Differential evolution and Markov chain Monte Carlo analyses of layer disorder in nanosheet ensembles using total scattering

2018 ◽  
Vol 51 (5) ◽  
pp. 1437-1444 ◽  
Author(s):  
Peter C. Metz ◽  
Robert Koch ◽  
Scott T. Misture
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Differential Evolution ◽  
Scattering Data ◽  
Type Model ◽  
Total Scattering ◽  
X Ray ◽  
Layer Disorder ◽  
Layer Position

Assemblies of nanosheets are often characterized by extensive layer-position disorder. Coupled with the often minute coherent scattering domain size and relaxation of the nanosheet structure itself, unambiguous interpretation of X-ray and neutron scattering data from such materials is non-trivial. This work demonstrates a general approach towards refinement of layer-disorder information from atomic pair distribution function (PDF) data for materials that span the gap between turbostratism and ordered stacking arrangements. X-ray total scattering data typical of a modern rapid-acquisition PDF instrument are simulated for a hypothetical graphene-like structure using the program DIFFaX, from which atomic PDFs are extracted. Small 1 × 1 × 20 supercell models representing the stacking of discrete layer types are combined to model a continuous distribution of layer-position disorder. Models optimized using the differential evolution algorithm demonstrate improved fit quality over 75 Å when a single mean layer-type model is replaced with a constrained 31-layer-type model. Posterior distribution analyses using the Markov chain Monte Carlo algorithm demonstrate that the influence of layer disorder and finite particle size are correlated. However, the refined mean stacking vectors match well with the generative parameter set.

scholarly journals The atomic structure of a MgCo2O4 nanoparticle for a positive electrode of a Mg rechargeable battery

2019 ◽  
Vol 55 (17) ◽  
pp. 2517-2520 ◽  
Author(s):  
Naoto Kitamura ◽  
Yuhei Tanabe ◽  
Naoya Ishida ◽  
Yasushi Idemoto
Keyword(s):  
Monte Carlo ◽  
Atomic Structure ◽  
Positive Electrode ◽  
Scattering Data ◽  
Rechargeable Battery ◽  
Reverse Monte Carlo ◽  
Spinel Type ◽  
Total Scattering ◽  
X Ray ◽  
Neutron Total Scattering

The atomic structure of a spinel-type MgCo2O4 nanoparticle was investigated by the reverse Monte Carlo modelling using X-ray and neutron total scattering data.

scholarly journals Bayesian reconstruction ofP(r) directly from two-dimensional detector imagesviaa Markov chain Monte Carlo method

2013 ◽  
Vol 46 (2) ◽  
pp. 404-414 ◽  
Author(s):  
Sudeshna Paul ◽  
Alan M. Friedman ◽  
Chris Bailey-Kellogg ◽  
Bruce A. Craig
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Interatomic Distance ◽  
Scattering Data ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Image ◽  
Two Dimensional Image

The interatomic distance distribution,P(r), is a valuable tool for evaluating the structure of a molecule in solution and represents the maximum structural information that can be derived from solution scattering data without further assumptions. Most current instrumentation for scattering experiments (typically CCD detectors) generates a finely pixelated two-dimensional image. In continuation of the standard practice with earlier one-dimensional detectors, these images are typically reduced to a one-dimensional profile of scattering intensities,I(q), by circular averaging of the two-dimensional image. Indirect Fourier transformation methods are then used to reconstructP(r) fromI(q). Substantial advantages in data analysis, however, could be achieved by directly estimating theP(r) curve from the two-dimensional images. This article describes a Bayesian framework, using a Markov chain Monte Carlo method, for estimating the parameters of the indirect transform, and thusP(r), directly from the two-dimensional images. Using simulated detector images, it is demonstrated that this method yieldsP(r) curves nearly identical to the referenceP(r). Furthermore, an approach for evaluating spatially correlated errors (such as those that arise from a detector point spread function) is evaluated. Accounting for these errors further improves the precision of theP(r) estimation. Experimental scattering data, where no ground truth referenceP(r) is available, are used to demonstrate that this method yields a scattering and detector model that more closely reflects the two-dimensional data, as judged by smaller residuals in cross-validation, thanP(r) obtained by indirect transformation of a one-dimensional profile. Finally, the method allows concurrent estimation of the beam center andDmax, the longest interatomic distance inP(r), as part of the Bayesian Markov chain Monte Carlo method, reducing experimental effort and providing a well defined protocol for these parameters while also allowing estimation of the covariance among all parameters. This method provides parameter estimates of greater precision from the experimental data. The observed improvement in precision for the traditionally problematicDmaxis particularly noticeable.

Markov chain Monte Carlo algorithms for optimizing grazing incidence optics for wide-field x-ray survey imaging

2002 ◽  
Author(s):  
Peter W. A. Roming ◽  
John C. Liechty ◽  
David H. Sohn ◽  
Jared R. Shoemaker ◽  
David N. Burrows ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Grazing Incidence ◽  
Wide Field ◽  
X Ray ◽  
Monte Carlo Algorithms ◽  
Grazing Incidence Optics

scholarly journals Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

2017 ◽  
Author(s):  
Dan Lu ◽  
Daniel Ricciuto ◽  
Anthony Walker ◽  
Cosmin Safta ◽  
William Munger
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Differential Evolution ◽  
Terrestrial Ecosystem ◽  
Predictive Performance ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Single Chain ◽  
Ecosystem Models

Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The DREAM is a multi-chain method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. It reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.

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