On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

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.

Application of the manakov-PMD equation to a computational investigation of low-PMD fibres

The phenomenon of low-PMD fibres is examined through numerical simulations. Instead of the coarse-step method we are using an algorithm developed through the Manakov-PMD equation. With the integration of the Manakov-PMD equation we have access to the fibre spin which relates to the orientation of the birefringence. The simulation results produced correspond to the behaviour of a low-PMD spun fibre. Furthermore we provide an analytical approximation compared to the numerical data. © 2005 Optical Society of America.

Numerical implementation of the Manakov-PMD equation with precomputed M(Ω) matrices

The Manakov-PMD equation can be integrated with the same numerical efficiency as the coarse-step method by using precomputed M(Ω) matrices, which entirely avoids the somewhat ad-hoc rescaling of coefficients necessary in the coarse-step method.

Effects of inducer continuity on auditory stream segregation:comparison of physical and perceived continuity in different contexts

The factors influencing the stream segregation of discrete tones and the perceived continuity of discrete tones as continuing through an interrupting masker are well understood as separate phenomena. Two experiments tested whether perceived continuity can influence the build-up of stream segregation by manipulating the perception of continuity during an induction sequence and measuring streaming in a subsequent test sequence comprising three triplets of low and high frequency tones (LHL-…). For experiment 1, a 1.2-s standard induction sequence comprising six 100-ms L-tones strongly promoted segregation, whereas a single extended L-inducer (1.1 s plus 100-ms silence) did not. Segregation was similar to that following the single extended inducer when perceived continuity was evoked by inserting noise bursts between the individual tones. Reported segregation increased when the noise level was reduced such that perceived continuity no longer occurred. Experiment 2 presented a 1.3-s continuous inducer created by bridging the 100-ms silence between an extended L-inducer and the first test-sequence tone. This configuration strongly promoted segregation. Segregation was also increased by filling the silence after the extended inducer with noise, such that it was perceived like a bridging inducer. Like physical continuity, perceived continuity can promote or reduce test-sequence streaming, depending on stimulus context.

Equation of state for water in the small compressibility region

The equation of state for dense fluids has been derived within the framework of the Sutherland and Katz potential models. The equation quantitatively agrees with experimental data on the isothermal compression of water under extrapolation into the high pressure region. It establishes an explicit relationship between the thermodynamic experimental data and the effective parameters of the molecular potential.

A post-structural analysis of perceptions and experiences of continuity and change within the UK automotive supplier base

Firms acting as suppliers to the British automotive industry have a long history of so doing, with some evidencing histories that predate even the invention of the motor car. In exploring the challenges faced by the descendants of these firms in the 1990s, a review is undertaken of the bodies of literature surrounding the changes wrought through the increased globalisation of the industry; the impact of new manufacturing technologies and techniques; the rising levels of co-operation between firms; and the growing impact of the automotive 'service sector'. Moreover, an exploration is undertaken of the perceived 'realities' of the automotive industry as constructed through discourse, including the ways in which discourse effects a continual reinterpretation and re-evaluation of the historical evolution of the industry. Attention is focused on the implications of the above for the automotive supply chain, and the means for its rationalisation proposed by the major car manufacturers and their partner-suppliers. Post-structuralist approaches are introduced as part of an attempt to establish and appropriate research methodology that can explore and deconstruct the discourses surrounding 'modernity', 'supply chain rationalisation', 'flexible specialisation' and 'globalisation' within the automotive industry. Analytical research is conducted into the small- to medium-sized business that constitute the majority of the supplier base in the United Kingdom, and the findings of this research are compared with those of a similar study conducted a quarter-century ago. In this way, the relationships of these firms with their customers, suppliers, and peers are investigated, as are their perceptions of a changing marketplace and their reactions to the impact of policies such as the 'supply chain rationalisation' pursued by the major automotive manufacturers. Authoritative discourses of industry form, function, and structure are challenged, with voice being granted to the marginalised: small suppliers, 'service sector' firms, or those only partly involved in the automotive industry.

A three dimensional numerical investigation of hillslope flow processes

Physically based distributed models of catchment hydrology are likely to be made available as engineering tools in the near future. Although these models are based on theoretically acceptable equations of continuity, there are still limitations in the present modelling strategy. Of interest to this thesis are the current modelling assumptions made concerning the effects of soil spatial variability, including formations producing distinct zones of preferential flow. The thesis contains a review of current physically based modelling strategies and a field based assessment of soil spatial variability. In order to investigate the effects of soil nonuniformity a fully three dimensional model of variability saturated flow in porous media is developed. The model is based on a Galerkin finite element approximation to Richards equation. Accessibility to a vector processor permits numerical solutions on grids containing several thousand node points. The model is applied to a single hillslope segment under various degrees of soil spatial variability. Such variability is introduced by generating random fields of saturated hydraulic conductivity using the turning bands method. Similar experiments are performed under conditions of preferred soil moisture movement. The results show that the influence of soil variability on subsurface flow may be less significant than suggested in the literature, due to the integrating effects of three dimensional flow. Under conditions of widespread infiltration excess runoff, the results indicate a greater significance of soil nonuniformity. The recognition of zones of preferential flow is also shown to be an important factor in accurate rainfall-runoff modelling. Using the results of various fields of soil variability, experiments are carried out to assess the validity of the commonly used concept of `effective parameters'. The results of these experiments suggest that such a concept may be valid in modelling subsurface flow. However, the effective parameter is observed to be event dependent when the dominating mechanism is infiltration excess runoff.

Random input problem for the nonlinear Schrödinger equation

We consider the random input problem for a nonlinear system modeled by the integrable one-dimensional self-focusing nonlinear Schrödinger equation (NLSE). We concentrate on the properties obtained from the direct scattering problem associated with the NLSE. We discuss some general issues regarding soliton creation from random input. We also study the averaged spectral density of random quasilinear waves generated in the NLSE channel for two models of the disordered input field profile. The first model is symmetric complex Gaussian white noise and the second one is a real dichotomous (telegraph) process. For the former model, the closed-form expression for the averaged spectral density is obtained, while for the dichotomous real input we present the small noise perturbative expansion for the same quantity. In the case of the dichotomous input, we also obtain the distribution of minimal pulse width required for a soliton generation. The obtained results can be applied to a multitude of problems including random nonlinear Fraunhoffer diffraction, transmission properties of randomly apodized long period Fiber Bragg gratings, and the propagation of incoherent pulses in optical fibers.

Using organoclay to promote morphology refinement and co-continuity in high-density polyethylene/polyamide 6 blends - Effect of filler content and polymer matrix composition

We investigate the gradual changes of the microstructure of two blends of high-density polyethylene (HDPE) and polyamide 6 (PA6) at opposite composition filled with increasing amounts of an organomodified clay. The filler locates preferentially inside the polyamide phase, bringing about radical alterations in the micron-scale arrangement of the polymer phases. When the host polyamide represents the major constituent, a sudden reduction of the average sizes of the polyethylene droplets was observed upon addition of even low amounts of organoclay. A morphology refinement was also noticed at low filler contents when the particles distributes inside the minor phase. In this case, however, keep increasing the organoclay content eventually results in a high degree of PA6 phase continuity. Rheological analyses reveal that the filler loading at which the polyamide assembles in a continuous network corresponds to the critical threshold for its rheological transition from a liquid- to a gel-like behaviour, which is indicative of the structuring of the filler inside the host PA6. On the basis of this finding, a schematic mechanism is proposed in which the role of the filler in driving the space arrangement of the polymer phases is discussed. Finally, we show that the synergism between the reinforcing action of the filler and its ability to affect the blend microstructure can be exploited in order to enhance relevant technological properties of the materials, such as their high temperature structural integrity.

Strategic practices:an activity theory perspective on continuity and change

This paper draws upon activity theory- to analyse an empirical investigation of the micro practices of strategy in three UK universities. Activity theory provides a framework of four interactive components from which strategy emerges; the collective structures of the organization, the primary actors, in this research conceptualized as the top management team (TMT), the practical activities in which they interact and the strategic practices through which interaction is conducted. Using this framework, the paper focuses specifically on the formal strategic practices involved in direction setting, resource allocation, and monitoring and control. These strategic practices arc associated with continuity of strategic activity in one case study but are involved in the reinterpretation and change of strategic activity in the other two cases. We model this finding into activity theory-based typologies of the cases that illustrate the way that practices either distribute shared interpretations or mediate between contested interpretations of strategic activity. The typologies explain the relationships between strategic practices and continuity and change of strategy as practice. The paper concludes by linking activity theory to wider change literatures to illustrate its potential as an integrative methodological framework for examining the subjective and emergent processes through which strategic activity is constructed. © Blackwell Publishing Ltd 2003.

Topic continuity in informal conversations between native and non-native speakers of English

Topic management by non-native speakers (NNSs) during informal conversations has received comparatively little attention from researchers, and receives surprisingly little attention in second language learning and teaching. This article reports on one of the topic management strategies employed by international students during informal, social interactions with native-speaker peers, exploring the process of maintaining topic continuity following temporary suspensions of topics. The concept of side sequences is employed to illustrate the nature of different types of topic suspension, as well as the process of jointly negotiating a return to the topic. Extracts from the conversations show that such sequences were not exclusively occasioned by language difficulties, and that the non-native speaker participants were able to effect successful returns to the main topic of the conversations.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.