Minimal three-component SU(2) gadget for polarization optics

Two identities involving quarter-wave plates and half-wave plates are established. These are used to improve on an earlier gadget involving four wave plates leading to a new gadget involving just three plates, a half-wave plate and two quarter-wave plates, which can realize all SU(2) polarization transformations. This gadget is shown to involve the minimum number of quarter-wave and half-wave plates. The analysis leads to a decomposition theorem for SU (2) matrices in terms of factors which are symmetric fourth and eighth roots of the identity.

Influence of strain softening on the fracture of plain concrete beams

Fracture behaviour of notched and un-notched plain concrete slender beams subjected to three-point or four-point bending is analyzed through a one-dimensional model, also called Softening Beam Model. Fundamental equations of equilibrium are used to develop the model. The influence of structural size in altering the fracture mode from brittle fracture to plastic collapse is explained through the stress distribution across the uncracked ligament obtained by varying the strain softening modulus. It is found that at the onset of fracture instability, stress at the crack tip is equal to zero. The maximum load and fracture load are found to be different and a unique value for the fracture load is obtained. It is shown that the length of the fracture process zone depends on the value of the strain softening modulus. Theoretical limits for fracture process zone length are also calculated. Several nonlinear fracture parameters, such as, crack tip opening displacement, crack mouth opening displacement and fracture energy are computed for a wide variety of beam specimens reported in the literature and are found to compare very well with experimental and theoretical results. It is demonstrated that by following a simple procedure, both pre-peak and post-peak portions of load versus crack mouth opening displacement curve can be obtained quite accurately. Further, a simple procedure to calculate the maximum load is also developed. The predicted values of maximum load are found to agree well with the experimental values. The Softening Beam Model (SBM), proposed in this investigation is very simple and is based on rational considerations. It can completely describe the fracture process from the beginning of formation of the fracture process zone till the onset of fracture instability.A l'aide d'un modèle unidimensionnel dit ldquoSoftening Beam Modelrdquo (SBM), on analyse le comportement à rupture de poutres élancées pleines entaillées ou non, soumises en flexion en trois ou quatre points. Des équations fondamentales d'équilibre sont utilisées pour développer le modèle. On explique l'influence de la taille du composant sur l'altération du mode de rupture en rupture fragile et en effondrement plastique par la distribution par la distribution des contraintes sur le ligament non fissuré lorsque varie le module d'adoucissement. On trouve que la contrainte à l'extrémité de la fissure est nulle est nulle au début de l'instabilité de la rupture. La charge maximum et la charge à la rupture sont trouvées différentes, et on obtient une valeur unique de la charge à la rupture. On montre que la longueur de la zone concernée par le processus de rupture d'pend de la valeur du module d'adoucissement. On calcule également les limites théoriques de longueur de cette zone. Divers paramètres de rupture non linéaire sont calculés pour une large gamme d'éprouvettes en poutres reprises dans la littérature; on trouve qu'il existe une bonne concordance avec les résultats expérimentaux et théoriques. On démontre qu'en suivant une procédure simple on peut obtenir avec une bonne précision la courbe reliant les portions avant et après le pic de sollicitation en fonction du COD de la fissure. En outre, on développe une procédure simple pour calculer la charge maximum. Les valeurs prédites sont en bon accord avec les valeurs expérimentales. Le modèle SBM proposé est très simple et est basé sur des considérations rationnelles. Il est susceptible de décrire complètement le processus de rupture depuis le début de la formation de la zone intéressée jusqu'à l'amorçage de la rupture instable.

A photoelastic approach to framed structure-foundation beam-soil interaction

The interaction of a framed structure with a foundation beam resting on an elastic medium, representing the soil, has been studied using the photoelastic method. The contact pressure distribution, the fibre stress in the foundation beam and frame structure, as well as the stresses in the elastic medium, have been obtained. These have been compared with theoretical results obtained by idealizing the soil as (a) elastic half plane, and (b) elastic half space. It is shown that the photoelastic method can provide an easy solution to this type of problem if the soil can be idealized as an elastic continuum.

Broadband stacked three-layer circular microstrip antenna arrays

The broadband aspects of stacked three-layer electromagnetically coupled circular microstrip antenna arrays are investigated experimentally. Experiments carried out on 8-element linear microstrip antenna arrays, using optimized stacked three-layer circular microstrip antenna elements, configured in E- and H-planes, have exhibited an impedance bandwidth of 20 percent, with a high gain and a good pattern shape with sidelobe as well as crosspolarization levels better than -20 dB through a scan angle of 40 deg from the broadside.

Three Dimensional Line-Clipping by Systematic Enumeration

Three dimensional clipping is a critical component of the 3D graphics pipeline. A new 3D clipping algorithm is presented in this paper. An efficient 2D clipping routine reported earlier has been used as a submodule. This algorithm uses a new classification scheme for lines of all possible orientations with respect to a rectangular parallelopiped view volume. The performance of this algorithm has been evaluated using exact arithmetic operation counts. It is shown that our algorithm requires less arithmetic operations than the Cyrus-Beck 3D clipping algorithm in all cases. It is also shown that for lines that intersect the clipping volume, our algorithm performs better than the Liang-Barsky 3D clipping algorithm.

Analysis of the evanescent field coupling between a fiber and a planar waveguide using the explicit finite difference method with a nonuniform mesh (Journal Paper)

We investigate an optical waveguide system consisting of an unclad fiber core suspended at a constant distance parallel to the surface of a planar waveguide. The coupling and propagation of light in the combined system is studied using the three-dimensional explicit finite difference beam propagation method with a nonuniform mesh configuration. The power loss in the fiber and the field distribution in the waveguide are studied as a function of various parameters, such as index changes, index profile, and propagation distance, for the combined system.

Promoting the European Union : Attitudinal stance adjectives in three genres of EU communication to the public

Målet för Pro Gradu-avhandlingen är att undersöka hur Europeiska unionen (EU) marknadsförs genom användningen av värderande adjektiv i tre genrer av skriftlig kommunikation från EU till medlemsstaternas medborgare. Undersökningen är inriktad på tre forskningsfrågor: hur marknadsföringen av EU syns i användningen av värderande adjektiv i de tre genrerna, vilka de centrala skillnaderna mellan de tre genrerna är gällande användningen av värderande adjektiv, samt på vilket sätt texterna uppfyller sitt kommunikativa syfte, nämligen att informera allmänheten om EU:s verksamhet och marknadsföra EU som en giltig och handlingskraftig union. Den teoretiska ramen för undersökningen grundar sig på genreanalys, kommunikationsteori och teorier om hur författarens värdering (stance) syns i texter. Skillnaden mellan genre, texttyp och register diskuteras, och teoridelen redogör även för begreppet diskurssamfund, dvs. den grupp personer som i ett yrkesmässigt eller institutionellt sammanhang producerar och använder sig av en genre enligt dess kommunikativa konventioner. Materialet behandlas även utgående från Egon Werlichs indelning av texttyper i deskriptiva, narrativa, expositära, argumentativa och instruktiva texter. Materialet består av tre delar som representerar var sin genre: informationsbroschyrer, pressmeddelanden och den Allmänna rapporten om Europeiska unionens verksamhet, som utges av EU varje år. Storleken på varje del av materialet varierar mellan 20 000 - 30 000 ord. Materialet har valts på basis av de teman texterna behandlar, och kriterierna för urvalet är bl.a. att texterna behandlar ämnen som har anknytning till medborgarnas vardag, att de är riktade till allmänheten, och att de finns tillgängliga på Internet. Undersökningen är genomförd som en kvalitativ genreanalys. Materialet analyseras först utgående från kontexten och det samhälleliga sammanhanget enligt Vijay K. Bhatias metodik för analys av obekanta genrer. Det kommunikativa syftet, författaren och den tilltänkta läsarkretsen, dvs. målgruppen för kommunikationen, fastställs. Värderande adjektiv som uttrycker författarens hållning har plockats ur texten manuellt och med hjälp av konkordansprogrammet AntConc, och placerats i 16 kategorier enligt de värden de uttrycker. Varje genre analyseras sedan språkligt med utgångspunkt i adjektivlistorna, varefter resultaten jämförs med varandra. Undersökningen visar att pressmeddelandena innehåller det största antalet värderande adjektiv, medan informationsbroschyrerna innehåller det minsta antalet värderande adjektiv. Den Allmänna rapporten om Europeiska unionens verksamhet innehåller delar med tätt förekommande värderande adjektiv, i synnerhet i stycken som behandlar mer kontroversiella ämnen. I alla tre genrer sammanfaller ett högt antal värderande adjektiv med argumentativ text, och argumentativ text förekommer främst då ämnet som diskuteras rör sig på en mer abstrakt nivå, t.ex. om EU:s värderingar och grundläggande principer, eller då texten behandlar sådan politik som delar allmänhetens uppfattning. För EU utgör alla tre genrer viktiga kanaler för kommunikationen till medlemsstaternas medborgare, och EU kan genom sitt informationsmaterial och sina officiella publikationer informera om, förklara och marknadsföra sin verksamhet på ett sätt som avser att upprätthålla och förbättra EU:s image. Utarbetandet av lämpliga texter är ändå krävande på grund av den heterogena målgruppen, och det är en utmaning i sig att få fram rätt budskap bland det stora utbudet information som finns tillgängligt på Internet.

Covalent attachment of two important dicopper(II) systems in a one-dimensional polymeric chain: An x-ray structure of [Cu2(en)2(OH)2·Cu2(O2CMe)4](PF6)2·0.5EtOH]α showing the shortest Cucdots, three dots, centeredCu Distance in the tetraacetato core

Reaction of Cu2(O2CMe)4(H2O)2 with 1,2-diaminoethane(en) in ethanol, followed by the addition of NH4PF6, led to the formation of a covalently linked 1D polymeric copper(II) title complex showing alternating [Cu2(en)2(OH)22+] and [Cu2(O2CMe)4] units in the chain and the shortest Cucdots, three dots, centeredCu separation of 2.558(2) Å in the tetraacetato core.

Dynamic response of a beam on elastic foundation of finite depth under a moving force

In this paper, dynamic response of an infinitely long beam resting on a foundation of finite depth, under a moving force is studied. The effect of foundation inertia is included in the analysis by modelling the foundation as a series of closely spaced axially vibrating rods of finite depth, fixed at the bottom and connected to the beam at the top. Viscous damping in the beam and foundation is included in the analysis. Steady state response of the beam-foundation system is obtained. Detailed numerical results are presented to study the effect of various parameters such as foundation mass, velocity of the moving load, damping and axial force on the beam. It is shown that foundation inertia can considerably reduce the critical velocity and can also amplify the beam response.

Electron-beam weld microstructures and properties of aluminium-lithium alloy 8090

Lithium-containing aluminium alloys are of considerable current interest in the aerospace and aircraft industries because lithium additions to aluminium improve the modulus and decrease the density compared to conventional aluminium alloys. Few commercial aluminium-lithium alloys have emerged for use in the aerospace industry. One such candidate is 8090, a precipitation-hardenable Al-Li-Cu-Mg alloy. The influence of electron-beam welding on the microstructure and mechanical properties of alloy 8090 material has been evaluated through microscopical observations and mechanical tests. Microscopic observations of the electronbeam welds revealed an absence of microporosity and hot cracking, but revealed presence of microporosity in the transverse section of the weld. Mechanical tests revealed the electronbeam weld to have lower strength, elongation and joint efficiency. A change in microscopic fracture mode was observed for the welded material when compared to the unwelded counterpart. An attempt is made to rationalize the behaviour in terms of competing mechanistic effects involving the grain structure of the material, the role of matrix deformation characteristics, grain-boundary chemistry and grain-boundary failure.

Flap‐Lag Damping in Hover and Forward Flight with a Three‐Dimensional Wake

Prediction of lag damping is difficult owing to the delicate balance of drag, induced drag and Coriolis forces in the in‐plane direction. Moreover, induced drag” is sensitive to dynamic wake, bath shed and trailing components, and thus its prediction requires adequate unsteady‐wake representation. Accordingly, rigid‐blade flap‐lag equations are coupled with a three‐dimensional finite‐state wake model; three isolatcd rotor canfigurations with three, four and five blades are treated over a range of thrust levels, tack numbers, lag frequencies and advance ratios. The investigation includes convergence characteristics of damping with respect to the number of radial shape functions and harmonics of the wake model for multiblade modes of low frequency (< 1/ rev.) to high frequency (> 1/rev.). Predicted flap and lag damping levels are then compared with similar predictions with 1) rigid wake (no unsteady induced now), 2) Loewy lift deficiency and 3) dynamic inflow. The coverage also includes correlations with the measured lag regressive‐mode damping in hover and forward flight and comparisons with similar correlations with dynamic inflow. Lag‐damping predictions with the dynamic wake model are consistently higher than the predictions with the dynamic inflow model; even for the low frequency lag regressive mode, the number of wake harmonics should at least be equal to twice the number of blades.

The Commercial Structure of Pedestrian Streets and Shopping Districts - Three Cases from Finland

Kävelykadut ovat tunnustettu tapa elävöittää keskusta-alueiden kauppaa. Aluksi moni kauppias epäilee kävelykadun tuomia muutoksia, mutta kokemus osoittaa, että kävelykadut ovat olleet menestyksekkäitä ja nostavat siellä olevien yritysten myyntiä. Jotkut yritykset eivät kuitenkin hyödy kävelykaduista, kun taas toiset hyötyvät paljon kun katu muuttuu kävelykaduksi. Tämä pro gradu -tutkielma tutkii kävelykatujen kaupallista rakennetta, jotta saataisiin selville minkätyyppiset yritykset löytyvät kävelykadulta. Tuloksia verrataan sen kaupallisen keskusvyöhykkeen kaupalliseen rakenteeseen missä kävelykatu sijaitsee. Näin saadaan selville erot kaupallisessa rakenteessa. Pro gradu tutkii myös miten tavallisia ketjuyritykset ovat kävelykaduilla ja kaupallisissa keskusvyöhykkeissä. Tutkimusaineisto koottiin kaupallisen inventoinnin avulla, joka suoritettiin kolmessa suomalaisessa kaupungissa: Tammisaaressa, Keravalla ja Porissa. Saatu aineisto luokiteltiin ja tulokset piirrettiin kartalle. Perustilastollisia menetelmiä käytettiin tulosten analysoimisessa. Tulokset eriteltiin kävelykadun, kauppakeskusten ja muiden paikkojen osalta ja luokiteltiin yleisluokkiin vähittäiskauppa, ravintola ja muu palvelu. Tulokset näyttävät, että on olemassa selkeitä eroja kun vertaa kävelykatuja ja kaupallisia keskusvyöhykkeitä. Kävelykaduilla on paljon enemmän vähittäiskauppoja, etenkin muotikauppoja, kuin muilla kaduilla. Kauppakeskuksilla on samantapainen kaupallinen rakenne kuin kävelykaduilla kun taas muilla kaduilla esiintyy vähemmän vähittäiskauppoja ja enemmän palveluyrityksiä. Ravintolat ovat melkein yhtä tavallisia koko kaupallisessa keskusvyöhykkeessä. Ketjuyritysten osalta tulokset ovat epäselviä. On olemassa osviittaa siitä, että ne ovat tavallisempia kävelykaduilla, etenkin suurissa kaupungeissa. Saatua tulosta ei ole kuitenkin tarpeeksi, jotta varmaa tietoa olisi saatu. Viimeisten 10–15 vuoden ajan Suomen kävelykadut ovat muuttuneet enemmän ravintolavaltaisiksi muiden palveluiden kustannuksella. Vähittäiskauppojen määrä on pysynyt vakaana. Suomalaiset kävelykadut eroavat kaupalliselta rakenteeltaan pohjoismaisista kävelykaduista, joilla on enemmän vähittäiskauppoja ja vähemmän palveluyrityksiä. Tapauskohtaisissa tuloksissa esiintyy paljon eroavaisuuksia. Paikalliset tekijät ovat usein voimakkaampia kuin yleiset teoriat kauppojen sijainnista kävelykaduilla. Yleisesti ottaen tulokset tukevat teoreettista viitekehystä. Tulokset antavat tarkempaa tietoa kävelykatujen ja kaupallisten keskusvyöhykkeiden kaupallisesta rakenteesta ja siitä, mitkä tekijät tähän vaikuttaa.

Prediction of load-deflection behaviour using fracture energy GF: A comparative study of two fracture models for concrete

Load-deflection curves for a notched beam under three-point load are determined using the Fictitious Crack Model (FCM) and Blunt Crack Model (BCM). Two values of fracture energy GF are used in this analysis: (i) GF obtained from the size effect law and (ii) GF obtained independently of the size effect. The predicted load-deflection diagrams are compared with the experimental ones obtained for the beams tested by Jenq and Shah. In addition, the values of maximum load (Pmax) obtained by the analyses are compared with the experimental ones for beams tested by Jenq and Shah and by Bažant and Pfeiffer. The results indicate that the descending portion of the load-deflection curve is very sensitive to the GF value used.