830 research outputs found
Compensation for the setup instability in ptychographic imaging
The high-frequency vibration of the imaging system degrades the quality of
the reconstruction of ptychography by acting as a low-pass filter on ideal
diffraction patterns. In this study, we demonstrate that by subtracting the
deliberately blurred diffraction patterns from the recorded patterns and adding
the properly amplified subtraction to the original data, the high-frequency
components lost by the vibration of the setup can be recovered, and thus the
image quality can be distinctly improved. Because no prior knowledge regarding
the vibrating properties of the imaging system is needed, the proposed method
is general and simple and has applications in several research fields.Comment: 13pages, 10figure
Strong convergence in the infinite horizon of numerical methods for stochastic differential equations
The strong convergence of numerical methods for stochastic differential
equations (SDEs) for is proved. The result is applicable to
any one-step numerical methods with Markov property that have the finite time
strong convergence and the uniformly bounded moment. In addition, the
convergence of the numerical stationary distribution to the underlying one can
be derived from this result. To demonstrate the application of this result, the
strong convergence in the infinite horizon of the backward Euler-Maruyama
method in the sense for some small is proved for SDEs with
super-linear coefficients, which is also a a standalone new result. Numerical
simulations are provided to illustrate the theoretical results.Comment: 16 pages, 2 figure
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Bond-Order Time Series Analysis for Detecting Reaction Events in Ab Initio Molecular Dynamics Simulations.
Ab initio molecular dynamics is able to predict novel reaction mechanisms by directly observing the individual reaction events that occur in simulation trajectories. In this article, we describe an approach for detecting reaction events from simulation trajectories using a physically motivated model based on time series analysis of ab initio bond orders. We found that applying a threshold to the bond order was insufficient for accurate detection, whereas peak finding on the first time derivative resulted in significantly improved accuracy. The model is trained on a reference set of reaction events representing the ideal result given unlimited computing resources. Our study includes two model systems: a heptanylium carbocation that undergoes hydride shifts and an unsaturated iron carbonyl cluster that features CO ligand migration and bridging behavior. The results indicate a high level of promise for this analysis approach to be used in mechanistic analysis of reactive AIMD simulations more generally
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