We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities a...We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.展开更多
When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by Verlinde's paper, ...When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.展开更多
A high-flux circulating fluidized bed （CFB） riser （0.076-m I.D. and 10-m high） was operated in a wide range of operating conditions to study its chaotic dynamics, using FCC catalyst particles （dp= 67μm, ρp = 15...A high-flux circulating fluidized bed （CFB） riser （0.076-m I.D. and 10-m high） was operated in a wide range of operating conditions to study its chaotic dynamics, using FCC catalyst particles （dp= 67μm, ρp = 1500 kg·m^-3）. Local solids concentration fluctuations measured using a reflective-type fiber optic probe were processed to determine chaotic invariants （Kolmogorov entropy and correlation dimension）, Radial and axial profiles of the chaotic invariants at different operating conditions show that the core region exhibits higher values of the chaotic invariants than the wall region. Both invariants vary strongly with local mean solids concentration. The transition section of the riser exhibits more complex dynamics while the bottom and top sections exhibit a more uniform macroscopic and less-complex microscopic flow structure. Increasing gas velocity leads to more complex and less predictable solids concentration fluctuations, while increasing solids flux generally lowers complexity and increases predictability. Very high solids flux, however, was observed to increase the entropy.展开更多
基金The NSF (10271057 and 10571086) of ChinaQing-lan Project in Nanjing Universityof Posts and Telecommunications (NY206053)
文摘We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.
基金supported by the National Natural Science Foundation of China(Grant Nos.61471356,and 11647060)the Fundamental Research Funds of Xianyang Normal University(Grant No.15XSYK034)
文摘When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.
文摘A high-flux circulating fluidized bed （CFB） riser （0.076-m I.D. and 10-m high） was operated in a wide range of operating conditions to study its chaotic dynamics, using FCC catalyst particles （dp= 67μm, ρp = 1500 kg·m^-3）. Local solids concentration fluctuations measured using a reflective-type fiber optic probe were processed to determine chaotic invariants （Kolmogorov entropy and correlation dimension）, Radial and axial profiles of the chaotic invariants at different operating conditions show that the core region exhibits higher values of the chaotic invariants than the wall region. Both invariants vary strongly with local mean solids concentration. The transition section of the riser exhibits more complex dynamics while the bottom and top sections exhibit a more uniform macroscopic and less-complex microscopic flow structure. Increasing gas velocity leads to more complex and less predictable solids concentration fluctuations, while increasing solids flux generally lowers complexity and increases predictability. Very high solids flux, however, was observed to increase the entropy.
