Viewpoint of the coupling model on relaxation and diffusion in various complex systems

1999 ◽  
Author(s):  
K. L. Ngai
Keyword(s):  
Complex Systems ◽  
Coupling Model ◽  
And Diffusion

scholarly journals On the existence of solutions to the fractional derivative equations d(alpha)u/dt(alpha)+Au = f, of relevance to diffusion in complex systems

2012 ◽  
Vol 17 (2) ◽  
pp. 153-168
Author(s):  
Arnaud Heibig ◽  
Liviu Iulian Palade
Keyword(s):  
Complex Systems ◽  
Fractional Derivative ◽  
Existence Of Solutions ◽  
Diffusion Processes ◽  
Adjoint Operator ◽  
Von Neumann ◽  
Random Walker ◽  
Glassy Materials ◽  
And Diffusion ◽  
Position Probability

Fractional derivative equations account for relaxation and diffusion processes in a large variety of condensed matter systems. For instance, diffusion of position probability density displayed by a random walker in complex systems – such as glassy materials – is often modeled by fractional derivative partial differential equations. This paper deals with the existence of solutions to the general fractional derivative equation dαu/dtα+Au = f for 0 < α < 1, with A a self-adjoint operator. The results are proved using the von Neumann–Dixmier theorem.

A METHOD FOR FINDING AGGREGATED REPRESENTATIONS OF LINEAR DYNAMICAL SYSTEMS

2010 ◽  
Vol 13 (02) ◽  
pp. 199-215 ◽  
Author(s):  
OLOF GÖRNERUP ◽  
MARTIN NILSSON JACOBI
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Markov Chains ◽  
Complex Systems ◽  
Diffusion Processes ◽  
Coarse Grained ◽  
Hierarchical Level ◽  
Permutation Symmetry ◽  
Linear Dynamical Systems ◽  
And Diffusion

A central problem in the study of complex systems is to identify hierarchical and intertwined dynamics. A hierarchical level is defined as an aggregation of the system's variables such that the aggregation induces its own closed dynamics. In this paper, we present an algorithm that finds aggregations of linear dynamical systems, e.g. including Markov chains and diffusion processes on weighted and directed networks. The algorithm utilizes that a valid aggregation with n states correspond to a set of n eigenvectors of the dynamics matrix such that these respect the same permutation symmetry with n orbits. We exemplify the applicability of the algorithm by employing it to identify coarse grained representations of cellular automata.

A coupling model of light propagation based on the radiative transfer and diffusion equations

2013 ◽  
Author(s):  
Hiroyuki Fujii ◽  
Yoko Hoshi ◽  
Shinpei Okawa ◽  
Tetsuya Yoshinaga ◽  
Satoru Kohno ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Light Propagation ◽  
Coupling Model ◽  
Diffusion Equations ◽  
And Diffusion

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

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