Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.

Measurements of the top-quark mass using charged particle tracking

We present three measurements of the top-quark mass in the lepton plus jets channel with approximately 1.9 fb-1 of integrated luminosity collected with the CDF II detector using quantities with minimal dependence on the jet energy scale. One measurement exploits the transverse decay length of b-tagged jets to determine a top-quark mass of 166.9+9.5-8.5 (stat) +/- 2.9 (syst) GeV/c2, and another the transverse momentum of electrons and muons from W-boson decays to determine a top-quark mass of 173.5+8.8-8.9 (stat) +/- 3.8 (syst) GeV/c2. These quantities are combined in a third, simultaneous mass measurement to determine a top-quark mass of 170.7 +/- 6.3 (stat) +/- 2.6 (syst) GeV/c2.

Measurements of the top-quark mass using charged particle tracking

We present three measurements of the top-quark mass in the lepton plus jets channel with approximately 1.9 fb-1 of integrated luminosity collected with the CDF II detector using quantities with minimal dependence on the jet energy scale. One measurement exploits the transverse decay length of b-tagged jets to determine a top-quark mass of 166.9+9.5-8.5 (stat) +/- 2.9 (syst) GeV/c2, and another the transverse momentum of electrons and muons from W-boson decays to determine a top-quark mass of 173.5+8.8-8.9 (stat) +/- 3.8 (syst) GeV/c2. These quantities are combined in a third, simultaneous mass measurement to determine a top-quark mass of 170.7 +/- 6.3 (stat) +/- 2.6 (syst) GeV/c2.

Measurement of Particle Production and Inclusive Differential Cross Sections in pbar{p} Collisions at sqrt{s}=1.96 TeV

We report a set of measurements of particle production in inelastic pbar{p} collisions collected with a minimum-bias trigger at the Tevatron Collider with the CDF II experiment. The inclusive charged particle transverse momentum differential cross section is measured, with improved precision, over a range about ten times wider than in previous measurements. The former modeling of the spectrum appears to be incompatible with the high particle momenta observed. The dependence of the charged particle transverse momentum on the event particle multiplicity is analyzed to study the various components of hadron interactions. This is one of the observable variables most poorly reproduced by the available Monte Carlo generators. A first measurement of the event transverse energy sum differential cross section is also reported. A comparison with a Pythia prediction at the hadron level is performed. The inclusive charged particle differential production cross section is fairly well reproduced only in the transverse momentum range available from previous measurements. At higher momentum the agreement is poor. The transverse energy sum is poorly reproduced over the whole spectrum. The dependence of the charged particle transverse momentum on the particle multiplicity needs the introduction of more sophisticated particle production mechanisms, such as multiple parton interactions, in order to be better explained.

Measurement of particle production and inclusive differential cross sections in pp̅ collisions at √s=1.96 TeV

We report a set of measurements of particle production in inelastic pbar{p} collisions collected with a minimum-bias trigger at the Tevatron Collider with the CDF II experiment. The inclusive charged particle transverse momentum differential cross section is measured, with improved precision, over a range about ten times wider than in previous measurements. The former modeling of the spectrum appears to be incompatible with the high particle momenta observed. The dependence of the charged particle transverse momentum on the event particle multiplicity is analyzed to study the various components of hadron interactions. This is one of the observable variables most poorly reproduced by the available Monte Carlo generators. A first measurement of the event transverse energy sum differential cross section is also reported. A comparison with a Pythia prediction at the hadron level is performed. The inclusive charged particle differential production cross section is fairly well reproduced only in the transverse momentum range available from previous measurements. At higher momentum the agreement is poor. The transverse energy sum is poorly reproduced over the whole spectrum. The dependence of the charged particle transverse momentum on the particle multiplicity needs the introduction of more sophisticated particle production mechanisms, such as multiple parton interactions, in order to be better explained.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Identification of Hadronically Decaying Tau Leptons in Searches for Heavy MSSM Higgs Bosons with the CMS Detector at the CERN LHC

This thesis describes methods for the reliable identification of hadronically decaying tau leptons in the search for heavy Higgs bosons of the minimal supersymmetric standard model of particle physics (MSSM). The identification of the hadronic tau lepton decays, i.e. tau-jets, is applied to the gg->bbH, H->tautau and gg->tbH+, H+->taunu processes to be searched for in the CMS experiment at the CERN Large Hadron Collider. Of all the event selections applied in these final states, the tau-jet identification is the single most important event selection criterion to separate the tiny Higgs boson signal from a large number of background events. The tau-jet identification is studied with methods based on a signature of a low charged track multiplicity, the containment of the decay products within a narrow cone, an isolated electromagnetic energy deposition, a non-zero tau lepton flight path, the absence of electrons, muons, and neutral hadrons in the decay signature, and a relatively small tau lepton mass compared to the mass of most hadrons. Furthermore, in the H+->taunu channel, helicity correlations are exploited to separate the signal tau jets from those originating from the W->taunu decays. Since many of these identification methods rely on the reconstruction of charged particle tracks, the systematic uncertainties resulting from the mechanical tolerances of the tracking sensor positions are estimated with care. The tau-jet identification and other standard selection methods are applied to the search for the heavy neutral and charged Higgs bosons in the H->tautau and H+->taunu decay channels. For the H+->taunu channel, the tau-jet identification is redone and optimized with a recent and more detailed event simulation than previously in the CMS experiment. Both decay channels are found to be very promising for the discovery of the heavy MSSM Higgs bosons. The Higgs boson(s), whose existence has not yet been experimentally verified, are a part of the standard model and its most popular extensions. They are a manifestation of a mechanism which breaks the electroweak symmetry and generates masses for particles. Since the H->tautau and H+->taunu decay channels are important for the discovery of the Higgs bosons in a large region of the permitted parameter space, the analysis described in this thesis serves as a probe for finding out properties of the microcosm of particles and their interactions in the energy scales beyond the standard model of particle physics.

On formation, growth and concentrations of air ions

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.

Understanding the chemistry of atmospheric aerosol particle formation via observations of physical properties

It is widely accepted that the global climate is heating up due to human activities, such as burning of fossil fuels. Therefore we find ourselves forced to make decisions on what measures, if any, need to be taken to decrease our warming effect on the planet before any irrevocable damage occurs. Research is being conducted in a variety of fields to better understand all relevant processes governing Earth s climate, and to assess the relative roles of anthropogenic and biogenic emissions into the atmosphere. One of the least well quantified problems is the impact of small aerosol particles (both of anthropogenic and biogenic origin) on climate, through reflecting solar radiation and their ability to act as condensation nuclei for cloud droplets. In this thesis, the compounds driving the biogenic formation of new particles in the atmosphere have been examined through detailed measurements. As directly measuring the composition of these newly formed particles is extremely difficult, the approach was to indirectly study their different characteristics by measuring the hygroscopicity (water uptake) and volatility (evaporation) of particles between 10 and 50 nm. To study the first steps of the formation process in the sub-3 nm range, the nucleation of gaseous precursors to small clusters, the chemical composition of ambient naturally charged ions were measured. The ion measurements were performed with a newly developed mass spectrometer, which was first characterized in the laboratory before being deployed at a boreal forest measurement site. It was also successfully compared to similar, low-resolution instruments. The ambient measurements showed that sulfuric acid clusters dominate the negative ion spectrum during new particle formation events. Sulfuric acid/ammonia clusters were detected in ambient air for the first time in this work. Even though sulfuric acid is believed to be the most important gas phase precursor driving the initial cluster formation, measurements of the hygroscopicity and volatility of growing 10-50 nm particles in Hyytiälä showed an increasing role of organic vapors of a variety of oxidation levels. This work has provided additional insights into the compounds participating both in the initial formation and subsequent growth of atmospheric new aerosol particles. It will hopefully prove an important step in understanding atmospheric gas-to-particle conversion, which, by influencing cloud properties, can have important climate impacts. All available knowledge needs to be constantly updated, summarized, and brought to the attention of our decision-makers. Only by increasing our understanding of all the relevant processes can we build reliable models to predict the long-term effects of decisions made today.

Observations on the first steps of atmospheric particle formation and growth

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.

Observations of production and transport of NOx formed by energetic particle precipitation in the polar night atmosphere

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.

Hybrid Modelling of Titan's Interaction with the Magnetosphere of Saturn

In this dissertation we study the interaction between Saturn's moon Titan and the magnetospheric plasma and magnetic field. The method of research is a three-dimensional computer simulation model, that is used to simulate this interaction. The simulation model used is a hybrid model. Hybrid models enable individual tracking or tracing of ions and also take into account the particle motion in the propagation of the electromagnetic fields. The hybrid model has been developed at the Finnish Meteorological Institute. This thesis gives a general description of the effects that the solar wind has on Earth and other planets of our solar system. Planetary satellites can also have similar interactions with the solar wind but also with the plasma flows of planetary magnetospheres. Titan is clearly the largest among the satellites of Saturn and also the only known satellite with a dense atmosphere. It is the atmosphere that makes Titan's plasma interaction with the magnetosphere of Saturn so unique. Nevertheless, comparisons with the plasma interactions of other solar system bodies are valuable. Detecting charged plasma particles requires in situ measurements obtainable through scientific spacecraft. The Cassini mission has been one of the most remarkable international efforts in space science. Since 2004 the measurements and images obtained from instruments onboard the Cassini spacecraft have increased the scientific knowledge of Saturn as well as its satellites and magnetosphere in a way no one was probably able to predict. The current level of science on Titan is practically unthinkable without the Cassini mission. Many of the observations by Cassini instrument teams have influenced this research both the direct measurements of Titan as well as observations of its plasma environment. The theoretical principles of the hybrid modelling approach are presented in connection to the broader context of plasma simulations. The developed hybrid model is described in detail: e.g. the way the equations of the hybrid model are solved is shown explicitly. Several simulation techniques, such as the grid structure and various boundary conditions, are discussed in detail as well. The testing and monitoring of simulation runs is presented as an essential routine when running sophisticated and complex models. Several significant improvements of the model, that are in preparation, are also discussed. A main part of this dissertation are four scientific articles based on the results of the Titan model. The Titan model developed during the course of the Ph.D. research has been shown to be an important tool to understand Titan's plasma interaction. One reason for this is that the structures of the magnetic field around Titan are very much three-dimensional. The simulation results give a general picture of the magnetic fields in the vicinity of Titan. The magnetic fine structure of Titan's wake as seen in the simulations seems connected to Alfvén waves an important wave mode in space plasmas. The particle escape from Titan is also a major part of these studies. Our simulations show a bending or turning of Titan's ionotail that we have shown to be a direct result of the basic principles in plasma physics. Furthermore, the ion flux from the magnetosphere of Saturn into Titan's upper atmosphere has been studied. The modelled ion flux has asymmetries that would likely have a large impact in the heating in different parts of Titan's upper atmosphere.

Search for Long-Lived Massive Charged Particles in 1.96 TeV pp̅ Collisions

We performed a signature-based search for long-lived charged massive particles (CHAMPs) produced in 1.0 $\rm{fb}^{-1}$ of $\bar{p}p$ collisions at $\sqrt{s}=1.96$ TeV, collected with the CDF II detector using a high transverse-momentum ($p_T$) muon trigger. The search used time-of-flight to isolate slowly moving, high-$p_T$ particles. One event passed our selection cuts with an expected background of $1.9 \pm 0.2$ events. We set an upper bound on the production cross section, and, interpreting this result within the context of a stable scalar top quark model, set a lower limit on the particle mass of 249 GeV/$c^2$ at 95% C.L.