Decelerating Airy pulses

It is shown that an electromagnetic wave equation in time domain is reduced in paraxial approximation to an equation similar to the Schrodinger equation but in which the time and space variables play opposite roles. This equation has solutions in form of time-varying pulses with the Airy function as an envelope. The pulses are generated by a source point with an Airy time varying field and propagate in vacuum preserving their shape and magnitude. The motion is according to a quadratic law with the velocity changing from infinity at the source point to zero in infinity. These one-dimensional results are extended to the 3D+time case when a similar Airy-Bessel pulse is excited by the field at a plane aperture. The same behaviour of the pulses, the non-diffractive preservation and their deceleration, is found. © 2011 IEEE.

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.

Stimuli of varying spatial scale induce gamma activity with distinct temporal characteristics in human visual cortex

Gamma activity to stationary grating stimuli was studied non-invasively using MEG recordings in humans. Using a spatial filtering technique, we localized gamma activity to primary visual cortex. We tested the hypothesis that spatial frequency properties of visual stimuli may be related to the temporal frequency characteristics of the associated cortical responses. We devised a method to assess temporal frequency differences between stimulus-related responses that typically exhibit complex spectral shapes. We applied this methodology to either single-trial (induced) or time-averaged (evoked) responses in four frequency ranges (0-40, 20-60, 40-80 and 60-100 Hz) and two time windows (either the entire duration of stimulus presentation or the first second following stimulus onset). Our results suggest that stimuli of varying spatial frequency induce responses that exhibit significantly different temporal frequency characteristics. These effects were particularly accentuated for induced responses in the classical gamma frequency band (20-60 Hz) analyzed over the entire duration of stimulus presentation. Strikingly, examining the first second of the responses following stimulus onset resulted in significant loss in stimulus specificity, suggesting that late signal components contain functionally relevant information. These findings advocate a functional role of gamma activity in sensory representation. We suggest that stimulus specific frequency characteristics of MEG signals can be mapped to processes of neuronal synchronization within the framework of coupled dynamical systems.

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.

Integration of the Manakov-PMD Equation with Precomputed M(w) Matrices for PMD Simulation

A novel direct integration technique of the Manakov-PMD equation for the simulation of polarisation mode dispersion (PMD) in optical communication systems is demonstrated and shown to be numerically as efficient as the commonly used coarse-step method. The main advantage of using a direct integration of the Manakov-PMD equation over the coarse-step method is a higher accuracy of the PMD model. The new algorithm uses precomputed M(w) matrices to increase the computational speed compared to a full integration without loss of accuracy. The simulation results for the probability distribution function (PDF) of the differential group delay (DGD) and the autocorrelation function (ACF) of the polarisation dispersion vector for varying numbers of precomputed M(w) matrices are compared to analytical models and results from the coarse-step method. It is shown that the coarse-step method achieves a significantly inferior reproduction of the statistical properties of PMD in optical fibres compared to a direct integration of the Manakov-PMD equation.

Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500 ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100 ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

Modified hydrogel matrices in fibre optic sensors

Common problems encountered in clinical sensing are those of non-biocompatibility, and slow response time of the device. The latter, also applying to chemical sensors, is possibly due to a lack of understanding of polymer support or membrane properties and hence failure to optimise membranes chosen for specific sensor applications. Hydrogels can be described as polymers which swell in water. In addition to this, the presence of water in the polymer matrix offers some control of biocompatibility. They thus provide a medium through which rapid transport of a sensed species to an incorporated reagent could occur. This work considers the feasibility of such a system, leading to the design and construction of an optical sensor test bed. The development of suitable membrane systems and of suitable coating techniques in order to apply them to the fibre optics is described. Initial results obtained from hydrogel coatings implied that the refractive index change in the polymer matrix, due to a change in water content with pH is the major factor contributing to the sensor response. However the presence of the colourimetric reagent was also altering the output signal obtained. An analysis of factors contributing to the overall response, such as colour change and membrane composition were made on both the test bed, via optical response, and on whole membranes via measurement of water content change. The investigation of coatings with low equilibrium water contents, of less than 10% was carried out and in fact a clearer signal response from the test bed was noted. Again these membranes were suprisingly responding via refractive index change, with the reagent playing a primary role in obtaining a sensible or non-random response, although not in a colourimetric fashion. A photographic study of these coatings revealed some clues as to the physical nature of these coatings and hence partially explained this phenomenon. A study of the transport properties of the most successful membrane, on a coated wire electrode and also on the fibre optic test bed, in a series of test environments, indicated that the reagent was possibly acting as an ion exchanger and hence having a major influence on transport and therefore sensor characteristics.

Time controlled photo-oxidation of polyolefins by polymer bound additives

A variety of iron compounds containing vinyl or thiol functional groups (used as photoactivators) have been synthesised and some of these were successfully bound to both polyethylene and polypropylene backbones during processing in the presence of peroxide and interlinking agent. Concentrates (masterbatches) of the photoactivators in PP and PE were prepared and the pro-oxidant effect of the diluted masterbatches in absence and presence of an antioxidant was evaluated. An antioxidant photoactivator (FeDNC ) was found to sensitise the photoactivity of pro-oxidants (Metone A / Metone M) whereas an antioxidant (ZnDNC) was found to stabilise the polymer (PP and PE) containing both of these combinations. It was observed that the lower concentration of FeDNC sensitises the stability of the polymer containing very small concentration of NiDNC whereas higher concentration of FeDNC stabilises the polymer (LDPE) containing same amount of NiDNC compared to FeDNC alone. The photostability of unstabilised PP containing FeAc could be varied by varying the concentration of ZnDEC. Both the induction period and the UV - life time of the polymer increased by increasing concentration of ZnDEC. It is suggested that ligand exchange reaction may take place between FeAc and ZnDNC. A polymer bound UV stabiliser (HAEB) and a thermal stabiliser (DBBA) were used with a non extractable photoactivator (FeAc) in PP. Small concentrations of the stabilisers (HAEB and DBBA) in combination with the photoactivator (FeAc) sensitise the polymer. The antioxidant present in commercial polymer (LDPE and PP) was found to be of a hindered phenol type, which was found to antagonise with ZnDNC when used in combination with the photoactivators.

The effects of varying forms and degrees of government intervention upon the effective competitiveness of UK small businesses

This doctoral thesis responds to the need for greater understanding of small businesses and their inherent unique problem-types. Integral to the investigation is the theme that for governments to effectively influence small business, a sound understanding of the factors they are seeking to influence is essential. Moreover, the study, in its recognition of the many shortcomings in management research and, in particular that the research methods and approaches adopted often fail to give adequate understanding of issues under study, attempts to develop an innovative and creative research approach. The aim thus being to produce, not only advances in small business management knowledge from the standpoints of government policy makers and `lq recipient small business, but also insights into future potential research method for the continued development of that knowledge. The origins of the methodology lay in the non-acceptance of traditional philosophical positions in epistemology and ontology, with a philosophical standpoint of internal realism underpinning the research. Internal realism presents the basis for the potential co-existence of qualitative and quantitative research strategy and underlines the crucial contributory role of research method in provision of ultimate factual status of the assertions of research findings. The concept of epistemological bootstrapping is thus used to develop a `lq partial research framework to foothold case study research, thereby avoiding limitations of objectivism and brute inductivism. The major insights and issues highlighted by the `lq bootstrap, guide the researcher around the participant case studies. A novel attempt at contextualist (linked multi-level and processual) analysis was attempted in the major in-depth case study, with two further cases playing a support role and contributing to a balanced emphasis of empirical research within the context of time constraints inherent within part-time research.

Enhancing the humidity response time of polymer optical fiber Bragg grating by using laser micromachining

The humidity sensors constructed from polymer optical fiber Bragg gratings (POFBG) respond to the water content change in the fiber induced by varying environmental condition. The water content change is a diffusion process. Therefore the response time of the POFBG sensor strongly depends on the geometry and size of the fiber. In this work we investigate the use of laser micromachining of D-shaped and slotted structures to improve the response time of polymer fiber grating based humidity sensors. A significant improvement in the response time has been achieved in laser micromachined D-shaped POFBG humidity sensors. The slotted geometry allows water rapid access to the core region but this does not of itself improve response time due to the slow expansion of the bulk of the cladding. We show that by straining the slotted sensor, the expansion component can be removed resulting in the response time being determined only by the more rapid, water induced change in core refractive index. In this way the response time is reduced by a factor of 2.5.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Stochastic calculations for fibre Raman amplifiers with randomly varying birefringence

For the first time for the model of real-world forward-pumped fibre Raman amplifier with the randomly varying birefringence, the stochastic calculations have been done numerically based on the Kloeden-Platen-Schurz algorithm. The results obtained for the averaged gain and gain fluctuations as a function of polarization mode dispersion (PMD) parameter agree quantitatively with the results of previously developed analytical model. Simultaneously, the direct numerical simulations demonstrate an increased stochastisation (maximum in averaged gain variation) within the region of the polarization mode dispersion parameter of 0.1÷0.3 ps/km1/2. The results give an insight into margins of applicability of a generic multi-scale technique widely used to derive coupled Manakov equations and allow generalizing analytic model with accounting for pump depletion, group-delay dispersion and Kerr-nonlinearity that is of great interest for development of the high-transmission-rates optical networks.

The time course of changes in retinal vessel diameter in response to differing durations of flicker light provocation

Purpose: To determine the response of retinal vessels to differing durations of flicker light (FL) sitmulation. Methods: We recorded retinal arterial and venous vessel dilation to 12.5 Hz flicker light provocation (Retinal Vessel Analyzer, Imedos Systems) of varying duration (5, 7, 10 and 20 seconds) in twelve healthy young individuals (age range 26-45 yrs). All participants underwent a full ocular examination including intraocular pressure and blood pressure measurements. Results: Maximum dilation (MD) did not show a significant dependence on flicker duration in arteries whereas maximum constriction (MC) did. However, in veins MD significantly increased with flicker duration. Approximately 80-90% of MD in arteries is reached within 10 seconds of flicker light stimulation. Conclusions: The vast majority of arterial dilatory capacity is reached within 10 seconds of flicker light stimulation even though venous dilation continues strongly. Since the MC of arteries shows a significant dependence on flicker duration measurements at two different durations can provide more information about the retinal vascular system than at a single flicker duration alone.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.