Bayesian analysis of community dynamics

Elucidating the mechanisms responsible for the patterns of species abundance, diversity, and distribution within and across ecological systems is a fundamental research focus in ecology. Species abundance patterns are shaped in a convoluted way by interplays between inter-/intra-specific interactions, environmental forcing, demographic stochasticity, and dispersal. Comprehensive models and suitable inferential and computational tools for teasing out these different factors are quite limited, even though such tools are critically needed to guide the implementation of management and conservation strategies, the efficacy of which rests on a realistic evaluation of the underlying mechanisms. This is even more so in the prevailing context of concerns over climate change progress and its potential impacts on ecosystems. This thesis utilized the flexible hierarchical Bayesian modelling framework in combination with the computer intensive methods known as Markov chain Monte Carlo, to develop methodologies for identifying and evaluating the factors that control the structure and dynamics of ecological communities. These methodologies were used to analyze data from a range of taxa: macro-moths (Lepidoptera), fish, crustaceans, birds, and rodents. Environmental stochasticity emerged as the most important driver of community dynamics, followed by density dependent regulation; the influence of inter-specific interactions on community-level variances was broadly minor. This thesis contributes to the understanding of the mechanisms underlying the structure and dynamics of ecological communities, by showing directly that environmental fluctuations rather than inter-specific competition dominate the dynamics of several systems. This finding emphasizes the need to better understand how species are affected by the environment and acknowledge species differences in their responses to environmental heterogeneity, if we are to effectively model and predict their dynamics (e.g. for management and conservation purposes). The thesis also proposes a model-based approach to integrating the niche and neutral perspectives on community structure and dynamics, making it possible for the relative importance of each category of factors to be evaluated in light of field data.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Quorum sensing in the plant pathogen Erwinia carotovora subsp. carotovora

Erwinia carotovora subsp. carotovora (Ecc) is a Gram-negative enterobacterium that causes soft-rot in potato and other crops. The main virulence determinants, the extracellular plant cell wall -degrading enzymes (PCWDEs), lead to plant tissue maceration. In order to establish a successful infection the production of PCWDEs are controlled by a complex regulatory network, including both specific and global activators and repressors. One of the most important virulence regulation systems in Ecc is mediated by quorum sensing (QS), which is a population density -dependent cell-to-cell communication mechanism used by many Gram-negative bacteria. In these bacteria N-acylhomoserine lactones (AHSL), act as diffusible signaling molecules enabling communication between bacterial cells. The AHSLs are structurally diverse and differ in their acyl chain length. This gives the bacteria signaling specificity and enables the recognition and communication within its own species. In order to detect and respond to the AHSLs the bacteria use QS regulators, LuxR-type proteins. The aim of this study was to get a deeper understanding of the Ecc QS system. In the first part of the study we showed that even different strains of Ecc use different dialects and of physiological concentrations, only the cognate AHSL with the correct acyl chain is recognized as a signal that can switch on virulence genes. The molecular basis of the substrate specificity of the AHSL synthase ExpI was investigated in order to recognize the acyl chain length specificity determinants of distinct AHSL synthases. Several critical residues that define the size of the substrate-binding pocket were identified. We demonstrated that in the ExpISCC1 mutations M127T and F69L are sufficient to change the N-3-oxohexanoyl-L-homoserine lactone producing ExpISCC1 to an N-3-oxooctanoyl-L-homoserine lactone (3-oxo-C8-HSL) producing enzyme. In the second study the means of sensing specificity and response to the AHSL signaling molecule were investigated. We demonstrated that the AHSL receptor ExpR1 of Ecc strain SCC3193 has strict specificity for the cognate AHSL 3-oxo-C8-HSL. In addition we identified a second AHSL receptor ExpR2 with a novel property to sense AHSLs with different acyl chain lengths. In the absence of AHSLs ExpR1 and ExpR2 were found to act synergistically to repress the virulence gene expression. This repression was shown to be released by addition of AHSLs and appears to be largely mediated by the global negative regulator RsmA. In the third study random transposon mutagenesis was used to widen the knowledge of the Ecc QS regulon. Two new QS-controlled target genes, encoding a DNA-binding regulator Hor and a plant ferredoxin-like protein FerE, were identified. The QS control of the identified genes was executed by the QS regulators ExpR1 and ExpR2 and as expression of PCWDE genes mediated by the RsmA repressor. Hor was shown to contribute to bacterial virulence at least partly through its control of PCWDE production, while FerE was shown to contribute to oxidative stress tolerance and in planta fitness of the bacteria. In addition our results suggest that QS is central to the control of oxidative stress tolerance in Ecc. In conclusion, these results indicate that Ecc strain SCC3193 is able to react and respond both to the cognate AHSL signal and the signals produced by other bacterial species, in order to control a wide variety of functions in the plant pathogen Ecc.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

Individuals on the Move : Body Condition Dependent Dispersal and Quasi-Local Competition in Metapopulations

Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

Computationally Efficient Methods for MDL-Optimal Density Estimation and Data Clustering

The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

Production of F4 Fimbrial Adhesin in Plants: a Model for Oral Porcine Vaccine against Enterotoxigenic Escherichia coli

F4 fimbriae of enterotoxigenic Escherichia coli (ETEC) are highly stable multimeric structures with a capacity to evoke mucosal immune responses. With these characters F4 offer a unique model system to study oral vaccination against ETEC-induced porcine postweaning diarrhea. Postweaning diarrhea is a major problem in piggeries worldwide and results in significant economic losses. No vaccine is currently available to protect weaned piglets against ETEC infections. Transgenic plants provide an economically feasible platform for large-scale production of vaccine antigens for animal health. In this study, the capacity of transgenic plants to produce FaeG protein, the major structural subunit and adhesin of F4 fimbria, was evaluated. Using the model plant tobacco, the optimal subcellular location for FaeG accumulation was examined. Targeting of FaeG into chloroplasts offered a superior accumulation level of 1% of total soluble proteins (TSP) over the other investigated subcellular locations, namely, the endoplasmic reticulum and the apoplast. Moreover, we determined whether the FaeG protein, when isolated from its fimbrial background and produced in a plant cell, would retain the key properties of an oral vaccine, i.e. stability in gastrointestinal conditions, binding to porcine intestinal F4 receptors (F4R), and inhibition of the F4-possessing (F4+) ETEC attachment to F4R. The chloroplast-derived FaeG protein did show resistance against low pH and proteolysis in the simulated gastrointestinal conditions and was able to bind to the F4R, subsequently inhibiting the F4+ ETEC binding in a dose-dependent manner. To investigate the oral immunogenicity of FaeG protein, the edible crop plant alfalfa was transformed with the chloroplast-targeting construct and equally to tobacco plants, a high-yield FaeG accumulation of 1% of TSP was obtained. A similar yield was also obtained in the seeds of barley, a valuable crop plant, when the FaeG-encoding gene was expressed under an endosperm-specific promoter and subcellularly targeted into the endoplasmic reticulum. Furthermore, desiccated alfalfa plants and barley grains were shown to have a capacity to store FaeG protein in a stable form for years. When the transgenic alfalfa plants were administred orally to weaned piglets, slight F4-specific systemic and mucosal immune responses were induced. Co-administration of the transgenic alfalfa and the mucosal adjuvant cholera toxin enhanced the F4-specific immune response; the duration and number of F4+ E. coli excretion following F4+ ETEC challenge were significantly reduced as compared with pigs that had received nontransgenic plant material. In conclusion, the results suggest that transgenic plants producing the FaeG subunit protein could be used for production and delivery of oral vaccines against porcine F4+ ETEC infections. The findings here thus present new approaches to develop the vaccination strategy against porcine postweaning diarrhea.

Molecular details of phage phi6 RNA-dependent RNA synthesis

For most RNA viruses RNA-dependent RNA polymerases (RdRPs) encoded by the virus are responsible for the entire RNA metabolism. Thus, RdRPs are critical components in the viral life cycle. However, it is not fully understood how these important enzymes function during viral replication. Double-stranded RNA (dsRNA) viruses perform the synthesis of their RNA genome within a proteinacous viral particle containing an RdRP as a minor constituent. The phi6 bacteriophage is the best-studied dsRNA virus, providing an excellent background for studies of its RNA synthesis. The purified recombinant phi6 RdRP is highly active in vitro and it possesses both RNA replication and transcription activities. The crystal structure of the phi6 polymerase, solved in complex with a number of ligands, provides a working model for detailed in vitro studies of RNA-dependent RNA polymerization. In this thesis, the primer-independent initiation of the phi6 RdRP was studied in vitro using biochemical and structural methods. A C-terminal, four-amino-acid-long loop protruding into the central cavity of the phi6 RdRP has been suggested to stabilize the incoming nucleotides of the initiation complex formation through stacking interactions. A similar structural element has been found from several other viral RdRPs. In this thesis, this so-called initiation platform loop was subjected to site-directed mutagenesis to address its role in the initiation. It was found that the initiation mode of the mutants is primer-dependent, requiring either an oligonucleotide primer or a back-priming initiation mechanism for the RNA synthesis. The crystal structure of a mutant RdRP with altered initiation platform revealed a set of contacts important for primer-independent initiation. Since phi6 RdRP is structurally and functionally homologous to several viral RdRPs, among them the hepatitis C virus RdRP, these results provide further general insight to understand primer-independent initiation. In this study it is demonstrated that manganese phasing could be used as a practical tool for solving structures of large proteins with a bound manganese ion. The phi6 RdRP was used as a case study to obtain phases for crystallographic analysis. Manganese ions are naturally bound to the phi6 RdRP at the palm domain of the enzyme. In a crystallographic experiment, X-ray diffraction data from a phi6 RdRP crystal were collected at a wavelength of 1.89 Å, which is the K edge of manganese. With this data an automatically built model of the core region of the protein could be obtained. Finally, in this work terminal nucleotidyl transferase (TNTase) activity of the phi6 RdRP was documented in the isolated polymerase as well as in the viral particle. This is the first time that such an activity has been reported in a polymerase of a dsRNA virus. The phi6 RdRP used uridine triphosphates as the sole substrate in a TNTase reaction but could accept several heterologous templates. The RdRP was able to add one or a few non-templated nucleotides to the 3' end of the single- or double-stranded RNA substrate. Based on the results on particle-mediated TNTase activity and previous structural information of the polymerase, a model for termination of the RNA-dependent RNA synthesis is suggested in this thesis.

The effect of lignin content and lignin modification on Norway spruce wood properties and decay resistance

Three different Norway spruce cutting clones growing in three environments with different soil and climatic conditions were studied. The purpose was to follow variation in the radial growth rate, wood properties and lignin content and to modify wood lignin with a natural monolignol, coniferyl alcohol, by making use of inherent wood peroxidases. In addition, the incorporation of chlorinated anilines into lignin was studied with synthetic model compounds and synthetic lignin preparations to show whether unnatural compounds originating from pesticides could be bound in the lignin polymer. The lignin content of heartwood, sapwood and earlywood was determined by applying Fourier transform infrared (FTIR) spectroscopy and a principal component regression (PCR) technique. Wood blocks were treated with coniferyl alcohol by using a vacuum impregnation method. The effect of impregnation was assessed by FTIR and by a fungal decay test. Trees from a fertile site showed the highest growth rate and sapwood lignin content and the lowest latewood proportion, weight density and modulus of rupture (MOR). Trees from a medium fertile site had the lowest growth rate and the highest latewood proportion, weight density, modulus of elasticity (MOE) and MOR. The most rapidly growing clone showed the lowest latewood proportion, weight density, MOE and MOR. The slowest growing clone had the lowest sapwood lignin content and the highest latewood proportion, weight density, MOE and MOR. Differences between the sites and clones were small, while fairly large variation was found between the individual trees and growing seasons. The cutting clones maintained clone-dependent wood properties in the different growing sites although variation between trees was high and climatic factors affected growth. The coniferyl alcohol impregnation increased the content of different lignin-type phenolic compounds in the wood as well as wood decay resistance against a white-rot fungus, Coriolus versicolor. During the synthetic lignin preparation 3,4-dichloroaniline became bound by a benzylamine bond to β-O-4 structures in the polymer and it could not be released by mild acid hydrolysis. The natural monolignol, coniferyl alcohol, and chlorinated anilines could be incorporated into the lignin polymer in vivo and in vitro, respectively.

Monte Carlo Simulations of Molecular Clusters in Nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Aspects of Inflationary Models at Low Energy Scales

Cosmological inflation is the dominant paradigm in explaining the origin of structure in the universe. According to the inflationary scenario, there has been a period of nearly exponential expansion in the very early universe, long before the nucleosynthesis. Inflation is commonly considered as a consequence of some scalar field or fields whose energy density starts to dominate the universe. The inflationary expansion converts the quantum fluctuations of the fields into classical perturbations on superhorizon scales and these primordial perturbations are the seeds of the structure in the universe. Moreover, inflation also naturally explains the high degree of homogeneity and spatial flatness of the early universe. The real challenge of the inflationary cosmology lies in trying to establish a connection between the fields driving inflation and theories of particle physics. In this thesis we concentrate on inflationary models at scales well below the Planck scale. The low scale allows us to seek for candidates for the inflationary matter within extensions of the Standard Model but typically also implies fine-tuning problems. We discuss a low scale model where inflation is driven by a flat direction of the Minimally Supersymmetric Standard Model. The relation between the potential along the flat direction and the underlying supergravity model is studied. The low inflationary scale requires an extremely flat potential but we find that in this particular model the associated fine-tuning problems can be solved in a rather natural fashion in a class of supergravity models. For this class of models, the flatness is a consequence of the structure of the supergravity model and is insensitive to the vacuum expectation values of the fields that break supersymmetry. Another low scale model considered in the thesis is the curvaton scenario where the primordial perturbations originate from quantum fluctuations of a curvaton field, which is different from the fields driving inflation. The curvaton gives a negligible contribution to the total energy density during inflation but its perturbations become significant in the post-inflationary epoch. The separation between the fields driving inflation and the fields giving rise to primordial perturbations opens up new possibilities to lower the inflationary scale without introducing fine-tuning problems. The curvaton model typically gives rise to relatively large level of non-gaussian features in the statistics of primordial perturbations. We find that the level of non-gaussian effects is heavily dependent on the form of the curvaton potential. Future observations that provide more accurate information of the non-gaussian statistics can therefore place constraining bounds on the curvaton interactions.

Studies on orographic effects in a numerical weather prediction model

Numerical models, used for atmospheric research, weather prediction and climate simulation, describe the state of the atmosphere over the heterogeneous surface of the Earth. Several fundamental properties of atmospheric models depend on orography, i.e. on the average elevation of land over a model area. The higher is the models' resolution, the more the details of orography directly influence the simulated atmospheric processes. This sets new requirements for the accuracy of the model formulations with respect to the spatially varying orography. Orography is always averaged, representing the surface elevation within the horizontal resolution of the model. In order to remove the smallest scales and steepest slopes, the continuous spectrum of orography is normally filtered (truncated) even more, typically beyond a few gridlengths of the model. This means, that in the numerical weather prediction (NWP) models, there will always be subgridscale orography effects, which cannot be explicitly resolved by numerical integration of the basic equations, but require parametrization. In the subgrid-scale, different physical processes contribute in different scales. The parametrized processes interact with the resolved-scale processes and with each other. This study contributes to building of a consistent, scale-dependent system of orography-related parametrizations for the High Resolution Limited Area Model (HIRLAM). The system comprises schemes for handling the effects of mesoscale (MSO) and small-scale (SSO) orographic effects on the simulated flow and a scheme of orographic effects on the surface-level radiation fluxes. Representation of orography, scale-dependencies of the simulated processes and interactions between the parametrized and resolved processes are discussed. From the high-resolution digital elevation data, orographic parameters are derived for both momentum and radiation flux parametrizations. Tools for diagnostics and validation are developed and presented. The parametrization schemes applied, developed and validated in this study, are currently being implemented into the reference version of HIRLAM.

Primordial Perturbations from a Self-interacting Curvaton

Inflation is a period of accelerated expansion in the very early universe, which has the appealing aspect that it can create primordial perturbations via quantum fluctuations. These primordial perturbations have been observed in the cosmic microwave background, and these perturbations also function as the seeds of all large-scale structure in the universe. Curvaton models are simple modifications of the standard inflationary paradigm, where inflation is driven by the energy density of the inflaton, but another field, the curvaton, is responsible for producing the primordial perturbations. The curvaton decays after inflation as ended, where the isocurvature perturbations of the curvaton are converted into adiabatic perturbations. Since the curvaton must decay, it must have some interactions. Additionally realistic curvaton models typically have some self-interactions. In this work we consider self-interacting curvaton models, where the self-interaction is a monomial in the potential, suppressed by the Planck scale, and thus the self-interaction is very weak. Nevertheless, since the self-interaction makes the equations of motion non-linear, it can modify the behaviour of the model very drastically. The most intriguing aspect of this behaviour is that the final properties of the perturbations become highly dependent on the initial values. Departures of Gaussian distribution are important observables of the primordial perturbations. Due to the non-linearity of the self-interacting curvaton model and its sensitivity to initial conditions, it can produce significant non-Gaussianity of the primordial perturbations. In this work we investigate the non-Gaussianity produced by the self-interacting curvaton, and demonstrate that the non-Gaussianity parameters do not obey the analytically derived approximate relations often cited in the literature. Furthermore we also consider a self-interacting curvaton with a mass in the TeV-scale. Motivated by realistic particle physics models such as the Minimally Supersymmetric Standard Model, we demonstrate that a curvaton model within the mass range can be responsible for the observed perturbations if it can decay late enough.

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

Monte Carlo simulations of molecular clusters in nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.