Transition from time-continuous systems to discrete mappings

Detailed transport studies in plasmas require the solution of the time evolution of many different initial positions of test particles in the phase space of the systems to be investigated. To reduce this amount of numerical work, one would like to replace the integration of the time-continues system with a mapping.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Osmotic dehydration in plant tissues

The primary aim of the thesis is to provide a comprehensive investigation of the osmotic dehydration processes in plant tissue. Effort has been concentrated on the modelling for simulating the processes. Two mathematical models for simulating the mass transfer during osmotic dehydration processes in plant tissues are developed and verified using existing experimental data. Both models are based on the mechanism of diffusion and convection of any mobile material that can transport in plant tissues. The mass balance equation for the transport of each constituent is established separately for intracellular and extra-cellular volumes with taking into account the mass transfer across the cell membrane the intracellular and extra-cellular volumes and the shrinkage of the whole tissue. The contribution from turgor pressure is considered in both models. Model two uses Darcy’s law to build the relation between shrinkage velocity and hydrostatic pressure in each volume because the plant tissue can be considered as the porous medium. Moreover, it has been extended to solve the multi-dimensional problems. A lot of efforts have been made to the parameter study and the sensitivity analyses. The parameters investigated including the concentration of the osmotic solution, diffusion coefficient, permeability of the cell membrane, elastic modulus of the cell wall, critical cell volume etc. The models allow us to quantitatively simulate the time evolution of intracellular and extra-cellular volumes as well as the time evolution of concentrations in each cross-section.

Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

T-cell epitope prediction and immune complex simulation using molecular dynamics:state of the art and persisting challenges

Atomistic Molecular Dynamics provides powerful and flexible tools for the prediction and analysis of molecular and macromolecular systems. Specifically, it provides a means by which we can measure theoretically that which cannot be measured experimentally: the dynamic time-evolution of complex systems comprising atoms and molecules. It is particularly suitable for the simulation and analysis of the otherwise inaccessible details of MHC-peptide interaction and, on a larger scale, the simulation of the immune synapse. Progress has been relatively tentative yet the emergence of truly high-performance computing and the development of coarse-grained simulation now offers us the hope of accurately predicting thermodynamic parameters and of simulating not merely a handful of proteins but larger, longer simulations comprising thousands of protein molecules and the cellular scale structures they form. We exemplify this within the context of immunoinformatics.

Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

New oil modified acrylic polymer for pH sensitive drug release:experimental results and statistical analysis

We report results of an experimental study, complemented by detailed statistical analysis of the experimental data, on the development of a more effective control method of drug delivery using a pH sensitive acrylic polymer. New copolymers based on acrylic acid and fatty acid are constructed from dodecyl castor oil and a tercopolymer based on methyl methacrylate, acrylic acid and acryl amide were prepared using this new approach. Water swelling characteristics of fatty acid, acrylic acid copolymer and tercopolymer respectively in acid and alkali solutions have been studied by a step-change method. The antibiotic drug cephalosporin and paracetamol have also been incorporated into the polymer blend through dissolution with the release of the antibiotic drug being evaluated in bacterial stain media and buffer solution. Our results show that the rate of release of paracetamol getss affected by the pH factor and also by the nature of polymer blend. Our experimental data have later been statistically analyzed to quantify the precise nature of polymer decay rates on the pH density of the relevant polymer solvents. The time evolution of the polymer decay rates indicate a marked transition from a linear to a strictly non-linear regime depending on the whether the chosen sample is a general copolymer (linear) or a tercopolymer (non-linear). Non-linear data extrapolation techniques have been used to make probabilistic predictions about the variation in weight percentages of retained polymers at all future times, thereby quantifying the degree of efficacy of the new method of drug delivery.

Numerical simulation of mass transfer during the osmotic dehydration of biological tissues

In this paper a mathematical model based on mass transfer in plant tissues is developed. The model takes into account the diffusion and convection of each constituent within the tissue. The driving force for the convection is assumed to be the gradient of hydrostatic pressure. The mass balance equation for the transport of each constituent is established separately for intracellular and extracellular volumes but taking into account the mass exchange across the cell membrane between the intracellular and extracellular volumes. The mass transfer results in not only the change of intracellular and extracellular volumes but also the shrinkage of whole tissue. The model allows us to quantitatively simulate the time evolution of intracellular and extracellular volumes, which was observed in histological sections under the microscope. © 2005 Elsevier B.V. All rights reserved.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Time-dependent evolution of tissue markers by MALDI-MS imaging

We have used MALDI-MS imaging (MALDI-MSI) to monitor the time dependent appearance and loss of signals when tissue slices are brought rapidly to room temperature for short to medium periods of time. Sections from mouse brain were cut in a cryostat microtome, placed on a MALDI target and allowed to warm to room temperature for 30 s to 3 h. Sections were then refrozen, fixed by ethanol treatment and analysed by MALDI-MSI. The intensity of a range of markers were seen to vary across the time course, both increasing and decreasing, with the intensity of some markers changing significantly within 30 s and markers also showed tissue location specific evolution. The markers resulting from this autolysis were compared directly to those that evolved in a comparable 16 h on-tissue trypsin digest, and the markers that evolved in the two studies were seen to be substantially different. These changes offer an important additional level of location-dependent information for mapping changes and seeking disease-dependent biomarkers in the tissue. They also indicate that considerable care is required to allow comparison of biomarkers between MALDI-MSI experiments and also has implications for the standard practice of thaw-mounting multiple tissue sections onto MALDI-MS targets.

Towards a framework for combining stochastic and deterministic descriptions of nonstationary financial time series

We present in this paper ideas to tackle the problem of analysing and forecasting nonstationary time series within the financial domain. Accepting the stochastic nature of the underlying data generator we assume that the evolution of the generator's parameters is restricted on a deterministic manifold. Therefore we propose methods for determining the characteristics of the time-localised distribution. Starting with the assumption of a static normal distribution we refine this hypothesis according to the empirical results obtained with the methods anc conclude with the indication of a dynamic non-Gaussian behaviour with varying dependency for the time series under consideration.

Evolution of capital structure in East Asia - corporate inertia of endeavours?

The paper examines the capital structure adjustment dynamics of listed non-financial corporations in seven east Asian countries before, during and after the crisis of 1997–1998. Our methodology allows for speeds of adjustment to vary, not only among firms, but also over time, distinguishing between cases of sudden and smooth adjustment.Whereas, compared with firms in the least affected countries, average leverages were much higher, generalized method-ofmoments analysis of the Worldscope panel data suggests that average speeds of adjustment were lower in the worst affected countries. This holds also for the severely financially distressed firms in some worst affected countries, though the trend reversed in the post-crisis period. These findings have important implications for the regulatory environment as well as access to market finance.

The evolution of "classical mythology" within marketing measure development

Purpose - This paper provides a deeper examination of the fundamentals of commonly-used techniques - such as coefficient alpha and factor analysis - in order to more strongly link the techniques used by marketing and social researchers to their underlying psychometric and statistical rationale. Design/methodology approach - A wide-ranging review and synthesis of psychometric and other measurement literature both within and outside the marketing field is used to illuminate and reconsider a number of misconceptions which seem to have evolved in marketing research. Findings - The research finds that marketing scholars have generally concentrated on reporting what are essentially arbitrary figures such as coefficient alpha, without fully understanding what these figures imply. It is argued that, if the link between theory and technique is not clearly understood, use of psychometric measure development tools actually runs the risk of detracting from the validity of the measures rather than enhancing it. Research limitations/implications - The focus on one stage of a particular form of measure development could be seen as rather specialised. The paper also runs the risk of increasing the amount of dogma surrounding measurement, which runs contrary to the spirit of this paper. Practical implications - This paper shows that researchers may need to spend more time interpreting measurement results. Rather than simply referring to precedence, one needs to understand the link between measurement theory and actual technique. Originality/value - This paper presents psychometric measurement and item analysis theory in easily understandable format, and offers an important set of conceptual tools for researchers in many fields. © Emerald Group Publishing Limited.

Numerically optimized implementations, mitigation and simulations of polarisation mode dispersion in real-time transmission systems

The aim of this thesis is to present numerical investigations of the polarisation mode dispersion (PMD) effect. Outstanding issues on the side of the numerical implementations of PMD are resolved and the proposed methods are further optimized for computational efficiency and physical accuracy. Methods for the mitigation of the PMD effect are taken into account and simulations of transmission system with added PMD are presented. The basic outline of the work focusing on PMD can be divided as follows. At first the widely-used coarse-step method for simulating the PMD phenomenon as well as a method derived from the Manakov-PMD equation are implemented and investigated separately through the distribution of a state of polarisation on the Poincaré sphere, and the evolution of the dispersion of a signal. Next these two methods are statistically examined and compared to well-known analytical models of the probability distribution function (PDF) and the autocorrelation function (ACF) of the PMD phenomenon. Important optimisations are achieved, for each of the aforementioned implementations in the computational level. In addition the ACF of the coarse-step method is considered separately, based on the result which indicates that the numerically produced ACF, exaggerates the value of the correlation between different frequencies. Moreover the mitigation of the PMD phenomenon is considered, in the form of numerically implementing Low-PMD spun fibres. Finally, all the above are combined in simulations that demonstrate the impact of the PMD on the quality factor (Q=factor) of different transmission systems. For this a numerical solver based on the coupled nonlinear Schrödinger equation is created which is otherwise tested against the most important transmission impairments in the early chapters of this thesis.

The design of a real-time nowcasting system for localised weather

National meteorological offices are largely concerned with synoptic-scale forecasting where weather predictions are produced for a whole country for 24 hours ahead. In practice, many local organisations (such as emergency services, construction industries, forestry, farming, and sports) require only local short-term, bespoke, weather predictions and warnings. This thesis shows that the less-demanding requirements do not require exceptional computing power and can be met by a modern, desk-top system which monitors site-specific ground conditions (such as temperature, pressure, wind speed and direction, etc) augmented with above ground information from satellite images to produce `nowcasts'. The emphasis in this thesis has been towards the design of such a real-time system for nowcasting. Local site-specific conditions are monitored using a custom-built, stand alone, Motorola 6809 based sub-system. Above ground information is received from the METEOSAT 4 geo-stationary satellite using a sub-system based on a commercially available equipment. The information is ephemeral and must be captured in real-time. The real-time nowcasting system for localised weather handles the data as a transparent task using the limited capabilities of the PC system. Ground data produces a time series of measurements at a specific location which represents the past-to-present atmospheric conditions of the particular site from which much information can be extracted. The novel approach adopted in this thesis is one of constructing stochastic models based on the AutoRegressive Integrated Moving Average (ARIMA) technique. The satellite images contain features (such as cloud formations) which evolve dynamically and may be subject to movement, growth, distortion, bifurcation, superposition, or elimination between images. The process of extracting a weather feature, following its motion and predicting its future evolution involves algorithms for normalisation, partitioning, filtering, image enhancement, and correlation of multi-dimensional signals in different domains. To limit the processing requirements, the analysis in this thesis concentrates on an `area of interest'. By this rationale, only a small fraction of the total image needs to be processed, leading to a major saving in time. The thesis also proposes an extention to an existing manual cloud classification technique for its implementation in automatically classifying a cloud feature over the `area of interest' for nowcasting using the multi-dimensional signals.