Monte Carlo simulation sampling procedures

In order to describe the fluorescence radiation profile of scattering samples in total, Eqs. (8.3) and (8.4) have to be coupled. This system of differential equations is not soluble exactly, and even if simple boundary conditions are introduced the solution is possible only by numerical approximation. The most flexible procedure to overcome all analytical difficulties is to use a Monte Carlo simulation. However, this method is little elegant, gives noisy results, and allows resimulation only according to the method of trial and error which can be very time consuming, even in the age of fast computers. Therefore different steps of simplifications have been introduced that allow closed analytical approximations of sufficient accuracy for most practical purposes. In a first... 

A probabilistic model is available for predicting the average log-tissue residue as a function of the water concentration at the site, and a set of site-specific tissue residue measurements is available. The water concentration to which the fish were exposed is known, so the average log-tissue residue can be predicted with the model. A Monte Carlo simulation will provide a set of equally probable predictions of the average log-tissue residue. The BMC acceptance-rejection procedure then boils down to estimating, for each model prediction, the probability of getting the observed sample average log-tissue residue concentration if the model prediction is correct. 

Combinatorial chemistry differs from usual Monte Carlo simulations in that several simultaneous searches of the variable space are carried out. That is, in a typical combinatorial chemistry experiment, several samples, e.g., 10,000, are synthesized and screened for figure of merit at one time. With the results of this first round, a new set of samples can be synthesized and screened. This procedure can be repeated for several rounds, although current materials discovery experiments have not systematically exploited this feature. 

Details on how to perform the calculations are given in [18], Here, it shall be sufficient to roughly describe the procedure Conformational sampling is performed by an in-house Monte-Carlo/simulated annealing algorithm ]36], based on the MMFF94s ]37-38] forcefield as implemented in Sybyl ]39], Typically, the Fukui ffinctions of different conformers do not exhibit different features... 

The MSI Polymorph Predictor (PP) is based on a four-step method. " " Sampling via Monte Carlo simulated annealing provides a starting set of trial structures. These are clustered to delete similar structures, minimized to create low energy crystal packings, and once more clustered to remove duplicates. Since the method is under continuous development and the current implementation differs significantly in some places from the procedure originally published, we present it below in relative detail. 

Again a Monte-Carlo simulation with a sample size of 10,000 is used. The estimation procedure is the same as described before. 

Stage 4 To run a pseudorandom sampling. The procedure to generate pseudorandom samples for the Monte Carlo simulation was performed. The results obtained until this step fed the economic evaluation database, which included the... 

A longstanding ambition has been to obtain dynamical information from Monte Carlo simulations. Of coinse, formally MC has no inherent timescale and is a, albeit sophisticated, phase space sampling procedure. Huitma and van Eerden have looked at this issue again. They ascribed the following definition of the physical time per MC step,... 

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