By using numerical simulation, we confirm that Takayasu–Sato–Takayasu (TST) model which leads Pareto’s law satisfies the detailed balance under Gibrat’s law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the equation which gives the Pareto index μ in TST model. Moreover, we extend the ...

Γ-convergence results for power-law functionals with variable exponents are obtained. The main motivation comes from the study of (first-failure) dielectric breakdown. Some connections with the generalization of the ∞-Laplace equation to the variable exponent setting are also explored. 2000 Mathematics Subject Classification:

This paper deals with free vibration analysis of continuously graded fiber reinforced (CGFR) truncated conical shell based on third-order shear deformation theory (TSDT), by developing special power-law distributions. The orthotropic (CGFR) truncated conical shell are clamped and simply supported at the both ends. It is assumed to have a smooth variation of fibers volume fraction in the thickne...

This paper obtains solitary waves, shock waves and singular solitons alon with conservation laws of the Rosenau Kortewegde Vries regularized long wave (R-KdV-RLW) equation with power law nonlinearity that models the dynamics of shallow water waves. The ansatz approach and the semi-inverse variational principle are used to obtain these solutions. The constraint conditions for the existence of so...

We consider the Tsallis distribution as a source of the apparent slope of one-particle spectra in heavy-ion collisions and investigate the equation of state of this special kind of quark matter in the framework of non-extensive thermodynamics. We relate the energy per particle to the power-law tail of spectra at a given temperature.

A model for the growth of weighted networks is proposed. The model is based on the edge preferential selection. By the master equation approach, the distributions of strength, weight and degree are provided and results show that each distribution has a power-law tail. Particularly, the network has a high clustering coefficient.

Liquid paraffin can be used as a coolant fluid in electronic and cutting devices due to its suitable capabilities such as electrical insulating, high heat capacity, chemical, and thermal stability, and high boiling point. In this study, the dynamic viscosity of paraffin containing the alumina nanoparticles has been examined experimentally. The nanofluids with different composition of alumina (0...

We prove a lower bound on the rate of relaxation to equilibrium in the H1 norm for a thin film equation. We find a two stage relaxation, with power law decay in an initial interval, followed by exponential decay, at an essentially optimal rate, for large times. The waiting time until the exponential decay sets in is explicitly estimated.

A model for the weighted bipartite network is proposed and the growth mechanism is based on the strength preferential attachment. By the rate equation approach, the strength distribution of the bottom nodes is provided and it has a shifted power-law tail, i.e., P (s) ∝ (s + θ)−γ , for large s. The expressions of the parameters θ and γ are also given.