Reaction time distribution

The IRT model has been developed in detail in a series of papers of Green, Pimblott and coworkers and has been validated by comparison with full random flight simulations [47,49,51]. The IRT treatment of the radiation chemistry relies upon the generation of random reaction times from initial coordinate positions from pair reaction time distribution functions. A simulation, such as a random flight calculation, starts with the initial spatial distribution of the reactants. The separations between all the pairs of particles are evaluated... 

In conclusion to this section, research in the RTD area is always active and the initial concepts of Danckwerts are gradually being completed and extended. The population balance approach provides a theoretical framework for this generalization. However, in spite of the efforts of several authors, simple procedures, easy to use by practitioners, would still be welcome in the field of unsteady state systems (variable volumes and flow rates), multiple inlet/outlet reactors, variable density mixtures, systems in which the mass-flowrate is not conserved, etc... On the other hand, the promising "generalized reaction time distribution" approach could be developed if suitable experimental methods were available for its determination. 

Mechanistic analysis of the chlorite-thiosulfate reaction, as well as consideration of the reaction time distributions, leads to the following qualitative explanation for the observed behavior. The pH rise and subsequent drop result from competition between two reaction pathways starting from chlorite and thiosulfate ... 

Orcutt JC, Davidson JF, Pigford RL. Reaction time distributions in fluidized catalytic reactors. Chem Eng Prog S5m Series 58(38) 1-15, 1962. 

Orcutt, J. C., J. F. Davidson and R. L. Pigford. Reaction Time Distributions in Fluidized Catalytic Reactors. Chem. Engr. Progress Symp. Series No. 38, Vol. 58 (1962) 1. 

Fig. 35. The location of the earliest peak in a reaction time distribution...

The second problem is the interpeak distance in the reaction time distribution. If the cycle time is not prolonged too much, the maximal distance used to compute the mean cycle time is 50 ms (maximum < 2 normal cycle time). With a cycle time of about 30 ms, the maximum of 50 ms is a good upper boundary. 

The first peak, FP, of a reaction time distribution is an indicator for the... 

This is another important point at the x-axis of the reaction time distribution. Its meaning can only be understood on a theoretical basis. The hypothetical neural representation suggests that there are two parts of the pathway within the cortex a linear part and a cyclical part. According to this theory, the point (Fp-2ET) divides these two parts in the minimal stimulus-response pathway. It has to be shown that this division by (Fp-2ET) is valid in all pathways. 

Example of the NESTLE results and the reaction times distribution of... 

Fig. 45. The NESTLE results (left) and the reaction time distribution (right) of the task allrH23. The length of the linear pathway is linEN = (Fp- con)/ET - 2 = (150-70)/15 - 2 = 80/15 -2 = 5.3-2 = 33, and the length of the cyclical pathway cycEN = (median - Fp)/ET + 2 = (195-150)/15 + 2 = 45/15 + 2 = 5 The constant time, the first peak and the median reaction time are indicated by the program...

Simulation of a reaction time distribution using the program SIMxlly... 

Fig. 51. Part of the reaction time distribution of the task a221S13A...

Now, the final elementary times are used to calculate the linEN and cycEN in the reaction time distribution. The table below is used to get the mode and the number of search processes from the cycEN. 

With the help of the elementary times and the reaction time distributions the lengths of the linear and the cyclical pathways are calculated. 

The conclusion therefore is that in some subjects (with triple search) the reaction time distribution does not show a first peak in the expected place at mincycEN = 2 but at mincycEN = 4. This implies an additional reduction of the linear pathway of 2ET and a prolongation of the cyclical pathway of the same amount. To take the decision where the first peak may be localized, ERP data may be helpful. It is not convenient to change the linear pathways in all subjects with triple search. In this work the linear pathways have not been changed at all after knowing the ERP data but the necessity to reduce the linear pathway may be assumed in some subjects. 

In this fast mode, the minimal pathways (first peak pathways in the reaction time distribution) last only 5 linET (like the xl ly trial). An example of this mode is subject HOI (see his results). 

The low probability of mincycEN = 2 in slow mode, triple search is the reason why the length of the linear pathway in the event-related potentials of subjects using this variant is shorter than the reaction time data (with mincycEN = 2) suggest. In the reaction time distribution of these subjects the break between the linear and the cyclical pathway does not lie mincycEN = 2ET left of the first peak but for example 4ET left of the first peak (see above). 

Figure 5-4. Cumulative brake reaction time distributions of young drivers to a high-contrast obstacle on the road under three levels of expectancy x = unalerted , o = surprise , and A = brake . See text for explanation (from Olson and Sivak, 1986, reprinted with permission from the Human Factors and Ergonomics Society).

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