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We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…
A random distribution of poroelastic spheres in a poroelastic medium obeying Biot's theory is considered. The scattering coefficients of the fast and the slow waves are computed in the low frequency limit using the sealed pore boundary…
Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations…
A growth model for porous sedimentary rocks is proposed, using a simple computer simulation algorithm. We generate the structure by ballistic deposition of particles with a bimodal size distribution. Porosity and specific surface area are…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
We study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in micro-fluidic micro-models of porous media.…
Understanding porous media properties and their scale dependence have been an active subject of research in the past several decades in hydrology, geosciences and petroleum engineering. The scale dependence of flow in porous media is…
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
We explore the experimental observation that complex networks of porous media exhibit the property that the porous coordination number is proportional to its size. Based in this geometry-topology duality we developed an analytical approach…
Fluid stretching in porous media governs the mixing of reactants, contaminants, and nutrients, yet how the solid microstructure controls the stretching statistics remains poorly understood. We investigate how porous-medium heterogeneity…
We study the effect of spatially-correlated heterogeneity on isothermal drying of porous media. We combine a minimal pore-scale model with microfluidic experiments with the same pore geometry. Our simulated drying behavior compare favorably…
We consider $N$ circles of equal radii, $r$, having their centers randomly placed within a square domain $\mathcal{D}$ of size $L \times L$ with periodic boundary conditions ($\mathcal{D} \in \mathbb{R}^2$). When two or more circles…
Information delivery via molecular signals is abundant in nature and potentially useful for industry sensing. Many propagation channels (e.g., tissue membranes and catalyst beds) contain porous medium materials and the impact this has on…
We investigate the upscaling of diffusive transport parameters as function of pore scale material structure using a stochastic framework. We focus on sub-REV (representative elementary volume) scale where the complexity of pore space…
The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray…
We have experimentally studied the distribution of the spatial extent of modes, and the crossover from essentially single-mode to distinctly multi-mode behavior inside a porous gallium phosphide random laser. This system serves as a paragon…