F Semeriyanov et al 2009 J. Phys. A: Math. Theor. 42 465001 doi:10.1088/1751-8113/42/46/465001
Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice
F Semeriyanov, M Saphiannikova and G Heinrich
Show affiliationsOur study is based on the work of Stinchcombe (1974 J. Phys. C: Solid State Phys. 7 179) and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of the inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi (1974 Phys. Rev. B 9 4575) for the regular lattice.
- PACS
-
84.32.Ff Conductors, resistors (including thermistors, varistors, and photoresistors)
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
-
82B43 Percolation (See also 60K35)
82B23 Exactly solvable models; Bethe ansatz
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
- Subjects
- Dates
-
Issue 46 (20 November 2009)
Received 16 March 2009, in final form 21 September 2009
Published 22 October 2009
-
Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice
F Semeriyanov et al 2009 J. Phys. A: Math. Theor. 42 465001
-
Dynamic investigation of mode transition in inductively coupled plasma with a hybrid model
Shu-Xia Zhao et al 2009 J. Phys. D: Appl. Phys. 42 225203
-
Modeling of ionic polymer metal composite actuator dynamics using a large deflection beam model
Shivakanth Gutta et al 2009 Smart Mater. Struct. 18 115023
-
Neutron star equation of state via gravitational wave observations
C Markakis et al 2009 J. Phys.: Conf. Ser. 189 012024
-
Solid Au nanoparticles as a catalyst for growing aligned ZnO nanowires: a new understanding of the vapour–liquid–solid process
Melanie Kirkham et al 2007 Nanotechnology 18 365304
-
Transformation optics for the full dielectric electromagnetic cloak and metal–dielectric planar hyperlens
D P Gaillot et al 2008 New J. Phys. 10 115039
-
Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class
Florian Beyer 2009 Class. Quantum Grav. 26 235016
-
Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments
Changbong Hyeon and D Thirumalai 2007 J. Phys.: Condens. Matter 19 113101
-
Naturally light hidden photons in LARGE volume string compactifications
Mark Goodsell et al JHEP11(2009)027
-
Full potential multiple scattering calculations of transition metals K-edges
Keisuke Hatada et al 2009 J. Phys.: Conf. Ser. 190 012010
Users also read
What's this?-
A derivation of an off-shell 2D,
supergravity chiral projection operator
- Thermodynamics and fluctuation theorems for a strongly coupled open quantum system: an exactly solvable case
- Non-skew-symmetric classical r-matrices and integrable cases of the reduced BCS model
Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- On the uncertainty in the regularized solution