An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Methods for Determining Blood Flow Through Intact Vessels of Experimental Animals Under Conditions of Gravitational Stress and in Extra-terrestrial Space Capsules Final Report, 1 Nov. 1960 - 31 Dec. 1964

Electromagnetic blood flow meter to determine blood flow through intact vessels of test animals in gravitational stress and in extraterrestrial space capsule

Measurements, Models, Systems and Design

531 s.

Gradient and Passive Circuit Structure in a Class of Non-linear Dynamics on a Graph

We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the assumption of detailed balance, we provide a method to formulate the governing ODE system in gradient descent form of sum-separable energy functions, which thus represent a class of Lyapunov functions; this class coincides with Csisz\'{a}r's information divergences. Our approach bases on a transformation of the original problem to a mass-preserving transport problem and it reflects a little-noticed general structure result for passive network synthesis obtained by B.D.O. Anderson and P.J. Moylan in 1975. The proposed gradient formulation extends known gradient results in dynamical systems obtained recently by M. Erbar and J. Maas in the context of porous medium equations. Furthermore, we exhibit a novel relationship between inhomogeneous Markov chains and passive non-linear circuits through gradient systems, and show that passivity of resistor elements is equivalent to strict convexity of sum-separable stored energy. Eventually, we discuss our results at the intersection of Markov chains and network systems under sinusoidal coupling

A survey of methods for deciding whether a reaction network is multistationary

Which reaction networks, when taken with mass-action kinetics, have the capacity for multiple steady states? There is no complete answer to this question, but over the last 40 years various criteria have been developed that can answer this question in certain cases. This work surveys these developments, with an emphasis on recent results that connect the capacity for multistationarity of one network to that of another. In this latter setting, we consider a network $N$ that is embedded in a larger network $G$, which means that $N$ is obtained from $G$ by removing some subsets of chemical species and reactions. This embedding relation is a significant generalization of the subnetwork relation. For arbitrary networks, it is not true that if $N$ is embedded in $G$, then the steady states of $N$ lift to $G$. Nonetheless, this does hold for certain classes of networks; one such class is that of fully open networks. This motivates the search for embedding-minimal multistationary networks: those networks which admit multiple steady states but no proper, embedded networks admit multiple steady states. We present results about such minimal networks, including several new constructions of infinite families of these networks

Hall Effect Gyrators and Circulators

The electronic circulator, and its close relative the gyrator, are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory, but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative non-reciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an ohmically-contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90 degrees. In this limit we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the a.c. wavelength. An experiment is proposed to achieve GHz-band gyration in millimetre (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realising a Hall gyrator is also analysed.Comment: 18 pages, 15 figures, ~5 MB. V3: sections V-VIII revisited plus other minor changes, Fig 2 added. Submitted to PR