Breaking probability

ANSPIPE Calculates pipe break probability using the Thomas Model BETA Calculates and draws event trees using word processor and other input BNLDATA Failure rate data... 

The second trajectory or interaction rule is the breaking probability,... 

In this application the reader will examine the influence of the interrelation between the two liquids on the extent and rate of the demixing process. In Example 5.1, the two liquids have a modest affinity for each other, characterized by rules describing a relatively low breaking probability rule between them. These setup data are found in Parameter setup 5.1. 

It is now interesting to see if changing the breaking probability Pb(A,B) or the joining parameter J(A,B) affects the reaction rate. For this we first set up the situation as in Example 8.2 above, with a 100 x 100 grid and 500 A and 500 B cells, but now set Pb(AB) = 0.5 (instead of Pb = 1.0). This means that the A and B cells in contact with each other have some tendency to stay in contact. 

A fiirther test of the equilibrium concept, introduced in Example 8.3, involves introducing the influence of the breaking probability into the equilibrium process. In this case repeat the process of Example 8.2, but with the change of Pb(AB) to 0.5. Do you expect an effect What do you observe What is Kgq for this case ... 

There is no reason to believe that any of these reactions involve formation of an intermediate acylium ion (Bentley et al., 1984) but the extent of C—Cl bond breaking probably increases markedly with increasing electron release from a substituent. Kinetic primary chloride isotope effects show that C—Cl bond breaking increases with increasing electron release in hydrolyses of 4-substituted benzoyl chlorides in aqueous acetone (Fry, 1970)... 

The breaking and joining rules described above have a physical parallel in studies of water and solution phenomena. The breaking probability, PB(W), governs the self-affinity of a water molecule, W. This probability has a relationship to the boiling point, described by the equation ... 

The hydrophobic effect is a term describing the influence of relatively nonpolar (lipophilic) substances on the collective behavior of water molecules in their vicinity. The common expression is that water is more structured or organized when in contact with a lipophilic solute. This behavior was observed in a cellular automata model of a solute in water,42,43 which led to a study in more detail.44 The hydrophobic effect was modeled by systematically increasing the breaking probability, PB(WS), value, encoding an increasing probability of a solute molecule, S, not to associate with water. 

Rules selected for this reaction included the joining and breaking probabilities as described earlier. In addition, it was necessary to include a probability of conversion, Pc, of an enzyme-substrate pair, ES, to an enzyme-product pair, EP, that was programmed to be an irreversible event. The cells designated as enzymes, E, were not permitted to move, and their random distribution in the grid limited them to a separation of at least 10 cells. Once a substrate molecule joined with an enzyme, no other pairings were possible. The lipophilicity of the substrate and product molecules were varied using the PB(WS) and PB(WP) rules. 

Both oxygen and hydrogen peroxide are good electron acceptors. The latter has the higher affinity, but may react less rapidly because (H202) is not stable, and bond-breaking probably occurs as the electron transfers, whereas for dioxygen, the... 

It is by no means certain that the mechanism of fracture-induced decomposition reaction will be the same as that described for slow decomposition. For example, when the crack is running at its maximum velocity, chemical bonds are broken on a time scale comparable to that required for a bond to make one vibration. It can be imagined, therefore, that those bonds which are near their maximum amplitude of vibration when the crack approaches wiU be most likely to break, probably leaving the surface in a highly active state and producing free radicals in the gas phase. Such a process was envisaged by Taylor and Weale... 

For RBMKs of the first generation, guillotine breaks of the main feedwater pipe and of the main steam line should be treated as BDBAs [6]. Intensive in-service inspection and other feasible actions are undertaken to prevent breaks in these pipes (with the break probability reduced to below 10 per reactor-year). 

Elementary probabilistic theory of branching chain reactions. If branching occurs in a chain reaction then expression (1.1) for the average chain length includes the branching probability (<, which acts to decrease the chain breaking probability... 

The final clever approximation is to define the temperature as an energy analog related to the make/break probability. It takes scientific creativity to postulate these relationships but they are based on experience and physical reasoning in an analog way. What are the results ... 

We note that this result could have been deduced directly from Table 12.1 by remembering that the probability of passing from X to the next X is the product of ot2. We can generalize relation [12.7], which gives the mean length of a chain as the reverse of the breaking probability. 

WSRC, DPST-88-546 (ECS-LOCA-11), "Indirect Pipe Break Probability (K)."... 

WSRC, DPST-88-468 (ECS-LOCA-12), "Direct Pipe Break Probability."... 

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