Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms

We demonstrate a novel experimental arrangement which rotates a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.Comment: 7 pages, 5 figures, final versio

Bio-Inspired Active Skins for Surface Morphing.

Mechanical metamaterials that leverage precise geometrical designs and imperfections to induce unique material behavior have garnered significant attention. This study proposes a Bio-Inspired Active Skin (BIAS) as a new class of instability-induced morphable structures, where selective out-of-plane material deformations can be pre-programmed during design and activated by in-plane strains. The deformation mechanism of a unit cell geometrical design is analyzed to identify how the introduction of hinge-like notches or instabilities, versus their pristine counterparts, can pave way for controlling bulk BIAS behavior. Two-dimensional arrays of repeating unit cells were fabricated, with notches implemented at key locations throughout the structure, to harvest the instability-induced surface features for applications such as camouflage, surface morphing, and soft robotic grippers

Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.Comment: To appear in IEEE Trans. Automat. Control; 15 pages, 2 figure

Design and analysis considerations for deployment mechanisms in a space environment

On the second flight of the INTELSAT V spacecraft the time required for successful deployment of the north solar array was longer than originally predicted. The south solar array deployed as predicted. As a result of the difference in deployment times a series of experiments was conducted to locate the cause of the difference. Deployment rate sensitivity to hinge friction and temperature levels was investigated. A digital computer simulation of the deployment was created to evaluate the effects of parameter changes on deployment. Hinge design was optimized for nominal solar array deployment time for future INTELSAT V satellites. The nominal deployment times of both solar arrays on the third flight of INTELSAT V confirms the validity of the simulation and design optimization

Kirigami-inspired, highly stretchable micro-supercapacitor patches fabricated by laser conversion and cutting.

The recent developments in material sciences and rational structural designs have advanced the field of compliant and deformable electronics systems. However, many of these systems are limited in either overall stretchability or areal coverage of functional components. Here, we design a construct inspired by Kirigami for highly deformable micro-supercapacitor patches with high areal coverages of electrode and electrolyte materials. These patches can be fabricated in simple and efficient steps by laser-assisted graphitic conversion and cutting. Because the Kirigami cuts significantly increase structural compliance, segments in the patches can buckle, rotate, bend and twist to accommodate large overall deformations with only a small strain (<3%) in active electrode areas. Electrochemical testing results have proved that electrical and electrochemical performances are preserved under large deformation, with less than 2% change in capacitance when the patch is elongated to 382.5% of its initial length. The high design flexibility can enable various types of electrical connections among an array of supercapacitors residing in one patch, by using different Kirigami designs

Origami Reconfigurable Electromagnetic Systems

With the ever-increasing demand for wireless communications, there is a great need for efficient designs of electromagnetic systems. Reconfigurable electromagnetic systems are very useful because such designs can provide multi-functionality and support different services. The geometrical topology of an electromagnetic element is very important as it determines the element’s RF performance characteristics. Origami geometries have significant advantages for launch-and-carry electromagnetic devices where devices need to fold in order to miniaturize their size during launch and unfold in order to operate after the platform has reached orbit. This dissertation demonstrates a practical process for designing reconfigurable electromagnetic devices using origami structures. Four different origami structures are studied and the integrated Mathematical-Computational-Electromagnetic models of origami antennas, origami reflectors and origami antenna arrays are developed and analyzed. These devices provide many unique capabilities compared with the traditional designs, such as band-switching, frequency tuning, polarization adjustment and mode reconfigurability. Prototypes are also manufactured to validate the performances of the designs. These designs change their geometry naturally, and they can be compactly packaged into small volume, which make them very suitable for spaceborne and satellite communication. Origami antennas and origami electromagnetics are expected to impact a variety of applications related to communications, surveillance and sensing

Eisenstein Series on Covers of Odd Orthogonal Groups

We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the $n$-fold cover of the split odd orthogonal group $SO_{2r+1}$. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured that the $p$-power contributions to the Whittaker coefficients may be computed using the theory of crystal graphs of type C, by attaching to each path component a Gauss sum or a degenerate Gauss sum depending on the fine structure of the path. We establish their conjecture using a combination of automorphic and combinatorial-representation-theoretic methods. Surprisingly, we must make use of the type A theory, and the two different crystal graph descriptions of Brubaker, Bump and Friedberg available for type A based on different factorizations of the long word into simple reflections. We also establish a formula for the Whittaker coefficients in the even degree cover case, again based on crystal graphs of type C. As a further consequence, we establish a Lie-theoretic description of the coefficients for $n$ sufficiently large, thereby confirming a conjecture of Brubaker, Bump and Friedberg.Comment: 62 page

Small Solutions to the Large Telescope Problem: A Massively Replicated MEMS Spectrograph

In traditional seeing-limited observations the spectrograph aperture scales with telescope aperture, driving sizes and costs to enormous proportions. We propose a new solution to the seeing-limited spectrograph problem. A massively fiber-sliced configuration feeds a set of small diffraction-limited spectrographs. We present a prototype, tunable, J-band, diffraction grating, designed specifically for Astronomical applications: The grating sits at the heart of a spectrograph, no bigger than a few inches on a side. Throughput requirements dictate using tens-of-thousands of spectrographs on a single 10 to 30 meter telescope. A full system would cost significantly less than typical instruments on 10m or 30m telescopes.Comment: 9 pages, 5 figures, presented at SPIE Astronomical Telescopes and Instrumentation, 23 - 28 June 2008, Marseille, France. See http://www.ucolick.org/~npk/MEMS for video