7,312 research outputs found

    The N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane

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    The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified

    Statistics of Cycles: How Loopy is your Network?

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    We study the distribution of cycles of length h in large networks (of size N>>1) and find it to be an excellent ergodic estimator, even in the extreme inhomogeneous case of scale-free networks. The distribution is sharply peaked around a characteristic cycle length, h* ~ N^a. Our results suggest that h* and the exponent a might usefully characterize broad families of networks. In addition to an exact counting of cycles in hierarchical nets, we present a Monte-Carlo sampling algorithm for approximately locating h* and reliably determining a. Our empirical results indicate that for small random scale-free nets of degree exponent g, a=1/(g-1), and a grows as the nets become larger.Comment: Further work presented and conclusions revised, following referee report

    Scalable Noise Estimation with Random Unitary Operators

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    We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation -- quantified by the trace of the superoperator describing the non--unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies additional information about the noise can be determined.Comment: 8 pages; v2: published version (typos corrected; reference added

    OpenFOAM Simulations of Atmospheric-Entry Capsules in the Subsonic Regime

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    The open-source Computational Fluid Dynamics software OpenFOAM is gaining wider acceptance in industry and academia for incompressible flow simulations. To date, there has been relatively little utilization of OpenFOAM for compressible external aerodynamic applications. The numerous turbulence models available in OpenFOAM makes it an attractive option for evaluating alternate Reynolds-Averaged Navier-Stokes (RANS) turbulent models to assess separated flow on atmospheric entry vehicles in the subsonic regime, where traditional turbulent models show reduced accuracy. This paper presents simulations of an axisymmetric capsule geometry at subsonic conditions using an OpenFOAM compressible flow solver. These results are compared with results from the NASA CFD code OVERFLOW and experimental data. These OpenFOAM simulations serve as a basis to explore OpenFOAMs extended turbulence models on compressible separated flows such as found on entry capsules

    Dramatic Shape Sensitivity of Directional Emission Patterns from Similarly Deformed Cylindrical Polymer Lasers

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    Recent experiments on similarly shaped polymer micro-cavity lasers show a dramatic difference in the far-field emission patterns. We show for different deformations of the ellipse, quadrupole and hexadecapole that the large differences in the far-field emission patterns is explained by the differing ray dynamics corresponding to each shape. Analyzing the differences in the appropriate phase space for ray motion, it is shown that the differing geometries of the unstable manifolds of periodic orbits are the decisive factors in determining the far-field pattern. Surprisingly, we find that strongly chaotic ray dynamics is compatible with highly directional emission in the far-field.Comment: 14 pages, 16 figures (eps), RevTeX 4, submitted to JOSA

    Mechanical Effects of Fine-Wire Climbing on the Hindlimb Skeleton of Mice

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    poster abstractHigh-impact exercise (running/jumping) can stimulate multiple anabolic responses (increased trabecular bone volume, BV/TV) in the skeleton, but is also linked to an increased incidence of skeletal fracture. Thus, it is not an appropriate treatment for patients with elevated fracture risks. However, multi-directional offaxis mechanical loading can also elicit anabolic responses, even when magnitudes are relatively low. This represents a potential alternative to high-impact exercise for improving skeletal mechanical properties. To test this hypothesis, we raised twelve weanling female C57BL/6 mice to 4 months of age in custom enclosures that prevent (control) or require (experimental) manual and pedal grasping while balancing and climbing above narrow wire substrates. At sacrifice, we measured whole mouse bone density (DEXA) and performed architectural (μCT) and mechanical (4-pt bending) analyses of the femur and tibia. Body mass was similar between groups, although exercised mice were leaner (-35% fat mass). Bone mineral density was also similar, while bone mineral content was increased (+7%) in the exercised mice. Femoral midshaft polar moment of inertia was similar between groups, but exercised mice had lower BV/TV (-46%) of the distal femur and greater trabecular spacing (+21%). Exercised femora showed more total displacement (+58%) and post yield displacement (+115%) in bending than controls, and increased material toughness (+40%). Patterns were similar for the tibia. Mechanical data are consistent with high-impact exercise studies, but architectural data are not. Together they suggest that our exercise model may improve bone mechanical properties by redistributing mineral within the skeleton, and not by increasing net bone formation

    Coherent states for continuous spectrum operators with non-normalizable fiducial states

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    The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the formalism to particular cases involving systems with a continuous spectrum: coherent states for the free particle and for the inverted oscillator (p2x2)(p^2 - x^2) are explicitly provided. Similar ideas can be used for other systems having non-normalizable fiducial states.Comment: 17 pages, typos corrected, references adde

    Uniformity in the Wiener-Wintner theorem for nilsequences

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    We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem.Comment: v3: 18 p., proof that the cube construction produces compact homogeneous spaces added, measurability issues in the proof of Theorem 1.5 addressed. We thank the anonymous referees for pointing out these gaps in v

    Late-time Light Curves of Type II Supernovae: Physical Properties of SNe and Their Environment

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    We present BVRIJHK band photometry of 6 core-collapse supernovae, SNe 1999bw, 2002hh, 2003gd, 2004et, 2005cs, and 2006bc measured at late epochs (>2 yrs) based on Hubble Space Telescope (HST), Gemini north, and WIYN telescopes. We also show the JHK lightcurves of a supernova impostor SN 2008S up to day 575. Of our 43 HST observations in total, 36 observations are successful in detecting the light from the SNe alone and measuring magnitudes of all the targets. HST observations show a resolved scattered light echo around SN 2003gd at day 1520 and around SN 2002hh at day 1717. Our Gemini and WIYN observations detected SNe 2002hh and 2004et, as well. Combining our data with previously published data, we show VRIJHK-band lightcurves and estimate decline magnitude rates at each band in 4 different phases. Our prior work on these lightcurves and other data indicate that dust is forming in our targets from day ~300-400, supporting SN dust formation theory. In this paper we focus on other physical properties derived from the late time light curves. We estimate 56Ni masses for our targets (0.5-14 x 10^{-2} Msun) from the bolometric lightcurve of each for days ~150-300 using SN 1987A as a standard (7.5 x 10^{-2} Msun). The flattening or sometimes increasing fluxes in the late time light curves of SNe 2002hh, 2003gd, 2004et and 2006bc indicate the presence of light echos. We estimate the circumstellar hydrogen density of the material causing the light echo and find that SN 2002hh is surrounded by relatively dense materials (n(H) >400 cm^{-3}) and SNe 2003gd and 2004et have densities more typical of the interstellar medium (~1 cm^{-3}). The 56Ni mass appears well correlated with progenitor mass with a slope of 0.31 x 10^{-2}, supporting the previous work by Maeda et al. (2010), who focus on more massive Type II SNe. The dust mass does not appear to be correlated with progenitor mass.Comment: We corrected the 56Ni mass of SN2005cs and Figures 8 (a) and 8 (c
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