Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.

Passive vector turbulence

This thesis consists of three articles on passive vector fields in turbulence. The vector fields interact with a turbulent velocity field, which is described by the Kraichnan model. The effect of the Kraichnan model on the passive vectors is studied via an equation for the pair correlation function and its solutions. The first paper is concerned with the passive magnetohydrodynamic equations. Emphasis is placed on the so called "dynamo effect", which in the present context is understood as an unbounded growth of the pair correlation function. The exact analytical conditions for such growth are found in the cases of zero and infinite Prandtl numbers. The second paper contains an extensive study of a number of passive vector models. Emphasis is now on the properties of the (assumed) steady state, namely anomalous scaling, anisotropy and small and large scale behavior with different types of forcing or stirring. The third paper is in many ways a completion to the previous one in its study of the steady state existence problem. Conditions for the existence of the steady state are found in terms of the spatial roughness parameter of the turbulent velocity field.

On global solar dynamo simulations

Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age-old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal rotation of the Sun, which plays a crucual role in the dynamo process, has also turned out to be a very difficult problem. In the present paper the current status of global dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to understand how the large-scale magnetic fields, i.e. whose length scale is greater than the scale of turbulence, are generated in the Sun. Some lessons from mean-field theory and local simulations are reviewed and their possible implications to the global models are discussed. Possible remedies to some of the current issues of the solar simulations are put forward.

3D MHD simulations of subsurface convection in OB stars

During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection.

Relocating the American Dream : The America of the 1960s as Portrayed by the New Journalists Norman Mailer, Hunter S. Thompson, and Tom Wolfe

The concept of the American Dream was subject to a strong re-evaluation process in the 1960s, as counterculture became a prominent force in American society. A massive generation of young people, moved by the Vietnam War, the hippie movement, and psychedelic experimentation, created substantial social turbulence in their efforts to break out of conventional patterns and to create a new kind of society. This thesis outlines and analyses the concept of the American Dream in popular imagination through three works of new journalism. My primary data consists of Tom Wolfe’s The Electric Kool-Aid Acid Test (1967), Hunter S. Thompson’s Fear and Loathing in Las Vegas: A Savage Journey to the Heart of the American Dream (1971), and Norman Mailer’s Armies of the Night: History as a Novel, the Novel as History (1968). In defining the American Dream, I discuss the history of the concept as well as its manifestations in popular culture. Because of its elusive and amorphous nature, the concept of the American Dream can only be examined in cultural texts that portray the values, sentiments, and customs of a certain era. I have divided the analytical section of my thesis into three parts. In the first part I examine how the authors discuss the American society of their time in relation to ideology, capitalism, and the media. In the second part I focus on the Vietnam War and the controversy it creates in relation to the notions of freedom and patriotism. In the third part I discuss how the authors portray the countercultural visions of a better America that challenged the traditional interpretations of the American Dream. I also discuss the dark side of the new dream: the problems and disillusions that came with the effort to change the world. This thesis is an effort to trace the relocation of the American Dream in the context of the 1960s counterculture and new journalism. It hopes to provide a valuable addition to the cultural history of the sixties and to the effort of conceptualizing the American Dream.

Wind drift of snowfall between the radar volume and ground

This study evaluates how the advection of precipitation, or wind drift, between the radar volume and ground affects radar measurements of precipitation. Normally precipitation is assumed to fall vertically to the ground from the contributing volume, and thus the radar measurement represents the geographical location immediately below. In this study radar measurements are corrected using hydrometeor trajectories calculated from measured and forecasted winds, and the effect of trajectory-correction on the radar measurements is evaluated. Wind drift statistics for Finland are compiled using sounding data from two weather stations spanning two years. For each sounding, the hydrometeor phase at ground level is estimated and drift distance calculated using different originating level heights. This way the drift statistics are constructed as a function of range from radar and elevation angle. On average, wind drift of 1 km was exceeded at approximately 60 km distance, while drift of 10 km was exceeded at 100 km distance. Trajectories were calculated using model winds in order to produce a trajectory-corrected ground field from radar PPI images. It was found that at the upwind side from the radar the effective measuring area was reduced as some trajectories exited the radar volume scan. In the downwind side areas near the edge of the radar measuring area experience improved precipitation detection. The effect of trajectory-correction is most prominent in instant measurements and diminishes when accumulating over longer time periods. Furthermore, measurements of intensive and small scale precipitation patterns benefit most from wind drift correction. The contribution of wind drift on the uncertainty of estimated Ze (S) - relationship was studied by simulating the effect of different error sources to the uncertainty in the relationship coefficients a and b. The overall uncertainty was assumed to consist of systematic errors of both the radar and the gauge, as well as errors by turbulence at the gauge orifice and by wind drift of precipitation. The focus of the analysis is error associated with wind drift, which was determined by describing the spatial structure of the reflectivity field using spatial autocovariance (or variogram). This spatial structure was then used with calculated drift distances to estimate the variance in radar measurement produced by precipitation drift, relative to the other error sources. It was found that error by wind drift was of similar magnitude with error by turbulence at gauge orifice at all ranges from radar, with systematic errors of the instruments being a minor issue. The correction method presented in the study could be used in radar nowcasting products to improve the estimation of visibility and local precipitation intensities. The method however only considers pure snow, and for operational purposes some improvements are desirable, such as melting layer detection, VPR correction and taking solid state hydrometeor type into account, which would improve the estimation of vertical velocities of the hydrometeors.

Foreign Capital and Finland : Central government's first period of reliance on international financial markets, 1862-1938

The main objective of the study is to evaluate the Finnish central government s foreign borrowing between the years 1862 and 1938. Most of this period was characterised by deep capital market integration that bears resemblance to the liberal world financial order at the turn of the millennium. The main aim is to analyse the credit risk associated with the state and its determination by evaluating the world financial market centres perception of Finland. By doing this, the study is also expected to provide an additional dimension to Finland s political and economic history by incorporating into the research the assessments of international capital markets regarding Finland during a period that witnessed profound political and economic changes in Finnish society. The evaluation of the credit risk mainly relies on exchange-rate risk free time series of the state s foreign bonds. They have been collected from quotations in the stock exchanges in Helsinki, Hamburg, Paris and London. In addition, it investigates Finland s exposure to short-term debt and Moody s credit ratings assigned to Finland. The study emphasises the importance of the political risk. It suggests that the hey-day of the state s reliance on foreign capital markets took place during last few decades of the 19th century when Finland enjoyed a wide autonomy in the Russian Empire and prudently managed its economy, highlighted in Finland s adherence to the international gold standard. Political confrontations in Finland and, in particular, in Russia and the turbulence of the world financial system prevented the return of this beneficial position again. Through its issuance of foreign bonds the state was able to import substantial amounts of foreign capital, which was sorely needed to foster economic development in Finland. Moreover, the study argues that the state s presence in the western capital markets not only had economic benefits, but it also increased the international awareness of Finland s distinct and separate status in the Russian Empire and later underlined its position as an independent republic.

Road Dust from Pavement Wear and Traction Sanding

Vehicles affect the concentrations of ambient airborne particles through exhaust emissions, but particles are also formed in the mechanical processes in the tire-road interface, brakes, and engine. Particles deposited on or in the vicinity of the road may be re-entrained, or resuspended, into air through vehicle-induced turbulence and shearing stress of the tires. A commonly used term for these particles is road dust . The processes affecting road dust emissions are complex and currently not well known. Road dust has been acknowledged as a dominant source of PM10 especially during spring in the sub-arctic urban areas, e.g. in Scandinavia, Finland, North America and Japan. The high proportion of road dust in sub-arctic regions of the world has been linked to the snowy winter conditions that make it necessary to use traction control methods. Traction control methods include dispersion of traction sand, melting of ice with brine solutions, and equipping the tires with either metal studs (studded winter tires), snow chains, or special tire design (friction tires). Several of these methods enhance the formation of mineral particles from pavement wear and/or from traction sand that accumulate in the road environment during winter. When snow and ice melt and surfaces dry out, traffic-induced turbulence makes some of the particles airborne. A general aim of this study was to study processes and factors underlying and affecting the formation and emissions of road dust from paved road surfaces. Special emphasis was placed on studying particle formation and sources during tire road interaction, especially when different applications of traction control, namely traction sanding and/or winter tires were in use. Respirable particles with aerodynamic diameter below 10 micrometers (PM10) have been the main concern, but other size ranges and particle size distributions were also studied. The following specific research questions were addressed: i) How do traction sanding and physical properties of the traction sand aggregate affect formation of road dust? ii) How do studded tires affect the formation of road dust when compared with friction tires? iii) What are the composition and sources of airborne road dust in a road simulator and during a springtime road dust episode in Finland? iv) What is the size distribution of abrasion particles from tire-road interaction? The studies were conducted both in a road simulator and in field conditions. The test results from the road simulator showed that traction sanding increased road dust emissions, and that the effect became more dominant with increasing sand load. A high percentage of fine-grained anti-skid aggregate of overall grading increased the PM10 concentrations. Anti-skid aggregate with poor resistance to fragmentation resulted in higher PM levels compared with the other aggregates, and the effect became more significant with higher aggregate loads. Glaciofluvial aggregates tended to cause higher particle concentrations than crushed rocks with good fragmentation resistance. Comparison of tire types showed that studded tires result in higher formation of PM emissions compared with friction tires. The same trend between the tires was present in the tests with and without anti-skid aggregate. This finding applies to test conditions of the road simulator with negligible resuspension. Source and composition analysis showed that the particles in the road simulator were mainly minerals and originated from both traction sand and pavement aggregates. A clear contribution of particles from anti-skid aggregate to ambient PM and dust deposition was also observed in urban conditions. The road simulator results showed that the interaction between tires, anti-skid aggregate and road surface is important in dust production and the relative contributions of these sources depend on their properties. Traction sand grains are fragmented into smaller particles under the tires, but they also wear the pavement aggregate. Therefore particles from both aggregates are observed. The mass size distribution of traction sand and pavement wear particles was mainly coarse, but fine and submicron particles were also present.

Population dynamics of blue mussels in a variable environment at the edge of their range

Spatial and temporal variation in the abundance of species can often be ascribed to spatial and temporal variation in the surrounding environment. Knowledge of how biotic and abiotic factors operate over different spatial and temporal scales in determining distribution, abundance, and structure of populations lies at the heart of ecology. The major part of the current ecological theory stems from studies carried out in central parts of the distributional range of species, whereas knowledge of how marginal populations function is inadequate. Understanding how marginal populations, living at the edge of their range, function is however in a key position to advance ecology and evolutionary biology as scientific disciplines. My thesis focuses on the factors affecting dynamics of marginal populations of blue mussels (Mytilus edulis) living close to their tolerance limits with regard to salinity. The thesis aims to highlight the dynamics at the edge of the range and contrast these with dynamics in more central parts of the range in order to understand the potential interplay between the central and the marginal part in the focal system. The objectives of the thesis are approached by studies on: (1) factors affecting regional patterns of the species, (2) long-term temporal dynamics of the focal species spaced along a regional salinity gradient, (3) selective predation by increasing populations of roach (Rutilus rutilus) when feeding on their main food item, the blue mussel, (4) the primary and secondary effects of local wave exposure gradients and (5) the role of small-scale habitat heterogeneity as determinants of large-scale pattern. The thesis shows that populations of blue mussels are largely determined by large scale changes in sea water salinity, affecting mainly recruitment success and longevity of local populations. In opposite to the traditional view, the thesis strongly indicate that vertebrate predators strongly affect abundance and size structure of blue mussel populations, and that the role of these predators increases towards the margin where populations are increasingly top-down controlled. The thesis also indicates that the positive role of biogenic habitat modifiers increases towards the marginal areas, where populations of blue mussels are largely recruitment limited. Finally, the thesis shows that local blue mussel populations are strongly dependent on high water turbulence, and therefore, dense populations are constrained to offshore habitats. Finally, the thesis suggests that ongoing sedimentation of rocky shores is detrimental for the species, affecting recruitment success and post-recruit survival, pushing stable mussel beds towards offshore areas. Ongoing large scale changes in the Baltic Sea, especially dilution processes with attendant effects, are predicted to substantially contract the distributional range of the mussel, but also affect more central populations. The thesis shows that in order to understand the functioning of marginal populations, research should (1) strive for multi-scale approaches in order to link ecosystem patterns with ecosystem processes, and (2) challenge the prevailing tenets that origin from research carried out in central areas that may not be valid at the edge.

Rekonnektio Maan magnetosfäärissä

Tässä väitöskirjassa perehdytään magneettisen rekonnektion ilmenemismuotoihin ja vaikutuksiin Maan magnetosfäärissä. Keskeisenä tutkimusvälineenä käytetään magnetohydrodynaamista (MHD) Gumics-magnetosfäärisimulaatiota. Työssä kehitetään myös uusia menetelmiä simulaatiossa ilmenevän rekonnektion tunnistamiseksi ja mittaamiseksi. MHD-simulaatio sopii suuren mittakaavan ilmiöiden tarkasteluun, joten kuvaa rekonnektiosta täydennetään pienen mittakaavan piirteiden osalta Cluster-satelliittien avulla. Tärkein tutkimuksen tuoma edistysaskel menetelmien saralla on rekonnektioviivan paikallistaminen topologisesti erityyppisten magneettikenttäviivojen alueiden liitoskohdassa olevana erottajaviivana neljän kentän tienoon menetelmää käyttäen. Tämä topologinen lähestymistapa on hyödyllinen erityisesti magnetopausilla, jonka monimutkainen geometria tekee magneettikentän paikalliseen käyttäytymiseen perustuvien rekonnektioviivan etsintätapojen soveltamisen hankalaksi. Topologisesti määritelty rekonnektioviiva on myös helppo tunnistaa magnetosfäärin globaalin konvektion solmukohdaksi. Magnetopausin rekonnektioviivan käyttäytyminen Gumicsissa noudattaa komponenttirekonnektio-olettamaan pohjautuvia teoreettisia ennusteita. Rekonnektion kvantitatiivinen tarkastelu Gumics-simulaatiossa perustuu energian muuntumiseen, joka lasketaan Poyntingin vektorin divergenssinä tai Poyntingin vuona valitun umpinaisen pinnan läpi. Rekonnektioon liittyvän energian muuntumisen jakautumista magnetopausilla tarkastellaan energian muuntumisen pintatiheyden avulla ja rekonnektion kokonaismäärää rekonnektiotehon avulla. Magnetopausin ja pyrstön rekonnektiotehot ovat simulaatiossa samaa suuruusluokkaa. Tärkeimmät magnetopausin rekonnektiotehoa säätelevät parametrit ovat aurinkotuulen nopeus ja aurinkotuulen magneettikentän suunta. Magnetopausin rekonnektio puolestaan säätelee energian ja aineen pääsyä magnetosfääriin, joskaan magnetopausin läpäisevät vuot eivät ole aivan suoraan verrannollisia rekonnektiotehoon. Pyrstön rekonnektioteho sen sijaan on suoraan verrannollinen magnetopausilta tulevaan energiavuohon; pyrstörekonnektio Gumicsissa on siis ulkoista pakotetta seuraava passiivinen energian käsittelijä. Simulaation tuottama rekonnektio on realistinen magnetosfäärin globaalissa mittakaavassa tarkasteltuna, mutta satelliittihavainnot paljastavat rekonnektiosta simulaation erottelukykyä pienimittakaavaisempia piirteitä. Havaintopuolella tämän väitöstutkimuksen tärkein löytö on protonien diffuusioalueen rakenteeseen kuuluvien Hallin kenttien kääntyminen pyrstön virtalevyn aaltoilun mukana.

Effects of climate and morphology on temperature conditions of lakes

To a large extent, lakes can be described with a one-dimensional approach, as their main features can be characterized by the vertical temperature profile of the water. The development of the profiles during the year follows the seasonal climate variations. Depending on conditions, lakes become stratified during the warm summer. After cooling, overturn occurs, water cools and an ice cover forms. Typically, water is inversely stratified under the ice, and another overturn occurs in spring after the ice has melted. Features of this circulation have been used in studies to distinguish between lakes in different areas, as basis for observation systems and even as climate indicators. Numerical models can be used to calculate temperature in the lake, on the basis of the meteorological input at the surface. The simple form is to solve the surface temperature. The depth of the lake affects heat transfer, together with other morphological features, the shape and size of the lake. Also the surrounding landscape affects the formation of the meteorological fields over the lake and the energy input. For small lakes the shading by the shores affects both over the lake and inside the water body bringing limitations for the one-dimensional approach. A two-layer model gives an approximation for the basic stratification in the lake. A turbulence model can simulate vertical temperature profile in a more detailed way. If the shape of the temperature profile is very abrupt, vertical transfer is hindered, having many important consequences for lake biology. One-dimensional modelling approach was successfully studied comparing a one-layer model, a two-layer model and a turbulence model. The turbulence model was applied to lakes with different sizes, shapes and locations. Lake models need data from the lakes for model adjustment. The use of the meteorological input data on different scales was analysed, ranging from momentary turbulent changes over the lake to the use of the synoptical data with three hour intervals. Data over about 100 past years were used on the mesoscale at the range of about 100 km and climate change scenarios for future changes. Increasing air temperature typically increases water temperature in epilimnion and decreases ice cover. Lake ice data were used for modelling different kinds of lakes. They were also analyzed statistically in global context. The results were also compared with results of a hydrological watershed model and data from very small lakes for seasonal development.

Molecular line and continuum studies of the early stages of star formation

New stars form in dense interstellar clouds of gas and dust called molecular clouds. The actual sites where the process of star formation takes place are the dense clumps and cores deeply embedded in molecular clouds. The details of the star formation process are complex and not completely understood. Thus, determining the physical and chemical properties of molecular cloud cores is necessary for a better understanding of how stars are formed. Some of the main features of the origin of low-mass stars, like the Sun, are already relatively well-known, though many details of the process are still under debate. The mechanism through which high-mass stars form, on the other hand, is poorly understood. Although it is likely that the formation of high-mass stars shares many properties similar to those of low-mass stars, the very first steps of the evolutionary sequence are unclear. Observational studies of star formation are carried out particularly at infrared, submillimetre, millimetre, and radio wavelengths. Much of our knowledge about the early stages of star formation in our Milky Way galaxy is obtained through molecular spectral line and dust continuum observations. The continuum emission of cold dust is one of the best tracers of the column density of molecular hydrogen, the main constituent of molecular clouds. Consequently, dust continuum observations provide a powerful tool to map large portions across molecular clouds, and to identify the dense star-forming sites within them. Molecular line observations, on the other hand, provide information on the gas kinematics and temperature. Together, these two observational tools provide an efficient way to study the dense interstellar gas and the associated dust that form new stars. The properties of highly obscured young stars can be further examined through radio continuum observations at centimetre wavelengths. For example, radio continuum emission carries useful information on conditions in the protostar+disk interaction region where protostellar jets are launched. In this PhD thesis, we study the physical and chemical properties of dense clumps and cores in both low- and high-mass star-forming regions. The sources are mainly studied in a statistical sense, but also in more detail. In this way, we are able to examine the general characteristics of the early stages of star formation, cloud properties on large scales (such as fragmentation), and some of the initial conditions of the collapse process that leads to the formation of a star. The studies presented in this thesis are mainly based on molecular line and dust continuum observations. These are combined with archival observations at infrared wavelengths in order to study the protostellar content of the cloud cores. In addition, centimetre radio continuum emission from young stellar objects (YSOs; i.e., protostars and pre-main sequence stars) is studied in this thesis to determine their evolutionary stages. The main results of this thesis are as follows: i) filamentary and sheet-like molecular cloud structures, such as infrared dark clouds (IRDCs), are likely to be caused by supersonic turbulence but their fragmentation at the scale of cores could be due to gravo-thermal instability; ii) the core evolution in the Orion B9 star-forming region appears to be dynamic and the role played by slow ambipolar diffusion in the formation and collapse of the cores may not be significant; iii) the study of the R CrA star-forming region suggests that the centimetre radio emission properties of a YSO are likely to change with its evolutionary stage; iv) the IRDC G304.74+01.32 contains candidate high-mass starless cores which may represent the very first steps of high-mass star and star cluster formation; v) SiO outflow signatures are seen in several high-mass star-forming regions which suggest that high-mass stars form in a similar way as their low-mass counterparts, i.e., via disk accretion. The results presented in this thesis provide constraints on the initial conditions and early stages of both low- and high-mass star formation. In particular, this thesis presents several observational results on the early stages of clustered star formation, which is the dominant mode of star formation in our Galaxy.

Shock acceleration in the solar corona

In this thesis acceleration of energetic particles at collisionless shock waves in space plasmas is studied using numerical simulations, with an emphasis on physical conditions applicable to the solar corona. The thesis consists of four research articles and an introductory part that summarises the main findings reached in the articles and discusses them with respect to theory of diffusive shock acceleration and observations. This thesis gives a brief review of observational properties of solar energetic particles and discusses a few open questions that are currently under active research. For example, in a few large gradual solar energetic particle events the heavy ion abundance ratios and average charge states show characteristics at high energies that are typically associated with flare-accelerated particles, i.e. impulsive events. The role of flare-accelerated particles in these and other gradual events has been discussed a lot in the scientific community, and it has been questioned if and how the observed features can be explained in terms of diffusive shock acceleration at shock waves driven by coronal mass ejections. The most extreme solar energetic particle events are the so-called ground level enhancements where particle receive so high energies that they can penetrate all the way through Earth's atmosphere and increase radiation levels at the surface. It is not known what conditions are required for acceleration into GeV/nuc energies, and the presence of both very fast coronal mass ejections and X-class solar flares makes it difficult to determine what is the role of these two accelerators in ground level enhancements. The theory of diffusive shock acceleration is reviewed and its predictions discussed with respect to the observed particle characteristics. We discuss how shock waves can be modeled and describe in detail the numerical model developed by the author. The main part of this thesis consists of the four scientific articles that are based on results of the numerical shock acceleration model developed by the author. The novel feature of this model is that it can handle complex magnetic geometries which are found, for example, near active regions in the solar corona. We show that, according to our simulations, diffusive shock acceleration can explain the observed variations in abundance ratios and average charge states, provided that suitable seed particles and magnetic geometry are available for the acceleration process in the solar corona. We also derive an injection threshold for diffusive shock acceleration that agrees with our simulation results very well, and which is valid under weakly turbulent conditions. Finally, we show that diffusive shock acceleration can produce GeV/nuc energies under suitable coronal conditions, which include the presence of energetic seed particles, a favourable magnetic geometry, and an enhanced level of ambient turbulence.