Slow Relaxation, Anomalous Diffusion, and Aging in Equilibrated or Nonequilibrated Environments

2005 ◽  
pp. 257-325
Author(s):  
Noëlle Pottier
Keyword(s):  
Anomalous Diffusion ◽  
Slow Relaxation

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

PHASE TRANSFORMATION AND SLOW RELAXATION IN FLUOSILICATES

1976 ◽  
Vol 37 (C6) ◽  
pp. C6-481-C6-481
Author(s):  
J. CHAPPERT ◽  
G. JEHANNO ◽  
F. VARRET
Keyword(s):  
Phase Transformation ◽  
Slow Relaxation

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.

scholarly journals New Radical Cation Salts Based on BDH-TTP Donor: Two Stable Molecular Metals with a Magnetic [ReF6]2− Anion and a Semiconductor with a [ReO4]− Anion

2021 ◽  
Vol 7 (4) ◽  
pp. 54
Author(s):  
Nataliya D. Kushch ◽  
Gennady V. Shilov ◽  
Lev I. Buravov ◽  
Eduard B. Yagubskii ◽  
Vladimir N. Zverev ◽  
...  
Keyword(s):  
Radical Cation ◽  
Low Temperatures ◽  
Ac Susceptibility ◽  
Slow Relaxation ◽  
Organic Radical ◽  
Inorganic Anion ◽  
Distinctive Features ◽  
Metallic Character ◽  
Radical Cation Salts ◽  
Partial Population

Three radical cation salts of BDH-TTP with the paramagnetic [ReF6]2− and diamagnetic [ReO4]− anions have been synthesized: κ-(BDH-TTP)4ReF6 (1), κ-(BDH-TTP)4ReF6·4.8H2O (2) and pseudo-κ″-(BDH-TTP)3(ReO4)2 (3). The crystal and band structures, as well as the conducting properties of the salts, have been studied. The structures of the three salts are layered and characterized by alternating κ-(1, 2) and κ″-(3) type organic radical cation layers with inorganic anion sheets. Similar to other κ-salts, the conducting layers in the crystals of 1 and 2 are formed by BDH-TTP dimers. The partial population of positions of Re atoms and disorder in the anionic layers of 1–3 are their distinctive features. Compounds 1 and 2 show the metallic character of conductivity down to low temperatures, while 3 is a semiconductor. The ac susceptibility of crystals 1 was investigated in order to test the possible slow relaxation of magnetization associated with the [ReF6]2− anion.

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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