Stationary scattering from a nonlinear network

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.

Exits, entrances and entrepreneurship : an exploration of economic theories of entrepreneurship through new independent entry and infant exit

The thesis began as a study of new firm formation. Preliminary research suggested that infant death rate was considered to be a closely related problem and the search was for a theory of new firm formation which would explain both. The thesis finds theories of exit and entry inadequate in this respect and focusses instead on theories of entrepreneurship, particularly those which concentrate on entrepreneurship as an agent of change. The role of information is found to be fundamental to economic change and an understanding of information generation and dissemination and the nature and direction of information flows is postulated to lead coterminously to an understanding of entrepreneurhsip and economic change. The economics of information is applied to theories of entrepreneurhsip and some testable hypotheses are derived. The testing relies on etablishing and measuring the information bases of the founders of new firms and then testing for certain hypothesised differences between the information bases of survivors and non-survivors. No theory of entrepreneurship is likely to be straightforwardly testable and many postulates have to be established to bring the theory to a testable stage. A questionnaire is used to gather information from a sample of firms taken from a new micro-data set established as part of the work of the thesis. Discriminant Analysis establishes the variables which best distinguish between survivors and non-survivors. The variables which emerge as important discriminators are consistent with the theory which the analysis is testing. While there are alternative interpretations of the important variables, collective consistency with the theory under test is established. The thesis concludes with an examination of the implications of the theory for policy towards stimulating new firm formation.

A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

Wave kinetics of random fibre lasers

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.

Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

The adoption of value-based management in large UK companies:a case for diffusion theory

Purpose – In the 1990s, a growing number of companies adopted value-based management (VBM) techniques in the UK. The purpose of this paper is to explore the motivations for the adoption or non-adoption of VBM for managing a business. Design/methodology/approach – An interview-based study of 37 large UK companies. Insights from diffusion theory and institutional theory are utilised to theorise these motivations. Findings – It was found that the rate of adoption of VBM in the sample companies does follow the classical S-shape. It also suggests that the supply-side of the diffusion process, most notably the role played by consultants, was an influence on many companies. This was not, however, a sufficient condition for companies to adopt the technique. The research also finds evidence of relocation diffusion, as several adopters are influenced by new officers, for example chief executive officers and finance directors, importing VBM techniques that they have used in organizations within which they have previously worked. Research limitations/implications – It is quite a small scale study and further work would be needed to develop the findings. Practical implications – Understanding and theorising the adoption of new management techniques will help understand the management of a business. Originality/value – This research adds further evidence to the value of studying management accounting, and more specifically management accounting change, in practice. It shows the developments in the adoption of a new technique and hence how a technique becomes accepted in practice.

On the opportunism-independent theory of the firm

Previous developments in the opportunism-independent theory of the firm are either restricted to special cases or are derived from the capabilities or resource-based perspective. However, a more general opportunism-independent approach can be developed, based on the work of Demsetz and Coase, which is nevertheless contractual in nature. This depends on 'direction', that is, deriving economic value by permitting one set of actors to direct the activities of another, and of non-human factors of production. Direction helps to explain not only firm boundaries and organisation, but also the existence of firms, without appealing to opportunism or moral hazard. The paper also considers the extent to which it is meaningful to speak of 'contractual' theories in the absence of opportunism, and whether this analysis can be extended beyond the employment contract to encompass ownership of assets by the firm. © The Author 2005. Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved.

Blood glucose self-monitoring in non-insulin-treated type 2 diabetes:a qualitative study of patients' perspectives

Background: Self-monitoring of blood glucose is controversial in the management of type 2 diabetes. Some research suggests that self-monitoring improves glycaemic control, whereas other research is sceptical about its value for people with type 2 diabetes who are not on insulin. Although blood glucose meters are widely available and used by this group, patients' own views are absent from the debate. Aim: To explore the pros and cons of glucose monitoring from the patients' perspectives. Design of study: Qualitative repeat-interview study. Setting: Patients were recruited from 16 general practices and three hospital clinics within four local healthcare cooperatives in Lothian, Scotland. Method: Interview data from 40 patients diagnosed with type 2 diabetes within the previous 6 months were analysed using thematic analysis informed by grounded theory. We report findings from round 1 and round 2 interviews. Results: Glucose monitoring can heighten patients' awareness of the impact of lifestyle; for example, dietary choices, on blood glucose levels. Glucose monitoring amplifies a sense of 'success' or 'failure' about self-management, often resulting in anxiety and self-blame if glucose readings remain consistently high. Moreover, monitoring can negatively effect patients' self-management when readings are counter-intuitive. Conclusion: Our analysis highlights the importance of understanding the meanings that newly diagnosed patients attach to glucose self-monitoring. To maximise the positive effects of self-monitoring, health professionals should ensure that patients understand the purpose of monitoring and should clarify with patients how readings should be interpreted. © British Journal of General Practice.

Design and development of a time of flight fast scattering spectrometer : a quantitative surface analysis technique and a new approach towards the experimental investigation of the surface particle interactions

A new surface analysis technique has been developed which has a number of benefits compared to conventional Low Energy Ion Scattering Spectrometry (LEISS). A major potential advantage arising from the absence of charge exchange complications is the possibility of quantification. The instrumentation that has been developed also offers the possibility of unique studies concerning the interaction between low energy ions and atoms and solid surfaces. From these studies it may also be possible, in principle, to generate sensitivity factors to quantify LEISS data. The instrumentation, which is referred to as a Time-of-Flight Fast Atom Scattering Spectrometer has been developed to investigate these conjecture in practice. The development, involved a number of modifications to an existing instrument, and allowed samples to be bombarded with a monoenergetic pulsed beam of either atoms or ions, and provided the capability to analyse the spectra of scattered atoms and ions separately. Further to this a system was designed and constructed to allow incident, exit and azimuthal angles of the particle beam to be varied independently. The key development was that of a pulsed, and mass filtered atom source; which was developed by a cyclic process of design, modelling and experimentation. Although it was possible to demonstrate the unique capabilities of the instrument, problems relating to surface contamination prevented the measurement of the neutralisation probabilities. However, these problems appear to be technical rather than scientific in nature, and could be readily resolved given the appropriate resources. Experimental spectra obtained from a number of samples demonstrate some fundamental differences between the scattered ion and neutral spectra. For practical non-ordered surfaces the ToF spectra are more complex than their LEISS counterparts. This is particularly true for helium scattering where it appears, in the absence of detailed computer simulation, that quantitative analysis is limited to ordered surfaces. Despite this limitation the ToFFASS instrument opens the way for quantitative analysis of the 'true' surface region to a wider range of surface materials.

Synapses, quantum theory and panpsychism

The introduction situates the ‘hard problem’ in its historical context and argues that the problem has two sides: the output side (the Kant-Eccles problem of the freedom of the Will) and the input side (the problem of qualia). The output side ultimately reduces to whether quantum mechanics can affect the operation of synapses. A discussion of the detailed molecular biology of synaptic transmission as presently understood suggests that such affects are unlikely. Instead an evolutionary argument is presented which suggests that our conviction of free agency is an evolutionarily induced illusion and hence that the Kant-Eccles problem is itself illusory. This conclusion is supported by well-known neurophysiology. The input side, the problem of qualia, of subjectivity, is not so easily outflanked. After a brief review of the neurophysiological correlates of consciousness (NCC) and of the Penrose-Hameroff microtubular neuroquantology it is again concluded that the molecular neurobiology makes quantum wave-mechanics an unlikely explanation. Instead recourse is made to an evolutionarily- and neurobiologically-informed panpsychism. The notion of an ‘emergent’ property is carefully distinguished from that of the more usual ‘system’ property used by most dual-aspect theorists (and the majority of neuroscientists) and used to support Llinas’ concept of an ‘oneiric’ consciousness continuously modified by sensory input. I conclude that a panpsychist theory, such as this, coupled with the non-classical understanding of matter flowing from quantum physics (both epistemological and scientific) may be the default and only solution to the problem posed by the presence of mind in a world of things.

The impact of brand owner on consumers' brand perceptions : a development of Heider's Balance Theory

Studies have shown that the brand “owner” is very influential in positioning the brand and when the brand “owner” ceases his or her active role the brand will be perceived differently by the consumers. Balance Theory (HBT), a cognitive psychological theory, studies the triadic relationships between two persons and an entity and predicts that when a person’s original perception of the relationship is disturbed, the person restructures to a new balanced perception. Consequently, this research was undertaken to: conceptualize the brand owner’s impact on consumer’s brand perception; test the applicability of both the static and dynamic predictions of the Heider’s Balance Theory in brand owner-consumer-brand relation (OCB); construct and test a model of brand owner-consumer-brand relation; and examine if personality has an influence on OCB. A discovery-oriented approach was taken to understand the selected market segment, the ready-to-wear and diffusion lines of international designer labels. Chinese Brand Personality Scale, fashion proneness and hedonic and utilitarian shopping scales were developed, and validated. 51 customers were surveyed. Both traditional and extended methods used in the Balance Theory were employed in this study. Responses to liked brand have been used to test and develop the model, while those for disliked brand were used for test and confirmation. A “what if’ experimental approach was employed to test the applicability of dynamic HBT theory in OCB Model. The hypothesized OCB Model has been tested and validated. Consumers have been found to have separate views on the brand and the brand owner; and their responses to contrasting ethical and non-ethical news of the brand owner are different. Personality has been found to have an influence and two personality adapted models have been tested and validated. The actual results go beyond the prediction of the Balance Theory. Dominant triple positive balance mode, dominant negative balance mode, and mode of extreme antipathy have been found. It has been found that not all balanced modes are good for the brand. Contrary to Heider’s findings, simply liking may not necessarily lead to unit relation in the OCB Model.

Non-Linear oil firm force coefficients for a journal bearing operating under aligned and misaligned conditions

It is well established that hydrodynamic journal bearings are responsible for self-excited vibrations and have the effect of lowering the critical speeds of rotor systems. The forces within the oil film wedge, generated by the vibrating journal, may be represented by displacement and velocity coefficient~ thus allowing the dynamical behaviour of the rotor to be analysed both for stability purposes and for anticipating the response to unbalance. However, information describing these coefficients is sparse, misleading, and very often not applicable to industrial type bearings. Results of a combined analytical and experimental investigation into the hydrodynamic oil film coefficients operating in the laminar region are therefore presented, the analysis being applied to a 120 degree partial journal bearing having a 5.0 in diameter journal and a LID ratio of 1.0. The theoretical analysis shows that for this type of popular bearing, the eight linearized coefficients do not accurately describe the behaviour of the vibrating journal based on the theory of small perturbations, due to them being masked by the presence of nonlinearity. A method is developed using the second order terms of Taylor expansion whereby design charts are provided which predict the twentyeight force coefficients for both aligned, and for varying amounts of journal misalignment. The resulting non-linear equations of motion are solved using a modified Newton-Raphson method whereby the whirl trajectories are obtained, thus providing a physical appreciation of the bearing characteristics under dynamically loaded conditions.