In a recent Letter, Buhot [1] proposes that entropy driven phase separation in hard-core binary mixtures is directly related to a bond-percolation transition. In particular, Buhot suggests that a phase instability occurs when the coordination number n b , defined as n b ෇ r l Z s l #r#s l ͑11R͒ g ll ͑r͒ dr , (1) is equal to zp c , where z is the coordination number of a particular crystal lattice, ...

The aim of this paper is to generalize the well-known asymptotic shape result for first-passage percolation on Zd to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet points to a deterministic shape that does not depend on the random environment. As a special cas...

The word percolation, borrowed from the Latin, refers to the seeping or oozing of a liquid through a porous medium, usually to be strained. In this and related senses it has been in use since the seventeenth century. It was introduced more recently into mathematics by S. R. Broadbent and J. M. Hammersley ([BH]) and is a branch of probability theory that is especially close to statistical mechan...

A computer algorithm is implemented to construct 3D cubic pore networks that simultaneously honor nuclear magnetic resonance (NMR) and mercury injection capillary pressure (MICP) measurements on core samples. The algorithm uses discretized pore-body size distributions from NMR and pore-throat size vs. incremental pore-volume fraction information from MICP as initial inputs. Both pore-throat rad...

PURPOSE To evaluate the safety and performance of a second-generation device for CO2 laser-assisted sclerectomy surgery system in experimental models. MATERIALS AND METHODS Laser-assisted deep sclerectomy using a modified CO2 laser system (OT-134-"IOPtiMate"; IOPtima Ltd, Israel) was performed in 3 experimental models: enucleated pig eyes, human cadaver eyes, and live rabbit eyes. A half-thic...

Flow in a porous medium, a problem with important practical applications, has motivated a large number of theoretical and experimental studies [1]. Aiming to understand the complex interplay between the dynamics of flow processes and randomness characterizing the porous medium, a number of models have been introduced that capture different aspects of various experimental situations. One of the ...

The measured values of the matter energy density and the vacuum energy density are obtained using an adiabatic black hole percolating model at the critical point. The percolation of black holes is related with an expanding isotropic universe filled with the most entropic fluid saturating the holographic bound.

The measured values of the matter energy density and the vacuum energy density are obtained using an adiabatic black hole percolating model at the critical point. The percolation of black holes is related with an expanding isotropic universe filled with the most entropic fluid saturating the holographic bound.

We investigate the multiscaling behaviour of usual and directed invasion percolation, with and without a power-law decay with the distance from an initial seed in the distribution of random numbers. We find universal multiscaling behaviour only in the presence of a power-law gradient in space. Invasion percolation [ 11 is a geometrical growth model that has been used to describe the penetration...

The equilibrium as well as nonequilibrium phase behaviors of colloidal dispersions have been investigated using statistical-mechanical theories of fluids and solids in complement with the renormalization-group (RG) theory. It is shown that the osmotic second virial coefficient at the critical point of the fluid-fluid transition varies with the range of attractions and is sensitive to specific f...