Recursion-transform method on computing the complex resistor network with three arbitrary boundaries

We perfect the recursion-transform method to be a complete theory, which can derive the general exact resistance between any two nodes in a resistor network with several arbitrary boundaries. As application of the method, we give a profound example to illuminate the usefulness on calculating resistance of a nearly $m\times n$ resistor network with a null resistor and three arbitrary boundaries, which has never been solved before since the Greens function technique and the Laplacian matrix approach are invalid in this case. Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of finite network. For the first time, seven general formulae of resistance between any two nodes in a nearly $m\times n$ resistor network in both finite and infinite cases are given by our theory. In particular, we give eight special cases by reducing one of general formulae to understand its application and meaning

Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks

This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic results related to percolation: namely, the conduction properties of a large random resistor network as the fraction of resistors is varied. We focus on how the conductance of such a network vanishes as the percolation threshold is approached from above. We also discuss the more microscopic current distribution within each resistor of a large network. At the percolation threshold, this distribution is multifractal in that all moments of this distribution have independent scaling properties. We will discuss the meaning of multifractal scaling and its implications for current flows in networks, especially the largest current in the network. Finally, we discuss the relation between resistor networks and random walks and show how the classic phenomena of recurrence and transience of random walks are simply related to the conductance of a corresponding electrical network.Comment: 27 pages & 10 figures; review article for the Encyclopedia of Complexity and System Science (Springer Science

Nonlinear DC-response in Composites: a Percolative Study

The DC-response, namely the $I$-$V$ and $G$-$V$ charateristics, of a variety of composite materials are in general found to be nonlinear. We attempt to understand the generic nature of the response charactersistics and study the peculiarities associated with them. Our approach is based on a simple and minimal model bond percolative network. We do simulate the resistor network with appropritate linear and nonlinear bonds and obtain macroscopic nonlinear response characteristics. We discuss the associated physics. An effective medium approximation (EMA) of the corresponding resistor network is also given.Comment: Text written in RevTEX, 15 pages (20 postscript figures included), submitted to Phys. Rev. E. Some minor corrections made in the text, corrected one reference, the format changed (from 32 pages preprint to 15 pages

Amplifier for measuring low-level signals in the presence of high common mode voltage

A high common mode rejection differential amplifier wherein two serially arranged Darlington amplifier stages are employed and any common mode voltage is divided between them by a resistance network. The input to the first Darlington amplifier stage is coupled to a signal input resistor via an amplifier which isolates the input and presents a high impedance across this resistor. The output of the second Darlington stage is transposed in scale via an amplifier stage which has its input a biasing circuit which effects a finite biasing of the two Darlington amplifier stages

Quadrature LC VCO with passive coupling and phase combining network

A circuit and method for generating a signal is disclosed. The circuit includes a set of wide tuning LC tanks, a set of core transistors cross coupled to the set of wide tuning LC tanks, and a combining network coupled to the set of wide tuning LC tanks and the set of core transistors. The combining network further includes a set of inputs connected to the set of wide tuning LC tanks and the set of core transistors, a set of coupling transistors connected to the set of inputs, a set of source inductors connected to the set of coupling transistors, a coupling capacitor connected to the set of source inductors, a load resistor connected to the coupling capacitor. The combining network combines the set of inputs and the signal is delivered to the load resistor as a fourth order harmonic.Board of Regents, University of Texas Syste

Multifractal Properties of the Random Resistor Network

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 current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/\nu$ to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E (Rapid Comm

Punch-magnet delay eliminated by modification of circuit

Reduction of retardation by diode-resistor networks of the current-decay time of a punch magnet by connection of a Zener diode in series with the damping network increases the reliability of data on paper tape

"Weak Quantum Chaos" and its resistor network modeling

Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with displaceable wall ("piston"). The motion is completely chaotic but with small Lyapunov exponent. The Hamiltonian matrix does not look like one taken from a Gaussian ensemble, but rather it is very sparse and textured. This can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity, respectively. For $g$ we use a resistor network calculation that has a direct relation to the semi-linear response characteristics of the system, hence leading to a novel prediction regarding the rate of heating of cold atoms in optical billiards with vibrating walls.Comment: 18 pages, 11 figures, improved PRE accepted versio