The graph-theoretic field model— II. application of multi-terminal representations to field problems

This paper is a sequel to a paper entitled “The Graph-Theoretic Field Model—I: Modelling and Formulations” (1). Herein, the Theory of Multi-Terminal Representations is applied to the Graph-Theoretic Field Model to provide mathematical models of finite elements. The element models are obtained solely from the algebraic building blocks of the Graph-Theoretic Field Model, without recourse to any functional mathematics. The theory of Multi-Terminal Representations is developed for both linear and non-linear problems. Examples of the application of the theory to one- and two-dimensional field problems are presented from heat conduction and electrostatics.     

Energy conversion in biological systems—part II. heat production in brown adipose tissue

This study involves the application of bond graphs to the generation of heat by cells in brown adipose tissue. In the first portion of this paper, data are presented to show the types of signals that can be measured at several sites in the system controlling thermogenesis—signals travelling from the brain to the tissue as well as signals over a feedback pathway from spinal cord temperature receptors back to the brain. Bond graphs are developed for several components of the system with an emphasis being placed on graphs describing the alternative mechanisms proposed for cellular energy conversion. The power flow is calculated using ENPORT for one mechanism for different values of plasma membrane resistance.     

Structural aspects of controllability and Sobservability—II. digraph decomposition

The graph theoretic aspects of controllability and observability are examined and related to the tensorial formulation of Part I of the paper. Particular emphasis is given to the significance of the system digraph decomposition and the relevance of this to certain system algebraic properties of interest in control theory.     

Model transformation based sliding mode control of discrete-time two-dimensional Fornasini–Marchesini systems

This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time.     

Outline of colloid chemistry.—III

In this paper there has been given a discussion of: types of precipitates; theory of peptization; condensation methods; dispersion methods. Under condensation methods there are two subdivisions, in which the stability is due chiefly to the presence of strongly adsorbed substances of chiefly to the low concentration of agglomerating agents. Under dispersion methods the subdivision are disintegration by removing an agglomerating agent, by adding a peptizing agent, by mechanical methods, by electrical methods, by electrochemical methods.     

Energy conversion in biological systems—part I. chemical reactions and ion transport

Constitutive equations for nonisothermal chemical reactions are derived with attention to temperature dependent parameters. Equations are also developed for the coupling of chemical reactions to ion transport. The equations are shown to be consistent with the laws of thermodynamics.