Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T21:13:37.005Z Has data issue: false hasContentIssue false

A stochastic model for polymer degradation

Published online by Cambridge University Press:  14 July 2016

S. K. Srinivasan
Affiliation:
Indian Institute of Technology, Madras
K. M. Mehata
Affiliation:
Indian Institute of Technology, Madras

Abstract

The stochastic model for breaking of molecular segments proposed by Bithell is analysed and some results relating to the distribution of the number of fragments are obtained by using a slightly more general model which allows multiple ruptures. The product density technique is employed to derive the mean and mean square number of segments at any time t and the number of segments with length greater than y at time of production.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bellman, R. E., Kalaba, R. and Wing, G. M. (1960) Invariant imbedding and mathematical physics — I. Particle processes. J. Math. Phys. 1, 280308.Google Scholar
[2] Bithell, J. F. (1969) A stochastic model for the breaking of molecular segments. J. Appl. Prob. 6, 5973.Google Scholar
[3] Ramakrishnan, A. (1950) Stochastic process relating to particles distributed to a continuous infinity of states. Proc. Camb. Phil. Soc. 46, 595602.Google Scholar
[4] Ramakrishnan, A. (1952) A note on Jánossy's mathematical model of a nucleon cascade. Proc. Camb. Phil. Soc. 48, 451456.Google Scholar
[5] Ramakrishnan, A. and Srinivasan, S. K. (1956) A new approach to cascade theory. Proc. Ind. Acad. Sci. A 44, 263.Google Scholar
[6] Srinivasan, S. K. (1969) Stochastic Theory and Cascade Processess. American Elsevier. Pub. Co., New York. Chapter 7.Google Scholar
[7] Roberts, G. E. and Kaufman, H. (1966) Tables of Laplace Transforms. W. B. Saunders Company, Philadelphia and London.Google Scholar