Modern silencers for heavy vehicle applications are designed to cancel out the sound generated by the effects of combustion and propagation of exhaust gases through the engine after-treatment system. The complex geometry within the compact silencer give rise to self generated (or flow-) noise that contribute to the total sound power radiated at the exhaust outlet. To evaluate the magnitude and spectral frequency content of this self-generated noise, accurate non-reflective boundary conditions need to be applied along with a solver optimized for low dissipation and dispersion of acoustic waves. Parametric studies have been preformed to construct and evaluate the non-reflectiveness of stretched grids in combination with the buffer-zone technique for low- to mid- frequency noise. The Proudman noise source model have been used to identify the sources of sound within the computational domain and Detached Eddy Simulations have been used with full silencer geometries. Finally, the non-reflective performance of the stretched grid and buffer-zone technique have been evaluated using the acoustic beamforming method to spatially filter out and estimate the amount of reflections present in the final simulations. Detached Eddy Simulations can with success be used to resolve flow noise in exhaust gas geometries and allow reasonable comparisons. Steady models have been included in the comparisons but can only be used to estimate the amount of production of acoustic energy, not the radiated sound pressure levels related to the suppression of sound due to flow characteristics within the silencer geometries. Finally, the rough beamforming method confirmed the function of the non-reflective boundary conditions by finding major differences in magnitude for the sound being radiated towards the measurement point in different directions. / Ljuddämpare för lastbilar och bussar är konstruerade för att dämpa det ljud som genereras i förbränningsmotorn och i avgasreningssystemet. Moderna ljuddämpare består av komplexa geometrier som avgaserna flödar igenom och som släcker ut oönskat ljud. När avgaserna, bärandes ljud ifrån förbränningsmotorn flödar i hög hastighet genom den komplexa geometrin alstras ytterligare buller, så kallat själv-genererat ljud. För att ta fram frekensspektrat och ljudtrycksnivån ifrån detta bidragande ljud kan Detached Eddy Simulations utföras. Denna metod av strömningsmekaniska beräkningar kräver dock icke-reflektiva randvilkor. Randvilkor som uppfyller kraven har konstruerats genom parameterstudier tillsammans med en numerisk lösare som med låg dissipation och dispersion beräknar de akustiska pertubationerna i fjärfältet på ett fysikaliskt korrekt sätt. Vidare har även akustiska källmetoder används för att uppskatta närfältets storlek. Magnituden hos de kvarvarande reflektionerna har sedan uppskattas med hjälp av en förenklad Beamforming metod. Detached Eddy Simulations kan på ett framgångsfullt sätt användas för att ta fram det egengenererade ljudet ifrån ljuddämpargeometrier och möjliggör därigenom rimliga jämförelser mellan olika avgasgeometrier. De akusiska källmetoderna kan med säkerhet anvädas för att uppskatta den akustiska effekten som genereras i geometrierna men kan inte användas för att ta fram de dämpande effekterna som turbulenta strukturer eller hastighetsgradienter medför. Den förenklade Beamforming metoden har även bekräftat funtionen hos de icke-reflectiva randvilkoren genom att påvisa stora skillander i den ljudnivån som radierars ifrån olika riktingar mot den punkt som anvädas för att extrahera ljuddämparens ljudtrycksnivå.

By studying self-avoiding polygons (SAPs) in (L, M )-tubes (a tubular sublattice of the simple cubic lattice) as a sequence of 2-spans, transfer matrices can be used to obtain theoretical and numerical results for these SAPs. As a result, asymptotic properties of these SAPs, such as pattern densities in a random SAP and the expected span of a random SAP, can be calculated directly from these transfer matrices. These same results can also be obtained for compact polygons, as well as SAPs under the influence of an external force (called compressed or stretched polygons). These results can act as tools for examining the entanglement complexity of SAPs in (L, M )-tubes. In this thesis, it is examined how transfer matrices can be used to develop these tools. The transfer matrix method is reviewed, and previous transfer matrix results for SAPs in (L, M )-tubes, as well as SAPs subjected to an external force, are presented. The transfer matrix method is then similarly applied to compact polygons, where new results regarding compact polygons are obtained, including proofs for a compact concatenation theorem and for a compact pattern theorem. Also in this thesis, transfer matrices are actually generated (via the computer) for relatively small tube sizes. This is done for the general case of SAPs in (L, M )-tubes, as well as for the compact and external force cases. New numerical results are obtained directly from these transfer matrices, and a new algorithm for generating polygons is also developed from these transfer matrices. Compact polygons are actually generated (via the computer) for relatively small tube sizes and spans by using the developed polygon generation algorithm, and new numerical results for pattern densities and limiting free energies are obtained for stretched and compressed polygons.

Fluid dynamics considers the physics of liquids and gases. This is a branch of classical physics and is totally based on Newton's laws of motion. Nevertheless, the equation of fluid motion, Navier-Stokes equation, becomes very complicated to solve even for very simple configurations. This thesis treats mainly analytical vortex solutions to Navier-Stokes equations. Vorticity is usually concentrated to smaller regions of the flow, sometimes isolated objects, called vortices. If one are able to describe vortex structures exactly, important information about the flow properties are obtained. Initially, the modeling of a conical vortex geometry is considered. The results are compared with wind-tunnel measurements, which have been analyzed in detail. The conical vortex is a very interesting phenomenaon for building engineers because it is responsible for very low pressures on buildings with flat roofs. Secondly, a suggested analytical solution to Navier-Stokes equation for internal flows is presented. This is based on physical argumentation concerning the vorticity production at solid boundaries. Also, to obtain the desired result, Navier-Stokes equation is reformulated and integrated. In addition, a model for required information of vorticity production at boundaries is proposed. The last part of the thesis concerns the examples of vortex models in 2-D and 3-D. In both cases, analysis of the Navier-Stokes equation, leads to the opportunity to construct linear solutions. The 2-D studies are, by the use of diffusive elementary vortices, describing experimentally observed vortex statistics and turbulent energy spectrums in stratified systems and in soapfilms. Finally, in the 3-D analysis, three examples of recent experimentally observed vortex objects are reproduced theoretically. First, coherent structures in a pipe flow is modeled. These vortex structures in the pipe are of interest since they appear for Re in the range where transition to turbulence is expected. The second example considers the motion in a viscous vortex ring. The model, with diffusive properties, describes the experimentally measured velocity field as well as the turbulent energy spectrum. Finally, a streched spiral vortex is analysed. A rather general vortex model that has many degrees of freedom is proposed, which also may be applied in other configurations.

Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For isotropic meshes such estimators are known but they fail when applied to anisotropic meshes. Rectangular (or cuboidal) anisotropic meshes were already investigated. In this paper an error estimator is presented for tetrahedral or triangular meshes which offer a much greater geometrical flexibility.

This diploma thesis deals with the measurement of mechanical properties and accelerated aging of monoaxially stretched polyethylene strips coming from three types of polymeric mesh, which serves to pack hay on baling machines. The strength of the strips is evaluated from two points of view. The first one is static tensile strength measured before and after accelerated aging at 23 °C and 40 °C, the second one determines the strength as the weight that causes the strip failure on a simple machine at 23, 40, 60 and 80 ° C. The results show that the smallest static strength has the least stabilized strip, which, on the other hand, revealed the highest strength in a dynamic loading. The change of supermolecular structure was evaluated by calorimetric measurements. The data shown only very little change of inner structure due to the average response of the whole crystalline phase comprising relatively wide distribution of crystallites. It is more than probable that supermolecular structure had been changed but the method is not sensitive to see the change of orientation of lamellae and macromolecular chains in them.

Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter. The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well. A numerical example supports the analysis of our anisotropic error estimator.

A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that the upper error bound depends on the alignment of the anisotropies of the mesh and of the solution. Hence reliable error estimation is possible for suitable anisotropic meshes. The lower error bound depends on the problem data via a local mesh Peclet number. Thus efficient error estimation is achieved for small mesh Peclet numbers. Altogether, error estimation approaches for isotropic meshes are successfully extended to anisotropic elements. Several numerical experiments support the analysis.

Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. An estimator that has shown to be one of the most reliable for reaction-diffusion problem is the <i>equilibrated residual method</i> and its modification done by Ainsworth and Babuška for singularly perturbed problem. However, even the modified method is not robust in the case of anisotropic meshes. The present work modifies the equilibrated residual method for anisotropic meshes. The resulting error estimator is equivalent to the equilibrated residual method in the case of isotropic meshes and is proved to be robust on anisotropic meshes as well. A numerical example confirms the theory.

Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. The simplest local error estimator from the implementation point of view is the so-called hierarchical error estimator. The reliability proof is usually based on two prerequisites: the saturation assumption and the strengthened Cauchy-Schwarz inequality. The proofs of these facts are extended in the present work for the case of the singularly perturbed reaction-diffusion equation and of the meshes with anisotropic elements. It is shown that the constants in the corresponding estimates do neither depend on the aspect ratio of the elements, nor on the perturbation parameters. Utilizing the above arguments the concluding reliability proof is provided as well as the efficiency proof of the estimator, both independent of the aspect ratio and perturbation parameters.

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