On position-space renormalization group approach to percolation

In a position-space renormalization group (PSRG) approach to percolation one calculates the probabilityR(p,b) that a finite lattice of linear sizeb percolates, wherep is the occupation probability of a site or bond. A sequence of percolation thresholdsp _c (b) is then estimated fromR(p _c ,b)=p _c (b) and extrapolated to the limitb to obtainp _c =p _c (). Recently, it was shown that for a certain spanning rule and boundary condition,R(p _c ,)=R _c is universal, and sincep _c is not universal, the validity of PSRG approaches was questioned. We suggest that the equationR(p _c ,b)=, where isany number in (0,1), provides a sequence ofp _c (b)'s thatalways converges top _c asb. Thus, there is anenvelope from any point inside of which one can converge top _c . However, the convergence is optimal if =R _c . By calculating the fractal dimension of the sample-spanning cluster atp _c , we show that the same is true aboutany critical exponent of percolation that is calculated by a PSRG method. Thus PSRG methods are still a useful tool for investigating percolation properties of disordered systems.     

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.     

Molecular dynamics simulation of pressure-driven water flow in silicon-carbide nanotubes

Many properties of silicon carbide (SiC) nanotubes, such as their high mechanical strength and resistance to corrosive environments, are superior to those of their carboneous counterparts, namely, carbon nanotubes (CNTs) and, therefore, SiC nanotubes can be a viable alternative to CNTs in a variety of applications. We employ molecular dynamics simulations to examine flow of water in SiC nanotubes and to study the differences and similarities with the same phenomenon in the CNTs. The simulations indicate that SiC nanotubes always provide larger flow enhancements than those reported for the CNTs. Moreover, a given flow enhancement in SiC nanotubes requires an applied pressure gradient that is at least an order of magnitude smaller than the corresponding value in a CNT of the same size.     

A Langevin equation for the rates of currency exchange based on the Markov analysis

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D⁽¹⁾ and D⁽²⁾, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.     

Shape of a wave front in a heterogenous medium

Wave propagation in a heterogeneous medium, characterized by a distribution of local elastic moduli, is studied. Both acoustic and elastic waves are considered, as are spatially random and power-law correlated distributions of the elastic moduli with nondecaying correlations. Three models--a continuum scalar model, and two discrete models--are utilized. Numerical simulations indicate the existence, at all times, of the relation, alpha = H, where alpha is the roughness exponent of the wave front in the medium, and H is the Hurst exponent that characterizes the spatial correlations in the distribution of the local elastic moduli. Hence, a direct relation between the static morphology of an inhomogeneous correlated medium and its dynamical properties is established. In contrast, for a wave front in random media, alpha = 0 (logarithmic growth) at short times, followed by a crossover to the classical value, alpha = 1/2, at long times.     

A Study of the Role of Microfractures in Counter-Current Spontaneous Imbibition by Lattice Boltzmann Simulation

Transport in Porous Media - During waterflooding, spontaneous imbibition is a fundamental recovery mechanism in fractured reservoirs. A large number of numerical and experimental studies have been...