in this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. in particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.

Fluidized fractal clusters of fine particles display critical-like dynamics at the jamming transition, characterized by a power law relating consolidation stress with volume fraction increment [sigma--(c) proportional, variant(Deltaphi)(beta)]. At a critical stress clusters are disrupted and there is a crossover to a logarithmic law (Deltaphi = nu logsigma--(c)) resembling the phenomenology of ...

Here we show theoretically that the history of solid growth during ‘‘rapid’’ solidification must be S-shaped, in accord with the constructal law of design in nature. In the beginning the rate of solidification increases and after reaching amaximum it decreasesmonotonically as the volume of solid tends toward a plateau. The S-history is a consequence of four configurations for the flow of heat f...

We have characterized a montmorillonite-based organoclay dispersed in three different nonaqueous solvents using a combination of x-ray scattering, small-angle neutron scattering (SANS), and ultrasmall angle neutron scattering (USANS), together with rheological measurements. Consistent with these measurements, we present a structural model for the incompletely dispersed clay as consisting of ran...

In this work, we consider the existence of global solution and exponential decay a nonlinear porous elastic system with time delay. The term as well delay acting in equation volume fraction. order to obtain uniqueness solution, will use semigroup theory linear operators under certain relation involving coefficients together Lyapunov functional, establish energy associated system.

The first bibliometric law appeared in Alfred J. Lotka’s 1926 examination of author productivity in chemistry and physics. The result is that the productivity distribution is thought to be described by a power law. In this paper, Lotka’s original data on author productivity in chemistry is reconsidered by comparing the fit of the data to both a discrete power law and a discrete power law with e...

For better understanding the effect of nanofluid flow in a porous medium, a set of experiments were conducted on a horizontal glass micromodel for Al2O3-water nanofluids. To characterize the flow of nanofluids the same experiment was done by pure water. The glass micromodel was constructed by a photolithography techniqu...

Several acquisitions of x-ray microtomography have been performed on a beads packing while it compacts under vertical vibrations. An image analysis allows to study the evolution of the packing structure during its progressive densification. In particular, the volume distribution of the pores reveals a large tail, compatible to an exponential law, which slowly reduces as the system gets more com...

Recently, Fabrikant, Koutsoupias and Papadimitriou [7] introduced a natural and beautifully simple model of network growth involving a trade-off between geometric and network objectives, with relative strength characterized by a single parameter which scales as a power of the number of nodes. In addition to giving experimental results, they proved a power-law lower bound on part of the degree s...

A two-phase flow model with liquid-solid transformation [M. Hütter, Phys. Rev. E 64, 011209 (2001)] is discussed, focusing on two elements: (1) the driving force for nucleation and growth and (2) the contribution of phase interfaces to the momentum balance. According to the model, nucleation and growth are partly driven by deviations from the equilibrium pressure difference between the phases, ...