Particle transport method for convection-diffusion-reaction problems

Convective transport, both pure and combined with diffusion and reaction, can be observed in a wide range of physical and industrial applications, such as heat and mass transfer, crystal growth or biomechanics. The numerical approximation of this class of problemscan present substantial difficulties clue to regions of high gradients (steep fronts) of the solution, where generation of spurious oscillations or smearing should be precluded. This work is devoted to the development of an efficient numerical technique to deal with pure linear convection and convection-dominated problems in the frame-work of convection-diffusion-reaction systems. The particle transport method, developed in this study, is based on using rneshless numerical particles which carry out the solution along the characteristics defining the convective transport. The resolution of steep fronts of the solution is controlled by a special spacial adaptivity procedure. The serni-Lagrangian particle transport method uses an Eulerian fixed grid to represent the solution. In the case of convection-diffusion-reaction problems, the method is combined with diffusion and reaction solvers within an operator splitting approach. To transfer the solution from the particle set onto the grid, a fast monotone projection technique is designed. Our numerical results confirm that the method has a spacial accuracy of the second order and can be faster than typical grid-based methods of the same order; for pure linear convection problems the method demonstrates optimal linear complexity. The method works on structured and unstructured meshes, demonstrating a high-resolution property in the regions of steep fronts of the solution. Moreover, the particle transport method can be successfully used for the numerical simulation of the real-life problems in, for example, chemical engineering.

Effect of Mechanical and Geometric Mismatching on Fatigue and Damage of Welded Joints

The future of high technology welded constructions will be characterised by higher strength materials and improved weld quality with respect to fatigue resistance. The expected implementation of high quality high strength steel welds will require that more attention be given to the issues of crack initiation and mechanical mismatching. Experiments and finite element analyses were performed within the framework of continuum damage mechanics to investigate the effect of mismatching of welded joints on void nucleation and coalescence during monotonic loading. It was found that the damage of undermatched joints mainly occurred in the sandwich layer and the damageresistance of the joints decreases with the decrease of the sandwich layer width. The damage of over-matched joints mainly occurred in the base metal adjacent to the sandwich layer and the damage resistance of the joints increases with thedecrease of the sandwich layer width. The mechanisms of the initiation of the micro voids/cracks were found to be cracking of the inclusions or the embrittled second phase, and the debonding of the inclusions from the matrix. Experimental fatigue crack growth rate testing showed that the fatigue life of under-matched central crack panel specimens is longer than that of over-matched and even-matched specimens. Further investigation by the elastic-plastic finite element analysis indicated that fatigue crack closure, which originated from the inhomogeneousyielding adjacent to the crack tip, played an important role in the fatigue crack propagation. The applicability of the J integral concept to the mismatched specimens with crack extension under cyclic loading was assessed. The concept of fatigue class used by the International Institute of Welding was introduced in the parametric numerical analysis of several welded joints. The effect of weld geometry and load condition on fatigue strength of ferrite-pearlite steel joints was systematically evaluated based on linear elastic fracture mechanics. Joint types included lap joints, angle joints and butt joints. Various combinations of the tensile and bending loads were considered during the evaluation with the emphasis focused on the existence of both root and toe cracks. For a lap joint with asmall lack-of-penetration, a reasonably large weld leg and smaller flank angle were recommended for engineering practice in order to achieve higher fatigue strength. It was found that the fatigue strength of the angle joint depended strongly on the location and orientation of the preexisting crack-like welding defects, even if the joint was welded with full penetration. It is commonly believed that the double sided butt welds can have significantly higher fatigue strength than that of a single sided welds, but fatigue crack initiation and propagation can originate from the weld root if the welding procedure results in a partial penetration. It is clearly shown that the fatigue strength of the butt joint could be improved remarkably by ensuring full penetration. Nevertheless, increasing the fatigue strength of a butt joint by increasing the size of the weld is an uneconomical alternative.

Immersioultraäänitutkimuksen kehittäminen

Teräksenvalmistajilta edellytetään jatkuvasti panostusta laadun ja laadunvarmistuksen kehittämiseen. Teräksen laatu ja puhtaus korostuvat varsinkin silloin, kun terästä käytetään vaativiin käyttökohteisiin, kuten autoteollisuuden tarpeisiin. Ultraäänitarkastusmenetelmää käytetään laadun-varmistuksessa teräksen sisävikojen etsimiseen. Ultraäänitarkastuksessa lähetetään suuritaajuuksista ääntä kappaleeseen. Ääni etenee materiaalissa ja heijastuu erilaisista epäjatkuvuuskohdista. Luotaimeen palaavaa ääntä analysoimalla saadaan tietoa teräksestä ja sen sisävioista. Ultraäänitarkastuksen ongelmana on vian tyypin määrittäminen hankaluus sekä herkkyys tutkittavan materiaalin aineominaisuuksille. Työn tavoitteena oli immersioultraäänitarkastuksen kehittäminen sovellettuna teräksenvalmistajan tarpeisiin. Materiaalin aineominaisuuksista tutkittiin seostuksen vaikutusta. Teräslajit tarkastettiin valssitilaisena, karkaistuna ja normalisoituna. Lisäksi tutkittiin kappaleen pinnankarheuden ja -muodon vaikutusta tarkastukseen. Vikatyyppien tunnistamisen mahdollisuuksia ultra-äänitarkastuksessa selvitettiin käyttäen FFT- taajuusanalyysiä. Erilailla lämpökäsitellyillä teräslajeilla näytti eniten tuloksiin vaikuttavan terästen raekoko. Valssitilaisilla teräksillä raekoko on suuri, jolloin ultraääni vaimenee voimakkaasti teräksessä. Huomattavaa kuitenkin oli, että mikäli lämpö-käsittelyillä ei teräksen raekokoa saada juuri pienennettyä, ei myöskään vaimeneminen vähene. Tämän vuoksi lämpökäsittely ei välttämättä ole aina tarpeellinen valmisteltaessa ultraääninäytteitä. Fourier’n taajuusanalyysissä huomattiin olevan eroavaisuuksia verrattaessa huokosista ja sulkeumista palaavien kaikujen taajuusspektrejä. Näiden tulosten perusteella näyttäisi olevan mahdollista käyttää FFT- menetelmää ultraääni-tarkastuksessa vikojen luokitteluun.

Opettajan monikulttuurinen työ

Teacher's multicultural work The purpose of the present study is to explore teachers’ conceptions of their work as teachers of multicultural students. Teachers’ experiences of multicultural work and conceptions derived from them are part of the teacher’s multicultural competence which is seen as a key component of the teacher’s multicultural teachership. The teacher’s multicultural competence consists of the teacher’s cultural knowledge, pedagogical skills and experiences and attitudes related to multiculturalism. The teacher’s multicultural competence constitutes the basis on which the teacher implements multicultural education. The foundation for the teacher’s work is laid by laws and decrees, curricula, regulations issued by authorities in charge of the education of immigrant students, resources available and other demands and expectations set by the ambient society. The study was conducted in the city of Turku, Finland. The sample consisted of class teachers who taught both immigrant and majority students. Main objects of study in the theoretical part are the multicultural and pluralistic school and the multicultural teachership. The basic assumption is that the multicultural and pluralistic school forms the frame of activity in which the teacher implements multicultural teaching. The research strategy is based on methodological triangulation. The quantitative part of the study was carried out using a questionnaire typical of survey methods. The questionnaire was returned by 71 teachers. The qualitative part was conducted using theme-based interviews typical of phenomenological philosophical research. Of the total of teachers who returned the questionnaire, twelve (12) teachers were selected for interviews. According to the results, the participating teachers enjoyed their work regardless of the ample extra work caused by the students with immigrant backgrounds. The teachers experienced their work as teachers of multicultural student groups as strenuous, yet challenging. Students with immigrant backgrounds had caused many changes in the teacher’s work. The teachers regarded their multicultural skills as inadequate in relation to the demands of the work. They had not received education related to teaching students with immigrant backgrounds, but they were ready for in-service education. The teachers’ previous attitudes concerning immigrant students had been enforced. Teaching experiences strengthened the earlier, both positive and negative, attitudes. The central problems related to multiculturalism in the teacher’s work were caused by the deficient Finnish skills of the students with immigrant background. This was apparent in both teaching and learning as well as in contacts with parents. The teachers reported on relatively few inclusions of multicultural angles in their teaching. However, they believed that they could aid students with different cultural backgrounds in their integration process. At the same time they felt that their own chances to enhance the students’ cultural identities were slim. On the basis of the interviews conducted in connection with the teacher’s multicultural competence, the teachers were divided into three groups: assimilative, indeterminate and integrating multicultural teachers. The present study provides a strong indication that teachers tend to interpret multiculturalism in narrow terms. School activities, such as Finnish as a second language, first language and religious instruction, which were targeted exclusively at immigrant students were in most cases considered adequate. A holistic, cross-disciplinary, all-inclusive multicultural education that would permeate all school activities remains largely unimplemented.

Leimuhitsauksen kokonaisvaltainen laadunhallinta päättymättömässä valssauksessa

Leimuhitsauksen laadunhallinnassa tärkeää on prosessimainen toiminta ja toimintojen kokonaisvaltaisuuden hahmottaminen. Leimuhitsauksen ollessa osana päättymätöntä valssausta hitsauksen laadunhallinta voidaan jakaa kolmeen päävaiheeseen: ennen hitsausta, hitsauksen aikana ja hitsauksen jälkeen vaikuttaviin laaduntuottotekijöihin. Leimuhitsauksen laaduntuottotekijöiden määritys ja jaottelu kaavioiksi on toteutettu tässä työssä. Leimuhitsin tekniseen laatuun vaikuttavat monet ilmiöt ja parametrit hitsauksen aikana. Tärkeimpiä hitsausparametreista ovat hitsausjännite, alustan liikenopeus, tyssäysmatka sekä leimutusaika. Väärät hitsausolosuhteet tai hitsausparametrit aiheuttavat erilaisia mekaanisia ja metallurgisia vikoja leimuhitsiin. Eräs metallurginen vikatyyppi ovat oksidisulkeumat hitsialueella. Nämä hapettuneet alueet voivat johtaa juurensa erilaisista syistä ja esimerkiksi leimutusajan ja epätasaisen liitospinnan yhteyttä sulkeumien syntyyn on epäilty. Pidennetyillä leimutusajoilla tehtyjen hitsauskokeiden ja hitsien rikkovien aineenkoetuskokeiden tuloksena todettiin tässä tutkittujen koehitsien oksidisulkeumien syntyvän hapettumalla leimutuksen aikana tai juuri hetkellä ennen tyssäystä, minkä lisäksi kosteat olosuhteet hitsausatmosfäärin ympärillä heikentävät lopputuloksen laatua. Leimutusajalla on tärkein osa leimutettavia pintoja tasaavana tekijänä ja mitä epätasaisempi liitettävä pinta on, sitä pidemmän leimutusajan se tarvitsee.

Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Artificial reflecting structures based on metamaterials

This thesis studies metamaterial-inspired mirrors which provide the most general control over the amplitude and phase of the reflected wavefront. The goal is to explore practical possibilities in designing fully reflective electromagnetic structures with full control over reflection phase. The first part of the thesis describes a planar focusing metamirror with the focal distance less than the operating wavelength. Its practical applicability from the viewpoint of aberrations when the incident angle deviates from the normal one is verified numerically and experimentally. The results indicate that the proposed focusing metamirror can be efficiently employed in many different applications due to its advantages over other conventional mirrors. In the second part of the thesis a new theoretical concept of reflecting metasurface operation is introduced based on Huygens’ principle. This concept in contrast to known approaches takes into account all the requirements of perfect metamirror operation. The theory shows a route to improve the previously proposed metamirrors through tilting the individual inclusions of the structure at a chosen angle from normal. It is numerically tested and the results demonstrate improvements over the previous design.