Although the physics of materials at surfaces and edges has been extensively studied, the movement of individual atoms at an isolated edge has not been directly observed in real time. With a transmission electron aberration-corrected microscope capable of simultaneous atomic spatial resolution and 1-second temporal resolution, we produced movies of the dynamics of carbon atoms at the edge of a ...

We have developed a numerical scheme for exact diagonalization of the few-particle electron–hole interaction Hamiltonians with a simultaneous resolution of several discrete conserved quantum numbers such as total electron or hole spins, total angular momentum, or parity. The method was applied to a simple model of a two-dimensional rectangular quantum box of arbitrary size and anisotropy, and c...

Complex multi-holed-region entity scenes (i.e., sets of random region with holes) are common in spatial database systems, spatial query languages, and the Geographic Information System (GIS). A multi-holed-region (region with an arbitrary number of holes) is an abstraction of the real world that primarily represents geographic objects that have more than one interior boundary, such as areas tha...

Using ShotLink data that records information on every stroke taken on the PGA Tour, this paper introduces a new metric to assess putting. The methodology is based on ideas from spatial statistics where a spatial map of each green is constructed. The spatial map provides estimates of the expected number of putts from various green locations. The difficulty of a putt is a function of both its dis...

We analyze the global structure of a family of Einstein-Maxwell solutions parametrized by mass, charge and cosmological constant. In a qualitative classification there are: (i) generic black-hole solutions, describing a Wheeler wormhole in a closed cosmos of spatial topology S × S; (ii) generic naked-singularity solutions, describing a pair of “point” charges in a closed cosmos; (iii) extreme b...

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasize the general character of this gravitational analogy by showing theoretically that the white hole horizon constit...

A strong electron-hole exchange interaction (EI) in semiconductor nanocrystals (NCs) gives rise to a large (up to tens of meV) splitting between optically active ('bright') and optically passive ('dark') excitons. This dark-bright splitting has a significant effect on the optical properties of band-edge excitons and leads to a pronounced temperature and magnetic field dependence of radiative de...

The ETS-NOCV analysis was applied to describe the σ-hole in a systematic way in a series of halogen compounds, CF3-X (X = I, Br, Cl, F), CH3I, and C(CH3)nH3-n-I (n = 1,2,3), as well as for the example germanium-based systems. GeXH3, X = F, Cl, H. Further, the ETS-NOCV analysis was used to characterize bonding with ammonia for these systems. The results show that the dominating contribution to t...

The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein’s vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the exterior area (r > 2GM) to the interior one (r < 2GM). As a contrast to its maximally extension in the Kruskal coordinates, we provide a comoving coordinate system ...