Verification of Biomedical Processes with Anomalous Diffusion, Transport and Interaction of Species

2020 ◽  
pp. 65-74
Author(s):  
Messoud Efendiev ◽  
Vitali Vougalter
Keyword(s):  
Anomalous Diffusion ◽  
Diffusion Transport

scholarly journals Some basic mathematical features of the simultaneous convection anomalous diffusion transport processes

2014 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
Ágnes Bálint ◽  
Csaba Mészáros
Keyword(s):  
Anomalous Diffusion ◽  
Diffusion Processes ◽  
Practical Importance ◽  
Transport Processes ◽  
Bulk Materials ◽  
Engineering Applications ◽  
Diffusion Transport ◽  
Open Research

The basic mathematical features of the anomalous diffusion processes are discussed in detail, together with some of the open research subdomains belonging to it. Due to its practical importance in engineering applications, the possibilities of the necessary mathematical refinements are proposed and justified for the general case of the simultaneous convection-anomalous diffusion processes taking place through porous bulk materials.

Anomalous diffusion in presence of boundary conditions

1990 ◽  
Vol 51 (13) ◽  
pp. 1387-1402 ◽  
Author(s):  
A. Giacometti ◽  
A. Maritan
Keyword(s):  
Boundary Conditions ◽  
Anomalous Diffusion

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

Magnetized wake driven anomalous diffusion in complex plasma

2021 ◽  
Vol 28 (8) ◽  
pp. 083703
Author(s):  
Biswajit Dutta ◽  
Pratikshya Bezbaruah ◽  
Nilakshi Das
Keyword(s):  
Anomalous Diffusion ◽  
Complex Plasma

Anomalous diffusion near structural-glass transformations

2001 ◽  
Vol 280 (1-2) ◽  
pp. 97-103 ◽  
Author(s):  
V.B. Kokshenev ◽  
N.S. Sullivan
Keyword(s):  
Anomalous Diffusion ◽  
Structural Glass

scholarly journals Caputo Fractional Derivative and Quantum-Like Coherence

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 211
Author(s):  
Garland Culbreth ◽  
Mauro Bologna ◽  
Bruce J. West ◽  
Paolo Grigolini
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Anomalous Diffusion ◽  
Caputo Fractional Derivative ◽  
Quantum Coherence ◽  
Time Derivative ◽  
The Other ◽  
Diffusion Equations ◽  
Self Organization ◽  
Ordinary Time

We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.

scholarly journals Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes

2021 ◽  
Vol 40 (1) ◽  
Author(s):  
Khaled M. Furati ◽  
Kassem Mustapha ◽  
Ibrahim O. Sarumi ◽  
Olaniyi S. Iyiola
Keyword(s):  
Anomalous Diffusion ◽  
Numerical Algorithms ◽  
Two Parameter
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