Optimal guidance of low-thrust interplanetary space vehicles

The low-thrust guidance problem is defined as the minimum terminal variance (MTV) control of a space vehicle subjected to random perturbations of its trajectory. To accomplish this control task, only bounded thrust level and thrust angle deviations are allowed, and these must be calculated based solely on the information gained from noisy, partial observations of the state. In order to establish the validity of various approximations, the problem is first investigated under the idealized conditions of perfect state information and negligible dynamic errors. To check each approximate model, an algorithm is developed to facilitate the computation of the open loop trajectories for the nonlinear bang-bang system. Using the results of this phase in conjunction with the Ornstein-Uhlenbeck process as a model for the random inputs to the system, the MTV guidance problem is reformulated as a stochastic, bang-bang, optimal control problem. Since a complete analytic solution seems to be unattainable, asymptotic solutions are developed by numerical methods. However, it is shown analytically that a Kalman filter in cascade with an appropriate nonlinear MTV controller is an optimal configuration. The resulting system is simulated using the Monte Carlo technique and is compared to other guidance schemes of current interest.

IPCC WGII Fifth Assessment Report (AR5): Expanding the solution space for adaptation

6 p.

Advancing EDL technologies for future space missions : from ground testing facilities to ablative heatshields

Motivated by recent MSL results where the ablation rate of the PICA heatshield was over-predicted, and staying true to the objectives outlined in the NASA Space Technology Roadmaps and Priorities report, this work focuses on advancing EDL technologies for future space missions.

Due to the difficulties in performing flight tests in the hypervelocity regime, a new ground testing facility called the vertical expansion tunnel is proposed. The adverse effects from secondary diaphragm rupture in an expansion tunnel may be reduced or eliminated by orienting the tunnel vertically, matching the test gas pressure and the accelerator gas pressure, and initially separating the test gas from the accelerator gas by density stratification. If some sacrifice of the reservoir conditions can be made, the VET can be utilized in hypervelocity ground testing, without the problems associated with secondary diaphragm rupture.

The performance of different constraints for the Rate-Controlled Constrained-Equilibrium (RCCE) method is investigated in the context of modeling reacting flows characteristic to ground testing facilities, and re-entry conditions. The effectiveness of different constraints are isolated, and new constraints previously unmentioned in the literature are introduced. Three main benefits from the RCCE method were determined: 1) the reduction in number of equations that need to be solved to model a reacting flow; 2) the reduction in stiffness of the system of equations needed to be solved; and 3) the ability to tabulate chemical properties as a function of a constraint once, prior to running a simulation, along with the ability to use the same table for multiple simulations.

Finally, published physical properties of PICA are compiled, and the composition of the pyrolysis gases that form at high temperatures internal to a heatshield is investigated. A necessary link between the composition of the solid resin, and the composition of the pyrolysis gases created is provided. This link, combined with a detailed investigation into a reacting pyrolysis gas mixture, allows a much needed consistent, and thorough description of many of the physical phenomena occurring in a PICA heatshield, and their implications, to be presented.

Through the use of computational fluid mechanics and computational chemistry methods, significant contributions have been made to advancing ground testing facilities, computational methods for reacting flows, and ablation modeling.

Space-charge-limited current in fast neutron irradiated silicon

DC and transient measurements of space-charge-limited currents through alloyed and symmetrical n^+ν n^+ structures made of nominally 75 kΩcm ν-type silicon are studied before and after the introduction of defects by 14 MeV neutron radiation. In the transient measurements, the current response to a large turn-on voltage step is analyzed. Right after the voltage step is applied, the current transient reaches a value which we shall call "initial current" value. At longer times, the transient current decays from the initial current value if traps are present.

Before the irradiation, the initial current density-voltage characteristics J(V) agree quantitatively with the theory of trap-free space-charge-limited current in solids. We obtain for the electron mobility a temperature dependence which indicates that scattering due to impurities is weak. This is expected for the high purity silicon used. The drift velocity-field relationships for electrons at room temperature and 77°K, derived from the initial current density-voltage characteristics, are shown to fit the relationships obtained with other methods by other workers. The transient current response for t > 0 remains practically constant at the initial value, thus indicating negligible trapping.

Measurement of the initial (trap-free) current density-voltage characteristics after the irradiation indicates that the drift velocity-field relationship of electrons in silicon is affected by the radiation only at low temperature in the low field range. The effect is not sufficiently pronounced to be readily analyzed and no formal description of it is offered. In the transient response after irradiation for t > 0, the current decays from its initial value, thus revealing the presence of traps. To study these traps, in addition to transient measurements, the DC current characteristics were measured and shown to follow the theory of trap-dominated space-charge-limited current in solids. This theory was applied to a model consisting of two discrete levels in the forbidden band gap. Calculations and experiments agreed and the capture cross-sections of the trapping levels were obtained. This is the first experimental case known to us through which the flow of space-charge-limited current is so simply representable.

These results demonstrate the sensitivity of space-charge-limited current flow as a tool to detect traps and changes in the drift velocity-field relationship of carriers caused by radiation. They also establish that devices based on the mode of space-charge-limited current flow will be affected considerably by any type of radiation capable of introducing traps. This point has generally been overlooked so far, but is obviously quite significant.

A movable-cavity cold atom space clock

We present an experimental scheme of a cold atom space clock with a movable cavity. By using a single microwave cavity, we find that the clock has a significant advantage, i.e. the longitudinal cavity phase shift is eliminated. A theoretical analysis has been carried out in terms of the relation between the atomic transition probability and the velocity of the moving cavity by taking into account the velocity distribution of cold atoms. The requirements for the microwave power and its stability for atomic pi/2 excitation at different moving velocities of the cavity lead to the determination of the proper working parameters of the rubidium clock in frequency accuracy 10(-17). Finally, the mechanical stability for the scheme is analysed and the ways of solving the possible mechanical instability of the device are proposed.

Magnetospheric access of solar particles and the configuration of the distant geomagnetic field

The access of 1.2-40 MeV protons and 0.4-1.0 MeV electrons from interplanetary space to the polar cap regions has been investigated with an experiment on board a low altitude, polar orbiting satellite (OG0-4).

A total of 333 quiet time observations of the electron polar cap boundary give a mapping of the boundary between open and closed geomagnetic field lines which is an order of magnitude more comprehensive than previously available.

Persistent features (north/south asymmetries) in the polar cap proton flux, which are established as normal during solar proton events, are shown to be associated with different flux levels on open geomagnetic field lines than on closed field lines. The pole in which these persistent features are observed is strongly correlated to the sector structure of the interplanetary magnetic field and uncorrelated to the north/south component of this field. The features were observed in the north (south) pole during a negative (positive) sector 91% of the time, while the solar field had a southward component only 54% of the time. In addition, changes in the north/south component have no observable effect on the persistent features.

Observations of events associated with co-rotating regions of enhanced proton flux in interplanetary space are used to establish the characteristics of the 1.2 - 40 MeV proton access windows: the access window for low polar latitudes is near the earth, that for one high polar latitude region is ~250 R_⊕ behind the earth, while that for the other high polar latitude region is ~1750 R_⊕ behind the earth. All of the access windows are of approximately the same extent (~120 R_⊕). The following phenomena contribute to persistent polar cap features: limited interplanetary regions of enhanced flux propagating past the earth, radial gradients in the interplanetary flux, and anisotropies in the interplanetary flux.

These results are compared to the particle access predictions of the distant geomagnetic tail configurations proposed by Michel and Dessler, Dungey, and Frank. The data are consistent with neither the model of Michel and Dessler nor that of Dungey. The model of Frank can yield a consistent access window configuration provided the following constraints are satisfied: the merging rate for open field lines at one polar neutral point must be ~5 times that at the other polar neutral point, related to the solar magnetic field configuration in a consistent fashion, the migration time for open field lines to move across the polar cap region must be the same in both poles, and the open field line merging rate at one of the polar neutral points must be at least as large as that required for almost all the open field lines to have merged in 0 (one hour). The possibility of satisfying these constraints is investigated in some detail.

The role played by interplanetary anisotropies in the observation of persistent polar cap features is discussed. Special emphasis is given to the problem of non-adiabatic particle entry through regions where the magnetic field is changing direction. The degree to which such particle entry can be assumed to be nearly adiabatic is related to the particle rigidity, the angle through which the field turns, and the rate at which the field changes direction; this relationship is established for the case of polar cap observations.

Coherent spectroscopy of the Rb-87 Fg=1 -> F-e=0 closed transition

This paper has observed linewidth narrowing of dark states in rubidium cell by using the Hanle configuration. The reduction of the coherent resonance width under the transition of Rb-87 F-g = 1 -> F-e = 0 is observed and the qualitative explanation about its mechanism is presented. Multiple subnatural width dips are obtained with a linearly polarized laser beam for the transition of Rb-87 F-g = 0, 1, 2. The feature of negative and positive slope, namely dispersionlike feature, is observed in the transmitted light.

Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.

Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.

Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.

It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.

A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.

Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Strong atom-light interactions along nanostructures: Transition from free-space to nanophotonic interfaces

An exciting frontier in quantum information science is the integration of otherwise "simple'' quantum elements into complex quantum networks. The laboratory realization of even small quantum networks enables the exploration of physical systems that have not heretofore existed in the natural world. Within this context, there is active research to achieve nanoscale quantum optical circuits, for which atoms are trapped near nano-scopic dielectric structures and "wired'' together by photons propagating through the circuit elements. Single atoms and atomic ensembles endow quantum functionality for otherwise linear optical circuits and thereby enable the capability of building quantum networks component by component. Toward these goals, we have experimentally investigated three different systems, from conventional to rather exotic systems : free-space atomic ensembles, optical nano fibers, and photonics crystal waveguides. First, we demonstrate measurement-induced quadripartite entanglement among four quantum memories. Next, following the landmark realization of a nanofiber trap, we demonstrate the implementation of a state-insensitive, compensated nanofiber trap. Finally, we reach more exotic systems based on photonics crystal devices. Beyond conventional topologies of resonators and waveguides, new opportunities emerge from the powerful capabilities of dispersion and modal engineering in photonic crystal waveguides. We have implemented an integrated optical circuit with a photonics crystal waveguide capable of both trapping and interfacing atoms with guided photons, and have observed the collective effect, superradiance, mediated by the guided photons. These advances provide an important capability for engineered light-matter interactions, enabling explorations of novel quantum transport and quantum many-body phenomena.