Extending the theory of Owicki and Gries with a logic of progress

This paper describes a logic of progress for concurrent programs. The logic is based on that of UNITY, molded to fit a sequential programming model. Integration of the two is achieved by using auxiliary variables in a systematic way that incorporates program counters into the program text. The rules for progress in UNITY are then modified to suit this new system. This modification is however subtle enough to allow the theory of Owicki and Gries to be used without change

Temporal moments of a tracer pulse in a perfectly parallel flow system

Perfectly parallel groundwater transport models partition water flow into isolated one-dimensional stream tubes which maintain total spatial correlation of all properties in the direction of flow. The case is considered of the temporal moments of a conservative tracer pulse released simultaneously into N stream tubes with arbitrarily different advective–dispersive transport and steady flow speeds in each of the stream tubes. No assumptions are made about the form of the individual stream tube arrival-time distributions or about the nature of the between-stream tube variation of hydraulic conductivity and flow speeds. The tracer arrival-time distribution g(t,x) is an N-component finite-mixture distribution, with the mean and variance of each component distribution increasing in proportion to tracer travel distance x. By utilising moment relations of finite mixture distributions, it is shown (to r=4) that the rth central moment of g(t,x) is an rth order polynomial function of x or φ, where φ is mean arrival time. In particular, the variance of g(t,x) is a positive quadratic function of x or φ. This generalises the well-known quadratic variance increase for purely advective flow in parallel flow systems and allows a simple means of regression estimation of the large-distance coefficient of variation of g(t,x). The polynomial central moment relation extends to the purely advective transport case which arises as a large-distance limit of advective–dispersive transport in parallel flow models. The associated limit g(t,x) distributions are of N-modal form and maintain constant shapes independent of travel distance. The finite-mixture framework for moment evaluation is also a potentially useful device for forecasting g(t,x) distributions, which may include multimodal forms. A synthetic example illustrates g(t,x) forecasting using a mixture of normal distributions

Foundations of the B method

B is a method for specifying, designing and coding software systems. It is based on Zermelo-Fraenkel set theory with the axiom of choice, the concept of generalized substitution and on structuring mechanisms (machine, refinement, implementation). The concept of refinement is the key notion for developing B models of (software) systems in an incremental way. B models are accompanied by mathematical proofs that justify them. Proofs of B models convince the user (designer or specifier) that the (software) system is effectively correct. We provide a survey of the underlying logic of the B method and the semantic concepts related to the B method; we detail the B development process partially supported by the mechanical engine of the prover

Applying the Herman-Beta probabilistic method to MV feeders

Includes bibliographical references.The assessment of voltage drop in radial feeders is an important element in the process of network design and planning. This task is however not straight forward as the operation of modern power systems is highly influenced by a variety of uncertain and random variables such as stochasticity in load demand and power generation from renewable energy resources. Classic deterministic methods which model load demand and generation with fixed mean values consequently turn out to be inadequate and inaccurate tools for the analysis of power flow in the uncertainty-filled system. Statistically based methods become more suitable for such a task as they account for input variable uncertainties in their calculation of load flow. In the South African context, the Herman Beta algorithm, a probabilistic load flow tool developed by Herman et al. was adopted as the method for voltage assessment in Low Voltage (LV) network. The method was shown to have significant advantages compared with many other probabilistic methods for LV feeders, as investigated by Sellick and Gaunt. Its performance with regards to speed and accuracy is superior to deterministic, numeric probabilistic and other analytical probabilistic methods. The evolving connections of smaller generators, referred to as Distributed Generators (DGs), to the utility grid inspired the extension of the HB algorithm to active LV distribution networks. The HB algorithm was however formulated specifically for LV feeders. The assumptions of purely resistive feeders and unity power factor loads make it unsuitable for the Medium Voltage (MV) distribution network. In South Africa, deterministic methods are still being used for network design in MV distribution networks. This means that the drawbacks of such methods, for example inaccuracy and computational burden with large systems, are characteristic of the quality of network design in MV feeders. The performance of the HB algorithm together with the advantages and superiority of load modelling using the Beta probability density function (Beta pdf) suggested that modifying the input parameters could allow the HB algorithm to be used for voltage calculations on MV networks. This work therefore involves the adaptation of the way the HB algorithm is used, to make it suitable for voltage calculations on MV feeders. The HB algorithm for LV feeders is firstly analysed, coded into MATLAB, tested and then validated. Following this, the input parameters for feeder impedance and load current are modified to include the effects of reactance and non-unity power factor loads, using approximate modelling techniques. For reactance, the modulus or absolute value of the complex impedance is used in place of the resistance, to compensate for the line reactance. The load current is adjusted by inflating it by the power factor. The results of calculations with the HB algorithm are tested against a Monte-Carlo Simulation (MCS) solution of the feeder with an accurate model (full representation of feeder impedance and load power factor). The approach is extended to include shunt capacitor connections and DG in voltage calculations using the HB algorithm and testing the results with MCS. The outcomes of this research are that the approach of adjusting the input parameters of line resistance and load current significantly improves the accuracy of calculations using the HB algorithm for MV feeders. Comparison with the results of MC simulations indicates that the error of voltage calculations on MV feeders will be less than 2% of the 'accurate probabilistic value'. However, it is not possible to predict the error for a particular application

Normalized analysis and design of LCC resonant converters

Abstract—A normalization of the LCC voltage-output resonant converter performance characteristics, in terms of the tank gain at resonance and the parallel-to-series-capacitor ratio, is presented. The resulting description is subsequently used for the derivation of a design procedure that incorporates the effects of diode losses and the finite charge/discharge time of the parallel capacitor. Unlike previously reported techniques, the resulting normalized behavior of the converter is used to identify design regions to facilitate a reduction in component electrical stresses, and the use of harmonics to transfer real power. Consideration of the use of preferred component values is also given. The underlying methodology is ultimately suitable for incorporation into a software suite for use as part of a rapid interactive design tool. Both simulation results and experimental measurements from a prototype converter are included to demonstrate the attributes of the proposed analysis and design methodologies

A continuum model of multi-phase reactive transport in igneous systems

Multi-phase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquid-dominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds, and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase- and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum, and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two- and three-phase flow problems in igneous systems.Comment: Revised preprint submitted for peer-reviewed publication: main text with 8 figures, 1 table; appendix with 3 figures and 2 table

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described

A Graph Transformation Approach to Software Architecture Reconfiguration

The ability of reconfiguring software architectures in order to adapt them to new requirements or a changing environment has been of growing interest. We propose a uniform algebraic approach that improves on previous formal work in the area due to the following characteristics. First, components are written in a high-level program design language with the usual notion of state. Second, the approach deals with typical problems such as guaranteeing that new components are introduced in the correct state (possibly transferred from the old components they replace) and that the resulting architecture conforms to certain structural constraints. Third, reconfigurations and computations are explicitly related by keeping them separate. This is because the approach provides a semantics to a given architecture through the algebraic construction of an equivalent program, whose computations can be mirrored at the architectural level