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  • Tuovinen, Antti-Pekka (Helsingin yliopisto, 2002)
  • Brücken, Jens Erik (Helsingin yliopisto, 2013)
    We have observed exclusive γγ production in proton-antiproton collisions at the Tevatron at sqrt(s) = 1.96 TeV. We use data corresponding to 1.11 ± 0.07 fb^{−1} integrated luminosity taken by the Run II Collider Detector at Fermilab, with a trigger requiring two electromagnetic showers, each with transverse energy ET > 2 GeV, and vetoing on hits in the forward beam shower counters. We select events with two electromagnetic showers, each with transverse energy ET > 2.5 GeV and pseudorapidity |η| < 1.0, with no other particles detected in −7.4 < η < +7.4. The two showers have similar ET and an azimuthal angle separation ∆φ ∼ π; we find 34 events with exactly two matching charged particle tracks, agreeing with expectations for the QED process p pbar → p + e^+ e^− + pbar by two photon exchange; and we find 43 events with no tracks. The latter are candidates for the exclusive process p pbar → p + γγ + pbar by double pomeron exchange. We use the strip and wire chambers at the longitudinal shower maximum position within the calorimeter to measure a possible exclusive background from IP + IP → π^0 π^0 , and conclude that it is consistent with zero and is < 15 events at 95% C.L. The measured cross section is σ_{γγ,excl} (|η| < 1, ET (γ) > 2.5 GeV) = 2.48 +0.40 -0.35 (stat) +0.40 -0.51 (syst) pb and in agreement with the theoretical predictions. This process is closely related to exclusive Higgs boson production pp → p + H + p at the Large Hadron Collider. The observation of the exclusive production of diphotons shows that exclusive Higgs production can happen and could be observed with a proper experimental setup.
  • Seppälä, Annika (Helsingin yliopisto, 2007)
    This work is focused on the effects of energetic particle precipitation of solar or magnetospheric origin on the polar middle atmosphere. The energetic charged particles have access to the atmosphere in the polar areas, where they are guided by the Earth's magnetic field. The particles penetrate down to 20-100 km altitudes (stratosphere and mesosphere) ionising the ambient air. This ionisation leads to production of odd nitrogen (NOx) and odd hydrogen species, which take part in catalytic ozone destruction. NOx has a very long chemical lifetime during polar night conditions. Therefore NOx produced at high altitudes during polar night can be transported to lower stratospheric altitudes. Particular emphasis in this work is in the use of both space and ground based observations: ozone and NO2 measurements from the GOMOS instrument on board the European Space Agency's Envisat-satellite are used together with subionospheric VLF radio wave observations from ground stations. Combining the two observation techniques enabled detection of NOx enhancements throughout the middle atmosphere, including tracking the descent of NOx enhancements of high altitude origin down to the stratosphere. GOMOS observations of the large Solar Proton Events of October-November 2003 showed the progression of the SPE initiated NOx enhancements through the polar winter. In the upper stratosphere, nighttime NO2 increased by an order of magnitude, and the effect was observed to last for several weeks after the SPEs. Ozone decreases up to 60 % from the pre-SPE values were observed in the upper stratosphere nearly a month after the events. Over several weeks the GOMOS observations showed the gradual descent of the NOx enhancements to lower altitudes. Measurements from years 2002-2006 were used to study polar winter NOx increases and their connection to energetic particle precipitation. NOx enhancements were found to occur in a good correlation with both increased high-energy particle precipitation and increased geomagnetic activity. The average wintertime polar NOx was found to have a nearly linear relationship with the average wintertime geomagnetic activity. The results from this thesis work show how important energetic particle precipitation from outside the atmosphere is as a source of NOx in the middle atmosphere, and thus its importance to the chemical balance of the atmosphere.
  • Juusola, Liisa (Helsingin yliopisto, 2009)
    In this thesis, the solar wind-magnetosphere-ionosphere coupling is studied observationally, with the main focus on the ionospheric currents in the auroral region. The thesis consists of five research articles and an introductory part that summarises the most important results reached in the articles and places them in a wider context within the field of space physics. Ionospheric measurements are provided by the International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer network, by the low-orbit CHAllenging Minisatellite Payload (CHAMP) satellite, by the European Incoherent SCATter (EISCAT) radar, and by the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) satellite. Magnetospheric observations, on the other hand, are acquired from the four spacecraft of the Cluster mission, and solar wind observations from the Advanced Composition Explorer (ACE) and Wind spacecraft. Within the framework of this study, a new method for determining the ionospheric currents from low-orbit satellite-based magnetic field data is developed. In contrast to previous techniques, all three current density components can be determined on a matching spatial scale, and the validity of the necessary one-dimensionality approximation, and thus, the quality of the results, can be estimated directly from the data. The new method is applied to derive an empirical model for estimating the Hall-to-Pedersen conductance ratio from ground-based magnetic field data, and to investigate the statistical dependence of the large-scale ionospheric currents on solar wind and geomagnetic parameters. Equations describing the amount of field-aligned current in the auroral region, as well as the location of the auroral electrojets, as a function of these parameters are derived. Moreover, the mesoscale (10-1000 km) ionospheric equivalent currents related to two magnetotail plasma sheet phenomena, bursty bulk flows and flux ropes, are studied. Based on the analysis of 22 events, the typical equivalent current pattern related to bursty bulk flows is established. For the flux ropes, on the other hand, only two conjugate events are found. As the equivalent current patterns during these two events are not similar, it is suggested that the ionospheric signatures of a flux rope depend on the orientation and the length of the structure, but analysis of additional events is required to determine the possible ionospheric connection of flux ropes.
  • Koponen, Ismo (Helsingin yliopisto, 2003)
  • Mönkkönen, Petteri (Helsingin yliopisto, 2005)
  • Riipinen, Ilona (Helsingin yliopisto, 2008)
    Atmospheric aerosol particles have a significant impact on air quality, human health and global climate. The climatic effects of secondary aerosol are currently among the largest uncertainties limiting the scientific understanding of future and past climate changes. To better estimate the climatic importance of secondary aerosol particles, detailed information on atmospheric particle formation mechanisms and the vapours forming the aerosol is required. In this thesis we studied these issues by applying novel instrumentation in a boreal forest to obtain direct information on the very first steps of atmospheric nucleation and particle growth. Additionally, we used detailed laboratory experiments and process modelling to determine condensational growth properties, such as saturation vapour pressures, of dicarboxylic acids, which are organic acids often found in atmospheric samples. Based on our studies, we came to four main conclusions: 1) In the boreal forest region, both sulphurous compounds and organics are needed for secondary particle formation, the previous contributing mainly to particle formation and latter to growth; 2) A persistent pool of molecular clusters, both neutral and charged, is present and participates in atmospheric nucleation processes in boreal forests; 3) Neutral particle formation seems to dominate over ion-mediated mechanisms, at least in the boreal forest boundary layer; 4) The subcooled liquid phase saturation vapour pressures of C3-C9 dicarboxylic acids are of the order of 1e-5 1e-3 Pa at atmospheric temperatures, indicating that a mixed pre-existing particulate phase is required for their condensation in atmospheric conditions. The work presented in this thesis gives tools to better quantify the aerosol source provided by secondary aerosol formation. The results are particularly useful when estimating, for instance, anthropogenic versus biogenic influences and the fractions of secondary aerosol formation explained by neutral or ion-mediated nucleation mechanisms, at least in environments where the average particle formation rates are of the order of some tens of particles per cubic centimeter or lower. However, as the factors driving secondary particle formation are likely to vary depending on the environment, measurements on atmospheric nucleation and particle growth are needed from around the world to be able to better describe the secondary particle formation, and assess its climatic effects on a global scale.
  • Kaila, Risto (Helsingin yliopisto, 2001)
  • Yang, Fan (Helsingin yliopisto, 2014)
    Dependence logic is a new logic which incorporates the notion of dependence , as well as independence between variables into first-order logic. In this thesis, we study extensions and variants of dependence logic on the first-order, propositional and modal level. In particular, the role of intuitionistic connectives in this setting is emphasized. We obtain, among others, the following results: 1. First-order intuitionistic dependence logic is proved to have the same expressive power as the full second-order logic. 2. Complete axiomatizations for propositional dependence logic and its variants are obtained. 3. The complexity of model checking problem for modal intuitionistic dependence logic is analyzed.
  • Hirsikko, Anne (Helsingin yliopisto, 2011)
    Aerosol particles have effect on climate, visibility, air quality and human health. However, the strength of which aerosol particles affect our everyday life is not well described or entirely understood. Therefore, investigations of different processes and phenomena including e.g. primary particle sources, initial steps of secondary particle formation and growth, significance of charged particles in particle formation, as well as redistribution mechanisms in the atmosphere are required. In this work sources, sinks and concentrations of air ions (charged molecules, cluster and particles) were investigated directly by measuring air molecule ionising components (i.e. radon activity concentrations and external radiation dose rates) and charged particle size distributions, as well as based on literature review. The obtained results gave comprehensive and valuable picture of the spatial and temporal variation of the air ion sources, sinks and concentrations to use as input parameters in local and global scale climate models. Newly developed air ion spectrometers (Airel Ltd.) offered a possibility to investigate atmospheric (charged) particle formation and growth at sub-3 nm sizes. Therefore, new visual classification schemes for charged particle formation events were developed, and a newly developed particle growth rate method was tested with over one year dataset. These data analysis methods have been widely utilised by other researchers since introducing them. This thesis resulted interesting characteristics of atmospheric particle formation and growth: e.g. particle growth may sometimes be suppressed before detection limit (~ 3 nm) of traditional aerosol instruments, particle formation may take place during daytime as well as in the evening, growth rates of sub-3 nm particles were quite constant throughout the year while growth rates of larger particles (3-20 nm in diameter) were higher during summer compared to winter. These observations were thought to be a consequence of availability of condensing vapours. The observations of this thesis offered new understanding of the particle formation in the atmosphere. However, the role of ions in particle formation, which is not well understood with current knowledge, requires further research in future.
  • Pauna, Matti (Helsingin yliopisto, 2007)
    In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.
  • Nikula, Miika (Helsingin yliopisto, 2014)
    Mandelbrot cascades and multiplicative chaos are two related natural constructions of random multifractal measures, or rather families of such measures indexed by a single real parameter. While these models were first defined decades ago, they have recently become topical again after they were applied in the field of planar random geometry. In that context, multiplicative chaos provides one rigorous way of defining the exponential of the Gaussian free field. Typically, for a Mandelbrot cascade or multiplicative chaos there exists a critical parameter value at which the behavior of the measure changes drastically. Away from criticality, the geometric properties of cascade and chaos measures have been studied intensively and much of the theory is by now classical. For small values of the parameter, the random measures considered here are natural examples of multifractality. The measures are exact dimensional with the dimension, depending deterministically on the parameter, strictly between 0 and the dimension of the ambient space in which the measure is constructed. For large values of the parameter the construction of the measures is a rather subtle issue, but it is known that in this case the measures are atomic. The main theme of this dissertation is the study of geometric properties of cascade and chaos measures at the critical parameter value. To mention one main result, it is shown that while the critical measures are almost surely supported on sets of Hausdorff dimension 0, they do not have atoms. Improving on the qualitative result, almost sure quantitative bounds are given for the mass carried by a set of a given size in the ambient geometry. One part of the analysis of the geometric properties of cascade and chaos measures is understanding the probability distributions of the mass of a given set. Since the measures are built to exhibit strong statistical self-similarity, this is a major part of understanding the full law of the measure, i.e. the joint laws arbitrary collections of sets. Results concerning the law of the mass of a fixed set are another main theme of this dissertation.
  • Lehtomaa, Jaakko (Helsingin yliopisto, 2016)
    This book is about heavy-tailed random variables and the phenomena they induce to mathematical models. It has become clear that the classical models employing light-tailed variables have an inherent tendency to underestimate the magnitude of extremal events. Recent developments in the financial world (financial crises) suggest that such shortcomings are not merely theoretical curiosities, but game-changing phenomena that can solely determine the fate of an agent. To overcome the obstacles set by the classical lines of thought an agent must consider ways to improve the way risk is modelled and assessed. The book proposes two ways to do this. Firstly, the existing models are reconfigured to include the effects of different types of risks. Secondly, heavy-tailed effects such as the principle of a single big jump are made more transparent by a detailed investigation. The mathematical theory of this book is based on the theory of random walks and their generalisations. Special attention is paid to randomly weighted random walks and randomly stopped random walks that are commonly encountered in the field of insurance mathematics.
  • Järvinen, Riku (Helsingin yliopisto, 2011)
    This doctoral thesis is about the solar wind influence on the atmosphere of the planet Venus. A numerical plasma simulation model was developed for the interaction between Venus and the solar wind to study the erosion of charged particles from the Venus upper atmosphere. The developed model is a hybrid simulation where ions are treated as particles and electrons are modelled as a fluid. The simulation was used to study the solar wind induced ion escape from Venus as observed by the European Space Agency's Venus Express and NASA's Pioneer Venus Orbiter spacecraft. Especially, observations made by the ASPERA-4 particle instrument onboard Venus Express were studied. The thesis consists of an introductory part and four peer-reviewed articles published in scientific journals. In the introduction Venus is presented as one of the terrestrial planets in the Solar System and the main findings of the work are discussed within the wider context of planetary physics. Venus is the closest neighbouring planet to the Earth and the most earthlike planet in its size and mass orbiting the Sun. Whereas the atmosphere of the Earth consists mainly of nitrogen and oxygen, Venus has a hot carbon dioxide atmosphere, which is dominated by the greenhouse effect. Venus has all of its water in the atmosphere, which is only a fraction of the Earth's total water supply. Since planets developed presumably in similar conditions in the young Solar System, why Venus and Earth became so different in many respects? One important feature of Venus is that the planet does not have an intrinsic magnetic field. This makes it possible for the solar wind, a continuous stream of charged particles from the Sun, to flow close to Venus and to pick up ions from the planet's upper atmosphere. The strong intrinsic magnetic field of the Earth dominates the terrestrial magnetosphere and deflects the solar wind flow far away from the atmosphere. The region around Venus where the planet's atmosphere interacts with the solar wind is called the plasma environment or the induced magnetosphere. Main findings of the work include new knowledge about the movement of escaping planetary ions in the Venusian induced magnetosphere. Further, the developed simulation model was used to study how the solar wind conditions affect the ion escape from Venus. Especially, the global three-dimensional structure of the Venusian particle and magnetic environment was studied. The results help to interpret spacecraft observations around the planet. Finally, several remaining questions were identified, which could potentially improve our knowledge of the Venus ion escape and guide the future development of planetary plasma simulations.
  • Jääskeläinen, Jarmo (Helsingin yliopisto, 2012)
    The dissertation consists of an introductory part and three articles. The starting point of the work is the consideration of quasiregular mappings in the plane. These are characterized by the Beltrami equation. One of the foundational results of the theory of quasiregular mappings is that the derivative of a nonconstant map does not vanish almost everywhere. The first paper (in collaboration with Kari Astala) shows that the same is true for so-called reduced quasiregular mappings when the function is one-to-one. The second paper studies linear classes of planar quasiregular mappings. In addition, it shows that the derivative of a nonconstant reduced quasiregular map is non-vanishing even in subdomains and without assuming injectivity. The principal tool of the proof is a reverse Hölder inequality for the adjoint equation of a 2nd order uniformly elliptic operator in the nondivergence form. The non-vanishing fact is used to show Wronsky-type theorem for general linear Beltrami systems. This result is applied to prove that the associated Beltrami equation of a linear quasiregular family is unique. The third article (joint work with Kari Astala, Albert Clop, Daniel Faraco, and László Székelyhidi Jr) tackles the problem of uniqueness of normalized solutions to the nonlinear Beltrami equation. It turns out that the uniqueness holds under explicit bounds in the ellipticity constant of the equation at infinity, but not in general. The fact is complemented with counterexamples.
  • Bissell-Siders, Ryan (Helsingin yliopisto, 2008)
    We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.
  • Petäjä, Tuukka (Helsingin yliopisto, 2006)
    Atmospheric aerosol particles affect the global climate as well as human health. In this thesis, formation of nanometer sized atmospheric aerosol particles and their subsequent growth was observed to occur all around the world. Typical formation rate of 3 nm particles at varied from 0.01 to 10 cm-3s-1. One order of magnitude higher formation rates were detected in urban environment. Highest formation rates up to 105 cm-3s-1 were detected in coastal areas and in industrial pollution plumes. Subsequent growth rates varied from 0.01 to 20 nm h-1. Smallest growth rates were observed in polar areas and the largest in the polluted urban environment. This was probably due to competition between growth by condensation and loss by coagulation. Observed growth rates were used in the calculation of a proxy condensable vapour concentration and its source rate in vastly different environments from pristine Antarctica to polluted India. Estimated concentrations varied only 2 orders of magnitude, but the source rates for the vapours varied up to 4 orders of magnitude. Highest source rates were in New Delhi and lowest were in the Antarctica. Indirect methods were applied to study the growth of freshly formed particles in the atmosphere. Also a newly developed Water Condensation Particle Counter, TSI 3785, was found to be a potential candidate to detect water solubility and thus indirectly composition of atmospheric ultra-fine particles. Based on indirect methods, the relative roles of sulphuric acid, non-volatile material and coagulation were investigated in rural Melpitz, Germany. Condensation of non-volatile material explained 20-40% and sulphuric acid the most of the remaining growth up to a point, when nucleation mode reached 10 to 20 nm in diameter. Coagulation contributed typically less than 5%. Furthermore, hygroscopicity measurements were applied to detect the contribution of water soluble and insoluble components in Athens. During more polluted days, the water soluble components contributed more to the growth. During less anthropogenic influence, non-soluble compounds explained a larger fraction of the growth. In addition, long range transport to a measurement station in Finland in a relatively polluted air mass was found to affect the hygroscopicity of the particles. This aging could have implications to cloud formation far away from the pollution sources.