Single-molecule microscopy of nanocatalysis

Nanoparticles are important catalysts. Understanding their structure-activity correlation is paramount for developing better catalysts, but hampered by their inherent inhomogeneity: individual nanoparticles differ from one to another, and for every nanoparticle, it can change from time to time, especially during catalysis. Furthermore, each nanoparticle presents on its surface various types of sites, which are often unequal in catalytic activity. I will present our work of using single-molecule fluorescence microscopy to overcome these challenges and study single-nanoparticle catalysis at the single-turnover resolution and nanometer precision. I will present how we interrogate the catalytic activity and dynamics of individual metal nanoparticles, map the reactivity of different surface sites, and uncover surprising spatial reactivity patterns within single facets at the nanoscale. This spatiotemporally resolved catalysis mapping also enables us to probe the communication between catalytic reactions at different locations on a single nanocatalyst, in much relation to allosteric effects in enzymes.Ope

Sparse Quadrature for High-Dimensional Integration with Gaussian Measure

In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions of high-dimensional parameters with Gaussian measure. Under certain assumptions of the exactness and the boundedness of univariate quadrature rules as well as the regularity of the parametric functions with respect to the parameters, we obtain the convergence rate $O(N^{-s})$, where $N$ is the number of indices, and $s$ is independent of the number of the parameter dimensions. Moreover, we propose both an a-priori and an a-posteriori schemes for the construction of a practical sparse quadrature rule and perform numerical experiments to demonstrate their dimension-independent convergence rates

Frictional interface crack-tip singular stress field in anisotropic

This study presents the asymptotic displacement and stress fields at the crack tip of frictional interface where slip can occur along the interface between two anisotropic composite laminates. The results show that real values corresponding to the order of stress singularities may exit at the crack tip of the frictional interface between two anisotropic layers. The order of stress singularity largely depends on the coefficient of friction within the interface and the material properties of anisotropic composite laminates such as fibre orientations