Error Analysis in Molecular Dynamics Simulation
In molecular dynamics (MD) simulations, there are errors due to inadequate sampling of the phase space or infrequently occurring events, these lead to the statistical error due to random fluctuation in the measurements.
For a series of M measurements of a fluctuating property A, the mean value is:
When these M measurements are independent, the variance of the mean <A> is:
but in most MD simulations, there is correlation between quantity A at different time, so the variance of the mean <A> will be underestimated as the effective number of independent measurements is actually less than M. In such situations we rewrite the variance as :
where is the autocorrelation function defined by
We can then use the autocorrelation function to estimate the error bar. Luckily, we have a much simpler method based on block averaging.
Read more about this topic: Error Analysis
Famous quotes containing the words error, analysis, dynamics and/or simulation:
“In religion,
What damned error but some sober brow
Will bless it, and approve it with a text,
Hiding the grossness with fair ornament?”
—William Shakespeare (1564–1616)
“Whatever else American thinkers do, they psychologize, often brilliantly. The trouble is that psychology only takes us so far. The new interest in families has its merits, but it will have done us all a disservice if it turns us away from public issues to private matters. A vision of things that has no room for the inner life is bankrupt, but a psychology without social analysis or politics is both powerless and very lonely.”
—Joseph Featherstone (20th century)
“Anytime we react to behavior in our children that we dislike in ourselves, we need to proceed with extreme caution. The dynamics of everyday family life also have a way of repeating themselves.”
—Cathy Rindner Tempelsman (20th century)
“Life, as the most ancient of all metaphors insists, is a journey; and the travel book, in its deceptive simulation of the journey’s fits and starts, rehearses life’s own fragmentation. More even than the novel, it embraces the contingency of things.”
—Jonathan Raban (b. 1942)