Introduction to Tsallis Entropy Theory

Entropy ◽  
2017 ◽  
Vol 19 (12) ◽  
pp. 641 ◽  
Author(s):  
Vijay Singh ◽  
Bellie Sivakumar ◽  
Huijuan Cui

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 55 ◽  
Author(s):  
Zhongfan Zhu ◽  
Hongrui Wang ◽  
Dingzhi Peng ◽  
Jie Dou

The settling velocity of a sediment particle is an important parameter needed for modelling the vertical flux in rivers, estuaries, deltas and the marine environment. It has been observed that a particle settles more slowly in the presence of other particles in the fluid than in a clear fluid, and this phenomenon has been termed ‘hindered settling’. The Richardson and Zaki equation has been a widely used expression for relating the hindered settling velocity of a particle with that in a clear fluid in terms of a concentration function and the power of the concentration function, and the power index is known as the exponent of reduction of the settling velocity. This study attempts to formulate the model for the exponent of reduction of the settling velocity by using the probability method based on the Tsallis entropy theory. The derived expression is a function of the volumetric concentration of the suspended particle, the relative mass density of the particle and the particle’s Reynolds number. This model is tested against experimental data collected from the literature and against five existing deterministic models, and this model shows good agreement with the experimental data and gives better prediction accuracy than the other deterministic models. The derived Tsallis entropy-based model is also compared with the existing Shannon entropy-based model for experimental data, and the Tsallis entropy-based model is comparable to the Shannon entropy-based model for predicting the hindered settling velocity of a falling particle in a particle-fluid mixture. This study shows the potential of using the Tsallis entropy together with the principle of maximum entropy to predict the hindered settling velocity of a falling particle in a particle-fluid mixture.


1991 ◽  
Vol 36 (4) ◽  
pp. 347-347
Author(s):  
No authorship indicated
Keyword(s):  

Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.


2013 ◽  
Vol 33 (9) ◽  
pp. 2490-2492
Author(s):  
Yuanxiang QIN ◽  
Liang DUAN ◽  
Kun YUE

ROBOT ◽  
2010 ◽  
Vol 32 (3) ◽  
pp. 289-297
Author(s):  
Xudong TANG ◽  
Yongjie PANG ◽  
Tiedong ZHANG ◽  
Ye LI

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