Intersection theory of punctured pseudoholomorphic curves

We study the intersection theory of punctured pseudoholomorphic curves in $4$-dimensional symplectic cobordisms. We first study the local intersection properties of such curves at the punctures. We then use this to develop topological controls on the intersection number of two curves. We also prove an adjunction formula which gives a topological condition that will guarantee a curve in a given homotopy class is embedded, extending previous work of Hutchings. We then turn our attention to curves in the symplectization $\mathbb{R}\times M$ of a $3$-manifold $M$ admitting a stable Hamiltonian structure. We investigate controls on intersections of the projections of curves to the $3$-manifold, and we present conditions that will guarantee the projection of a curve to the $3$-manifold is an embedding. Finally we consider an application concerning pseudoholomorphic curves in manifolds admitting a certain class of holomorphic open book decomposition, and an application concerning the existence of generalized pseudoholomorphic curves.Comment: 109 pages; updated so that section numbering matches that of published versio

Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium phases in which the polarization is confined not to a symmetry axis but to a symmetry plane. One of these phases provides a natural description of the newly observed monoclinic phase. Moreover, the theory makes testable predictions about the nature of the phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A ferroelectric phase of the lowest (triclinic) symmetry type, in which the polarization is not constrained by symmetry, does not emerge until the Devonshire theory is carried to twelfth order. A topological analysis of the critical points of the free-energy surface facilitates the discussion of the phase transition sequences.Comment: 10 pages, with 5 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/dv_pzt/index.htm

Digital participation in the VisLab: Sketching urban visions for the harbour of Lachen (Switzerland) online

For decades, citizen participation has been recognised as a crucial part of urban planning. Simultaneously, as our everyday life become more digital, digital tools are being increasingly used in the involvement of citizens and their perspectives on urban issues. In particular, 3D visualisation tools based on point cloud visualisations may have the potential to further enhance opportunities for citizen participation digitally. Yet, research on their application in digital participation processes has been limited. Therefore, this study attempts to bridge this gap by developing the Urban Sketch Tool (UST) and initiating a digital participation process VisLab with local stakeholders in Lachen (Switzerland). The aim was to investigate how the UST facilitates the sketching of urban visions for the harbour of Lachen, and how it supports a discussion between stakeholders. Furthermore, how stakeholders discuss their urban visions and whether they reach consensus or dissent was examined. The study’s findings indicate that the Urban Sketch Tool is simple to use and allows for the sketching of urban visions, which facilitates discussion about urban issues by providing a common language for participants. With regard to the stakeholder discussion, the results suggest that the stakeholder mainly reach consensus through an exchange of knowledge and perspectives. However, dissent rarely occurs, because participants tend to avoid conflict or shift their opinion toward consensus. Notably, the current findings do indicate some limitations associated with the use of the UST and digital participation. As it turns out, the UST and digital access to participation may introduce new barriers, particularly for stakeholder who experience technical difficulties during the process or have a deficiency in digital skills. This results in the exclusion of individuals and unequal access to the digital participation process, resulting in unbalanced outcomes. Thus, it is recommended that digital tools be developed for those who face the greatest barriers to digital participation in planning. Additionally, it is advised that in digital participation, particular attention is being paid to conflict and the voices of marginalised participants. Finally, it can be concluded that digital participation and digital tools such as the UST such as the UST should not replace more traditional forms of participation, but rather complement them and thereby enable them to reach their full potential

High-Efficiency Nested Hall Thrusters for Robotic Solar System Exploration

This work describes the scaling and design attributes of Nested Hall Thrusters (NHT) with extremely large operational envelopes, including a wide range of throttleability in power and specific impulse at high efficiency (>50%). NHTs have the potential to provide the game changing performance, powerprocessing capabilities, and cost effectiveness required to enable missions that cannot otherwise be accomplished. NHTs were first identified in the electric propulsion community as a path to 100- kW class thrusters for human missions. This study aimed to identify the performance capabilities NHTs can provide for NASA robotic and human missions, with an emphasis on 10-kW class thrusters well-suited for robotic exploration. A key outcome of this work has been the identification of NHTs as nearly constant-efficiency devices over large power throttling ratios, especially in direct-drive power systems. NHT systems sized for robotic solar system exploration are predicted to be capable of high-efficiency operation over nearly their entire power throttling range. A traditional Annular Hall Thruster (AHT) consists of a single annular discharge chamber where the propellant is ionized and accelerated. In an NHT, multiple annular channels are concentrically stacked. The channels can be operated in unison or individually depending on the available power or required performance. When throttling an AHT, performance must be sacrificed since a single channel cannot satisfy the diverse design attributes needed to maintain high thrust efficiency. NHTs can satisfy these requirements by varying which channels are operated and thereby offer significant benefits in terms of thruster performance, especially under deep power throttling conditions where the efficiency of an AHT suffers since a single channel can only operate efficiently (>50%) over a narrow power throttling ratio (3:1). Designs for 10-kW class NHTs were developed and compared with AHT systems. Power processing systems were considered using either traditional Power Processing Units (PPU) or Direct Drive Units (DDU). In a PPU-based system, power from the solar arrays is transformed from the low voltage of the arrays to the high voltage needed by the thruster. In a DDU-based system, power from the solar arrays is fed to the thruster without conversion. DDU-based systems are attractive for their simplicity since they eliminate the most complex and expensive part of the propulsion system. The results point to the strong potential of NHTs operating with either PPUs or DDUs to benefit robotic and human missions through their unprecedented power and specific impulse throttling capabilities. NHTs coupled to traditional PPUs are predicted to offer high-efficiency (>50%) power throttling ratios 320% greater than present capabilities, while NHTs with direct-drive power systems (DDU) could exceed existing capabilities by 340%. Because the NHT-DDU approach is implicitly low-cost, NHT-DDU technology has the potential to radically reduce the cost of SEP-enabled NASA missions while simultaneously enabling unprecedented performance capability

High-Specific Impulse Hall Thrusters, Part 2: Efficiency Analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77163/1/AIAA-15954-346.pd

The Role of Magnetic Field Topography in Improving the Performance of a High Voltage Hall Thruster

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76735/1/AIAA-2002-4111-487.pd

Compact Rare Earth Emitter Hollow Cathode

A compact, high-current, hollow cathode utilizing a lanthanum hexaboride (LaB6) thermionic electron emitter has been developed for use with high-power Hall thrusters and ion thrusters. LaB6 cathodes are being investigated due to their long life, high current capabilities, and less stringent xenon purity and handling requirements compared to conventional barium oxide (BaO) dispenser cathodes. The new cathode features a much smaller diameter than previously developed versions that permit it to be mounted on axis of a Hall thruster ( internally mounted ), as opposed to the conventional side-mount position external to the outer magnetic circuit ("externally mounted"). The cathode has also been reconfigured to be capable of surviving vibrational loads during launch and is designed to solve the significant heater and materials compatibility problems associated with the use of this emitter material. This has been accomplished in a compact design with the capability of high-emission current (10 to 60 A). The compact, high-current design has a keeper diameter that allows the cathode to be mounted on the centerline of a 6- kW Hall thruster, inside the iron core of the inner electromagnetic coil. Although designed for electric propulsion thrusters in spacecraft station- keeping, orbit transfer, and interplanetary applications, the LaB6 cathodes are applicable to the plasma processing industry in applications such as optical coatings and semiconductor processing where reactive gases are used. Where current electrical propulsion thrusters with BaO emitters have limited life and need extremely clean propellant feed systems at a significant cost, these LaB6 cathodes can run on the crudest-grade xenon propellant available without impact. Moreover, in a laboratory environment, LaB6 cathodes reduce testing costs because they do not require extended conditioning periods under hard vacuum. Alternative rare earth emitters, such as cerium hexaboride (CeB6) can be used in this configuration with possibly an even longer emitter life. This cathode is specifically designed to integrate on the centerline of a high-power Hall thruster, thus eliminating the asymmetries in the plasma discharge common to cathodes previously mounted externally to the thruster s magnetic circuit. An alternative configuration for the cathode uses an external propellant feed. This diverts a fraction of the total cathode flow to an external feed, which can improve the cathode coupling efficiency at lower total mass flow rates. This can improve the overall thruster efficiency, thereby decreasing the required propellant loads for different missions. Depending on the particular mission, reductions in propellant loads can lead to mission enabling capabilities by allowing launch vehicle step-down, greater payload capability, or by extending the life of a spacecraft

Co-Flow Hollow Cathode Technology

Hall thrusters utilize identical hollow cathode technology as ion thrusters, yet must operate at much higher mass flow rates in order to efficiently couple to the bulk plasma discharge. Higher flow rates are necessary in order to provide enough neutral collisions to transport electrons across magnetic fields so that they can reach the discharge. This higher flow rate, however, has potential life-limiting implications for the operation of the cathode. A solution to the problem involves splitting the mass flow into the hollow cathode into two streams, the internal and external flows. The internal flow is fixed and set such that the neutral pressure in the cathode allows for a high utilization of the emitter surface area. The external flow is variable depending on the flow rate through the anode of the Hall thruster, but also has a minimum in order to suppress high-energy ion generation. In the co-flow hollow cathode, the cathode assembly is mounted on thruster centerline, inside the inner magnetic core of the thruster. An annular gas plenum is placed at the base of the cathode and propellant is fed throughout to produce an azimuthally symmetric flow of gas that evenly expands around the cathode keeper. This configuration maximizes propellant utilization and is not subject to erosion processes. External gas feeds have been considered in the past for ion thruster applications, but usually in the context of eliminating high energy ion production. This approach is adapted specifically for the Hall thruster and exploits the geometry of a Hall thruster to feed and focus the external flow without introducing significant new complexity to the thruster design

High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors

This innovation has been developed to improve the resolutions of future spacebased active and passive microwave antennas for earth-science remote sensing missions by maintaining surface figure precisions of large membrane/thin-shell reflectors during orbiting. The intention is for these sensing instruments to be deployable at orbit altitudes one or two orders of magnitude higher than Low Earth Orbit (LEO), but still being able to acquire measurements at spatial resolution and sensitivity similar to those of LEO. Because active and passive microwave remote sensors are able to penetrate through clouds to acquire vertical profile measurements of geophysical parameters, it is desirable to elevate them to the higher orbits to obtain orbital geometries that offer large spatial coverage and more frequent observations. This capability is essential for monitoring and for detailed understanding of the life cycles of natural hazards, such as hurricanes, tropical storms, flash floods, and tsunamis. Major components of this high-precision antenna-surface-control system include a membrane/thin shell reflector, a metrology sensor, a controller, actuators, and corresponding power amplifier and signal conditioning electronics (see figure). Actuators are attached to the back of the reflector to produce contraction/ expansion forces to adjust the shape of the thin-material reflector. The wavefront-sensing metrology system continuously measures the surface figure of the reflector, converts the surface figure to digital data and feeds the data to the controller. The controller determines the control parameters and generates commands to the actuator system. The flexible, piezoelectric polymer actuators are thus activated, providing the control forces needed to correct any distortions that exist in the reflector surface. Piezoelectric polymer actuators are very thin and flexible. They can be implemented on the back of the membrane/thin-shell reflector without introducing significant amounts of mass or stiffness to the reflector. They can be rolled up or folded to accommodate the packaging needed for launch. An analytical model of the system, which includes the membrane reflector, actuator, and controller has been developed to investigate the functionality of this control system on a 35-meter-diameter membrane reflector. The performance of this system under external disturbances such as in space thermal loads and W-error due to inflation has been investigated. A subscale breadboard has been developed, and the functionality of this control concept has been demonstrated by this breadboard

Neutral Flow Evolution in a Six-Kilowatt Hall Thruster

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90645/1/AIAA-54141-803.pd