Abstract
The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage.
Lewins, J D
[1]
- Cambridge Univ. (UK). Dept. of Engineering
Citation Formats
Lewins, J D.
Equations for the stochastic cumulative multiplying chain.
United Kingdom: N. p.,
1980.
Web.
doi:10.1016/0306-4549(80)90096-1.
Lewins, J D.
Equations for the stochastic cumulative multiplying chain.
United Kingdom.
https://doi.org/10.1016/0306-4549(80)90096-1
Lewins, J D.
1980.
"Equations for the stochastic cumulative multiplying chain."
United Kingdom.
https://doi.org/10.1016/0306-4549(80)90096-1.
@misc{etde_6616963,
title = {Equations for the stochastic cumulative multiplying chain}
author = {Lewins, J D}
abstractNote = {The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage.}
doi = {10.1016/0306-4549(80)90096-1}
journal = []
volume = {7:9}
journal type = {AC}
place = {United Kingdom}
year = {1980}
month = {Jan}
}
title = {Equations for the stochastic cumulative multiplying chain}
author = {Lewins, J D}
abstractNote = {The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage.}
doi = {10.1016/0306-4549(80)90096-1}
journal = []
volume = {7:9}
journal type = {AC}
place = {United Kingdom}
year = {1980}
month = {Jan}
}