User:Kjhuston/sandbox

Todo: - Calculating ensemble average values in a single biased simulation is what's covered in the US article now - More commonly, people use umbrella sampling to calculate free energy profiles/landscapes - Cover umbrella sampling - what is single histogram equation

History
- Torrie and Valleau (1976) - combining histograms? the difference in umbrella potentials has a coordinate-dependent direct influence on the histogram which can be removed (subtract on log p plot) the indirect influence of umbrella potentials on the system results in a free energy difference for the entire simulation (shift histos on log p plot)

- Weighted Histogram Analysis Method

i think the most straightforward way to make the animation is actually to run tiny 1D monte carlo simulations.


 * (1) Show the true unbiased free energy profile (FEP) with a big barrier (3 seconds)
 * (2) Show an MC simulation on the true unbiased FEP, and how it can't sample high energy states well, so doesn't generate the FEP (5 seconds)
 * (3) Show the biasing potentials on the true free energy profile (3 seconds)
 * (4) Removing the true free energy profile, run biased simulations, show resulting histograms (5 seconds)
 * (5) Turn histograms into free energy profiles for each biased simulation (3 seconds)
 * (6) Remove biasing potential (3 seconds)
 * (7) Shift FEPs to overlap (3 seconds)
 * (8) Compare generated unbiased FEP to true unbiased FEP (3 seconds)

The whole thing comes to 28 seconds, which might be pushing it for animation length