A quantum bound on the compactness

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes.

Inhomogeneous spacetimes in Weyl integrable geometry with matter source

We investigate the existence of inhomogeneous exact solutions in Weyl Integrable theory with a matter source. In particular, we consider the existence of a dust fluid source while for the underlying geometry we assume a line element which belongs to the family of silent universes. We solve explicitly the field equations and we find the Szekeres spacetimes in Weyl Integrable theory. We show that only the isotropic family can describe inhomogeneous solutions where the LTB spacetimes are included. A detailed analysis of the dynamics of the field equations is given where the past and future attractors are determined. It is interesting that the Kasner spacetimes can be seen as past attractors for the gravitation models, while the unique future attractor describes the Milne universe similar with the behaviour of the gravitational model in the case of General Relativity.

Classification and susceptibility assessment of debris flow based on a semi-quantitative method combination of the fuzzy <i>C</i>-means algorithm, factor analysis and efficacy coefficient

The existence of debris flows not only destroys the facilities but also seriously threatens human lives, especially in scenic areas. Therefore, the classification and susceptibility analysis of debris flow are particularly important. In this paper, 21 debris flow catchments located in Huangsongyu Township, Pinggu District, Beijing, China, were investigated. Besides field investigation, a geographic information system, a global positioning system and remote-sensing technology were applied to determine the characteristics of debris flows. This article introduced a clustering validity index to determine the clustering number, and the fuzzy C-means algorithm and factor analysis method were combined to classify 21 debris flow catchments in the study area. The results were divided into four types: debris flow closely related to scale–topography–human activity, topography–human activity–matter source, scale–matter source–geology and topography–scale–matter source–human activity. Nine major factors screened from the classification result were selected for susceptibility analysis, using both the efficacy coefficient method and the combination weighting. Susceptibility results showed that the susceptibility levels of 2 debris flow catchments were high, 6 were moderate and 13 were low. The assessment results were consistent with the field investigation. Finally, a comprehensive assessment including classification and susceptibility evaluation of debris flow was obtained, which was useful for risk mitigation and land use planning in the study area and provided a reference for the research on related issues in other areas.