Anomalous Diffusion in Associative Networks of High-Sticker-Density Polymers

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.

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Algebra

10.1093/oso/9780198809982.003.0003 ◽

2018 ◽

Author(s):

Andrea Henderson

Keyword(s):

Euclidean Geometry ◽

Symbolic Logic ◽

Associative Networks ◽

Aristotelian Logic ◽

Modern Algebra ◽

Symbolic Systems ◽

The Difference ◽

Founding Principle ◽

Conventional Symbol

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean geometry and the latter with algebra. Rather than trying to bridge this divide, practitioners of modern algebra and the pioneers of symbolic logic made it the founding principle of their work. Regarding the content of claims as a matter of “indifference,” they concerned themselves solely with the formal interrelations of the symbolic systems devised to represent those claims. In its celebration of artificial algorithmic structures, symbolic logician Lewis Carroll’s Sylvie and Bruno dramatizes the power of this new formalist ideal not only to revitalize the moribund field of Aristotelian logic but also to redeem symbolism itself, conceived by Carroll and his mathematical, philosophical, and symbolist contemporaries as a set of harmonious associative networks rather than singular organic correspondences.

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Generation of condition-dependent reaching movements based on layered associative networks

2012 IEEE International Conference on Development and Learning and Epigenetic Robotics (ICDL) ◽

10.1109/devlrn.2012.6400581 ◽

2012 ◽

Cited By ~ 1

Author(s):

Masaki Ogino ◽

Mai Hikita ◽

Sawa Fuke ◽

Minoru Asada

Keyword(s):

Reaching Movements ◽

Associative Networks

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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

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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

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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.

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