arXiv subjects

Muhammad Sahimi

Publications and source records attributed to Muhammad Sahimi.

At least 19 recordsLinked to original sources

arXiv2025

Heterogeneous Wettability Alters Methane Migration and Leakage in Shallow Aquifers

Capillary heterogeneity is increasingly recognized as a first-order control on gas plume migration and trapping in aquifers and storage formations. We show that spatial variability in the water-methane contact angle, determined by mineralogy and salinity, alters capillary entry pressures and migration pathways. Using molecular dynamics simulations, we estimate contact angles on quartz and kaolinite under fresh and saline conditions and incorporate these results into continuum-scale multiphase flow simulations via a contact-angle-informed Leverett J function, mapping wettability directly onto continuum-scale flow properties. Accounting for contact angle heterogeneity affects methane behavior: mobile and residually trapped methane in aquifers decrease by up to 10 percent, while leakage to the atmosphere increases by as much as 20 percent. The magnitude of this effect depends on permeability contrast, leakage rate, salinity, and facies proportions. By coupling molecular-scale wettability to continuum-scale flow and transport, this cross-scale framework provides a physically grounded basis for groundwater protection and risk assessment and yields more reliable emissions estimates. The approach can be generalized to other subsurface gas transport problems, including hydrogen and carbon dioxide storage, as well as natural releases such as methane from permafrost thaw.

physics.flu-dyn↗

arXiv2023

Data-Driven Reconstruction of Stochastic Dynamical Equations based on Statistical Moments

Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid. If such processes are Markov, then their probability distribution is governed by the Kramers-Moyal (KM) equation, a partial differential equation that involves an infinite number of coefficients, which depend on the state variable. The KM coefficients must be evaluated based on measured time series for a data-driven reconstruction of the governing equations for the stochastic dynamics. We present an accurate method of computing the KM coefficients, which relies on computing the coefficients' conditional moments based on the statistical moments of the time series. The method's advantages over state-of-the-art approaches are demonstrated by investigating prototypical stochastic processes with well-known properties.

cond-mat.stat-mech↗

arXiv2023

Physics-Informed and Data-Driven Discovery of Governing Equations for Complex Phenomena in Heterogeneous Media

Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition softwares/hardwares are providing vast amounts of data for various complex phenomena, ranging from those in atomospheric environment, to large-scale porous formations, and biological systems. The tremendous increase in the speed of scientific computing has also made it possible to emulate diverse high-dimensional, multiscale and multiphysics phenomena that contain elements of stochasticity, and to generate large volumes of numerical data for them in heterogeneous systems. The difficulty is, however, that often the governing equations for such phenomena are not known. A prime example is flow, transport, and deformation processes in macroscopically-heterogeneous materials and geomedia. In other cases, the governing equations are only partially known, in the sense that they either contain various coefficients that must be evaluated based on data, or that they require constitutive relations, such as the relationship between the stress tensor and the velocity gradients for non-Newtonian fluids in the momentum conservation equation, in order for them to be useful to the modeling. Several classes of approaches are emerging to address such problems that are based on machine learning, symbolic regression, the Mori-Zwanzig projection operator formulation, sparse identification of nonlinear dynamics, data assimilation, and stochastic optimization and analysis, or a combination of two or more of such approaches. This Perspective describes the latest developments in this highly important area, and discusses possible future directions.

cs.CE↗

arXiv2023

Percolation and conductivity in evolving disordered media

Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the networks' bonds remains constant throughout the entire process. There are, however, many important problems in which the conductance of the bonds evolves over time and does not remain constant. Examples include clogging, dissolution and precipitation, catalytic processes in porous materials, as well as the deformation of a porous medium by applying an external pressure or stress to it that reduces the size of its pores. We introduce two percolation models to study the evolution of the conductivity of such networks. The two models are related to natural and industrial processes involving clogging, precipitation, and dissolution processes in porous media and materials. The effective conductivity of the models is shown to follow known power laws near the percolation threshold, despite radically different behavior both away from and even close to the percolation threshold. The behavior of the networks close to the percolation threshold is described by critical exponents, yielding bounds for traditional percolation exponents. We show that one of the two models belongs to the traditional universality class of percolation conductivity, while the second model yields non-universal scaling exponents.

cond-mat.stat-mech↗

arXiv2022

AC Hopping Conduction At Extreme Disorder Takes Place On The Bond Invasion Percolation Cluster

It has been suggested that ac conduction in extremely disordered solids occurs on the critical percolation cluster. In this note, we argue that in fact the transport process takes place on the bond invasion percolation cluster (BIPC). The structure of the BIPC is universal independent of the conductances of the bonds, which explains why the rescaled ac conductivity is a universal function of the rescaled frequency. It also explains why the effective-medium approximation provides quantitatively accurate predictions for the effective conductivity.

cond-mat.dis-nn↗

arXiv2020

Nanoscale detection of metastable states in porous and granular media

Microseismicity in subsurface geologic environments, such as sandstone gas reservoirs, is expected in the presence of liquid or gas injection. Although difficult to predict, the potential for microseismic events is important to field-scale projects, such as geologic storage of CO2 whereby the gas is injected into natural sandstone formations. We conjecture that a primary factor causing microseismicity is the existence of metastable states in granular porous medium and provide experimental evidence for its validity. External perturbation trigger abrupt relaxation events, which, with a certain probability, can grow into macroscopic microseismic events. Here the triggering perturbation is produced by cooling to a cryogenic temperature. As the "sensor" for the abrupt relaxation events we use thin Al films deposited on the sandstone surface. We show that as the temperature is varied, the films' resistance exhibits sharp jumps, which we attribute to mechanical restructuring or microfractures in the fabric of the sandstone. We checked the superconducting characteristics of the Al thin films on the sandstone and found microwave-induced Shapiro steps on the voltage-current diagrams. Such quantized steps provide indicates that the film is made of a network of nanobridges, which makes it ever more sensitive to abrupt relaxation events occurring in the substrate, i.e., in the underlying sandstone.

physics.app-ph↗

arXiv2020

Numerical Simulation and the Universality Class of the KPZ Equation for Curved Substrates

The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades. Some experiments indicated the power law for the interface width, $w(t)\sim t^\beta$, remains the same as in growth on planar surfaces. Escudero (Phys. Rev. Lett. {\bf 100}, 116101, 2008) argued, however, that for the radial KPZ equations in (1+1)-dimension $w(t)$ should increase as $w(t)\sim [\ln(t)]^{1/2}$ in the long-time limit. Krug (Phys. Rev. Lett. {\bf 102}, 139601, 2009) argued, however, that the dynamics of the interface must remain unchanged with a change in the geometry. Other studies indicated that for radial growth the exponent $\beta$ should remain the same as that of the planar case, regardless of whether the growth is linear or nonlinear, but that the saturation regime will not be reached anymore. We present the results of extensive numerical simulations in (1+1)-dimensions of the radial KPZ equation, starting from an initial circular substrate. We find that unlike the KPZ equation for flat substrates, the transition from linear to nonlinear universality classes is not sharp. Moreover, in the long-time limit the interface width exhibits logarithmic growth with the time, instead of saturation. We also find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that the average radius of the interface decreases with time and reaches a minimum but not zero value.

cond-mat.stat-mech↗

arXiv2019

Effect of heterogeneity and spatial correlations on the structure of tumor invasion front in cellular environments

Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the biological mechanisms of tumor growth have been gained. We develop a model to study how tumors' invasion front depends on the relevant properties of a cellular environment. To do so, we develop a model based on a nonlinear reaction-diffusion equation, the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation, to model tumor growth. Our study aims to understand how heterogeneity in the cellular environment's stiffness, as well as spatial correlations in its morphology, the existence of both of which has been demonstrated by experiments, affects the properties of tumor invasion front. It is demonstrated that three important factors affect the properties of the front, namely, the spatial distribution of the local diffusion coefficients, the spatial correlations between them, and the ratio of the cells' duplication rate and their average diffusion coefficient. Analyzing the scaling properties of tumor invasion front computed by solving the governing equation, we show that, contrary to several previous claims, the invasion front of tumors and cancerous cell colonies cannot be described by the well-known models of kinetic growth, such as the Kardar-Parisi-Zhang equation.

cond-mat.stat-mech↗

arXiv2019

Efficient Simulation of Fluid Flow and Transport in Heterogeneous Media Using Graphics Processing Units (GPUs)

Networks of interconnected resistors, springs and beams, or pores are standard models of studying scalar and vector transport processes in heterogeneous materials and media, such as fluid flow in porous media, and conduction, deformations, and electric and dielectric breakdown in heterogeneous solids. The computation time and required memory are two limiting factors that hinder the scalability of the computations to very large sizes. We present a dual approach, based on the use of a combination of the central processing units (CPUs) and graphics processing units (GPUs), to simulation of flow, transport, and similar problems using the network models. A mixed-precision algorithm, together with the conjugate-gradient method is implemented on a single GPU solver. The efficiency of the method is tested with a variety of cases, including pore- and random-resistor network models in which the conductances are long-range correlated, and also contain percolation disorder. Both isotropic and anisotropic networks are considered. To put the method to a stringent test, the long-range correlations are generated by a fractional Brownian motion (FBM), which we generate by a message-passing interface method. For all the cases studied an overall speed-up factor of about one order of magnitude or better is obtained, which increases with the size of the network. Even the critical slow-down in networks near the percolation threshold does not decrease the speed-up significantly. We also obtain approximate but accurate bounds for the permeability anisotropy $K_x/K_y$ for stratified porous media.

physics.comp-ph↗

arXiv2019

Regulation of Migration of Chemotactic Tumor Cells by the Spatial Distribution of the Collagen Fibers' Orientation

Collagen fibers, an important component of the extracellular matrix (ECM), can both inhibit and promote cellular migration. {\it In-vitro} studies have revealed that the fibers' orientations are crucial to cellular invasion, while {\it in-vivo} investigations have led to the development of tumor-associated collagen signatures (TACS) as an important prognostic factor. Studying biophysical regulation of cell invasion and the effect of the fibers' oritentation not only deepens our understanding of the phenomenon, but also helps classifying the TACSs precisely, which is currently lacking. We present a stochastic model for random/chemotactic migration of cells in fibrous ECM, and study the role of the various factors in it. The model provides a framework, for the first time to our knowledge, for quantitative classification of the TACSs, and reproduces quantitatively recent experimental data for cell motility. It also indicates that the spatial distribution of the fibers' orientations and extended correlations between them, hitherto ignored, as well as dynamics of cellular motion all contribute to regulation of the cells' invasion length, which represents a measure of metastatic risk. Although the fibers' orientations trivially affect randomly moving cells, their effect on chemotactic cells is completely nontrivial and unexplored, which we study in this paper.

q-bio.CB↗

arXiv2019

Exact enumeration approach to first-passage time distribution of non-Markov random walks

We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of a fractional Brownian motion with a Hurst exponent $H\in(1/2,1)$ that describes numerous non-Markov stochastic phenomena in physics, biology and geology, and for which the limit $H=1/2$ represents a Markov process.

cond-mat.stat-mech↗

arXiv2019

Morphology and Kinetics of Random Sequential Adsorption of Superballs: From Hexapods to Cubes

Superballs represent a class of particles whose shapes are defined by ${|x|}^{2p}+{|y|}^{2p}+{|z|}^{2p} \le R^{2p}$, with $p\in(0,\infty)$ being the "deformation parameter". $0 1$ one has, respectively, families of convex octahedrallike and cubelike particles, with $p=1,\;0.5$ and $\infty$ representing spheres, octahedra, and cubes. Colloidal zeolite suspensions, catalysis, and adsorption, as well as biomedical magnetic nanoparticles are but a few of the applications of packing of superballs. We introduce a universal method for simulating random sequential adsorption of superballs, which we refer to as "low-entropy" algorithm, in contrast with the conventional algorithm that represents a "high-entropy" method. The two algorithms yield, respectively, precise estimates of the jamming fraction $\phi_\infty(p)$ and $\nu(p)$, the exponent that characterizes the kinetics of adsorption at long times $t$, $\phi(\infty)-\phi(t)\sim t^{-\nu(p)}$. Precise estimates of $\phi_\infty(p)$ and $\nu(p)$ are obtained and shown to be in agreement, in some special limits, with the existing analytical and numerical results.

cond-mat.soft↗

arXiv2018

Role of the Interplay Between the Internal and External Conditions in Invasive Behavior of Tumors

Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the dynamic interactions between the two. A stem cell theory of cancer has recently been developed that suggests the existence of a subpopulation of self-renewing tumor cells which is responsible for tumorigenesis, and is able to initiate metastatic spreading. The question of abundance of the cancer stem cells (CSCs) and its relation to tumor malignancy has, however, remained an unsolved problem and has been a subject of recent debates. In this paper, we propose a novel model beyond the standard stochastic models of tumor development, in order to explore the effect of the density of the CSCs and oxygen on the tumor's invasive behavior. The model identifies natural selection as the underlying process for complex morphology of tumors, which has been observed experimentally, and indicates that their invasive behavior depends on {\it both} the number of the CSCs and the oxygen density in the microenvironment. The interplay between the external and internal conditions may pave the way for a new cancer therapy.

physics.bio-ph↗

arXiv2017

Hysteretic behavior of electrical conductivity in packings of particles

We address the problem of predicting saturation-dependent electrical conductivity {\sigma} in packings of spheres during drainage and imbibition. The effective-medium approximation (EMA) and the universal power law of percolation for {\sigma} are used, respectively, at higher and low water saturations to predict the conductivity, with the crossover between the two occurring at some intermediate saturation Swx. The main input to the theory is a single parameter that we estimate using the capillary pressure data. The predictions are compared with experimental, as well as numerical data for three distinct types of packings. The results for drainage in all the packings indicate that the universal power law of percolation is valid over the entire range of Sw. For imbibition, however, the universal power law crosses over to the EMA at Swx = 0.5. We also find that the effect of the pore-size distribution on the {\sigma}-Sw relation is minimal during both drainage and imbibition.

physics.flu-dyn↗

arXiv2013

Dynamic renormalization group analysis of propagation of elastic waves in two-dimensional heterogeneous media

We study localization of elastic waves in two-dimensional heterogeneous solids with randomly distributed Lam\'e coefficients, as well as those with long-range correlations with a power-law correlation function. The Matin-Siggia-Rose method is used, and the one-loop renormalization group (RG) equations for the the coupling constants are derived in the limit of long wavelengths. The various phases of the coupling constants space, which depend on the value $\rho$, the exponent that characterizes the power-law correlation function, are determined and described. Qualitatively different behaviors emerge for $\rho<1$ and $\rho>1$. The Gaussian fixed point (FP) is stable (unstable) for $\rho<1$ ($\rho>1$). For $\rho<1$ there is a region of the coupling constants space in which the RG flows are toward the Gaussian FP, implying that the disorder is irrelevant and the waves are delocalized. In the rest of the disorder space the elastic waves are localized. We compare the results with those obtained previously for acoustic wave propagation in the same type of heterogeneous media, and describe the similarities and differences between the two phenomena.

cond-mat.dis-nn↗

arXiv2013

Numerical simulation of the localization of elastic waves in two- and three-dimensional heterogeneous media

Localization of elastic waves in two-dimensional (2D) and three-dimensional (3D) media with random distributions of the Lam\'e coefficients (the shear and bulk moduli) is studied, using extensive numerical simulations. We compute the frequency-dependence of the minimum positive Lyapunov exponent $\gamma$ (the inverse of the localization length) using the transfer-matrix method, the density of states utilizing the force-oscillator method, and the energy-level statistics of the media. The results indicate that all the states may be localized in the 2D media, up to the disorder width and the smallest frequencies considered, although the numerical results also hint at the possibility that there might a small range of the allowed frequencies over which a mobility edge might exist. In the 3D media, however, most of the states are extended, with only a small part of the spectrum in the upper band tail that contains localized states, even if the Lam\'e coefficients are randomly distributed. Thus, the 3D heterogeneous media still possess a mobility edge. If both Lam\'e coefficients vary spatially in the 3D medium, the localization length $\Lambda$ follows a power law near the mobility edge, $\Lambda\sim(\Omega-\Omega_c)^{-\nu}$, where $\Omega_c$ is the critical frequency. The numerical simulation yields, $\nu \simeq 1.89\pm 0.17$, significantly larger than the numerical estimate, $\nu\simeq 1.57\pm 0.01$, and $\nu=3/2$, which was recently derived by a semiclassical theory for the 3D Anderson model of electron localization...

cond-mat.dis-nn↗

arXiv2009

Turbulent-Like Behavior of Seismic Time Series

We report on a novel stochastic analysis of seismic time series for the Earth's vertical velocity, by using methods originally developed for complex hierarchical systems, and in particular for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced change of the shapes of the probability density functions (PDF) of the series' increments. Before and close to an earthquake the shape of the PDF and the long-range correlation in the increments both manifest significant changes. For a moderate or large-size earthquake the typical time at which the PDF undergoes the transition from a Gaussian to a non-Gaussian is about 5-10 hours. Thus, the transition represents a new precursor for detecting such earthquakes.

physics.geo-ph↗

arXiv2007

Uncertainty in the Fluctuations of the Price of Stocks

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.

q-fin.ST↗