A Parallel Manipulator with Only Translational Degrees of Freedom

This report presents a novel three degree of freedom parallel manipulator that employs only revolute joints and constrains the manipulator output to translational motion. Closed-form solutions are developed for both the inverse and forward kinematics. It is shown that the inverse kinematics problem has up to four real solutions, and the forward kinematics problem has up to 16 real solutions

Optimization of a Three DOF Translational Platform for Well- Conditioned Workspace

Two optimization studies on the design of a three degree of freedom translational parallel platform are conducted and the results are compared. The objective function of the first study maximizes total volume of the manipulator workspace without regard to the quality of the workspace. The second study optimizes the total volume of well conditioned workspace by maximizing a global condition index. The global condition index is a function of the condition number of the Jacobian matrix, providing a means of measuring the amplification error between the actuators and the end effector. Both objective functions involve an integration over the workspace of the manipulator. This integral is approximated using the Monte Carlo method

Ferromagnetic phase transition and Bose-Einstein condensation in spinor Bose gases

Phase transitions in spinor Bose gases with ferromagnetic (FM) couplings are studied via mean-field theory. We show that an infinitesimal value of the coupling can induce a FM phase transition at a finite temperature always above the critical temperature of Bose-Einstein condensation. This contrasts sharply with the case of Fermi gases, in which the Stoner coupling $I_s$ can not lead to a FM phase transition unless it is larger than a threshold value $I_0$. The FM coupling also increases the critical temperatures of both the ferromagnetic transition and the Bose-Einstein condensation.Comment: 4 pages, 4 figure

Beyond Gross-Pitaevskii Mean Field Theory

A large number of effects related to the phenomenon of Bose-Einstein Condensation (BEC) can be understood in terms of lowest order mean field theory, whereby the entire system is assumed to be condensed, with thermal and quantum fluctuations completely ignored. Such a treatment leads to the Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although this theory works remarkably well for a broad range of experimental parameters, a more complete treatment is required for understanding various experiments, including experiments with solitons and vortices. Such treatments should include the dynamical coupling of the condensate to the thermal cloud, the effect of dimensionality, the role of quantum fluctuations, and should also describe the critical regime, including the process of condensate formation. The aim of this Chapter is to give a brief but insightful overview of various recent theories, which extend beyond the GPE. To keep the discussion brief, only the main notions and conclusions will be presented. This Chapter generalizes the presentation of Chapter 1, by explicitly maintaining fluctuations around the condensate order parameter. While the theoretical arguments outlined here are generic, the emphasis is on approaches suitable for describing single weakly-interacting atomic Bose gases in harmonic traps. Interesting effects arising when condensates are trapped in double-well potentials and optical lattices, as well as the cases of spinor condensates, and atomic-molecular coupling, along with the modified or alternative theories needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer Verlag

Basic Atomic Physics

Contains reports on five research projects.National Science Foundation Grant PHY 96-024740National Science Foundation Grant PHY 92-21489U.S. Navy - Office of Naval Research Contract N00014-96-1-0484Joint Services Electronics Program Grant DAAHO4-95-1-0038National Science Foundation Grant PHY95-14795U.S. Army Research Office Contract DAAHO4-94-G-0170U.S. Army Research Office Contract DAAG55-97-1-0236U.S. Army Research Office Contract DAAH04-95-1-0533U.S. Navy - Office of Naval Research Contract N00014-96-1-0432National Science Foundation Contract PHY92-22768David and Lucile Packard Foundation Grant 96-5158National Science Foundation Grant PHY 95-01984U.S. Army Research OfficeU.S. Navy - Office of Naval Research Contract N00014-96-1-0485AASERT N00014-94-1-080

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.Peer reviewedFinal Published versio

Discrete-Position Solar Tracking for Photovoltaic System

The purpose of this research is to design a new tracking system for solar panels using the idea of discrete-position tracking. Compared with the traditional fixed solar panel, discrete-position trackers have a higher gain of harvesting solar radiation with smaller misalignment angles. Also, since we are trying to design the a passive tracker with solely mechanical structure to do the kinetics, a discrete-position tracker can decrease the cost of the maintenance to a huge extent in contrast to both one-axis and two-axis continuous tracking systems. The majority of the cost of maintaining a continuous tracker is the motor or hydraulic ram. These devices not only are relatively expensive but also do not adapt robust to different weather condition. Therefore, the major part of this summer research is to develop the algorithm of calculating the gain of discrete-position tracker for solar panels comparing with fixed tracker and continuous tracker. The report will introduce the background information of current solar trackers and explain the initiative of new design. The majority of work done in this summer was developing a mathematical model that quantifies the energy output with several specific inputs. The report uses a lot of space defining the variables of the model, including the input and output of the system. These variables are strictly and scientifically defined so that they meet the standards of corresponding science institutions, such International Astronomical Union. The final model gives the approximate numbers of energy harvested for fixed and discrete-position trackers compared with the two-axis continuous trackers, noted as the optimum trackers in the code. Because of the time limitation, the team did not start the optimization for the discrete-position angles. The current model with the given position at latitude of 40 degrees north and longitude of 0 degrees can generate approximately 20 percent more electricity than fixed solar panel with the slope of 10 degrees and orientation of 20 degrees west. However, this configuration of discrete-position tracker only makes up 62.89% electricity compared with continuous trackers based on the calculation. The number could be higher after the optimization for the system, and the optimization will be the next direction of the research

Petrology of Plutonic Xenoliths and Volcanic Rocks from Grenada, Lesser Antilles

Grenada is the southernmost island in the Lesser Antilles arc, a chain of subduction-related volcanoes distinguished by its diversity of magma composition and unusually abundant plutonic xenoliths, many with cumulate textures. We have determined the mineral compositions of a newly collected, extensive suite of plutonic xenoliths from Grenada and examined their relationship with the lavas in an attempt to explore the role of intra-crustal processes on magmatic evolution. The plutonic assemblages are dominated by mafic phases with abundant hornblende and clinopyroxene, and include the only known plagioclase-free examples in the Lesser Antilles. Bulk compositions are unlike those of natural silicate melts and are consistent with the majority of the xenoliths having a cumulate origin. Experimental and thermobarometric evidence shows that the entire cumulate suite can be generated in a narrow pressure range (0.2-0.5 GPa) with different assemblages resulting from small variations in melt chemistry and temperature. Temperature estimates are consistent with the observed crystallization sequence of olivine → clinopyroxene → hornblende → plagioclase. A spinel phase is present throughout ranging from Cr- to Fe3+-rich. The crystallization sequence requires elevated magmatic H2O contents (̃7 wt % H2O) sufficient both to suppress plagioclase crystallization and to render this phase extremely rich in anorthite upon appearance; this is a characteristic of many island arc settings. Studied lavas from the M- and C-series span picrites and ankaramites to hornblende- and orthopyroxene-bearing andesites. MELTS modelling confirms experimental hypotheses that the two lava series can be derived from a common picritic magma, with M-series differentiation occurring in the uppermost mantle (~1.4-1.8 GPa) and C-series in the shallow crust (~0.2 GPa). Plutonic xenoliths from Grenada are notably different from those of the neighbouring island of St Vincent, the respective assemblages and mineral chemistry demonstrating the effect of small-scale changes in melt composition and magma storage conditions between these two islands. We suggest that the unusual petrological and geochemical characteristics of Grenada magmas are a result of proximity to the South American continent and associated localized thickening of the oceanic lithosphere. This increases the depth of magma generation and is reflected in the elevated LREE/HREE of the Grenada lavas, indicating that last equilibration with a garnet lherzolite source occurred at a depth of ≥60 km