<p>The aim of this study is to examine the vocabulary and receptive collocation knowledge in English among Swedish upper secondary school students. The primary material consists of two vocabulary tests, one collocation test, and a background questionnaire.</p><p>The first research question concerns whether the students who receive a major part of their education in English have a higher level of vocabulary and receptive collocation knowledge in English than those who are taught primarily in Swedish. The second concerns if the students who started to learn English before the age of 7 have a higher level of vocabulary and receptive collocation knowledge in English than those who started after 7. The third concerns if the level of the students' vocabulary and receptive collocation knowledge correlates. The fourth addresses whether external inputs of English may have had an effect on the students' vocabulary and receptive collocation knowledge level.</p><p>The results indicate that reinforcement of English through an education mostly in English has rendered a higher level of vocabulary and receptive collocation knowledge in English. In addition, starting to learn English before age 7 also appeared to have had a positive effect on these levels. In addition, the results suggest that an early onset (before 7) of English compensates for lack of reinforcement of English. Conversely, reinforcement of English compensates for a late onset (after 7) of English. However, the results imply that the combination of an early onset (before 7) of English and reinforcement of English is the most efficient means to achieve a high level of vocabulary and receptive collocation knowledge.</p><p>Moreover, a clear correlation was found between vocabulary knowledge and receptive collocation knowledge, which also points to the importance of a large exposure to English.</p><p>For the high performance students, external influences such as English in primary and secondary school, and a high motivation to learn English may have contributed to a higher language confidence, and possibly a higher level of vocabulary and receptive collocation knowledge.</p><p> </p>

Computation methods based on the Wiener chaos expansion have been developed to study the behaviors of the aeroelastic system with randomparameters. It is proven that the discrete wavelet transformation is one ofthe most accurate and efficient numerical schemes for this uncertainty quantizationproblem. In this thesis, we propose the stochastic collocation methods(SCM), whichis a type of sampling method combining the strength of the MonteCarlo simulation and the stochastic Galerkin method. The convergence with respect to the number of the nodal points is investigated, and simulation results to aeroelastic models in the presence of uncertainty in the system parameter and due to the initial condition are reported. It is demonstrated that the accuracy of the SCM is comparable to those achieved by using the wavelet chaos expansion. However, the SCM is more straightforward, efficient and easy to implement. / Applied Mathematics

Increased national and international travel over the lastdecades has caused an increase in the global number ofpassengers using different means of transportation. Greateffort is being directed to improving the noisy environment inthe residential community. This is to face the growing strictnoise requirements which are implemented by international noiseregulatory authorities, governments, and local airports. Thereis also a strong competition between different manufacturers tomake their products quieter. The propulsion system in anaircraft is the major source of noise during relevant flightconditions. The engine noise in a vehicle dominates the totalradiated noise at low speeds especially inside cities. Manyrecent studies on noise reduction involve the use of perforatedplates in the air and gas flow ducting connected to the engine.This thesis deals with the modelling of perforates as anabsorbent. There are many difficulties in using liners in theseapplications. The most important is that there is no largesurface area to which the linings may be applied. Equally, theenvironment in which linings have to survive is hostile.Therefore, liners have to be carefully tailored in order toachieve the most efficient attenuation. The full-scalesimulation testing, which is usually necessary to define thenoise attenuation produced by a liner installation, is bothtime-consuming and expensive. Therefore, a need for accuratemodels is a must. This thesis fills some gaps in the impedancemodelling of perforated liners. It also concentrates on thosecomplicated situations of sound propagation in ducts that weresolved earlier using Finite Element Methods. Alternateanalytical solutions to these problems are developed here,which gives more physical insight into the results. The key design parameter of perforates is the acousticimpedance. The impedance is what determines their efficiency toabsorb sound waves. A semi empirical impedance model wasdeveloped to be capable of accurately predicting the linerimpedance as a function of its physical properties and thesurrounding conditions. It was compared to all previous modelsin the literature. Nothing in the literature has been reportedon the effect of temperature on the perforate impedance,therefore a complete study was performed. A new inverseanalytical impedance measurement technique was proposed. It isbased on educing the impedance value based on the measurementof the attenuation across a lined duct section. Twoapplications were further considered: The effect of hard stripsin lined ducts on there attenuation properties; and themodelling of perforations in a complicated automotive mufflersystem. Keywords:Perforates–Liners–Acousticimpedance–Hot stream liners–Hard splices–Mufflers–Lined ducts–Collocation–Flowduct.

The stochastic Galerkin and collocation methods are used to solve an advection-diusion equation with uncertain and spatially varying viscosity. We investigate well-posedness, monotonicity and stability for the extended system resulting from the Galerkin projection of the advection-diusion equation onto the stochastic basis functions. High-order summationby- parts operators and weak imposition of boundary conditions are used to prove stability of the semi-discrete system. It is essential that the eigenvalues of the resulting viscosity matrix of the stochastic Galerkin system are positive and we investigate conditions for this to hold. When the viscosity matrix is diagonalizable, stochastic Galerkin and stochastic collocation are similar in terms of computational cost, and for some cases the accuracy is higher for stochastic Galerkin provided that monotonicity requirements are met. We also investigate the total spatial operator of the semi-discretized system and its impact on the convergence to steadystate

Two basic approaches to reduce computational requirements for solving distillation problems have been studied: simplifications of the model based on physical approximations and order reduction techniques based on numerical approximations. Several problems have been studied using full and reduced-order techniques along with the following distillation models: Constant Molar Overflow, Constant Molar Holdup and Time-Dependent Molar Holdup. Steady-state results show excellent agreement in the profiles obtained using orthogonal collocation and demonstrate that with an order reduction of up to 54%, reduced-order models yield better results than physically simpler models. Step responses demonstrate that with a reduction in computing time of the order of 60% the method still provides better dynamic simulations than those obtained using physical simplifications. Frequency response data obtained from pulse tests has been used to verify that reduced-order solutions preserve the dynamic characteristics of the original full-order system while physical simplifications do not. The orthogonal collocation technique is also applied to a coupled columns scheme with good results. / Graduation date: 1992

Hydraulic fracturing is an important and abundant process in both industrial applications and natural environments. The current work is the first systematic quantitative study of the effect of interaction in and between complex hydraulic fractures at different spatial scales. A mathematical model, based on the boundary collocation method, has been developed. The model has been employed for a typical field case, a highly segmented vein. This vein is well-mapped, and therefore, represents a well constrained example. The computed apertures are compared to the measured apertures. By using the simplest constitutive model, based on an ideal elastic material, and including the effect of interaction between the segments, it was possible to obtain an excellent match at all considered scales. It was also shown that the concept of effective fracture, as currently accepted in the literature, is not always applicable and may lead to unbounded inaccuracy. Unfortunately, in most cases, very little (if any) directly measured data on fracture and material properties is available. An important example of such a weakly constrained case, involving hydraulic fracturing, is diking beneath the seafloor at mid-oceanic ridges. In this study, it is shown that the commonly accepted scenario of a dike propagating from the center of the pressurized magma chamber to the ocean floor is not consistent with conventional fracture mechanics due to the fact that the chamber has the shape of a thin lens. Even at such a large scale (i.e., a kilometer or more), the mechanical principles of elastic interaction appear to be applicable. Since diking is likely to generate a region of high permeability near its margin, in addition to heat, the ongoing hydrothermal activity becomes localized. Our modeling suggests the probable positions of the propagating dikes. Consequently, comparing the observed locations of hydrothermal sites with respect to that of the magma chamber could be useful for constraining the mechanisms of magma lens evolution.

In this dissertation we discuss some upscaling methods for flow and transport in heterogeneous reservoirs. We studied realization-based multi-phase flow and transport upscaling and ensemble-level flow upscaling. Multi-phase upscaling is more accurate than single-phase upscaling and is often required for high level of coarsening. In multi-phase upscaling, the upscaled transport parameters are time-dependent functions and are challenging to compute. Due to the hyperbolic feature of the saturation equation, the nonlocal effects evolve in both space and time. Standard local two-phase upscaling gives significantly biased results with reference to fine-scale solutions. In this work, we proposed two types of multi-phase upscaling methods, TOF (time-offlight)- based two-phase upscaling and local-global two-phase upscaling. These two methods incorporate global flow information into local two-phase upscaling calculations. A linear function of time and time-of-flight and a global coarse-scale two-phase solution (time-dependent) are used respectively in these two approaches. The local boundary condition therefore captures the global flow effects both spatially and temporally. These two methods are applied to permeability distributions with various correlation lengths. Numerical results show that they consistently improve existing two-phase upscaling methods and provide accurate coarse-scale solutions for both flow and transport. We also studied ensemble level flow upscaling. Ensemble level upscaling is up scaling for multiple geological realizations and often required for uncertainty quantification. Solving the flow problem for all the realizations is time-consuming. In recent years, some stochastic procedures are combined with upscaling methods to efficiently compute the upscaled coefficients for a large set of realization. We proposed a fast perturbation approach in the ensemble level upscaling. By Karhunen-Lo`eve expansion (KLE), we proposed a correction scheme to fast compute the upscaled permeability for each realization. Then the sparse grid collocation and adaptive clustering are coupled with the correction scheme. When we solve the local problem, the solution can be represented by a product of Green's function and source term. Using collocation and clusering technique, one can avoid the computation of Green's function for all the realizations. We compute Green's function at the interpolation nodes, then for any realization, the Green's function can be obtained by interpolation. The above techniques allow us to compute the upscaled permeability rapidly for all realizations in stochastic space.

In this thesis, we extend the spectral collocation methods(SCM) (i.e., pseudo-spectral method) in Quarteroni and Valli [27] for the semilinear, parameter-dependentproblems(PDP) in the square with the Dirichlet boundary condition. The optimal error bounds are derived in this thesis for both H1 and L2 norms. For the solutions sufficiently smooth, the very high convergence rates can be obtained. The algorithms of the SCM are simple and easy to carry out. Only a few of basis functions are needed so that not only can the high accuracy of the PDP solutions be achieved, but also a great deal of CPU time may be saved. Moreover, for PDP the stability analysis of SCM is also made, to have the same growth rates of condition number as those for Poisson¡¦s equation. Numerical experiments are carried out to verify the theoretical analysis made.

For the method of fundamental solutions(MFS), many reports deal with 2D problems. Since the MFS is more advantageous for 3D problems, this thesis is devoted to Laplace's equation in 3D problems. Since the fundamental solutions(FS) £X(x,y)=1/(4£k||x-y||), x,y∈R^3 are known, the location of source points is important in real computation. In this thesis, we choose a cylinder as the solution domain, and the source points on larger cylinders and spheres. Numerical results are reported, to draw some useful conclusions. The theoretical analysis will be explored in the future.

<p>English prepositions cause problems for learners of English. The way prepositions are taught has impact on how students learn. Using corpora in teaching makes it possible for teachers and pupils to explore language together and is a good alternative to filling in missing prepositions on worksheets. Sometimes linguistic errors are caused by mother tongue interference. Little research has been made earlier with a Swedish contrastive approach to prepositions but a great deal of literature concern language transfer and mother tongue interference. This essay is written on the assumption that Swedish as a first language interferes with English and causes prepositional mistakes.</p><p>Two classes of ninth graders participated in my investigation. I wanted to find out if students performed better when they had given answers to choose from or when they had to produce the preposition themselves. My study proved that pupils had a better knowledge of prepositions perceptively than productively. It also proved that learners resorted to Swedish when they did not know the correct answer. Many learners fail to recognise prepositions as parts of multiword expressions. By teaching students how to notice grammatical collocations and lexical chunks we can help them to achieve acceptable levels of language proficiency and accuracy.</p>