<p>A major fraction of stars will pass through a short period of dramatic events in their final evolutionary stage. Low- to intermediate-mass stars, studied here, are stripped of their outer parts in a slow massive wind. This mass loss reshapes both the star and the surrounding medium. The formation of the wind is a consequence of the non-linear interaction of a number of physical processes. Stellar pulsations and efficient dust formation are examples of such key processes. Time-dependent theoretical models, in combination with observations, are useful tools for understanding these winds.</p><p>The main object of this thesis has been the physical improvement of a theoretical wind model. Here the coupling between the dust and gas in the wind is studied in further detail, allowing drift. The methods that have been developed earlier to describe the micro-physical interaction are overviewed and summarized. Previously dust has often been assumed to move at the same velocity as gas. New time-dependent wind models are presented where grain drift has been treated self-consistently. Specifically, the coupling between dust and gas in the wind has been modeled more realistically, with descriptions of both the modified momentum and energy balances, and drift dependent dust formation. The results of these new ``drift models'' have been compared with the results of non-drift models. </p><p>A general result of the study is that the effects of drift are significant and difficult to predict if a simple analytical theory is used. It has been found that dust in drift models tends to accumulate in certain dense regions, an accumulation that was not possible without drift. Moreover the new models show an increased variability in the wind structure. The use of drift in dust formation tends to markedly increase the produced dust. Some sets of model parameters lead to a wind without including drift, but a corresponding wind does not form when drift is included -- and vice versa. The effects of drift are important and can probably not be ignored in realistic models.</p>

<p>The magnetospheric cusps are two funnel-like regions of Earth's magnetosphere where solar wind plasma can have direct access to the ionosphere. The cusps are very dynamic regions where wave-particle interactions continuously take place and redistribute energy among different particle populations. In this thesis, both low and high frequency plasma waves in the cusp have been studied in detail using data from the Cluster spacecraft mission. The waves were studied with respect to frequency, Poynting flux and polarization. Wavelengths have also been estimated using multi-spacecraft techniques. At low frequencies, kinetic Alfvén waves and nonpotential ion cyclotron waves are identified and at high frequencies, electron cyclotron waves, whistler waves, upper-hybrid and RX-waves are observed. A common generation mechanism called the shell-instability is proposed for several of the wave modes present in the cusp, both at low and high frequencies. </p><p>The plasma in the cusp is shown to be strongly inhomogeneous. In an inhomogeneous low-frequency magnetoplasma, kinetic Alfvén waves couple to drift-waves. Such drift-kinetic Alfvén waves have long been believed to nonlinearly self-interact and form coherent structures in the form of drift-kinetic Alfvén vortices. In this thesis the first unambiguous direct measurements confirming the existence of such vortices in a turbulent space plasma are presented. Some of the crucial parameters such as the vortex radius are determined. </p><p>Plasma theory is electrodynamics applied to a large collection of charged particles. In this thesis a new way of looking at the fundamental Maxwell tensor is presented. A covariant spectral density tensor containing information on electromagnetic waves is formed. This tensor is then decomposed into irreducible components by using the spinor formalism for an arbitrary metric. The obtained fundamental tensors are shown to correspond both to well known tensors in Maxwell's theory, as well as several physically interesting new tensors.</p>

A major fraction of stars will pass through a short period of dramatic events in their final evolutionary stage. Low- to intermediate-mass stars, studied here, are stripped of their outer parts in a slow massive wind. This mass loss reshapes both the star and the surrounding medium. The formation of the wind is a consequence of the non-linear interaction of a number of physical processes. Stellar pulsations and efficient dust formation are examples of such key processes. Time-dependent theoretical models, in combination with observations, are useful tools for understanding these winds. The main object of this thesis has been the physical improvement of a theoretical wind model. Here the coupling between the dust and gas in the wind is studied in further detail, allowing drift. The methods that have been developed earlier to describe the micro-physical interaction are overviewed and summarized. Previously dust has often been assumed to move at the same velocity as gas. New time-dependent wind models are presented where grain drift has been treated self-consistently. Specifically, the coupling between dust and gas in the wind has been modeled more realistically, with descriptions of both the modified momentum and energy balances, and drift dependent dust formation. The results of these new ``drift models'' have been compared with the results of non-drift models. A general result of the study is that the effects of drift are significant and difficult to predict if a simple analytical theory is used. It has been found that dust in drift models tends to accumulate in certain dense regions, an accumulation that was not possible without drift. Moreover the new models show an increased variability in the wind structure. The use of drift in dust formation tends to markedly increase the produced dust. Some sets of model parameters lead to a wind without including drift, but a corresponding wind does not form when drift is included -- and vice versa. The effects of drift are important and can probably not be ignored in realistic models.

It is relatively straightforward to establish equilibrium inmagnetically confined plasmas, but the plasma is frequentlysucceptible to a variety of instabilities that are driven bythe free energy in the magnetic field or in the pressuregradient. These unstable modes exhibit effects that affect theparticle, momentum and heat confinement properties of theconfiguration. Studies of the dynamics of several of the mostimportant modes are the subject of this thesis. The studies arecarried out on plasmas in the reversed field pinch (RFP)configuration. One phenomenon commonly observed in RFPs is mode walllocking. The localized nature of these phase- and wall lockedstructures results in localized power loads on the wall whichare detrimental for confinement. A detailed study of the walllocked mode phenomenon is performed based on magneticmeasurements from three RFP devices. The two possiblemechanisms for wall locking are investigated. Locking as aresult of tearing modes interacting with a static field errorand locking due to the presence of a non-ideal boundary. Thecharacteristics of the wall locked mode are qualitativelysimilar in a device with a conducting shell system (TPE-RX)compared to a device with a resistive shell (Extrap T2). Atheoretical model is used for evaluating the threshold valuesfor wall locking due to eddy currents in the vacuum vessel inthese devices. A good correlation with experiment is observedfor the conducting shell device. The possibility of succesfully sustaining discharges in aresistive shell RFP is introduced in the recently rebuiltdevice Extrap T2R. Fast spontaneous mode rotation is observed,resulting in low magnetic fluctuations, low loop voltage andimproved confinement. Wall locking is rarely observed. The lowtearingmode amplitudes allow for the theoretically predictedinternal nonresonant on-axis resistive wall modes to beobserved. These modes have not previously been distinguisheddue to the formation of wall locked modes. The internal andexternal nonresonant resistive wall modes grow on the timescale of the shell penetration time. These growth rates dependon the RFP equilibrium. The internal nonresonant resistive wallmodes dominate in Extrap T2R, especially for shallow reverseddischarges. The external nonresonant modes grow solely in deepreversal discharges. <b>Keywords</b>Nuclear fusion, reversed field pinch, resistiveinstabilities, wall locked modes, tearing modes, resistiveshell modes, field errors, EXTRAP-T2, EXTRAP-T2R, TPE-RX

The magnetospheric cusps are two funnel-like regions of Earth's magnetosphere where solar wind plasma can have direct access to the ionosphere. The cusps are very dynamic regions where wave-particle interactions continuously take place and redistribute energy among different particle populations. In this thesis, both low and high frequency plasma waves in the cusp have been studied in detail using data from the Cluster spacecraft mission. The waves were studied with respect to frequency, Poynting flux and polarization. Wavelengths have also been estimated using multi-spacecraft techniques. At low frequencies, kinetic Alfvén waves and nonpotential ion cyclotron waves are identified and at high frequencies, electron cyclotron waves, whistler waves, upper-hybrid and RX-waves are observed. A common generation mechanism called the shell-instability is proposed for several of the wave modes present in the cusp, both at low and high frequencies. The plasma in the cusp is shown to be strongly inhomogeneous. In an inhomogeneous low-frequency magnetoplasma, kinetic Alfvén waves couple to drift-waves. Such drift-kinetic Alfvén waves have long been believed to nonlinearly self-interact and form coherent structures in the form of drift-kinetic Alfvén vortices. In this thesis the first unambiguous direct measurements confirming the existence of such vortices in a turbulent space plasma are presented. Some of the crucial parameters such as the vortex radius are determined. Plasma theory is electrodynamics applied to a large collection of charged particles. In this thesis a new way of looking at the fundamental Maxwell tensor is presented. A covariant spectral density tensor containing information on electromagnetic waves is formed. This tensor is then decomposed into irreducible components by using the spinor formalism for an arbitrary metric. The obtained fundamental tensors are shown to correspond both to well known tensors in Maxwell's theory, as well as several physically interesting new tensors.

The current paradigm in planet formation theory is developed around a hierarquical growth of solid bodies, from interstellar dust grains to rocky planetary cores. A particularly difficult phase in the process is the growth from meter-size boulders to planetary embryos of the size of our Moon or Mars. Objects of this size are expected to drift extremely rapid in a protoplanetary disk, so that they would generally fall into the central star well before larger bodies can form. In this thesis, we used numerical simulations to find a physical mechanism that may retain solids in some parts of protoplanetary disks long enough to allow for the formation of planetary embryos. We found that such accumulation can happen at the borders of so-called dead zones. These dead zones would be regions where the coupling to the ambient magnetic field is weaker and the turbulence is less strong, or maybe even absent in some cases. We show by hydrodynamical simulations that material accumulating between the turbulent active and dead regions would be trapped into vortices to effectively form planetary embryos of Moon to Mars mass. We also show that in disks that already formed a giant planet, solid matter accumulates on the edges of the gap the planet carves, as well as at the stable Lagrangian points. The concentration is strong enough for the solids to clump together and form smaller, rocky planets like Earth. Outside our solar system, some gas giant planets have been detected in the habitable zone of their stars. Their wakes may harbour rocky, Earth-size worlds.

In this thesis we address several analytical and numerical problems related with the general relativistic study of black hole space-times and boson stars. We have developed a new centered finite volume method based on the flux splitting approach. The techniques for dealing with the singularity, steep gradients and apparent horizon location, are studied in the context of a single Schwarzschild black hole, in both spherically symmetric and full 3D simulations. We present an extended study of gauge instabilities related with a class of singularity avoiding slicing conditions and show that, contrary to previous claims, these instabilities are not generic for evolved gauge conditions. We developed an alternative to the current space coordinate conditions, based on a generalized Almost Killing Equation. We performed a general relativistic study regarding the long term stability of Mixed-State Boson Stars configurations and showed that they are suitable candidates for dark matter models. / En esta tesis abordamos varios problemas analíticos y numéricos relacionados con el estudio de agujeros negros relativistas y modelos de materia oscura. Hemos desarrollado un nuevo método de volúmenes finitos centrados basado en el enfoque de la división de flujo. Discutimos las técnicas para tratar con la singularidad, los gradientes abruptos y la localización del horizonte aparente en el contexto de un solo agujero negro de Schwarzschild, en simulaciones tanto con simetría esférica como completamente tridimensionales. Hemos extendido el estudio de una familia de condiciones de foliaciones evitadoras de singularidad y mostrado que ciertas inestabilidades no son genéricas para condiciones de gauge dinámicas. Desarrollamos una alternativa a las prescripciones actuales basada en una Almost Killing Equation generalizada. Hemos realizado también un estudio con respecto a la estabilidad a largo plazo de configuraciones de Mixed-State Boson Stars, el cual sugiere que estas podrían ser candidatas apropiadas para modelos de materia oscura.

Nuclear spinodal instabilities are investigated in non-relativistic and relativistic stochastic mean-field approaches for charge asymmetric and charge symmetric nuclear matter. Quantum statistical effect on the growth of instabilities are calculated in non-relativistic approach. Due to quantal effects, in both symmetric and asymmetric matter, dominant unstable modes shift towards longer wavelengths and modes with wave numbers larger than the Fermi momentum are strongly suppressed. As a result of quantum statistical effects, in particular at lower temperatures, amplitude of density fluctuations grows larger than those calculated in semi-classical approximation. Relativistic calculations in the semi-classical limit are compared with the results of non-relativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around $rho_{B}=0.4 rho_{0}$ in the relativistic approach while most unstable behavior occurs at lower baryon densities around $rho_{B}=0.2 rho_{0}$ in the non-relativistic calculations.

The nuclear matter liquid-gas phase transition is expected to be a signal of nuclear spinodal instabilities as a result of density fluctuations. Nuclear spinodal instabilities in symmetric nuclear matter are studied within a stochastic relativistic density-dependent model in semi-classical approximation. We use two parameterization for the Lagrange density, DDME1 and TW sets. The early growth of density fluctuations is investigated by employing relativistic Vlasov equation based on QHD and discussed the cluster size of the condensations from the early growth of density correlation functions. Expectations are that hot nuclear matter behaves unstable around &rho / b &asymp / &rho / 0/4 (below the saturation density) and at low temperatures. We therefore present our results at low temperature T=1 MeV and at higher temperature T=5 MeV, and also at a lower initial baryon density &rho / b = 0.2 &rho / 0 and a higher value &rho / b = 0.4 &rho / 0 where unstable behavior is within them. Calculations in density-dependent model are compared with the other calculations obtained in a relativistic non-linear model and in a Skyrme type nonivrelativistic model. Our results are consistent with them. Qualitatively similar results show that the physics of the quantities are model-independent. The size of clusterization is estimated in two ways, by using half-wavelength of the most unstable mode and from the width of correlation function at half maximum. Furthermore, the average speed of condensing fragments during the initial phase of spinodal decomposition are determined by using the current density correlation functions.

<p>It is relatively straightforward to establish equilibrium inmagnetically confined plasmas, but the plasma is frequentlysucceptible to a variety of instabilities that are driven bythe free energy in the magnetic field or in the pressuregradient. These unstable modes exhibit effects that affect theparticle, momentum and heat confinement properties of theconfiguration. Studies of the dynamics of several of the mostimportant modes are the subject of this thesis. The studies arecarried out on plasmas in the reversed field pinch (RFP)configuration.</p><p>One phenomenon commonly observed in RFPs is mode walllocking. The localized nature of these phase- and wall lockedstructures results in localized power loads on the wall whichare detrimental for confinement. A detailed study of the walllocked mode phenomenon is performed based on magneticmeasurements from three RFP devices. The two possiblemechanisms for wall locking are investigated. Locking as aresult of tearing modes interacting with a static field errorand locking due to the presence of a non-ideal boundary. Thecharacteristics of the wall locked mode are qualitativelysimilar in a device with a conducting shell system (TPE-RX)compared to a device with a resistive shell (Extrap T2). Atheoretical model is used for evaluating the threshold valuesfor wall locking due to eddy currents in the vacuum vessel inthese devices. A good correlation with experiment is observedfor the conducting shell device.</p><p>The possibility of succesfully sustaining discharges in aresistive shell RFP is introduced in the recently rebuiltdevice Extrap T2R. Fast spontaneous mode rotation is observed,resulting in low magnetic fluctuations, low loop voltage andimproved confinement. Wall locking is rarely observed. The lowtearingmode amplitudes allow for the theoretically predictedinternal nonresonant on-axis resistive wall modes to beobserved. These modes have not previously been distinguisheddue to the formation of wall locked modes. The internal andexternal nonresonant resistive wall modes grow on the timescale of the shell penetration time. These growth rates dependon the RFP equilibrium. The internal nonresonant resistive wallmodes dominate in Extrap T2R, especially for shallow reverseddischarges. The external nonresonant modes grow solely in deepreversal discharges.</p><p><b>Keywords</b>Nuclear fusion, reversed field pinch, resistiveinstabilities, wall locked modes, tearing modes, resistiveshell modes, field errors, EXTRAP-T2, EXTRAP-T2R, TPE-RX</p>