A general formulation for the spectral noise S& of random linear resistor networks of arbitrary topology is given. General calculational methods based on Tellegen's theorem are illustrated for oneand two-probe configurations. For self-similar networks, we show the existence of a new exponent b, member of a whole new hierarchy of exponents characterizing the size dependence of the normalized noi...

The qth moment M(q) of the growth probability of diffusion-limited aggregates is studied for q<0 in terms of the value [M(q,N)]av obtained by averaging M(q) over the ensemble of all aggregates of a given number of particles N. For a range of structures that are susceptible to precise analysis, we verify that all moments, even those for q<0, obey asymptotic power-law scaling in N. Since we canno...

We present a reanalysis of the renormalization-group calculation to first order in ε=6−d, where d is the spatial dimensionality, of the exponent, t, which describes the behavior of the conductivity of a percolating network at the percolation threshold. If we set t=(d−2)νp+ζ, where νp is the correlation-length exponent, then our result is ζ=1+(ε/42). This result clarifies several previously para...

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i) approximately 1/i, where i is the current. As a...

We present numerical data and scaling theories for the critical behavior of random resistor networks near the percolation threshold. We determine the critical exponents of a suitably defined resistance correlation function by a Padé analysis of low-concentration expansions as a function of dimensionality. We verify that d=6 is the critical dimensionality for the onset of mean-field behavior. We...

To date, the design of surface-printed resistors has utilised the time-consuming moment method. The synthetic asymptote technique usually generates simple design formulae, and this technique has been extended and applied to the design of surface-printed resistors. It is found that the derived resistance is immune to change even at high frequencies. In addition, it is found that the novel formul...

We find new facet-defining inequalities for the linear ordering polytope generalizing the well-known Möbius ladder inequalities. Our starting point is to observe that the natural derivation of the Möbius ladder inequalities as {0, 1 2 }-cuts produces triangulations of the Möbius band and of the corresponding (closed) surface, the projective plane. In that sense, Möbius ladder inequalities have ...

The resistance R(x,x’) between two connected terminals in a randomly diluted resistor network is studied on a d-dimensional hypercubic lattice at the percolation threshold pc. When each individual resistor has a small random component of resistance, R(x,x’) becomes a random variable with an associated probability distribution, which contains information on the distribution of currents in the in...

This paper proposes a new floating gate MOSFET (FGMOS) based voltage-controlled grounded resistor. In the proposed circuit FGMOS operating in the ohmic region is linearized by another conventional MOSFET operating in the saturation region. The major advantages of FGMOS based voltage-controlled grounded resistor (FGVCGR) are simplicity, low total harmonic distortion (THD), and low power consumpt...

Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the nonpercolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are go...