Related papers: Fractal continuum model for the adsorption-diffusi…
A Monte Carlo model of radiative transfer in multi-phase dusty media is applied to the situation of stars and clumpy dust in a sphere or a disk. The distribution of escaping and absorbed photons are shown for various filling factors and…
Fluid flow through bimodal porous media, characterized by a distinct separation in pore size distribution, is critical in various scientific and engineering applications, including groundwater management, oil and gas production, and carbon…
Mathematically modeling complex transport phenomena at the molecular level can be a powerful tool for identifying transport mechanisms and predicting macroscopic properties. We use two different stochastic time series models, parameterized…
This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel $L^2$-projection variational transfer approach. This…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
The relationship between geometric and dynamic properties of fractal-like aggregates is studied in the continuum mass and momentum-transfer regimes. The synthetic aggregates were generated by a cluster-cluster aggregation algorithm. The…
In this paper we present a mathematical model and a numerical workflow for the simulation of a thermal single-phase flow with reactive transport in porous media, in the presence of fractures. The latter are thin regions which might behave…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Many theoretical and experimental results show that solute transport in heterogeneous porous media exhibits multi-scaling behaviors. To describe such non-Fickian diffusions, this work provides a distributed order Hausdorff diffusion model…
We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via…
During the hydraulically induced compaction of a granular layer fracture patterns arise. In numerical simulations we study how these patterns depend on the gas properties as well as on the properties of the porous medium. In particular the…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
Transient dynamics of heat conduction in isotropic fractal metamaterials is investigated. By using the Laplacian operator in non-integer dimension, we analytically and numerically study the effect of fractal dimensionality on the evolution…
A time series of fractal dimension values of urban form can form a fractal dimension curve and reflects urban growth. In many cases, the fractal dimension curves of cities can be modeled with logistic function, which in turn can be used to…
The paper develops a new integral micromorphic elastic continuum model, which can describe dispersion properties of band-gap metamaterials, i.e., metamaterials that inhibit propagation of waves in a certain frequency range. The enrichment…
We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as an $(d-1)$-dimensional interface within the…
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal…
A computer simulation technique, suited to replicate real adsorption experiments, was applied to pure simulated silica in order to gain insight into the fractal regime of its surface. The previously reported experimental fractal dimension…
We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…