We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1 < h < 2, a fractal distribution function associated with a fractal von Newmann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational ...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...

Fractal geometry (fractional Brownian motion—FBM) is introduced to characterize the pore distribution of porous material. Based on this fractal characterization, a mathematical model of heat conduction is presented to study heat conduction behaviors in porous material with a focus on effective thermal conductivity. The role of pore structure on temperature distribution and heat flux is examined...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...

Sewage solids are usually characterized by non-specific parameters such as suspended solids. The suspended solids has been shown to be an inadequate index for advanced water treatment processes. In this study, the sewages solids particle size distribution was used to provide more detailed information on sewage characteristic. It is hoped that, by introducing particle size distribution, the mech...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...

We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution à la Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticl...