Pressure of the standard model

We review the computation of the thermodynamic pressure of the entire minimal standard model to three loop order, performed in hep-ph/0510375 and hep-ph/0512177.Comment: 4 pages, 3 figures, to appear in the proceedings of Strong and Electroweak Matter 200

Pressure of the Standard Model Near the Electroweak Phase Transition

We extend our previous determination of the thermodynamic pressure of the Standard Model so that the result can be applied down to temperatures corresponding to the electroweak crossover. This requires a further resummation which can be cleanly organised within the effective theory framework. The result allows for a precise determination of the expansion rate of the Universe for temperatures around the electroweak crossover.Comment: 16 pages, 6 figures. v2: published versio

Pressure of the Standard Model at High Temperatures

We compute the pressure of the standard model at high temperatures in the symmetric phase to three loops, or to O(g^5) in all coupling constants. We find that the terms of the perturbative expansion in the SU(2) + Higgs sector decrease monotonically with increasing order, but the large values of the strong coupling constant g_s and the Yukawa coupling of the top quark g_Y make the expansion in the full theory converge more slowly. The final result is observed to be about 10% smaller than the ideal gas pressure commonly used in cosmological calculations.Comment: 30 pages, 4 figures. v2: one reference added, minor revisions, accepted for publication in JHE

Screened perturbation theory at four loops

We study the thermodynamics of massless phi-fourth theory using screened perturbation theory, which is a way to systematically reorganise the perturbative series. The free energy and pressure are calculated through four loops in a double expansion in powers of g^2 and m/T, where m is a thermal mass of order gT. The result is truncated at order g^7. We find that the convergence properties are significantly improved compared to the weak-coupling expansion.Comment: Talk given at Strong and Electroweak Matter 2008, Amsterdam, Aug. 25-29 2008. 4 pages, 1 figur

The N_f^3 g^6 term in the pressure of hot QCD

We determine the first independent part of the g^6 coefficient in the weak coupling expansion of the QCD pressure at high temperatures, the one proportional to the maximal power of the number of quark flavors N_f. In addition to introducing and developing computational methods that can be used in evaluating other parts of the expansion, our calculation provides a result that becomes dominant in the limit of large N_f and a fixed effective coupling g_{eff}^2 = g^2 N_f/2.Comment: 9 pages, 2 figures, revtex, v2: minor modifications and additional reference

Mesonic screening masses at high temperature and finite density

We compute the first perturbative correction to the static correlation lengths of light quark bilinears in hot QCD with finite quark chemical potentials. The correction is small and positive, with mu-dependence depending on the relative sign of chemical potentials and the number of dynamical flavors. The computation is carried out using a three-dimensional effective theory for the lowest fermionic Matsubara mode. We also compute the full correlator in free theory and find a rather complicated general mu-dependence at shorter distances. Finally, rough comparisons with lattice simulations are discussed.Comment: 24 pages, 5 figures, JHEP style. Minor corrections and clarifications, version to appear in JHE

Teaching in the Montessori Classroom: Investigating Variation Theory and Embodiment as a Foundation of Teachers’ Development

The theory of Montessori education has been interpreted by some researchers to be vaguely formulated. However, as shown in previous research, Maria Montessori’s didactic approach to teaching and learning mathematics is fully consistent with variation theory and the theory of embodiment. Dr. Montessori used the theoretical concept of isolation of quality, which means that the learning objects have to be kept identical except for one variable, which has to differ to be perceptible. This concept is in alignment with variation theory, which emphasizes variation as a necessary condition for learners to discern aspects of an object of learning. The other theory applied in this article is the theory of embodiment: important cognitive functions are fundamentally grounded in action that is concordant with Dr. Montessori’s view that mind and movement are parts of the same entity.                 This article reports on a qualitative single-case study with a formative intention in which we investigated the significance of being acquainted with variation theory and the theory of embodiment when working with Montessori material. The study analyzes a teacher’s mathematics presentations with the Montessori material and the children’s work with this material, using Epistemological Move Analysis, which focuses on how the teacher directs children’s learning. The analysis was shared with the teacher to support her awareness of the ways teaching can be developed from a variation and embodiment theoretical perspective. Results show that the teacher’s awareness of why a specific learning object be treated in accordance with variation theory and embodiment seems to promote a more constructive and effective way to direct children’s learning

Four-loop pressure of massless O(N) scalar field theory

Inspired by the corresponding problem in QCD, we determine the pressure of massless O(N) scalar field theory up to order g^6 in the weak-coupling expansion, where g^2 denotes the quartic coupling constant. This necessitates the computation of all 4-loop vacuum graphs at a finite temperature: by making use of methods developed by Arnold and Zhai at 3-loop level, we demonstrate that this task is manageable at least if one restricts to computing the logarithmic terms analytically, while handling the ``constant'' 4-loop contributions numerically. We also inspect the numerical convergence of the weak-coupling expansion after the inclusion of the new terms. Finally, we point out that while the present computation introduces strategies that should be helpful for the full 4-loop computation on the QCD-side, it also highlights the need to develop novel computational techniques, in order to be able to complete this formidable task in a systematic fashion.Comment: 34 page

NESTE OILIN HAMINAN TERMINAALIN PI-KAAVIOIDEN PÄIVITYS

Tämän opinnäytetyön aiheena oli päivittää Neste Oil Oyj:n Haminan terminaalin PI-kaaviot Tukesin turvallisuusohjeiden vaatimusten mukaisiksi. Käytössä olevat PI-kaaviot olivat vanhentuneita ja alueelle oli tehty useita muutostöitä ilman, että muutoksia olisi merkitty kaavioihin. Vanhat kaaviot olivat turvallisuusriski ja hankaloittivat operaattoreiden ja käyttöhenkilökunnan toimintaa. Vika- tai vaaratilanteen sattuessa ajantasainen PI-kaavio on ratkaisevassa roolissa tilanteen korjaamiseksi. Päivitettyjen PI-kaavioiden avulla voidaan kustannustehokkaasti suunnitella ennakkohuoltoja ja muutostöitä. Työkaluina olivat vanhat PI-kaaviot, joihin merkittiin eroavaisuuksia kentällä. Jos eroavaisuuksia oli paljon, piirrettiin prosessin osa muistiinpanoihin ja myöhemmin lisättiin kokonaisuuteen. Piirrosmerkkien päivittämisen yhteydessä perehdyttiin standardiin SFS-14617-6. Työssä perehdyttiin myös ATEX-säädökseen SFS EN 1127. Vanhentuneiden kaavioiden päivittäminen erillisenä projektina on todella haastavaa ja työlästä, minkä vuoksi on suositeltavaa päivittää muutokset PI-kaaviohin muutostöiden yhteydessä. Toimilaitteiden nimeäminen positiotunnuksilla helpottaa kenttätyöskentelyä huomattavasti.The purpose of this thesis was to update the P&I diagrams (P&ID) of Neste Oil Hamina terminal according to the regulations issued by Tukes. The diagrams in use were out of date and numerous changes had been introduced without modifying the diagrams. For this reason, the old diagrams were a safety risk and posed difficulties to operational staff. In case of a fault condition, P&IDs are important to solve the situation. The updated P&IDs can be used to efficiently improve preventive maintenance and alteration work. The diagrams were updated by comparing outdated diagrams and the as-built assembly off the terminal. In case of numerous modifications, the said part of the process was sketched to notes and later added to that specific process sheet. Standard SFS-14617-6 was used to update the graphic symbols and SFS EN 1127 was used regarding ATEX regulations. Updating the diagrams as an individual project is challenging and time-consuming which is why it is recommended that diagrams be updated in conjunction with or immediately after the alteration work is complete. Tagging actuators with position facilitates field work