Precise velocity and acceleration information is required for many real time applications. A standalone GPS receiver can be used to derive such information; however, there are many unsolved problems in this regard. This thesis establishes the theoretical basis for precise velocity and acceleration determination using a standalone GPS receiver in real time. An intensive investigation has been conducted into the Doppler effect in GPS. A highly accurate Doppler shift one-way observation equation is developed based on a comprehensive error analysis of each contributing factor including relativistic effects. Various error mitigation/elimination methods have been developed to improve the measurement accuracy of both the Doppler and Doppler-rate. Algorithms and formulae are presented to obtain real-time satellite velocity and acceleration in the ECEF system from the broadcast ephemeris. Low order IIR differentiators are designed to derive Doppler and Doppler-rate measurements from the raw GPS data for real-time applications. Abnormalities and their corresponding treatments in real-time operations are also discussed. In addition to the velocity and acceleration determination, this thesis offers a good tool for GPS measurement modelling and for design of interpolators, differentiators, as well as Kalman filters. The relativistic terms presented by this thesis suggest that it is possible to measure the geopotential directly using Doppler shift measurements. This may lead to a foundation for the development of a next generation satellite system for geodesy in the future.

<p>Oscillator strengths and transition energies are calculated for several mono-substitutes of benzene and naphthalene molecules. The substituents investigated are chlorine, bromine and iodine. Calculations for these molecules are presented, at the Hartree-Fock and DFT level of theory. The functional used in DFT is CAM-B3LYP.</p>

This Thesis puts its focus on the physics of neutron stars and its description with methods of numerical relativity. In the first step, a new numerical framework the Whisky2D code will be developed, which solves the relativistic equations of hydrodynamics in axisymmetry. Therefore we consider an improved formulation of the conserved form of these equations. The second part will use the new code to investigate the critical behaviour of two colliding neutron stars. Considering the analogy to phase transitions in statistical physics, we will investigate the evolution of the entropy of the neutron stars during the whole process. A better understanding of the evolution of thermodynamical quantities, like the entropy in critical process, should provide deeper understanding of thermodynamics in relativity. More specifically, we have written the Whisky2D code, which solves the general-relativistic hydrodynamics equations in a flux-conservative form and in cylindrical coordinates. This of course brings in 1/r singular terms, where r is the radial cylindrical coordinate, which must be dealt with appropriately. In the above-referenced works, the flux operator is expanded and the 1/r terms, not containing derivatives, are moved to the right-hand-side of the equation (the source term), so that the left hand side assumes a form identical to the one of the three-dimensional (3D) Cartesian formulation. We call this the standard formulation. Another possibility is not to split the flux operator and to redefine the conserved variables, via a multiplication by r. We call this the new formulation. The new equations are solved with the same methods as in the Cartesian case. From a mathematical point of view, one would not expect differences between the two ways of writing the differential operator, but, of course, a difference is present at the numerical level. Our tests show that the new formulation yields results with a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. The second part of the Thesis uses the new code for investigations of critical phenomena in general relativity. In particular, we consider the head-on-collision of two neutron stars in a region of the parameter space where two final states a new stable neutron star or a black hole, lay close to each other. In 1993, Choptuik considered one-parameter families of solutions, S[P], of the Einstein-Klein-Gordon equations for a massless scalar field in spherical symmetry, such that for every P > P⋆, S[P] contains a black hole and for every P < P⋆, S[P] is a solution not containing singularities. He studied numerically the behavior of S[P] as P → P⋆ and found that the critical solution, S[P⋆], is universal, in the sense that it is approached by all nearly-critical solutions regardless of the particular family of initial data considered. All these phenomena have the common property that, as P approaches P⋆, S[P] approaches a universal solution S[P⋆] and that all the physical quantities of S[P] depend only on |P − P⋆|. The first study of critical phenomena concerning the head-on collision of NSs was carried out by Jin and Suen in 2007. In particular, they considered a series of families of equal-mass NSs, modeled with an ideal-gas EOS, boosted towards each other and varied the mass of the stars, their separation, velocity and the polytropic index in the EOS. In this way they could observe a critical phenomenon of type I near the threshold of black-hole formation, with the putative solution being a nonlinearly oscillating star. In a successive work, they performed similar simulations but considering the head-on collision of Gaussian distributions of matter. Also in this case they found the appearance of type-I critical behaviour, but also performed a perturbative analysis of the initial distributions of matter and of the merged object. Because of the considerable difference found in the eigenfrequencies in the two cases, they concluded that the critical solution does not represent a system near equilibrium and in particular not a perturbed Tolmann-Oppenheimer-Volkoff (TOV) solution. In this Thesis we study the dynamics of the head-on collision of two equal-mass NSs using a setup which is as similar as possible to the one considered above. While we confirm that the merged object exhibits a type-I critical behaviour, we also argue against the conclusion that the critical solution cannot be described in terms of equilibrium solution. Indeed, we show that, in analogy with what is found in, the critical solution is effectively a perturbed unstable solution of the TOV equations. Our analysis also considers fine-structure of the scaling relation of type-I critical phenomena and we show that it exhibits oscillations in a similar way to the one studied in the context of scalar-field critical collapse. / Diese Arbeit legt seinen Schwerpunkt auf die Physik von Neutronensternen und deren Beschreibung mit Methoden der numerischen Relativitätstheorie. Im ersten Schritt wird eine neue numerische Umgebung, der Whisky2D Code entwickelt, dieser löst die relativistischen Gleichungen der Hydrodynamik in Axialymmetrie. Hierzu betrachten wir eine verbesserte Formulierung der sog. "flux conserved formulation" der Gleichungen. Im zweiten Teil wird der neue Code verwendet / um das kritische Verhalten zweier kollidierenden Neutronensternen zu untersuchen. In Anbetracht der Analogie, um Übergänge in der statistischen Physik Phase werden wir die Entwicklung der Entropie der Neutronensterne während des gesamten Prozesses betrachten. Ein besseres Verständnis der Evolution von thermodynamischen Größen, wie der Entropie in kritischer Prozess, sollte zu einem tieferen Verständnis der relativistischen Thermodynamik führen. Der Whisky2D Code, zur Lösung Gleichungen relativistischer Hydrodynamik wurde in einer „flux conserved form“ und in zylindrischen Koordinaten geschrieben. Hierdurch entstehen 1 / r singuläre Terme, wobei r der ist, die entsprechend behandelt werden müssen. In früheren Arbeiten, wird der Operator expandiert und die 1 / r spezifisch Therme auf die rechte Seite geschrieben, so dass die linke Seite eine Form annimmt, die identisch ist mit der kartesischen Formulierung. Wir nennen dies die Standard-Formulierung. Eine andere Möglichkeit ist, die Terme nicht zu expandieren, den und den 1/r Term in die Gleichung hinein zu ziehen. Wir nennen dies die Neue-Formulierung. Die neuen Gleichungen werden mit den gleichen Verfahren wie im kartesischen Fall gelöst. Aus mathematischer Sicht ist keine Unterschiede zwischen den beiden Formulierungen zu erwarten, erst die numerische Sicht zeigt die Unterschiede auf. Versuche zeigen, dass die Neue-Formulierung numerische Fehler um mehrere Größenordnungen reduziert. Der zweite Teil der Dissertation verwendet den neuen Code für die Untersuchung kritischer Phänomene in der allgemeinen Relativitätstheorie. Insbesondere betrachten wir die Kopf-auf-Kollision zweier Neutronensterne in einem Bereich des Parameter Raums, deren zwei mögliche Endzustände entweder einen neuen stabilen Neutronenstern oder ein Schwarzes Loch darstellen. Im Jahr 1993, betrachtete Choptuik Ein-Parameter-Familien von Lösungen, S [P], der Einstein-Klein-Gordon-Gleichung für ein masseloses Skalarfeld in sphärischer Symmetrie, so dass für jedes P> P ⋆, S[P] ein Schwarzes Loch enthalten ist und jedes P <P ⋆, S [P] eine Lösung ohne eine Singularität. Er studierte das numerisch Verhalten von S [P] als P → P ⋆ und stellte fest, dass die kritische Lösung, S[P ⋆], universell in dem Sinne ist, dass die Lösung nahe des kritischen Wertes unabhängig von den Anfangsdaten ist. Alle diese Phänomene haben die gemeinsame Eigenschaft, dass sobald sich P P ⋆ annähert, auch S[P] S [P ⋆] annähert und dass alle physikalischen Größen von S [P] nur noch von | P - P ⋆ | abhängen. Die erste Studie der kritischen Phänomene über den Frontalzusammenstoß von zwei Neutronensternen wurde von Jin und Suen im Jahr 2007 durchgeführt. Insbesondere untersuchten sie eine Reihe von Anfangsdaten gleicher Neutronensternmasse, mit einer idealen EOS, die aufeinander zu beschleunigt werden. Variiert wurden die Massen der Sterne, ihr Abstand, die Geschwindigkeit und die polytropen Index der EOS. Auf diese Weise konnten sie kritische Phänomen des Typ I beobachten. In weiteren Versuchen, führten sie ähnliche Simulationen frontal kollidierender Materie in Gauß Verteilungen durch. Auch in diesem Fall fanden sie Typ-I-kritisches Verhalten. Zudem führten sie eine störungstheoretische Analyse der Anfangsobjekte als auch der stabilen Endobjekte durch. Wegen der beträchtlichen Unterschiede in den Eigenfrequenzen in beiden Fallen, schlossen sie daraus, dass die kritische Lösung keine linear-gestörten Tolmann-Oppenheimer-Volkoff (TOV) Sterne im Gleichgewicht darstellen. In dieser Arbeit untersuchen wir die Dynamik der Frontalzusammenstoß zweier Neutronensterne gleicher Masse mit ähnlichem Setup wie oben besprochen. Während wir bestätigen, dass die erzeugten Objekte ebenfalls ein Typ-I-kritische Verhalten aufweisen, wiedersprechen wir der der Aussage, dass sich die kritische Lösung nicht als Gleichgewichtslösung dargestellt werden kann. In der Tat zeigen wir, dass die kritische Lösung als linear-gestörte instabile Lösung eines TOV-Sterns dargestellt werden kann. Unsere Analyse berücksichtigt auch die Feinstruktur der Skalenverhältnisse Typ-I-kritischer Phänomene und wir zeigen ebenfalle, dass hier Oszillationen auftreten, die bereits in ähnlichen Studien zum Kollaps kritischer Skalar-Feld gefunden wurden.

In this thesis we study the relativistic multipole moments for stationary asymptotically flat spacetimes as introduced by Geroch and Hansen. These multipole moments give an asymptotic description of the gravitational field in a coordinate independent way. Due to this good description of the spacetimes, it is natural to try to construct a spacetime from only the set of multipole moments. Here we present a simple method to do this for the static axisymmetric case. We also give explicit solutions for the cases where the number of non-zero multipole moments are finite. In addition, for the general stationary axisymmetric case, we present methods to generate solutions. It has been a long standing conjecture that the multipole moments give a complete characterization of the stationary spacetimes. Much progress toward a proof has been made over the years. However, there is one remaining difficult task: to prove that a spacetime exists with an a-priori given arbitrary set of multipole moments subject to some given condition. Here we present such a condition for the axisymmetric case, and prove that it is both necessary and sufficient. We also extend this condition to the general case without axisymmetry, but in this case we only prove the necessity of our condition.

Oscillator strengths and transition energies are calculated for several mono-substitutes of benzene and naphthalene molecules. The substituents investigated are chlorine, bromine and iodine. Calculations for these molecules are presented, at the Hartree-Fock and DFT level of theory. The functional used in DFT is CAM-B3LYP.

The Quark Gluon Plasma (QGP) is a form of matter in which quarks and gluons are deconfined, and was suggested to be formed in high-energy heavy-ion collisions. Since the discovery of high-pT hadron suppression in central Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), and the related discovery of the quenching of the away-side jet in these collisions, the role of jets as key probes of the QGP was re-affirmed. The Solenoidal Tracker At RHIC (STAR) detector system, which is suited for jet studies because of its large solid-angle coverage, has produced a number of interesting jet measurements in recent years, including gamma-jet measurements, attempts at full heavy-ion jet reconstruction, and two-dimensional correlations. A long-range correlation in pseudorapidity (the ?Ridge?) was studied (with statistical significance) out to pT^trig. <? 7 GeV /c and was assumed to have an integrated yield independent of pT^trig. Further studies out to higher pT were limited by the minimum biased statistics taken in Run 4 (2004) with STAR. This work presents results of a ridge analysis with (non-reconstructed) pi0s and direct-gamma-rich triggers out to ?13.5 GeV /c in pT^trig. Using triggered data from Run 7 (2007) and Run 10 (2010) Au+Au collisions detected with STAR. Preliminary results seem to indicate that the ridge yield decreases with pT^trig., and that the ridge yield for direct-?-rich triggers is consistent with zero.

In this thesis we present a time-dependent multi-zone radiative transfer code and its applications to study the multiwavelength emission of blazars. The multiwavelength variability of blazars is widely believed to be a direct manifestation of the formation and propagation of relativistic jets, and hence the related physics of the black hole - accretion disk - jet system. However, the understanding of these variability demands highly sophisticated theoretical analysis and numerical simulations. Especially, the inclusion of the light travel time effects(LTTEs) in these calculations has long been realized important, but very difficult. The code we use couples Fokker-Planck and Monte Carlo methods, in a 2 dimensional (cylindrical) geometry. For the first time all the LTTEs are fully considered, along with a proper, full, self-consistent treatment of Compton cooling, which depends on the LTTEs. Using this code, we studied a set of physical processes that are relevant to the variability of blazars, including electron injection and escape, radiative cooling, and stochastic particle acceleration. Our comparison of the observational data and the simulation results revealed that a combination of all those processes is needed to reproduce the observed behaviors of the emission of blue blazars. The simulation favors that the high energy emission at quiet and flare stages comes from the same location. We have further modeled red blazars PKS 1510-089. External radiation, which comes from the broad line region (BLR) or infrared torus, is included in the model. The results confirm that external Compton model can adequately describe the emission from red blazars. The emission from BLR is favored as the source of Inverse Compton seed photons, compared to synchrotron and IR torus radiation.

This dissertation presents a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map a subsonic flow into a canonical Laplacian flow with the same boundary conditions. The method represents the generalization of the methods of Prandtl-Glauert and Karman-Tsien and gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by the analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the wave equation under Lorentz transformations. Whereas elements of the special theory can be invoked for linear and global compressibility effects, the question posed in this work is whether other techniques from relativity theory could be used for effects that are nonlinear and local. This line of thought leads to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. The dissertation presents the theory and a numerical method for practical solutions of equivalent incompressible flows over arbitrary profiles. The numerical method employs an iterative approach involving the solution of the incompressible flow with a panel method and the solution of the coordinate mapping to the canonical flow with a finite difference approach. This method is demonstrated for flow over a circular cylinder and over a NACA 0012 profile. Results are validated with subcritical full potential test cases available in the literature. Two areas of applicability of the method have been identified. The first is airfoil inverse design leveraging incompressible flow knowledge and empirical data for the potential field effects on boundary layer transition and separation. The second is aerodynamic testing using distorted models.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 178-185).

We study particle production and its density evolution and equilibration in hot dense medium, such as hadronic gas after quark gluon plasma hadronization and relativistic electron positron photon plasma. For this study we use kinetic momentum integrated equations for particles density evolution with Lorentz invariant reaction rates. We extend these equations, used before for two-to-two particles reactions (1 + 2 ↔ 3 + 4), to the case of two-to-one and backward reactions (1 + 2 ↔ 3). One type of hot dense medium, which we study, is hadronic gas produced at quark gluon plasma hadronization in heavy ions collisions in SPS, RHIC and LHC experiments. We study hadron production at quark gluon plasma hadronization and their evolution in thermal hadronic gas phase. We consider non-equilibrium hadronization model, for which the yields of the light quark hadrons are defined by entropy conservation. Yields of hadrons containing heavier (strange, charm, bottom) quarks are mainly controlled by flavor conservation. We predict yields of charm and bottom hadrons within this non-equilibrium statistical hadronization model. Then we use this non-equilibrium hadronization as the initial condition in the study of hadronic kinetic phase. During this time period some hadronic resonances can be produced in lighter hadrons fusion. This reaction is opposite to resonance decay. Production of resonances is dominant over decay if there is non-equilibrium excess of decay products. Within this model we explain apparently contradictory experimental results reported in RHIC experiments: ∑(1385) yield is enhanced while ∧(1520) yield is suppressed compared to the statistical hadronization model expectation obtained without kinetic phase. We also predict Δ(1232) enhancement. The second type of plasma medium we consider is the relativistic electron position photon plasma (EP³) drop. This plasma is expected to be produced in decay of supercritical field created in ultrashort laser pulse. We study at what conditions this plasma drop is opaque for photons and therefore may reach thermal and chemical equilibrium. Further we consider muon and pion production in this plasma also as a diagnostic tool. Such heavy particles can be diagnostic tool to study the properties of EP³ plasma, similar to the role taken by heavy hadrons production in heavy ions collisions. Finally all these theoretical developments can be applied to begin a study of particles evolution in early universe in temperatures domain from QGP hadronization (160 MeV) to nucleosynthesis (0.1 MeV). The first results on pion equilibration are presented here.