We consider the problem of two-point resistance in a resistor network previously studied by one of us (Wu 2004 J. Phys. A: Math. Gen. 37 6653). By formulating the problem differently, we obtain a new expression for the two-point resistance between two arbitrary nodes which is simpler and can be easier to use in practice. We apply the new formulation to the cobweb resistor network to obtain the ...

We consider circular planar graphs and circular planar resistor networks. Associated with each circular planar graph F there is a set n(F) = { (P; Q) } of pairs of sequences of boundary nodes which are connected through F. A graph F is called critical if removing any edge breaks at least one of the connections (P: Q) in n(F). We prove that two critical circular planar graphs are Y-A equivalent ...

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation ...

A novel CMOS monolithic analog multiplier capable of operating in two quadrants is described in this thesis. The multiplier incorporates a voltage-controlled variable linear resistor comprised of two FET transistors in the feedback network of an operational amplifier. This novel approach to implementing an analog multiplier results in good linearity and wide input dynamic range when compared to...

We propose the notion of {\it resistance of a graph} as an accompanying notion of the structure entropy to measure the force of the graph to resist cascading failure of strategic virus attacks. We show that for any connected network $G$, the resistance of $G$ is $\mathcal{R}(G)=\mathcal{H}^1(G)-\mathcal{H}^2(G)$, where $\mathcal{H}^1(G)$ and $\mathcal{H}^2(G)$ are the one- and two-dimensional s...