Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

Transition and foreign aid policies in the Visegrád countries:a path dependant approach

The paper argues that the current emerging international development policies of the Visegrád (V4) countries are heavily influenced by the certain aspects of the Communist past and the transition process. Due to these influences, the V4 countries have difficulties in adapting the foreign aid practices of Western donors and this leads to the emergence of a unique Central and Eastern European development cooperation model. As an analytical background, the paper builds on the path dependency theory of transition. A certain degree of path dependence is clearly visible in V4 foreign aid policies, and the paper analyses some aspects of this phenomenon: how these new emerging foreign aid donors select their partner countries, how much they spend on aid, how they formulate their aid delivery policies and institutions and what role the non-state actors play. The main conclusions of the paper are that the legacies of the Communist past have a clear influence and the V4 countries still have a long way to go in adapting their aid policies to international requirements.

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.

Token codeswitching and language alternation in narrative discourse: a functional-pragmatic approach

This study is concerned with two phenomena of language alternation in biographic narrations in Yiddish and Low German, based on spoken language data recorded between 1988 and 1995. In both phenomena language alternation serves as an additional communicative tool which can be applied by bilingual speakers to enlarge their set of interactional devices in order to ensure a smoother or more pointed processing of communicative aims. The first phenomenon is a narrative strategy I call Token Cod-eswitching: In a bilingual narrative culminating in a line of reported speech, a single element of L2 indicates the original language of the reconstructed dialogue – a token for a quote. The second phenomenon has to do with directing procedures, carried out by the speaker and aimed at guiding the hearer's attention, which are frequently carried out in L2, supporting the hearer's attention at crucial points in the interaction. Both phenomena are analyzed following a model of narrative discourse as proposed in the framework of Functional Pragmatics. The model allows the adoption of an integral approach to previous findings in code-switching research.

Response-based segmentation using Finite Mixture Partial Least Squares: theoretical foundations and an application to American Customer Satisfaction Index Data

When applying multivariate analysis techniques in information systems and social science disciplines, such as management information systems (MIS) and marketing, the assumption that the empirical data originate from a single homogeneous population is often unrealistic. When applying a causal modeling approach, such as partial least squares (PLS) path modeling, segmentation is a key issue in coping with the problem of heterogeneity in estimated cause-and-effect relationships. This chapter presents a new PLS path modeling approach which classifies units on the basis of the heterogeneity of the estimates in the inner model. If unobserved heterogeneity significantly affects the estimated path model relationships on the aggregate data level, the methodology will allow homogenous groups of observations to be created that exhibit distinctive path model estimates. The approach will, thus, provide differentiated analytical outcomes that permit more precise interpretations of each segment formed. An application on a large data set in an example of the American customer satisfaction index (ACSI) substantiates the methodology’s effectiveness in evaluating PLS path modeling results.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

Modified nonlinear inverse synthesis for optical links with distributed Raman amplification

We propose a modification of the nonlinear digital signal processing technique based on the nonlinear inverse synthesis for the systems with distributed Raman amplification. The proposed path-average approach offers 3 dB performance gain, regardless of the signal power profile.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

A path-dependent contingent-claims approach to capacity investments

This note presents a contingent-claims approach to strategic capacity planning. We develop models for capacity choice and expansion decisions in a single firm environment where investment is irreversible and demand is uncertain. These models illustrate specifically the relevance of path-dependent options analysis to planning capacity investments when the firm adopts demand tracking or average capacity strategies. It is argued that Asian/average type real options can explain hysteresis phenomena in addition to providing superior control of assets in place.

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.

Creation of relational assets through the 'library of equipment' model:an industrial modernization approach of Japan's local technology centres

SMEs with a weak internal R&D capacity show the tendency to shy away from using external sources of technical expertise. The tendency deters providers of industrial modernization services from supporting such structurally weak SMEs. This paper examines how Japan's local technology centres - kosetsushi - remove the bottleneck and reach out to a significant proportion of SMEs with a weak R&D capacity in their localities. Kosetsushi centres sustain habitual interactions with client firms through 'low information gap' services solving immediate needs and lead the clients to a riskier and longer path toward innovation capacity building. This gives kosetsushi centres a position distinct from universities and consultancies in the regional innovation system. While long-term relationships between kosetsushi centres and their client firms can increase switching costs and produce lock-in effects, a case study of two kosetsushi centres illustrates the importance of 'low-information gap' services and relational assets created thereby to the modernization of SMEs with a weak internal R&D capacity. The paper calls for long-term commitment by the public sector if it addresses the issue through modernization services.

Evaluating and developing project-based learning:an empirical approach to evaluating CDIO

As a global profession, engineering is integral to the maintenance and further development of society. Indeed, contemporary social problems requiring engineering solutions are not only a consequence of natural and ‘manmade’ disasters (such as the Japanese earthquake or the oil leakage in the Gulf of Mexico) but also encapsulate 21st Century dilemmas around sustainability, poverty and pollution [2,6,7]. Given the complexity of such problems and the constant need for innovation, the demand for engineering education to provide a ready supply of suitably qualified engineering graduates, able to make innovative decisions has never been higher [3,5]. Bearing this in mind, and taking account problems of attrition in engineering education [1,6,4] innovation in the way in which the curriculum is developed and delivered is crucial. CDIO [Conceive, Design, Implement, Operate] provides a potentially ground-breaking solution to such dilemmas. Aimed at equipping students with practical engineering skills supported by the necessary theoretical background, CDIO could potentially change the way engineering is perceived and experienced within higher education. Aston University introduced CDIO into its Mechanical Engineering and Design programmes in October 2011. From its induction, engineering education researchers have ‘shadowed’ the staff responsible for developing and teaching the programme. Utilising an Action Research Design, and adopting a mixed methodological research design, the researchers have worked closely with the teaching team to critically reflect on the processes involved in introducing CDIO into the curriculum. Concurrently, research has been conducted to capture students’ perspectives of CDIO. In evaluating the introduction of CDIO at Aston, the researchers have developed a distinctive research strategy with which to evaluate CDIO. It is the emergent findings from this research that form the basis of this paper. Although early-on in its development CDIO is making a significant difference to engineering education at the University. The paper draws attention to pedagogical, practical and professional issues – discussing each one in turn and in doing so critically analysing the value of CDIO from academic, student and industrial perspectives. The paper concludes by noting that whilst CDIO represents a forwardthinking approach to engineering education, the need for constant innovation in learning and teaching should not be forgotten. Indeed, engineering education needs to put itself at the forefront of pedagogic practice. Providing all-rounded engineers, ready to take on the challenges of the 21st Century!