The "universal property" of Horizon Entropy Sum of Black Holes in Four Dimensional Asymptotical (anti-)de-Sitter Spacetime Background

We present a new ``universal property'' of entropy, that is the ``entropy sum'' relation of black holes in four dimensional (anti-)de-Sitter asymptotical background. They depend only on the cosmological constant with the necessary effect of the un-physical ``virtual'' horizon included in the spacetime where only the cosmological constant, mass of black hole, rotation parameter and Maxwell field exist. When there is more extra matter field in the spacetime, one will find the ``entropy sum'' is also dependent of the strength of these extra matter field. For both cases, we conclude that the ``entropy sum'' does not depend on the conserved charges $M$, $Q$ and $J$, while it does depend on the property of background spacetime. We will mainly test the ``entropy sum'' relation in static, stationary black hole and some black hole with extra matter source (scalar hair and higher curvature) in the asymptotical (anti-)de-sitter spacetime background. Besides, we point out a newly found counter example of the mass independence of the ''entropy product'' relation in the spacetime with extra scalar hair case, while the ``entropy sum'' relation still holds. These result are indeed suggestive to some underlying microscopic mechanism. Moreover, the cosmological constant and extra matter field dependence of the ``entropy sum'' of all horizon seems to reveal that ``entropy sum'' is more general as it is only related to the background field. For the case of asymptotical flat spacetime without any matter source, we give a note for the Kerr black hole case in appendix. One will find only mass dependence of ``entropy sum'' appears. It makes us believe that, considering the dependence of ``entropy sum'', the mass background field may be regarded as the next order of cosmological constant background field and extra matter field.Comment: 14 pages, no figures, JHEP forma

Thermodynamic relations for entropy and temperature of multi-horizons black holes

We present some entropy and temperature relations of multi-horizons, even including the "virtual" horizon. These relations are related to product, division and sum of entropy and temperature of multi-horizons. We obtain the additional thermodynamic relations of both static and rotating black holes in three and four dimensional (A)dS spacetime. Especially, a new dimensionless, charges-independence and $T_+S_+=T_-S_-$ like relation is presented. This relation does not depend on the mass, electric charge, angular momentum and cosmological constant, as it is always a constant. These relations lead us to get some interesting thermodynamic bound of entropy and temperature, including the Penrose inequality which is the first geometrical inequality of black holes. Besides, based on these new relations, one can obtain the first law of thermodynamics and Smarr relation for all horizons of black hole.Comment: 12 pages, no figures, title changed, references adde

Hydrodynamics of a Gas-Driven Gas-Liquid-Solid Spouted Bed

A novel cylindrical gas-driven gas-liquid-solid spouted bed was developed in this project, which has a high potential to be used for a biological wastewater treatment process. Solids motion, flow regimes, and regime transitions in this system were studied. With increasing gas velocity, four regimes were identified, including: fixed bed, semi spouted bed, full spouted bed and internal circulating fluidized bed. The respective gas velocities for the transitions between the four regimes were experimentally identified and termed as minimum spouting velocity, full spouting velocity and minimum circulating velocity. A new “basketing” method was adopted to measure the minimum spouting velocity while the particle velocity and dense phase retraction in the annulus were monitored to determine the full spouting velocity and minimum circulating velocity. The effects of key operating parameters on the three transitional velocities were examined in this novel spouted bed. When a draft tube was present, these three velocities increased with increasing particle density and draft tube length. The minimum spouting velocity and full spouting velocity were not affected when varying the nozzle-tube gap, while the minimum circulating velocity increased with longer nozzle-tube gaps. Without a draft tube, the gas-driven gas-liquid-solid spouted bed stability is reduced, where results were mainly obtained in terms of the water level, initial static bed height and gas flowrate

Citation Function and Polarity Classification in Biomedical Papers

The traditional reference evaluation method treats all citations equally. However, a citation can serve various functions. It may reflect the citing paper author’s motivation as well as his/her true attitude towards the cited paper. Investigating such information can be achieved through citation content analysis. This thesis develops an 8-category classification scheme on citation function and polarity to help understand what role a citation played in scientific papers. A biomedical citation corpus is annotated with this scheme and experimented with supervised machine learning methods. Several types of features that capture the characteristics of citation sentences are extracted by natural language processing techniques to serve as the inputs of automatic classifiers. The importance of cue phrases in citation classification is also addressed and discussed