Talk:Umbrella sampling

a figure of the idea like http://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/umbrella.png should be included
I'm planning to make an animated figure that shows the whole process of calculating a free energy profile in umbrella sampling as described by Kumar et al. : 1) running simulations called windows, each with a biasing potential 2) generating histograms from these simulations to get biased 1D free energy profiles 3) removing direct bias from the biased 1D FEPs 4) shifting each FEP to match overlapping parts. This also requires significant overhaul of the article. Right now it covers calculation of the average of some property within a single biased simulation, but I believe most people use umbrella sampling to generate histograms from many overlapping biased simulations, from which unbiased free energy profiles/landscapes can be calculated. Kjhuston (talk) 19:24, 10 April 2014 (UTC)

I should clarify, the animation will not step through WHAM from Kumar et al., but will approximately describe Eqn. 9 from Kumar et al.

$$W_{\{0\},\beta}(\xi)=-\sum_{j=1}^L \lambda_j \hat{V}_j(\xi)+W_{\{\lambda\},\beta}(\xi)+C(\{\lambda\},\beta)$$

Starting with the biased free energy profiles generated from the umbrella sampling windows in part (2): $$W_{\{\lambda\},\beta}(\xi)$$

Part (3) is removal of the biasing potential $$-\sum_{j=1}^L \lambda_j \hat{V}_j(\xi)$$

and part (4) is shifting of each FEP to match overlapping parts, effectively calculating free energy differences between biased simulations $$C(\{\lambda\},\beta)$$

and thereby giving the unbiased free energy profile: $$W_{\{0\},\beta}(\xi)$$

Kjhuston (talk) 19:37, 10 April 2014 (UTC)

umbrella windows missing
umbrella windows missing, as well as WHAM.--2001:7C0:710:726:6437:7752:52C5:9B20 (talk) 23:48, 8 August 2015 (UTC)