Related papers: Possible Experimental Test of Continuous Medium Mo…
In this paper we investigate the dynamical behavior of fractional differential system associated to 5D Maxwell-Bloch model in terms of fractional Caputo derivatives.
Mathematical models that accurately predict the mechanical behavior of blood can contribute to the development of biomedical devices and medications which are relevant in clinical applications. The models existing in the literature are…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
We use contraction method in probabilistic metric spaces to prove existence and uniqueness of selfsimilar random fractal measures.
In this review article we consider the crack growth resistance ofmicrometer and submicrometer sized samples from the fracture mechanics point of view. Standard fracture mechanics test procedures were developed for macroscale samples, and…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
We introduce a method of estimating parameters associated with a fractal random scattering medium, which utilizes the multiscale properties of the scattered field. The example of ray-density fluctuations beyond a phase screen with fractal…
Partial derivatives are used in a variety of different ways within physics. Most notably, thermodynamics uses partial derivatives in ways that students often find confusing. As part of a collaboration with mathematics faculty, we are at the…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…
We study a porous medium equation with right hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator. The derivative in time is also fractional of Caputo-type and which takes into account…
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…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models both in the context of finite…
The box method discrete fracture model (Box-DFM) is an important finite volume-based discrete fracture model (DFM) to simulate flows in fractured porous media. In this paper, we investigate a simple but effective extension of the box method…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…
For spherical and parabolic averages of the Fourier transform of fractal measures, we obtain new upper bounds on rates of decay by an "intermediate dimension" trick.
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
The formalism proposed in Phys. Rev. Lett. 116, 078001 (2016) for determination of the normal and tangential inter-particle forces in frictional disks from visual data was criticized in a comment to that paper. However the theory developed…