A rigorous upper bound in electrostatics on a random lattice ensemble
Article
Received:
Revised:
- 48 Downloads
- 2 Citations
Abstract
We consider a Kirchhoff network on a random two-dimensional lattice with links and weights as previously specified, and a circular boundary of radiusR. We show rigorously that the resistance between the central point and the boundary, averaged over all placements of the remaining sites with site density ϱ, is bounded above by
$$\begin{array}{*{20}c} {(4\pi )^{ - 1} [\ln (4\pi \rho R^2 ) + 1] + 16[\tan ^{ - 1} 5^{ - {1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} + 5^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} /(\sqrt 5 + 1)^2 ]} \\ { \simeq (4\pi )^{ - 1} \ln (4\pi \rho R^2 ) + 12.0.} \\ \end{array} $$
Keywords
Neural Network Statistical Physic Complex System Nonlinear Dynamics Central Point
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Christ, N.H., Friedberg, R., Lee, T.D.: Random lattice field theory. Nucl. Phys. B202, 89–125 (1982)Google Scholar
- 2.Christ, N.H., Friedberg, R., Lee, T.D.: Gauge theory on a Random lattice. Nucl. Phys. B210, 310–336 (1982)Google Scholar
- 3.Christ, N.H., Friedberg, R., Lee, T.D.: Weights of links and plaquettes in a Random lattice. Nucl. Phys. B210, 337–346 (1982)Google Scholar
- 4.Christ, N.H., Friedberg, R., Lee, T.D., Ren, H.C.: Numerical computations on a Random lattice. Columbia University preprint CU-TP-245Google Scholar
Copyright information
© Springer-Verlag 1983