We are concerned with the probability that a standard Brownian motion W(t) crosses a curved boundary c(t) on a finite interval [0, T]. Let this probability be denoted by Q(c(t); T). Due to recent advances in research a new way of estimating Q(c(t); T) seems feasible: Monte Carlo Simulation. Wang and Pötzelberger (1997) derived an explicit formula for the boundary crossing probability of piecewise linear functions which has the form of an expectation. Based on this formula we proceed as follows: First we approximate the general boundary c(t) by a piecewise linear function cm(t) on a uniform partition. Then we simulate Brownian sample paths in order to evaluate the expectation in the formula of the authors for cm(t). The bias resulting when estimating Q(c_m(t); T) rather than Q(c(t); T) can be bounded by a formula of Borovkov and Novikov (2005). Here the standard deviation - or the variance respectively - is the main limiting factor when increasing the accuracy. The main goal of this dissertation is to find and evaluate variance reducing techniques in order to enhance the quality of the Monte Carlo estimator for Q(c(t); T). Among the techniques we discuss are: Antithetic Sampling, Stratified Sampling, Importance Sampling, Control Variates, Transforming the original problem. We analyze each of these techniques thoroughly from a theoretical point of view. Further, we test each technique empirically through simulation experiments on several carefully chosen boundaries. In order to asses our results we set them in relation to a previously established benchmark. As a result of this dissertation we derive some very potent techniques that yield a substantial improvement in terms of accuracy. Further, we provide a detailed record of our simulation experiments. (author's abstract)

This thesis is a blend of neutron transport theory and numerical analysis. We start with the study of the problem of the Mika/Case eigenexpansion used in the solution process of the homogeneous one-speed Boltzmann neutron transport equation with anisotropic scattering for plane symmetry. The anisotropic scattering is expressed as a finite Legendre series in which the coefficients are the ``scattering coefficients'. This eigenexpansion consists of a discrete spectrum of eigenvalues with its corresponding eigenfunctions and the continuous spectrum [-1,+1] with its corresponding eigendistributions. In the general case where the anisotropic scattering can be of any (finite) order, multiple discrete eigenvalues exist and these have to be located to have the complete spectrum. We have devised a stable and robust method that locates all these discrete eigenvalues. The method is a two-step process: first the number of discrete eigenvalues is calculated and this is followed by the calculation of the discrete eigenvalues themselves, now being able to count them down and make sure none are forgotten. During our numerical experiments, we came across what we called near-singular eigenvalues: discrete eigenvalues that are located extremely close to the continuum and hence lead to near-singular behaviour in the eigenfunction. Our solution method has been adapted and allows for the automatic detection of such a near-singular eigenvalue. For the elements of the continuous spectrum [-1,+1], there is no non-zero function satisfying the associated eigenequation but there is a non-zero distribution that does satisfy it. It is not feasible to compute a distribution as such but one can evaluate integrals in which this distribution appears. The continuum part of the eigenexpansion can hence only be characterised by its (angular) moments. Accurate and fast numerical quadrature is needed to evaluate these integrals. Several quadrature methods have been evaluated on a representative test function. The eigenexpansion was proved to be orthogonal and complete and hence can be used to represent the infinite medium Green's function. The latter is the building block of the Boundary Sources Method, an integral solution method for the neutron transport equation. Using angular and angular/spatial moments of the Green's function, it is possible to solve with high accuracy slab problems. We have written a one-dimensional slab code implementing this Boundary Sources Method allowing for media with arbitrary order anisotropic scattering. Our results are very good and the code can be considered as a benchmark code for others. As a final application, we have used our code to study the discrete spectrum of a well-known scattering kernel in radiative transfer, the Henyey-Greenstein kernel. This kernel has one free parameter which is used to fit the kernel to experimental data. Since the kernel is a continuous function, a finite Legendre approximation needs to be adopted. Depending on the free parameter, the approximation order and the number of secondaries per collision, the number of discrete eigenvalues ranges from two to thirty and even more. Bounds for the minimum approximation order are derived for different requirements on the approximation: non-negativity, an absolute and relative error tolerance.

<p>In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction.</p><p>In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view.</p><p><b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering</p>

Unsteady two-dimensional laminar flow of an incompressible viscous fluid over a periodically grooved wall is investigated by numerical simulation using two independent finite-difference methods. One is the vorticity-stream function method, and the other involves the vorticity-velocity induction law formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The flow field, which includes the time development of the shear layer and the recirculating flow in the zone of separation, is examined in detail during the transient phase to the steady-state condition. The analytical and numerical formulations, which include the implementation of the boundary conditions, are derived in detail. The generation of vorticity at the solid surfaces is modelled differently in the two approaches. This vorticity production plays an important role in determining the surface-pressure distribution and the drag coefficient. Characteristics of the transient solution for a moderate Reynolds number in the laminar range are presented. Included with the graphical results are the temporal development of the constant stream function contours, including the dividing contour between the zone of separation and the main flow, and the constant vorticity contours. These latter contours show the interactions of separated vortices. The flow is found to approach a steady-state condition comprising an undisturbed uniform flow, a nonuniform irrotational flow, a shear layer adjacent to the grooved wall, and a recirculating vortex flow in the groove. Results also include the time development of the surface shear stress, surface pressure, drag coefficient and several typical velocity profiles, which characterize the flow in the recirculating region. Comparisons of the results obtained by the two numerical methods are made during the major development of the flow. The results showing the general features of the flow development including the time development of the shear layer, free shear layer and recirculating vortex flow are in good agreement. However, a significant deviation does exist at early times for the distribution of surface pressure, which accordingly has noticeable effect on the drag coefficient. Nevertheless, the gap between the distributions of surface pressure and drag coefficients dies out gradually as time progresses. The form of the stream function and vorticity contours at the steady state agrees well with those obtained from a recent numerical investigation of the steady flow in grooved channels.

Transition in high-speed boundary layers is investigated using direct numerical simulation (DNS). A compressible Navier-Stokes code that is specifically tailored towards accurate and efficient simulations of boundary layer stability and boundary layer transition was developed and thoroughly validated. Particular emphasis was put into the adoption of a high-order accurate spatial discretization including a boundary closure with the same stencil width as the interior scheme. Oblique breakdown has been shown, using both temporal and spatial DNS, to be a viable route to transition for the boundary layer of the sharp 7° cone at Mach 3.5 investigated by Corke 2002. A 'wedge-shaped' transitional regime was observed to be characteristic for this type of breakdown on the cone geometry. Furthermore, it was shown that the dominance of the longitudinal mode in the nonlinear transition regime of oblique breakdown is due to a continuously nonlinear forced transient growth. That is the primary pair of oblique waves permanently 'seeds' disturbances into the longitudinal mode, where these disturbances exhibit non-modal unstable behavior. In addition to the simulations of controlled transition via oblique breakdown, six simulations have been conducted and analyzed where transition is initiated by multiple primary waves. Despite the broader spectrum of primary waves, typical features of oblique breakdown are still apparent in these simulations and therefore, it may be conjectured, that oblique breakdown initiated by one primary pair of waves is a good model for the nonlinear processes in natural transition. Furthermore, hypersonic boundary layer stability and transition for a flared and a straight cone at Mach 6 was investigated. In particular, a comparative investigation between both geometries regarding the K-type breakdown was performed in order to give some indications towards the open question how strong the nonlinear transition processis altered by the cone flare.

During the late 19th Century there was considerable debate in the United States among members of the legal profession, the general public and even some scientists about the validity of using tree rings to determine tree age. In an earlier boundary dispute case in Maryland (1830) the Honorable Theodorick Bland rejected the use of tree rings to establish the date when a purported witness tree was marked with an identifying blaze. Bland did not believe that there was enough scientific evidence or legal precedent to support this idea. A review of the current scientific literature of the time, however, indicates that most scientists, especially in Europe, accepted that tree rings could be used to determine age. In the United States, however, this idea was debated, particularly in the late 19th Century, in both the popular press and scientific publications. The main argument of opponents such as A. L. Child was that the number of tree rings was often wildly in excess of the known age of the tree. These inconsistencies were likely because of the inexperience of the observer, mistaking earlywood and latewood for separate rings, and the presence of a small number of false rings, sometimes called secondary rings. The great ages reported for the giant sequoias may have also raised doubts among the public. Among scientists, however, the relationship between ring number and tree age and between ring width and climate became widely accepted. Several cases heard in both Federal and State Courts as well as Bernhard E. Fernow’s Age of Trees and Time of Blazing Determined by Annual Rings laid to rest any doubt of the relationship between tree rings and age in temperate forests, i.e. one ring equals one year’s growth, and showed that the date when a witness tree was blazed could be easily determined from a cross-section of the trunk.

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In the service economy of the 21st century, companies face intense competition in providing customer-centric products and services. In an environment where emerging technologies constantly stimulate innovative methods of service delivery, customer and technological knowledge remain the primary types of information applied by a company in providing customers with quality products and services. Managing knowledge interactions for synergetic business operations is critical in building a service-oriented infrastructure for continuous innovation. This study explores the pattern of knowledge interaction between R&D and marketing departments. Knowledge possessed by R&D department is defined as technological knowledge, while knowledge possessed by marketing department is defined as customer knowledge. First, the concepts, theories, and relevant research regarding the relationship between customer and technological knowledge is reviewed. Based on boundary-spanning theory, this study conducts an exploratory case study to examine the interaction between customer and technological knowledge. The case study focuses on the interaction between sales personnel and R&D employees across three levels of interaction, the syntactic, semantic, and pragmatic. This study found that different types of knowledge and activities between R&D and marketing departments generate different results. This study also found that most business knowledge for innovation is generated at the knowledge interaction between semantic and pragmatic level. Another finding is that Field Application Engineers play the important roles of boundary spanner because they possess both technological knowledge and customer knowledge for their specialized field. Boundary spanners serve as both filters and facilitators in information transmittal between internal units, and play an important role in the transfer of ideas within organizations. To develop critical innovations, businesses should interact according to what type of knowledge accessed.

The thesis numerically explores the use and behavior of Active Hydraulic Devices (AHDs), creating a new capability to simulate and control a pipe system’s transient performance. Automatic control valves are the first type of AHDs studied in this research. Due to the challenges inherent in the design of a pressure relief valve (PRV), the general principles of PRV use and selection are studied along with the system’s response to the PRV parameters. A new application of PID (proportional, integral and derivative) control valve is envisioned that combines a remote sensor at the upstream end of a pipeline to create a non- or semi- reflective boundary at the downstream end. Case studies show that, with such a boundary, the reflection and resonance of pressure waves within the pipeline are sometimes eliminated and invariably limited. The second type of AHDs studied in this research is the governed hydro turbine, the most complicated hydraulic component in terms of transient analysis and waterhammer control. A complete numerical model is developed for the turbine installations in either urban water networks or conventional hydropower generation systems. Using the model, transient simulations for several realistic hydro projects are presented along with various transient control measures.