Molecular dynamics studies of nanoparticle impacts

This thesis concerns the dynamics of nanoparticle impacts on solid surfaces. These impacts occur, for instance, in space, where micro- and nanometeoroids hit surfaces of planets, moons, and spacecraft. On Earth, materials are bombarded with nanoparticles in cluster ion beam devices, in order to clean or smooth their surfaces, or to analyse their elemental composition. In both cases, the result depends on the combined effects of countless single impacts. However, the dynamics of single impacts must be understood before the overall effects of nanoparticle radiation can be modelled. In addition to applications, nanoparticle impacts are also important to basic research in the nanoscience field, because the impacts provide an excellent case to test the applicability of atomic-level interaction models to very dynamic conditions. In this thesis, the stopping of nanoparticles in matter is explored using classical molecular dynamics computer simulations. The materials investigated are gold, silicon, and silica. Impacts on silicon through a native oxide layer and formation of complex craters are also simulated. Nanoparticles up to a diameter of 20 nm (315000 atoms) were used as projectiles. The molecular dynamics method and interatomic potentials for silicon and gold are examined in this thesis. It is shown that the displacement cascade expansionmechanism and crater crown formation are very sensitive to the choice of atomic interaction model. However, the best of the current interatomic models can be utilized in nanoparticle impact simulation, if caution is exercised. The stopping of monatomic ions in matter is understood very well nowadays. However, interactions become very complex when several atoms impact on a surface simultaneously and within a short distance, as happens in a nanoparticle impact. A high energy density is deposited in a relatively small volume, which induces ejection of material and formation of a crater. Very high yields of excavated material are observed experimentally. In addition, the yields scale nonlinearly with the cluster size and impact energy at small cluster sizes, whereas in macroscopic hypervelocity impacts, the scaling 2 is linear. The aim of this thesis is to explore the atomistic mechanisms behind the nonlinear scaling at small cluster sizes. It is shown here that the nonlinear scaling of ejected material yield disappears at large impactor sizes because the stopping mechanism of nanoparticles gradually changes to the same mechanism as in macroscopic hypervelocity impacts. The high yields at small impactor size are due to the early escape of energetic atoms from the hot region. In addition, the sputtering yield is shown to depend very much on the spatial initial energy and momentum distributions that the nanoparticle induces in the material in the first phase of the impact. At the later phases, the ejection of material occurs by several mechanisms. The most important mechanism at high energies or at large cluster sizes is atomic cluster ejection from the transient liquid crown that surrounds the crater. The cluster impact dynamics detected in the simulations are in agreement with several recent experimental results. In addition, it is shown that relatively weak impacts can induce modifications on the surface of an amorphous target over a larger area than was previously expected. This is a probable explanation for the formation of the complex crater shapes observed on these surfaces with atomic force microscopy. Clusters that consist of hundreds of thousands of atoms induce long-range modifications in crystalline gold.

Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 0.9 and 2.36 TeV

Measurements of inclusive charged-hadron transverse-momentum and pseudorapidity distributions are presented for proton-proton collisions at sqrt(s) = 0.9 and 2.36 TeV. The data were collected with the CMS detector during the LHC commissioning in December 2009. For non-single-diffractive interactions, the average charged-hadron transverse momentum is measured to be 0.46 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 0.9 TeV and 0.50 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 2.36 TeV, for pseudorapidities between -2.4 and +2.4. At these energies, the measured pseudorapidity densities in the central region, dN(charged)/d(eta) for |eta|

Remote sensing of leaf area index: enhanced retrieval from close-range and remotely sensed optical observations

A wide range of models used in agriculture, ecology, carbon cycling, climate and other related studies require information on the amount of leaf material present in a given environment to correctly represent radiation, heat, momentum, water, and various gas exchanges with the overlying atmosphere or the underlying soil. Leaf area index (LAI) thus often features as a critical land surface variable in parameterisations of global and regional climate models, e.g., radiation uptake, precipitation interception, energy conversion, gas exchange and momentum, as all areas are substantially determined by the vegetation surface. Optical wavelengths of remote sensing are the common electromagnetic regions used for LAI estimations and generally for vegetation studies. The main purpose of this dissertation was to enhance the determination of LAI using close-range remote sensing (hemispherical photography), airborne remote sensing (high resolution colour and colour infrared imagery), and satellite remote sensing (high resolution SPOT 5 HRG imagery) optical observations. The commonly used light extinction models are applied at all levels of optical observations. For the sake of comparative analysis, LAI was further determined using statistical relationships between spectral vegetation index (SVI) and ground based LAI. The study areas of this dissertation focus on two regions, one located in Taita Hills, South-East Kenya characterised by tropical cloud forest and exotic plantations, and the other in Gatineau Park, Southern Quebec, Canada dominated by temperate hardwood forest. The sampling procedure of sky map of gap fraction and size from hemispherical photographs was proven to be one of the most crucial steps in the accurate determination of LAI. LAI and clumping index estimates were significantly affected by the variation of the size of sky segments for given zenith angle ranges. On sloping ground, gap fraction and size distributions present strong upslope/downslope asymmetry of foliage elements, and thus the correction and the sensitivity analysis for both LAI and clumping index computations were demonstrated. Several SVIs can be used for LAI mapping using empirical regression analysis provided that the sensitivities of SVIs at varying ranges of LAI are large enough. Large scale LAI inversion algorithms were demonstrated and were proven to be a considerably efficient alternative approach for LAI mapping. LAI can be estimated nonparametrically from the information contained solely in the remotely sensed dataset given that the upper-end (saturated SVI) value is accurately determined. However, further study is still required to devise a methodology as well as instrumentation to retrieve on-ground green leaf area index . Subsequently, the large scale LAI inversion algorithms presented in this work can be precisely validated. Finally, based on literature review and this dissertation, potential future research prospects and directions were recommended.

Heavy-light mesons on a lattice

Several excited states of Ds and Bs mesons have been discovered in the last six years: BaBar, Cleo and Belle discovered the very narrow states D(s0)*(2317)+- and D(s1)(2460)+- in 2003, and CDF and DO Collaborations reported the observation of two narrow Bs resonances, B(s1)(5830)0 and B*(s2)(5840)0 in 2007. To keep up with experiment, meson excited states should be studied from the theoretical aspect as well. The theory that describes the interaction between quarks and gluons is quantum chromodynamics (QCD). In this thesis the properties of the meson states are studied using the discretized version of the theory - lattice QCD. This allows us to perform QCD calculations from first principles, and "measure" not just energies but also the radial distributions of the states on the lattice. This gives valuable theoretical information on the excited states, as we can extract the energy spectrum of a static-light meson up to D wave states (states with orbital angular momentum L=2). We are thus able to predict where some of the excited meson states should lie. We also pay special attention to the order of the states, to detect possible inverted spin multiplets in the meson spectrum, as predicted by H. Schnitzer in 1978. This inversion is connected to the confining potential of the strong interaction. The lattice simulations can also help us understand the strong interaction better, as the lattice data can be treated as "experimental" data and used in testing potential models. In this thesis an attempt is made to explain the energies and radial distributions in terms of a potential model based on a one-body Dirac equation. The aim is to get more information about the nature of the confining potential, as well as to test how well the one-gluon exchange potential explains the short range part of the interaction.

Canopy processes, fluxes and microclimate in a pine forest

Interaction between forests and the atmosphere occurs by radiative and turbulent transport. The fluxes of energy and mass between surface and the atmosphere directly influence the properties of the lower atmosphere and in longer time scales the global climate. Boreal forest ecosystems are central in the global climate system, and its responses to human activities, because they are significant sources and sinks of greenhouse gases and of aerosol particles. The aim of the present work was to improve our understanding on the existing interplay between biologically active canopy, microenvironment and turbulent flow and quantify. In specific, the aim was to quantify the contribution of different canopy layers to whole forest fluxes. For this purpose, long-term micrometeorological and ecological measurements made in a Scots pine (Pinus sylvestris) forest at SMEAR II research station in Southern Finland were used. The properties of turbulent flow are strongly modified by the interaction between the canopy elements: momentum is efficiently absorbed in the upper layers of the canopy, mean wind speed and turbulence intensities decrease rapidly towards the forest floor and power spectra is modulated by spectral short-cut . In the relative open forest, diabatic stability above the canopy explained much of the changes in velocity statistics within the canopy except in strongly stable stratification. Large eddies, ranging from tens to hundred meters in size, were responsible for the major fraction of turbulent transport between a forest and the atmosphere. Because of this, the eddy-covariance (EC) method proved to be successful for measuring energy and mass exchange inside a forest canopy with exception of strongly stable conditions. Vertical variations of within canopy microclimate, light attenuation in particular, affect strongly the assimilation and transpiration rates. According to model simulations, assimilation rate decreases with height more rapidly than stomatal conductance (gs) and transpiration and, consequently, the vertical source-sink distributions for carbon dioxide (CO2) and water vapor (H2O) diverge. Upscaling from a shoot scale to canopy scale was found to be sensitive to chosen stomatal control description. The upscaled canopy level CO2 fluxes can vary as much as 15 % and H2O fluxes 30 % even if the gs models are calibrated against same leaf-level dataset. A pine forest has distinct overstory and understory layers, which both contribute significantly to canopy scale fluxes. The forest floor vegetation and soil accounted between 18 and 25 % of evapotranspiration and between 10 and 20 % of sensible heat exchange. Forest floor was also an important deposition surface for aerosol particles; between 10 and 35 % of dry deposition of particles within size range 10 30 nm occurred there. Because of the northern latitudes, seasonal cycle of climatic factors strongly influence the surface fluxes. Besides the seasonal constraints, partitioning of available energy to sensible and latent heat depends, through stomatal control, on the physiological state of the vegetation. In spring, available energy is consumed mainly as sensible heat and latent heat flux peaked about two months later, in July August. On the other hand, annual evapotranspiration remains rather stable over range of environmental conditions and thus any increase of accumulated radiation affects primarily the sensible heat exchange. Finally, autumn temperature had strong effect on ecosystem respiration but its influence on photosynthetic CO2 uptake was restricted by low radiation levels. Therefore, the projected autumn warming in the coming decades will presumably reduce the positive effects of earlier spring recovery in terms of carbon uptake potential of boreal forests.

Observation of the Ωb- baryon and measurement of the properties of the Ξb- and Ωb- baryons

We report the observation of the bottom, doubly-strange baryon Omega^-_b through the decay chain Omega^-_b -> J/psi Omega^-, where J/psi -> mu^+ mu^-, Omega^- -> Lambda K^-, and Lambda -> p pi^-, using 4.2 fb^{-1} of data from p\bar p collisions at sqrt{s}=1.96 TeV, and recorded with the Collider Detector at Fermilab. A signal is observed whose probability of arising from a background fluctuation is 4.0 * 10^{-8}, or 5.5 Gaussian standard deviations. The Omega^-_b mass is measured to be 6054.4 +/- 6.8 (stat.) +/- 0.9 (syst.) MeV/c^2. The lifetime of the Omega^-_b baryon is measured to be 1.13^{+0.53}_{-0.40}(stat.) +/- 0.02(syst.)$ ps. In addition, for the \Xi^-_b baryon we measure a mass of 5790.9 +/- 2.6(stat.) +/- 0.8(syst.) MeV/c^2 and a lifetime of 1.56^{+0.27}_{-0.25}(stat.) +/-0.02(syst.) ps. Under the assumption that the \Xi_b^- and \Omega_b^- are produced with similar kinematic distributions to the \Lambda^0_b baryon, we find sigma(Xi_b^-) B(Xi_b^- -> J/psi Xi^-)}/ sigma(Lambda^0_b) B(Lambda^0_b -> J/psi Lambda)} = 0.167^{+0.037}_{-0.025}(stat.) +/-0.012(syst.) and sigma(Omega_b^-) B(Omega_b^- -> J/psi Omega^-)/ sigma(Lambda^0_b) B(Lambda^0_b -> J/psi Lambda)} = 0.045^{+0.017}_{-0.012}(stat.) +/- 0.004(syst.) for baryons produced with transverse momentum in the range of 6-20 GeV/c.

Evaluating the Predictability of the Volatility Smile Using Return Distributions

In this paper, we examine the predictability of observed volatility smiles in three major European index options markets, utilising the historical return distributions of the respective underlying assets. The analysis involves an application of the Black (1976) pricing model adjusted in accordance with the Jarrow-Rudd methodology as proposed in 1982. Thereby we adjust the expected future returns for the third and fourth central moments as these represent deviations from normality in the distributions of observed returns. Thus, they are considered one possible explanation to the existence of the smile. The obtained results indicate that the inclusion of the higher moments in the pricing model to some extent reduces the volatility smile, compared with the unadjusted Black-76 model. However, as the smile is partly a function of supply, demand, and liquidity, and as such intricate to model, this modification does not appear sufficient to fully capture the characteristics of the smile.

Toxicant distributions and impact models in environmental risk analysis of waste sites

Myrkyllisten aineiden jakaumat ja vaikutusmallit jätealueiden ympäristöriskien analyysissä.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Structure of Relativistic States

QCD factorization in the Bjorken limit allows to separate the long-distance physics from the hard subprocess. At leading twist, only one parton in each hadron is coherent with the hard subprocess. Higher twist effects increase as one of the active partons carries most of the longitudinal momentum of the hadron, x -> 1. In the Drell-Yan process \pi N -> \mu^- mu^+ + X, the polarization of the virtual photon is observed to change to longitudinal when the photon carries x_F > 0.6 of the pion. I define and study the Berger-Brodsky limit of Q^2 -> \infty with Q^2(1-x) fixed. A new kind of factorization holds in the Drell-Yan process in this limit, in which both pion valence quarks are coherent with the hard subprocess, the virtual photon is longitudinal rather than transverse, and the cross section is proportional to a multiparton distribution. Generalized parton distributions contain information on the longitudinal momentum and transverse position densities of partons in a hadron. Transverse charge densities are Fourier transforms of the electromagnetic form factors. I discuss the application of these methods to the QED electron, studying the form factors, charge densities and spin distributions of the leading order |e\gamma> Fock state in impact parameter and longitudinal momentum space. I show how the transverse shape of any virtual photon induced process, \gamma^*(q)+i -> f, may be measured. Qualitative arguments concerning the size of such transitions have been previously made in the literature, but without a precise analysis. Properly defined, the amplitudes and the cross section in impact parameter space provide information on the transverse shape of the transition process.