Weiqi Wang — Page 6

arXiv2020

Numerical solution for the stress near a hole with corners in an infinite plate under biaxial loading

We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting in a set of singular integro-differential equations on the boundary. The resulting boundary integral equations are solved numerically using a Chebyshev collocation method which is augmented by a fractional power term, derived by asymptotic analysis of the corner region, to resolve stress singularities at corners of the hole. We apply our numerical method to the test case of the hole formed by two partially-overlapping circles, which can include either a corner pointing into the solid or a corner pointing out of the solid. Our numerical results recover the exact stress on the boundary to within relative error $10^{-3}$ for modest computational effort.

math.AP↗

arXiv2018

(Meta-)stability and Core-Shell Dynamics of Gold Nanoclusters at Finite Temperature

Gold nanoclusters have been the focus of numerous computational studies but an atomistic understanding of their structural and dynamical properties at finite temperature is far from satisfactory. To address this deficiency, we investigate gold nanoclusters via ab initio molecular dynamics, in a range of sizes where a core-shell morphology is observed. We analyze their structure and dynamics using of state-of-the-art techniques, including unsupervised machine-learning nonlinear dimensionality reduction (sketch-map) for describing the similarities and differences among the range of sampled configurations. We find that, whereas the gold nanoclusters exhibit continuous structural rearrangement, they clearly show persistent motifs: a cationic core of one to five atoms is loosely bound to a shell which typically displays a substructure resulting from the competition between locally spherical vs planar fragments. Besides illuminating the properties of core-shell gold nanoclusters, the present study proposes a set of useful tools for understanding their nature in operando.

cond-mat.mes-hall↗