Computational Analysis and Optimization of Real Gas Flow In Small Centrifugal Compressors

Small centrifugal compressors are more and more widely used in many industrialsystems because of their higher efficiency and better off-design performance comparing to piston and scroll compressors as while as higher work coefficient perstage than in axial compressors. Higher efficiency is always the aim of the designer of compressors. In the present work, the influence of four partsof a small centrifugal compressor that compresses heavy molecular weight real gas has been investigated in order to achieve higher efficiency. Two parts concern the impeller: tip clearance and the circumferential position of the splitter blade. The other two parts concern the diffuser: the pinch shape and vane shape. Computational fluid dynamics is applied in this study. The Reynolds averaged Navier-Stokes flow solver Finflo is used. The quasi-steady approach is utilized. Chien's k-e turbulence model is used to model the turbulence. A new practical real gas model is presented in this study. The real gas model is easily generated, accuracy controllable and fairly fast. The numerical results and measurements show good agreement. The influence of tip clearance on the performance of a small compressor is obvious. The pressure ratio and efficiency are decreased as the size of tip clearance is increased, while the total enthalpy rise keeps almost constant. The decrement of the pressure ratio and efficiency is larger at higher mass flow rates and smaller at lower mass flow rates. The flow angles at the inlet and outlet of the impeller are increased as the size of tip clearance is increased. The results of the detailed flow field show that leakingflow is the main reason for the performance drop. The secondary flow region becomes larger as the size of tip clearance is increased and the area of the main flow is compressed. The flow uniformity is then decreased. A detailed study shows that the leaking flow rate is higher near the exit of the impeller than that near the inlet of the impeller. Based on this phenomenon, a new partiallyshrouded impeller is used. The impeller is shrouded near the exit of the impeller. The results show that the flow field near the exit of the impeller is greatly changed by the partially shrouded impeller, and better performance is achievedthan with the unshrouded impeller. The loading distribution on the impeller blade and the flow fields in the impeller is changed by moving the splitter of the impeller in circumferential direction. Moving the splitter slightly to the suction side of the long blade can improve the performance of the compressor. The total enthalpy rise is reduced if only the leading edge of the splitter ismoved to the suction side of the long blade. The performance of the compressor is decreased if the blade is bended from the radius direction at the leading edge of the splitter. The total pressure rise and the enthalpy rise of thecompressor are increased if pinch is used at the diffuser inlet. Among the fivedifferent pinch shape configurations, at design and lower mass flow rates the efficiency of a straight line pinch is the highest, while at higher mass flow rate, the efficiency of a concave pinch is the highest. The sharp corner of the pinch is the main reason for the decrease of efficiency and should be avoided. The variation of the flow angles entering the diffuser in spanwise direction is decreased if pinch is applied. A three-dimensional low solidity twisted vaned diffuser is designed to match the flow angles entering the diffuser. The numerical results show that the pressure recovery in the twisted diffuser is higher than in a conventional low solidity vaned diffuser, which also leads to higher efficiency of the twisted diffuser. Investigation of the detailed flow fields shows that the separation at lower mass flow rate in the twisted diffuser is later than in the conventional low solidity vaned diffuser, which leads to a possible wider flow range of the twisted diffuser.

Torque vibration model of axial-flux surface-mounted permanent magnet synchronous machine

In order that the radius and thus ununiform structure of the teeth and otherelectrical and magnetic parts of the machine may be taken into consideration the calculation of an axial flux permanent magnet machine is, conventionally, doneby means of 3D FEM-methods. This calculation procedure, however, requires a lotof time and computer recourses. This study proves that also analytical methods can be applied to perform the calculation successfully. The procedure of the analytical calculation can be summarized into following steps: first the magnet is divided into slices, which makes the calculation for each section individually, and then the parts are submitted to calculation of the final results. It is obvious that using this method can save a lot of designing and calculating time. Thecalculation program is designed to model the magnetic and electrical circuits of surface mounted axial flux permanent magnet synchronous machines in such a way, that it takes into account possible magnetic saturation of the iron parts. Theresult of the calculation is the torque of the motor including the vibrations. The motor geometry and the materials and either the torque or pole angle are defined and the motor can be fed with an arbitrary shape and amplitude of three-phase currents. There are no limits for the size and number of the pole pairs nor for many other factors. The calculation steps and the number of different sections of the magnet are selectable, but the calculation time is strongly depending on this. The results are compared to the measurements of real prototypes. The permanent magnet creates part of the flux in the magnetic circuit. The form and amplitude of the flux density in the air-gap depends on the geometry and material of the magnetic circuit, on the length of the air-gap and remanence flux density of the magnet. Slotting is taken into account by using the Carter factor in the slot opening area. The calculation is simple and fast if the shape of the magnetis a square and has no skew in relation to the stator slots. With a more complicated magnet shape the calculation has to be done in several sections. It is clear that according to the increasing number of sections also the result will become more accurate. In a radial flux motor all sections of the magnets create force with a same radius. In the case of an axial flux motor, each radial section creates force with a different radius and the torque is the sum of these. The magnetic circuit of the motor, consisting of the stator iron, rotor iron, air-gap, magnet and the slot, is modelled with a reluctance net, which considers the saturation of the iron. This means, that several iterations, in which the permeability is updated, has to be done in order to get final results. The motor torque is calculated using the instantaneous linkage flux and stator currents. Flux linkage is called the part of the flux that is created by the permanent magnets and the stator currents passing through the coils in stator teeth. The angle between this flux and the phase currents define the torque created by the magnetic circuit. Due to the winding structure of the stator and in order to limit the leakage flux the slot openings of the stator are normally not made of ferromagnetic material even though, in some cases, semimagnetic slot wedges are used. In the slot opening faces the flux enters the iron almost normally (tangentially with respect to the rotor flux) creating tangential forces in the rotor. This phenomenon iscalled cogging. The flux in the slot opening area on the different sides of theopening and in the different slot openings is not equal and so these forces do not compensate each other. In the calculation it is assumed that the flux entering the left side of the opening is the component left from the geometrical centre of the slot. This torque component together with the torque component calculated using the Lorenz force make the total torque of the motor. It is easy to assume that when all the magnet edges, where the derivative component of the magnet flux density is at its highest, enter the slot openings at the same time, this will have as a result a considerable cogging torque. To reduce the cogging torquethe magnet edges can be shaped so that they are not parallel to the stator slots, which is the common way to solve the problem. In doing so, the edge may be spread along the whole slot pitch and thus also the high derivative component willbe spread to occur equally along the rotation. Besides forming the magnets theymay also be placed somewhat asymmetric on the rotor surface. The asymmetric distribution can be made in many different ways. All the magnets may have a different deflection of the symmetrical centre point or they can be for example shiftedin pairs. There are some factors that limit the deflection. The first is that the magnets cannot overlap. The magnet shape and the relative width compared to the pole define the deflection in this case. The other factor is that a shifting of the poles limits the maximum torque of the motor. If the edges of adjacent magnets are very close to each other the leakage flux from one pole to the other increases reducing thus the air-gap magnetization. The asymmetric model needs some assumptions and simplifications in order to limit the size of the model and calculation time. The reluctance net is made for symmetric distribution. If the magnets are distributed asymmetrically the flux in the different pole pairs will not be exactly the same. Therefore, the assumption that the flux flows from the edges of the model to the next pole pairs, in the calculation model from one edgeto the other, is not correct. If it were wished for that this fact should be considered in multi-pole pair machines, this would mean that all the poles, in other words the whole machine, should be modelled in reluctance net. The error resulting from this wrong assumption is, nevertheless, irrelevant.

Lämmönsiirron numeerinen laskenta profiloidulle kanavalle.

Työn tavoitteena oli tutkia aaltomaisen profiloinnin vaikutusta suorien jäähdytyskanavien lämmönsiirtoon ja painehäviöön. Erilaisia profiileja oli kymmenen kappaletta ja ne olivat 5mm leveitä ja 30cm pitkiä kukin. Ne laskettiin kolmeulotteisina tapauksina FINFLO-virtausratkaisijalla kolmella eri Reynoldsin luvulla, jotka vastasivat laminaarista, osittain turbulenttista ja lähes kokonaan turbulenttista virtausta. Lämmönsiirtoaine oli kuiva +30°C ilma ja profiloinnin toteutustapa oli toisiaan sivuavat ympyräkaaret kolmella erilaisella säteen arvolla ja kolmella erilaisella aallonpituuden arvolla. Lisäksi laskettiin saman levyisen tasokanavan arvot jokaisella Reynoldsin luvulla kaksiulotteisina tapauksina. Näitä profiloimattomia kanavia pidettiin referenssitapauksina. Tuloksena havaittiin että profiloimalla saadaan yksiselitteisesti suurempi lämpöteho ulos samasta tilavuudesta. Lämmönsiirtokerroin kasvaa profiloinnin avulla parhaimmillaan n. 20% käytetystä turbulenssimallista tai lämmönsiirtokertoimen määritelmästä riippumatta. Painehäviö kasvaa myös aina, mutta kitkakerroin voi hieman pienentyä. Profiilin varsinaisena hyvyyskriteerinä pidettiin lämmönsiirtokertoimen ja kitkakertoimen suhdetta h/f. Se osoittautui riippuvaksi Reynoldsin luvusta ja turbulenssimallista; ASM ja Chien k-έ -mallit ennustavat transitioetäisyyden eri tavalla. Laminaarisilla virtauksilla h/f :n vaihtelu oli vähäistä; suhde vaihteli vain ±5% eri profiilien kesken. ASM-mallilla havaittiin sekundääripyörteilyä, ehkä siksi että se mallintaa anisotrooppisen turbulenssin. Chien k-έ malli ennusti suuremman ja aikaisemmin alkavan turbulenttisuuden kuin ASM. Lisäksi havaittiin mm. että tietyillä profiileilla muodostuu kanavan kapeimpaan kohtaan selvä virtausnopeuden paikallinen minimi seinämän läheisyyden takia.

Relation between plaque type, plaque thickness, blood shear stress, and plaque stress in coronary arteries assessed by X-ray Angiography and Intravascular Ultrasound

Purpose: Atheromatic plaque progression is affected, among others phenomena, by biomechanical, biochemical, and physiological factors. In this paper, the authors introduce a novel framework able to provide both morphological (vessel radius, plaque thickness, and type) and biomechanical (wall shear stress and Von Mises stress) indices of coronary arteries. Methods: First, the approach reconstructs the three-dimensional morphology of the vessel from intravascular ultrasound(IVUS) and Angiographic sequences, requiring minimal user interaction. Then, a computational pipeline allows to automatically assess fluid-dynamic and mechanical indices. Ten coronary arteries are analyzed illustrating the capabilities of the tool and confirming previous technical and clinical observations. Results: The relations between the arterial indices obtained by IVUS measurement and simulations have been quantitatively analyzed along the whole surface of the artery, extending the analysis of the coronary arteries shown in previous state of the art studies. Additionally, for the first time in the literature, the framework allows the computation of the membrane stresses using a simplified mechanical model of the arterial wall. Conclusions: Circumferentially (within a given frame), statistical analysis shows an inverse relation between the wall shear stress and the plaque thickness. At the global level (comparing a frame within the entire vessel), it is observed that heavy plaque accumulations are in general calcified and are located in the areas of the vessel having high wall shear stress. Finally, in their experiments the inverse proportionality between fluid and structural stresses is observed.

Analytical Study on the Influence of Geometrical Parameters on the Fatigue Strength of Welds with Undercuts

The purpose of this study is to analyze the influence of geometric parameters on the fatigue strength of the welded joint. The thesis includes the analytical study pertaining to variation of undercut and the weld toe radius. The theoretical part includes the concepts of fracture mechanics, different stages of the crack propagation and finally the results. The numerical results are obtained from FRANC2D/L. The results show that the fatigue strength of the welded structure depends on the parameters of the welds such as the weld toe radius, weld angle, height of the undercut and plate thickness. The results show that the fatigue life can be improved by having the undercut as minimum as possible. However there has been significant variation on the fatigue life of the structure when the weld toe radius is increased.

Internet-palveluntarjoajan luotettava autentikointijärjestelmä

Internet-palveluntarjoaja haluaa tarjota palveluitaan vain omille asiakkailleen. Niinpä Internetin käyttäjien autentikointi on tärkeä osa Internet-palveluntarjoajan kokonaisjärjestelmässä. Jopa asiakkaiden laskutus saattaa perustua luotettavaan autentikointiin. Internet-palveluntarjoajan autentikointijärjestelmä perustuu usein AAA-malliin, joka pitää sisällään käyttäjien autentikoinnin, auktorisoinnin ja käyttötilastojen keräämisen. Tässä työssä esitellään AAA-mallia ja autentikointijärjestelmään läheisesti liittyviä muita teknologioita. Työn käytännön osassa tutustutaan Internet-palveluntarjoajan AAA-ohjelmiston uusimiseen. Tuloksena oli tulevaisuuden tarpeisiin paremmin sopiva AAAjärjestelmä. Samalla esitellään myös joitakin ideoita järjestelmän kehittämiseksi edelleen.

Effects of adult dysthyroidism on the morphology of hippocampal neurons.

This study investigates the effect of thyroid hormones on the morphology of hippocampal neurons in adult rats. Hypo- and hyperthyroidism were induced by adding 0.02% methimazole and 1% l-thyroxine, in drinking water from 40 days of age, respectively. When the rats were 89 days old their brains were removed and stained by a modified Golgi method and blood samples were collected in order to measure T4 serum levels. Neurons were selected and drawn using a camera lucida. Our results show that methimazole administration reduces the dendritic branching of the apical shafts of CA3 and CA1 pyramidal neurons mainly by increasing the distance to the first branch point in both types of neurons, and reducing branch points in the radius of 50 μm from the soma in CA1 neurons. Nevertheless, it was observed an increase of apical spine density in CA3 neurons from this group. Thyroxine reduces apical and basal tree of CA3 pyramidal neurons increasing the distance to the first branch point, reducing branch points in the radius of 50 μm from the soma and increases their apical and basal spine density. In CA1 field, thyroxine reduces the number of basal branch points. Both treatments seems to provoke alterations in the same direction reducing the dendritic branching and increasing spine density, although no significances appeared in some of the parameters analyzed. The effects are more evident in thyroxine than methimazole group; and in CA3 neurons than in CA1 neurons. In discussion it is pointed that the increase of spine density could be a mechanism to compensate the functionality reduction that can be provoke by the treatment effect on dendritic branching.

Kromaattisuuserojen laskentamalli

Työssä esitellään Lappeenrannan teknillisen yliopiston Tietotekniikan osastolla kehitettyä kromaattisuuserojen laskentamallia. Työn keskeisimpinä tavoitteina on luoda tiivis katsaus jo olemassa oleviin värierojen laskentamenetelmien tekniikoihin ja käydä läpi värien havaitsemiseen liittyviä yksityiskohtia. Työn käytännön osuudessa tutkitaan kehitettyä mallia ja esitetään ideoita kehittäen mallia täsmällisemmäksi. Kromaattisuuserojen laskentamalli perustuu MacAdamin määrittelemien ellipsien hyödyntämiseen CIE-1931 kromaattisuusdiagrammissa. Ideana on projisoida ellipsit iso- ja pikkuakseleidensa suhteen vakiosäteisiksi ympyröiksi kolmiulotteiselle pinnalle. Kromaattisuuserot lasketaan pinnalta käyttämällä numeerista menetelmää. Tuloksena todetaan mallin täyttävän osittain sille asetetut vaatimukset ja parantavan CIE-1931 kromaattisuusdiagrammin yhtenäisyyttä erityisesti diagrammin vihreän ja sinisen värin alueilla.

Metsäpalveluyritysten menestyminen ja siihen vaikuttavat tekijät

Tutkimuksessa kartoitettiin metsäpalveluyritysten toimintaympäristöä sekä menestymistä ja siihen vaikuttavia tekijöitä. Tutkimusta varten haastateltiin 27 metsäpalveluyrittäjää kesäkuussa 1999. Heikommin menestyneiden ja Menestyneimpien metsäpalveluyritysten löytämiseksi luotiin kaksi menestyspistejärjestelmää: KASKARA (KASvu, KAnnattavuus & RAhoitus) -mittaristo ja Tasapainotettu (Balanced Scorecard) mittaristo. KASKARA-mittaristossa tarkastelun kohteena olivat yrityksen kasvu (yrityksen liikevaihdon kasvuprosentti ja investoinnit) ja kannattavuus sekä rahoituksellinen tila (maksuvalmius ja vakavaraisuus) yrittäjän itsensä arvioimana. Toisaalta käytettäessä Tasapainotettua mittaristoa KASKARA-mittaristoon liitettiin vielä neljä muuttujaa: yrityksen tärkeimmän asiakkaan antama palaute yrittäjälle, yrittäjän hankkima täydennyskoulutus, kovien kilpailijoiden lukumäärä yrityksen nykyisellä toiminta-alueella ja yrittäjän oma arvio yrityksensä paremmuudesta kilpailijoihin nähden. Tutkimuksen Menestyneimpiä yrityksiä voitiin kuvata seuraavasti: yrittäjä kertoi olleensa luottavainen yritystä perustaessaan; yhtenä tärkeimmistä motiiveista yrityksensä perustamiseen yrittäjä piti pyrkimystä ansiotulojen kasvattamiseen; hieman alle puolet yrityksistä oli hakkuuseen painottuneita yrityksiä - muut päätoimialat olivat puukauppa, metsätalouden suunnittelupalvelut sekä mittauspalvelut; yrittäjän lisäksi yritykseen on palkattu keskimäärin kaksi vakinaista työntekijää; yrityksen kirjanpidosta huolehtii joku muu (useimmiten tilitoimisto) kuin yrittäjä; yrityksen kaluston määrä on kasvanut yrityksen perustamisvuodesta, mutta yrityksen asiakaskunta on pysynyt lähes samana; yrityksen tärkeimmän asiakkaan osuus yrityksen liikevaihdosta on 90%; tulevaisuudessa yrittäjä haluaa ylläpitää nykyisiä asiakassuhteita; ja kartoitettaessa yrittäjän halukkuutta ryhtyä uudelleen yrittäjäksi saamien kokemustensa pohjalta valtaosin yrittäjät sanoivat varmasti ryhtyvänsä uudelleen metsäpalveluyrittäjäksi. Vastaavasti Heikommin menestyneitä yrityksiä ja niiden toimintaa voitiin luonnehtia seuraavien tekijöiden avulla: yrittäjä oli ollut iältään yli 40-vuotias, kun hän oli perustanut metsäpalveluyrityksensä; yrittäjä oli toiminut maanviljelijänä ennen metsäpalveluyrittäjäuraansa; lähes puolet yrittäjistä olivat olleet melko epävarmoja yritystä käynnistäessään; yrityksen päätoimiala on useimmiten hakkuu; yrityksessä ei ole yrittäjän lisäksi palkattua, vakinaista henkilöstöä; yrityksen toiminta-alueen säde on alle 40 kilometriä; valtaosin yrittäjät hoitavat itse yrityksensä kirjanpidon; yrityksen kaluston määrä ei ole kasvanut yrityksen perustamisvuodesta; yrityksellä on nykyisin alle viisi asiakasta; tärkeimmän asiakkaan osuus yrityksen liikevaihdosta on noin 60%; tulevaisuudessa yrittäjä suunnittelee hankkivansa uusia asiakkaita nykyisten asiakassuhteiden ylläpidon lisäksi; ja jos yrittäjä saisi tehdä uudelleen yrityksensä perustamispäätöksen, runsas kaksi kolmasosaa yrittäjistä kertoi harkitsevansa tarkkaan perustamispäätöstä, mutta perustavansa uudelleen metsäpalveluyrityksen.

Analysis of bulk and surface contributions in the neutron skin of nuclei

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy and has multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult to obtain. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.

Patterns of primary growth increments in otoliths of Sparus aurata larvae in relation to water temperature and food consumption

Sparus aurata larvae reared under controlled water-temperature conditions during the first 24 days after hatching displayed a linear relationship between age (t) and standard length (SL): SL = 2.68 + 0.19 t (r2 = 0.91l). Increments were laid down in the sagittae with daily periodicity starting on day of hatching. Standard length (SL) and sagittae radius (OR) were correlated: SL(mm) = 2.65 + 0.012 OR(mm). The series of measurements of daily growth increment widths (DWI), food density and water temperature were analyzed by means of time series analysis. The DWI series were strongly autocorrelated, the growth on any one day was dependent upon growth on the previous day. Time series of water temperatures showed, as expected, a random pattern of variation, while food consumed daily was a function of food consumed the two previous days. The DWI series and the food density were correlated positively at lags 1 and 2. The results provided evidence of the importance of food intake upon the sagittae growth when temperature is optimal (20ºC). Sagittae growth was correlated with growth on the previous day, so this should be taken into account when fish growth is derived from sagittae growth rates.

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

Bone structure assessed by HR-pQCT, TBS and DXL in adult patients with different types of osteogenesis imperfecta.

UNLABELLED: Bone microarchitecture by high-resolution peripheral quantitative computed tomography (HR-pQCT) was assessed in adult patients with mild, moderate, and severe osteogenesis imperfecta (OI). The trabecular bone score (TBS), bone mineral density (BMD) by dual-energy X-ray absorptiometry (DXA), and dual X-ray and laser (DXL) at the calcaneus were likewise assessed in patients with OI. Trabecular microstructure and BMD in particular were severely altered in patients with OI. INTRODUCTION: OI is characterized by high fracture risk but not necessarily by low BMD. The main purpose of this study was to assess bone microarchitecture and BMD at different skeletal sites in different types of OI. METHODS: HR-pQCT was performed in 30 patients with OI (mild OI-I, n = 18 (41.8 [34.7, 55.7] years) and moderate to severe OI-III-IV, n = 12 (47.6 [35.3, 58.4] years)) and 30 healthy age-matched controls. TBS, BMD by DXA at the lumbar spine and hip, as well as BMD by DXL at the calcaneus were likewise assessed in patients with OI only. RESULTS: At the radius, significantly lower trabecular parameters including BV/TV (p = 0.01 and p < 0.0001, respectively) and trabecular number (p < 0.0001 and p < 0.0001, respectively) as well as an increased inhomogeneity of the trabecular network (p < 0.0001 and p < 0.0001, respectively) were observed in OI-I and OI-III-IV in comparison to the control group. Similar results for trabecular parameters were found at the tibia. Microstructural parameters were worse in OI-III-IV than in OI-I. No significant differences were found in cortical thickness and cortical porosity between the three subgroups at the radius. The cortical thickness of the tibia was thinner in OI-I (p < 0.001), but not OI-III-IV, when compared to controls. CONCLUSIONS: Trabecular BMD and trabecular bone microstructure in particular are severely altered in patients with clinical OI-I and OI-III-IV. Low TBS and DXL and their significant associations to HR-pQCT parameters of trabecular bone support this conclusion.

Assessment of meshing techniques for fatigue analysis of load carrying welded joints using the effective notch approach

The effective notch stress approach for the fatigue strength assessment of welded structures as included in the Fatigue Design Recommendation of the IIW requires the numerical analysis of the elastic notch stress in the weld toe and weld root which is fictitiously rounded with a radius of 1mm. The goal of this thesis work was to consider alternate meshing strategies when using the effective notch stress approach to assess the fatigue strength of load carrying partial penetration fillet-welded cruciform joints. In order to establish guidelines for modeling the joint and evaluating the results, various two-dimensional (2D) finite element analyses were carried out by systematically varying the thickness of the plates, the weld throat thickness, the degree of bending, and the shape and location of the modeled effective notch. To extend the scope of this work, studies were also carried out on the influence of

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.