论文标题

部分可观测时空混沌系统的无模型预测

Proper usage of Scherrer's and Guinier's formulas in X-ray analysis of size distribution in systems of monocrystalline CeO2 nanoparticles

论文作者

Valério, Adriana, Trindade, Fabiane J., Penacchio, Rafaela F. S., Ramos, Bria C., Damasceno, Sérgio, Estradiote, Maurício B., Rodella, Cristiane B., Ferlauto, André S., Kycia, Stefan W., Morelhão, Sérgio L.

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

Small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD) techniques are widely used as analytical tools in the optimization and control of nanomaterial synthesis processes. In crystalline nanoparticle systems with size distribution, the discrepant size values determined by using SAXS and XRD still lacks a well-established description in quantitative terms. To address fundamental questions, the isolated effect of size distribution is investigated by SAXS and XRD simulation in polydisperse systems of virtual nanoparticles. It quantitatively answered a few questions, among which the most accessible and reliable size values and what they stand for regarding the size distribution parameters. When a finite size distribution is introduced, the two techniques produce differing results even in perfectly crystalline nanoparticles. Once understood, the deviation in resulting size values can, in principle, resolve two parameters size distributions of crystalline nanoparticles. To demonstrate data analysis procedures in light of this understanding, XRD and SAXS experiments were carried out on a series of powder samples of cubic ceria nanoparticles. Besides changes in the size distribution related to the synthesis parameters, proper comparison of XRD and SAXS results revealed particle-particle interaction effects underneath the SAXS intensity curves. It paves the way for accurate and reliable methodologies to assess size, size dispersion, and degree of crystallinity in synthesized nanoparticles.

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