system with cubic autocatalysis coupled with decay. Here a term af)2 must compete with the removal k2/ . For a 1 and 1 it is not immediately obvious that any wave solutions will exist at all. Such considerations also suggest that wave formation will be favoured by particularly high autocatalyst concentrations at the point of initiation, so / > 1 in a localized region. Thus we may expect some threshold for the initiation. 

The I- V characteristic in vacuum shows a slight ohmic behaviour without any threshold voltage or NDR region. Contrary to these curves, the same device behaves very similarly in air and dry O2. In general, the threshold voltage and the NDR region varied from sweep to sweep and no relationship could be noticed between the condition in air or pure O2. 

First, the proper switching function of the device was verified. Both device parts were tested and each of them showed bistable behaviour as it can be seen for device part A11 in Figure 27.13. The NDR region and the threshold bias were shifted to higher voltages and appeared at 10-14 V as compared with a few volts in the stacked devices. Additionally, the current did not rise as fast and abruptly at the threshold voltage. 

Calculations for H + H2 at energies below threshold for excitation of the first vibrational level were compared with two approximations which assumed separability of motions along the reaction path and transversal to it. One approximation assumed conservation of transversal vibrational energy, and the second one conservation of transversal vibrational quantum number, i.e. adiabatic motion. The second assumption was closer to the exact results both in magnitude and in the shape of the reaction threshold region. However, as collision energies were increased and other vibrational states of products became excitable, the behaviour became more nearly statistical, in that probabilities of reactions tended to decrease and become comparable. 

If phase plane analysis thus accounts for relay behaviour, can it also explain the existence of an abrupt threshold for the amplification of perturbations When the steady state is located at A as in fig. 5.20, a tiny displacement of y towards the right will suffice to produce the excitable response. However, when the substrate nullcline is located more to the left (for example, for smaller values of parameter v), the steady state moves further away from the region of negative slope. A... 

On the other hand, the strong collision treatment is quite poor in describing the shapes of the fall-off in rate with pressure for the reactions of many simpler molecules, as is shown for the case of the thermal dissociation of nitrous oxide in Figure 8.1 here, the experimental measurements [66.0] lie rather close to a strict Lindemann curve, whereas the strong collision shape exhibits a much more gradual decline. This approach to strict Lindemann behaviour is easily understood in terms of a sequential activation process as the pressure declines and we enter the fall-off region, the states just above threshold decay so quickly... 

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