Universal relaxation and diffusion in interacting complex systems: Fundamental physics and rich applications

2013 ◽  
Author(s):  
K. L. Ngai
Keyword(s):  
Complex Systems ◽  
Fundamental Physics ◽  
And Diffusion

New Horizons of Predictability in Complex Dynamical Systems: From Fundamental Physics to Climate and Society

2021 ◽  
Author(s):  
Rui A. P. Perdigão
Keyword(s):  
Complex Systems ◽  
Stochastic Dynamic ◽  
Earth System ◽  
Fundamental Physics ◽  
Linear Dynamics ◽  
New Horizons ◽  
Intelligence System ◽  
Consistent Manner ◽  
Dynamic Resonance ◽  
Climate And Society

Discerning the dynamics of complex systems in a mathematically rigorous and physically consistent manner is as fascinating as intimidating of a challenge, stirring deeply and intrinsically with the most fundamental Physics, while at the same time percolating through the deepest meanders of quotidian life. The socio-natural coevolution in climate dynamics is an example of that, exhibiting a striking articulation between governing principles and free will, in a stochastic-dynamic resonance that goes way beyond a reductionist dichotomy between cosmos and chaos. Subjacent to the conceptual and operational interdisciplinarity of that challenge, lies the simple formal elegance of a lingua franca for communication with Nature. This emerges from the innermost mathematical core of the Physics of Coevolutionary Complex Systems, articulating the wealth of insights and flavours from frontier natural, social and technical sciences in a coherent, integrated manner. Communicating thus with Nature, we equip ourselves with formal tools to better appreciate and discern complexity, by deciphering a synergistic codex underlying its emergence and dynamics. Thereby opening new pathways to see the “invisible” and predict the “unpredictable” – including relative to emergent non-recurrent phenomena such as irreversible transformations and extreme geophysical events in a changing climate. Frontier advances will be shared pertaining a dynamic that translates not only the formal, aesthetical and functional beauty of the Physics of Coevolutionary Complex Systems, but also enables and capacitates the analysis, modelling and decision support in crucial matters for the environment and society. By taking our emerging Physics in an optic of operational empowerment, some of our pioneering advances will be addressed such as the intelligence system Earth System Dynamic Intelligence and the Meteoceanics QITES Constellation, at the interface between frontier non-linear dynamics and emerging quantum technologies, to take the pulse of our planet, including in the detection and early warning of extreme geophysical events from Space.

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.

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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