Biomedical subjects

Muhammad Sahimi

Publications and source records attributed to Muhammad Sahimi.

13 recordsLinked to original sources

PubMed2006

Development of optimal models of porous media by combining static and dynamic data: the porosity distribution.

This paper is part of a project, the goal of which is the development of the optimal spatial distributions of the porosity and permeability of a large-scale porous medium by using complementary static and dynamic data for the medium. The data include limited measurements of the porosity, which the method honors (preserves) in the optimal model and utilizes its correlation function, together with the first-arrival (FA) times, at a certain number of receivers, of seismic waves that have propagated in the medium and the time dependence of the pressure of a fluid flowing in the medium. The method uses the simulated-annealing (SA) technique in order to develop the optimal model. In the present paper we utilize the porosity and FA times data in order to develop the optimal spatial distribution of the porosity. This is accomplished by combining the SA method with a simulator that solves for the numerical solution of the acoustic-wave equation from which the FA times are estimated, limited porosity, and FA times data. We show that the optimal model not only honors the data, but also provides accurate estimates of the porosities in the rest of the porous medium. The efficiency of the computations is discussed in detail.

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PubMed2006

Generation of long-range correlations in large systems as an optimization problem.

We propose an efficient method of generating long-range correlations in large systems. The development of this method was motivated by the problem of constructing an optimal model for a large-scale porous medium. There are typically long-range correlations in the properties of such porous media, such as their permeability and porosity, for which there are usually only limited data. The optimal model must not only honor (preserve) the available data and their correlation function, but also accurately predict the future behavior of fluid flow in the media. We formulate the problem of generating the long-range correlations as one of optimization, and utilize simulated annealing to generate a d-dimensional array which contains the correlations and honors the existing data. The optimization process is based on the data's correlation function. The method is, therefore, free of the many numerical difficulties and/or limitations that most previous techniques suffer from. It is completely general and may be used for generating long-range correlations with any type of correlation function, in both isotropic and anisotropic media. Representative examples are presented, and the method's efficiency and accuracy are discussed.

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PubMed2006

Supercritical fluids in porous composite materials: direction-dependent flow properties.

The results of extensive nonequilibrium molecular dynamics simulations of flow and transport of a pure fluid, as well as a binary fluid mixture, through a porous material composed of a macropore, a mesopore, and a nanopore, in the presence of an external pressure gradient, are reported. We find that under supercritical conditions, unusual phenomena occur that give rise to direction-dependent and pressure-dependent permeabilities for the fluids' components. The results, which are also in agreement with a continuum formulation of the problem, indicate that the composite nature of the material, coupled with condensation, give rise to the direction-dependent permeabilities. Therefore, modeling flow and transport of fluids, in the supercritical regime, in porous materials with the type of morphology considered in this paper (such as supported porous membranes) would require using effective permeabilities that depend on both the external pressure drop and the direction along which it is applied to the materials.

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PubMed2006

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.

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PubMed2005

Diffusion in scale-free networks with annealed disorder.

The scale-free (SF) networks that have been studied so far contained quenched disorder generated by random dilution which does not vary with the time. In practice, if a SF network is to represent, for example, the worldwide web, then the links between its various nodes may temporarily be lost and reestablished again later on. This gives rise to SF networks with annealed disorder. Even if the disorder is quenched, it may be more realistic to generate it by a dynamical process that is happening in the network. In this paper, we study diffusion in SF networks with annealed disorder generated by various scenarios, as well as in SF networks with quenched disorder which, however, is generated by the diffusion process itself. Several quantities of the diffusion process are computed, including the mean number of distinct sites visited, the mean number of returns to the origin, and the mean number of connected nodes that are accessible to the random walkers at any given time. The results, including (1) greatly reduced growth with the time of the mean number of distinct sites visited, (2) blocking of the random walkers, (3) the existence of a phase diagram that separates the region in which diffusion is possible from one in which diffusion is impossible, and (4) a transition in the structure of the networks at which the mean number of distinct sites visited vanishes, indicate completely different behavior for the computed quantities than those in SF networks with quenched disorder generated by simple random dilution.

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PubMed2005

Atomistic simulation of nanoporous layered double hydroxide materials and their properties. I. Structural modeling.

An atomistic model of layered double hydroxides, an important class of nanoporous materials, is presented. These materials have wide applications, ranging from adsorbents for gases and liquid ions to nanoporous membranes and catalysts. They consist of two types of metallic cations that are accommodated by a close-packed configuration of OH- and other anions in a positively charged brucitelike layer. Water and various anions are distributed in the interlayer space for charge compensation. A modified form of the consistent-valence force field, together with energy minimization and molecular dynamics simulations, is utilized for developing an atomistic model of the materials. To test the accuracy of the model, we compare the vibrational frequencies, x-ray diffraction patterns, and the basal spacing of the material, computed using the atomistic model, with our experimental data over a wide range of temperature. Good agreement is found between the computed and measured quantities.

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PubMed2005

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.

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PubMed2005

Self-affine fractal distributions of the bulk density, elastic moduli, and seismic wave velocities of rock.

The scale dependence of the bulk density rho and seismic wave velocities V(p) and V(s) and the possibility of the existence of long-range correlations in such properties in field-scale porous media (FSPM) are investigated. We analyze measured data for rho, V(p), and V(s) for nine FSPM, using the maximum entropy method and the wavelet decomposition technique. The analysis indicates the existence of long-range correlations in the data, characterized by self-affine fractal distributions that follow the statistics of the fractional Brownian motion. Therefore, the elastic moduli of the FSPM should also be fractally distributed and contain long-range correlations; our analysis confirms this. The implications of the results for modeling elastic moduli of porous rock, fracture propagation in FSPM, and the interpretation of seismic wave recordings of FSPM are discussed, and the possible deviations from the classical analysis of such phenomena are pointed out.

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PubMed2004

Numerical simulation of a continuum model of growth of thin composite films.

We present the results of extensive numerical integration in ( 1+1 ) dimensions of a set of equations that couple the Kardar-Parisi-Zhang (KPZ) equation to the time-dependent Ginzburg-Landau (TDGL) equation, recently proposed for modeling the growth of thin composite solid films. We find that for times t shorter than a crossover time t(c) the mean domain size L(t) grows logarithmically with the time, whereas for t>> t(c) L(t) grows as t(1/ z(m) ), with z(m) being nonuniversal and depending on the parameters of the model. The roughness exponent is also found to be nonuniversal. Thus, neither the dynamics of the domains' growth is governed by the TDGL equation, nor is the scaling of the surface roughness described by the KPZ equation.

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PubMed2004

Molecular dynamics simulations of transport and separation of carbon dioxide-alkane mixtures in carbon nanopores.

The configurational-bias Monte Carlo method, which is used for efficient generation of molecular models of n-alkane chains, is combined for the first time with the dual control-volume grand-canonical molecular-dynamics simulation, which has been developed for studying transport of molecules in pores under an external potential gradient, to investigate transport and separation of binary mixtures of n-alkanes, as well as mixtures of CO2 and n-alkanes, in carbon nanopores. The effect of various factors, such as the temperature of the system, the composition of the mixture, and the pore size, on the separation of the mixtures is investigated. We also report the preliminary results of an experimental study of transport and separation of some of the same mixtures in a carbon molecular-sieve membrane with comparable pore sizes. The results indicate that, for the mixtures considered in this paper, even in very small carbon nanopores the energetic effects still play a dominant role in the transport and separation properties of the mixtures, whereas in a real membrane they are dominated by the membrane's morphological characteristics. As a result, for the mixtures considered, a single pore may be a grossly inadequate model of a real membrane, and hence one must resort to three-dimensional molecular pore network models of the membrane.

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PubMed2003

Lattice Boltzmann simulation of fluid flow in fracture networks with rough, self-affine surfaces.

Using the lattice Boltzmann method, we study fluid flow in a two-dimensional (2D) model of fracture network of rock. Each fracture in a square network is represented by a 2D channel with rough, self-affine internal surfaces. Various parameters of the model, such as the connectivity and the apertures of the fractures, the roughness profile of their surface, as well as the Reynolds number for flow of the fluid, are systematically varied in order to assess their effect on the effective permeability of the fracture network. The distribution of the fractures' apertures is approximated well by a log-normal distribution, which is consistent with experimental data. Due to the roughness of the fractures' surfaces, and the finite size of the networks that can be used in the simulations, the fracture network is anisotropic. The anisotropy increases as the connectivity of the network decreases and approaches the percolation threshold. The effective permeability K of the network follows the power law K approximately (beta), where is the average aperture of the fractures in the network and the exponent beta may depend on the roughness exponent. A crossover from linear to nonlinear flow regime is obtained at a Reynolds number Re approximately O(1), but the precise numerical value of the crossover Re depends on the roughness of the fractures' surfaces.

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PubMed2002

Diffusion in disordered media with long-range correlations: anomalous, Fickian, and superdiffusive transport and log-periodic oscillations.

We present the results of extensive Monte Carlo simulation of diffusion in disordered media with long-range correlations, a problem which is relevant to transport of contaminants in field-scale porous media, such as aquifers, gas transport in soils, and transport in composite materials. The correlations are generated by a fractional Brownian motion characterized by a Hurst exponent H. For H>1/2 the correlations appear to have no effect, and the transport process is diffusive. However, for H<1/2 and depending on the morphology of the medium, three distinct types of transport processes, namely, anomalous, Fickian, and superdiffusive transport may emerge. Moreover, if the medium is anisotropic and stratified, biased diffusion in it is characterized by power-law growth of the mean square displacements with the time in which the effective exponents characterizing the power-law oscillates log periodically with the time. This result cannot be predicted by any of the currently available continuum theories of transport in disordered media.

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PubMed2002

Nonuniversality of invasion percolation in two-dimensional systems.

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension D(f) of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, D(f) approximately equal to 1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.

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