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Gene networks can be modeled by piecewise-linear (PL) switching systems of differential equations, called Glass networks after their originator. Networks of interacting genes that regulate each other may have complicated interactions. From a `systems biology' point of view, it would be useful to know what types of dynamical behavior are possible for certain classes of network interaction structure. A useful way to describe the activity of this network symbolically is to represent it as a directed graph on a hypercube of dimension $n$ where $n$ is the number of elements in the network. Our work here is considering this problem backwards, i.e. we consider different types of cycles on the $n$-cube and show that there exist parameters, consistent with the directed graph on the hypercube, such that a periodic orbit exists. For any simple cycle on the $n$-cube with a non-branching vertex, we prove by construction that it is possible to have a stable periodic orbit passing through the corresponding orthants for some sets of focal points $F$ in Glass networks. When the simple cycle on the $n$-cube doesn't have a non-branching vertex, a structural principle is given to determine whether it is possible to have a periodic orbit for some focal points. Using a similar construction idea, we prove that for self-intersecting cycles where the vertices revisited on the cycle are not adjacent, there exist Glass networks which have a periodic orbit passing through the corresponding orthants of the cycle. For figure-8 patterns with more than one common vertex, we obtain results on the form of the return map (Poincar{\'e} map) with respect to how the images of the returning cones of the 2 component cycle intersect the returning cone themselves. Some of these allow complex behaviors.

In the recent years, interest in TM oxides with 5d valence electrons has grown immensely due to the realization of novel spin-orbit coupled ground states. In these compounds, e.g., iridates and osmates, the intriguing situation arises where the spin-orbit and electron-electron interactions meet on the same energy scale. This has created a new window of interest in these compounds since the interplay of crystal field effects, local multiplet physics, spin-orbit couplings, and intersite hopping can offer novel types of correlated ground states and excitations. In 5d5 iridates, a spin-orbit entangled j = 1/2 Mott insulating state has been realized recently. A remarkable feature of such a ground state is that it gives rise to anisotropic magnetic interactions. The 2D honeycomb-lattice 213 iridium oxides, A2IrO3 (A=Li,Na), have been put forward to host highly anisotropic bond-dependent spin-spin interactions that resemble the Kitaev spin model, which supports various types of topological phases relevant in quantum computing. The 2D square-lattice 214 iridates Sr2IrO4 and Ba2IrO4 are, on the other hand, appealing because of their perceived structural and magnetic simi- larity to La2CuO4, the mother compound of the cuprate high-Tc superconductors. This has promoted the latter iridium oxide compounds as novel platforms for the search of high-Tc superconductivity. To put such considerations on a firm footing, it is essential to quantify the different coupling strengths and energy scales, as they for instance appear in effective Hamiltonian descriptions of these correlated systems. Moreover, it is important to correctly describe their effects. In this thesis, the electronic structure and magnetic properties of 5d5 (mainly 214 and 213) iridates are studied using wave-function-based quantum chemistry methods. These methods are fully ab initio and are capable of accurately treating the electron-electron interactions without using any ad hoc parameters. The spin-orbit entangled j = 1/2 ground state in 214, 213 and other lower symmetry Sr3CuIrO6 and Na4Ir3O8 iridates is first analyzed in detail, by studying the local electronic structure of the 5d5 Ir4+ ion. We establish that the longer-range crystal anisotropy, i.e., low-symmetry fields related to ionic sites beyond the nearest neighbor oxygen cage, strongly influence the energies of Ir d levels. The ground state in all the compounds studied is j = 1/2 like with admixture from j ≃ 3/2 states ranging from 1 – 15 %. Further, the average j ≃ 1/2 → j ≃ 3/2 excitation energy we find is around 0.6 eV. The NN magnetic exchange interactions we computed for 214 iridates are predominantly isotropic Heisenberg-like with J ~ 60 meV, 3 – 4 times smaller than found in isostructural copper oxides. However, the anisotropic interactions are an order of magnitude larger than those in cuprates. Our estimates are in excellent agreement with those extracted from experiments, e.g., resonant inelastic x-ray scattering measurements. For the 213 honeycomb-lattice Na2IrO3 our calculations show that the relevant spin Hamiltonian contains further anisotropic terms beyond the Kitaev-Heisenberg model. Nevertheless, we predict that the largest energy scale is the Kitaev interaction, 10 to 20 meV, while the Heisenberg superexchange and off-diagonal symmetric anisotropic couplings are significantly weaker. In the sister compound Li2IrO3, we find that the structural inequivalence between the two types of Ir-Ir links has a striking influence on the effective spin Hamiltonian, leading in particular to two very different NN superexchange pathways, one weakly AF (~ 1 meV) and another strongly FM (−19 meV). The latter gives rise to rigid spin-1 triplets on a triangular lattice.

This study aims to investigate different orbit determination algorithms for the first Turkish remote sensing satellite, BiLSAT-1. The micro-satellite carries an onboard GPS receiver. Pseudorange measurements simulated from the position and velocity data supplied by T&Uuml / BiTAK-BiLTEN are used for the implementation of different orbit determination algorithms concluding to an estimate of the satellite&rsquo / s state. Satellite&rsquo / s position, velocity components and the GPS receiver&rsquo / s clock bias are selected as the state parameters to be estimated. Kalman filter algorithms are used for the estimation of these state parameters. The modeled affecting force components include / geopotential and atmospheric drag. The global gravity models EGM96 and EIGEN-CG03C have been utilized together with Harris Priester atmospheric density model for the force modeling. The effect of the changes during the implementation of the force models, numerical integration, and estimation algorithms are investigated. Software has been developed using MATLAB programming language for the implementation of all algorithms performed in this study for orbit determination.

Let G be a compact Lie group and let π be an irreducible representation of G of highest weight λ. We study the operator-valued Fourier transform of the product of the j-function and the pull-back of ?? by the exponential mapping. We show that the set of extremal points of the convex hull of the support of this distribution is the coadjoint orbit through ?? + ??. The singular support is furthermore the union of the coadjoint orbits through ?? + w??, as w runs through the Weyl group. Our methods involve the Weyl functional calculus for noncommuting operators, the Nelson algebra of operants and the geometry of the moment set for a Lie group representation. In particular, we re-obtain the Kirillov-Duflo correspondence for compact Lie groups, independently of character formulae. We also develop a "noncommutative" version of the Kirillov character formula, valid for noncentral trigonometric polynomials. This generalises work of Cazzaniga, 1992.

Stuttgart, Univ., Diss., 2001.

Universiẗat, Diss., 2003--Stuttgart.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

A growing interest in distributed systems of small satellites has recently emerged due to their ability to perform a variety of new mission types, increasing technical capability, and reduced time and cost for development. However, the lack of available and dedicated small launch services currently restricts the establishment of these systems in orbit. Secondary payload launch opportunities and alternative deployment strategies can address the issue of access-to-orbit and support the delivery of the constellation to the correct orbit configuration following launch. Of these deployment strategies, the method of indirect plane separation, which utilises the natural precession of Earth orbits, is particularly applicable to the deployment of small satellite constellations due to the potential to significantly reduce propulsive requirements, albeit at the cost of increased deployment time. A review of satellite constellation design revealed that existing methods and tools are not suitable for the analysis of small satellite constellations and are not equipped to investigate alternative deployment strategies, despite the potential benefits of improved access-to-orbit, reduced system complexity, and reduced cost. To address the identified gaps in the design process, a methodology in which the analysis of small satellite constellation deployment is integrated into the system design framework is presented in this thesis. The corresponding system design-space is subsequently explored using a numerical optimisation method, which aids the identification of effective system designs and promotes the understanding of relationships between the design variables and output objectives. The primary objectives of this methodology are to ensure that the different opportunities for deployment of small satellite constellations are thoroughly examined during the design process and to support the development of improved mission and system designs. The presented methodology is demonstrated using a reduced order framework comprised of an analysis for the deployment of small satellite constellations, preliminary vehicle and propulsion system sizing processes, and system cost estimating relationships. Using this simplified mission design framework, the design space-exploration of three small satellite constellation mission case-studies is performed by application of a multiobjective genetic algorithm. Objectives of time-to-deploy, system mass, and system cost are used to direct the optimisation process and search for the most effective solutions in the system design-space. In order to perform the analysis of constellation deployment by the process of indirect plane separation, a simulation method using a semi-analytical propagation technique and time-varying atmospheric density model was developed and verified by comparison to the actual deployment of the FORMOSAT-3/COSMIC mission. The results of the case-studies presented illustrate the ability of the developed methodology to support the design process for satellite constellations and enable the identification of promising and improved system architectures for further development. Moreover, through the enumeration and quantification of the system design-space and tradespace, the methodology is shown to support the identification of relationships and trends between the design variables and selected output objectives, increasing the knowledge available to the system design team during the design process.

In recent years the space industry has seen significant growth in numbers of sub 10kg satellite platforms now known more broadly in the industry as nanosatellites. Nanosatellites potential applicability is driven by flourishing technologies miniaturisation in the consumer electronics market and commercialisation of space. Currently nanosatellite mission operations are limited in both lifetime and manoeuvrability due to limitations in on board propulsion technologies. Further enhancement of mission operations relies on more effective integration of current reaction-mass-based propulsion technologies and further development of miniaturised propulsion systems. Paradoxically, the compact spacecraft size and mass that facilitate nanosatellite access to space is presently a drawback in terms of acceptable systems performance and propulsion systems capacity. Moreover characteristic power density and vulnerability to the space environment is already high in nanosatellites in contrast to major satellites, rendering the design, inclusion, and optimisation of propulsion technologies a challenging task. This thesis focuses on techniques to support mission planning and characterisation of propulsion technologies for nanosatellites. Acknowledging the outweighing significance of solar activity modulating space environment perturbations and particularly atmospheric drag, a robust solar forecast method is proposed to support lifetime estimations. Complementing the pivotal framework information for propulsion system design and management, the vulnerability to atmospheric drag is assessed to identify the profile of the current vaguely defined drag coefficient of standard nanosatellites. Finally, addressing a crucial task on emerging propulsion technologies for nanosatellite systems, a method to improve low thrust characterisation via in-orbit manoeuvres using standard elementary attitude determination resources is devised. The robust solar activity forecast is carried out using observed historic and reconstructed Sun’s polar magnetic field, to define the initial state of an up-to-date solar magnetohydrodynamics computational model; the method successfully reproduces recent solar cycles activity, anticipating moderate-to-low activity during the next 25th cycle. The identification of the drag coefficient profile in standard nanosatellites is enabled by the statistical assessment of observed orbital decay through an iterative fitting process of propagated orbits; the profile is physically consistent and descriptive mostly in orbits below 350km during moderate-to-high solar activity. Finally, the devised thrust characterisation method exploits the regular geometry and mass distribution of standard nanosatellites to identify low thrust actuation via actuated body angular rotation rates in an intermediate axis spinner; precise computer simulations show that it is possible to improve low thrust estimations from weak and noisy sensor signals using the proposed method against typical methods using body angular acceleration.