143 research outputs found

    Accurate Estimation of Diffusion Coefficients and their Uncertainties from Computer Simulation

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    Self-diffusion coefficients, D∗D^*, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation suffer from statistical noise, which introduces uncertainty in the resulting estimate of D∗D^*. An optimal scheme for estimating D∗D^* will minimise this uncertainty, i.e., will have high statistical efficiency, and will give an accurate estimate of the uncertainty itself. We present a scheme for estimating D∗D^* from a single simulation trajectory with high statistical efficiency and accurately estimating the uncertainty in the predicted value. The statistical distribution of MSDs observable from a given simulation is modelled as a multivariate normal distribution using an analytical covariance matrix for an equivalent system of freely diffusing particles, which we parameterise from the available simulation data. We then perform Bayesian regression to sample the distribution of linear models that are compatible with this model multivariate normal distribution, to obtain a statistically efficient estimate of D∗D^* and an accurate estimate of the associated statistical uncertainty

    A general approach to maximise information density in neutron reflectometry analysis

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    Neutron and X-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of a model-dependent methods. This can lead to the over- and under- analysis of experimental data, when too many or too few parameters are allowed to vary in the model. In this work, we outline a robust and generic framework for the determination of the set of free parameters that is capable of maximising the in-formation density of the model. This framework involves the determination of the Bayesian evidence for each permutation of free parameters; and is applied to a simple phospholipid monolayer. We believe this framework should become an important component in reflectometry data analysis, and hope others more regularly consider the relative evidence for their analytical models

    Kinisi:Bayesian analysis of mass transport from molecular dynamics simulations

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    kinisi is a Python package for estimating transport coefficients—e.g., self-diffusion coefficients, ∗—and their corresponding uncertainties from molecular dynamics simulation data. It includes an implementation of the approximate Bayesian regression scheme described in McCluskey etal. (2023), wherein the mean-squared displacement (MSD) of mobile atoms is modelled as a multivariate normal distribution that is parametrised from the input simulation data. kinisi uses Markov-chain Monte Carlo (Foreman-Mackey et al., 2019; Goodman &amp; Weare, 2010) to sample this model multivariate normal distribution to give a posterior distribution of linear model ensemble MSDs that are compatible with the observed simulation data. For each linear ensemble MSD, x(), a corresponding estimate of the diffusion coefficient, ̂∗ is given via the Einstein relation, ̂∗ =1d x() / 6 d where is time. The posterior distribution of compatible model ensemble MSDs calculated by kinisi gives a point estimate for the most probable value of ∗ , given the observed simulation data, and an estimate of the corresponding uncertainty in ̂∗. kinisi also provides equivalent functionality for estimating collective transport coefficients, i.e., jump-diffusion coefficients and ionic conductivities<br/

    Assessing molecular simulation for the analysis of lipid monolayer reflectometry

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    Using molecular simulation to aid in the analysis of neutron reflectometry measurements is commonplace. However, reflectometry is a tool to probe large-scale structures, and therefore the use of all-atom simulation may be irrelevant. This work presents the first direct comparison between the reflectometry profiles obtained from different all-atom and coarse-grained molecular dynamics simulations. These are compared with a traditional model layer structure analysis method to determine the minimum simulation resolution required to accurately reproduce experimental data. We find that systematic limits reduce the efficacy of the MARTINI potential model, while the Berger united-atom and Slipids all-atom potential models agree similarly well with the experimental data. The model layer structure gives the best agreement, however, the higher resolution simulation-dependent methods produce an agreement that is comparable. Finally, we use the atomistic simulation to advise on possible improvements that may be offered to the model layer structures, creating a more realistic monolayer model.Comment: Electronic Supplementary Information (ESI) available: All analysis/plotting scripts and figure files, allowing for a fully reproducible, and automated, analysis workflow for the work presented is available at \url{https://github.com/arm61/sim_vs_trad} (DOI: 10.5281/zenodo.2600729) under a CC BY-SA 4.0 licens

    Overscreening and Underscreening in Solid-Electrolyte Grain Boundary Space-Charge Layers

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    Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions adjacent to grain boundaries. The general analytical form of these space-charge regions is known only in the dilute limit, where defect-defect correlations can be neglected. Using kinetic Monte Carlo simulations of a three-dimensional Coulomb lattice gas, we show that grain-boundary space-charge regions in non-dilute solid electrolytes exhibit overscreening -- damped oscillatory space-charge profiles -- and underscreening -- decay lengths that are longer than the corresponding Debye length and that increase with increasing defect-defect interaction strength. Overscreening and underscreening are known phenomena in concentrated liquid electrolytes, and the observation of functionally analogous behaviour in solid electrolyte space-charge regions suggests that the same underlying physics drives behaviour in both classes of systems. We therefore expect theoretical approaches developed to study non-dilute liquid electrolytes to be equally applicable to future studies of solid electrolytes

    An introduction to classical molecular dynamics simulation for experimental scattering users

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    Classical molecular dynamics simulations are a common component of multi-modal analyses from scattering measurements, such as small-angle scattering and diffraction. Users of these experimental techniques often have no formal training in the theory and practice of molecular dynamics simulation, leading to the possibility of these simulations being treated as a "black box" analysis technique. In this article, we describe an open educational resource (OER) designed to introduce classical molecular dynamics to users of scattering methods. This resource is available as a series of interactive web pages, which can be easily accessed by students, and as an open source software repository, which can be freely copied, modified, and redistributed by educators. The topic covered in this OER includes classical atomistic modelling, parameterising interatomic potentials, molecular dynamics simulations, typical sources of error, and some of the approaches to using simulations in the analysis of scattering data.Comment: Electronic Supplementary Information (ESI) available: All analysis/plotting scripts and figure files, allowing for a fully reproducible, and automated, analysis workflow for the work presented is available at \url{https://github.com/arm61/sim_and_scat_paper} (DOI: 10.5281/zenodo.2556826) under a CC BY-SA 4.0 licens
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