Multiple histograms

The coil-to-globule transition was studied for designed HP copolymer chains both by means of lattice Monte Carlo simulations using bond fluctuation algorithms and multiple histogram reweighting [100,101] and by a numer-... 

For obtaining the canonical distributions, the multiple-histogram reweighting techniques [9,10] are particularly suitable. Suppose we have made a single... 

Although these equations are expressions for the density of states as a function of both energy and reaction coordinate, the free energies are identical to those obtained from the standard one-dimensional multiple histogram equation. 

Multiple histograms obtained at different temperatures can be used to broaden the accessible temperature range [77,78]. 

Shi, W., Zhao, X., and Johnson, J.K. (2002). Phase transitions of adsorbed fluids computed from multiple-histogram reweighting. Mol. Phys., 100, 2139-50. 

Nearest neighbor (NN) interpolation and trilinear (bilinear in the present 2D example) interpolation find the reference image intensity value at position p, and update the corresponding joint histogram entry at p, while partial volume (PV) interpolation distributes the contribution of this sample over multiple histogram entries defined by its NN intensities, using the same weights as for bilinear interpolation. 

In the third step, our ZT-TBMD method has been extended by incorporating the Nose-bath (Nose 1984) and the Multiple Histogram approximations (Fanourgakis et al. 1997), so as to be applicable to cluster studies at finite temperatures in an efficient way (Andriotis et al. 2006, 2007 Fthenakis et al. 2003). This generalization allows one to calculate the caloric curve for the cluster and use this to study the effect of temperature on the structural, electronic, and magnetic properties of transition metal clusters and binary systems containing transition metal and semiconductor atoms. The method has been used to study the variation of structural and magnetic properties with temperature as well as to obtain the caloric curves of the Ni-clusters (Andriotis et al. 2006,2007 Fthenakis et al. 2003). 

A. Ghoufi, F. Goujon, V. Lachet, and P. Malfreyt,/. Chem. Phys., 128, 154716 (2008). Multiple Histogram Reweighting Method for the Surface Tension Calculation. 

Thus, the question is whether the combination of Metropolis data obtained in simulations at different temperatures can yield an improved estimate g E). This is indeed possible by means of the multiple-histogram reweighting method [86], sometimes also called weighted histogram analysis method (WHAM) [87]. Even though the general idea is simple, the actual implementation is not trivial. The reason is that conventional Monte Carlo simulation techniques such as the Metropolis method cannot yield absolute estimates for the partition sum Z T)= g E) i. e., estimates for the density of states at differ-... 

The efficiency of PERM depends on the simulation temperature. Therefore, a precise estimation of the density of states requires separate simulations at different temperatures. Then, the density of states can be constructed by means of the multiple-histogram reweighting method [86]. Although being a powerful method, it is difficult to keep track of the statistical errors involved in the individual histograms obtained in the simulations. 

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