Non-Gaussianities and Preheating from N-flation and Magnetogenesis via rotating cosmic string loops

In this thesis we examine multi-field inflationary models of the early Universe. Since non-Gaussianities may allow for the possibility to discriminate between models of inflation, we compute deviations from a Gaussian spectrum of primordial perturbations by extending the delta-N formalism. We use N-flation as a concrete model; our findings show that these models are generically indistinguishable as long as the slow roll approximation is still valid. Besides computing non-Guassinities, we also investigate Preheating after multi-field inflation. Within the framework of N-flation, we find that preheating via parametric resonance is suppressed, an indication that it is the old theory of preheating that is applicable. In addition to studying non-Gaussianities and preheatng in multi-field inflationary models, we study magnetogenesis in the early universe. To this aim, we propose a mechanism to generate primordial magnetic fields via rotating cosmic string loops. Magnetic fields in the micro-Gauss range have been observed in galaxies and clusters, but their origin has remained elusive. We consider a network of strings and find that rotating cosmic string loops, which are continuously produced in such networks, are viable candidates for magnetogenesis with relevant strength and length scales, provided we use a high string tension and an efficient dynamo.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Formation of structure in dark energy cosmologies

Acceleration of the universe has been established but not explained. During the past few years precise cosmological experiments have confirmed the standard big bang scenario of a flat universe undergoing an inflationary expansion in its earliest stages, where the perturbations are generated that eventually form into galaxies and other structure in matter, most of which is non-baryonic dark matter. Curiously, the universe has presently entered into another period of acceleration. Such a result is inferred from observations of extra-galactic supernovae and is independently supported by the cosmic microwave background radiation and large scale structure data. It seems there is a positive cosmological constant speeding up the universal expansion of space. Then the vacuum energy density the constant describes should be about a dozen times the present energy density in visible matter, but particle physics scales are enormously larger than that. This is the cosmological constant problem, perhaps the greatest mystery of contemporary cosmology. In this thesis we will explore alternative agents of the acceleration. Generically, such are called dark energy. If some symmetry turns off vacuum energy, its value is not a problem but one needs some dark energy. Such could be a scalar field dynamically evolving in its potential, or some other exotic constituent exhibiting negative pressure. Another option is to assume that gravity at cosmological scales is not well described by general relativity. In a modified theory of gravity one might find the expansion rate increasing in a universe filled by just dark matter and baryons. Such possibilities are taken here under investigation. The main goal is to uncover observational consequences of different models of dark energy, the emphasis being on their implications for the formation of large-scale structure of the universe. Possible properties of dark energy are investigated using phenomenological paramaterizations, but several specific models are also considered in detail. Difficulties in unifying dark matter and dark energy into a single concept are pointed out. Considerable attention is on modifications of gravity resulting in second order field equations. It is shown that in a general class of such models the viable ones represent effectively the cosmological constant, while from another class one might find interesting modifications of the standard cosmological scenario yet allowed by observations. The thesis consists of seven research papers preceded by an introductory discussion.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

Joseph A. Schumpeter's Theory of Social and Economic Evolution : a Reconstruction and Critique

The book presents a reconstruction, interpretation and critical evaluation of the Schumpeterian theoretical approach to socio-economic change. The analysis focuses on the problem of social evolution, on the interpretation of the innovation process and business cycles and, finally, on Schumpeter s optimistic neglect of ecological-environmental conditions as possible factors influencing social-economic change. The author investigates how the Schumpeterian approach describes the process of social and economic evolution, and how the logic of transformations is described, explained and understood in the Schumpeterian theory. The material of the study includes Schumpeter s works written after 1925, a related part of the commentary literature on these works, and a selected part of the related literature on the innovation process, technological transformations and the problem of long waves. Concerning the period after 1925, the Schumpeterian oeuvre is conceived and analysed as a more or less homogenous corpus of texts. The book is divided into 9 chapters. Chapters 1-2 describe the research problems and methods. Chapter 3 is an effort to provide a systematic reconstruction of Schumpeter's ideas concerning social and economic evolution. Chapters 4 and 5 focus their analysis on the innovation process. In Chapters 6 and 7 Schumpeter's theory of business cycles is examined. Chapter 8 evaluates Schumpeter's views concerning his relative neglect of ecological-environmental conditions as possible factors influencing social-economic change. Finally, chapter 9 draws the main conclusions.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Non-Fermi liquid theory of quantum hall effects

Within the Grassmannian U(2N)/U(N) x U(N) nonlinear sigma-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping. (C) 2005 Pleiades Publishing, Inc.

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m =1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian discm must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

Surface instability of confined elastic bilayers: Theory and simulations

The surface of a soft elastic film becomes unstable and forms a self-organized undulating pattern because of adhesive interactions when it comes in contact proximity with a rigid surface. For a single film, the pattern length scale lambda, which is governed by the minimization of the elastic stored energy, gives lambda similar to 3h, where h is the film thickness. Based on a linear stability analysis and simulations of adhesion and debonding, we consider the contact instability of an elastic bilayer, which provides greater flexibility in the morphological control of interfacial instability. Unlike the case of a single film, the morphology of the contact instability patterns, debonding distance, and debonding force in a bilayer can be controlled in a nonlinear way by varying the thicknesses and shear moduli of the films. Interestingly, the pattern wavelength in a bilayer can be greatly increased or decreased compared to a single film when the adhesive contact is formed by the stiffer or the softer of the two films, respectively. In particular, lambda as small as 0.5h can be obtained. This indicates a new strategy for pattern miniaturization in elastic contact lithography.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

Interculturality in Theory and Practice in the Master's Programme of Intercultural Bilingual Education in Bolivia

Tämän tutkielman aiheena on kulttuurienvälisyys kulttuurienvälisessä kaksikielisessä opetuksessa (Educación Intercultural Bilingüe, EIB) Boliviassa ja erityisesti kulttuurienvälisen kaksikielisen koulutuksen maisteriohjelmassa (Maestría en Educación Intercultural Bilingüe), jota koordinoi PROEIB Andes -järjestö yhteistyössä Cochabamban Universidad Mayor de San Simónin kanssa. Tutkielman tarkoituksena on selvittää, miten kulttuurienvälisyys määritellään ja mitä se käytännössä merkitsee opetuksen eri osa-alueilla: sisällöissä, opetusmetodeissa ja -materiaaleissa sekä arvioinnissa. Koska kulttuurienvälisen kaksikielisen opetuksen toteutus ja tutkiminen eri Latinalaisen Amerikan maissa on tähän asti painottunut lähes yksinomaan perusopetukseen, pyrin työssäni keskittymään kulttuurienvälisyyden ilmentymiin nimenomaan bolivialaisessa korkeakoulukontekstissa. Tutkielman aineistona on käytetty kahdeksaa EIB -asiantuntijoiden teemahaastattelua, jotka FM Eila Isotalus on tehnyt Boliviassa vuonna 2004. Haastatteluaineisto analysoitiin teoriasidonnaista eli abduktiivista sisällönanalyysiä käyttäen. Tutkielman teoriatausta koostuu yhtäältä kulttuurienvälisyyteen ja monikulttuurisuuteen liittyvien käsitteiden määrittelystä, ja toisaalta kulttuurienväliseen opetukseen liittyvien mallien esittelystä. Aineiston analyysissä avuksi on ollut etenkin James A. Banksin teoria monikulttuurisen opetuksen viidestä ulottuvuudesta, joiden kautta on voitu pohtia kulttuurienvälisyyden toteutumista opetuksen eri osa-alueilla ja nostaa esille bolivialaisen kulttuurienvälisen opetuksen erityispiirteitä. Aineiston analyysissä ilmenee, että kulttuurienvälisyyden käsitteen määrittely on vahvasti kontekstisidonnainen ja jatkuva prosessi, johon vaikuttavat eri toimijoiden näkemykset ja vaatimukset. EIB -asiantuntijoiden esittämät määrittelyt voidaan jakaa makro- ja mikrososiaaliseen kategoriaan sen mukaan, nähdäänkö kulttuurienvälisyys ensisijaisesti yhteiskunnallisena vai yksilötason käsitteenä. Aineistossa korostuu ajatus latinalaisamerikkalaisesta kulttuurienvälisyydestä poliittisena käsitteenä, jonka keskiössä on vaatimus yhteiskunnallisten valtasuhteiden muutoksesta. Yksi suurimmista haasteista kulttuurienvälisyyden toteuttamisessa bolivialaisessa korkeakouluopetuksessa ovat akateemiseen kulttuuriin liittyvät perinteet, jotka vaikeuttavat uusien toimintatapojen omaksumista. Kulttuurienvälisyys opetuksessa on toistaiseksi tarkoittanut etupäässä sisältöjen monipuolistamista lisäämällä opetusohjelmiin elementtejä paikallisista kulttuureista. Tärkeänä askeleena EIB:n kehityksessä voidaan pitää painopisteen siirtymistä sisältökysymyksistä kulttuurienvälisten opetusmetodien luomiseen. Näiden opetusmenetelmien tulisi pohjautua ymmärrykseen oppimisesta kokonaisvaltaisena, yhteisöllisenä prosessina ja siten kuroa umpeen kuilua koulun ja yhteisöjen arkielämän välillä. Opetusmenetelmien ja -materiaalien suhteen keskeinen kulttuurienvälisyyteen liittyvä kysymys on intiaanikansojen suullisen kulttuurin ja tiedon jakamisen perinteiden hyödyntäminen opetuksessa. Maisteriohjelman opiskelijoiden arvioinnissa pyritään huomioimaan yksilön kokonaisvaltainen kehitys pelkkien opintosuoritusten sijasta, mutta arvosanoihin pohjautuvasta arvostelukäytännöstä ei ole toistaiseksi voitu luopua yliopiston vaatimusten vuoksi. Kaiken kaikkiaan kulttuurienvälisyyden toteuttaminen EIB:ssä ja maisteriohjelmassa on pitkän tähtäimen prosessi, joka vaatii perinteisten opetuskäytäntöjen kyseenalaistamista ja korkeakouluopetuksessa myös akateemisen kulttuurin haastamista. On oleellisen tärkeää, että prosessiin osallistuvat asiantuntijoiden ohella myös esimerkiksi opiskelijat, intiaaniyhteisöt ja -järjestöaktiivit.

A generalized mathematical theory and experimental verification of proportional notches

A theory and generalized synthesis procedure is advocated for the design of weir notches and orifice-notches having a base in any given shape, to a depth a, such that the discharge through it is proportional to any singular monotonically-increasing function of the depth of flow measured above a certain datum. The problem is reduced to finding an exact solution of a Volterra integral equation in Abel form. The maximization of the depth of the datum below the crest of the notch is investigated. Proof is given that for a weir notch made out of one continuous curve, and for a flow proportional to the mth power of the head, it is impossible to bring the datum lower than (2m − 1)a below the crest of the notch. A new concept of an orifice-notch, having discontinuity in the curve and a division of flow into two distinct portions, is presented. The division of flow is shown to have a beneficial effect in reducing the datum below (2m − 1)a from the crest of the weir and still maintaining the proportionality of the flow. Experimental proof with one such orifice-notch is found to have a constant coefficient of discharge of 0.625. The importance of this analysis in the design of grit chambers is emphasized.