Upper Estimates on the Higher-dimensional Multifractal Spectrum of Local Entropy

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.

Gravitational correlation, black hole entropy,and information conservation

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.

A MNCIE method for registration of ultrasound images

A new approach to the problem of registration of ultrasound images is presented, using a concept of Nonlinear Correlation Information Entropy (NCIE) as the matching criterion. The proposed method applies NCIE to measure the correlation degree between the image intensities of corresponding voxel in the floating and reference images. Registration is achieved by adjustment of the relative position until NCIE between the images is maximized. However, unlike mutual information (MI), NCIE varies in the closed interval [0, 1], and around the extremum it varies sharply, which makes it possible that thresholds of NCIE can be used to boost the search for the registration transformation. Using this feature of NCIE, we combine the downhill simplex searching algorithm to register the ultrasound images. The simulations are conducted to testify the effectiveness and rapidity of the proposed registration method, in which the ultrasound floating images are aligned to the reference images with required registration accuracy. Moreover, the NCIE based method can overcome local minima problem by setting thresholds and can take care of the differences in contrast between the floating and reference images.

ANALYSIS OF THE CHAOTIC DYNAMICS OF A HIGH-FLUX CFB RISER USING SOLIDS CONCENTRATION MEASUREMENTS

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.