Related papers: A note on fractional derivative modeling of broadb…
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…
The diffraction of ultrashort pulse changes its spatial and temporal structure that is crucial for multi-channel communication and location via such pulses. The features of the evolution of broadband pulses discussed for two general…
In this paper we discuss some general properties of viscoelastic models defined in terms of constitutive equations involving infinitely many derivatives (of integer and fractional order). In particular, we consider as a working example the…
Ultrasound imaging is widely used for real-time, noninvasive diagnosis, but speckle and related artifacts reduce image quality and can hinder interpretation. We present a diffusion-based ultrasound despeckling method built on the Image…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
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…
We describe and implement a numerical method for modelling the frequency-dependent power-law absorption of ultrasound in tissue, as governed by the first order linear wave equations with a loss taking the form of a fractional time…
A simple design paradigm for making broad-band ultra-thin plasmonic absorbers is introduced. The absorber's unit cell is composed of sub-units of various sizes, resulting in nearly 100% absorbance at multiple adjacent frequencies and high…
Deep learning (DL) methods typically require large datasets to effectively learn data distributions. However, in the medical field, data is often limited in quantity, and acquiring labeled data can be costly. To mitigate this data scarcity,…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
In this study, a reduced micromorphic model for multiscale materials is developed. In the context of this model, multiscale materials are modeled with deformable microstructures. The deformation energy is formed depending on microstrain and…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
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…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…
In this paper we consider a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject…
This paper presents a time-space Hausdorff derivative model for depicting solute transport in aquifers or water flow in heterogeneous porous media. In this model, the time and space Hausdorff derivatives are defined on non-Euclidean fractal…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…