Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

Description and Theoretical Analysis (Using Schemata) of Planner: A Language for Proving Theorems and Manipulating Models in a Robot

Planner is a formalism for proving theorems and manipulating models in a robot. The formalism is built out of a number of problem-solving primitives together with a hierarchical multiprocess backtrack control structure. Statements can be asserted and perhaps later withdrawn as the state of the world changes. Under BACKTRACK control structure, the hierarchy of activations of functions previously executed is maintained so that it is possible to revert to any previous state. Thus programs can easily manipulate elaborate hypothetical tentative states. In addition PLANNER uses multiprocessing so that there can be multiple loci of changes in state. Goals can be established and dismissed when they are satisfied. The deductive system of PLANNER is subordinate to the hierarchical control structure in order to maintain the desired degree of control. The use of a general-purpose matching language as the basis of the deductive system increases the flexibility of the system. Instead of explicitly naming procedures in calls, procedures can be invoked implicitly by patterns of what the procedure is supposed to accomplish. The language is being applied to solve problems faced by a robot, to write special purpose routines from goal oriented language, to express and prove properties of procedures, to abstract procedures from protocols of their actions, and as a semantic base for English.

Process control in agile supply chain network.

The work comprises a new theoretical development applied to aid decision making in an increasingly important commercial sector. Agile supply, where small volumes of high margin, short life cycle innovative products are offered, is increasingly carried out through a complex global supply chain network. We outline an equilibrium solution in such a supply chain network, which works through limited cooperation and coordination along edges (links) in the network. The links constitute the stochastic modelling entities rather than the nodes of the network. We utilise newly developed phase plane analysis to identify, model and predict characteristic behaviour in supply chain networks. The phase plane charts profile the flow of inventory and identify out of control conditions. They maintain quality within the network, as well as intelligently track the way the network evolves in conditions of changing variability. The methodology is essentially distribution free, relying as it does on the study of forecasting errors, and can be used to examine contractual details as well as strategic and game theoretical concepts between decision-making components (agents) of a network. We illustrate with typical data drawn from supply chain agile fashion products.

Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction

Peron, N., Cox, S.J., Hutzler, S. and Weaire, D. (2007) Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction. The European Physical Journal E - Soft Matter. 22: 341-351. Sponsorship: This research was supported by the European Space Agency (14914/02/NL/SH, 14308/00/NL/SG) (AO-99-031) CCN 002 MAP Project AO-99-075) and Science Foundation Ireland (RFP 05/RFP/PHY0016). SJC acknowledges support from EPSRC (EP/D071127/1).

Metallic foam processing from the liquid state

Cox, S.J., Bradley, G. and Weaire, D. (2001) Metallic foam processing from the liquid state: the competition between solidification and drainage. Eur. Phys. J. AP 14:87-97. Sponsorship: This research was supported by the Prodex programme of ESA, and is a contribution to ESA contract C14308/AO-075-99. SJC was supported by Enterprise Ireland and a Marie Curie fellowship. GB was supported by the HPC Programme of TCD.

Comparison of blinkers and explosive events: A case study

Bewsher, D., Innes, D.E., Parnell, C.E. and Brown, D.S., 2005, Comparison of blinkers and explosive events, Astronomy and Astrophysics, 432, 307. Sponsorship: PPARC

Non-commutative symbolic coding

Gohm, Rolf; Kummerer, B.; Lang, T., (2006) 'Non-commutative symbolic coding', Ergodic Theory and Dynamical Systems 26(5) pp.1521-1548 RAE2008