Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion

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.

Download Full-text

Pattern selection in a ring of Kuramoto oscillators

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2019.104868 ◽

2019 ◽

Vol 78 ◽

pp. 104868 ◽

Cited By ~ 2

Author(s):

Károly Dénes ◽

Bulcsú Sándor ◽

Zoltán Néda

Keyword(s):

Pattern Selection ◽

Kuramoto Oscillators

Download Full-text

Automatic Gait Pattern Selection for Legged Robots

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) ◽

10.1109/iros45743.2020.9340789 ◽

2020 ◽

Author(s):

Jiayi Wang ◽

Iordanis Chatzinikolaidis ◽

Carlos Mastalli ◽

Wouter Wolfslag ◽

Guiyang Xin ◽

...

Keyword(s):

Gait Pattern ◽

Legged Robots ◽

Pattern Selection ◽

Selection For

Download Full-text

Parametric resonance and pattern selection in an array of microcantilevers interacting through fringing electrostatic fields

Nonlinear Dynamics ◽

10.1007/s11071-021-06755-y ◽

2021 ◽

Author(s):

Nir Dick ◽

Slava Krylov

Keyword(s):

Parametric Resonance ◽

Pattern Selection ◽

Electrostatic Fields

Download Full-text

Magnetized wake driven anomalous diffusion in complex plasma

Physics of Plasmas ◽

10.1063/5.0055139 ◽

2021 ◽

Vol 28 (8) ◽

pp. 083703

Author(s):

Biswajit Dutta ◽

Pratikshya Bezbaruah ◽

Nilakshi Das

Keyword(s):

Anomalous Diffusion ◽

Complex Plasma

Download Full-text

Anomalous diffusion near structural-glass transformations

Physics Letters A ◽

10.1016/s0375-9601(00)00807-0 ◽

2001 ◽

Vol 280 (1-2) ◽

pp. 97-103 ◽

Cited By ~ 8

Author(s):

V.B. Kokshenev ◽

N.S. Sullivan

Keyword(s):

Anomalous Diffusion ◽

Structural Glass

Download Full-text

Caputo Fractional Derivative and Quantum-Like Coherence

Entropy ◽

10.3390/e23020211 ◽

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.

Download Full-text