Spinor Bose-Einstein Condensates and Topological Defects

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.

Effect of supplemental vitamin E on the performance of growing-finishing pigs fed stored versus freshly harvested barley and on the storage stability and eating quality of frozen pork

Lihasikojen E-vitamiinin tarve ruokittaessa vastapuidulla ohralla ja rehuun lisätyn E-vitamiinin vaikutus lihan pakastussäilyvyyteen ja syöntilaatuun

Stability Evaluation of a Paper Machine Wet End

Työssä analysoidaanprosessin vaikutusta paperikoneen stabiiliuteen. Kaksi modernia sanomalehtipaperikonetta analysoitiin ja sen perusteella molemmista prosesseista rakennettiin fysiikan lakeihin perustuvat simulointimallit APROS Paper simulointiohjelmistolla. Työn tavoitteena on selvittää, miten kyseisten koneiden prosessit eroavat toisistaan ja arvioida, miten havaitut erot vaikuttavat prosessien stabiiliuteen. Työssä tarkastellaan periodisten häiriöiden vaimenemista prosessissa. Simuloinnissa herätteenä käytettiin puhdasta valkoista kohinaa, jonka avulla eri taajuistenperiodisten häiriöiden vaimenemista analysoitiin. Prosessien häiriövasteet esitetään taajuuskoordinaatistossa. Suurimmat erot prosessien välillä löytyivät viirakaivosta ja sen sekoitusdynamiikasta. Perinteisen viirakaivon todettiin muistuttavan käyttäytymiseltään sarjaan kytkettyjä ideaalisekoittimia, kun taas pienempitilavuuksisen fluumin todettiin käyttäytyvän lähes kuin putkiviive. Vaikka erotprosessitilavuudessa sekä viirakaivon sekoitusdynamiikassa olivat hyvin selkeät, havaittiin vain marginaalinen ero prosessin välillä periodisten häiriöiden vaimenemisessa, koska erot viiraretentiotasoissa vaikuttivat eniten simulointituloksia. Matalammalla viiraretentiolla operoivan paperikoneen todettiin vaimentavan tehokkaammin prosessihäiriöitä. Samalla retentiotasolla pienempitilavuuksisen prosessin todettiin vaimentavan hitaita prosessihäiriöitä marginaalisesti paremmin. Tutkituista paperikoneista toisella simuloitiin viiraosan vedenpoistomuutoksenvaikutusta viiraretentioon ja paperin koostumukseen. Lisäksi arvioitiin viiraretention säädön toimivuutta. Viiraosan listakengän vedenpoiston todettiin aiheuttavan merkittäviä sakeus- ja retentiohäiriöitä, mikäli sen avulla poistettavan kiintoaineen virtaus tuplaantuisi. Viiraretention säädön todettiin estävän häiriöiden kierron prosessissa, mutta siirtävän ne suoraan rainaan. Retention säädön eikuitenkaan todettu olevan suoranainen häiriön lähde.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Biocide analysis, usability and stability

Biosidien toimittajat tavallisesti suorittavat biosidien annostelumäärien hallinnan paperi- ja kartonkiteollisuudessa. Useimmiten annostelun hallinta määritetään epäsuorilla menetelmillä, kuten esimerkiksi määrittämällä bakteerien kasvua. Biosidien tehoaineiden todellista konsentraatiota tai määrää prosessivesissä tai lopputuotteessa ei tavallisesti mitata. Diplomityössä kehitettiin kolmelle paperiteollisuudessa yleisesti käytetyllä biosidin tehoaineelle analyyttiset menetelmät. Menetelmät kehitettiin glutaraldehydille, 2,2-dibromi-3-nitriilipropionamidi:lle (DBNPA) ja 5-kloori-2-metyyli-4-isotiatsoliini-3-oni:lle (CMI). Kehitettyjä menetelmiä käytettiin tehoaineiden stabiilisuuden seuraamiseen vesiliuoksessa eri pH:ssa ja lämpötilassa. Lisäksi kartonkinäytteistä tehtiin uuttokokeita ja yritettiin kehittää uuttomenetelmät, joilla pystyttäisiin määrittämään biosidien tehoaineiden jäännöspitoisuuksia lopputuotteesta. Glutaraldehydille ja CMI:lle onnistuttiin kehittämään uuttomenetelmät, joilla pystyttiin määrittämään kartongista tutkittujen tehoaineiden jäännöspitoisuudet. Saadut tulokset vaikuttavat realistisilta. Glutaraldehydille ja DBNPA:lle tehtiin stabiilisuuskokeita ja tulokset ovat samankaltaisia mitä muut tutkijat ovat saaneet.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

On Topological Solitons in The Faddeev-Skyrme Model and its Extensions

The topological solitons of two classical field theories, the Faddeev-Skyrme model and the Ginzburg-Landau model are studied numerically and analytically in this work. The aim is to gain information on the existence and properties of these topological solitons, their structure and behaviour under relaxation. First, the conditions and mechanisms leading to the possibility of topological solitons are explored from the field theoretical point of view. This leads one to consider continuous deformations of the solutions of the equations of motion. The results of algebraic topology necessary for the systematic treatment of such deformations are reviewed and methods of determining the homotopy classes of topological solitons are presented. The Faddeev-Skyrme and Ginzburg-Landau models are presented, some earlier results reviewed and the numerical methods used in this work are described. The topological solitons of the Faddeev-Skyrme model, Hopfions, are found to follow the same mechanisms of relaxation in three different domains with three different topological classifications. For two of the domains, the necessary but unusual topological classification is presented. Finite size topological solitons are not found in the Ginzburg-Landau model and a scaling argument is used to suggest that there are indeed none unless a certain modification to the model, due to R. S. Ward, is made. In that case, the Hopfions of the Faddeev-Skyrme model are seen to be present for some parameter values. A boundary in the parameter space separating the region where the Hopfions exist and the area where they do not exist is found and the behaviour of the Hopfion energy on this boundary is studied.

The effect of microfibrillated cellulose addition on drying shrinkage and dimensional stability of wood-free paper

Microfibrillated cellulose (MFC) is known to enhance strength properties of paper. Improved strength usually means increased bonding which is strongly connected to dimensional instability of paper. Dimensional instability is due to changes in moisture content of paper; when paper is moistened it expands and when dried, it shrinks. Hygroexpansion is linked to end-use problems and excessive drying shrinkage consumes strength potential. Effective use of materials requires controlling of these phenomena. There isn’t yet data concerning dimensional stability of papers containing MFC which restricts wider use of MFC. Main objective of the work was to evaluate dimensional stability of wood-free paper containing different amounts of MFC. Sheets were dried with different methods to see how drying strains effected on drying shrinkage and hygroexpansion. Also tensile strength was measured to find out the effect of MFC. Results were compared to sheets containing kraft fines and in some test points cationic starch was used alongside with MFC. MFC increased the dimensional instability of freely dried sheets. As the amounts of MFC increased the effects on dimensional stability became more severe. However the fineness of MFC didn’t play any important role. Both hygroexpansion and drying shrinkage were decreased with cationic starch addition. Prevention of drying shrinkage over powered the effects of additives on hygroexpansion. Tensile strength improved up till 7 % addition amount which could be set as the upper limit of MFC addition when paper preparation and tensile strength are concerned.