In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical...

Many natural phenomena display "self-organized criticality" (SOC), (Bak et al., 1987). This refers to spatially extended systems for which patterns of activity characterized by different lengthscales can occur with a probability density that follows a power law with pattern size. Differently from power laws at phase transitions, systems displaying SOC do not need the tuning of an external param...

The study of boundary layer flow and heat transfer of an electrically conducting visco-elastic second grade fluid in a porous medium past a stretching sheet is conducting with power law surface temperature or power law surface heat flux. The flow in boundary layer is considered to be generated solely by the linear stretching of the boundary sheet adjacent to porous medium in a magnetic field wi...

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and the frequently used thermodynamic model are shown to be special cases of a more general distribution that contains a parameter a. This parameter is related to the Lévy index and the Fisher critical exponent , the latter of which describes the power-law fall...

this article introduces a new tri-parameter law of corresponding states from the known regularities, namely the lir and zeno line for dense fluids (when tz=tc). two of these parameters are the zeno line parameters and the third parameter (the fluid parameter), has been obtained from the lir, this parameter is solely dependent upon the fluid characteristics. the third parameter can be obtaind fr...

A maximum entropy framework based on Tsallis entropy is proposed to depict long tail behavior of queue lengths in broadband networks. Queue length expression as measured in terms of number of packets involves Hurwitz-zeta function. When the entropy parameter q in Tsallis entropy is less than unity, the distribution of packets yields power law behavior. In the limit q tending to unity, Tsallis e...

The method of higher-order L-moments (LH-moment) was proposed as a more robust alternative compared to classical characterize extreme events. new derivation will be done for Mielke-Johnson’s Kappa and Three-Parameters Type-II (K3D-II) distributions based on the LH-moments approach. data maximum monthly rainfall Embong station in Terengganu were used case study. analyses conducted using with η=0...

We consider the connected component of the partial duplication model for a random graph, a model which was introduced by Bhan, Galas and Dewey as a model for gene expression networks. The most rigorous results are due to Hermann and Pfaffelhuber, who show a phase transition between a subcritical case where in the limit almost all vertices are isolated and a supercritical case where the proporti...