Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

Recently, we developed and implemented the bond propagation algorithm for calculating the partition function and correlation functions of random bond Ising models in two dimensions. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function, and we derive explicit expressions for this transformation. We also discuss variations of the original bond propagation procedure within the larger context of Y-Delta-Y-reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.Comment: 12 pages, 10 figures; submitte

Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan

The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan have been calculated exactly for arbitrary size as well as arbitrary individual edge and node reliabilities, using transfer matrices of dimension four at most. While the all-terminal reliabilities of these graphs are identical, the special case of identical edge ($p$) and node ($\rho$) reliabilities shows that their two-terminal reliabilities are quite distinct, as demonstrated by their generating functions and the locations of the zeros of the reliability polynomials, which undergo structural transitions at $\rho = \displaystyle {1/2}$

Vectorial formalism for analysis and design of polyphase synchronous machines

A vectorial formalism for analysis and design of polyphase synchronous machines without reluctance and saturation effects is described. We prove the equivalence of such a machine with a set of magnetically independent machines, which are electrically and mechanically coupled. Specific problems of polyphase machines can thus be favorably analyzed with this concept. Rules of conception and constraints on electric supply can be deduced. Moreover the vectorial approach, which generalizes the complex phasor method, can also be used to control n-leg Voltage Source Inverters. This methodology is applied to 3-phase and 6- phase synchronous machines

Assessment of Reliability of Composite Power System Including Smart Grids

The large service interruptions of power supply in the transmission system have significant impact on modern society. The aim of the power system engineers is to prevent and mitigate such events with optimal decisions in design, planning, operation and maintenance. Due to the rapid growth in the power demand and competitive power market scenario, the transmission and distribution systems are frequently being operated under heavily loaded conditions. This tends to make failure of components more frequent in the power system necessitating large downtime to repair or replace the equipment. A majority of the service interruptions are happening due to lack of proper planning and operation of power system. Therefore, complete reliability assessment in generation, transmission and distribution systems is needed at the planning stage. The reliability assessment in smart grids is very much beneficial to the power operator and reduces the risk of grid failure due to failure of major components in power systems. This chapter is confined to composite power system reliability assessment. The composite power system combines both the generation and transmission systems’ adequacy. The generation system in the composite power system includes both conventional and renewable sources. The composite power system reliability assessment is quite difficult due to the large number of equipment, interconnected network topology and uncertainties in generation capacity. The reliability assessment concentrates mainly on the use of probabilistic states of components in generation and transmission systems to evaluate the overall reliability. This analysis will result in a cost-effective system configuration to provide continuous power supply to the consumers at reasonable cost. The reliability level of the system is measured by the defined indices. One of these indices is the probability of average power availability at load bus. This reliability assessment mainly focuses on development of methods to evaluate the probability of average power availability at load buses for a specified system configuration. This chapter discusses the two main techniques called node elimination method and modified minimal cut set method

Exact Failure Frequency Calculations for Extended Systems

This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to $k$-out-of-$n$:G and linear consecutive $k$-out-of-$n$:F systems, and to a simple ladder network in which each edge and node may fail. We also give the associated generating functions when the components have identical availabilities and failure rates. For large systems, the failure rate of the whole system is asymptotically proportional to its size. This paves the way to ready-to-use formulae for various architectures, as well as proof that the differential operator approach to failure frequency calculations is very useful and straightforward

A new approach to solving three combinatorial enumeration problems on planar graphs

The purpose of this paper is to show how the technique of delta-wye graph reduction provides an alternative method for solving three enumerative function evaluation problems on planar graphs. In particular, it is shown how to compute the number of spanning trees and perfect matchings, and how to evaluate energy in the Ising spin glass model of statistical mechanics. These alternative algorithms require O(n2) arithmetic operations on an n-vertex planar graph, and are relatively easy to implement