Fiedler trees for multiscale surface analysis

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales. Published by Elsevier Ltd.

Engineering of 3D self-directed quantum dot ordering in multilayer InGaAs/GaAs nanostructures by means of flux gas composition

Lateral ordering of InGaAs quantum dots on the GaAs (001) surface has been achieved in earlier reports, resembling an anisotropic pattern. In this work, we present a method of breaking the anisotropy of ordered quantum dots (QDs) by changing the growth environment. We show experimentally that using As(2) molecules instead of As(4) as a background flux is efficient in controlling the diffusion of distant Ga adatoms to make it possible to produce isotropic ordering of InGaAs QDs over GaAs (001). The control of the lateral ordering of QDs under As(2) flux has enabled us to improve their optical properties. Our results are consistent with reported experimental and theoretical data for structure and diffusion on the GaAs surface.