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I have half life of single connection between strands element. How can I count half life of a strand if strand has 10 of such a connections.

My current approach Lets say that I have 10 strands, each strand has 10 connections. So there is 100 connections. After time $t_{HalfLife}$ there will be only 50 connections. But I have no idea how to convert this 50 to number of strands with 10 connections.

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    $\begingroup$ Does a strand die when 1 of its 10 connections breaks, or when all 10 connections break? $\endgroup$
    – Henry
    Jun 7, 2011 at 13:47
  • $\begingroup$ One break is enough to kill strand $\endgroup$
    – Darqer
    Jun 7, 2011 at 14:02

1 Answer 1

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This assumes that a single break causes the strand to fail. The probability of no break of one connection in an interval of length $t$ is $\exp (-\lambda t)$. The half life is $\frac{\log 2}{\lambda}$ as that is the time for half the connections to break. Given $10$ connections, the failure rate is $10 \lambda$, so ...

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    $\begingroup$ So it gives me $N(t)=N_{0}e^{-\lambda t}$, then $t_{1/2}=\frac{log2}{10\lambda}$ -> $\lambda=\frac{log2}{10t_{1/2}}$ so I have $N(t)=N_{0}e^{-\frac{t (log2)}{10t_{1/2}}}$. Is it correct ? $\endgroup$
    – Darqer
    Jun 7, 2011 at 14:14
  • $\begingroup$ @Darqer: Looks good. $\endgroup$ Jun 7, 2011 at 15:55

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