An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach

We summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity (an integer multiple of some basic unit size). In particular, we discuss Smoluchowski's equation for aggregation, the Becker-Döring model of simultaneous aggregation and fragmentation, and more general models involving coagulation and fragmentation.

Organizational, systems and human issues in production planning, scheduling and control

With global markets and global competition, pressures are placed on manufacturing organizations to compress order fulfillment times, meet delivery commitments consistently and also maintain efficiency in operations to address cost issues. This chapter argues for a process perspective on planning, scheduling and control that integrates organizational planning structures, information systems as well as human decision makers. The chapter begins with a reconsideration of the gap between theory and practice, in particular for classical scheduling theory and hierarchical production planning and control. A number of the key studies of industrial practice are then described and their implications noted. A recent model of scheduling practice derived from a detailed study of real businesses is described. Socio-technical concepts are then introduced and their implications for the design and management of planning, scheduling and control systems are discussed. The implications of adopting a process perspective are noted along with insights from knowledge management. An overview is presented of a methodology for the (re-)design of planning, scheduling and control systems that integrates organizational, system and human perspectives. The most important messages from the chapter are then summarized.

Chiral polymerisation and the RNA world

The purpose of this paper is to review two mathematical models: one for the formation of homochiral polymers from an originally chirally symmetric system; and the other, to show how, in an RNA-world scenario, RNA can simultaneously act both as information storage and a catalyst for its own production. We note the similarities and differences in chemical mechanisms present in the systems. We review these two systems, analysing steady-states, interesting kinetics and the stability of symmetric solutions. In both systems we show that there are ranges of parameter values where some chains increase their own concentrations faster than others.

Chiral polymerisation and the RNA world

The purpose of this paper is to review two mathematical models: one for the formation of homochiral polymers from an originally chirally symmetric system; and the other, to show how, in an RNA-world scenario, RNA can simultaneously act both as information storage and a catalyst for its own production. We note the similarities and differences in chemical mechanisms present in the systems. We review these two systems, analysing steady-states, interesting kinetics and the stability of symmetric solutions. In both systems we show that there are ranges of parameter values where some chains increase their own concentrations faster than others.