Related papers: Precise algorithms to compute surface correlation …
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
The pore-surface and surface-surface correlation functions are structural characteristics that play an important role in theoretical materials science and in small-angle scattering theory. Exact analytical expressions for the surface…
By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts, including porous and…
It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function $S_2(\mathbf{r})$ is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye…
Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…
In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient…
Understanding structure-function relationships is essential to advance the manufacturing of next-gen materials with desired properties and functionalities. Precise and rapid measurement of features like wrinkle size, droplet diameter, and…
We compare theoretical, experimental, and computational approaches to random rough surfaces. The aim is to produce rough surfaces with desirable correlations and to analyze the correlation functions extracted from the surface profiles.…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such {\it Debye…
Microfluidic devices offer unique opportunities to directly observe multiphase flow in porous media. However, as a direct representation of flow in geological pore networks, conventional microfluidics face several challenges. One is that…
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of correlation…
The ability to image materials at the microscale from long-wavelength wave data is a major challenge to the geophysical, engineering and medical fields. Here, we present a framework to constrain microstructure geometry and properties from…
Two-phase random textures abound in a host of contexts, porous and composite media, ecological structures, biological media and astrophysical structures. Questions surrounding the spatial structure of such textures continue to pose many…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…