Free Energy Level Correction by Monte Carlo Resampling with Weighted Histogram Analysis Method

Free energy calculations may provide vital information for studying various chemical and biological processes.Quantum mechanical methods are required to accurately describe interaction energies,but their computations are often too demanding for conformational sampling.As a remedy,level correction schemes that allow calculating high level free energies based on conformations from lower level simulations have been developed.Here,we present a variation of a Monte Carlo(MC)resampling approach in relation to the weighted histogram analysis method(WHAM).We show that our scheme can generate free energy surfaces that can practically converge to the exact one with sufficient sampling,and that it treats cases with insufficient sampling in a more stable manner than the conventional WHAM-based level correction scheme.It can also provide a guide for checking the uncertainty of the levelcorrected surface and a well-defined criterion for deciding the extent of smoothing on the free energy surface for its visual improvement.We demonstrate these aspects by obtaining the free energy maps associated with the alanine dipeptide and proton transfer network of the KillerRed protein in explicit water,and exemplify that the MC resampled WHAM scheme can be a practical tool for producing free energy surfaces of realistic systems.

A WEIGHTED PENALTY FINITE ELEMENT METHOD FOR THE ANALYSIS OF POWER-LAW FLUID FLOW PROBLEMS

In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.

Evolved clustering analysis of 300 MW boiler furnace pressure sequence based on entropy characterization

The furnace process is very important in boiler operation,and furnace pressure works as an important parameter in furnace process.Therefore,there is a need to analyze and monitor the pressure signal in furnace.However,little work has been conducted on the relationship with the pressure sequence and boiler’s load under different working conditions.Since pressure sequence contains complex information,it demands feature extraction methods from multi-aspect consideration.In this paper,fuzzy c-means analysis method based on weighted validity index(VFCM)has been proposed for the working condition classification based on feature extraction.To deal with the fluctuating and time-varying pressure sequence,feature extraction is taken as nonlinear analysis based on entropy theory.Three kinds of entropy values,extracted from pressure sequence in time-frequency domain,are studied as the clustering objects for work condition classification.Weighted validity index,taking the close and separation degree into consideration,is calculated on the base of Silhouette index and Krzanowski-Lai index to obtain the optimal clustering number.Each time FCM runs,the weighted validity index evaluates the clustering result and the optimal clustering number will be obtained when it reaches the maximum value.Four datasets from UCI Machine Learning Repository are presented to certify the effectiveness in VFCM.Pressure sequences got from a 300 MW boiler are then taken for case study.The result of the pressure sequence case study with an error rate of 0.5332%shows the valuable information on boiler’s load and pressure sequence in furnace.The relationship between boiler’s load and entropy values extracted from pressure sequence is proposed.Moreover,the method can be considered to be a reference method for data mining in other fluctuating and time-varying sequences.