The quantitative assessment of uncertainty and sampling quality is essential in molecular simulation. Many systems of interest are highly complex, often at the edge of current computational capabilities. Modelers must therefore analyze and communicate statistical uncertainties so that “consumers” of simulated data understand its significance and limitations. This article covers key analyses appropriate for trajectory data generated by conventional simulation methods such as molecular dynamics and (single Markov chain) Monte Carlo. It also provides guidance for analyzing some ‘enhanced’ sampling approaches. We do not discuss systematic errors arising, e.g., from inaccuracy in the chosen model or force field.
The composites industry is increasingly using molecular dynamics (MD) simulations to inform its materials development decisions. As a result, there is growing awareness that simulated predictions require quantitative assessments of their quality in order to routinely provide reliable and actionable information. In the following, we develop a suite of uncertainty quantification (UQ) tools designed to assess simulation-based estimates of the glass transition temperature T g of polymer systems for aerospace applications. We consider contributions to this uncertainty arising from: (i) identification of asymptotic regimes in density versus temperature relations; (ii) fluctuations associated with limited time-averaging of dynamical noise; (iii) and finite-size effects associated with partial averaging over polymer-network configurations. We present a sequence of analyses by which we assess each of these contributions and quantify their net effect on estimates of T g. Importantly, these methods suggest more efficient workflows by indicating when multiple small simulations can be combined to yield estimates with uncertainties comparable to larger, more expensive simulations. We expect that related approaches will, in the future, be applicable to other physical quantities of interest as well as to a broader class of computational tools.
We measure the microvortical flows around gold nanorods propelled by ultrasound in water using polystyrene nanoparticles as optical tracers. We infer the rotational frequencies of such nanomotors assuming a hydrodynamic model of this interaction. In this way, we find that nanomotors rotate around their longitudinal axes at frequencies of up to ≈ 2.5 kHz, or ≈ 150 000 rpm, in the planar pressure node of a half-wavelength layered acoustic resonator driven at ≈ 3 MHz with an acoustic energy density of <10 J·m(-3). The corresponding tangential speeds of up to ≈ 2.5 mm·s(-1) at a nanomotor radius of ≈ 160 nm are 2 orders of magnitude faster than the translational speeds of up to ≈ 20 μm·s(-1). We also find that rotation and translation are independent modes of motion within experimental uncertainty. Our study is an important step toward understanding the behavior and fulfilling the potential of this dynamic nanotechnology for hydrodynamically interacting with biological media, as well as other applications involving nanoscale transport, mixing, drilling, assembly, and rheology. Our results also establish the fastest reported rotation of a nanomotor in aqueous solution.
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