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.

Coherent quantum Boltzmann equations from cQPA

We reformulate and extend our recently introduced quantum kinetic theory for interacting fermion and scalar fields. Our formalism is based on the coherent quasiparticle approximation (cQPA) where nonlocal coherence information is encoded in new spectral solutions at off-shell momenta. We derive explicit forms for the cQPA propagators in the homogeneous background and show that the collision integrals involving the new coherence propagators need to be resummed to all orders in gradient expansion. We perform this resummation and derive generalized momentum space Feynman rules including coherent propagators and modified vertex rules for a Yukawa interaction. As a result we are able to set up self-consistent quantum Boltzmann equations for both fermion and scalar fields. We present several examples of diagrammatic calculations and numerical applications including a simple toy model for coherent baryogenesis.

Kosteikkosedimentin fosforivarat ja niiden käyttökelpoisuus kasveille

Maatalouden ympäristötukiohjelmalla pyritään vähentämään maatalouden ravinnekuormitusta, sillä valtaosa fosforin hajakuormituksesta on peräisin maataloudesta. Maataloudesta peräisin olevan fosforin rehevöittävää vaikutusta vesistöissä voidaan pyrkiä vähentämään kosteikoilla, joiden päätarkoituksena on saada valumaveden mukana erodoitunut maa-aines sedimentoitumaan kosteikon pohjalle. Kosteikkojen toimivuudesta ja vesiensuojelun merkityksestä on kuitenkin Suomessa tehdyissä tutkimuksissa saatu ristiriitaisia tuloksia. Tämän työn tavoitteena on selvittää maa-analyysien avulla, mitä valuma-alueelta erodoitunut fosforille tapahtuu kosteikon sedimentissä ja kuinka hyvin sedimentoitunut aines soveltuu kasvualustaksi kasvintuotannossa. Valuma-alueen maanäytteitä ja kosteikon sedimenttinäytteitä vertailemalla havaittiin kosteikossa tapahtuvan erodoituneen maa-aineksen lajittumista. Kosteikosta otetussa sedimenttinäytteessä oli 48 % enemmän savesta kuin valumapellon muokkauskerroksen maanäytteissä. Lisäksi havaittiin, että savespitoisuuden lisääntyminen lisäsi sedimentin reaktiivista pinta-alaa, koska sedimentissä oli 45 % enemmän alumiini- ja rautahydroksideja kuin valuma-alueelta otetuissa maanäytteissä. Hydroksidien runsauden takia fosforin sorptiokapasiteetti oli sedimentissä 52 % suurepi kuin valuma-alueelta otetuissa näytteissä. Sedimenttinäytteiden fosforin sorptiokyllästysaste oli kuitenkin samansuuruinen verrattuna valuma-alueelta otettuihin näytteisiin, sillä hapettuneessa sedimentissä oli 50 % enemmän alumiini- ja rautahydroksidien sitomaa fosforia. Näytteenottohetkellä sedimentti oli pelkistyneessä tilassa, jolloin sen vesiuuttoisen fosforin määrä oli huomattavasti suurempi kuin hapettuneessa sedimentissä. Vastaavasti sedimentin hapettuessa fosforin sorptiokyky kasvoi huomattavasti, sillä pelkistyneestä sedimentistä desorboitui fosforia kosteikon veteen. Tämä havaittiin myös astiakokeessa, sillä sedimentissä kasvanut raiheinä kärsi voimakkaasta fosforin puutoksesta niillä lannoitustasoilla, joilla valuma-alueen maanäytteessä kasvaneella raiheinällä ei silmämääräisesti havaittu esiintyvän puutosoireita. Sedimentin toiselle sadolle annetulla kolminkertaisella fosforin lisälannoituksella saavutettiin samansuuruiset sadon kuiva-ainemäärät, fosforipitoisuudet ja fosforin otot kuin valuma-alueen maanäytteissä kasvaneella ensimmäisellä sadolla oli. Astiakokeen tulosten perusteella pelkistyneessä tilassa ollut sedimentti soveltuu heikosti kasvintuotannon kasvualustaksi suuren fosforisorptiokykynsä ansiosta. Parhaiten sedimentti soveltuisi runsaasti helppoliukoista fosforia sisältäville alueille, kuten karjan jalottelutarhan pohjamateriaaliksi, vähentämään ympäristöön kohdistuvaa fosforikuormitusta.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Cohésion modale et subordination : Le conditionnel et le jussif finnois au miroir de la valeur sémantique et discursive du subjonctif français

Modal cohesion and subordination. The Finnish conditional and jussive moods in comparison to the French subjunctive This study examines verb moods in subordinate clauses in French and Finnish. The first part of the analysis deals with the syntax and semantics of the French subjunctive, mood occurring mostly in subordinate positions. The second part investigates Finnish verb moods. Although subordinate positions in Finnish grammar have no special finite verb form, certain uses of Finnish verb moods have been compared to those of subjunctives and conjunctives in other languages. The present study focuses on the subordinate uses of the Finnish conditional and jussive (i.e. the third person singular and plural of the imperative mood). The third part of the analysis discusses the functions of subordinate moods in contexts beyond complex sentences. The data used for the analysis include 1834 complex sentences gathered from newspapers, online discussion groups and blog texts, as well as audio-recorded interviews and conversations. The data thus consist of both written and oral texts as well as standard and non-standard variants. The analysis shows that the French subjunctive codes theoretical modality. The subjunctive does not determine the temporal and modal meaning of the event, but displays the event as virtual. In a complex sentence, the main clause determines the temporal and modal space within which the event coded by the subjunctive clause is interpreted. The subjunctive explicitly indicates that the space constructed in the main clause extends its scope over the subordinate clause. The subjunctive can therefore serve as a means for creating modal cohesion in the discourse. The Finnish conditional shares the function of making explicit the modal link between the components of a complex construction with the French subjunctive, but the two moods differ in their semantics. The conditional codes future time and can therefore occur only in non-factual or counterfactual contexts, whereas the event expressed by French subjunctive clauses can also be interpreted as realized. Such is the case when, for instance, generic and habitual meaning is involved. The Finnish jussive mood is used in a relatively limited number of subordinate clause types, but in these contexts its modal meaning is strikingly close to that of the French subjunctive. The permissive meaning, typical of the jussive in main clause positions, is modified in complex sentences so that it entails inter-clausal relation, namely concession. Like the French subjunctive, the jussive codes theoretical modal meaning with no implication of the truth value of the proposition. Finally, the analysis shows that verb moods mark modal cohesion, not only on the syntagmatic level (namely in complexe sentences), but also on the paradigmatic axis of discourse in order to create semantic links over entire segments of talk. In this study, the subjunctive thus appears, not as an empty category without function, as it is sometimes described, but as an open form that conveys the temporal and modal meanings emerging from the context.

Phytophthora in Finnish nurseries

Human-mediated movement of plants and plant products is now generally accepted to be the primary mode of introduction of plant pathogens. Species of the genus Phytophthora are commonly spread in this way and have caused severe epidemics in silviculture, horticulture as well as natural systems all over the world. The aims of the study were to gather information on the occurrence of Phytophthora spp. in Finnish nurseries, to produce information for risk assessments for these Phytophthora spp. by determining their host ranges and tolerance of cold temperatures, and to establish molecular means for their detection. Phytophthora cactorum was found to persist in natural waterbodies and results suggest that irrigation water might be a source of inoculum in nurseries. In addition to P. cactorum, isolates from ornamental nursery Rhododendron yielded three species new to Finland: P. ramorum, P. plurivora and P. pini. The only species with quarantine status, P. ramorum, was most adapted to growth in cold temperatures and able to persist in the nursery in spite of an annual sanitation protocol. Phytophthora plurivora and the closely related P. pini had more hosts among Nordic tree and plant species than P. ramorum and P. cactorum, and also had higher infectivity rates. All four species survived two weeks in -5 °C , and thus soil survival of these Phytophthoras in Finland is likely under current climatic conditions. The most common tree species in Finnish nurseries, Picea abies, was highly susceptible to P. plurivora and P. pini in pathogenicity trials. In a histological examination of P. plurivora in P. abies shoot tissues, fast necrotrophic growth was observed in nearly all tissues. The production of propagules in P. abies shoot tissue was only weakly indicated. In this study, a PCR DGGE technique was developed for simultaneous detection and identification of Phytophthora spp. It reliably detected Phytophthora in plant tissues and could discriminate most test species as well as indicate instances of multiple-species infections. It proved to be a useful detection and identification tool either applied alone or in concert with traditional isolation culture techniques. All of the introduced species of Phytophthora had properties that promote a high risk of establishment and spread in Finland. It is probable that more pathogens of this genus will be introduced and become established in Finland and other Nordic countries unless efficient phytosanitary control becomes standard practice in the international plant trade.

Dependence of the large-scale vortex instability on latitude, stratification and domain size

In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions for the onset of the instability were investigated in terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification, and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the colatitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.