UK Nonlinear News, May 1998

Recent Theses

Construction of Molecular Dynamics Like Cellular Automata Models for Simulation of Compressible Fluid Dynamic Systems

Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur -- 208 016, INDIA

Himanshu Agrawal

Supervisor: Professor E. Rathakrishan


This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results indicate, the attempt is successful. A systematic method for constructing cellular automata models of fluid dynamic systems is discovered and proposed following a review of the existing developments. The considerations required for constructing such models for fluid dynamic systems consisting of particles with arbitrary interaction potentials and existing over arbitrary spatial lattices are outlined. The method is illustrated by constructing a model for simulation of systems of particles moving with unit speed along the links of an underlying square spatial lattice. Using this model, two two-dimensional systems are simulated and studied for a number of model and system parameters. For almost all the model and system parameters, the results are found to be in complete agreement with the available theoretical predictions. For some model parameters, results show (expected) departure from theoretical predictions which is explained.

Source: Himanshu Agrawal (

Chaotic Vibrations of Heated plates

Mechanical and Aerospace Engineering, University of Dayton, USA

Muge Fermen-Coker

Supervisor: Professor Glen E. Johnson


In recent years, the investigation of dynamical behavior of plates under thermal loads has become important due to the high temperatures reached on external skin panels of hypersonic vehicles. It has been shown by other researchers that the skin panels may encounter chaotic vibrations about their thermally buckled positions.

In this research, the chaotic vibrations of simply supported plates under thermal and sinusoidal excitation is studied in order to predict the vibratory behavior of a representative class of such skin panels. A method for the development of equations of motion, that forms a foundation for further investigation of the response of elastic panels under general thermal, mechanical and aerodynamic loading and various boundary conditions, is presented and discussed.

The boundaries of regular and chaotic regions of motion are defined and the sensitivity of these boundaries to changes in design parameters is explored for the purpose of developing useful design criteria. The onset of chaos is predicted through the computation of Lyapunov exponents. The sensitivity of Lyapunov exponent calculations to the choice of numerical method of integration, numerical precision and the magnitude of coefficients as functions of design variables, is discussed. The effects of thermal moment, thermal buckling, amplitude and frequency of excitation, damping, thickness and length to width ratio of panels on the onset of chaos is studied. The results of the research are presented as a contribution to the panel design of hypersonic vehicles.

Source: Muge Fermen-Coker (

The Dynamics of Open-Ocean Plankton Ecosystem Models

Department of Biological Sciences, University of Warwick

Andrew Yool

Supervisor: Professor J. M. McGlade


In contributing around 40% of total annual primary productivity, the plankton ecosystems of the world ocean play a significant part in the global cycle of carbon. The formulation of dynamic models of plankton ecology is one facet of the study of this cycle, and though much progress has been made, considerable uncertainty still surrounds many aspects of their construction. This thesis focuses on one such plankton model, the nitrogen mixed-layer ecosystem model of Fasham (1993), and several investigations of its structure and parameterisation have been undertaken.

In the first of these the importance of the model's structure has been studied by rationally reducing the full seven compartment form of the model to a simple phytoplankton-zooplankton ecology, and then gradually re-assembling it. This work found the presence of detritus key to the success of the reduced models, while also finding bacteria to be a mostly redundant component of the full model.

A notable feature of modelled summers at OSW "India" in the North Atlantic (and tentatively in data from this location) is the occurrence of predator-prey oscillations. Since such behaviour has consequences for tests of the model, these oscillations were investigated numerically to establish their true nature. Although it was found that they were really transients towards a stable fixed point, further explorations of the parameter space of the model located regions in which stable limit cycle behaviour occurred, and these regions suggested situations under which oscillatory behaviour might be observed in the real world. Of particular importance in the construction of models is the assignment of parameter values. As estimating most of these requires difficult or time-consuming experiments, knowing which parameters most strongly influence model behaviour can optimise the development of a model. To this end, a sensitivity study of the model was performed, primarily using stochastic techniques. This study found that phytoplankton photosynthesis and zooplankton grazing parameters topped the rankings of parameter sensitivity. Further work explored the sensitivity technique known as stochastic parameters (Kremer, 1983).

Finally, a variant of the Fasham (1993) model in which vertical space was represented by two communicating layers was constructed, and several facets of its behaviour explored. The importance of latitude and zooplankton migration, as well as the properties of Taylor (1988) were examined, with particular emphasis on the significance of any DCM that formed in the model solutions. Throughout the thesis results are related to the literature and, where possible, to data. Most sections, however, refer to comparisons between models or parts of models, but the analysis always aims to place results in context within plankton modelling.

The entire thesis will soon be available on the internet from the Ecosystems Analysis & Management Group's Thesis Archive, which can be accessed from:

Source: Andrew Yool (

UK Nonlinear News Issue 12 Index Page May 1998).
Last Updated: 1st May 1998.