Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

Free space communications with beam steering a two-electrode tapered laser diode using liquid-crystal slm

A free space optical wireless communication system with 3 degree angular coverage and 1.25 GHz modulation bandwidth is reported, in which relatively narrow laser beam of a simultaneous high power, high modulation speed and ultra high modulation efficiency directly modulated two-electrode tapered laser diode is steered using a nematic phase-only Liquid-Crystal On Silicon Spatial Light Modulator (LCOS SLM) by displaying reconfigurable 256 phase level gratings. © 1983-2012 IEEE.

Fluid-structure interaction simulations of a tension-cone inflatable aerodynamic decelerator

A series of fluid-structure interaction simulations of an aerodynamic tension-cone supersonic decelerator prototype intended for large mass payload deployment in planetary explorations are discussed. The fluid-structure interaction computations combine large deformation analysis of thin shells with large-eddy simulation of compressible turbulent flows using a loosely coupled approach to enable quantification of the dynamics of the vehicle. The simulation results are compared with experiments carried out at the NASA Glenn Research Center. Reasonably good agreement between the simulations and the experiment is observed throughout a deflation cycle. The simulations help to illuminate the details of the dynamic progressive buckling of the tension-cone decelerator that ultimately results in the collapse of the structure as the inflation pressure is decreased. Furthermore, the tension-cone decelerator exhibits a transient oscillatory behavior under impulsive loading that ultimately dies out. The frequency of these oscillations was determined to be related to the acoustic time scale in the compressed subsonic region between the bow shock and the structure. As shown, when the natural frequency of the structure and the frequency of the compressed subsonic region approximately match, the decelerator exhibits relatively large nonaxisymetric oscillations. The observed response appears to be a fluid-structure interaction resonance resulting from an acoustic chamber (pistonlike) mode exciting the structure. Copyright © 2013 by Christopher Porter, R. Mark Rennie, Eric J. Jumper.

Electron-beam-induced direct etching of graphene

We present electron-beam-induced oxidation of single- and bilayer graphene devices in a low-voltage scanning electron microscope. We show that the injection of oxygen leads to targeted etching at the focal point, enabling us to pattern graphene with a resolution of better than 20 nm. Voltage-contrast imaging, in conjunction with finite-element simulations, explain the secondary-electron intensities and correlate them to the etch profile. © 2013 Elsevier Ltd. All rights reserved.

A computational fluid-structure interaction study of inflation cycles of a tension cone decelerator

Inflatable aerodynamic decelerators present potential advantages for planetary entry in missions of robotic and human exploration. The design of these structures face many engineering challenges, including complex deformable geometries, anisotropic material response, and coupled shockturbulence interactions. In this paper, we describe a comprehensive computational fluid-structure interaction study of an inflation cycle of a tension cone decelerator in supersonic flow and compare the simulations with earlier published experimental results. The aeroshell design and flow conditions closely match recent experiments conducted at Mach 2.5. The structural model is a 16-sided polygonal tension cone with seams between each segment. The computational model utilizes adaptive mesh refinement, large-eddy simulation, and shell mechanics with self-contact modeling to represent the flow and structure interaction. This study focuses on the dynamics of the structure as the inflation pressure varies gradually, and the behavior of forces experienced by the flexible and rigid (the payload capsule) structures. © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Collapse of a composite beam made from ultra high molecular-weight polyethylene fibres

Hot-pressed laminates with a [0/90]48 lay-up, consisting of 83% by volume of ultra high molecular-weight polyethylene (UHMWPE) fibres, and 17% by volume of polyurethane (PU) matrix, were cut into cantilever beams and subjected to transverse end-loading. The collapse mechanisms were observed both visually and by X-ray scans. Short beams deform elastically and collapse plastically in longitudinal shear, with a shear strength comparable to that observed in double notch, interlaminar shear tests. In contrast, long cantilever beams deform in bending and collapse via a plastic hinge at the built-in end of the beam. The plastic hinge is formed by two wedge-shaped microbuckle zones that grow in size and in intensity with increasing hinge rotation. This new mode of microbuckling under macroscopic bending involves both elastic bending and shearing of the plies, and plastic shear of the interface between each ply. The double-wedge pattern contrasts with the more usual parallel-sided plastic microbuckle that occurs in uniaxial compression. Finite element simulations and analytical models give additional insight into the dominant material and geometric parameters that dictate the collapse response of the UHMWPE composite beam in bending. Detailed comparisons between the observed and predicted collapse responses are used in order to construct a constitutive model for laminated UHMWPE composites. © 2013 Elsevier Ltd.

Electron-beam patterning of polymer electrolyte films to make multiple nanoscale gates for nanowire transistors

We report an electron-beam based method for the nanoscale patterning of the poly(ethylene oxide)/LiClO4 polymer electrolyte. We use the patterned polymer electrolyte as a high capacitance gate dielectric in single nanowire transistors and obtain subthreshold swings comparable to conventional metal/oxide wrap-gated nanowire transistors. Patterning eliminates gate/contact overlap, which reduces parasitic effects and enables multiple, independently controllable gates. The method's simplicity broadens the scope for using polymer electrolyte gating in studies of nanowires and other nanoscale devices. © 2013 American Chemical Society.

Wave dispersion and power flow analysis of an infinite aerofoil-shaped beam

Classic flutter analysis models an aerofoil as a two degree-of-freedom rigid body supported by linear and torsional springs, which represent the bending and torsional stiffness of the aerofoil section. In this classic flutter model, no energy transfer or dissipation can occur in the span-wise direction of the aerofoil section. However, as the aspect ratio of an aerofoil section increases, this span-wise energy transfer - in the form of travelling waves - becomes important to the overall system dynamics. This paper extends the classic flutter model to include travelling waves in the span-wise direction. Namely, wave dispersion and power flow analysis of an infinite, aerofoil-shaped beam, subject to bending, torsion, tension and a constant wind excitation, is used to investigate the overall system stability. Examples of potential applications for these high aspect ratio aerofoil sections include high-altitude balloon tethers, towed cables, offshore risers and mooring lines.