Software Monte Carlo

All the data processing was performed with Matlab software. Monte-Carlo simulations were used for error calculations with 200 iterations. All self-diffusion coefficients were calculated from the following equation ... 

A comprehensive and up-to-date introduction to the ideas of molecular dynamics and Monte Carlo, with statistical mechanical background, advanced teclmiques and case studies, supported by a Web page for software download. 

A.4 MOLECULAR MECHANICS/MOLECULAR DYNAMICS/MONTE CARLO SOFTWARE... 

Many more special-purpose software packages have been developed, particularly in teaching and research institutions. SMCM is software designed at the University of California in Los Angeles for partitioning of pollutants (19). Monte Carlo and molecular dynamic techniques have been adapted in a... 

Modeling studies are most useful when experimentally detenriined structures are of modest quality and suitable force-field potentials and modeling software are available. Although statistical methods such as Monte Carlo and molecular dynamics would be preferred in solution or other disordered states, we feel that energy minimization criteria are valid for static, ordered structures such as crystals. 

Supposing that one has decided on bounds for a variable, one can fit a distribution that has a bounded support, such as the beta distribution or Johnson SB distribution. Alternatively, in a Monte Carlo implementation, one may sample the unbounded distribution and discard values that fall beyond the bounds. However, then a source of some discomfort is that the parameters of the distribution truncated in this way may deviate from the specification of the distribution (e.g., the mean and variance will be modified by truncation). It seems reasonable for Monte Carlo software to report the percentage discarded, and report means and variances of the distributions as truncated, for comparison to means and variances specified. 

The popularity of Monte Carlo for risk-based uncertainty analysis is somewhat driven by the fact that Monte Carlo is fundamentally easy to implement, particularly with the advent of the personal computer, and graphically based software like Crystal Ball (www.decisioneering.com) and Risk (www.palisade. com/risk.html). The availability of such software systems generally promotes the use of uncertainty analysis in ecological risk assessments, reducing the amount of mathematical and statistical knowledge required of the user to implement the... 

Keep it simple. Generally, uncertainty analyses need not be complex, although many investigators tend to make them so. While available software enables rather complicated Monte Carlo approaches, simple approaches usually provide defendable results that can be easily communicated to others. 

Efforts should be made to provide and improve user-friendly software, especially for those approaches where it currently appears to be lacking (e.g., Bayesian methods and Monte Carlo with more than 2 dimensions). 

Each vendor of SPICE simulation software has added features such as Monte Carlo analysis, schematic entry, and post simulation waveform processing, as well as extensive model libraries. In most cases, the manufacturers have modified the algorithms for controlling convergence and have added new parameters or syntax for component models. As a result, each electronic design automaton (EDA) tool vendor has the basic Berkeley SPICE 2 features and a unique set of capabilities and performance enhancements. 

Conformational expansion of molecules (also called conformation hunting in Cressets XedeX software module) applies a Monte Carlo approach combined with fast molecular dynamics for ring conformations. The minimization of the conformations is done using the XED force field, in order to assign correct charges. Based on the results obtained by Bostrom [99], this method performs comparably to other available methods when considering the RMS difference... 

The Monte Carlo exposure calculations described in this chapter are carried out with a flexible computer software program named DistGEN (Sielken Inc., 1995). This program allows exposure equations to be specified in the general computer language called FORTRAN, so they can have practically any form. Furthermore, the user-specified distributions for the components of the exposure equations can be selected from a wide variety of classical statistical distributions (normal, log-normal, etc. with user-specified parameter values) or from sample data (either the sample... 

Monte Carlo simulation can involve several methods for using a pseudo-random number generator to simulate random values from the probability distribution of each model input. The conceptually simplest method is the inverse cumulative distribution function (CDF) method, in which each pseudo-random number represents a percentile of the CDF of the model input. The corresponding numerical value of the model input, or fractile, is then sampled and entered into the model for one iteration of the model. For a given model iteration, one random number is sampled in a similar way for all probabilistic inputs to the model. For example, if there are 10 inputs with probability distributions, there will be one random sample drawn from each of the 10 and entered into the model, to produce one estimate of the model output of interest. This process is repeated perhaps hundreds or thousands of times to arrive at many estimates of the model output. These estimates are used to describe an empirical CDF of the model output. From the empirical CDF, any statistic of interest can be inferred, such as a particular fractile, the mean, the variance and so on. However, in practice, the inverse CDF method is just one of several methods used by Monte Carlo simulation software in order to generate samples from model inputs. Others include the composition and the function of random variable methods (e.g. Ang Tang, 1984). However, the details of the random number generation process are typically contained within the chosen Monte Carlo simulation software and thus are not usually chosen by the user. 

Point and range estimates as well as probabilistic models (Monte Carlo simulation) must show complete reproducibility per programming environment, since the underlying algorithms are deterministic. They should show asymptotic equivalence of results over different software environments and simulation techniques. 

Recent software, taking advantage of fast computing, directly use the powder diffraction profiles instead of peak positions for indexing. Softwares such as X-Celft (based on successive dichotomy approach similar to DICVOL) and TOPAS-I (based on Monte Carlo methods) are examples. 

The XD, ND as well as molecular dynamics (MD) and Monte Carlo (MC) computer simulation methods are considered well-est lished since a great number of investigation has been performed with them. With rare exceptions, experiments on liquids at normal conditions are considered as routine laboratory work by now. Similarly, even commercially available computer software helps the researchers to run simple simulations. However, the interpretation of the results is complicated and therefore a continuous improvement of the interpretation techniques is required. The XD experimental structure functions ate often... 

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