Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

Modelling of femtosecond inscription in fused silica

We present theoretical and numerical analysis of the femtosecond processing of silica by laser beam with power below self-focusing threshold.

Computer aided form roll design

Cold roll forming is an extremely important but little studied sheet metal forming process. In this thesis, the process of cold roll forming is introduced and it is seen that form roll design is central to the cold roll forming process. The conventional design and manufacture of form rolls is discussed and it is observed that surrounding the design process are a number of activities which although peripheral are time consuming and a possible source of error. A CAD/CAM system is described which alleviates many of the problems traditional to form roll design. New techniques for the calculation of strip length and controlling the means of forming bends are detailed. The CAD/CAM system's advantages and limitations are discussed and, whilst the system has numerous significant advantages, its principal limitation can be said to be the need to manufacture form rolls and test them on a mill before a design can be stated satisfactory. A survey of the previous theoretical and experimental analysis of cold roll forming is presented and is found to be limited. By considering the previous work, a method of numerical analysis of the cold roll forming process is proposed based on a minimum energy approach. Parallel to the numerical analysis, a comprehensive range of software has been developed to enhance the designer's visualisation of the effects of his form roll design. A complementary approach to the analysis of form roll design is the generation of form roll design, a method for the partial generation of designs is described. It is suggested that the two approaches should continue in parallel and that the limitation of each approach is knowledge of the cold roll forming process. Hence, an initial experimental investigation of the rolling of channel sections is described. Finally, areas of potential future work are discussed.

Alginates as therapeutic and drug delivery systems

Alginate is widely used as a viscosity enhancer in many different pharmaceutical formulations. The aim of this thesis is to quantitatively describe the functions of this polyelectrolyte in pharmaceutical systems. To do this the techniques used were Viscometry, Light Scattering, Continuous and Oscillatory Shear Rheometry, Numerical Analysis and Diffusion. Molecular characterization of the Alginate was carried out using Viscometry and Light Scattering to determine the molecular weight, the radius of gyration, the second virial coefficient and the Kuhn statistical segment length. The results showed good agreement with similar parameters obtained in previous studies. By blending Alginate with other polyelectrolytes, Xanthan Gum and 'Carbopol', in various proportions and with various methods of low and high shear preparation, a very wide range of dynamic rheological properties was found. Using oscillatory testing, the parameters often varied over several decades of magnitude. It was shown that the determination of the viscous and elastic components is particularly useful in describing the rheological 'profiles' of suspending agent blends and provides a step towards the non-empirical formulation of pharmaceutical disperse systems. Using numerical analysis of equations describing planar diffusion, it was shown that the analysis of drug release profiles alone does not provide unambiguous information about the mechanism of rate control. These principles were applied to the diffusion of Ibuprofen in Calcium Alginate gels. For diffusion in such non-Newtonian systems, emphasis was placed on the use of the elastic as well as the viscous component of viscoelasticity. It was found that the diffusion coefficients were relatively unaffected by increases in polymer concentration up to 5 per cent, yet the elasticities measured by oscillatory shear rheometry were increased. This was interpreted in the light of several theories of diffusion in gels.