Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Effects of living crown reduction on needle element status of Scots pine

A wide range of biotic and abiotic factors, operating over different time perspectives and intensities, cause defoliation and a rapid decrease in the crown size of trees. Scleroderris canker disease [Gremmeniella abietina (Lagerb.) Morelet] has caused widespread crown reduction and tree mortality in Scots pine (Pinus sylvestris L) in forests in Scandinavia during the last three decades. In the 1980's, attempts were made to show, on the basis of the higher foliar N and S concentrations of affected pines in the diseased area, that sulphur and nitrogen deposition predispose trees to G. abietina. Unfortunately, in many studies on defoliated trees, exceptionally high or low needle mineral nutrient concentrations are still often interpreted as one of the causes of tree injury and not, conversely, as the result. In this thesis, three different field experiments, with foliar analysis as the main study method, were conducted in order to asses the possible long-term effects of living crown reduction on the needle nutrient concentrations of Scots pine trees in southern Finland. The crown ratio and length of the living crown were used to estimate the amount of defoliation in the reduced canopies. The material for the partial studies was collected and a total of 968 foliar samples were analysed individually (15-17 elements/sample) on a total of 488 sample trees (140 diseased, 116 pruned and 232 control trees) during the years 1987-1996 in 13 Scots pine stands. All the three experiments of this thesis provided significant evidence that severe, disease-induced defoliation or artificial pruning of the living branches can induce long-lasting nutritional changes in the foliage of the recovering trees under the typical growing conditions for Scots pine. The foliar concentrations of all the 17 mineral nutrients/elements analysed were affected, to a varying degree, by artificial pruning during the following three years. Although Scots pine, as an evergreen conifer, is considered to have low induced chemical responses to defoliation, this study proved experimentally under natural forest conditions that severe artificial pruning or disease-induced defoliation of Scots pine trees may induce biologically significant changes in the concentrations of most of the important macro- and micronutrients, as well as of carbon, in refoliated needles. Concerning the studies in this thesis, I find the results significant in providing new information about the long-term effects of rapid living crown reduction on the foliar nutrient and element status of Scots pine trees. Key words: Foliar analysis, defoliation, needle loss, pruning, nutrients, Pinus sylvestris, Gremmeniella abietina

The white-rot fungi Phlebia radiata and Dichomitus squalens in wood-based cultures: expression of laccases, lignin peroxidases, and oxalate decarboxylase

Basidiomycetous white-rot fungi are the only organisms that can efficiently decompose all the components of wood. Moreover, white-rot fungi possess the ability to mineralize recalcitrant lignin polymer with their extracellular, oxidative lignin-modifying enzymes (LMEs), i.e. laccase, lignin peroxidase (LiP), manganese peroxidase (MnP), and versatile peroxidase (VP). Within one white-rot fungal species LMEs are typically present as several isozymes encoded by multiple genes. This study focused on two effi cient lignin-degrading white-rot fungal species, Phlebia radiata and Dichomitus squalens. Molecular level knowledge of the LMEs of the Finnish isolate P. radiata FBCC43 (79, ATCC 64658) was complemented with cloning and characterization of a new laccase (Pr-lac2), two new LiP-encoding genes (Pr-lip1, Pr-lip4), and Pr-lip3 gene that has been previously described only at cDNAlevel. Also, two laccase-encoding genes (Ds-lac3, Ds-lac4) of D. squalens were cloned and characterized for the first time. Phylogenetic analysis revealed close evolutionary relationships between the P. radiata LiP isozymes. Distinct protein phylogeny for both P. radiata and D. squalens laccases suggested different physiological functions for the corresponding enzymes. Supplementation of P. radiata liquid culture medium with excess Cu2+ notably increased laccase activity and good fungal growth was achieved in complex medium rich with organic nitrogen. Wood is the natural substrate of lignin-degrading white-rot fungi, supporting production of enzymes and metabolites needed for fungal growth and the breakdown of lignocellulose. In this work, emphasis was on solid-state wood or wood-containing cultures that mimic the natural growth conditions of white-rot fungi. Transcript analyses showed that wood promoted expression of all the presently known LME-encoding genes of P. radiata and laccase-encoding genes of D. squalens. Expression of the studied individual LME-encoding genes of P. radiata and D. squalens was unequal in transcript quantities and apparently time-dependent, thus suggesting the importance of several distinct LMEs within one fungal species. In addition to LMEs, white-rot fungi secrete other compounds that are important in decomposition of wood and lignin. One of these compounds is oxalic acid, which is a common metabolite of wood-rotting fungi. Fungi produce also oxalic-acid degrading enzymes of which the most widespread is oxalate decarboxylase (ODC). However, the role of ODC in fungi is still ambiguous with propositions from regulation of intra and extracellular oxalic acid levels to a function in primary growth and concomitant production of ATP. In this study, intracellular ODC activity was detected in four white-rot fungal species, and D. squalens showed the highest ODC activity upon exposure to oxalic acid. Oxalic acid was the most common organic acid secreted by the ODC-positive white-rot fungi and the only organic acid detected in wood cultures. The ODC-encoding gene Ds-odc was cloned from two strains of D. squalens showing the first characterization of an odc-gene from a white-rot polypore species. Biochemical properties of the D. squalens ODC resembled those described for other basidiomycete ODCs. However, the translated amino acid sequence of Ds-odc has a novel N-terminal primary structure with a repetitive Ala-Ser-rich region of ca 60 amino acid residues in length. Expression of the Ds-odc transcripts suggested a constitutive metabolic role for the corresponding ODC enzyme. According to the results, it is proposed that ODC may have an essential implication for the growth and basic metabolism of wood-decaying fungi.

Dispersal and related life history traits in the Glanville fritillary butterfly

Most studies of life history evolution are based on the assumption that species exist at equilibrium and spatially distinct separated populations. In reality, this is rarely the case, as populations are often spatially structured with ephemeral local populations. Therefore, the characteristics of metapopulations should be considered while studying factors affecting life history evolution. Theoretical studies have examined spatial processes shaping the evolution of life history traits to some extent, but there is little empirical data and evidence to investigate model predictions. In my thesis I have tried to bridge the gap between theoretical and empirical studies by using the well-known Glanville fritillary (Melitaea cinxia) metapopulation as a model system. The long-term persistence of classic metapopulations requires sufficient dispersal to establish new local populations to compensate for local extinctions. Previous studies on the Glanville fritillary have shown that females establishing new populations are not a random sample from the metapopulation, but they are in fact more dispersive than females in old populations. Many other life-history traits, such as body size, fecundity and lifespan, may be related to dispersal rate. Therefore, I examined a range of correlated traits for their evolutionary and ecological consequences. I was particularly interested in how the traits vary under natural environmental conditions, hence all studies were conducted in a large (32 x 26 m) outdoor population cage built upon a natural habitat patch. Individuals for the experiments were sampled from newly-established and old populations within a large metapopulation. Results show that females originating from newly-established populations had higher within-habitat patch mobility than females from old populations. I showed that dispersal rate is heritable and that flight activity is related to variation in a gene encoding the glycolytic enzyme phosphoglucose isomerase. Both among-individual and among-population variation in dispersal are correlated with the reproductive performance of females, though I found no evidence for a trade-off between dispersal and fecundity in terms of lifetime egg production or clutch size. Instead, the results suggest that highly dispersive females from newly-established populations have a shorter lifespan than females from old populations, and that dispersive females may pay a cost in terms of reduced lifetime reproductive success due to increased time spent outside habitat patches. In summary, the results of this thesis show that genotype-dependent dispersal rate correlates with other life history traits in the Glanville fritillary, and that the rapid turnover of local populations (extinctions and re-colonisations) is likely to be the mechanism that maintains phenotypic variation in many life history traits at the metapopulation level.

Theoretical modeling of ionospheric electrodynamics including induction effects

This thesis deals with theoretical modeling of the electrodynamics of auroral ionospheres. In the five research articles forming the main part of the thesis we have concentrated on two main themes: Development of new data-analysis techniques and study of inductive phenomena in the ionospheric electrodynamics. The introductory part of the thesis provides a background for these new results and places them in the wider context of ionospheric research. In this thesis we have developed a new tool (called 1D SECS) for analysing ground based magnetic measurements from a 1-dimensional magnetometer chain (usually aligned in the North-South direction) and a new method for obtaining ionospheric electric field from combined ground based magnetic measurements and estimated ionospheric electric conductance. Both these methods are based on earlier work, but contain important new features: 1D SECS respects the spherical geometry of large scale ionospheric electrojet systems and due to an innovative way of implementing boundary conditions the new method for obtaining electric fields can be applied also at local scale studies. These new calculation methods have been tested using both simulated and real data. The tests indicate that the new methods are more reliable than the previous techniques. Inductive phenomena are intimately related to temporal changes in electric currents. As the large scale ionospheric current systems change relatively slowly, in time scales of several minutes or hours, inductive effects are usually assumed to be negligible. However, during the past ten years, it has been realised that induction can play an important part in some ionospheric phenomena. In this thesis we have studied the role of inductive electric fields and currents in ionospheric electrodynamics. We have formulated the induction problem so that only ionospheric electric parameters are used in the calculations. This is in contrast to previous studies, which require knowledge of the magnetospheric-ionosphere coupling. We have applied our technique to several realistic models of typical auroral phenomena. The results indicate that inductive electric fields and currents are locally important during the most dynamical phenomena (like the westward travelling surge, WTS). In these situations induction may locally contribute up to 20-30% of the total ionospheric electric field and currents. Inductive phenomena do also change the field-aligned currents flowing between the ionosphere and magnetosphere, thus modifying the coupling between the two regions.

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.

Open and closed boundaries in large-scale convective dynamos

Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. To test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation level of large-scale dynamos. Open (vertical field) and closed (perfect conductor) boundary conditions are used for the magnetic field. The contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate in this regime increases proportional to Rm^(1/2). In the nonlinear regime, the saturation level of the energy of the mean magnetic field is independent of Rm when open boundaries are used. In the case of perfect conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm^(-1) for Rm > 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

Svekofennialaisen orogenian ylityönnön terminen mallinnus Itä-Suomen arkeeisella kratonilla

This study reviews the thermophysical properties of rocks and the lithosphere and describes a one dimensional thermal numeric model of hypothetical 20 km thick overthrust plate obtruded on to the Archeaen craton in the Svecofennian orogeny (1.92-1.77 Ga). The objective is to find out if the overthrust plate and its radiogenic heat sources were able to produce the thermal effects observed on the current erosion level of the Archaean craton. Heat transfer in lithosphere is assumed conductive, and advective heat transfer due to melting and melt transfer is supposed negligible. The study area is located in the Eastern Finland, approximately current Kainuu and Northern Karelia regions, east from the most active orogenic belt (Raahe-Ladoga zone), so that orogenic magmatism can be neglected. Physical parameters and boundary conditions for the model are from different earlier published sources: deep seismic profiles (rock variation in depth), laboratory measurements (heat production and conductivity of rocks), field measurements (heat flow densities), and pT(t) estimations from the Finnish precambrian to estimate the size and thickness of the sheet. Comparison of the modelling results to previous K-Ar datings and other pTt estimations show, that the effect of the overthrust sheet has been adequate (max. T 450°C at 4 kbar) to produce the K-Ar resetting ages measured from the Archaean bedrock at current erosion level. No other kind of thermal activation in lithosphere is required. Results show possibly very minor partial melting in upper middle crust underneath the overthrust sheet.

Overwintering ecology of northern field layer plants : snow and photosynthesis in Vaccinium vitis-idaea L.

Winter is a significant period for the seasonality of northern plants, but is often overlooked when studying the interactions of plants and their environment. This study focuses on the effects of overwintering conditions, including warm winter periods, snow, and snowmelt on boreal and sub-Arctic field layer plants. Wintertime photosynthesis and related physiological factors of evergreen dwarf shrubs, particularly of Vaccinium vitis-idaea, are emphasised. The work combines experiments both in the field and in growth chambers with measurements in natural field conditions. Evergreen dwarf shrubs are predominantly covered by snow in the winter. The protective snow cover provides favourable conditions for photosynthesis, especially during the spring before snowmelt. The results of this study indicate that photosynthesis occurs under the snow in V. vitis-idaea. The light response of photosynthesis determined in field conditions during the period of snow cover shows that positive net CO2 exchange is possible under the snow in the prevailing light and temperature. Photosynthetic capacity increases readily during warm periods in winter and the plants are thus able to replenish carbohydrate reserves lost through respiration. Exposure to low temperatures in combination with high light following early snowmelt can set back photosynthesis as sustained photoprotective measures are activated and photodamage begins to build up. Freezing may further decrease the photosynthetic capacity. The small-scale distribution of many field layer plants, including V. vitis-idaea and other dwarf shrubs, correlates with the snow distribution in a forest. The results of this study indicate that there are species-specific differences in the snow depth affinity of the field and ground layer species. Events and processes taking place in winter can have a profound effect on the overall performance of plants and on the interactions between plants and their environment. Understanding the processes involved in the overwintering of plants is increasingly important as the wintertime climate in the north is predicted to change in the future.

Magnetorotational instability driven dynamos at low magnetic Prandtl numbers

Numerical simulations of the magnetorotational instability (MRI) with zero initial net flux in a non-stratified isothermal cubic domain are used to demonstrate the importance of magnetic boundary conditions. In fully periodic systems the level of turbulence generated by the MRI strongly decreases as the magnetic Prandtl number (Pm), which is the ratio of kinematic viscosity and magnetic diffusion, is decreased. No MRI or dynamo action below Pm=1 is found, agreeing with earlier investigations. Using vertical field conditions, which allow magnetic helicity fluxes out of the system, the MRI is found to be excited in the range 0.1