Emergent behaviour in large electrical networks

Many complex systems have emergent behaviour which results from 6 the way in that the components of the system interact, rather than their individual 7 properties. However, it is often unclear as to what this emergent behaviour can be, 8 or inded how large the system should be for such behaviour to arise. In this paper we 9 will address these problems for the specific case of an electrical network comprising 10 a mixture of resistive and reactive elements. Using this model we will show, using 11 some spectral theory, the types of emergent behaviour that we expect and also how 12 large a system we need for this to be observed.

[1]  A. K. Jonscher,et al.  Universal relaxation law : a sequel to Dielectric relaxation in solids , 1996 .

[2]  Gérard Toulouse,et al.  Biology And Computation: A Physicist's Choice , 1993 .

[3]  Graeme W. Milton,et al.  Bounds on the complex dielectric constant of a composite material , 1980 .

[4]  Jeppe C. Dyre,et al.  Universality of ac conduction in disordered solids , 2000 .

[5]  C. T. White,et al.  On the origin of the universal dielectric response in condensed matter , 1979, Nature.

[6]  J. M. Luck,et al.  Dielectric resonances of binary random networks , 1998 .

[7]  Darryl P Almond,et al.  An evaluation of random R-C networks for modelling the bulk ac electrical response of ionic conductors , 1999 .

[8]  Christian Brosseau,et al.  Modelling and simulation of dielectric heterostructures: a physical survey from an historical perspective , 2006 .

[9]  K. D. Murphy,et al.  Evidence of emergent scaling in mechanical systems , 2006 .

[10]  A. K. Jonscher,et al.  The ‘universal’ dielectric response , 1977, Nature.

[11]  J. Luck,et al.  The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models , 1990 .

[12]  P. Anderson.  More is different. , 1972, Science.

[13]  University of Michigan,et al.  Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices , 1998 .

[14]  Van-Tan Truong,et al.  Complex conductivity of a conducting polymer composite at microwave frequencies , 1995 .

[15]  D. Almond,et al.  The 'emergent scaling' phenomenon and the dielectric properties of random resistor-capacitor networks , 2003 .