String Cosmological Models with Magnetic Field

Core-collapse supernovae (CCSNe) are among the most energetic explosions in the universe, liberating the prodigious amount of ~ 1053 erg, the binding energy of their compact remnants, neutron stars or stellar mass black holes. While 99% of this energy is emitted in neutrinos, 1% goes into the internal and asymptotic kinetic energy of the ejecta, and it is reasonable to assume that a tiny fraction is radiated in gravitational waves (GWs). Ever since the first experimental efforts to detect GWs, CCSNe have been considered prime sources of gravitational waves for interferometric detectors. Besides neutrinos, which have already been observed in the context of stellar core collapse of SN1987A, GWs could provide us access to the electromagnetically hidden compact inner core of some such cataclysmic events, supplying us for example with valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. However, GW astronomy strongly depends on the extensive data processing of the detector output on the basis of reliable GW estimates, which only recently have become feasible with the emerging power of supercomputers. The work presented in this thesis is concerned with numerical CCSN models and their imprints in GWs. I performed an extensive series of more than 30 three-dimensional magnetohydrodynamical (MHD) core-collapse simulations. My models are based on a 15M [...] progenitor stemming from stellar evolution calculations, an effective general relativistic potential and either the Lattimer-Swesty (with three possible compressibilities) or the Shen equation of state (EoS) for hot, dense matter. Furthermore, the neutrino transport is tracked by computationally efficient algorithms for the radiative transfer of massless fermions. I systematically investigated the effects of the microphysical finite-temperature nuclear EoS, the initial rotation rate, both the toroidal and the poloidal magnetic fields, and multidimensional gravitational potentials on the GW signature. Based on the results of these calculations, I obtained the largest – and also one of the most realistic – catalogue of GW signatures from 3D MHD stellar core collapse simulations at present. I stress the importance of including postbounce neutrino physics, since it quantitatively alters the GW signature. Non- and slowly-rotating models show GW emission caused by prompt and protoneutron star (PNS) convection. Moreover, the signal stemming from prompt convection allows for the distinction between the two different nuclear EoS indirectly by different properties of the fluid instabilities. For simulations with moderate or even fast rotation rates, I only find the axisymmetric type I wave signature at core bounce. In line with recent results, I could confirm that the maximum GW amplitude scales roughly linearly with the ratio of rotational to gravitational energy (T/|W|) at core bounce below a threshold value of about 10%. Furthermore, I point out that PNS can become dynamically unstable to rotational instabilities at T/|W| values as low as ~ 2% at core bounce. Apart from these two points, I show that it is generally very difficult to discern the effects of the individual features of the input physics in a GW signal from a rotating CCSN that can be attributed unambiguously to a specific model. Weak magnetic fields do not notably influence the dynamical evolution of the core and thus the GW emission. However, for strong initial poloidal magnetic fields ≥ 1012G, the combined action of flux-freezing and field winding leads to conditions where the ratio of magnetic field pressure to matter pressure reaches about unity which leads to the onset of a jet-like supernova explosion. The collimated bipolar out-stream of matter is then reflected in the emission of a type IV GW signal. In contradiction to axisymmetric simulations, I find evidence that nonaxisymmetric fluid modes can counteract or even suppress jet formation for models with strong initial toroidal magnetic fields. I emphasize the importance of including multidimensional gravitational potentials in rapidly rotating 3D CCSN simulations: taking them into account can alter the resulting GW amplitudes up to a factor of 2 compared to simulations which encounter gravity only by a monopolar approximation. Moreover, I show that the postbounce dynamics occuring in the outer layers (at radii R ≥ 200km) of models run with 3D gravity deviates vastly from the ones run with a 1D or 2D gravitational potential. The latter finding implies that both spherically symmetric and axisymmetric treatments of gravity are too restrictive for a quantitative description of the overall postbounce evolution of rapidly rotating CCSN models. The results of models with continued neutrino emission show that including deleptonization during the postbounce phase is an indispensable issue for the quantitative prediction of GWs from core-collapse supernovae, because it can alter the GW amplitude up to a factor of 10 compared to a pure hydrodynamical treatment. My collapse simulations indicate that corresponding events in our Galaxy would be detectable either by LIGO, if the source is rotating, or at least by the advanced LIGO detector, if it is not or only slowly rotating.

Electromagnetic Environment Associated with Lightning Strikes to Tall Strike Objects

In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N > 1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N = 2. We further show that this theorem does not hold for N > 2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity.

Edge Localized Mode Control in TCV

Thermodynamic and Gasdynamic Aspects of a Boiling Liquid Expanding Vapour Explosion

In radiation belt physics radial distance is often thought of by L*, which approximates the distance from the Earth’s centre to an equatorial point (if we were to assume a dipole magnetic field). Global magnetic field models allow a subset of locations on the ground to be mapped along field lines to a location in space and transformed into L*, provided that location maps to a closed drift path. This allows observations from ground, or low-altitude space-based platforms to be mapped into space in order to inform radiation belt modelling. In current modelling efforts a decision must therefore be made for the global magnetic field model to implement. Many data-based magnetic field models exist; however these models can significantly disagree on mapped L* values for a single point on the ground, during both quiet times and storms. We present a state of the art probabilistic L* mapping tool, Pro-L*, which produces probability distributions for L* corresponding to a given ground location. Pro-L* is an extensive dataset comprising 11 years worth of hourly L* values for 7 global magnetic field models, spanning a high resolution grid in the Northern Hemisphere where ground instruments for radiation belt studies are mostly located. Accompanying each L* approximation, the McIlwain L, magnetic field amplitude and Cartesian location are also stored. Data was generated using the International Radiation Belt Environment Modelling library (IRBEM-Lib), a collection of FORTRAN 77 processes for radiation belt modelling which compute magnetic coordinates and drift shells using various external magnetic field models, hosted in the Python package Spacepy. The data is formatted in yearly compressed csv files, with each row a particular hour containing all of the mentioned variables for each magnetic field model, the corresponding grid points’ magnetic latitude, magnetic longitude, and magnetic local time (MLT). Therefore, each hour index appears for each grid point.

A viable alternative to cosmological inflation is provided by the combined theory of quiescent cosmology and the Weyl curvature hypothesis. We augment the conformal framework of this theory by incorporating the spacetime property of self-similarity. A generalisation of the conformal Killing equation is developed as a definition of asymptotic self-similarity for use in the framework; we derive several propositions and theorems that facilitate the application of this definition, and demonstrate asymptotic self-similarity for FLRW and other models. We also detail the conditions under which self-similarity is preserved by conformal transformations, and investigate its relationship to other symmetry properties in the framework.

In this paper, dynamic response of the horizontal concrete beam subjected to seismic ground excitation is investigated. The structure is reinforced by Fe2O3 nanoparticles which have the magnetic properties. The hyperbolic shear deformation beam theory (HSDBT) is used for mathematical modeling of the structure. Based on the Mori-Tanaka model, the effective material properties of concrete beam is calculated considering the agglomeration of Fe2O3 nanoparticles. Applying energy method and Hamilton\'s principle, the motion equations are derived. Harmonic differential quadrature method (HDQM) along with Newmark method is utilized for numerical solution of the motion equations. The effects of different parameters such as volume fraction and agglomeration of Fe2O3 nanoparticles, magnetic field, boundary conditions and geometrical parameters of concrete beam are studied on the dynamic response of the structure. In order to validation of this work, an exact solution is used for comparing the numerical and analytical results. The results indicated that applying magnetic field decreases the of the structure up to 54 percent. In addition, increase too much the magnetic field (Hx>5e8 A/m) does not considerable effect on the reduction of the maximum dynamic displacement.

A class of exact non-static solutions to the Einstein field equations has been derived for Bianchi type-V space-time filled with a viscous perfect fluid in the presence and absence of a magnetic field. Some physical consequences of the models have also been discussed.

Magnetized, cold, dense molecular cloud cores provide the birth environment for stars, discs, and planets. The multi-scale scenario of low-mass star formation occurs via the formation of two quasi-hydrostatic cores. Furthermore, the conservation of angular momentum can lead to the formation of a disc around the second core (i.e.~the forming protostar). During these early stages of star formation, magnetically driven outflows and jets can be launched from the first and second cores, respectively. Star, disc, and outflow formation involve complex physical processes, which require a robust, self-consistent numerical treatment. In this thesis, we use numerical simulations to probe the gravitational collapse scenario that involves the transition of an isolated molecular cloud core to a hydrostatic core with a surrounding disc. We use the \emph{PLUTO} code to perform radiation (magneto-)hydrodynamic (MHD) collapse simulations, using one- and two-dimensional (2D) grids. We include the effects of self-gravity and a grey flux-limited diffusion approximation for the radiative transfer. Additionally, we use for the gas equation of state density- and temperature-dependent thermodynamic quantities to account for the dissociation, ionisation, and molecular vibrations and rotations. Our spherically symmetric simulations span seven orders of magnitude in spatial scale. We survey a wide range of initial low- to high-mass (0.5 -- 100~$M_{\odot}$) molecular cloud cores, yielding the largest parameter scan so far. Our results highlight the dependence of the first and second hydrostatic core properties on the initial cloud core properties. These simulations indicate that in the high-mass regime, the first hydrostatic cores do not have enough time to form due to large accretion rates. We further expand our studies to three different sets of 2D simulations using axial and midplane symmetry. First, we perform 2D simulations for non-rotating molecular cloud cores with masses of 1~$M_{\odot}$, 5~$M_{\odot}$, 10~$M_{\odot}$, and 20~$M_{\odot}$. For each of these cases, we use an unprecedented resolution to model the evolution of the second core for $\geq$~100 years after its formation. For the first time, we demonstrate that convection is generated in the outer layers of the second core. This supports the intriguing possibility that dynamo-driven magnetic fields may be generated during the earliest phases of star formation. Following which, for the 1~$M_{\odot}$ case, we analyse the effects of solid-body rotation on the properties of the hydrostatic cores and disc formation. In this model, the first hydrostatic core evolves into a more oblate, pseudo-disc like structure and a sub-au disc starts forming after the formation of the second core. Finally, we explore the effects of ideal and non-ideal (including Ohmic resistivity) MHD during the collapse of rotating molecular cloud cores. We investigate the dependence of molecular outflows and disc formation on the initial cloud core mass, rotation, resistivity, and magnetic field strength. We find the presence of magnetically driven outflows launched from both first and second cores in the resistive models. We also reveal ongoing disc formation in some of our resistive simulations. In conclusion, we use detailed thermodynamical modelling to quantify the properties of the hydrostatic cores, outflows, and discs for collapse scenarios with a wide range of initial cloud core properties. The models presented herein will serve as the foundation for follow-up studies that link these theoretical insights with observational signatures.

The major objective of this thesis is to reorient and analyze three component magnetic field data recorded in two boreholes during Integrated Ocean Drilling Program (IODP) Expedition 330 to the Louisville Seamount Chain. One aim of the expedition was to determine whether the hotspot that created the seamount chain during the past 80 million years is moving relative to the Hawaiian-Emperor hotspot or if it remained stationary within the mantle. The magnetic field measurements were conducted with the Gottinger Bohrlochmagnetometer, which comprises fibre optic gyros that measure the rotations of the tool within the borehole. In this thesis, I use different algorithms to reorient the measured magnetic field from the tools reference frame into the geographical reference frame. This purpose requires sensors of high accuracy and careful data processing. I present several reorientation algorithms; among others, I introduce two new sensor fusion algorithms for gyro and inclinometer data based on a Kalman filter. Oriented magnetic field data can be used to determine both the inclination and declination of the magnetization of the rocks surrounding the borehole by the application of appropriate models. Measurements on drill core samples can typically only be used to determine the inclination of magnetization, as cores are usually azimuthally unoriented. In the subsequent analysis of the oriented magnetic field data, I use different models for the drilled igneous layers to calculate the magnetization of the subsurface. As horizontal layers turn out to be insufficient to explain the data, I extend the interpretation to inclined layers. I introduce a new approximation for the magnetic field of inclined layers that can be used to separate the calculation of magnetization in an inversion using horizontal layers and a following consideration of potential layer geometries. My approximation additionally reveals possible ambiguities and errors of the measurements. Using images of the borehole wall that give additional information about the possible geometry of a drilled layer inside Burton Guyot (Site U1376), I determine a mean inclination of magnetization of 58.9° and a mean declination of magnetization of 0.4°. These results agree with current theories of a stationary Louisville hotspot. In addition, the result for the declination suggests that Burton Guyot has not been rotated since its formation.

We study under which conditions a space-time admits at each point coordinate systems with the same orientation. A generalization of the Fermi derivative to a linear connection compatible with the metric is considered: Fermi connection. Using techniques of Lie groups. it is proved that the parallel transport associated to the Fermi connection corresponds to spatial rotations. Hence, those space-times for which a Fermi connection with vanishing curvature can be defined admit at each point coordinate systems with the same orientation. Conformally flat solutions with a perfect fluid and the equation of state p = -3p are considered. These solutions. when Θ 2 = 24πρ, admit at each point coordinate systems with the same orientation. An example is the Robertson-Walker universe of infinite radius.

In magnetically confined fusion devices, the energy and particle transport is significantly larger than expected from purely collisional processes. This degraded confinement mostly results from small-scale turbulence and prevents from reaching self-sustained burning plasma conditions in present day experiments. A better understanding of these nonlinear phenomena is therefore of key importance on the way towards controlled fusion. The small-scale microinstabilities and associated turbulence are investigated for Tokamak plasmas by means of numerical simulations in the frame of the gyrokinetic theory. This model describes the evolution of the particle distribution functions in phase space together with self-consistent electromagnetic fields, while neglecting the fast motion associated with the Larmor orbit of particles around the magnetic field lines. In the course of this thesis work, substantial modifications to the existing Eulerian gyrokinetic code GENE have been carried out in collaboration with the Max-Planck-Institute für Plasmaphysik in Garching, Germany. The code has been extended from a local approximation, which only considers a reduced volume of a fusion plasma, to a global version which fully includes radial temperature and density profiles as well as radial magnetic equilibrium variations. To this end, the gyrokinetic equations have been formulated for general magnetic geometry, keeping radial variations of equilibrium quantities, and considering field aligned coordinates, suitable for their numerical implementation. The numerical treatment of the radial direction has been modified from a Fourier representation in the local approach to real space in the global code. This has in particular required to adapt the radial derivatives, the field solver, and to implement a real space dealiasing scheme for the treatment of the nonlinearity. A heat source was in addition introduced to allow for steady state global nonlinear simulations. An important part of this work also focused on the description of the magnetic equilibrium. A circular concentric flux surface model as well as an interface with an MHD equilibrium code were implemented. A detailed investigation concerning the s – α model, previously used in local codes, was also carried out. It was shown that inconsistencies in this model had resulted in misinterpreted agreement between local and global results at large ρ* = ρs/a values, with ρs the Larmor radius and a the minor radius of the Tokamak. True convergence between local and global simulations was finally obtained by correct treatment of the geometry in both cases and considering the appropriate ρ* → 0 limit in the latter case. The new global code was furthermore successfully tested and benchmarked against various other codes in the adiabatic electron limit in both the linear and nonlinear regime. A nonlinear ρ* scan was in addition carried out showing convergence to the local results in the limit ρ* → 0 and also providing further insight on previous disagreements between two other global gyrokinetic codes concerning ρ* convergence. Linear global simulations with kinetic electrons have shown consistent behavior with respect to local results. Using the interface with the MHD equilibrium code, the effects of plasma shaping on Ion Temperature Gradient (ITG) instabilities were investigated by means of local simulations. A favorable influence of elongation and negative triangularity was observed. It was shown that these effects could be mostly accounted for by the modifications of the effective flux-surface averaged temperature gradient. Most importantly, a unique effective nonlinear critical temperature gradient could be determined for the different considered elongations and triangularities. The local code was finally used to investigate particle and energy transport in the case of TCV discharges presenting an electron Internal Transport Barrier (eITB). It was shown that at the transition between ITG and Trapped Electron Mode (TEM) dominated turbulent regimes, the particle flux goes to zero. Interestingly, this effect could be well reproduced by a quasi-linear approach where all the different unstable wavenumbers are considered. The nonlinear simulations also revealed that a minimum of the electron heat diffusivity is observed at the transition between the TEM and ITG regimes. A strong dependence of this quantity was also noticed with respect to the density gradient. Quantitative comparisons with experimental results have shown that a reasonable agreement could only be reached in regions where the density gradient is small while the flux tube simulations seem to overestimate the heat transport if one accounts for gradient values in the center of the transport barrier. Some first nonlinear global simulations appear to indicate that finite ρ* effects could potentially play an important role and thus reduce the heat diffusivity to realistic values.

We investigate the numerical modelling of relativistic protons, so-called cosmic rays, in a magnetised plasma. For the first time we combine two different components of a cosmological simulation code that so far have only been tested and employed independently of each other. By means of magnetohydrodynamic shock tube calculations in a gas that contains a constant fraction of relativistic particles we check for the correct physical behaviour of the combined numerical models. For this purpose we derive an analytical expression for the magnetosonic shock and rarefaction waves in the MHD Riemann problem and solve for the resulting system of equations using an iterative scheme. Comparing the theoretical and numerical solutions of a number of shock tube calculations we assess the physical correctness of the simulation. After successful testing we simulate the structure formation of three galaxy clusters including the consistent modelling of magnetic fields and cosmic rays. By means of analytical models we compute the X-ray and radio emission of the simulated clusters and reveal the temporal correlation between both quantities. Through a comparison with the strong lensing cross sections we demonstrate that the observable radio emission of galaxy clusters is directly connected to the occurrence of substructure in their dark matter halos and is thus triggered by strong merger shocks.

A mathematical solution to Einstein's field equations with a perfect fluid source, with variable gravitational constant $G$ and Cosmological constant $\Lambda$ for FRW space-time in higher dimensions is obtained and case study has also been done where the values of $\rho(t), G(t), \Lambda(t), q(t),$ and $d_{H}(t)$ has been obtained and their nature is also analyzed.