Through calculation, and subsequent fabrication of, holographic optical devices, we can sculpt a single laser beam into a fully-configurable array of optical tweezers. Each spot in such an array is then capable of trapping and manipulating one particle, making possible simultaneous control over large collections of micro-objects. Our addition of holographic techniques has extended the basic capabilities of optical tweezing, making it a more viable tool for the assembly of nanodevices and the organization of specimens into user-defined structures.

Previously, a generalized Lorentz-Mie scattering theory has been used to model single (non-holographic) optical traps. Here, we develop a simpler and more intuitive approach to examine the trapping potential as a function of particle size, the polarizability of the particle material as compared to that of the surrounding medium, the power of the laser used to trap the particles, and the angular divergence of the optics used for promoting assembly. For this calculation we incorporate an approximate form for the energy density of the laser beam-one that is appropriate both within and outside of the Rayleigh limit. We believe that our conclusions remain viable in the intermediate case, where the particles to be trapped have dimensions on the order of the wavelength of visible light; this regime is of particular interest in applications involving assembly of photonic bandgap materials and other photonically-active structures. Notably, we are the first to address the key question regarding application of holographic optical tweezer arrays, namely the number of particles that can be simultaneously incorporated and manipulated.

There are many potential applications for such techniques; e.g., allowing for the construction of aggregations with tailor-made crystalline symmetries. Defects may be introduced in a controlled way allowing exploration of their role in phase transitions. Even biological specimens could be organized into useful configurations for studying how they behave in large, organized collections. In addition, there is growing interest in electronic devices, which exploit the confinement of electrons onto isolated nanoparticles. The application of our techniques might increase the yield during fabrication of these devices.

]]>Our primary extension of the Schelling model was to include social agents who can authentically 'see' their neighbors up to a distance R, called 'vision'. By exploring the consequences of systematically varying R, we have developed an understanding of how vision interacts with racial preferences and minority concentrations and leads to novel, complex segregation behavior. We have discovered three regimes: an unstable regime, where societies invariably segregate; a stable regime, where integrated societies remain stable; and an intermediate regime where a complex behavior is observed.

Since the primary audience of Urban Studies consists of sociologists and economists, we have not elaborated in the first chapter upon the phase transition which was strongly suggested by the "complex behavior" in the intermediate regime. The purpose of chapter two then, is to elucidate these additional physically interesting aspects of our model. Melting is a textbook example of first order (discontinuous) phase transitions. These are marked by two central features: a sharp temperature at which the transition occurs, and the coexistence of the two phases at that melting point. One can study the first-order phase transition that ice undergoes when melting into water by observing the ice while continuously raising its temperature. However, if you were only able to view the system at certain discrete temperatures, you would only see a either a piece of ice or a puddle of water during each observation. Thus in order to study the potential phase transition occurring in our model, we must be able to control the governing parameters continuously. However, in our original 'discrete' model, R measures how far an agent sees from its own home as an integer number of houses. Since we can only assign discrete values to R, it is meaningless to speak of a phase transition occurring as a function of this variable.

To overcome the limitations of our first model, we introduce a continuous model in chapter two where the range of vision (denoted R2 for notational clarity) can be varied continuously. This model uses a utility function that assigns greater weight to neighbors nearer an evaluating agent. The function used to model this decrease in utility contribution with distance is an exponentially decaying curve. We control the steepness of this curve (and thereby control the agents' vision) using R2. Since R2 can be set to equal any positive real number, we can indeed study the possible phase transition in our simulations' behavior as the function of a continuous variable.

Additionally, the continuous model demonstrates the robustness of the sociologically relevant conclusions drawn in chapter one. Our continuous model, a generalization of a model developed by Wasserman and Yohe (2001), is in fact more realistic than our first model. In particular, we were pleased to discover the same three behavioral regimes and all associated trends in both our discrete model and our continuous model. This confirms that our original results were robust and not merely algorithmic artifacts related to the specific treatment of vision used in our discrete model.

]]>We observed these and other objects with filters close to the Johnson-Kron-Cousins BVRl filters corresponding to the blue, visible, red, and near-IR wavelengths using the 0.9m SMARTS telescope at Cerro-Tololo Inter-American Observatory during October 2003. Using the image reduction routines (imred) of the Image Reduction and Analysis Facility (NOAO Xl IIIRAF), we removed the bias caused by dark currents, and flat fielded the data to improve the signal-to-noise ratio (SNR).

Instrumental magnitudes for all objects were extracted using the aperture photometry package (apphot). Landolt standard stars were used to solve the transformation equations and extract extinction coefficients. Photometric calibration routines (photcaI) allowed us to use the extinction coefficients and instrumental magnitudes to determine magnitudes in the Landolt standard system. We computed absolute magnitudes for 279 Thule and C/2002 CE10 (LINEAR) in the VR bands by correcting for the changing geocentric distance, heliocentric distance, and solar phase of the object. 279 Thule was found to have a mean absolute visual magnitude of 8.66±0.OJ and a V-R color of 0.44±0.03, when corrected for solar phase using the standard IAU phase relation (Bowell et al; J989). We discuss the suitability of the standard phase relation for 279 Thule. We place constraints on the size of the objects. We determine the rotation period for 279 Thule to be 7.6±0.5 hrs, using an implementation of the phase dispersion minimization (PDM) algorithm first developed by Stellingwerf (1978). It is likely that observations of C12002 CE lU (LINEAR) have been contaminated by near nucleus coma.

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