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Sample records for embedded phase singularity

  1. Transformation of optical-vortex beams by holograms with embedded phase singularity

    NASA Astrophysics Data System (ADS)

    Bekshaev, A. Ya.; Orlinska, O. V.

    2010-04-01

    Spatial characteristics of diffracted beams produced by the "fork" holograms from incident circular Laguerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram's groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed. The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.

  2. Phase singularity diffusion.

    PubMed

    Cheng, Xiaojun; Lockerman, Yitzchak; Genack, Azriel Z

    2014-06-01

    We follow the trajectories of phase singularities at nulls of intensity in the speckle pattern of waves transmitted through random media as the frequency of the incident radiation is scanned in microwave experiments and numerical simulations. Phase singularities are observed to diffuse with a linear increase of the square displacement 〈R2〉 with frequency shift. The product of the diffusion coefficient of phase singularities in the transmitted speckle pattern and the photon diffusion coefficient through the random medium is proportional to the square of the effective sample length. This provides the photon diffusion coefficient and a method for characterizing the motion of dynamic material systems.

  3. Singularity embedding method in potential flow calculations

    NASA Technical Reports Server (NTRS)

    Jou, W. H.; Huynh, H.

    1982-01-01

    The so-called H-type mesh is used in a finite-element (or finite-volume) calculation of the potential flow past an airfoil. Due to coordinate singularity at the leading edge, a special singular trial function is used for the elements neighboring the leading edge. The results using the special singular elements are compared to those using the regular elements. It is found that the unreasonable pressure distribution obtained by the latter is removed by the embedding of the singular element. Suggestions to extend the present method to transonic cases are given.

  4. Topological charge selection rule for phase singularities

    SciTech Connect

    Zacares, M.; Vijande, J.; Ferrando, A.; Merino, E.

    2009-10-15

    We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.

  5. Characterizing maximally singular phase-space distributions

    NASA Astrophysics Data System (ADS)

    Sperling, J.

    2016-07-01

    Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples.

  6. Phase singularities in cardiac electrical activity

    NASA Astrophysics Data System (ADS)

    Uzelac, Ilija; Sidorov, Veniamin; Wikswo, John

    2010-03-01

    theory of topological spaces has its analogy in biological systems, one of which is the heart. The heart is an excitable medium that can be represented as a set of excitable elements (cardiomyocytes) that behave similarly to hourglasses. Excitable element needs external stimuli to be excited and after finite time goes back to its initial state, so its natural topological space is a ring. Topological space set (phases) can be simple set as ``rest,'' ``excited,'' ``refractory,'' ``relatively refractory'', but it can be as continuous as a set of angles on a 2π circle. In topological spaces topological charge is defined by: [ W=12πldθ (l) ] where l is the integration path and dθ is the change in phase. Non zero topological charge is called phase singularity of mapping. Practical application of topological charge analysis is a powerful method to quantify electrical dynamics during ventricular fibrillation (VF). Particularly by means of phase singularity detection it is possible to track wave breaks which relate to anatomical and electrophysiological heterogeneities.

  7. Elimination of phase singularity to achieve superresolution in lossy metamaterials.

    PubMed

    Lee, Kwangchil; Jung, Youngjean; Padilla, Willie J; Kim, Kyoungsik

    2010-06-07

    The presence of absorption losses softens the singular behavior of transmission resonances and leads to a good image in spite of limited effective spatial frequency range. Nonetheless, we found that the phase singularity does not disappear despite the considerably reduced retardation effects by softening the transmission resonances. Because the phase singularity severely deteriorates the ideal image reconstruction, broad transmission bandwidth in spatial frequency domain is not sufficient enough to achieve superresolution in TiO(2) thin film lens. The present work predicts successful elimination of the phase singularity and the achievement of approximately lambda /12.9 superresolution in TiO(2) thin film lens through the phase correction method.

  8. Optical near-field phase singularities produced by microstructures

    NASA Astrophysics Data System (ADS)

    Nesci, Antonello; Daendliker, Rene; Salt, Martin; Herzig, Hans Peter

    2001-12-01

    An electromagnetic field is characterized by an amplitude, a phase and a polarization state. In this paper, we intend to gain an understanding of the interaction of light with microstructures in order to determine their optical properties. Measurements of the amplitude and phase close to gratings are presented using a heterodyne scanning probe microscope. We discuss some basic properties of phase distributions. Indeed, coherent light diffracted by microstructures can give birth to phase dislocations, also called phase singularities. Phase singularities are isolated points where the amplitude of the field is zero. The position of these special points can lead us to information about the structure (shape, surface defects, etc), by comparing with rigorous diffraction calculation using e.g. the Fourier Modal Method (FMM). We present high-resolution measurements of such phase singularities and compare them with theoretical results. Polarization effects have been studied in order to understand the field conversion by the fiber tip.

  9. Reduction of phase singularities in a speckle Michelson setup

    NASA Astrophysics Data System (ADS)

    Mantel, K.; Nercissian, V.

    2017-06-01

    Speckle interferometry is an optical metrology technique for characterizing rough surfaces. In one application, the deformation of a specimen under a load may be determined by comparing measurements before and after the load is applied. Owing to the surface roughness, however, the results are impaired by phase singularities, leading to a strong noise in the measurement results. Usually, filtering and smoothing operations are performed to reduce the noise. However, these procedures also affect the underlying systematic phase and are therefore disadvantageous. Instead, we examine incoherent averaging, a physical procedure, to reduce the number of phase singularities in the first place. We tailor the spatial coherence of the light using extended light sources of continuous or multipoint shape, achieving smoother phase distributions. The mechanism behind the reduction process involves subtle effects like enhancing phase singularity correlations in the fields before and after the deformation takes place.

  10. Phase singularity in the diffracted field from Fresnel's double mirror

    NASA Astrophysics Data System (ADS)

    Aalipour, Rasoul; Taghi Tavassoly, M.

    2013-05-01

    It is shown that when a coherent beam of light illuminates a Fresnel's double mirror, Fresnel diffraction becomes appreciable. The subject fundamentally differs from interference. We calculate the diffracted field by applying Fresnel-Kirchhoff integral. We modified the common Fresnel's double mirror by imposing an initial height between the mirrors, as the height is chosen small enough so that the application of Fresnel's double mirror is maintained. We show by simulation and experiment that a phase singularity causes from the initial height and modifies the diffracted field from the Fresnel's double mirror. One can adjust the location of the line singularity by changing the angle between the mirrors. Also, the anomalous behavior of a polychromatic beam diffracted from the modified Fresnel's double mirror at the neighborhood of the line singularity, is investigated by simulation.

  11. Cycle of phase, coherence and polarization singularities in Young's three-pinhole experiment.

    PubMed

    Pang, Xiaoyan; Gbur, Greg; Visser, Taco D

    2015-12-28

    It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to create a continuous cycle of transformations between classes of singularities, often accompanied by topological reactions in which different singularities are created and annihilated. This arrangement serves to clarify the relationships between the different singularity types, and provides a simple tool for further exploration.

  12. Turbulent diffusion phase transition is due to singular energy spectrum.

    PubMed

    Wallstrom, T C

    1995-11-21

    The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion.

  13. Turbulent diffusion phase transition is due to singular energy spectrum.

    PubMed Central

    Wallstrom, T C

    1995-01-01

    The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion. Images Fig. 2 PMID:11607590

  14. Phase singularity of surface plasmon polaritons generated by optical vortices.

    PubMed

    Tan, P S; Yuan, G H; Wang, Q; Zhang, N; Zhang, D H; Yuan, X-C

    2011-08-15

    We demonstrate an experimental result that shows the phase singularity of surface plasmon waves generated by the direct transform of optical vortices at normal incidence focused on a structureless metal surface. The near-field two-dimensional intensity distribution near the focal plane is experimentally examined by using near-field scanning optical microscopy and shows a good agreement with the finite-difference time-domain simulation result. The experimental realization demonstrates a potential of the proposed excitation scheme to be reconfigured locally with advantages over structures milled into optically thick metallic films for plasmonics applications involving plasmonic vortices.

  15. The Pancharatnam-Berry phase in polarization singular beams

    NASA Astrophysics Data System (ADS)

    Kumar, Vijay; Viswanathan, Nirmal K.

    2013-04-01

    Space-variant inhomogeneously polarized field formed due to superposition of orthogonally polarized Gaussian (LG00) and Laguerre-Gaussian (LG01) beams results in polarization singular beams with different morphology structures such as lemon, star and dipole patterns around the C-point in the beam cross-section. The Pancharatnam-Berry phase plays a critical role in the formation and characteristics of these spatially inhomogeneous fields. We present our experimental results wherein we measure the variable geometric phase by tracking the trajectory of the component vortices in the beam cross-section, by interfering with selective polarization states and by tracking different latitudes on the Poincaré sphere without the effect of a dynamic phase.

  16. Numerical generation of a polarization singularity array with modulated amplitude and phase.

    PubMed

    Ye, Dong; Peng, Xinyu; Zhao, Qi; Chen, Yanru

    2016-09-01

    A point having no defined polarized ellipse azimuthal angle (circularly polarized) in a space-variant vector field is called a polarization singularity, and it has three types: Lemon, Monstar, and Star. Recently, the connection of polarization singularities has been performed. Inspired by this, we conduct a numerical generation of a polarization singularity array. Our method is based on two orthogonal linearly polarized light beams with modulated amplitude and phase. With appropriate distribution functions of amplitudes and phases we can control the polarized states of polarization singularities, which offer a possibility to simulate a polarization singularity array.

  17. Near-field phase singularity in subwavelength metallic microstructures

    NASA Astrophysics Data System (ADS)

    Kang, Ming; Guo, Qing-Hua; Chen, Jing; Gu, Bing; Li, Yongnan; Wang, Hui-Tian

    2011-10-01

    A near-field phase singularity (NFPS) depending on the spin state of the incident electromagnetic (EM) radiation is very fascinating because it can enrich the functionality of the EM radiation in metamaterials. Here we present a microscopic dipole model to describe the NFPS effect under the time-harmonic quasistatic limit. The results reveal that NFPS exists for the longitudinal components of both electric and magnetic fields as well as the transverse component of time-averaged Poynting vector. The localized surface plasmon polariton in the subwavelength metallic structure contributes to enhance the generation efficiency of NFPS by introducing the resonance of the electric dipole. This effect not only is promising for microtrapping and manipulation but also enriches the functionality of the existing metamaterials.

  18. On the expanding phase of a singular bounce and intermediate inflation: The modified gravity description

    NASA Astrophysics Data System (ADS)

    Oikonomou, V. K.

    2017-03-01

    We demonstrate that the intermediate inflation scenario is a singular inflation cosmology, with the singularity at the origin t = 0 being a pressure and energy density singularity and particularly a Type III singularity. Also, we show that the expanding phase of a singular bounce can be identical to the intermediate inflation scenario, if the singular bounce has a Type III singularity at the origin. For the intermediate inflation scenario we examine the cosmological implications on the power spectrum in the context of various forms of modified gravity. Particularly, we calculate the power spectrum in the context of F(R), F(G) Gauss-Bonnet gravity and also for F(T) gravity and we discuss the viability of each scenario by comparing the resulting spectral index with the latest observational data.

  19. Singular diffraction-free surface plasmon beams generated by overlapping phase-shifted sources.

    PubMed

    Wei, Shibiao; Lin, Jiao; Wang, Qian; Yuan, Guanghui; Du, Luping; Wang, Rong; Xu, Le; Hong, Minghui; Min, Changjun; Yuan, Xiaocong

    2013-04-01

    We propose and experimentally demonstrate the singular surface plasmon beam that presents a dark channel generated by a point dislocation and a long diffraction-free propagation distance up to 70λ(sp). The singular surface beam is the result of the interference of two surface plasmon polariton (SPP) plane waves, which are launched by two coupling gratings with lateral displacement. An aperture-type near-field scanning optical microscope is used to map the intensity distribution of the singular SPP waves. The propagating point dislocation embedded in the beam is shown by full-wave calculations and is later verified by near-field interference in the experiment.

  20. Description of phase singularities and their application to focusing design.

    PubMed

    Martínez-Niconoff, G; Muñoz-Lopez, J; Méndez-Martínez, E

    2001-09-01

    We describe the focusing region associated with transmittances, analyzing its associated phase function. We show that generic features can be studied from the differential equation for focusing geometry, which is obtained through angular representation for diffraction fields. With the treatment, we recover the results for circular zone plates, and by introducing a linear transformation into the transmittance function we generate structures that keep the ability to generate focusing. According to the choice of the parameters involved, the diffraction field presents new focusing regions, whose three-dimensional geometry and spatial evolution can be described in a selective fashion with analysis of only the phase singularities associated with the diffraction field and avoidance of the integral representation. The treatment is also applied to a simple lens. We recover the theoretical predictions obtained by Berry and Upstill [M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. XVIII, p. 259], and these predictions are corroborated experimentally. The results obtained are shown.

  1. Multivariate singular spectrum analysis and the road to phase synchronization

    NASA Astrophysics Data System (ADS)

    Groth, Andreas; Ghil, Michael

    2010-05-01

    Singular spectrum analysis (SSA) and multivariate SSA (M-SSA) are based on the classical work of Kosambi (1943), Loeve (1945) and Karhunen (1946) and are closely related to principal component analysis. They have been introduced into information theory by Bertero, Pike and co-workers (1982, 1984) and into dynamical systems analysis by Broomhead and King (1986a,b). Ghil, Vautard and associates have applied SSA and M-SSA to the temporal and spatio-temporal analysis of short and noisy time series in climate dynamics and other fields in the geosciences since the late 1980s. M-SSA provides insight into the unknown or partially known dynamics of the underlying system by decomposing the delay-coordinate phase space of a given multivariate time series into a set of data-adaptive orthonormal components. These components can be classified essentially into trends, oscillatory patterns and noise, and allow one to reconstruct a robust "skeleton" of the dynamical system's structure. For an overview we refer to Ghil et al. (Rev. Geophys., 2002). In this talk, we present M-SSA in the context of synchronization analysis and illustrate its ability to unveil information about the mechanisms behind the adjustment of rhythms in coupled dynamical systems. The focus of the talk is on the special case of phase synchronization between coupled chaotic oscillators (Rosenblum et al., PRL, 1996). Several ways of measuring phase synchronization are in use, and the robust definition of a reasonable phase for each oscillator is critical in each of them. We illustrate here the advantages of M-SSA in the automatic identification of oscillatory modes and in drawing conclusions about the transition to phase synchronization. Without using any a priori definition of a suitable phase, we show that M-SSA is able to detect phase synchronization in a chain of coupled chaotic oscillators (Osipov et al., PRE, 1996). Recently, Muller et al. (PRE, 2005) and Allefeld et al. (Intl. J. Bif. Chaos, 2007) have

  2. Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces.

    PubMed

    Li, Ying; Liu, Yachao; Ling, Xiaohui; Yi, Xunong; Zhou, Xinxing; Ke, Yougang; Luo, Hailu; Wen, Shuangchun; Fan, Dianyuan

    2015-01-26

    Observation of photonic spin Hall effect (SHE) near the phase singularity at dielectric metasurfaces is presented. The structured metasurface works as a space-variant Pancharatnam-Berry phase element and produces a vortex beam with phase singularity. The dynamical vortex phase is introduced to eliminate or enhance the phase singularity, thus realizing the manipulation of spin-dependent Pancharatnam-Berry phase. The spin-orbit coupling near the singularity of the Pancharatnam-Berry phase leads to the observation of the photonic SHE which manifests itself as spin-dependent splitting. The underlying mechanism is significantly different from previously reported cases. It thereby provides an alternative way to manipulate the spin states of photons.

  3. Topological charge transformation of beams with embedded fractional phase step in the process of second harmonic generation

    NASA Astrophysics Data System (ADS)

    Stanislovaitis, Paulius; Matijosius, Aidas; Ivanov, Maksym; Smilgevicius, Valerijus

    2017-10-01

    We demonstrate collinear second harmonic generation performed with a beam with an embedded initial phase singularity of strength | l| =1/2. We examine the law of topological charge conservation during this process. Despite the instability of the initial singularity, we observe a counterintuitive topological charge doubling. In the second harmonic, we observe an optical vortex of strength (topological charge) | l| =1. The conservation of topological charge is confirmed by both numerical simulations and the experiment. We also provide a qualitative explanation of the process.

  4. Combined phase singularity and wavefront analysis for optical maps of ventricular fibrillation.

    PubMed

    Rogers, Jack M

    2004-01-01

    Much of the research into the mechanisms of ventricular fibrillation (VF) employs high-resolution mapping of electrical activation and recovery patterns. We previously developed a method for analyzing electrically mapped VF patterns that was based on identifying individual VF wavefronts. We now introduce a related method designed to take into account the information on repolarization that is present in optically mapped VF data. The new method first converts raw fluorescence data to an angular variable that tracks the phase of the mapped tissue through the depolarization-repolarization cycle. We define wavefronts in this context as isolines of phase that terminate either at boundaries or at singular points within the phase field. These singularities are the pivots of functional reentry and are important determinants of VF patterns. We parameterize VF by constructing data structures that describe wavefronts and singularities and also maintain wavefront-wavefront, wavefront-singularity, and singularity-singularity relationships. We describe one important application of this parameterization, which is to identify, localize, and characterize the importance of occurrences of propagation block during VF.

  5. LASER BEAMS: On a method for obtaining laser beams with a phase singularity

    NASA Astrophysics Data System (ADS)

    Malyutin, A. A.

    2004-03-01

    A method is analysed for obtaining laser beams with a phase singularity with the help of phase screens described by the function of the type exp(ilphi). It is shown that this method is used to obtain laser beams in the form of single rings with a smooth intensity distribution in the far-field radiation zone (at the lens focus) representing the superposition of Laguerre — Gaussian modes. In the near-field zone and, in the presence of aperture clipping, also in the focal region, the beams with a more complicated structure can be observed. The scaling of the radius corresponding to the maximum intensity of the beam both in the absence and presence of aperture clipping occurs linearly with the singularity charge l. The influence of the beam decentration and of the phase screen on the structure of phase-singularity beams is estimated.

  6. Evolution of phase singularities of vortex beams propagating in atmospheric turbulence.

    PubMed

    Ge, Xiao-Lu; Wang, Ben-Yi; Guo, Cheng-Shan

    2015-05-01

    Optical vortex beams propagating through atmospheric turbulence are studied by numerical modeling, and the phase singularities of the vortices existing in the turbulence-distorted beams are calculated. It is found that the algebraic sum of topological charges (TCs) of all the phase singularities existing in test aperture is approximately equal to the TC of the input vortex beam. This property provides us a possible approach for determining the TC of the vortex beam propagating through the atmospheric turbulence, which could have potential application in optical communication using optical vortices.

  7. A Singular Perturbation Approach for Time-Domain Assessment of Phase Margin

    NASA Technical Reports Server (NTRS)

    Zhu, J. Jim; Yang, Xiaojing; Hodel, A Scottedward

    2010-01-01

    This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter Epsilon. First, a bijective relationship between the Singular Perturbation Margin (SPM) max and the PM of the nominal (slow) system is established with an approximation error on the order of Epsilon(exp 2). In proving this result, relationships between the singular perturbation parameter Epsilon, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.

  8. Comparisons between singularities of pseudophase and speckle phase using binary diffusers in optical vortex metrology

    NASA Astrophysics Data System (ADS)

    Veiras, Francisco E.; Vadnjal, Ana Laura; Etchepareborda, Pablo; Bianchetti, Arturo; Federico, Alejandro; Kaufmann, Guillermo H.

    2016-12-01

    An analysis based on the comparison between singularities of speckle phase and pseudophase in the practice of optical vortex metrology is carried out by measuring the phase map of the speckle pattern obtained from the transmitted light through binary diffusers. In the characterization of the core structure of both phase singularities, the variation of the measured parameters is produced by means of in-plane linear displacements and rotations of the scattered speckle fields. These fields are addressed by using similar displacements of the binary phase masks recorded in a spatial light modulator (SLM). We complete these comparisons by measuring out-of-plane variations of the core structure parameters. In addition, we verified that the phase map of the transmitted light beam through the binary diffusers recorded in SLMs is actually characterized by a speckle phase with vortices of unitary charge. The presented analysis would be helpful for understanding the scope and limitations of the use of the singularities of speckle phase and pseudophase as position marking, and also for speckle measurement of in-plane rigid-body displacements of binary diffusers dynamically controlled by means of SLMs.

  9. Griffiths singularity of quantum phase transition in ion-gated ZrNCl

    NASA Astrophysics Data System (ADS)

    Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro

    Recent technological advances of thin films fabrication, especially mechanical exfoliation, led to discoveries of less-disordered highly-crystalline two-dimensional (2D) superconductors; atomically thin NbSe2 and ion-gated 2D materials, which show intrinsic properties of 2D superconductors with minimal disorder; for example, metallic ground state, and unconventional 2D Ising superconductivity due to pure spin-valley locking effect. In this talk, we focus on magnetotransport properties of an ionic-liquid gated ZrNCl, which exhibited Griffiths singularity-like behavior in superconductor-metal-insulator transition induced by magnetic fields at low carrier concentrations. The overall behavior is quite similar to the recent results of superconducting Ga thin films, in which quantum Griffiths singularity was observed in vortex-glass state. We will discuss the relationship between Griffiths singularity and quantum tunneling or flux flow of vortices phase (vortex liquid) in our system

  10. Robust three-dimensional best-path phase-unwrapping algorithm that avoids singularity loops.

    PubMed

    Abdul-Rahman, Hussein; Arevalillo-Herráez, Miguel; Gdeisat, Munther; Burton, David; Lalor, Michael; Lilley, Francis; Moore, Christopher; Sheltraw, Daniel; Qudeisat, Mohammed

    2009-08-10

    In this paper we propose a novel hybrid three-dimensional phase-unwrapping algorithm, which we refer to here as the three-dimensional best-path avoiding singularity loops (3DBPASL) algorithm. This algorithm combines the advantages and avoids the drawbacks of two well-known 3D phase-unwrapping algorithms, namely, the 3D phase-unwrapping noise-immune technique and the 3D phase-unwrapping best-path technique. The hybrid technique presented here is more robust than its predecessors since it not only follows a discrete unwrapping path depending on a 3D quality map, but it also avoids any singularity loops that may occur in the unwrapping path. Simulation and experimental results have shown that the proposed algorithm outperforms its parent techniques in terms of reliability and robustness.

  11. Automatic Detections of P and S Phases using Singular Value Decomposition Analysis

    NASA Astrophysics Data System (ADS)

    Kurzon, I.; Vernon, F.; Ben-Zion, Y.; Rosenberger, A.

    2012-12-01

    We implement a new method for the automatic detection of the primary P and S phases using Singular Value Decomposition (SVD) analysis. The method is based on a real-time iteration algorithm of Rosenberger (2010) for the SVD of three component seismograms. Rosenberger's algorithm identifies the incidence angle by applying SVD and separates the waveforms into their P and S components. We have been using the same algorithm, with the modification that we apply a set of filters prior to the SVD, and study the success of these filters in detecting correctly the P and S arrivals, in different stations and segments of the San Jacinto Fault Zone. A recent deployment in San Jacinto Fault Zone area provides a very dense seismic networks, with ~ 90 stations in a fault zone which is 150km long and 30km wide. Embedded in this network are 5 linear arrays crossing the fault trace, with ~ 10 stations at ~ 25-50m spacing in each array. This allows us to test the detection algorithm in a diverse setting, including events with different source mechanisms, stations with different site characteristics, and ray paths that diverge from the SVD approximation used in the algorithm, such as rays propagating within the fault and recorded on the linear arrays. Comparing our new method with classic automatic detection methods using Short Time Average (STA) to Long Time Average (LTA) ratios, we show the success of this SVD detection. Unlike the STA to LTA ratio methods that normally tend to detect the P phase, but in many cases cannot distinguish the S arrival, the main advantage of the SVD method is that almost all the P arrivals have an associated S arrival. Moreover, even for cases of short distance events, in which the S arrivals are masked by the P waves, the SVD algorithm under low band filters, manages to detect those S arrivals. The method is less consistent for stations located directly on the fault traces, in which the SVD approximation is not always valid; but even in such cases the

  12. Topology of phase and polarisation singularities in focal regions

    NASA Astrophysics Data System (ADS)

    Andrejic, Petar; Lekner, John

    2017-10-01

    The focal region of a beam contains circles of zeros of the beam wavefunction, on which surfaces of different phase meet. The existence of these zeros is topological in origin, and appears to be universal. Two examples of generalised Bessel beams are examined. One of these has zeros only in the focal plane. The other has focal plane zeros but also movement of the zeros away from the focal plane at certain values of a parameter which determines the tightness of the focus, as analysed by Berry in 1998. As tightness of focus increases these two families of beams coalesce into a common most-focused beam. The polarisation properties of both families and of their common limiting form are considered and correlated with the zeros (dislocations) of the beam wavefunctions. We find regions of circular polarisation in beams which are nominally linearly polarised, and rapid variation of the polarisation pattern as the tightness of focus passes through critical values.

  13. Hybrid method based on singular value decomposition and embedded zero tree wavelet technique for ECG signal compression.

    PubMed

    Kumar, Ranjeet; Kumar, A; Singh, G K

    2016-06-01

    In the field of biomedical, it becomes necessary to reduce data quantity due to the limitation of storage in real-time ambulatory system and telemedicine system. Research has been underway since very beginning for the development of an efficient and simple technique for longer term benefits. This paper, presents an algorithm based on singular value decomposition (SVD), and embedded zero tree wavelet (EZW) techniques for ECG signal compression which deals with the huge data of ambulatory system. The proposed method utilizes the low rank matrix for initial compression on two dimensional (2-D) ECG data array using SVD, and then EZW is initiated for final compression. Initially, 2-D array construction has key issue for the proposed technique in pre-processing. Here, three different beat segmentation approaches have been exploited for 2-D array construction using segmented beat alignment with exploitation of beat correlation. The proposed algorithm has been tested on MIT-BIH arrhythmia record, and it was found that it is very efficient in compression of different types of ECG signal with lower signal distortion based on different fidelity assessments. The evaluation results illustrate that the proposed algorithm has achieved the compression ratio of 24.25:1 with excellent quality of signal reconstruction in terms of percentage-root-mean square difference (PRD) as 1.89% for ECG signal Rec. 100 and consumes only 162bps data instead of 3960bps uncompressed data. The proposed method is efficient and flexible with different types of ECG signal for compression, and controls quality of reconstruction. Simulated results are clearly illustrate the proposed method can play a big role to save the memory space of health data centres as well as save the bandwidth in telemedicine based healthcare systems. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  14. Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities

    PubMed Central

    Ackerman, Paul J.; Qi, Zhiyuan; Lin, Yiheng; Twombly, Christopher W.; Laviada, Mauricio J.; Lansac, Yves; Smalyukh, Ivan I.

    2012-01-01

    Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable “optical drawing” of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators. PMID:22679553

  15. Laser-ablative engineering of phase singularities in plasmonic metamaterial arrays for biosensing applications

    SciTech Connect

    Aristov, Andrey I.; Kabashin, Andrei V.; Zywietz, Urs; Evlyukhin, Andrey B.; Reinhardt, Carsten; Chichkov, Boris N.

    2014-02-17

    By using methods of laser-induced transfer combined with nanoparticle lithography, we design and fabricate large-area gold nanoparticle-based metamaterial arrays exhibiting extreme Heaviside-like phase jumps in reflected light due to a strong diffractive coupling of localized plasmons. When employed in sensing schemes, these phase singularities provide the sensitivity of 5 × 10{sup 4} deg. of phase shift per refractive index unit change that is comparable with best values reported for plasmonic biosensors. The implementation of sensor platforms on the basis of such metamaterial arrays promises a drastic improvement of sensitivity and cost efficiency of plasmonic biosensing devices.

  16. Non-singular Brans–Dicke collapse in deformed phase space

    SciTech Connect

    Rasouli, S.M.M.; Ziaie, A.H.; Jalalzadeh, S.; Moniz, P.V.

    2016-12-15

    We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

  17. Non-singular Brans-Dicke collapse in deformed phase space

    NASA Astrophysics Data System (ADS)

    Rasouli, S. M. M.; Ziaie, A. H.; Jalalzadeh, S.; Moniz, P. V.

    2016-12-01

    We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

  18. Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection.

    PubMed

    Kravets, V G; Schedin, F; Jalil, R; Britnell, L; Gorbachev, R V; Ansell, D; Thackray, B; Novoselov, K S; Geim, A K; Kabashin, A V; Grigorenko, A N

    2013-04-01

    The non-trivial behaviour of phase is crucial for many important physical phenomena, such as, for example, the Aharonov-Bohm effect and the Berry phase. By manipulating the phase of light one can create 'twisted' photons, vortex knots and dislocations which has led to the emergence of the field of singular optics relying on abrupt phase changes. Here we demonstrate the feasibility of singular visible-light nano-optics which exploits the benefits of both plasmonic field enhancement and the peculiarities of the phase of light. We show that properly designed plasmonic metamaterials exhibit topologically protected zero reflection yielding to sharp phase changes nearby, which can be employed to radically improve the sensitivity of detectors based on plasmon resonances. By using reversible hydrogenation of graphene and binding of streptavidin-biotin, we demonstrate an areal mass sensitivity at a level of fg mm(-2) and detection of individual biomolecules, respectively. Our proof-of-concept results offer a route towards simple and scalable single-molecule label-free biosensing technologies.

  19. Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition

    NASA Astrophysics Data System (ADS)

    Singh, Phool; Yadav, A. K.; Singh, Kehar

    2017-04-01

    A novel scheme for image encryption of phase images is proposed, using fractional Hartley transform followed by Arnold transform and singular value decomposition in the frequency domain. Since the plaintext is a phase image, the mask used in the spatial domain is a random amplitude mask. The proposed scheme has been validated for grayscale images and is sensitive to the encryption parameters such as the order of the Arnold transform and the fractional orders of the Hartley transform. We have also evaluated the scheme's resistance to the well-known noise and occlusion attacks.

  20. Existence and boundedness of solutions for a singular phase field system

    NASA Astrophysics Data System (ADS)

    Bonetti, Elena; Colli, Pierluigi; Fabrizio, Mauro; Gilardi, Gianni

    This paper is devoted to the mathematical analysis of a thermo-mechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a presentation of the model. Then, the initial and boundary value problem is addressed for the related PDE system, which contains some nonlinear and singular terms with respect to the temperature variable. Existence of the solution is shown along with the boundedness of both phase variable χ and absolute temperature ϑ. Finally, uniqueness is proved in the framework of a source term depending Lipschitz continuously on ϑ.

  1. High-multipole excitations of atoms by twisted photons near phase singularity (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Afanasev, Andrei; Carlson, Carl E.; Mukherjee, Asmita

    2016-09-01

    We calculate transition amplitudes and cross sections for excitation of hydrogen-like atoms by the twisted photon states, or photon states with more than one unit of angular momentum projection along the direction of propagation. If the target atom is located at distances of the order of atomic size near the vortex center, the transitions rates into l_f>1 states become comparable with the rates for standard electric dipole transitions. It is shown that when the transition rates are normalized to the local photon flux, the resulting cross sections for l_f>1 are singular near the optical vortex center, i.e., high-multipole excitations take place in the region of zero field intensity near phase singularity. Relation to the "quantum core" concept introduced by Berry and Dennis is discussed.

  2. Spurious character of singularities associated with phase transitions in cylindrical pores

    NASA Astrophysics Data System (ADS)

    Binder, K.; Virnau, P.; Wilms, D.; Winkler, A.

    2011-08-01

    Phase transitions of simple fluids and binary fluid mixtures confined into long cylindrical pores are re-examined, such as capillary condensation/evaporation and wetting transitions. While a large part of the literature ignores the fact that due to the quasi-one-dimensional character of these systems a singular behavior associated with a sharp phase transition cannot occur, we pay attention to the extent in which these phase transitions are smoothed out (in relation to the magnitude of the pore cross-sectional area). We argue that the finiteness of the pore length is an important parameter which controls the physical phenomena that are observed in simulations (and presumably also experiments explaining the distinction between the apparent "pore critical temperature" and the "hysteresis critical temperature"). We illustrate our arguments with recent findings from simulations of a lattice gas/Ising system and of the Asakura-Oosawa model of colloid-polymer mixtures.

  3. Representation of image distortion by Moiré fringes at phase singularity state.

    PubMed

    Samavati, Katayoon; Taghi Tavassoly, M; Ghomi, Hamid

    2017-01-10

    When a grating is imaged by an optical imaging system, due to the aberrations of the system, the parameters of the image grating suffer minute gradual changes across the image. Superimposing an ideal grating image over the real grating image at the phase singularity state of the two gratings leads to phase contours, special Moiré fringes, which directly represent the distortions over the image. In this report, after a brief review of the required theoretical bases, we show when the parameters of a grating change linearly the corresponding Moiré fringes at the singularity state are represented by quadratic functions, and for nonlinear changes higher order functions are involved. Thus, by imposing desired changes on the parameters of a grating one can produce Moiré fringes satisfying functions of required orders. In the experimental part of the report we apply the technique to evaluate the image distortions imposed by a conventional camera and cameras installed in a mobile and in a tablet.

  4. Nanoparticle collisions in the gas phase in the presence of singular contact potentials

    NASA Astrophysics Data System (ADS)

    Ouyang, Hui; Gopalakrishnan, Ranganathan; Hogan, Christopher J.

    2012-08-01

    Collisional growth and ionization is commonplace for gas phase nanoparticles (i.e., in aerosols). Nanoparticle collisions in atmospheric pressure environments occur in the mass transfer transition regime, and further attractive singular contact potentials (which arise when modeling nanoparticles as condensed matter and for which the potential energy approaches -∞ when two entities contact) often have a non-negligible influence on collision processes. For these reasons collision rate calculations for nanoparticles in the gas phase are not straightforward. We use mean first passage time calculations to develop a simple relationship to determine the collision rate in the gas phase, accounting for the influences of both the transition regime and singular contact potentials (specifically the non-retarded van der Waals and image potentials). In the presented analysis, methods to determine the degree of enhancement in collision rate due to attractive singular potentials in the continuum (diffusive) regime, ηC, and the degree of enhancement in the free molecular (ballistic) regime, ηFM, are first reviewed. Accounting for these enhancement factors, with mean first passage time calculations it is found that the collision rate for gas phase nanoparticles with other gas phase entities can be determined from a relationship between the dimensionless collision rate coefficient, H, and the diffusive Knudsen number, KnD, i.e., the ratio of the mean collision persistence distance to the collision length scale. This coincides with the H(KnD) relationship found to appropriately describe collisions between entities interacting via a hard-sphere potential, but with ηC and ηFM incorporated into the definitions of both H and KnD, respectively. The H(KnD) relationship is compared to the predictions of flux matching theory, used prevalently in prior work for collision rate calculation, and through this comparison it is found that at high potential energy to thermal energy ratios, flux

  5. Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

    NASA Astrophysics Data System (ADS)

    Neupane, Madhab; Xu, Su-Yang; Sankar, R.; Gibson, Q.; Wang, Y. J.; Belopolski, I.; Alidoust, N.; Bian, G.; Shibayev, P. P.; Sanchez, D. S.; Ohtsubo, Y.; Taleb-Ibrahimi, A.; Basak, S.; Tsai, W.-F.; Lin, H.; Durakiewicz, Tomasz; Cava, R. J.; Bansil, A.; Chou, F. C.; Hasan, M. Z.

    2015-08-01

    We report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI), Pb1 -xSnxSe , as a function of various material parameters including composition x , temperature T , and crystal structure. Our spectroscopic data demonstrate the electronic ground-state condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states' response to circularly polarized light. Our results show that each material parameter can tune the system between the trivial and topological phase in a distinct way, unlike that seen in Bi2Se3 and related compounds, leading to a rich topological phase diagram. Our systematic studies of the TCI Pb1 -xSnxSe are a valuable materials guide to realize new topological phenomena.

  6. Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

    DOE PAGES

    Neupane, Madhab; Xu, Su-Yang; Sankar, R.; ...

    2015-08-20

    Here we report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI), Pb1more » $${-}$$xSnxSe, as a function of various material parameters including composition x, temperature T , and crystal structure. Our spectroscopic data demonstrate the electronic ground-state condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states’ response to circularly polarized light. Our results show that each material parameter can tune the system between the trivial and topological phase in a distinct way, unlike that seen in Bi2Se3 and related compounds, leading to a rich topological phase diagram. Our systematic studies of the TCI Pb1$${-}$$xSnxSe are a valuable materials guide to realize new topological phenomena.« less

  7. Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

    SciTech Connect

    Neupane, Madhab; Xu, Su-Yang; Sankar, R.; Gibson, Q.; Wang, Y. J.; Belopolski, I.; Alidoust, N.; Bian, G.; Shibayev, P. P.; Sanchez, D. S.; Ohtsubo, Y.; Taleb-Ibrahimi, A.; Tsai, W. -F.; Lin, H.; Durakiewicz, Tomasz; Cava, R. J.; Bansil, A.; Chou, F. C.; Hasan, M. Z.

    2015-08-20

    Here we report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI), Pb1${-}$xSnxSe, as a function of various material parameters including composition x, temperature T , and crystal structure. Our spectroscopic data demonstrate the electronic ground-state condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states’ response to circularly polarized light. Our results show that each material parameter can tune the system between the trivial and topological phase in a distinct way, unlike that seen in Bi2Se3 and related compounds, leading to a rich topological phase diagram. Our systematic studies of the TCI Pb1${-}$xSnxSe are a valuable materials guide to realize new topological phenomena.

  8. Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier.

    PubMed

    Federico, Alejandro; Kaufmann, Guillermo H

    2008-10-01

    We evaluate a method based on the two-dimensional directional wavelet transform and the introduction of a spatial carrier to retrieve optical phase distributions in singular scalar light fields. The performance of the proposed phase-retrieval method is compared with an approach based on Fourier transform. The advantages and limitations of the proposed method are discussed.

  9. Enhancing multivariate singular spectrum analysis for phase synchronization: The role of observability

    NASA Astrophysics Data System (ADS)

    Portes, Leonardo L.; Aguirre, Luis A.

    2016-09-01

    Multivariate singular spectrum analysis (M-SSA) was recently adapted to study systems of coupled oscillators. It does not require an a priori definition for phase nor detailed knowledge of the individual oscillators, but it uses all the variables of each system. This aspect could be restrictive for practical applications, since usually just a few (sometimes only one) variables are measured. Based on dynamical systems and observability theories, we first show how to apply the M-SSA with only one variable and show the conditions to achieve good performance. Next, we provide numerical evidence that this single-variable approach enhances the explanatory power compared to the original M-SSA when computed with all the system variables. This could have important practical implications, as pointed out using benchmark oscillators.

  10. Enhancing multivariate singular spectrum analysis for phase synchronization: The role of observability.

    PubMed

    Portes, Leonardo L; Aguirre, Luis A

    2016-09-01

    Multivariate singular spectrum analysis (M-SSA) was recently adapted to study systems of coupled oscillators. It does not require an a priori definition for phase nor detailed knowledge of the individual oscillators, but it uses all the variables of each system. This aspect could be restrictive for practical applications, since usually just a few (sometimes only one) variables are measured. Based on dynamical systems and observability theories, we first show how to apply the M-SSA with only one variable and show the conditions to achieve good performance. Next, we provide numerical evidence that this single-variable approach enhances the explanatory power compared to the original M-SSA when computed with all the system variables. This could have important practical implications, as pointed out using benchmark oscillators.

  11. Phase singularities in 3D plasmonic crystal metamaterials for ultra-sensitive biosensing

    NASA Astrophysics Data System (ADS)

    Danilov, Artem; Aristov, Andrey I.; Manousidaki, Maria; Terzaki, Konstantina; Fotakis, Costas; Farsari, Maria; Kabashin, Andrei V.

    2017-02-01

    Plasmonic biosensors form the core label-free technology for studies of biomolecular interactions, but they still need a drastic improvement of sensitivity and novel nano-architectural implementations to match modern trends of nanobiotechnology. Here, we consider the generation of resonances in light reflected from 3D woodpile plasmonic crystal metamaterials fabricated by Direct Laser Writing by Multi-Photon Polymerization, followed by silver electroless plating. We show that the generation of these resonances is accompanied by the appearance of singularities of phase of reflected light and examine the response of phase characteristics to refractive index variations inside the metamaterial matrix. The recorded phase sensitivity (3*104 deg. of phase shift per RIU change) outperforms most plasmonic counterparts and is attributed to particular conditions of plasmon excitation in 3D plasmonic crystal geometry. Combined with a large surface for biomolecular immobilizations offered by the 3D woodpile matrix, the proposed sensor architecture promises a new important landmark in the advancement of plasmonic biosensing technology.

  12. Lissajous singularities.

    PubMed

    Kessler, David A; Freund, Isaac

    2003-01-15

    Coherent optical Lissajous states are easily created by nonlinear processes such as second-harmonic generation (SHG). Singular properties of such states are discussed and illustrated theoretically with non-phase-matched SHG of an ellipse field containing a C point.

  13. Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence.

    PubMed

    Rao, Ruizhong

    2008-01-10

    Numerical experiments are carried out for a plane wave propagating in the atmospheric turbulence for a weak to strong fluctuation condition, i.e., the Rytov index being in a large range of 2x10(-3) to 20. Mainly two categories of propagation events are explored for the same range of Rytov index. In one category the propagation distance and also the Fresnel length are kept fixed with the turbulence strength changing. In the other the turbulence strength is kept fixed with the distance changing. The statistical characteristics of the scintillation index, the maximum and minimum of the intensity, the fractal dimension of the intensity image, and the number density of the phase singularity are analyzed. The behaviors of the fractal dimension and the density of the phase singularity present obvious differences for the two categories of propagation. The fractal dimension depends both on the Rytov index and the Fresnel length. In both weak and strong fluctuation conditions the dimension generally increases with the Rytov index, but is at minimum at the onset region. The phase singularity density is coincident with the theoretical results under a weak fluctuation condition, and has a slowly increasing manner with the Rytov index in the strong fluctuation condition. The dependence on the Fresnel size is confident and there is no saturation for the phase singularity.

  14. ALIGNMENT OF PROTOSTARS AND CIRCUMSTELLAR DISKS DURING THE EMBEDDED PHASE

    SciTech Connect

    Spalding, Christopher; Batygin, Konstantin; Adams, Fred C. E-mail: kbatygin@gps.caltech.edu

    2014-12-20

    Star formation proceeds via the collapse of a molecular cloud core over multiple dynamical timescales. Turbulence within cores results in a spatially non-uniform angular momentum of the cloud, causing a stochastic variation in the orientation of the disk forming from the collapsing material. In the absence of star-disk angular momentum coupling, such disk-tilting would provide a natural mechanism for the production of primordial spin-orbit misalignments in the resulting planetary systems. However, owing to high accretion rates in the embedded phase of star formation, the inner edge of the circumstellar disk extends down to the stellar surface, resulting in efficient gravitational and accretional angular momentum transfer between the star and the disk. Here, we demonstrate that the resulting gravitational coupling is sufficient to suppress any significant star-disk misalignment, with accretion playing a secondary role. The joint tilting of the star-disk system leads to a stochastic wandering of star-aligned bipolar outflows. Such wandering widens the effective opening angle of stellar outflows, allowing for more efficient clearing of the remainder of the protostar's gaseous envelope. Accordingly, the processes described in this work provide an additional mechanism responsible for sculpting the stellar initial mass function.

  15. Multivariate singular spectrum analysis and phase synchronization: An application to U.S. business cycles

    NASA Astrophysics Data System (ADS)

    Groth, Andreas; Ghil, Michael; Hallegatte, Stephane; Dumas, Patrice

    2010-05-01

    Over the last two decades, singular spectrum analysis (SSA) and multivariate SSA (M-SSA) have proven their power in the temporal and spatio-temporal analysis of short and noisy time series in numerous fields of the geosciences and of other disciplines. M-SSA provides insight into the unknown or partially known dynamics of the underlying system by decomposing the delay-coordinate phase space of a given multivariate time series into a set of data-adaptive orthonormal components. These components can be classified essentially into trends, oscillatory patterns and noise, and allow one to reconstruct a robust "skeleton" of the dynamical system's structure. For an overview we refer to Ghil et al. (Rev. Geophys., 2002). We first present M-SSA in the context of synchronization analysis and illustrate its ability to unveil information about the mechanisms behind the adjustment of rhythms in coupled dynamical systems. This poster deals with the special case of phase synchronization between coupled chaotic oscillators (Rosenblum et al., PRL, 1996). Several ways of measuring phase synchronization are in use, and the robust definition of a reasonable phase for each oscillator is critical in each of them. We illustrate here the advantages of M-SSA in the automatic identification of oscillatory modes and in drawing conclusions about the transition to phase synchronization. Without using any a priori definition of a suitable phase, we show that M-SSA is able to detect phase synchronization in a chain of coupled chaotic oscillators (Osipov et al., PRE, 1996). The key application of these theoretical results in this poster is to U.S. macroeconomic data for 1954--2005. M-SSA helps us draw conclusions about the cyclical behavior of the U.S. economy and its underlying dynamical properties. The recurrence of expansions and recessions, at approximately 5--6-year intervals, is referred to as business cycles; their origin is still a matter of considerable controversy. Our analysis sheds

  16. A New Efficient Method for Detecting Phase Singularity in Cardiac Fibrillation

    PubMed Central

    Hwang, Minki; Lim, Byounghyun; Joung, Boyoung; Pak, Hui-Nam

    2016-01-01

    Background The point of phase singularity (PS) is considered to represent a spiral wave core or a rotor in cardiac fibrillation. Computational efficiency is important for detection of PS in clinical electrophysiology. We developed a novel algorithm for highly efficient and robust detection of PS. Methods In contrast to the conventional method, which calculates PS based on the line integral of the phase around a PS point equal to ±2π (the Iyer-Gray method), the proposed algorithm (the location-centric method) looks for the phase discontinuity point at which PS actually occurs. We tested the efficiency and robustness of these two methods in a two-dimensional mathematical model of atrial fibrillation (AF), with and without remodeling of ionic currents. Results 1. There was a significant association, in terms of the Hausdorff distance (3.30 ± 0.0 mm), between the PS points measured using the Iyer-Gray and location-centric methods, with almost identical PS trajectories generated by the two methods. 2. For the condition of electrical remodeling of AF (0.3 × ICaL), the PS points calculated by the two methods were satisfactorily co-localized (with the Hausdorff distance of 1.64 ± 0.09 mm). 3. The proposed location-centric method was substantially more efficient than the Iyer-Gray method, with a 28.6-fold and 28.2-fold shorter run times for the control and remodeling scenarios, respectively. Conclusion We propose a new location-centric method for calculating PS, which is robust and more efficient compared with the conventionally used method. PMID:27907144

  17. Singularities and Closed String Tachyons

    SciTech Connect

    Silverstein, Eva; /SLAC /Stanford U., Phys. Dept.

    2006-03-17

    A basic problem in gravitational physics is the resolution of spacetime singularities where general relativity breaks down. The simplest such singularities are conical singularities arising from orbifold identifications of flat space, and the most challenging are spacelike singularities inside black holes (and in cosmology). Topology changing processes also require evolution through classically singular spacetimes. I briefly review how a phase of closed string tachyon condensate replaces, and helps to resolve, basic singularities of each of these types. Finally I discuss some interesting features of singularities arising in the small volume limit of compact negatively curved spaces and the emerging zoology of spacelike singularities.

  18. Molecular-level comparison of alkylsilane and polar-embedded reversed-phase liquid chromatography systems.

    PubMed

    Rafferty, Jake L; Siepmann, J Ilja; Schure, Mark R

    2008-08-15

    Stationary phases with embedded polar groups possess several advantages over conventional alkylsilane phases, such as reduced peak tailing, enhanced selectivity for specific functional groups, and the ability to use a highly aqueous mobile phase. To gain a deeper understanding of the retentive properties of these reversed-phase packings, molecular simulations were carried out for three different stationary phases in contact with mobile phases of various water/methanol ratios. Two polar-embedded phases were modeled, namely, amide and ether containing, and compared to a conventional octadecylsilane phase. The simulations show that, due to specific hydrogen bond interactions, the polar-embedded phases take up significantly more solvent and are more ordered than their alkyl counterparts. Alkane and alcohol probe solutes indicate that the polar-embedded phases are less retentive than alkyl phases for nonpolar species, whereas polar species are more retained by them due to hydrogen bonding with the embedded groups and the increased amount of solvent within the stationary phase. This leads to a significant reduction of the free-energy barrier for the transfer of polar species from the mobile phase to residual silanols, and this reduced barrier provides a possible explanation for reduced peak tailing.

  19. Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model

    NASA Astrophysics Data System (ADS)

    Suzuki, Akio; Konno, Hidetoshi

    2011-09-01

    The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.

  20. EVALUATING THE HYDROGEOCHEMICAL RESPONSE OF SPRINGS USING PHASE-PLANE PLOTS AND SINGULAR SPECTRUM ANALYSIS

    SciTech Connect

    B. NEWMAN; C. DUFFY; D. HICKMOTT

    2001-04-01

    An ongoing study is focused on understanding the hydrology and geochemistry of three contaminated, perennial, semi-arid zone springs at a high explosives production facility at Los Alamos National Laboratory, in northern New Mexico, USA. Springflow time series were examined using singular spectrum analysis (SSA) to identify the important time-scales affecting flow in the springs. SSA results suggest that springflow has two dominant patterns: a series of low-frequency modes which follow the seasonal and longer-term climate conditions at the site, and a large number of higher frequency modes which display the characteristic ''red noise'' spectrum related to local, short-term weather conditions. Phase-plane plots of {delta}{sup 18}O and spring discharge suggest that high flow conditions are dominated by snowmelt and summer monsoon inputs while low flow conditions can be affected by mixing of fast and slow flow components causing wide variations in {delta}{sup 18}O values. The analysis is being used for development of an efficient strategy for sampling design for environmental monitoring of contaminants that respond to multiple time scales.

  1. Measurement of in-plane displacements using the phase singularities generated by directional wavelet transforms of speckle pattern images.

    PubMed

    Vadnjal, Ana Laura; Etchepareborda, Pablo; Federico, Alejandro; Kaufmann, Guillermo H

    2013-03-20

    We present a method to determine micro and nano in-plane displacements based on the phase singularities generated by application of directional wavelet transforms to speckle pattern images. The spatial distribution of the obtained phase singularities by the wavelet transform configures a network, which is characterized by two quasi-orthogonal directions. The displacement value is determined by identifying the intersection points of the network before and after the displacement produced by the tested object. The performance of this method is evaluated using simulated speckle patterns and experimental data. The proposed approach is compared with the optical vortex metrology and digital image correlation methods in terms of performance and noise robustness, and the advantages and limitations associated to each method are also discussed.

  2. Charge Inversion and Topological Phase Transition at a Twist Angle Induced van Hove Singularity of Bilayer Graphene.

    PubMed

    Kim, Youngwook; Herlinger, Patrick; Moon, Pilkyung; Koshino, Mikito; Taniguchi, Takashi; Watanabe, Kenji; Smet, Jurgen H

    2016-08-10

    van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.

  3. Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems. [stability margins for wing flutter suppression and drone lateral attitude control

    NASA Technical Reports Server (NTRS)

    Mukhopadhyay, V.; Newsom, J. R.

    1982-01-01

    A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.

  4. Singularities and Topological Phase Transitions in Fluids: Breaking Away, Selective Withdrawal, and Islets in the Stream

    SciTech Connect

    Nagel, Sidney

    2007-01-17

    The exhilarating spray from waves crashing into the shore, the distressing sound of a faucet leaking in the night, and the indispensable role of bubbles dissolving gas into the oceans are but a few examples of the ubiquitous presence and profound importance of drop formation and splashing in our lives. During fission, a fluid forms a neck that becomes vanishingly thin at the point of breakup. This topological transition is accompanied by a dynamic singularity in which physical properties such as pressure diverge. Singularities of this sort often organize the overall dynamical evolution of nonlinear systems. I will first discuss the role of singularities in the breakup of droplets. I will then present a second experiment, selective withdrawal, in which we study the steady-state shape of a liquid as it is withdrawn by a nozzle through a surrounding fluid. Here, a change in topology may again be accompanied by a singularity. Applications of this geometry that rely on singular dynamical behavior are relevant for the coating of biological particles that may be of particular use in medical transplantation technologies.

  5. Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes

    NASA Astrophysics Data System (ADS)

    Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno

    2011-07-01

    We consider a cosmological model based upon a noncanonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of black holes whose interior are described by the Kantowski-Sachs metric and modeled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of these black holes and compare the results with the Hawking values. We observe that it is actually the noncommutativity in the momentum sector that allows for the existence of a minimum in the potential, which is the key to apply the Feynman-Hibbs procedure. It is shown that this noncommutative model generates a nonunitary dynamics that predicts a vanishing probability in the neighborhood of the singularity. This result effectively regularizes the Kantowski-Sachs singularity and generalizes a similar result, previously obtained for the case of Schwarzschild black holes.

  6. Behavior of embedded phase in shock-driven two-phase flow

    NASA Astrophysics Data System (ADS)

    Kuehner, Garrett; Wayne, Patrick; Olmstead, Dell; Corbin, Clint; Bernard, Tennille; Vorobieff, Peter; Truman, C. Randall

    2013-11-01

    We present an experimental study of droplet acceleration in a shock-driven two-phase flow (air with embedded liquid droplets). The droplets (propylene glycol, diameter 0.5-3 μm) were pre-mixed with the air in the test section of a shock tube, then impulsively accelerated with planar shock wave with a Mach number of 1.7. A cross-section of the flow is illuminated with multiple pulses from Nd:YAG lasers, producing time-resolved visualizations of the seeded volume. The images are then analyzed to quantify droplet velocity and acceleration from the shock passage to about 1.5 ms after the shock. Based on the velocity measurements, we can resolve the droplet lag after the shock, when the massive droplets ``catch up'' with the flow of the surrounding air, as well as validate our earlier estimates of boundary layer growth. This research is supported by NNSA (US National Nuclear Security Agency).

  7. A polar-embedded C30 stationary phase: preparation and evaluation.

    PubMed

    Zhang, Mingliang; Mai, Wenpeng; Zhao, Liang; Guo, Yong; Qiu, Hongdeng

    2015-04-03

    A novel polar-embedded C30 stationary phase has been synthesized and characterized. The polar carbamate group was generated homogeneously in situ by the catalytic reaction between isocyanate and primary alcohol. The simple one-pot synthetic strategy provided an efficient and effective strategy for modification of silica spheres. Efficiency, selectivity and silanol activity of the resulting column were characterized in detail with different classes of analytes that included Standard Reference Materials (SRM) 870, SRM 869b and SRM 1647e, alkylbenzene congeners, as well as polar-substituted aromatics. The polar-embedded C30 stationary phase was found to exhibit excellent shape selectivity.

  8. A theory of phase singularities for image representation and its applications to object tracking and image matching.

    PubMed

    Qiao, Yu; Wang, Wei; Minematsu, Nobuaki; Liu, Jianzhuang; Takeda, Mitsuo; Tang, Xiaoou

    2009-10-01

    This paper studies phase singularities (PSs) for image representation. We show that PSs calculated with Laguerre-Gauss filters contain important information and provide a useful tool for image analysis. PSs are invariant to image translation and rotation. We introduce several invariant features to characterize the core structures around PSs and analyze the stability of PSs to noise addition and scale change. We also study the characteristics of PSs in a scale space, which lead to a method to select key scales along phase singularity curves. We demonstrate two applications of PSs: object tracking and image matching. In object tracking, we use the iterative closest point algorithm to determine the correspondences of PSs between two adjacent frames. The use of PSs allows us to precisely determine the motions of tracked objects. In image matching, we combine PSs and scale-invariant feature transform (SIFT) descriptor to deal with the variations between two images and examine the proposed method on a benchmark database. The results indicate that our method can find more correct matching pairs with higher repeatability rates than some well-known methods.

  9. Singularity development and supersymmetry in holography

    NASA Astrophysics Data System (ADS)

    Buchel, Alex

    2017-08-01

    We study the effects of supersymmetry on singularity development scenario in holography presented in [1] (BBL). We argue that the singularity persists in a supersymmetric extension of the BBL model. The challenge remains to find a string theory embedding of the singularity mechanism.

  10. Formulation of the twisted-light-matter interaction at the phase singularity: Beams with strong magnetic fields

    NASA Astrophysics Data System (ADS)

    Quinteiro, G. F.; Reiter, D. E.; Kuhn, T.

    2017-01-01

    The formulation of the interaction of matter with singular light fields needs special care. In a recent article [G. F. Quinteiro et al., Phys. Rev. A 91, 033808 (2015), 10.1103/PhysRevA.91.033808] we have shown that the Hamiltonian describing the interaction of a twisted-light beam having parallel orbital and spin angular momenta with a small object located close to the phase singularity can be expressed only in terms of the electric field of the beam. Here we complement our study by providing an interaction Hamiltonian for beams having antiparallel orbital and spin angular momenta. Such beams may exhibit unusually strong magnetic effects. We further extend our formulation to radially and azimuthally polarized beams. The advantages of our formulation are that for all beams the Hamiltonian is written solely in terms of the electric and magnetic fields of the beam and as such it is manifestly gauge invariant. Furthermore, it is intuitive by resembling the well-known expressions in the dipole-electric and dipole-magnetic moment approximations.

  11. Observation of Phase-Filling Singularities in the Optical Dielectric Function of Highly Doped n -Type Ge

    NASA Astrophysics Data System (ADS)

    Xu, Chi; Fernando, Nalin S.; Zollner, Stefan; Kouvetakis, John; Menéndez, José

    2017-06-01

    Phase-filling singularities in the optical response function of highly doped (>1019 cm-3 ) germanium are theoretically predicted and experimentally confirmed using spectroscopic ellipsometry. Contrary to direct-gap semiconductors, which display the well-known Burstein-Moss phenomenology upon doping, the critical point in the joint density of electronic states associated with the partially filled conduction band in n -Ge corresponds to the so-called E1 and E1+Δ1 transitions, which are two-dimensional in character. As a result of this reduced dimensionality, there is no edge shift induced by Pauli blocking. Instead, one observes the "original" critical point (shifted only by band gap renormalization) and an additional feature associated with the level occupation discontinuity at the Fermi level. The experimental observation of this feature is made possible by the recent development of low-temperature, in situ doping techniques that allow the fabrication of highly doped films with exceptionally flat doping profiles.

  12. Phase and amplitude retrieval of objects embedded in a sinusoidal background from its diffraction pattern

    SciTech Connect

    Wu, Chu; Ng, Tuck Wah; Neild, Adrian

    2010-04-01

    Efforts of phase and amplitude retrieval from diffraction patterns have almost exclusively been applied for nonperiodic objects. We investigated the quality of retrieval of nonperiodic objects embedded in a sinusoidal background, using the approach of iterative hybrid input-output with oversampling. Two strategies were employed; one by filtering in the frequency domain prior to phase retrieval, and the other by filtering the phase or amplitude image after retrieval. Results obtained indicate better outcomes with the latter approach provided detector noise is not excessive.

  13. Resonance and phase shift in an open Aharonov-Bohm ring with an embedded quantum dot.

    PubMed

    Hedin, Eric R; Joe, Yong S; Satanin, Arkady M

    2009-01-07

    The transmission and phase properties of electron transport through a quantum dot (QD) with variable coupling to a third-terminal probe are investigated analytically for the case of the QD connected directly to source and drain reservoirs and when the QD is embedded in one arm of an Aharonov-Bohm (AB) ring. Using the tight-binding model, explicit analytical expressions of the transmission through the QD for each case are given. Expressions for the conductance with coupling to the third terminal, which breaks unitarity and phase-locking, are also given. It is shown that in a three-terminal interferometer the zero of the Fano resonance in the transmission moves off the real energy axis for finite values of the coupling parameter. The zero orbits around the pole in the complex energy plane as a function of magnetic flux through the ring, and can be returned to the real energy axis unless the coupling parameter exceeds a critical value. With the QD embedded in one arm of the AB ring, the electron transmission and the transmission phase, and the phase of the AB oscillations, are described in relation to the degree of coupling to the third-terminal probe which opens the interferometer. By tuning the degree of coupling to the probe, it is shown that the phase of the AB oscillations can be made to match the intrinsic phase of the QD, facilitating experimental characterization of the phase response of the QD.

  14. Measuring the Gouy Phase of Matter Waves using Singular Atom Optics with Spinor BECs

    NASA Astrophysics Data System (ADS)

    Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.

    2016-05-01

    The Gouy phase is a propagation-dependent geometric phase found in confined waves as they propagate through a focus. Although it has been observed and studied extensively both in scalar and vector optical beams as well as in electron vortex beams, it has not yet been directly observed in ultracold matter waves. The Schrödinger equation has the same form as the paraxial wave equation from electromagnetism; expansion of a BEC upon release from a trap has the same mathematical form as a beam propagating away from a focus. We employ and extend this analogy between coherent optical beams and coherent matter waves to include spin angular momentum (polarization), which enables us measure the matter wave Gouy phase using coreless vortex spin textures in spinor BECs. Because the Gouy phase is dependent on the orbital angular momentum of the wave, the vortex and core states acquire different Gouy phase shifts. Parameters that are sensitive to the relative phase such as two-dimensional maps of the Stokes parameters rotate during evolution due to this phase difference. Using atom-optic polarimetry we can access the evolution of the atomic Stokes parameters and observe this rotation.

  15. Anthracenyl polar embedded stationary phases with enhanced aromatic selectivity. Part II: A density functional theory study.

    PubMed

    Mignot, Mélanie; Schammé, Benjamin; Tognetti, Vincent; Joubert, Laurent; Cardinael, Pascal; Peulon-Agasse, Valérie

    2017-09-11

    New polar embedded aromatic stationary phases (mono- and trifunctional versions) that contain an amide-embedded group coupled with a tricyclic aromatic moiety were developed for chromatographic applications and described in the first paper of this series. These phases offered better separation performance for PAHs than for alkylbenzene homologues, and an enhanced ability to differentiate aromatic planarity to aromatic tridimensional conformation, especially for the trifunctional version and when using methanol instead of acetonitrile. In this second paper, a density functional theory study of the retention process is reported. In particular, it was shown that the selection of the suitable computational protocol allowed for describing rigorously the interactions that could take place, the solvent effects, and the structural changes for the monofunctional and the trifunctional versions. For the first time, the experimental data coupled with these DFT results provided a better understanding of the interaction mechanisms and highlighted the importance of the multimodal character of the designed stationary phases: alkyl spacers for interactions with hydrophobic solutes, amide embedded groups for dipole-dipole and hydrogen-bond interactions, and aromatic terminal groups for π-π interactions. Copyright © 2017 Elsevier B.V. All rights reserved.

  16. Ultrasound array transmitter architecture with high timing resolution using embedded phase-locked loops.

    PubMed

    Smith, Peter R; Cowell, David M J; Raiton, Benjamin; Ky, Chau Vo; Freear, Steven

    2012-01-01

    Coarse time quantization of delay profiles within ultrasound array systems can produce undesirable side lobes in the radiated beam profile. The severity of these side lobes is dependent upon the magnitude of phase quantization error--the deviation from ideal delay profiles to the achievable quantized case. This paper describes a method to improve interchannel delay accuracy without increasing system clock frequency by utilizing embedded phase-locked loop (PLL) components within commercial field-programmable gate arrays (FPGAs). Precise delays are achieved by shifting the relative phases of embedded PLL output clocks in 208-ps steps. The described architecture can achieve the necessary interelement timing resolution required for driving ultrasound arrays up to 50 MHz. The applicability of the proposed method at higher frequencies is demonstrated by extrapolating experimental results obtained using a 5-MHz array transducer. Results indicate an increase in transmit dynamic range (TDR) when using accurate delay profiles generated by the embedded-PLL method described, as opposed to using delay profiles quantized to the system clock.

  17. Preparation of a stationary phase with s-triazine ring embedded group for reversed phase high-performance LC.

    PubMed

    Li, Yingyu; Dai, Peichun; Ke, Yanxiong; Jin, Yu; Liang, Xinmiao

    2010-10-01

    This paper describes the synthesis and chromatographic evaluation of a new polar-embedded stationary phase, which utilized 2,4,6-trichloro-1,3,5-triazine as the spacer. The resulting materials were characterized by elemental analysis, IR, and solid-state (13)C NMR. Empirical test mixtures were utilized to evaluate the column, and showed that it had good performance for basic compounds and high selectivity for polyaromatic hydrocarbons. Moreover, the novel stationary phase has unique property, especially in the separation of "homologous alkaloids" from natural products.

  18. An embedded boundary method for soluble surfactants with interface tracking for two-phase flows

    NASA Astrophysics Data System (ADS)

    Khatri, Shilpa; Tornberg, Anna-Karin

    2014-01-01

    Surfactants, surface reacting agents, lower the surface tension of the interface between fluids in multiphase flow. This capability of surfactants makes them ideal for many applications, including wetting, foaming, and dispersing. Due to their molecular composition, surfactants are adsorbed from the bulk fluid to the interface between the fluids, leading to different concentrations on the interface and in the fluid. In a previous paper [21], we introduced a new second order method using uniform grids to simulate insoluble surfactants in multiphase flow. This method used Strang splitting allowing for a fully second order treatment in time. Here, we use the same numerical methods to explicitly represent the singular interface, treat the interfacial surfactant concentration, and couple with the Navier-Stokes equations. Now, we introduce a second order method for the surfactants in the bulk that continues to allow the use of regular grids for the full problem. Difficulties arise since the boundary condition for the bulk concentration, which handles the flux of surfactant between the interface and bulk fluid, is applied at the interface which cuts arbitrarily through the regular grid. We extend the embedded boundary method, introduced in [22], to handle this challenge. Through our results, we present the effect of the solubility of the surfactants. We show results of drop dynamics due to resulting Marangoni stresses and of drop deformations in shear flow in the presence of soluble surfactants. There is a large nondimensional parameter space over which we try to understand the drop dynamics.

  19. Tunable ferroelectric meta-material phase shifter embedded inside low temperature co-fired ceramics (LTCC)

    NASA Astrophysics Data System (ADS)

    Tork, Hossam S.

    This dissertation describes electrically tunable microwave devices utilizing low temperature co-fired ceramics (LTCC) and thick film via filled with the ferroelectric materials barium strontium titanate (BST) and barium zirconate titanate (BZT). Tunable ferroelectric capacitors, zero meta-material phase shifters, and tunable meta-material phase shifters are presented. Microwave phase shifters have many applications in microwave devices. They are essential components for active and passive phased array antennas and their most common use is in scanning phased array antennas. They are used in synthetic aperture radars (SAR), low earth orbit (LEO) communication satellites, collision warning radars, and intelligent vehicle highway systems (IVHS), in addition to various other applications. Tunable ferroelectric materials have been investigated, since they offer the possibility of lowering the total cost of phased arrays. Two of the most promising ferroelectric materials in microwave applications are BST and BZT. The proposed design and implementation in this research introduce new types of tunable meta-material phase shifters embedded inside LTCC, which use BST and BZT as capacitive tunable dielectric material controlled by changing the applied voltage. This phase shifter has the advantages of meta-material structures, which produce little phase error and compensation while having the simultaneous advantage of using LTCC technology for embedding passive components that improve signal integrity (several signal lines, power planes, and ground planes) by using different processes like via filling, screen printing, laminating and firing that can be produced in compact sizes at a low cost. The via filling technique was used to build tunable BST, BZT ferroelectric material capacitors to control phase shift. Finally, The use of the proposed ferroelectric meta-material phase shifter improves phase shifter performance by reducing insertion loss in both transmitting and receiving

  20. Singularity computations

    NASA Technical Reports Server (NTRS)

    Swedlow, J. L.

    1976-01-01

    An approach is described for singularity computations based on a numerical method for elastoplastic flow to delineate radial and angular distribution of field quantities and measure the intensity of the singularity. The method is applicable to problems in solid mechanics and lends itself to certain types of heat flow and fluid motion studies. Its use is not limited to linear, elastic, small strain, or two-dimensional situations.

  1. Observation of Phase-Filling Singularities in the Optical Dielectric Function of Highly Doped n-Type Ge.

    PubMed

    Xu, Chi; Fernando, Nalin S; Zollner, Stefan; Kouvetakis, John; Menéndez, José

    2017-06-30

    Phase-filling singularities in the optical response function of highly doped (>10^{19}  cm^{-3}) germanium are theoretically predicted and experimentally confirmed using spectroscopic ellipsometry. Contrary to direct-gap semiconductors, which display the well-known Burstein-Moss phenomenology upon doping, the critical point in the joint density of electronic states associated with the partially filled conduction band in n-Ge corresponds to the so-called E_{1} and E_{1}+Δ_{1} transitions, which are two-dimensional in character. As a result of this reduced dimensionality, there is no edge shift induced by Pauli blocking. Instead, one observes the "original" critical point (shifted only by band gap renormalization) and an additional feature associated with the level occupation discontinuity at the Fermi level. The experimental observation of this feature is made possible by the recent development of low-temperature, in situ doping techniques that allow the fabrication of highly doped films with exceptionally flat doping profiles.

  2. Metastable extensions of phase equilibrium lines and singular points of simple substance

    SciTech Connect

    Baidakov, V. G. Protsenko, S. P.

    2006-12-15

    The thermodynamic properties of crystal, liquid, and gas in the stable and metastable states have been determined by molecular dynamics simulation of a system of 2048 Lennard-Jones particles. The spinodals of a superheated crystal, a superheated liquid, and a supersaturated vapor have been approximated; the spinodal for a supercooled liquid turns out to be nonexistent. The liquid-vapor, liquid-crystal, and crystal-vapor equilibrium curves and their extensions beyond the triple point have been calculated. It has been shown that, as distinct from the metastable extension of the saturation curve, which terminates at the zero isotherm, the metastable melting and sublimation curves terminate at, respectively, the stretched liquid and superheated crystal spinodals. The properties of the critical end points of metastable equilibrium of extended phases are considered.

  3. Phase-space model of a collisionless stellar cylinder embedded in a rotating halo

    NASA Astrophysics Data System (ADS)

    Kondratyev, B. P.; Kireeva, E. N.

    The phase-space model of a stellar cylindrical bar embedded in a rotating triaxial halo is constructed. The equations of motion of an individual star in the bar are derived and solved. The model has three integrals of motion and the condition of the cylinder boundary conservation is derived. The model is found to represent a four-dimensional ellipsoid in six-dimensional phase space. The phase-space distribution function of stars is derived, which depends on isolating integrals of motion. The centroid velocity field describes longitudinal shear averaged flows in the cylinder. Two non-zero components of the velocity dispersion tensor depend quadratically on coordinates and vanish at the surface of the cylindrical bar.

  4. The Embedded Phase of Star Formation : Outflows, Envelopes, First Conditions of Disk Formation

    NASA Astrophysics Data System (ADS)

    Vorobyov, Eduard

    2017-06-01

    The embedded phase of star formation witnesses the birth of stars, the formation of circumstellar disks, and the launch of jets and outflows. It sets the stage for the disk and star evolution in the subsequent optically visible T Tauri phase, largely determining disk and stellar masses and paving the way for planet assembly. This phase is hard to observe and theory can provide valuable insights into the processes that take place in the depth of collapsing clouds. I will overview processes that are linked with the disk early evolution, such as gravitational instability and its implications, variable protostellar accretion with episodic bursts and its effect on the disk dynamical and chemical evolution, and initial stages of dust growth. The nature of very low luminosity objects (VELLOs) will also be discussed.

  5. Orientational phase transitions of a lattice of magnetic dots embedded in a London-type superconductor

    NASA Astrophysics Data System (ADS)

    Dzhezherya, Yuri I.; Novak, I. Yu; Kruchinin, Sergei P.

    2010-10-01

    In recent experiments, structured arrays of ferromagnetic nanoparticles in the bulk of a superconductor have been fabricated. We present the theory of orientational phase transitions in a planar regular lattice of nanoscale ferromagnetic particles embedded in a superconductor. In the London approximation, we show that the interactions between ferromagnetic particles can lead to either a parallel or antiparallel spin alignment depending on the ratio of the interparticle distance, the London penetration depth and the temperature. The extension of the results to systems of ferromagnetic nanoparticles with more complicated geometries is discussed.

  6. Imidazolium embedded C8 based stationary phase for simultaneous reversed-phase/hydrophilic interaction mixed-mode chromatography.

    PubMed

    Qiao, Xiaoqiang; Zhang, Lu; Zhang, Niu; Wang, Xin; Qin, Xinying; Yan, Hongyuan; Liu, Haiyan

    2015-06-26

    A new imidazolium embedded C8 based stationary phase (SIL-MPS-VOL) was facilely prepared by two steps and characterized by Fourier transform infrared spectrometry and thermogravimetric analysis. Due to the introduction of quaternary imidazolium group to the traditional C8 stationary phase, the developed SIL-MPS-VOL column demonstrated both reversed-phase liquid chromatography (RPLC) and hydrophilic interaction liquid chromatography (HILIC) retention mechanisms. A series of hydrophobic and hydrophilic test samples, including benzene homologues, anilines, positional isomers, nucleosides and nucleotides, were used to evaluate the developed SIL-MPS-VOL stationary phase. A rapid separation time, high separation efficiency and planar selectivity were achieved, compared with the commercially available C8 column. Moreover, the developed stationary phase was further used to detect and separate of melamine in powdered infant formula and high polar component of secondary metabolites of Trichoderma, and improved separation efficiency was achieved, indicating the potential merits of the developed SIL-MPS-VOL stationary phase for simultaneous separation of complex hydrophobic and hydrophilic samples with high selectivity.

  7. The state of globular clusters at birth: emergence from the gas-embedded phase

    NASA Astrophysics Data System (ADS)

    Leigh, Nathan; Giersz, Mirek; Webb, Jeremy J.; Hypki, Arkadiusz; De Marchi, Guido; Kroupa, Pavel; Sills, Alison

    2013-12-01

    In this paper, we discuss the origin of the observed correlation between the cluster concentration c and present-day mass function slope α reported by De Marchi, Paresce & Pulone. This relation can either be reproduced from universal initial conditions combined with some dynamical mechanism(s) that alter(s) the cluster structure and mass function over time, or it must arise early on in the cluster lifetime, such as during the gas-embedded phase of cluster formation. Using a combination of Monte Carlo and N-body models for globular cluster evolution performed with the MOCCA and NBODY6 codes, respectively, we explore a number of dynamical mechanisms that could affect the observed relation. For the range of initial conditions considered here, our results are consistent with a universal initial binary fraction ≈10 per cent (which does not, however, preclude 100 per cent) and a universal initial stellar mass function resembling the standard Kroupa distribution. Most of the dispersion observed in the c-α relation can be attributed to two-body relaxation and Galactic tides. However, dynamical processes alone could not have reproduced the dispersion in concentration, and we require at least some correlation between the initial concentration and the total cluster mass. We argue that the origin of this trend could be connected to the gas-embedded phase of cluster evolution.

  8. Engineering of chalcogenide materials for embedded applications of Phase Change Memory

    NASA Astrophysics Data System (ADS)

    Zuliani, Paola; Palumbo, Elisabetta; Borghi, Massimo; Dalla Libera, Giovanna; Annunziata, Roberto

    2015-09-01

    Phase Change Memory technology can be a real breakthrough for process cost saving and performances for embedded applications. The feasibility at 90 nm technology node has been solidly proven in an industrial environment and the added value of this solution demonstrated. Nevertheless, for specific applications some improvement in High Temperature Data Retention (HTDR) characteristics is needed. In this work we present the engineering of chalcogenide materials in order to increase the stability of RESET state as a function of temperature. This goal has been achieved by exploring Ge-rich compounds in the Ge-Sb-Te ternary diagram. In particular, an optimized GexSbyTez Phase Change material, able to guarantee code integrity of the memory content after soldering thermal profile and data retention in extended temperature range has been obtained. Extrapolation of data retention at 10 years for temperatures higher than 150 °C cell-level has been demonstrated, thus enabling automotive applications.

  9. Phase behavior of electrostatically complexed polyelectrolyte gels using an embedded fluctuation model.

    PubMed

    Audus, Debra J; Gopez, Jeffrey D; Krogstad, Daniel V; Lynd, Nathaniel A; Kramer, Edward J; Hawker, Craig J; Fredrickson, Glenn H

    2015-02-14

    Nanostructured, responsive hydrogels formed due to electrostatic interactions have promise for applications such as drug delivery and tissue mimics. These physically cross-linked hydrogels are composed of an aqueous solution of oppositely charged triblocks with charged end-blocks and neutral, hydrophilic mid-blocks. Due to their electrostatic interactions, the end-blocks microphase separate and form physical cross-links that are bridged by the mid-blocks. The structure of this system was determined using a new, efficient embedded fluctuation (EF) model in conjunction with self-consistent field theory. The calculations using the EF model were validated against unapproximated field-theoretic simulations with complex Langevin sampling and were found consistent with small angle X-ray scattering (SAXS) measurements on an experimental system. Using both the EF model and SAXS, phase diagrams were generated as a function of end-block fraction and polymer concentration. Several structures were observed including a body-centered cubic sphere phase, a hexagonally packed cylinder phase, and a lamellar phase. Finally, the EF model was used to explore how parameters that directly relate to polymer chemistry can be tuned to modify the resulting phase diagram, which is of practical interest for the development of new hydrogels.

  10. Phase segregation of polymerizable lipids to construct filters for separating lipid-membrane-embedded species

    PubMed Central

    Hu, Shu-Kai; Chen, Ya-Ming; Chao, Ling

    2014-01-01

    Supported lipid bilayer (SLB) platforms have been developed to transport and separate membrane-embedded species in the species' native bilayer environment. In this study, we used the phase segregation phenomenon of lipid mixtures containing a polymerizable diacetylene phospholipid, 1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine (DiynePC), and a nonpolymerizable phospholipid, 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), to create filter barrier structures in SLBs. Upon exposing the phase segregated samples to UV light, the DiynePC-rich domains could become crosslinked and remain fixed on the surface of the support, while the DOPC-rich regions, where no crosslinking could happen, could be removed later by detergent washing, and thus became the void regions in the filter. During the filter fabrication process, we used the laminar flow configuration in a microfluidic channel to control the spatial locations of the feed region and filter region in the SLB. The flow in a microfluidic channel was also used to apply a strong hydrodynamic shear stress to the SLB to transport the membrane-embedded species from the feed region to the filter region. We varied the DiynePC/DOPC molar ratio from 60/40 to 80/20 to adjust the cutoff size of the filter barriers and used two model membrane-embedded species of different sizes to examine the filtering capability. One of the model species, Texas Red 1,2-dihexa-decanoyl-sn-glycero-3-phosphoethanolamine triethylammonium salt (Texas Red DHPE), had a single-lipid size, and the other species, cholera toxin subunit B-GM1 complex, had a multilipid size. When the DiynePC/DOPC molar ratio was 60/40, both species had high penetration ratios in the filter region. However, when the ratio was increased to 70/30, only the Texas Red DHPE, which was the smaller of the two model species, could penetrate the filter to a considerable extent. When the ratio was increased to 80/20, neither of the model species could penetrate the filter

  11. A single-phase embedded Z-source DC-AC inverter.

    PubMed

    Kim, Se-Jin; Lim, Young-Cheol

    2014-01-01

    In the conventional DC-AC inverter consisting of two DC-DC converters with unipolar output capacitors, the output capacitor voltages of the DC-DC converters must be higher than the DC input voltage. To overcome this weakness, this paper proposes a single-phase DC-AC inverter consisting of two embedded Z-source converters with bipolar output capacitors. The proposed inverter is composed of two embedded Z-source converters with a common DC source and output AC load. Though the output capacitor voltages of the converters are relatively low compared to those of a conventional inverter, an equivalent level of AC output voltages can be obtained. Moreover, by controlling the output capacitor voltages asymmetrically, the AC output voltage of the proposed inverter can be higher than the DC input voltage. To verify the validity of the proposed inverter, experiments were performed with a DC source voltage of 38 V. By controlling the output capacitor voltages of the converters symmetrically or asymmetrically, the proposed inverter can produce sinusoidal AC output voltages. The experiments show that efficiencies of up to 95% and 97% can be achieved with the proposed inverter using symmetric and asymmetric control, respectively.

  12. A Single-Phase Embedded Z-Source DC-AC Inverter

    PubMed Central

    Kim, Se-Jin; Lim, Young-Cheol

    2014-01-01

    In the conventional DC-AC inverter consisting of two DC-DC converters with unipolar output capacitors, the output capacitor voltages of the DC-DC converters must be higher than the DC input voltage. To overcome this weakness, this paper proposes a single-phase DC-AC inverter consisting of two embedded Z-source converters with bipolar output capacitors. The proposed inverter is composed of two embedded Z-source converters with a common DC source and output AC load. Though the output capacitor voltages of the converters are relatively low compared to those of a conventional inverter, an equivalent level of AC output voltages can be obtained. Moreover, by controlling the output capacitor voltages asymmetrically, the AC output voltage of the proposed inverter can be higher than the DC input voltage. To verify the validity of the proposed inverter, experiments were performed with a DC source voltage of 38 V. By controlling the output capacitor voltages of the converters symmetrically or asymmetrically, the proposed inverter can produce sinusoidal AC output voltages. The experiments show that efficiencies of up to 95% and 97% can be achieved with the proposed inverter using symmetric and asymmetric control, respectively. PMID:25133241

  13. Modeling thermal insulation of firefighting protective clothing embedded with phase change material

    NASA Astrophysics Data System (ADS)

    Hu, Yin; Huang, Dongmei; Qi, Zhengkun; He, Song; Yang, Hui; Zhang, Heping

    2013-04-01

    Experiments and research on heat transport through firefighting protective clothing when exposed to high temperature or intensive radiation are significant. Phase change material (PCM) takes energy when changes from solid to liquid thus reducing heat transmission. A numerical simulation of heat protection of the firefighting protective clothing embedded with PCM was studied. We focused on the temperature variation by comparing different thicknesses and position conditions of PCM combined in the clothing, as well as the melting state of PCM and human irreversible burns through a simplified one-dimensional model. The results showed it was superior to place PCM between water and proof layer and inner layer, in addition, greater thickness increased protection time while might adding extra burden to the firefighter.

  14. FDTD analysis of silver-nanoparticle-embedded phase change recording pits

    NASA Astrophysics Data System (ADS)

    Lin, Jincheng; Huang, Huan; Wang, Yang; Wu, Yiqun

    Super-resolution near-field structure (super-RENS) is a functional structure which can overcome the optical diffraction limit and play an important role in nano scale optical data storage. The resolution enhancement of the scatter-type super- RENS optical disk is related to the localized surface plasmon of silver particles dissociated from the AgOx layer and its near-field interaction with the recording pits in the phase change layer. Recently, a new method for optically synthesizing silver nanoparticles in a phase change matrix has been proposed by our group [Mater. Chem. Phys. 135, 467-473(2012)], which provides a potential approach to forming a more simple plasmonic recording structure than the traditional AgOx-type structure. In this paper, field distribution of silver-nanoparticles-embedded Ge2Sb2Te5 phase change recording pits is numerically analyzed by the finite-difference time-domain (FDTD) method. The optical contrast enhancement capability is confirmed for the optimized recording structures when the pit size is smaller than the optical diffraction limit.

  15. Graphene-Embedded Hydrogel Nanofibers for Detection and Removal of Aqueous-Phase Dyes.

    PubMed

    Im, Kyungun; Nguyen, Duong Nguyen; Kim, Saerona; Kong, Hye Jeong; Kim, Yukyung; Park, Chul Soon; Kwon, Oh Seok; Yoon, Hyeonseok

    2017-03-16

    A facile route to graphene/polymer hydrogel nanofibers was developed. An aqueous dispersion of graphene (containing >40% bilayer graphene flakes) stabilized by a functionalized water-soluble polymer with phenyl side chains was successfully electrospun to yield nanofibers. Subsequent vapor-phase cross-linking of the nanofibers produced graphene-embedded hydrogel nanofibers (GHNFs). Interestingly, the GHNFs showed chemical sensitivity to the cationic dyes methylene blue (MB) and crystal violet (CV) in the aqueous phase. The adsorption capacities were as high as 0.43 and 0.33 mmol g(-1) s(-1) for MB and CV, respectively, even in a 1.5 mL s(-1) flow system. A density functional theory calculation revealed that aqueous-phase MB and CV dyes were oriented parallel to the graphene surface and that the graphene/dye ensembles were stabilized by secondary physical bonding mechanisms such as the π-π stacking interaction in an aqueous medium. The GHNFs exhibited electrochemical properties arising mainly from the electric double-layer capacitance, which were applied in a demonstration of GHNF-based membrane electrodes (5 cm in diameter) for detecting the dyes in the flow system. It is believed that the GHNF membrane can be a successful model candidate for commercialization of graphene due to its easy-to-fabricate process and remarkable properties.

  16. Reliability Analysis and Optimal Release Problem Considering Maintenance Time of Software Components for an Embedded OSS Porting Phase

    NASA Astrophysics Data System (ADS)

    Tamura, Yoshinobu; Yamada, Shigeru

    OSS (open source software) systems which serve as key components of critical infrastructures in our social life are still ever-expanding now. Especially, embedded OSS systems have been gaining a lot of attention in the embedded system area, i.e., Android, BusyBox, TRON, etc. However, the poor handling of quality problem and customer support prohibit the progress of embedded OSS. Also, it is difficult for developers to assess the reliability and portability of embedded OSS on a single-board computer. In this paper, we propose a method of software reliability assessment based on flexible hazard rates for the embedded OSS. Also, we analyze actual data of software failure-occurrence time-intervals to show numerical examples of software reliability assessment for the embedded OSS. Moreover, we compare the proposed hazard rate model for the embedded OSS with the typical conventional hazard rate models by using the comparison criteria of goodness-of-fit. Furthermore, we discuss the optimal software release problem for the porting-phase based on the total expected software maintenance cost.

  17. Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)

    SciTech Connect

    Zhao, C.Y.; Lu, W.; Tian, Y.

    2010-08-15

    In this paper the experimental investigation on the solid/liquid phase change (melting and solidification) processes have been carried out. Paraffin wax RT58 is used as phase change material (PCM), in which metal foams are embedded to enhance the heat transfer. During the melting process, the test samples are electrically heated on the bottom surface with a constant heat flux. The PCM with metal foams has been heated from the solid state to the pure liquid phase. The temperature differences between the heated wall and PCM have been analysed to examine the effects of heat flux and metal foam structure (pore size and relative density). Compared to the results of the pure PCM sample, the effect of metal foam on solid/liquid phase change heat transfer is very significant, particularly at the solid zone of PCMs. When the PCM starts melting, natural convection can improve the heat transfer performance, thereby reducing the temperature difference between the wall and PCM. The addition of metal foam can increase the overall heat transfer rate by 3-10 times (depending on the metal foam structures and materials) during the melting process (two-phase zone) and the pure liquid zone. The tests for investigating the solidification process under different cooling conditions (e.g. natural convection and forced convection) have been carried out. The results show that the use of metal foams can make the sample solidified much faster than pure PCM samples, evidenced by the solidification time being reduced by more than half. In addition, a two-dimensional numerical analysis has been carried out for heat transfer enhancement in PCMs by using metal foams, and the prediction results agree reasonably well with the experimental data. (author)

  18. Liquid-phase plasma synthesis of silicon quantum dots embedded in carbon matrix for lithium battery anodes

    SciTech Connect

    Wei, Ying; Yu, Hang; Li, Haitao; Ming, Hai; Pan, Keming; Huang, Hui; Liu, Yang; Kang, Zhenhui

    2013-10-15

    Graphical abstract: - Highlights: • Silicon quantum dots embedded in carbon matrix (SiQDs/C) were fabricated. • SiQDs/C exhibits excellent battery performance as anode materials with high specific capacity. • The good performance was attributed to the marriage of small sized SiQDs and carbon. - Abstract: Silicon quantum dots embedded in carbon matrix (SiQDs/C) nanocomposites were prepared by a novel liquid-phase plasma assisted synthetic process. The SiQDs/C nanocomposites were demonstrated to show high specific capacity, good cycling life and high coulmbic efficiency as anode materials for lithium-ion battery.

  19. Neural networks with non-uniform embedding and explicit validation phase to assess Granger causality.

    PubMed

    Montalto, Alessandro; Stramaglia, Sebastiano; Faes, Luca; Tessitore, Giovanni; Prevete, Roberto; Marinazzo, Daniele

    2015-11-01

    A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of assumptions in modeling the relevant features of the data. We tried to overcome those pitfalls using a neural network approach in which a model is built without any a priori assumptions. In this sense this method can be seen as a bridge between model-free and model-based approaches. The experiments performed will show that the method presented in this work can detect the correct dynamical information flows occurring in a system of time series. Additionally we adopt a non-uniform embedding framework according to which only the past states that actually help the prediction are entered into the model, improving the prediction and avoiding the risk of overfitting. This method also leads to a further improvement with respect to traditional Granger causality approaches when redundant variables (i.e. variables sharing the same information about the future of the system) are involved. Neural networks are also able to recognize dynamics in data sets completely different from the ones used during the training phase.

  20. Linear dichroism spectroscopy of gas phase biological molecules embedded in superfluid helium droplets

    NASA Astrophysics Data System (ADS)

    Kong, Wei; Pei, Linsen; Zhang, Jie

    This article presents the current status of gas phase linear dichroism (LD) spectroscopy, including the theoretical background, the experimental technique, and a few examples in the UV/VIS and IR. Orientation and alignment of gas phase samples are achieved using a DC electric field. To reach the necessary degree of alignment, biological molecules vaporized from a heated oven need to be embedded in superfluid helium droplets. Excitation under different polarization directions of the light source relative to the alignment field can then be used to derive the direction of the transition dipole, or the size of the permanent dipole, or both. For biological molecules that have no resonance lines or too many resonance lines, LD offers an additional parameter for spectroscopic assignment and tautomeric and conformational identification. The direction of the vibrational transition dipole is proven more reliable for vibrational and tautomeric assignment than the energy or frequency information, which is often problematic because of its sensitivity to basis sets and calculation methods. Several examples of vibrational LD of nucleic acid bases will be discussed. On the other hand, if a chromophore with a known electronic transition dipole is attached to a biological molecule, as demonstrated in the case of tryptamine, the permanent dipole determined from LD is then representative of the molecular conformation. This method of conformational determination does not rely on detailed spectroscopic assignment, thus it is applicable to molecules that do not have resolvable vibronic bands. However, its application is currently limited to the availability of an effective chromophore, and the search for such a chromophore is an on-going effort.

  1. An all digital phase locked loop for synchronization of a sinusoidal signal embedded in white Gaussian noise

    NASA Technical Reports Server (NTRS)

    Reddy, C. P.; Gupta, S. C.

    1973-01-01

    An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.

  2. Singularity classification as a design tool for multiblock grids

    NASA Technical Reports Server (NTRS)

    Jones, Alan K.

    1992-01-01

    A major stumbling block in interactive design of 3-D multiblock grids is the difficulty of visualizing the design as a whole. One way to make this visualization task easier is to focus, at least in early design stages, on an aspect of the grid which is inherently easy to present graphically, and to conceptualize mentally, namely the nature and location of singularities in the grid. The topological behavior of a multiblock grid design is determined by what happens at its edges and vertices. Only a few of these are in any way exceptional. The exceptional behaviors lie along a singularity graph, which is a 1-D construct embedded in 3-D space. The varieties of singular behavior are limited enough to make useful symbology on a graphics device possible. Furthermore, some forms of block design manipulation that appear appropriate to the early conceptual-modeling phase can be accomplished on this level of abstraction. An overview of a proposed singularity classification scheme and selected examples of corresponding manipulation techniques is presented.

  3. Understanding Singular Vectors

    ERIC Educational Resources Information Center

    James, David; Botteron, Cynthia

    2013-01-01

    matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so…

  4. Understanding Singular Vectors

    ERIC Educational Resources Information Center

    James, David; Botteron, Cynthia

    2013-01-01

    matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so…

  5. Two dimensional x-ray phase imaging using single grating interferometer with embedded x-ray targets.

    PubMed

    Morimoto, Naoki; Fujino, Sho; Yamazaki, Amane; Ito, Yasuhiro; Hosoi, Takuji; Watanabe, Heiji; Shimura, Takayoshi

    2015-06-29

    Using multidot metal targets embedded in a diamond substrate, we created a single-grating Talbot-Lau interferometer and used it to capture two dimensional (2D) x-ray phase images. The ensemble of these targets constitutes a tiny virtual array of x-ray source and enables x-ray phase-contrast imaging with no source or absorption grating within a 1 m source-detector distance for 8 keV x-rays. We directly resolved a dot-pattern self-image of the phase grating with 6 µm pitch by using an x-ray image detector with 24 µm pixels and obtained 2D differential-phase and dark-field images from a single-exposure. Using the 2D differential-phase images, we also obtained a phase image with no streak artifacts.

  6. Preparation and chromatographic evaluation of new branch-type diamide-embedded octadecyl stationary phase with enhanced shape selectivity.

    PubMed

    Zhang, Mingliang; Chen, Jia; Mallik, Abul K; Qiu, Hongdeng; Jiang, Shengxiang; Ihara, Hirotaka

    2014-06-23

    A novel branch-type diamide-embedded octadecyl stationary phase was prepared by facile amidation. The preparation of this new phase involves the synthesis of new bifunctional silane ligand and surface modification of spherical silica via anchoring of silane coupling agent. The obtained diamide-embedded octadecyl stationary phase demonstrated excellent hydrophobic selectivity, as well as enhanced shape and planarity selectivity in comparison to commercial polymeric and monomeric C18 phases, respectively, as revealed by the systematic investigation into its liquid chromatographic retention of isomeric polycyclic aromatic hydrocarbons. The applicability of this new stationary phase was further testified by the effective separation of isomeric compounds belong to different chemical classes, including chain isomers of alkylbenzenes, and positional isomers of substituted aromatics. An in-depth analysis of the separation mechanisms other than molecular shape recognition involved in the new stationary phase was performed using a linear solvation energy relationships model and compared with its monoamide and pure C18 counterparts correspondingly. The performance of the new stationary phase in quantitative analysis of phenols from real-world samples was also evaluated.

  7. Singular Continuous Spectrum for Singular Potentials

    NASA Astrophysics Data System (ADS)

    Jitomirskaya, Svetlana; Yang, Fan

    2017-05-01

    We prove that Schrödinger operators with meromorphic potentials {(H_{α,θ}u)_n=u_{n+1}+u_{n-1}+ g(θ+nα)/f(θ+nα) u_n} have purely singular continuous spectrum on the set {{E: L(E) < δ{(α, θ)}}}, where {δ} is an explicit function and L is the Lyapunov exponent. This extends results of Jitomirskaya and Liu (Arithmetic spectral transitions for the Maryland model. CPAM, to appear) for the Maryland model and of Avila,You and Zhou (Sharp Phase transitions for the almost Mathieu operator. Preprint, 2015) for the almost Mathieu operator to the general family of meromorphic potentials.

  8. Singularity in structural optimization

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Guptill, J. D.; Berke, L.

    1993-01-01

    The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.

  9. Solid-phase extraction of flavonoids in honey samples using carbamate-embedded triacontyl-modified silica sorbent.

    PubMed

    Liu, Houmei; Zhang, Mingliang; Guo, Yong; Qiu, Hongdeng

    2016-08-01

    In this study, carbamate-embedded triacontyl-modified silica (Sil-CBM-C30) is successfully prepared and used as an efficient sorbent for solid-phase extraction. The extraction performance of the resultant sorbent is evaluated with five flavonoids including myricetin, quercetin, luteolin, kaempferol and isorhamnetin. Main parameters, which affect extraction efficiencies, are carefully investigated and optimized. Comparative experiments between Sil-CBM-C30 and commercial C18 sorbents indicate that the extraction efficiencies of the former one surpass the latter one. The modification of carbamate-embedded triacontyl group on surface of silica causes analytes extracted by hydrophobic, hydrogen bonding and π-π interactions. Under optimal conditions, good linearities and satisfied LODs and LOQs are achieved. The SPE-HPLC-DAD method is successfully developed and applied for the honey sample analysis.

  10. Resolution of quantum singularities

    NASA Astrophysics Data System (ADS)

    Konkowski, Deborah; Helliwell, Thomas

    2017-01-01

    A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

  11. A chromatographic estimate of the degree of surface heterogeneity of RPLC packing materials. III. Endcapped amido-embedded reversed phase

    SciTech Connect

    Gritti, Fabrice; Guiochon, Georges A

    2006-01-01

    The difference in adsorption behavior between a conventional monomeric endcapped C{sub 18} stationary phase (3.43 {micro}mol/m{sup 2}) and an endcapped polymeric RP-Amide phase (3.31 {micro}mol/m{sup 2}) was investigated. The adsorption isotherms of four compounds (phenol, caffeine, sodium 2-naphthalene sulfonate, and propranololium chloride) were measured by frontal analysis (FA) and the degree of heterogeneity of each phase for each solute was characterized by their adsorption energy distributions (AED), derived using the Expectation-Maximization method. The results show that only certain analytes (phenol and 2-naphthalene sulfonate) are sensitive to the presence of the polar embedded amide groups within the RP phase. Their binding constants on the amide-bonded phase are significantly higher than on conventional RPLC phases. Furthermore, an additional type of adsorption sites was observed for these two compounds. However, these sites having a low density, their presence does not affect much the retention factors of the two analytes. On the other hand, the adsorption behavior of the other two analytes (caffeine and propranololium chloride) is almost unaffected by the presence of the amide group in the bonded layer. Strong selective interactions may explain these observations. For example, hydrogen-bond interactions between an analyte (e.g., phenol or naphthalene sulfonate) and the carbonyl group (acceptor) or the nitrogen (donor) of the amido-embedded group may take place. No such interactions may take place with either caffeine or the cation propranololium chloride. This study confirms the hypothesis that analytes have ready access to locations deep inside the bonded layer, where the amide groups are present.

  12. Defect reduction of SiNx embedded m-plane GaN grown by hydride vapor phase epitaxy

    NASA Astrophysics Data System (ADS)

    Woo, Seohwi; Kim, Minho; So, Byeongchan; Yoo, Geunho; Jang, Jongjin; Lee, Kyuseung; Nam, Okhyun

    2014-12-01

    Nonpolar (1 0 -1 0) m-plane GaN has been grown on m-plane sapphire substrates by hydride vapor phase epitaxy (HVPE). We studied the defect reduction of m-GaN with embedded SiNx interlayers deposited by ex-situ metal organic chemical vapor deposition (MOCVD). The full-width at half-maximum values of the X-ray rocking curves for m-GaN with embedded SiNx along [1 1 -2 0]GaN and [0 0 0 1]GaN were reduced to 528 and 1427 arcs, respectively, as compared with the respective values of 947 and 3170 arcs, of m-GaN without SiNx. Cross-section transmission electron microscopy revealed that the basal stacking fault density was decreased by approximately one order to 5×104 cm-1 due to the defect blocking of the embedded SiNx. As a result, the near band edge emission intensities of the room-temperature and low-temperature photoluminescence showed approximately two-fold and four-fold improvement, respectively.

  13. Column selectivity in reversed-phase liquid chromatography. VI. Columns with embedded or end-capping polar groups.

    PubMed

    Wilson, N S; Gilroy, J; Dolan, J W; Snyder, L R

    2004-02-13

    A previous model of column selectivity for reversed-phase liquid chromatography (RP-LC) has been applied to an additional 21 columns with embedded or end-capping polar groups (EPGs). Embedded-polar-group columns exhibit a significantly different selectivity vs. non-EPG, type-B columns, generally showing preferential retention of hydrogen-bond donors, as well as decreased retention for hydrogen-bond acceptors or ionized bases. EPG-columns are also generally less hydrophobic (more polar) than are non-EPG-columns. Interestingly, columns with polar end-capping tend to more closely resemble non-EPG columns, suggesting that the polar group has less effect on column selectivity when used to end-cap the column versus the case of an embedded polar group. Column selectivity data reported here for EPG-columns can be combined with previously reported values for non-EPG columns to provide a database of 154 different columns. This enables a comparison of any two of these columns in terms of selectivity. However, comparisons that involve EPG columns are more approximate.

  14. The Hamiltonian property of the flow of singular trajectories

    SciTech Connect

    Lokutsievskiy, L V

    2014-03-31

    Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles.

  15. Cosmological applications of singular hypersurfaces in general relativity

    NASA Astrophysics Data System (ADS)

    Laguna-Castillo, Pablo

    Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

  16. Quantum phase transition in a coupled two-level system embedded in anisotropic three-dimensional photonic crystals

    NASA Astrophysics Data System (ADS)

    Shen, H. Z.; Shao, X. Q.; Wang, G. C.; Zhao, X. L.; Yi, X. X.

    2016-01-01

    The quantum phase transition (QPT) describes a sudden qualitative change of the macroscopic properties mapped from the eigenspectrum of a quantum many-body system. It has been studied intensively in quantum systems with the spin-boson model, but it has barely been explored for systems in coupled spin-boson models. In this paper, we study the QPT with coupled spin-boson models consisting of coupled two-level atoms embedded in three-dimensional anisotropic photonic crystals. The dynamics of the system is derived exactly by means of the Laplace transform method, which has been proven to be equivalent to the dissipationless non-Markovian dynamics. Drawing on methods for analyzing the ground state, we obtain the phase diagrams through two exact critical equations and two QPTs are found: one QPT is that from the phase without one bound state to the phase with one bound state and another is that from one phase with the bound state having one eigenvalue to another phase where the bound state has two eigenvalues. Our analytical results also suggest a way of control to overcome the effect of decoherence by engineering the spectrum of the reservoirs to approach the non-Markovian regime and to form the bound state of the whole system for quantum devices and quantum statistics.

  17. Absolute phase unwrapping for dual-camera system without embedding statistical features

    NASA Astrophysics Data System (ADS)

    Jiang, Chufan; Zhang, Song

    2017-05-01

    This paper proposes an absolute phase unwrapping method for 3D measurement that uses two cameras and one projector. On the left camera image, each pixel has one wrapped phase value which corresponds to multiple projector candidates with different absolute phase values. We use geometric relationship of the system to map projector candidates into right camera candidates. By applying a series of candidate rejection criteria, a unique correspondence pair between two camera images can be determined. Then the absolute phase is obtained by tracing the correspondence point back to projector space. Experimental results demonstrate that the proposed absolute phase unwrapping algorithm can successfully work on both complex geometry and multiple isolated objects measurement.

  18. An Implementation of real-time phased array radar fundamental functions on DSP-focused, high performance embedded computing platform

    NASA Astrophysics Data System (ADS)

    Yu, Xining; Zhang, Yan; Patel, Ankit; Zahrai, Allen; Weber, Mark

    2016-05-01

    This paper investigates the feasibility of real-time, multiple channel processing of a digital phased array system backend design, with focus on high-performance embedded computing (HPEC) platforms constructed based on general purpose digital signal processor (DSP). Serial RapidIO (SRIO) is used as inter-chip connection backend protocol to support the inter-core communications and parallelisms. Performance benchmark was obtained based on a SRIO system chassis and emulated configuration similar to a field scale demonstrator of Multi-functional Phased Array Radar (MPAR). An interesting aspect of this work is comparison between "raw and low-level" DSP processing and emerging tools that systematically take advantages of the parallelism and multi-core capability, such as OpenCL and OpenMP. Comparisons with other backend HPEC solutions, such as FPGA and GPU, are also provided through analysis and experiments.

  19. Multiscale mimetic method for two-phase flow in fractured media using embedded discrete fracture model

    NASA Astrophysics Data System (ADS)

    Zhang, Qingfu; Huang, Zhaoqin; Yao, Jun; Wang, Yueying; Li, Yang

    2017-09-01

    A multiscale mimetic method is developed for the simulation of multiphase flow in fractured porous media in the context of an embedded discrete fracture model (EDFM). The EDFM constructs independent grids for matrix and fracture system. Therefore, it is an efficient and practical flow model as it avoids the complicated unstructured grid subdivision and computing process. In order to extend the EDFM to field-scale applications, we integrate EDFM into a multiscale mimetic method. In this work, we use the multiscale basis functions to capture the detailed interactions between the fractures and the background. The multiscale basis functions are calculated numerically by solving EDFM on the local fine-grid with mimetic finite difference (MFD) method. The MFD method is conservative and robust, which makes it possible to deal with highly complex grid systems. Through combination of multiscale mimetic method and EDFM, this formulation can generate accurate velocity field and pressure field on the fine-scale grid more efficiently than the traditional methods. Numerical results are presented for verification of this multiscale mimetic approach for embedded discrete fracture media, and demonstrate its computational efficiency. The results show that this method is an accurate and efficient method for flow simulation in real-field fractured heterogeneous reservoirs.

  20. The relationship among complex fractionated electrograms, wavebreak, phase singularity, and local dominant frequency in fibrillation wave-dynamics: a modeling comparison study.

    PubMed

    Yun, Yonghyeon; Hwang, Minki; Park, Jae Hyung; Shin, Hangsik; Shim, Eun Bo; Pak, Hui-Nam

    2014-03-01

    Although complex fractionated electrogram (CFE) is known to be a target for catheter ablation of fibrillation, its physiological meaning in fibrillation wave-dynamics remains to be clarified. We evaluated the spatiotemporal relationships among the parameters of fibrillation wave-dynamics by simulation modeling. We generated maps of CFE-cycle length (CFE-CL), local dominant frequency (LDF), wave break (WB), and phase singularity (PS) of fibrillation in 2-dimensional homogeneous bidomain cardiac modeling (1,000 × 1,000 cells ten Tusscher model). We compared spatiotemporal correlations by dichotomizing each maps into 10 × 10 lattice zones. In spatial distribution, WB and PS showed excellent correlation (R = 0.963, P < 0.001). CFE-CL had weak correlations with WB (R = 0.288, P < 0.001), PS (R = 0.313, P < 0.001), and LDF (R = -0.411, P < 0.001). However, LDF did not show correlation with PS or WB. PSs were mostly distributed at the periphery of low CFE-CL area. Virtual ablation (5% of critical mass) of CFE-CL < 100 ms terminated fibrillation at 14.3 sec, and high LDF ablation (5% of critical mass) changed fibrillation to organized tachycardia, respectively. In homogeneous 2D fibrillation modeling, CFE-CL was weakly correlated with WB, PS, and LDF, spatiotemporally. PSs are mostly positioned at the periphery of low CFE-CL areas, and virtual ablation targeting low CFE-CL regions terminated fibrillation successfully.

  1. Observation of a new superfluid phase for 3He embedded in nematically ordered aerogel

    NASA Astrophysics Data System (ADS)

    Zhelev, N.; Reichl, M.; Abhilash, T. S.; Smith, E. N.; Nguyen, K. X.; Mueller, E. J.; Parpia, J. M.

    2016-09-01

    In bulk superfluid 3He at zero magnetic field, two phases emerge with the B-phase stable everywhere except at high pressures and temperatures, where the A-phase is favoured. Aerogels with nanostructure smaller than the superfluid coherence length are the only means to introduce disorder into the superfluid. Here we use a torsion pendulum to study 3He confined in an extremely anisotropic, nematically ordered aerogel consisting of ~10 nm-thick alumina strands, spaced by ~100 nm, and aligned parallel to the pendulum axis. Kinks in the development of the superfluid fraction (at various pressures) as the temperature is varied correspond to phase transitions. Two such transitions are seen in the superfluid state, and we identify the superfluid phase closest to Tc at low pressure as the polar state, a phase that is not seen in bulk 3He.

  2. Observation of a new superfluid phase for 3He embedded in nematically ordered aerogel

    PubMed Central

    Zhelev, N.; Reichl, M.; Abhilash, T. S.; Smith, E. N.; Nguyen, K. X.; Mueller, E. J.; Parpia, J. M.

    2016-01-01

    In bulk superfluid 3He at zero magnetic field, two phases emerge with the B-phase stable everywhere except at high pressures and temperatures, where the A-phase is favoured. Aerogels with nanostructure smaller than the superfluid coherence length are the only means to introduce disorder into the superfluid. Here we use a torsion pendulum to study 3He confined in an extremely anisotropic, nematically ordered aerogel consisting of ∼10 nm-thick alumina strands, spaced by ∼100 nm, and aligned parallel to the pendulum axis. Kinks in the development of the superfluid fraction (at various pressures) as the temperature is varied correspond to phase transitions. Two such transitions are seen in the superfluid state, and we identify the superfluid phase closest to Tc at low pressure as the polar state, a phase that is not seen in bulk 3He. PMID:27669660

  3. Dimensional mutation and spacelike singularities

    SciTech Connect

    Silverstein, Eva

    2006-04-15

    I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent result that at finite volume, the effective dimensionality is increased by an amount of order 2h/V for a surface of genus h and volume V in string units. This arises in part from an exponentially growing density of states of winding modes supported by the fundamental group, and passes an interesting test of modular invariance. Further evidence for a plethora of examples with the spacelike singularity replaced by a higher dimensional phase arises from the fact that the sigma model on a Riemann surface can be naturally completed by many gauged linear sigma models, whose RG flows approximate time evolution in the full string backgrounds arising from this in the limit of large dimensionality. In recent examples of spacelike singularity resolution by tachyon condensation, the singularity is ultimately replaced by a phase with all modes becoming heavy and decoupling. In the present case, the opposite behavior ensues: more light degrees of freedom arise in the small radius regime. We comment on the emerging zoology of cosmological singularities that results.

  4. Embedding Game-Based Problem-Solving Phase into Problem-Posing System for Mathematics Learning

    ERIC Educational Resources Information Center

    Chang, Kuo-En; Wu, Lin-Jung; Weng, Sheng-En; Sung, Yao-Ting

    2012-01-01

    A problem-posing system is developed with four phases including posing problem, planning, solving problem, and looking back, in which the "solving problem" phase is implemented by game-scenarios. The system supports elementary students in the process of problem-posing, allowing them to fully engage in mathematical activities. In total, 92 fifth…

  5. Embedding Game-Based Problem-Solving Phase into Problem-Posing System for Mathematics Learning

    ERIC Educational Resources Information Center

    Chang, Kuo-En; Wu, Lin-Jung; Weng, Sheng-En; Sung, Yao-Ting

    2012-01-01

    A problem-posing system is developed with four phases including posing problem, planning, solving problem, and looking back, in which the "solving problem" phase is implemented by game-scenarios. The system supports elementary students in the process of problem-posing, allowing them to fully engage in mathematical activities. In total, 92 fifth…

  6. Development of graphene nanoplatelet embedded polymer microcantilever for vapour phase explosive detection applications

    SciTech Connect

    Ray, Prasenjit; Pandey, Swapnil; Ramgopal Rao, V.

    2014-09-28

    In this work, a graphene based strain sensor has been reported for explosive vapour detection applications by exploiting the piezoresistive property of graphene. Instead of silicon based cantilevers, a low cost polymeric micro-cantilever platform has been used to fabricate this strain sensor by embedding the graphene nanoplatelet layer inside the beam. The fabricated devices were characterized for their mechanical and electromechanical behaviour. This device shows a very high gauge factor which is around ~144. Also the resonant frequency of these cantilevers is high enough such that the measurements are not affected by environmental noise. These devices have been used in this work for reliable detection of explosive vapours such as 2,4,6-Trinitrotoluene down to parts-per-billion concentrations in ambient conditions.

  7. Embedded Electro-Optic Sensor Network for the On-Site Calibration and Real-Time Performance Monitoring of Large-Scale Phased Arrays

    DTIC Science & Technology

    2005-07-09

    This final report summarizes the progress during the Phase I SBIR project entitled "Embedded Electro - Optic Sensor Network for the On-Site Calibration...sensor network based on an electro - optic field-detection technique (the Electro - optic Sensor Network, or ESN) for the performance evaluation of phased

  8. c2d Spitzer IRS spectra of embedded low-mass young stars: gas-phase emission lines

    NASA Astrophysics Data System (ADS)

    Lahuis, F.; van Dishoeck, E. F.; Jørgensen, J. K.; Blake, G. A.; Evans, N. J.

    2010-09-01

    Context. A survey of mid-infrared gas-phase emission lines of H2, H2O and various atoms toward a sample of 43 embedded low-mass young stars in nearby star-forming regions is presented. The sources are selected from the Spitzer “Cores to Disks” (c2d) legacy program. Aims: The environment of embedded protostars is complex both in its physical structure (envelopes, outflows, jets, protostellar disks) and the physical processes (accretion, irradiation by UV and/or X-rays, excitation through slow and fast shocks) which take place. The mid-IR spectral range hosts a suite of diagnostic lines which can distinguish them. A key point is to spatially resolve the emission in the Spitzer-IRS spectra to separate extended PDR and shock emission from compact source emission associated with the circumstellar disk and jets. Methods: An optimal extraction method is used to separate both spatially unresolved (compact, up to a few hundred AU) and spatially resolved (extended, thousand AU or more) emission from the IRS spectra. The results are compared with the c2d disk sample and literature PDR and shock models to address the physical nature of the sources. Results: Both compact and extended emission features are observed. Warm (T_ex few hundred K) H2, observed through the pure rotational H2 S(0), S(1) and S(2) lines, and [S i] 25 μm emission is observed primarily in the extended component. [S i] is observed uniquely toward truly embedded sources and not toward disks. On the other hand hot (T_ex ⪆ 700 K) H2, observed primarily through the S(4) line, and [Ne ii] emission is seen mostly in the spatially unresolved component. [Fe ii] and [Si ii] lines are observed in both spatial components. Hot H2O emission is found in the spatially unresolved component of some sources. Conclusions: The observed emission on ≥1000 AU scales is characteristic of PDR emission and likely originates in the outflow cavities in the remnant envelope created by the stellar wind and jets from the embedded

  9. Enhancement of β-phase in PVDF films embedded with ferromagnetic Gd5Si4 nanoparticles for piezoelectric energy harvesting

    DOE PAGES

    Harstad, Shane; D’Souza, Noel; Soin, Navneet; ...

    2017-01-04

    Self-polarized Gd5Si4-polyvinylidene fluoride (PVDF) nanocomposite films have been synthesized via a facile phase-inversion technique. For the 5 wt% Gd5Si4-PVDF films, the enhancement of the piezoelectric β-phase and crystallinity are confirmed using Fourier transform infrared (FTIR) spectroscopy (phase fraction, FβFβ, of 81% as compared to 49% for pristine PVDF) and differential scanning calorimetry (crystallinity, ΔXcΔXc, of 58% as compared to 46% for pristine PVDF), respectively. The Gd5Si4 magnetic nanoparticles, prepared using high-energy ball milling were characterized using Dynamic Light Scattering and Vibrating Sample Magnetometry (VSM) to reveal a particle size of ~470 nm with a high magnetization of 11 emu/g. Themore » VSM analysis of free-standing Gd5Si4-PVDF films revealed that while the pristine PVDF membrane shows weak diamagnetic behavior, the Gd5Si4-PVDF films loaded at 2.5 wt% and 5 wt% Gd5Si4 show enhanced ferromagnetic behavior with paramagnetic contribution from Gd5Si3 phase. The interfacial interactions between Gd5Si4 and PVDF results in the preferential crystallization of the β-phase as confirmed via the shift in the CH2 asymmetric and symmetric stretching vibrations in the FTIR. These results confirm the magnetic Gd5Si4 nanoparticles embedded in the PVDF membrane lead to an increased β-phase fraction, which paves the way for future efficient energy harvesting applications using a combination of magnetic and piezoelectric effects.« less

  10. El Niño phases embedded in Asian and North American drought reconstructions

    NASA Astrophysics Data System (ADS)

    Li, Jinbao; Xie, Shang-Ping; Cook, Edward R.

    2014-02-01

    The amplitude of El Niño-Southern Oscillation (ENSO) varies substantially at each phase of its evolution, affecting the timing and patterns of atmospheric teleconnections around the globe. Instrumental records are too short to capture the full behavior of ENSO variability. Here we use the well-validated Monsoon Asia Drought Atlas (MADA) and North America Drought Atlas (NADA) for the past 700 years, and show that tree-ring records from different regions represent tropical sea surface temperature (SST) conditions at various phases of ENSO. Three modes of tree-ring based summer drought variability are found to be correlated with ENSO: summer droughts over the Maritime Continent and Southwest North America (NA), and a dipole mode between Central and South Asia. A lagged correlation analysis is performed to determine the time when precipitation and temperature anomaly imprints on summer droughts as recorded in tree-rings. Drought anomalies in the Maritime Continent and Southwest NA represent ENSO at the developing and peak phases respectively, while those over Central/South Asia are associated with tropical-wide SST anomalies (including the Indian Ocean) at the decay phase of ENSO. Thus proxy records from different regions can provide valuable information on long-term behavior of ENSO at different phases.

  11. Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry.

    PubMed

    Kulkarni, Rishikesh; Rastogi, Pramod

    2015-04-10

    A novel technique is proposed for the simultaneous measurement of all three components of displacement from a single recording of the interference field in digital holographic interferometry. The interference field is divided into a number of rectangular segments, and in each of these segments, the interference field is represented as a multicomponent low-order two-dimensional (2D) polynomial phase signal. 2D-product high-order ambiguity function based analysis is applied to obtain an accurate estimation of the 2D polynomial coefficients. These coefficients are further used to compute the interference phases. The simulation and experimental results show the robustness of the proposed method to noise and its effectiveness in multiple phase estimation.

  12. Singular Dynamic Holography

    NASA Astrophysics Data System (ADS)

    Tolstik, A. L.

    2016-02-01

    Basic patterns of interaction of Gaussian and singular light beams (optical vortices) in media with resonant and thermal nonlinearity are experimentally investigated. It is demonstrated that interference of the Gaussian and singular beams in a nonlinear medium leads to the formation of dynamic volume holograms characterized by a singular structure. Under conditions of nonlinear holographic recording and Bragg diffraction on singular volume holograms, multiplexing of a topological charge and frequency conversion of optical vortices (transition from the IR to the visible range of the spectrum) is observed. Polarization recording of singular holograms that allows dynamic control to be performed over polarization of singular light beams including rotation of the polarization plane and conversion of linearly polarized radiation into circularly or elliptically polarized radiation.

  13. Synergistic and singular effects of river discharge and lunar illumination on dam passage of upstream migrant yellow-phase American eels

    USGS Publications Warehouse

    Welsh, Stuart; Aldinger, Joni L.; Braham, Melissa; Zimmerman, Jennifer L.

    2016-01-01

    Monitoring of dam passage can be useful for management and conservation assessments of American eel, particularly if passage counts can be examined over multiple years. During a 7-year study (2007–2013) of upstream migration of American eels within the lower Shenandoah River (Potomac River drainage), we counted and measured American eels at the Millville Dam eel pass, where annual study periods were determined by the timing of the eel pass installation during spring or summer and removal during fall. Daily American eel counts were analysed with negative binomial regression models, with and without a year (YR) effect, and with the following time-varying environmental covariates: river discharge of the Shenandoah River at Millville (RDM) and of the Potomac River at Point of Rocks, lunar illumination (LI), water temperature, and cloud cover. A total of 17 161 yellow-phase American eels used the pass during the seven annual periods, and length measurements were obtained from 9213 individuals (mean = 294 mm TL, s.e. = 0.49, range 183–594 mm). Data on passage counts of American eels supported an additive-effects model (YR + LI + RDM) where parameter estimates were positive for river discharge (β = 7.3, s.e. = 0.01) and negative for LI (β = −1.9, s.e. = 0.34). Interestingly, RDM and LI acted synergistically and singularly as correlates of upstream migration of American eels, but the highest daily counts and multiple-day passage events were associated with increased RDM. Annual installation of the eel pass during late spring or summer prevented an early spring assessment, a period with higher RDM relative to those values obtained during sampling periods. Because increases in river discharge are climatically controlled events, upstream migration events of American eels within the Potomac River drainage are likely linked to the influence of climate variability on flow regime.

  14. w-cosmological singularities

    SciTech Connect

    Fernandez-Jambrina, L.

    2010-12-15

    In this paper we characterize barotropic index singularities of homogeneous isotropic cosmological models [M. P. Dabrowski and T. Denkiewicz, Phys. Rev. D 79, 063521 (2009).]. They are shown to appear in cosmologies for which the scale factor is analytical with a Taylor series in which the linear and quadratic terms are absent. Though the barotropic index of the perfect fluid is singular, the singularities are weak, as it happens for other models for which the density and the pressure are regular.

  15. 248-nm DUV MoSiON embedded phase-shifting mask for 0.25 micrometer lithography

    NASA Astrophysics Data System (ADS)

    Dao, Giang T.; Liu, Gang; Hainsey, Robert F.; Farnsworth, Jeff N.; Tokoro, Yasuo; Kawada, Susumu; Yamamoto, Tsuneo; Yoshioka, Nobuyuki; Chiba, Akira; Morimoto, Hiroaki

    1995-07-01

    Over the past five years worldwide efforts have been made to develop new techniques for optical lithography enhancement. These techniques include optical proximity correction, off-axis illumination, pupil filtering and phase-shifting mask (PSM). Among many phase-shifting mask approaches, embedded PSM (EPSM) method has drawn significant interest due to its relatively simple reticle fabrication process and excellent lithographic performance, in particular, for dark field mask layers such as contact and via holes. Perhaps, the most difficult task in materializing the EPSM technology is the creation of a thin film structure that controls both phase and transmission. In addition, this film structure must withstand severe environment of mask making process and yet can be inspected and repaired successfully using currently available tool sets. The newly developed MoSiON material meets these requirements and has demonstrated a feasibility for DUV EPSM pilot production. In this paper, characteristics of the DUV lifetime test results. Details of reticle fabrication process including e-beam writing, dry etching, inspection and repair will be presented along with chemical durability data and process capability. Finally, wafer level lithographic performance for contact holes printed on a step-and-scan and a projection aligner will be shown to demonstrate lithographic performance of 248 nm DUV EPSM for 0.25 micrometer lithography.

  16. Singularity v1.x

    SciTech Connect

    KURTZER, GREGORY; MURIKI, KRISHNA

    2016-04-12

    Singularity is a container solution designed to facilitate mobility of compute across systems and HPC infrastructures. It does this by creating minimal containers that are defined by a specfile and files from the host system are used to build the container. The resulting container can then be launched by any Linux computer with Singularity installed regardless if the programs inside the container are present on the target system, or if they are a different version, or even incompatible versions. Singularity achieves extreme portability without sacrificing usability thus solving the need of mobility of compute. Singularity containers can be executed within a normal/standard command line process flow.

  17. On singular and sincerely singular compact patterns

    NASA Astrophysics Data System (ADS)

    Rosenau, Philip; Zilburg, Alon

    2016-08-01

    A third order dispersive equation ut +(um)x +1/b[ua∇2ub]x = 0 is used to explore two very different classes of compact patterns. In the first, the prevailing singularity at the edge induces traveling compactons, solitary waves with a compact support. In the second, the singularity induced at the perimeter of the initial excitation, entraps the dynamics within the domain's interior (nonetheless, certain very singular excitations may escape it). Here, overlapping compactons undergo interaction which may result in an interchange of their positions, or form other structures, all confined within their initial support. We conjecture, and affirm it empirically, that whenever the system admits more than one type of compactons, only the least singular compactons may be evolutionary. The entrapment due to singularities is also unfolded and confirmed numerically in a class of diffusive equations ut =uk∇2un with k > 1 and n > 0 with excitations entrapped within their initial support observed to converge toward a space-time separable structure. A similar effect is also found in a class of nonlinear Klein-Gordon Equations.

  18. Wave Geometry: a Plurality of Singularities

    NASA Astrophysics Data System (ADS)

    Berry, M. V.

    Five interconnected wave singularities are discussed: phase monopoles, at eigenvalue degeneracies in parameter space, where the 2-form generating the geomeeic phase is singular, phase dislocations, at zeros of complex wavefunctions in position space, where different wavefronts (surfaces of constant phase) meet; caustics, that is envelopes (foci) of families of classical paths or geometrical rays, where real rays are born violently and which are complementary to dislocations; Stokes sets, at which a complex ray is born gently where it is maximally dominated by another ray; and complex degeneracies, which are the sources of adiabatic quantum transtions in analytic Hamiltonians.

  19. Digital holographic phase imaging of particles embedded in microscopic structures in three dimensions

    NASA Astrophysics Data System (ADS)

    Park, Jun Yong; Desta, Habben; Maloney, Maxwell C.; Sharikova, Anna; Khmaladze, Alexander

    2016-05-01

    We present a three-dimensional microscopic technique based on digital holographic imaging, which allows highly accurate axial localization of features inside of a three dimensional sample. When a light wave is propagating through, or reflecting from, a microscopic object, the phase changes can be converted into intensity variations using the existing digital microscopic techniques. The phase change indicates the change in the optical path length, which can be then converted to physical thickness, providing the sample height information. This property of holograms is used in phasecontrast techniques, and can also be used for quantitative 3D imaging. However, if the sample contains features with different indices of refraction, this method can only provide the overall optical thickness, and cannot determine where in the axial direction the particular feature is located. As a result, the application of Digital Holographic Microscopy to imaging of organelles within live cells, or defects within semiconductor substrates, is limited to overall morphology of the sample. To determine the axial location of features inside of a three dimensional sample, we developed a phase image processing method based on analyzing images taken from non-zero incident angles. When compared, these images can discriminate between various axial depths of features, while still retaining the information about the overall thickness profile of the sample.

  20. Singular finite element methods

    NASA Technical Reports Server (NTRS)

    Fix, George J.

    1987-01-01

    Singularities which arise in the solution to elliptic systems are often of great technological importance. This is certainly the case in models of fracture of structures. A survey of the ways singularities are modeled is presented with special emphasis on the effects due to nonlinearities.

  1. Scattering of shear waves by a two-phase multiferroic sensor embedded in a piezoelectric/piezomagnetic medium

    NASA Astrophysics Data System (ADS)

    Hashemi, Roohollah

    2017-03-01

    In this paper, a robust methodology with several desirable features is developed for the determination of the magneto-electro-elastic fields of a shear (SH) wave scattered by a two-phase multiferroic fiber embedded in an infinite transversely isotropic piezoelectric or piezomagnetic medium. While the traditional wave-function expansion approach commonly used in the literature ceases to hold when the geometry of the obstacle is not symmetric, the present theory is capable of treating eccentric coating-fiber ensemble. To put its wide range of applicability in perspective, my analytical methodology is applied to several descriptive examples with various degrees of complexity. The calculated results reveals the profound influence of material properties of constituent phases, the thickness and eccentricity of coating layer, as well as the frequency of propagating SH-wave on the pertinent scattered fields induced by the multiferroic fiber. It is expected that the formulation and numerical results of this paper serve as a useful reference for the design and manufacture of multiferroic materials with a durable and yet reliable performance under dynamics loadings.

  2. A Non Singular Universe

    NASA Astrophysics Data System (ADS)

    Hawking, Stephen

    2005-01-01

    The last chapter of my PhD thesis, contained my first singularity theorem. This showed that under certain reasonable conditions, any cosmological solution of the field equations, would have a big bang singularity. At this singularity, classical general relativity would break down, so one could not use it to predict how the universe began. It was therefore necessary to develop a quantum theory of gravity, in order to understand the origin of the universe. In this talk, I explore if the origin of the universe can be semi classical, and non singular. This is possible despite the singularity theorems, because like so many other no go theorems, they have a get out clause. In this case, the get out is the strong energy condition.

  3. Singular Atom Optics with Spinor BECs

    NASA Astrophysics Data System (ADS)

    Schultz, Justin T.; Hansen, Azure; Bigelow, Nicholas P.

    2015-05-01

    We create and study singular spin textures in pseudo-spin-1/2 BECs. A series of two-photon Raman interactions allows us to not only engineer the spinor wavefunction but also perform the equivalent of atomic polarimetry on the BEC. Adapting techniques from optical polarimetry, we can image two-dimensional maps of the atomic Stokes parameters, thereby fully reconstructing the atomic wavefunction. In a spin-1/2 system, we can represent the local spin superposition with ellipses in a Cartesian basis. The patterns that emerge from the major axes of the ellipses provide fingerprints of the singularities that enable us to classify them as lemons, stars, saddles, or spirals similar to classification schemes for singularities in singular optics, condensed matter, and liquid crystals. These techniques may facilitate the study of geometric Gouy phases in matter waves as well as provide an avenue for utilizing topological structures as quantum gates.

  4. Global existence for a singular Gierer-Meinhardt system

    NASA Astrophysics Data System (ADS)

    Chen, Shaohua; Salmaniw, Yurij; Xu, Runzhang

    2017-02-01

    This paper is concerned with existence results for a singular Gierer-Meinhardt system subject to zero Dirichlet boundary conditions, which originally arose in studies of pattern-formation in biology. The mathematical difficulties are that the system becomes singular near the boundary and it lacks a variational structure. We use a functional method to obtain both upper and lower bounds for the perturbed system and then use Sobolev embedding theorem to prove the existence of a pair of positive solutions under suitable conditions. This method is first used in a singular parabolic system and is completely different than the traditional methods of sub and super solutions.

  5. A family of three stages embedded explicit six-step methods with eliminated phase-lag and its derivatives for the numerical solution of second order problems

    NASA Astrophysics Data System (ADS)

    Simos, T. E.

    2017-07-01

    In the present paper we investigate a family of three stages high algebraic order embedded explicit six-step methods with eliminated phase-lag and its derivatives for the numerical solution of second order periodic initial or boundary-value problems. The basis of the construction of the new proposed family of embedded methods is (1) the elimination phase-lag and (2) the elimination of the phase-lag's derivatives. The produced methods with the above mentioned methodology are studied on:their local truncation error, the asymptotic form of the local truncation error which is produced applying them to the radial Schrödinger equation, the comparison of the asymptotic forms of the local truncation errors which leads to conclusions on the effectiveness of each method of the family, the stability and the interval of periodicity of the developed methods of the new family of embedded pairs, the application the new obtained family of embedded methods to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc in order to show their effectiveness.

  6. Endoluminal MR-guided ultrasonic applicator embedding cylindrical phased-array transducers and opposed-solenoid detection coil.

    PubMed

    Rata, Mihaela; Birlea, Vlad; Murillo, Adriana; Paquet, Christian; Cotton, François; Salomir, Rares

    2015-01-01

    MR-guided high-intensity contact ultrasound (HICU) was suggested as an alternative therapy for esophageal and rectal cancer. To offer high-quality MR guidance, two prototypes of receive-only opposed-solenoid coil were integrated with 64-element cylindrical phased-array ultrasound transducers (rectal/esophageal). The design of integrated coils took into account the transducer geometry (360° acoustic window within endoluminal space). The rectal coil was sealed on a plastic support and placed reversibly on the transducer head. The esophageal coil was fully embedded within the transducer head, resulting in one indivisible device. Comparison of integrated versus external coils was performed on a clinical 1.5T scanner. The integrated coils showed higher sensitivity compared with the standard extracorporeal coil with factors of up to 7.5 (rectal applicator) and 3.3 (esophageal applicator). High-resolution MR images for both anatomy (voxel 0.4 × 0.4 × 5 mm(3)) and thermometry (voxel 0.75 × 0.75 × 8 mm(3), 2 s/image) were acquired in vivo with the rectal endoscopic device. The temperature feedback loop accurately controlled multiple control points over the region of interest. This study showed significant improvement of MR data quality using endoluminal integrated coils versus standard external coil. Inframillimeter spatial resolution and accurate feedback control of MR-guided HICU thermotherapy were achieved. © 2014 Wiley Periodicals, Inc.

  7. Saddle-like deformation in a dielectric elastomer actuator embedded with liquid-phase gallium-indium electrodes

    SciTech Connect

    Wissman, J.; Finkenauer, L.; Deseri, L.; Majidi, C.

    2014-10-14

    We introduce a dielectric elastomer actuator (DEA) composed of liquid-phase Gallium-Indium (GaIn) alloy electrodes embedded between layers of poly(dimethylsiloxane) (PDMS) and examine its mechanics using a specialized elastic shell theory. Residual stresses in the dielectric and sealing layers of PDMS cause the DEA to deform into a saddle-like geometry (Gaussian curvature K<0). Applying voltage Φ to the liquid metal electrodes induces electrostatic pressure (Maxwell stress) on the dielectric and relieves some of the residual stress. This reduces the longitudinal bending curvature and corresponding angle of deflection ϑ. Treating the elastomer as an incompressible, isotropic, NeoHookean solid, we develop a theory based on the principle of minimum potential energy to predict the principal curvatures as a function of Φ. Based on this theory, we predict a dependency of ϑ on Φ that is in strong agreement with experimental measurements performed on a GaIn-PDMS composite. By accurately modeling electromechanical coupling in a soft-matter DEA, this theory can inform improvements in design and fabrication.

  8. Timelike naked singularity

    SciTech Connect

    Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis

    2004-10-15

    We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture.

  9. The Big Bang Singularity

    NASA Astrophysics Data System (ADS)

    Ling, Eric

    The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

  10. Symmetric embedded predictor-corrector (EP2CM) methods with vanished phase-lag and its derivatives for second order problems

    NASA Astrophysics Data System (ADS)

    Stasinos, P. I.; Simos, T. E.

    2017-07-01

    Embedded predictor-corrector methods with two-stages of prediction and with vanished phase-lag and its derivatives are described in this paper. We give the symbol (EP2CM) since these methods have two-stages of prediction. The first stage of the predictor of the new algorithm is based on the linear eight-step symmetric method of Quinlan-Tremaine [1]. The new scheme is non-linear since has three-stages. These methods can be used on the approximate solution of: 1. initial-value problems (IVPs) with oscillatory solutions, 2. boundary-value problems (IVPs) with oscillatory solutions, 3. orbital problems 4. the Schrödinger equation and related problems.The new presented algorithm belongs to the embedded methods. The numerical and theoretical achievements show the efficiency of the new produced embedded scheme.

  11. Generic singularity studies revisited

    NASA Astrophysics Data System (ADS)

    Barrow, John D.; Tipler, Frank J.

    1981-04-01

    We comment on a reply by Belinskii, Khalatnikov and Lifshitz to our analysis of their conclusions regarding the general structure of space-time singularities. We support our contention that it is impossible to provide a reliable analysis of the evolution of a general (or stable) solution with local techniques in a synchronous coordinate system having a simultaneous physical singularity. Work supported in part by the National Science Foundation under grant number PHY 78-26592.

  12. Resonance Van Hove singularities in wave kinetics

    NASA Astrophysics Data System (ADS)

    Shi, Yi-Kang; Eyink, Gregory L.

    2016-10-01

    Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D =(N - 2) d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D > 2 but produce divergences when D ≤ 2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D - δ ≤ 2, as we find for several physical examples, including electron-hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger-Dyson integral equations for the wave dynamics.

  13. Numerical Approaches to Spacetime Singularities.

    PubMed

    Berger, Beverly K

    1998-01-01

    This review updates a previous review article [22]. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.

  14. High numerical aperture focusing of singular beams

    NASA Astrophysics Data System (ADS)

    Normatov, Alexander; Spektor, Boris; Shamir, Joseph

    2009-02-01

    Rigorous vector analysis of high numerical aperture optical systems encounters severe difficulties. While existing analytic methods, based on the Richards-Wolf approach, allow focusing of nearly planar incident wavefronts, these methods break down for beams possessing considerable phase jumps, such as beams containing phase singularities. This work was motivated by the need to analyze a recently introduced metrological application of singular beams that demonstrated an experimental sensitivity of 20nm under a moderate numerical aperture of 0.4. One of the possibilities to obtain even better sensitivity is by increasing the numerical aperture of the optical system. In this work we address the issue of high numerical aperture focusing of the involved singular beams. Our solution exploits the superposition principle to evaluate the three dimensional focal distribution of the electromagnetic field provided the illuminating wavefront can be described as having piecewise quasi constant phase. A brief overview of singular beam microscopy is followed by deeper discussion of the involved high numerical aperture focusing issue. Further, a few examples of different singular beam focal field distributions are presented.

  15. Einstein and Singularities

    NASA Astrophysics Data System (ADS)

    Earman, John; Eisenstaedt, Jean

    Except for a few brief periods, Einstein was uninterested in analysing the nature of the spacetime singularities that appeared in solutions to his gravitational field equations for general relativity. The existence of such monstrosities reinforced his conviction that general relativity was an incomplete theory which would be superseded by a singularity-free unified field theory. Nevertheless, on a number of occasions between 1916 and the end of his life, Einstein was forced to confront singularities. His reactions show a strange asymmetry: he tended to be more disturbed by (what today we would call) merely apparent singularities and less disturbed by (what we would call) real singularities. Einstein had strong a priori ideas about what results a correct physical theory should deliver. In the process of searching through theoretical possibilities, he tended to push aside technical problems and jump over essential difficulties. Sometimes this method of working produced brilliant new ideas-such as the Einstein-Rosen bridge-and sometimes it lead him to miss important implications of his theory of gravity-such as gravitational collapse.

  16. Generalized teleparallel cosmology and initial singularity crossing

    NASA Astrophysics Data System (ADS)

    Awad, Adel; Nashed, Gamal

    2017-02-01

    We present a class of cosmological solutions for a generalized teleparallel gravity with f(T)=T+α˜ (‑T)n, where α˜ is some parameter and n is an integer or half-integer. Choosing α˜ ~ Gn‑1, where G is the gravitational constant, and working with an equation of state p=w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.

  17. On the SVMpath singularity.

    PubMed

    Dai, Jisheng; Chang, Chunqi; Mai, Fei; Zhao, Dean; Xu, Weichao

    2013-11-01

    This paper proposes a novel ridge-adding-based approach for handling singularities that are frequently encountered in the powerful SVMpath algorithm. Unlike the existing method that performs linear programming as an additional step to track the optimality condition path in a multidimensional feasible space, our new approach provides a simpler and computationally more efficient implementation, which needs no extra time-consuming procedures other than introducing a random ridge term to each data point. Contrary to the existing ridge-adding method, which fails to avoid singularities as the ridge terms tend to zero, our novel approach, for any small random ridge terms, guarantees the existence of the inverse matrix by ensuring that only one index is added into or removed from the active set. The performance of the proposed algorithm, in terms of both computational complexity and the ability of singularity avoidance, is manifested by rigorous mathematical analyses as well as experimental results.

  18. On integrable singularities and apparent contact angles within a classical paradigm: partial and complete wetting regimes with or without phase change

    NASA Astrophysics Data System (ADS)

    Colinet, Pierre; Rednikov, Alexey

    2011-11-01

    Far from claiming any ultimate resolution of the contact line paradoxes, we argue that a somewhat controversial paradigm, originally employed by de Gennes and collaborators, actually appears both to be quite reasonable at its foundations and to lead to physically consistent final results in a wide variety of situations. Curiously enough, while containing a singularity in itself, the approach nonetheless renders the classical contact-line singularities - both hydrodynamic and thermal - integrable, in particular as far as several quantities of interest are concerned. It is also readily applicable to quite a few situations: from equilibrium shapes and moving contact lines of a non-volatile liquid, to cases with evaporation into either a pure-vapor or an inert-gas atmosphere. The paradigm actually consists in an approach involving both the (positive or negative) spreading coefficient and the disjoining pressure in the form of a positive inverse cubic law, a conceptual framework that most notably describes structures with truncated precursor films on a macroscopically bare solid surface. Supported by ESA & BELSPO, by the EU-MULTIFLOW project, and by FRS-FNRS.

  19. Type I singularities and the phantom menace

    SciTech Connect

    Naskar, Tapan; Ward, John

    2007-09-15

    We consider the future dynamics of a transient phantom dominated phase of the universe in loop quantum cosmology (LQC) and in the Randall-Sundrum braneworld, which both have a nonstandard Friedmann equation. We find that for a certain class of potentials, the Hubble parameter oscillates with simple harmonic motion in the LQC case and therefore avoids any future singularity. For more general potentials we find that damping effects eventually lead to the Hubble parameter becoming constant. On the other hand in the braneworld case we find that although the type I singularity can be avoided, the scale factor still diverges at late times.

  20. Singularity perturbed zero dynamics of nonlinear systems

    NASA Technical Reports Server (NTRS)

    Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

    1992-01-01

    Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

  1. Finite time future singularities in the interacting dark sector

    NASA Astrophysics Data System (ADS)

    Cataldo, Mauricio; Chimento, Luis P.; Richarte, Martín G.

    2017-03-01

    We construct a piecewise model that gives a physical viable realization of finite-time future singularity for a spatially flat Friedmann-Robertson-Walker universe within the interacting dark matter-dark energy framework, with the latter in the form of a variable vacuum energy. The scale factor solutions provided by the model are accommodated in several branches defined in four regions delimited by the scale factor and the effective energy density. A branch starts from a big bang singularity and describes an expanding matter-dominated universe until the sudden future singularity occurs. Then, an expanding branch emerges from a past singularity, reaches a maximum, reverses its expansion, and possibly collapses into itself while another expanding branch emerges from the latter singularity and has a de Sitter phase which is intrinsically stable. We obtain a different piecewise scale factor which describes a contracting de Sitter universe in the distant past until the finite-time future singularity happens. It emerges and continues in a contracting phase, bounces at the minimum, reverses, and enters into a stable de Sitter phase without a dramatic final. Also, we explore the aforesaid cosmic scenarios by focusing on the leading contributions of some physical quantities near the sudden future singularity and applying the geometric Tipler and Królak criteria in order to inspect the behavior of timelike geodesic curves around such singularity.

  2. Singular Vectors' Subtle Secrets

    ERIC Educational Resources Information Center

    James, David; Lachance, Michael; Remski, Joan

    2011-01-01

    Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.

  3. Singular Vectors' Subtle Secrets

    ERIC Educational Resources Information Center

    James, David; Lachance, Michael; Remski, Joan

    2011-01-01

    Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.

  4. Numerical Approaches to Spacetime Singularities.

    PubMed

    Berger, Beverly K

    2002-01-01

    This Living Review updates a previous version [25] which is itself an update of a review article [31]. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.

  5. A simple method for the synthesis of a polar-embedded and polar-endcapped reversed-phase chromatographic packing with low activity of residue silanols.

    PubMed

    Liu, Hai-yan; Li, Zhi-yong; Liu, Dan; Xue, Ying-wen; Shi, Zhi-guo

    2016-04-22

    Octadecyl bonded silica (ODS) is the most popular packing for reversed-phase chromatography. However, it generally demonstrates bad resolution for polar analytes because of the residue silanols and its poor stability in aqueous mobile phase. To address the problem, a new reversed-phase packing containing both polar-embedded and polar-endcapped moieties was proposed. It was prepared by a very simple method, in which the epoxide addition reaction of 3-glycidoxypropyltrimethoxysilane with 1-octadecanethiol proceeded simultaneously with the reaction of silane coupling onto silica particles. By controlling the molecular ratio of 3-glycidoxypropyltrimethoxysilane to 1-octadecanethiol higher than 1.0 (1.56 for the present study), both polar-embedded and polar-endcapped moieties were achieved onto the packing. The performance of the packing was evaluated in detail. The results demonstrated that neutral, acidic and basic analytes were well separated on the packing. The column efficiency for phenanthrene was 34,200 theoretical plates per meter. In addition, four nucleotides can be separated in 100% phosphate buffered saline solution with good reproducibility, which indicates the packing has good stability in aqueous mobile phase. Amitriptyline, a typical basic analytes, was eluted out with relatively symmetric peak shape (asymmetry factor of 1.36), which implies that the packing has not suffered from the negative effect of residue silanols significantly. Good stability in buffer solution of pH ranging from 2.0 to 10.0 was also documented for the packing.

  6. Complete representation of a correlation singularity in a partially coherent beam.

    PubMed

    Stahl, C S D; Gbur, G

    2014-10-15

    An understanding of phase singularities of correlation functions is important in optical coherence theory and imaging science, but to date such singularities have only been theoretically studied in a single transverse plane, at most. In this Letter we evaluate the complete structure of a correlation singularity of a partially coherent Laguerre-Gauss beam, describing it in both the transverse and the propagation directions. These results agree with previously found solutions, and introduce new aspects of correlation singularities.

  7. Singularities in loop quantum cosmology.

    PubMed

    Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David

    2008-12-19

    We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.

  8. Singularities of interference of three waves with different polarization states.

    PubMed

    Kurzynowski, Piotr; Woźniak, Władysław A; Zdunek, Marzena; Borwińska, Monika

    2012-11-19

    We presented the interference setup which can produce interesting two-dimensional patterns in polarization state of the resulting light wave emerging from the setup. The main element of our setup is the Wollaston prism which gives two plane, linearly polarized waves (eigenwaves of both Wollaston's wedges) with linearly changed phase difference between them (along the x-axis). The third wave coming from the second arm of proposed polarization interferometer is linearly or circularly polarized with linearly changed phase difference along the y-axis. The interference of three plane waves with different polarization states (LLL - linear-linear-linear or LLC - linear-linear-circular) and variable change difference produce two-dimensional light polarization and phase distributions with some characteristic points and lines which can be claimed to constitute singularities of different types. The aim of this article is to find all kind of these phase and polarization singularities as well as their classification. We postulated in our theoretical simulations and verified in our experiments different kinds of polarization singularities, depending on which polarization parameter was considered (the azimuth and ellipticity angles or the diagonal and phase angles). We also observed the phase singularities as well as the isolated zero intensity points which resulted from the polarization singularities when the proper analyzer was used at the end of the setup. The classification of all these singularities as well as their relationships were analyzed and described.

  9. Quantum transitions through cosmological singularities

    NASA Astrophysics Data System (ADS)

    Bramberger, Sebastian F.; Hertog, Thomas; Lehners, Jean-Luc; Vreys, Yannick

    2017-07-01

    In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.

  10. Hard x-ray phase contrast imaging using a tabletop Talbot-Lau interferometer with multiline embedded x-ray targets.

    PubMed

    Shimura, Takayoshi; Morimoto, Naoki; Fujino, Sho; Nagatomi, Takaharu; Oshima, Keni-chi; Harada, Jimpei; Omote, Kazuhiko; Osaka, Naohisa; Hosoi, Takuji; Watanabe, Heiji

    2013-01-15

    We demonstrate hard x-ray phase contrast imaging (XPCI) using a tabletop Talbot-Lau interferometer in which the x-ray source and source grating are replaced with an x-ray source with multiline metal targets embedded in a diamond substrate. This source realizes an array of linear x-ray sources of a few micrometers width without fabrication difficulty because of the shallow penetration depth of electrons irradiated to the metal targets. This enhances the coherence of x rays from each linear source and allows XPCI within 45 cm source-detector distance under 1.2 W input power for 8 keV x rays.

  11. Singularities and internal rotational dynamics of electron beams

    NASA Astrophysics Data System (ADS)

    Velasco-Martínez, D.; Ibarra-Sierra, V. G.; Sandoval-Santana, J. C.; Cardoso, J. L.; Kunold, A.

    2016-12-01

    We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest nonvanishing terms of the wave function near the singularity, it is possible to infer the structure of the Bohmian streamlines. Conversely, starting from a map of the electron's Bohmian velocities, we demonstrate that it is possible to derive the form of the electron's wave function near the singularity. We outline a procedure that could yield an experimental method to determine the main parameters of the electron's wave function close to a singularity.

  12. Singularities in Optimal Structural Design

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Guptill, J. D.; Berke, L.

    1992-01-01

    Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

  13. Singularities in optimal structural design

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Guptill, J. D.; Berke, L.

    1992-01-01

    Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

  14. Resolving cosmological singularities

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Mukhanov, Viatcheslav

    2017-03-01

    We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the universe has a regular bounce which takes place during the time inversely proportional to the square root of the limiting curvature. Away from the bounce, corrections to General Relativity are negligible. In addition the non-singluar modification of General Relativity delivers for free a realistic candidate for Dark Matter.

  15. Dynamical singularities in ultradiffusion

    NASA Astrophysics Data System (ADS)

    Keirstead, W. P.; Huberman, B. A.

    1987-12-01

    We study ultradiffusion in systems with an arbitrary distribution of energy barriers and nearest-neighbor hopping processes. As the effective temperature R is increased, we find power-law decay of the autocorrelation function with an anomalous R-dependent exponent for Rsingular crossover at Rc to normal diffusion. The value of Rc depends on the average branching ratio of the system. We have also discovered a set of trees for which the R dependence of the exponent departs from the expected value based on universality arguments. Analytical results and computer experiments for several systems are presented.

  16. Singular eigenfunctions for shearing fluids I

    SciTech Connect

    Balmforth, N.J.; Morrison, P.J.

    1995-02-01

    The authors construct singular eigenfunctions corresponding to the continuous spectrum of eigenvalues for shear flow in a channel. These modes are irregular as a result of a singularity in the eigenvalue problem at the critical layer of each mode. They consider flows with monotonic shear, so there is only a single critical layer for each mode. They then solve the initial-value problem to establish that these continuum modes, together with any discrete, growing/decaying pairs of modes, comprise a complete basis. They also view the problem within the framework of Hamiltonian theory. In that context, the singular solutions can be viewed as the kernel of an integral, canonical transformation that allows us to write the fluid system, an infinite-dimensional Hamiltonian system, in action-angle form. This yields an expression for the energy in terms of the continuum modes and provides a means for attaching a characteristic signature (sign) to the energy associate with each eigenfunction. They follow on to consider shear-flow stability within the Hamiltonian framework. Next, the authors show the equivalence of integral superpositions of the singular eigenfunctions with the solution derived with Laplace transform techniques. In the long-time limit, such superpositions have decaying integral averages across the channel, revealing phase mixing or continuum damping. Under some conditions, this decay is exponential and is then the fluid analogue of Landau damping. Finally, the authors discuss the energetics of continuum damping.

  17. Singular behavior of jet substructure observables

    DOE PAGES

    Larkoski, Andrew J.; Moult, Ian

    2016-01-20

    Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the limit in which hard substructure is resolved, as well as the limit of a jet with a single hard core. In this paper we study in detail the perturbative structure of two prominent jet substructure observables, N-subjettiness and the energy correlation functions, as measured on background QCD jets. In particular, we focus on the distinction between the limits in which two-prong structure is resolved or unresolved. Dependingmore » on the choice of subjet axes, we demonstrate that at fixed order, N-subjettiness can manifest myriad behaviors in the unresolved region: smooth tails, end-point singularities, or singularities in the physical region. The energy correlation functions, by contrast, only have non-singular perturbative tails extending to the end point. We discuss the effect of hadronization on the various observables with Monte Carlo simulation and demonstrate that the modeling of these effects with non-perturbative shape functions is highly dependent on the N-subjettiness axes definitions. Lastly, our study illustrates those regions of phase space that must be controlled for high-precision jet substructure calculations, and emphasizes how such calculations can be facilitated by designing substructure observables with simple singular structures.« less

  18. Singular behavior of jet substructure observables

    SciTech Connect

    Larkoski, Andrew J.; Moult, Ian

    2016-01-20

    Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the limit in which hard substructure is resolved, as well as the limit of a jet with a single hard core. In this paper we study in detail the perturbative structure of two prominent jet substructure observables, N-subjettiness and the energy correlation functions, as measured on background QCD jets. In particular, we focus on the distinction between the limits in which two-prong structure is resolved or unresolved. Depending on the choice of subjet axes, we demonstrate that at fixed order, N-subjettiness can manifest myriad behaviors in the unresolved region: smooth tails, end-point singularities, or singularities in the physical region. The energy correlation functions, by contrast, only have non-singular perturbative tails extending to the end point. We discuss the effect of hadronization on the various observables with Monte Carlo simulation and demonstrate that the modeling of these effects with non-perturbative shape functions is highly dependent on the N-subjettiness axes definitions. Lastly, our study illustrates those regions of phase space that must be controlled for high-precision jet substructure calculations, and emphasizes how such calculations can be facilitated by designing substructure observables with simple singular structures.

  19. Data embedding

    DOEpatents

    Sandford, M.T. II; Handel, T.G.

    1997-08-19

    A method is disclosed for embedding auxiliary information into a set of host data, such as a photograph, television signal, facsimile transmission, or identification card. All such host data contain intrinsic noise, allowing pixels in the host data which are nearly identical and which have values differing by less than the noise value to be manipulated and replaced with auxiliary data. As the embedding method does not change the elemental values of the host data, the auxiliary data do not noticeably affect the appearance or interpretation of the host data. By a substantially reverse process, the embedded auxiliary data can be retrieved easily by an authorized user. 19 figs.

  20. Data embedding

    DOEpatents

    Sandford, II, Maxwell T.; Handel, Theodore G.

    1997-01-01

    A method of embedding auxiliary information into a set of host data, such as a photograph, television signal, facsimile transmission, or identification card. All such host data contain intrinsic noise, allowing pixels in the host data which are nearly identical and which have values differing by less than the noise value to be manipulated and replaced with auxiliary data. As the embedding method does not change the elemental values of the host data, the auxiliary data do not noticeably affect the appearance or interpretation of the host data. By a substantially reverse process, the embedded auxiliary data can be retrieved easily by an authorized user.

  1. Optical singularities in plasmonic fields near single subwavelength holes

    NASA Astrophysics Data System (ADS)

    de Hoogh, A.; Rotenberg, N.; Kuipers, L.

    2014-11-01

    We identify phase and polarization singularities in near-field measurements and theoretical modeling of the electric near-field distributions that result from the scattering of surface plasmon polaritons from single subwavelength holes in optically thick gold films. We discuss properties of the singularities, such as their topological charge or the field amplitudes at their locations. We show that it is possible to tune the in-plane field amplitude at the positions of the polarization singularities by three orders of magnitude simply by varying the hole or incident plasmon beam size.

  2. Enhanced Thermoelectricity in High-Temperature β-Phase Copper(I) Selenides Embedded with Cu2Te Nanoclusters.

    PubMed

    Butt, Sajid; Xu, Wei; Farooq, Muhammad U; Ren, Guang K; Zhang, Qinghua; Zhu, Yingcai; Khan, Sajid U; Liu, Lijuan; Yu, Meijuan; Mohmed, Fida; Lin, Yuanhua; Nan, Ce-Wen

    2016-06-22

    We report remarkably enhanced thermoelectric performance of Te doped Cu2Se in midtemperature range. Through ball-milling process followed by spark plasma sintering (SPS), nanoscale Cu2Te clusters were embeded in the matrix of Cu2Se, inducing a drastic enhancement of thermoelectric performance by reducing the thermal conductivity without degrading the power factor. A large ZT value of 1.9 was achieved at 873 K for Cu2Se1.9Te0.1, which is about 2 times larger than that of the pure Cu2Se. The nanoscale heat management by Cu2Te nanoclusters in superionic conductors opens up an avenue for thermoelectric materials research.

  3. Natural semidirect gauge mediation and D-branes at singularities

    SciTech Connect

    Argurio, Riccardo; Bertolini, Matteo; Ferretti, Gabriele; Mariotti, Alberto

    2009-08-15

    We consider semidirect gauge mediation models of supersymmetry breaking where the messengers are composite fields and their supersymmetric mass is naturally generated through quartic superpotential couplings. We show that such composite messenger models can be easily embedded in quiver gauge theories arising from D-branes at Calabi-Yau singularities, and argue that semidirect gauge mediation is in fact a very natural option for supersymmetry breaking in D-brane models. We provide several explicit examples and discuss their salient phenomenological properties.

  4. Art as a Singular Rule

    ERIC Educational Resources Information Center

    Avital, Doron

    2007-01-01

    This paper will examine an unresolved tension inherent in the question of art and argue for the idea of a singular rule as a natural resolution. In so doing, the structure of a singular rule will be fully outlined and its paradoxical constitution will be resolved. The tension I mention above unfolds both as a matter of history and as a product of…

  5. Double spaces with isolated singularities

    SciTech Connect

    Cheltsov, I A

    2008-02-28

    The non-rationality is proved for double covers of P{sup n} branched over a hypersurface F subset of P{sup n} of degree 2n>=8 with isolated singularities such that the multiplicity of each singular point of F does not exceed 2(n-2) and the projectivization of its tangent cone is smooth. Bibliography: 15 titles.

  6. Art as a Singular Rule

    ERIC Educational Resources Information Center

    Avital, Doron

    2007-01-01

    This paper will examine an unresolved tension inherent in the question of art and argue for the idea of a singular rule as a natural resolution. In so doing, the structure of a singular rule will be fully outlined and its paradoxical constitution will be resolved. The tension I mention above unfolds both as a matter of history and as a product of…

  7. Polarization singularity democracy:WYSIWYG

    NASA Astrophysics Data System (ADS)

    Freund, Isaac

    2004-08-01

    The canonical point singularity of elliptically polarized light is a C point, an isolated point of circular polarization surrounded by a field of polarization ellipses. The defining singular property of a C point is that the surrounding ellipses rotate about the point. It is shown that this rotation is seen only for a particular line of sight (LOS) and, conversely, that there exists a unique LOS for every ellipse along which the ellipse is seen as a singularity. It is also shown that changes in LOS can turn singularities into stationary points and vice versa. The democratic behavior of polarization singularities and stationary points is a consequence of the fundamental ''what you see is what you get'' property of ellipse fields. Simple experiments are proposed for observing this unusual property of elliptically polarized light.

  8. Computing singularities of perturbation series

    SciTech Connect

    Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

    2011-03-15

    Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schroedinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be useful for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with {delta}-function interactions for which Moeller-Plesset perturbation theory is considered and the radius of convergence found.

  9. Preservation in microbial mats: mineralization by a talc-like phase of a fish embedded in a microbial sarcophagus

    NASA Astrophysics Data System (ADS)

    Iniesto, Miguel; Zeyen, Nina; López-Archilla, Ana; Bernard, Sylvain; Buscalioni, Ángela; Guerrero, M. Carmen; Benzerara, Karim

    2015-09-01

    Microbial mats have been repeatedly suggested to promote early fossilization of macroorganisms. Yet, experimental simulations of this process remain scarce. Here, we report results of 5 year-long experiments performed onfish carcasses to document the influence of microbial mats on mineral precipitation during early fossilization. Carcasses were initially placed on top of microbial mats. After two weeks, fishes became coated by the mats forming a compact sarcophagus, which modified the microenvironment close to the corpses. Our results showed that these conditions favoured the precipitation of a poorly crystalline silicate phase rich in magnesium. This talc-like mineral phase has been detected in three different locations within the carcasses placed in microbial mats for more than 4 years: 1) within inner tissues, colonized by several bacillary cells; 2) at the surface of bones of the upper face of the corpse buried in the mat; and 3) at the surface of several bones such as the dorsal fin which appeared to be gradually replaced by the Mg-silicate phase. This mineral phase has been previously shown to promote bacteria fossilization. Here we provide first experimental evidence that such Mg-rich phase can also be involved in exceptional preservation of animals.

  10. Unstable horizons and singularity development in holography

    NASA Astrophysics Data System (ADS)

    Bosch, Pablo; Buchel, Alex; Lehner, Luis

    2017-07-01

    In holographic applications one can encounter scenarios where a long-wavelength instability can arise. In such situations, it is often the case that the dynamical end point of the instability is a new equilibrium phase with a nonlinear scalar hair condensate outside the black hole horizon. We here review holographic setups where symmetric horizons suffer from long-wavelength instabilities where a suitable equilibrium condensate phase does not exist. We study the dynamics of the simplest model in this exotic class, and show that it uncovers arbitrarily large curvatures in the vicinity of the horizon which asymptotically turn such region singular, at finite time with respect to the boundary theory.

  11. Low-temperature phase transition in nanostructured MnO embedded within the channels of MCM-41-type matrices

    SciTech Connect

    Golosovsky, I. V.; Mirebeau, I.; Fauth, F.; Kurdyukov, D. A.; Kumzerov, Yu. A.

    2006-08-01

    High-resolution x-ray-diffraction experiments of antiferromagnetic MnO nanostructured within the channels of mesoporous MCM-41 matrices reveal an unusual transition from a distorted, trigonal phase to a cubic phase at about 40 K, well below the magnetic transition temperature of 120 K. The disappearance of the structural distortion is accompanied by an increase of the unit-cell parameter, amplitude of atomic motion, and the appearance of inner stresses. Such behavior drastically differs from the behavior known for the bulk compound.

  12. EDITORIAL: The plurality of optical singularities

    NASA Astrophysics Data System (ADS)

    Berry, Michael; Dennis, Mark; Soskin, Marat

    2004-05-01

    This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the

  13. Loop quantum cosmology and singularities.

    PubMed

    Struyve, Ward

    2017-08-15

    Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

  14. Superior Dielectric Performance of Engineering Thermoplastic as a Result of In situ Embedding of Nanoscale Mixed-Phase Molybdenum Oxide

    NASA Astrophysics Data System (ADS)

    Qureshi, Nilam; Shinde, Manish; Ratheesh, R.; Bhalerao, Anand; Kale, Bharat; Mulik, Uttam; Amalnerkar, Dinesh P.

    2015-07-01

    To facilitate in situ generation of single and mixed-phase molybdenum oxide on the nanoscale in a network of polyphenylene sulfide (PPS), a novel polymer-inorganic solid-state reaction is proposed. Ammonium molybdate was homogeneously mixed with PPS in 1:1 molar ratio and heated at 285°C for different times (6 h, 24 h, or 48 h) under ambient conditions. The products were characterized by x-ray diffractometry, field emission scanning electron microscopy, and transmission electron microscopy. Structural investigations revealed the co-existence of mix-phased molybdenum oxide, i.e. dominant orthorhombic α-MoO3, and minor monoclinic Mo8O23 phases, within the modified PPS matrix. The resulting molybdenum oxide nanostructures had rod and sheet-like morphology in the PPS matrix. Dielectric measurements on pellets prepared from the resulting nanocomposites revealed improvement of the dielectric properties compared with values reported for pure PPS. The resulting nano-composites may exhibit properties synergistically derived from those of their components (molybdenum oxide and PPS), i.e. lower dielectric constant and loss tangent, enabling application as relatively high-temperature capacitors.

  15. Five-dimensional null-cone structure of big bang singularity

    SciTech Connect

    Lauro, S.; Schucking, E.L.

    1985-04-01

    The Friedmann model PHI of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five-dimensional Minkowski space MV is globally rigid: if F(PHI) and F'(PHI) are isometric embeddings in MV there is a motion of MV such that F'= F. The big bang singularity is the vertex of a null half-cone in MV. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.

  16. Singular field response and singular screening of vacancies in antiferromagnets.

    PubMed

    Wollny, Alexander; Andrade, Eric C; Vojta, Matthias

    2012-10-26

    For isolated vacancies in ordered local-moment antiferromagnets we show that the magnetic-field linear-response limit is generically singular: The magnetic moment associated with a vacancy in zero field is different from that in a finite field h in the limit h→0(+). The origin is a universal and singular screening cloud, which moreover leads to perfect screening as h→0(+) for magnets which display spin-flop bulk states in the weak-field limit.

  17. Singularity Expansion Method

    NASA Astrophysics Data System (ADS)

    Riggs, Lloyd Stephen

    In this work the transient currents induced on an arbitrary system of thin linear scatterers by an electromagnetic plane wave are solved by using an electric field integral equation (EFIE) formulation. The transient analysis is carried out using the singularity expansion method (SEM). The general analysis developed here is useful for assessing the vulnerability of military aircraft to a nuclear generated electromagnetic pulse (EMP). It is also useful as a modal synthesis tool in the analysis and design of frequency selective surfaces (FSS). SEM parameters for a variety of thin cylindrical geometries have been computed. Specifically, SEM poles, modes, coupling coefficients, and transient currents are given for the two and three element planar array. Poles and modes for planar arrays with a larger number (as many as eight) of identical equally spaced elements are also considered. SEM pole-mode results are given for identical parallel elements with ends located at the vertices of a regular N-agon. Pole-mode patterns are found for symmetric (and slightly perturbed) single junction N-arm elements and for the five junction Jerusalem cross. The Jerusalem cross element has been used extensively in FSS.

  18. Studies of nitride- and oxide-based materials as absorptive shifters for embedded attenuated phase-shifting mask in 193 nm

    NASA Astrophysics Data System (ADS)

    Lin, Cheng-ming; Chang, Keh-wen; Lee, Ming-der; Loong, Wen-An

    1999-07-01

    Abstract-Five materials which are PdSixOy, CrAlxOy, SiNx, TiSixNy, and TiSixOyNz as absorptive shifters for attenuated phase-shifting mask in 193 nm wavelength lithography are presented. PdSixOy films were deposited by dual e-gun evaporation. CrAlxOy, TiSixNy and TiSixOyNz films were formed by plasma sputtering and SiNx films were formed with LPCVD. All of these materials are shown to be capable of achieving 4 percent - 15 percent transmittance in 193 nm with thickness that produce a 180 degrees phase shift. Under BCl3:Cl2 equals 14:70 sccm; chamber pressure 5 mtorr and RF power 1900W, the dry etching selectivity of TiSixNy over DQN positive resist and fused silica, were found to be 2:1 and 4,8:1 respectively. An embedded layer TiSixNy with 0.5 micrometers line/space was successfully patterned.

  19. Visibility of a spacetime singularity

    SciTech Connect

    Joshi, Pankaj S.

    2007-02-15

    We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultradense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of nonspacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed nonspacelike curves which also necessarily escape from the same. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.

  20. A reversible bipolar WORM device based on AlOxNy thin film with Al nano phase embedded

    NASA Astrophysics Data System (ADS)

    Zhu, W.; Li, J.; Zhang, L.; Hu, X. C.

    2017-03-01

    An Al-rich AlOxNy thin film based reversible Write-Once-Read-Many-Times (WORM) memory device with MIS structure could transit from high resistance state (HRS, ∼1011 Ω) to low resistance state (LRS, ∼105 Ω) by sweeping voltage up to ∼20 V. The first switching could be recorded as writing process for WORM device which may relate to conductive path are formed through the thin film. The conductive path should be formed by both Al nano phase and oxygen vacancies. Among of them, Al nano phases are not easy to move, but oxygen vacancies could migrate under high E-field or at high temperature environment. Such conductive path is not sensitive to charging effect after it formed, but it could be broken by heating effect, which may relate to the migration of excess Al ions and oxygen vacancies at high temperature. After baking LRS (ON state) WORM device at 200 °C for 2 min, the conductivity will decrease to HRS which indicates conductive path is broken and device back to HRS (OFF state) again. This phenomenon could be recorded as recovery process. Both writing and recovery process related to migration of oxygen vacancies and could be repeated over 10 times in this study. It also indicates that there is no permanent breakdown occurred in MIS structured WORM device operation. We suggest that this conductive path only can be dissolved by a temperature sensitive electro-chemical action. This WORM device could maintain at LRS over 105 s with on-off ratio over 4 orders.

  1. Compression embedding

    DOEpatents

    Sandford, M.T. II; Handel, T.G.; Bradley, J.N.

    1998-03-10

    A method of embedding auxiliary information into the digital representation of host data created by a lossy compression technique is disclosed. The method applies to data compressed with lossy algorithms based on series expansion, quantization to a finite number of symbols, and entropy coding. Lossy compression methods represent the original data as integer indices having redundancy and uncertainty in value by one unit. Indices which are adjacent in value are manipulated to encode auxiliary data. By a substantially reverse process, the embedded auxiliary data can be retrieved easily by an authorized user. Lossy compression methods use loss-less compressions known also as entropy coding, to reduce to the final size the intermediate representation as indices. The efficiency of the compression entropy coding, known also as entropy coding is increased by manipulating the indices at the intermediate stage in the manner taught by the method. 11 figs.

  2. Compression embedding

    DOEpatents

    Sandford, II, Maxwell T.; Handel, Theodore G.; Bradley, Jonathan N.

    1998-01-01

    A method of embedding auxiliary information into the digital representation of host data created by a lossy compression technique. The method applies to data compressed with lossy algorithms based on series expansion, quantization to a finite number of symbols, and entropy coding. Lossy compression methods represent the original data as integer indices having redundancy and uncertainty in value by one unit. Indices which are adjacent in value are manipulated to encode auxiliary data. By a substantially reverse process, the embedded auxiliary data can be retrieved easily by an authorized user. Lossy compression methods use loss-less compressions known also as entropy coding, to reduce to the final size the intermediate representation as indices. The efficiency of the compression entropy coding, known also as entropy coding is increased by manipulating the indices at the intermediate stage in the manner taught by the method.

  3. Phase separation in SiGe nanocrystals embedded in SiO{sub 2} matrix during high temperature annealing

    SciTech Connect

    Mogaddam, N. A. P.; Turan, R.; Alagoz, A. S.; Yerci, S.; Foss, S.; Finstad, T. G.

    2008-12-15

    SiGe nanocrystals have been formed in SiO{sub 2} matrix by cosputtering Si, Ge, and SiO{sub 2} independently on Si substrate. Effects of the annealing time and temperature on structural and compositional properties are studied by transmission electron microscopy, x-ray diffraction (XRD), and Raman spectroscopy measurements. It is observed that Ge-rich Si{sub (1-x)}Ge{sub x} nanocrystals do not hold their compositional uniformity when annealed at high temperatures for enough long time. A segregation process leading to separation of Ge and Si atoms from each other takes place. This process has been evidenced by a double peak formation in the XRD and Raman spectra. We attributed this phase separation to the differences in atomic size, surface energy, and surface diffusion disparity between Si and Ge atoms leading to the formation of nonhomogenous structure consist of a Si-rich SiGe core covered by a Ge-rich SiGe shell. This experimental observation is consistent with the result of reported theoretical and simulation methods.

  4. Naked singularity resolution in cylindrical collapse

    SciTech Connect

    Kurita, Yasunari; Nakao, Ken-ichi

    2006-03-15

    In this paper, we study the gravitational collapse of null dust in cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the backreaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the naked singularity. In this case, although this naked singularity satisfies the strong curvature condition by Krolak (limiting focusing condition), geodesics which hit the singularity can be extended uniquely across the singularity. Therefore, we may say that the collapsing null dust passes through the singularity formed by itself and then leaves for infinity. Finally, the singularity completely disappears and the flat spacetime remains.

  5. Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes.

    PubMed

    Ando, Taro; Matsumoto, Naoya; Ohtake, Yoshiyuki; Takiguchi, Yu; Inoue, Takashi

    2010-12-01

    We investigate optical singularities in coaxial superpositions of two Laguerre-Gaussian (LG) modes with a common beam waist from the viewpoints of a general formulation of phase structure, experimental generation of various superposition beams, and evaluation of the generated beams' fidelity. By applying a holographic phase-amplitude modulation scheme using a phase-modulation-type spatial light modulator, output fidelity beyond 0.960 was observed under several typical conditions. Additionally, an elliptic-type folded singularity, which provides a different class of phase structures from familiar helical singularities, was predicted and observed in a superposition involving two LG modes of both radially and azimuthally higher orders.

  6. Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation

    NASA Astrophysics Data System (ADS)

    Guo, Zongming; Wei, Juncheng; Zhou, Feng

    2017-07-01

    Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem

  7. Spacetime singularity resolution in Snyder noncommutative space

    NASA Astrophysics Data System (ADS)

    Gorji, M. A.; Nozari, K.; Vakili, B.

    2014-04-01

    Inspired by quantum gravity proposals, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for the natural realization of inflation as a phase transition from the quantum gravity regime to the standard radiation dominated era. Also, we obtain finite energy and entropy densities for the Universe when at least the weak energy condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the big bang singularity is removed.

  8. Pre-service elementary science teaching self-efficacy and teaching practices: A mixed-methods, dual-phase, embedded case study

    NASA Astrophysics Data System (ADS)

    Sangueza, Cheryl Ramirez

    This mixed-method, dual-phase, embedded-case study employed the Social Cognitive Theory and the construct of self-efficacy to examine the contributors to science teaching self-efficacy and science teaching practices across different levels of efficacy in six pre-service elementary teachers during their science methods course and student teaching experiences. Data sources included the Science Teaching Efficacy Belief Instrument (STEBI-B) for pre-service teachers, questionnaires, journals, reflections, student teaching lesson observations, and lesson debriefing notes. Results from the STEBI-B show that all participants measured an increase in efficacy throughout the study. The ANOVA analysis of the STEBI-B revealed a statistically significant increase in level of efficacy during methods course, student teaching, and from the beginning of the study to the end. Of interest in this study was the examination of the participants' science teaching practices across different levels of efficacy. Results of this analysis revealed how the pre-service elementary teachers in this study contextualized their experiences in learning to teach science and its influences on their science teaching practices. Key implications involves the value in exploring how pre-service teachers interpret their learning to teach experiences and how their interpretations influence the development of their science teaching practices.

  9. Spacetime Singularities in Quantum Gravity

    NASA Astrophysics Data System (ADS)

    Minassian, Eric A.

    2000-04-01

    Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.

  10. Computing singularities of perturbation series

    NASA Astrophysics Data System (ADS)

    Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

    2011-03-01

    Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schrödinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be useful for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with δ-function interactions for which Møller-Plesset perturbation theory is considered and the radius of convergence found.

  11. Spiral-like singular beams in gyrotropic crystals

    NASA Astrophysics Data System (ADS)

    Rubass, A.; Fadeyeva, T.; Egorov, Yu.; Shvedov, V.; Volyar, A.; Desyatnikov, A.; Kivshar, Yu.

    2006-05-01

    Recent developments in solving a paraxial wave equation1 open new perspectives in theoretical analysis of different types of singular beams stimulating in turn a great series of experimental investigations 2,3. In particular, authors of Ref. 4 propose to use pure phase masks for creating a structurally stable helico-conical singular beam with spiral-like intensity distribution. On the other hand, artificial phase masks need a great precision in their manufacturing connected with a large industrial outlay. Because of a great interest is to use natural objects for generating singularities in beams. Such objects are anisotropic crystals. As is well-known, uniaxial and biaxial crystals serve as basic elements for generating optical vortices nested in different types of singular beams 5. The most amazing feature of the crystal is ability to create stable polychromatic vortices with high energy effectiveness. In contrast to the method of computer-generated holograms 6'7 the crystal forms a white vortex-bearing beam without any additional gadgets. The aim of the present article is to consider one more way permitting to generate singular beams bearing spiral edge dislocations and optical vortices with the help of two gyrotropic crystals.

  12. Compression embedding

    DOEpatents

    Sandford, II, Maxwell T.; Handel, Theodore G.; Bradley, Jonathan N.

    1998-01-01

    A method and apparatus for embedding auxiliary information into the digital representation of host data created by a lossy compression technique and a method and apparatus for constructing auxiliary data from the correspondence between values in a digital key-pair table with integer index values existing in a representation of host data created by a lossy compression technique. The methods apply to data compressed with algorithms based on series expansion, quantization to a finite number of symbols, and entropy coding. Lossy compression methods represent the original data as ordered sequences of blocks containing integer indices having redundancy and uncertainty of value by one unit, allowing indices which are adjacent in value to be manipulated to encode auxiliary data. Also included is a method to improve the efficiency of lossy compression algorithms by embedding white noise into the integer indices. Lossy compression methods use loss-less compression to reduce to the final size the intermediate representation as indices. The efficiency of the loss-less compression, known also as entropy coding compression, is increased by manipulating the indices at the intermediate stage. Manipulation of the intermediate representation improves lossy compression performance by 1 to 10%.

  13. Compression embedding

    DOEpatents

    Sandford, M.T. II; Handel, T.G.; Bradley, J.N.

    1998-07-07

    A method and apparatus for embedding auxiliary information into the digital representation of host data created by a lossy compression technique and a method and apparatus for constructing auxiliary data from the correspondence between values in a digital key-pair table with integer index values existing in a representation of host data created by a lossy compression technique are disclosed. The methods apply to data compressed with algorithms based on series expansion, quantization to a finite number of symbols, and entropy coding. Lossy compression methods represent the original data as ordered sequences of blocks containing integer indices having redundancy and uncertainty of value by one unit, allowing indices which are adjacent in value to be manipulated to encode auxiliary data. Also included is a method to improve the efficiency of lossy compression algorithms by embedding white noise into the integer indices. Lossy compression methods use loss-less compression to reduce to the final size the intermediate representation as indices. The efficiency of the loss-less compression, known also as entropy coding compression, is increased by manipulating the indices at the intermediate stage. Manipulation of the intermediate representation improves lossy compression performance by 1 to 10%. 21 figs.

  14. Naked singularities as particle accelerators

    SciTech Connect

    Patil, Mandar; Joshi, Pankaj S.

    2010-11-15

    We investigate here the particle acceleration by naked singularities to arbitrarily high center of mass energies. Recently it has been suggested that black holes could be used as particle accelerators to probe the Planck scale physics. We show that the naked singularities serve the same purpose and probably would do better than their black hole counterparts. We focus on the scenario of a self-similar gravitational collapse starting from a regular initial data, leading to the formation of a globally naked singularity. It is seen that when particles moving along timelike geodesics interact and collide near the Cauchy horizon, the energy of collision in the center of mass frame will be arbitrarily high, thus offering a window to Planck scale physics.

  15. Singular Spectrum Analysis in Astrometry and Geodynamics

    NASA Astrophysics Data System (ADS)

    Vityazev, V. V.; Miller, N. O.; Prudnikova, E. Ja.

    2010-10-01

    The paper presents the possibilities of the Singular Spectrum Analyses on the examples of its application to several astrometric and geodynamic time series. The comparisons of results obtained by other often used methods (Fourier transform, Wavelet Transform, different filter methods) are given. The Singular Spectrum Analyses method was used for the investigation of the Chandler wobble (CW), which was extracted from the IERS Pole coordinates and latitude variations at Pulkovo. The CW amplitude and phase variations were examined by means of the Hilbert transform. The main conclusion which can be made from this study is: we have found two epochs of deep CW amplitude decreases near 1850 and 2005, which are also accompanied by a large phase jump, similar to well known event in 1920s. The investigation of first latitude observations at Pulkovo (1840-1855) was executed with the aim to gain and analyse the sum of Chandler and annual components from very small quantity of very noisy observations. The SSA is applied for investigation of the zenith troposphere delay time-series derived from observations of several VLBI stations. Combined IVS time-series of the zenith wet and total troposphere delays obtained in IGG were used for analysis. For all stations under consideration the non-linear trends and the seasonal components with annual and semiannual periods were found. Some interesting peculiarities were found to be individual for every stations. Comparison of the trends with meteorological parameters is also presented.

  16. Cavity-controlled spectral singularity.

    PubMed

    Nireekshan Reddy, K; Dutta Gupta, S

    2014-08-01

    We study theoretically a parity-time (PT)-symmetric, saturable, balanced gain-loss system in a ring-cavity configuration. The saturable gain and loss are modeled by a two-level medium with or without population inversion. We show that the specifics of the spectral singularity can be fully controlled by the cavity and the atomic detuning parameters. The theory is based on the mean-field approximation, as in the standard theory of optical bistability. Further, in the linear regime we demonstrate the regularization of the singularity in detuned systems, while larger input power levels are shown to be adequate to limit the infinite growth in absence of detunings.

  17. Algebraic Singularity Method for Mass Measurements with Missing Energy

    SciTech Connect

    Kim, Ian-Woo

    2010-02-26

    We propose a novel generalized method for mass measurements based on phase space singularity structures that can be applied to any event topology with missing energy. Our method subsumes the well-known end point and transverse mass methods and yields new techniques for studying 'missing particle' events, such as the double chain production of stable neutral particles at the LHC.

  18. Ranging With Electromagnetic Singularities

    DTIC Science & Technology

    2008-04-01

    spatially filtered by a 10-μm-diameter pinhole and expanded using an inverse Kepler telescope . The Gaussian beam diverging from the pinhole is...to be construed as an official Department of the Army position unless so designated by other authorized documents. Citation of manufacturer’s or...imposes an amplitude null on an incoming beam. Since the spatial phase is a function of angular position to the optic axis, as the beam propagates

  19. The chemistry of episodic accretion in embedded objects. 2D radiation thermo-chemical models of the post-burst phase

    NASA Astrophysics Data System (ADS)

    Rab, Ch.; Elbakyan, V.; Vorobyov, E.; Güdel, M.; Dionatos, O.; Audard, M.; Kamp, I.; Thi, W.-F.; Woitke, P.; Postel, A.

    2017-07-01

    Context. Episodic accretion is an important process in the evolution of young stars and their environment. The observed strong luminosity bursts of young stellar objects likely have a long lasting (i.e. longer than the burst duration) impact on the chemical evolution of the disk and envelope of young stars. Aims: We aim to investigate the observational signatures of the chemical evolution in the post-burst phase for embedded sources. With such signatures it is possible to identify targets that experienced a recent luminosity burst. Methods: We present a new model for the chemistry of episodic accretion based on the two dimensional, radiation thermo-chemical disk code PRODIMO (PROtoplanetary DIsk MOdel). We have extended PRODIMO with a proper treatment for envelope structures. For a representative Class I model, we calculated the chemical abundances in the post-burst phase and produced synthetic observables such as intensity maps and radial intensity profiles. Results: During a burst, many chemical species, such as CO, sublimate from the dust surfaces. As the burst ends they freeze out again (post-burst phase). This freeze-out happens from inside-out due to the radial density gradient in the disk and envelope structure. This inside-out freeze-out produces clear observational signatures in spectral line emission, such as rings and distinct features in the slope of radial intensity profiles. We fitted synthetic C18O J = 2-1 observations with single and two component fits and find that post-burst images are much better matched by the latter. Comparing the quality of such fits therefore allows identification of post-burst targets in a model-independent way. Conclusions: Our models confirm that it is possible to identify post-burst objects from spatially resolved CO observations. However, to derive proper statistics, such as the strength and frequencies of bursts, from observations it is important to consider the inclination and structure of the target and dust

  20. Optimal singular control for nonlinear semistabilisation

    NASA Astrophysics Data System (ADS)

    L'Afflitto, Andrea; Haddad, Wassim M.

    2016-06-01

    The singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton-Jacobi-Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.

  1. The 1965 Penrose singularity theorem

    NASA Astrophysics Data System (ADS)

    Senovilla, José M. M.; Garfinkle, David

    2015-06-01

    We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of the closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belongs to its legacy.

  2. Specialty functions singularity mechanics problems

    NASA Technical Reports Server (NTRS)

    Sarigul, Nesrin

    1989-01-01

    The focus is in the development of more accurate and efficient advanced methods for solution of singular problems encountered in mechanics. At present, finite element methods in conjunction with special functions, boolean sum and blending interpolations are being considered. In dealing with systems which contain a singularity, special finite elements are being formulated to be used in singular regions. Further, special transition elements are being formulated to couple the special element to the mesh that models the rest of the system, and to be used in conjunction with 1-D, 2-D and 3-D elements within the same mesh. Computational simulation with a least squares fit is being utilized to construct special elements, if there is an unknown singularity in the system. A novel approach is taken in formulation of the elements in that: (1) the material properties are modified to include time, temperature, coordinate and stress dependant behavior within the element; (2) material properties vary at nodal points of the elements; (3) a hidden-symbolic computation scheme is developed and utilized in formulating the elements; and (4) special functions and boolean sum are utilized in order to interpolate the field variables and their derivatives along the boundary of the elements. It may be noted that the proposed methods are also applicable to fluids and coupled problems.

  3. Singularly Perturbed Lie Bracket Approximation

    SciTech Connect

    Durr, Hans-Bernd; Krstic, Miroslav; Scheinker, Alexander; Ebenbauer, Christian

    2015-03-27

    Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.

  4. Removable singularities of holomorphic functions

    NASA Astrophysics Data System (ADS)

    Chirka, E. M.

    2016-09-01

    Several sufficient conditions for the removability of singular sets with area zero are obtained for holomorphic functions in plane domains and on Riemann surfaces, under certain metric and topological assumptions about cluster sets of these functions and the limit sets of their graphs. Bibliography: 14 titles.

  5. Showtime: An Analysis of the Embedded News Media Program During the Pre-Combat and the Combat Phases of Operation Iraqi Freedom

    DTIC Science & Technology

    2005-05-26

    Network . 50 Margaret Belknap, The CNN Effect, p. 7. 51 General (Ret) Colin Powell with Joseph Perisco, My American Journey (New York: Random House...Enduring Freedom, helped blaze the path for a large-scale, embedded media program in Operation Iraqi Freedom. Reeder inferred that when journalists were...that needs an answer. Did the networks and publics from countries other than the United States welcome the reports of embedded media? And, were the

  6. Singularities from colliding plane gravitational waves

    NASA Astrophysics Data System (ADS)

    Tipler, Frank J.

    1980-12-01

    A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.

  7. Numerical simulations of stiff fluid gravitational singularities

    SciTech Connect

    Curtis, Joshua; Garfinkle, David

    2005-09-15

    Numerical simulations of the approach to the singularity in spacetimes with stiff fluid matter are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities in the presence of such matter. It is found that the singularity is spacelike and that as it is approached, the spacetime dynamics becomes local and nonoscillatory.

  8. Geodesic behavior of sudden future singularities

    SciTech Connect

    Fernandez-Jambrina, L.; Lazkoz, Ruth

    2004-12-15

    In this paper we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although tidal forces are not strong enough to produce a Big Rip. For the sake of completeness, we compare with the typical sudden future singularities of phantom cosmologies.

  9. G 2-Monopoles with Singularities (Examples)

    NASA Astrophysics Data System (ADS)

    Oliveira, Goncalo

    2016-11-01

    G 2-Monopoles are solutions to gauge theoretical equations on G 2-manifolds. If the G 2-manifolds under consideration are compact, then any irreducible G 2-monopole must have singularities. It is then important to understand which kind of singularities G 2-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.

  10. Splash singularity for water waves.

    PubMed

    Castro, Angel; Córdoba, Diego; Fefferman, Charles L; Gancedo, Francisco; Gómez-Serrano, Javier

    2012-01-17

    We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.

  11. Shadow of a naked singularity

    NASA Astrophysics Data System (ADS)

    Ortiz, Néstor; Sarbach, Olivier; Zannias, Thomas

    2015-08-01

    We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud, and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observer's eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.

  12. Quantum propagation across cosmological singularities

    NASA Astrophysics Data System (ADS)

    Gielen, Steffen; Turok, Neil

    2017-05-01

    The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

  13. Singular 7-manifolds with G2 holonomy and intersecting 6-branes

    NASA Astrophysics Data System (ADS)

    Behrndt, Klaus

    2002-07-01

    A 7-manifold with G2 holonomy can be constructed as a R3 bundle over a quaternionic space. We consider a quaternionic base space which is singular and its metric depends on three parameters, where one of them corresponds to an interpolation between S4 and CP 2 or its non-compact analogs. This 4d Einstein space has four isometries and the fixed point set of a generic Killing vector is discussed. When embedded into M-theory the compactification over a given Killing vector gives intersecting 6-branes as IIA configuration and we argue that membrane instantons may resolve the curvature singularity.

  14. Energy conditions of non-singular black hole spacetimes in conformal gravity

    NASA Astrophysics Data System (ADS)

    Toshmatov, Bobir; Bambi, Cosimo; Ahmedov, Bobomurat; Abdujabbarov, Ahmadjon; Stuchlík, Zdeněk

    2017-08-01

    Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase.

  15. Topological resolution of gauge theory singularities

    SciTech Connect

    Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

    2013-08-21

    Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

  16. Large-scale sparse singular value computations

    NASA Technical Reports Server (NTRS)

    Berry, Michael W.

    1992-01-01

    Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.

  17. Conformal anomaly around the sudden singularity

    NASA Astrophysics Data System (ADS)

    Houndjo, S. J. M.

    2010-10-01

    Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be p=-ρ-Aρα, the conformal anomaly can transform the sudden singularity into the singularity of type III for any α>1/2 and into the singularity of the type I (the big rip) or the big crunch for 1/2<α<3/2.

  18. Multichannel framework for singular quantum mechanics

    SciTech Connect

    Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.

    2014-01-15

    A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.

  19. The geometry of warped product singularities

    NASA Astrophysics Data System (ADS)

    Stoica, Ovidiu Cristinel

    In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

  20. Geometrically induced singular behavior of entanglement

    NASA Astrophysics Data System (ADS)

    Cavalcanti, D.; Saldanha, P. L.; Cosme, O.; Brandão, F. G. S. L.; Monken, C. H.; Pádua, S.; Santos, M. França; Cunha, M. O. Terra

    2008-07-01

    We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically, it is shown that singular points at the border of the set of unentangled states originate singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down-conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.

  1. Singularity analysis: theory and further developments

    NASA Astrophysics Data System (ADS)

    Cheng, Qiuming

    2015-04-01

    Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.

  2. Understanding singularities — Classical and quantum

    NASA Astrophysics Data System (ADS)

    Konkowski, Deborah A.; Helliwell, Thomas M.

    2016-01-01

    The definitions of classical and quantum singularities are reviewed. Examples are given of both as well as their utility in general relativity. In particular, the classical and quantum singularity structure of certain interesting conformally static spherically symmetric spacetimes modeling scalar field collapse are reviewed. The spacetimes include the Roberts spacetime, the Husain-Martinez-Nuñez spacetime and the Fonarev spacetime. The importance of understanding spacetime singularity structure is discussed.

  3. Singular Perturbation for Discontinuous Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

    Teixeira, M. A.; da Silva, P. R.

    In this article some qualitative aspects of non-smooth systems on ℝn are studied through methods of Geometric Singular Perturbation Theory (GSP-Theory). We present some results that generalize some settings in low dimension, that bridge the space between such systems and singularly perturbed smooth systems. We analyze the local behavior around typical singularities and prove that the dynamics of the so called Sliding Vector Field is determined by the reduced problem on the center manifold.

  4. Quantum dress for a naked singularity

    NASA Astrophysics Data System (ADS)

    Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge

    2016-09-01

    We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2 + 1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak) cosmic censorship.

  5. Overcoming Robot-Arm Joint Singularities

    NASA Technical Reports Server (NTRS)

    Barker, L. K.; Houck, J. A.

    1986-01-01

    Kinematic equations allow arm to pass smoothly through singular region. Report discusses mathematical singularities in equations of robotarm control. Operator commands robot arm to move in direction relative to its own axis system by specifying velocity in that direction. Velocity command then resolved into individual-joint rotational velocities in robot arm to effect motion. However, usual resolved-rate equations become singular when robot arm is straightened.

  6. Exact solutions and singularities in string theory

    SciTech Connect

    Horowitz, G.T. ); Tseytlin, A.A. )

    1994-10-15

    We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail.

  7. Acceleration of Dominant Supermassive Black Hole Singularities Serving as the Catalyst of Dark Energy in the Formation of Universes

    NASA Astrophysics Data System (ADS)

    Wilson, John

    2013-04-01

    Cosmological process analysis is used to develop the singularity acceleration hypothesis which is based on nine universe formation axioms. Singularity acceleration universe formation is a cyclic process analogous to a branching universe having the following seven phases reoccurring in each daughter universe: 1. A phase transition big bang that forms a new universe 2. Expansion of the new universe and its structure 3. Dispersion of its mass and increasing entropy 4. Isolation of its galaxy clusters and supercluster complexes beyond event horizons 5. Many separate consolidations of all forms of matter, forces, and energy within these supercluster complexes into dominant supermassive black hole gravitational singularities 6. The resulting acceleration of singularities warping space to the speed of light 7. The independent separation of each of these singularities from the universe causing a big bang phase transition and producing all forms of matter, forces, and energy in a new universe.

  8. Plasmonic resonance scattering from silver nanowire illuminated by tightly focused singular beam.

    PubMed

    Normatov, Alexander; Spektor, Boris; Leviatan, Yehuda; Shamir, Joseph

    2010-08-15

    We investigate scattering features of tightly focused singular beams by placing a cylindrical nanowire in the vicinity of a line phase singularity. Applying an illumination wavelength corresponding to silver cylinder plasmonic resonance, we compare the scattering response with that of a perfect conductor. The rigorous modeling employs a 2D version of the Richards-Wolf focusing method and the source model technique. It is found that a cylinder with a plasmonic resonance produces a strong scattering response by deflecting the power flow toward the optical singularity region, where otherwise the power approaches zero.

  9. Accurate Feeding of Nanoantenna by Singular Optics for Nanoscale Translational and Rotational Displacement Sensing

    NASA Astrophysics Data System (ADS)

    Xi, Zheng; Wei, Lei; Adam, A. J. L.; Urbach, H. P.; Du, Luping

    2016-09-01

    Identifying subwavelength objects and displacements is of crucial importance in optical nanometrology. We show in this Letter that nanoantennas with subwavelength structures can be excited precisely by incident beams with singularity. This accurate feeding beyond the diffraction limit can lead to dynamic control of the unidirectional scattering in the far field. The combination of the field discontinuity of the incoming singular beam with the rapid phase variation near the antenna leads to remarkable sensitivity of the far-field scattering to the displacement at a scale much smaller than the wavelength. This Letter introduces a far-field deep subwavelength position detection method based on the interaction of singular optics with nanoantennas.

  10. On local invariants of singular symplectic forms

    NASA Astrophysics Data System (ADS)

    Domitrz, Wojciech

    2017-04-01

    We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.

  11. On the spatial distribution of fingerprint singularities.

    PubMed

    Cappelli, Raffaele; Maltoni, Davide

    2009-04-01

    Fingerprint singularities play an important role in several fingerprint recognition and classification systems. Although some general relationships and constraints about the location of singularities in the different fingerprint classes are well known, to the best of our knowledge no statistical models have been developed until now. This paper studies the spatial distributions of singularity locations in nature and derives, from a representative dataset of labelled samples, the probability density functions of the four main fingerprint classes. The results obtained can be directly exploited to improve the accuracy of many techniques relying on the position of singularities, as confirmed by the results of two experiments on fingerprint classification and synthesis.

  12. Naked singularities and quantum gravity

    SciTech Connect

    Harada, Tomohiro; Iguchi, Hideo; Nakao, Ken-ichi; Singh, T. P.; Tanaka, Takahiro; Vaz, Cenalo

    2001-08-15

    There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e., quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches the Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state.

  13. Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect

    NASA Astrophysics Data System (ADS)

    Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang

    2014-05-01

    The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.

  14. Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect.

    PubMed

    Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang

    2014-05-02

    The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.

  15. The Semantics of Plurals: A Defense of Singularism

    ERIC Educational Resources Information Center

    Florio, Salvatore

    2010-01-01

    In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…

  16. Discrete wavelet transform and singular value decomposition based ECG steganography for secured patient information transmission.

    PubMed

    Edward Jero, S; Ramu, Palaniappan; Ramakrishnan, S

    2014-10-01

    ECG Steganography provides secured transmission of secret information such as patient personal information through ECG signals. This paper proposes an approach that uses discrete wavelet transform to decompose signals and singular value decomposition (SVD) to embed the secret information into the decomposed ECG signal. The novelty of the proposed method is to embed the watermark using SVD into the two dimensional (2D) ECG image. The embedding of secret information in a selected sub band of the decomposed ECG is achieved by replacing the singular values of the decomposed cover image by the singular values of the secret data. The performance assessment of the proposed approach allows understanding the suitable sub-band to hide secret data and the signal degradation that will affect diagnosability. Performance is measured using metrics like Kullback-Leibler divergence (KL), percentage residual difference (PRD), peak signal to noise ratio (PSNR) and bit error rate (BER). A dynamic location selection approach for embedding the singular values is also discussed. The proposed approach is demonstrated on a MIT-BIH database and the observations validate that HH is the ideal sub-band to hide data. It is also observed that the signal degradation (less than 0.6%) is very less in the proposed approach even with the secret data being as large as the sub band size. So, it does not affect the diagnosability and is reliable to transmit patient information.

  17. Strehl ratio: a tool for optimizing optical nulls and singularities.

    PubMed

    Hénault, François

    2015-07-01

    In this paper a set of radial and azimuthal phase functions are reviewed that have a null Strehl ratio, which is equivalent to generating a central extinction in the image plane of an optical system. The study is conducted in the framework of Fraunhofer scalar diffraction, and is oriented toward practical cases where optical nulls or singularities are produced by deformable mirrors or phase plates. The identified solutions reveal unexpected links with the zeros of type-J Bessel functions of integer order. They include linear azimuthal phase ramps giving birth to an optical vortex, azimuthally modulated phase functions, and circular phase gratings (CPGs). It is found in particular that the CPG radiometric efficiency could be significantly improved by the null Strehl ratio condition. Simple design rules for rescaling and combining the different phase functions are also defined. Finally, the described analytical solutions could also serve as starting points for an automated searching software tool.

  18. Regularizing cosmological singularities by varying physical constants

    SciTech Connect

    Dąbrowski, Mariusz P.; Marosek, Konrad E-mail: k.marosek@wmf.univ.szczecin.pl

    2013-02-01

    Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the Λ-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.

  19. An extension theorem for conformal gauge singularities

    NASA Astrophysics Data System (ADS)

    Lübbe, Christian; Tod, Paul

    2009-11-01

    We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.

  20. Secure Embedded Systems

    DTIC Science & Technology

    2016-02-26

    computing. An embedded computer system is designed for a dedicated function, in contrast to a general-purpose computer system , e.g., a desktop... embedded system is challenging because security requirements are rarely accurately identified at the start of the design process, and embedded ...architecture that will seamlessly work with various OSA components is a challenge. 3    Design Process (heading level 1) Embedded system CONOPS are

  1. Discrete singular convolution mapping methods for solving singular boundary value and boundary layer problems

    NASA Astrophysics Data System (ADS)

    Pindza, Edson; Maré, Eben

    2017-03-01

    A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions. The obtained results from discrete singular convolution methods based on single and double exponential transformations are compared with each other, and with the existing methods too. Numerical results confirm that these methods are considerably efficient and accurate in solving singular and regular problems. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.

  2. Tuning Li-Ion Diffusion in α-LiMn1-xFexPO4 Nanocrystals by Antisite Defects and Embedded β-Phase for Advanced Li-Ion Batteries.

    PubMed

    Hu, Jiangtao; Xiao, Yinguo; Tang, Hanting; Wang, Hongbin; Wang, Ziqi; Liu, Chaokun; Zeng, Hua; Huang, Qingzhen; Ren, Yang; Wang, Chongmin; Zhang, Wei; Pan, Feng

    2017-08-09

    Olivine-structured LiMn1-xFexPO4 has become a promising candidate for cathode materials owing to its higher working voltage of 4.1 V and thus larger energy density than that of LiFePO4, which has been used for electric vehicles batteries with the advantage of high safety but disadvantage of low energy density due to its lower working voltage of 3.4 V. One drawback of LiMn1-xFexPO4 electrode is its relatively low electronic and Li-ionic conductivity with Li-ion one-dimensional diffusion. Herein, olivine-structured α-LiMn0.5Fe0.5PO4 nanocrystals were synthesized with optimized Li-ion diffusion channels in LiMn1-xFexPO4 nanocrystals by inducing high concentrations of Fe(2+)-Li(+) antisite defects, which showed impressive capacity improvements of approaching 162, 127, 73, and 55 mAh g(-1) at 0.1, 10, 50, and 100 C, respectively, and a long-term cycling stability of maintaining about 74% capacity after 1000 cycles at 10 C. By using high-resolution transmission electron microscopy imaging and joint refinement of hard X-ray and neutron powder diffraction patterns, we revealed that the extraordinary high-rate performance could be achieved by suppressing the formation of electrochemically inactive phase (β-LiMn1-xFexPO4, which is first reported in this work) embedded in α-LiMn0.5Fe0.5PO4. Because of the coherent orientation relationship between β- and α-phases, the β-phase embedded would impede the Li(+) diffusion along the [100] and/or [001] directions that was activated by the high density of Fe(2+)-Li(+) antisite (4.24%) in α-phase. Thus, by optimizing concentrations of Fe(2+)-Li(+) antisite defects and suppressing β-phase-embedded olivine structure, Li-ion diffusion properties in LiMn1-xFexPO4 nanocrystals can be tuned by generating new Li(+) tunneling. These findings may provide insights into the design and generation of other advanced electrode materials with improved rate performance.

  3. Singularity analysis and robust neighborhood statistics

    NASA Astrophysics Data System (ADS)

    Zuo, Renguang

    2015-04-01

    Neighborhood statistics involving data within small neighborhoods have the advantages of revealing more detailed local structures and spatial variations of spatial patterns, and provide less biased information compared with global statistics. However, the resulting neighborhood statistics are influenced by the size of neighborhood. Singularity analysis can be regarded as a type of robust neighborhood statistics. It measures the gradient of relative change within small neighborhoods. The value of singularity index at a location of z rarely relies on the element concentration at that location, but depends on the changes around z. From the multifractal theory viewpoint, the singularity index is independent of the size of neighborhood. Singularity analysis is a powerful tool to identify geochemical and geophysical anomalies in mineral exploration. Recent studies demonstrated singularity analysis can well detect the weak geochemical anomalies related to mineralization due to decaying and masking effects of covers.

  4. Singularity: Scientific containers for mobility of compute.

    PubMed

    Kurtzer, Gregory M; Sochat, Vanessa; Bauer, Michael W

    2017-01-01

    Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and software engineers and researchers alike, and integrates seamlessly into common workflows for both of these groups. As its primary use case, Singularity brings mobility of computing to both users and HPC centers, providing a secure means to capture and distribute software and compute environments. This ability to create and deploy reproducible environments across these centers, a previously unmet need, makes Singularity a game changing development for computational science.

  5. Naked shell singularities on the brane

    SciTech Connect

    Seahra, Sanjeev S.

    2005-04-15

    By utilizing nonstandard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically-symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exotic equation of state and a pressure singularity where the brane crosses the bulk horizon. From a relativistic point of view, such a singularity is required to maintain matter infinitesimally above the surface of a black hole. From the point of view of the AdS/CFT conjecture, the singular horizon can be seen as one possible quantum correction to a classical black hole geometry. Various generalizations of planar slicings are also considered for a Ricci-flat bulk, and we find that singular horizons and exotic matter distributions are common features.

  6. Singular value decomposition with systolic arrays

    NASA Technical Reports Server (NTRS)

    Ipsen, I. C. F.

    1984-01-01

    Systolic arrays for determining the singular value decomposition of a mxn, m n, matrix A of bandwidth w are presented. After A has been reduced to bidiagonal form B by means of Givens plane rotations, the singular values of B are computed by the Golub-Reinsch iteration. The products of plane rotations form the matrices of left and right singular vectors. Assuming each processor can compute or supply a plane rotation, O(wn) processors accomplish the reduction to bidiagonal form in O(np) steps, where p is the number of superdiagonals. A constant number of processors then determines each singular value in about 6n steps. The singular vectors are computed by rerouting the rotations through the arrays used for the reduction to bidiagonal form, or else along the way by employing another rectangular array of O(wm) processors.

  7. Singularities and conjugate points in FLRW spacetimes

    NASA Astrophysics Data System (ADS)

    het Lam, Huibert; Prokopec, Tomislav

    2017-10-01

    Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a theorem that when a non-comoving, non-spacelike geodesic in a singular FLRW spacetime obeys conditions (39) and (40), every point on that geodesic is part of a pair of conjugate points. The proof is based on the Raychaudhuri equation. We find that the theorem is applicable to all non-comoving, non-spacelike geodesics in FLRW spacetimes with non-negative spatial curvature and scale factors that near the singularity have power law behavior or power law behavior times a logarithm. When the spatial curvature is negative, the theorem is applicable to a subset of these spacetimes.

  8. Singularities affect dynamics of learning in neuromanifolds.

    PubMed

    Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko

    2006-05-01

    The parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units. A parameter space forms a geometrical manifold, called the neuromanifold in the case of neural networks. Such a model is identified with a statistical model, and a Riemannian metric is given by the Fisher information matrix. However, the matrix degenerates at singularities. Such a singular structure is ubiquitous not only in multilayer perceptrons but also in the gaussian mixture probability densities, ARMA time-series model, and many other cases. The standard statistical paradigm of the Cramér-Rao theorem does not hold, and the singularity gives rise to strange behaviors in parameter estimation, hypothesis testing, Bayesian inference, model selection, and in particular, the dynamics of learning from examples. Prevailing theories so far have not paid much attention to the problem caused by singularity, relying only on ordinary statistical theories developed for regular (nonsingular) models. Only recently have researchers remarked on the effects of singularity, and theories are now being developed. This article gives an overview of the phenomena caused by the singularities of statistical manifolds related to multilayer perceptrons and gaussian mixtures. We demonstrate our recent results on these problems. Simple toy models are also used to show explicit solutions. We explain that the maximum likelihood estimator is no longer subject to the gaussian distribution even asymptotically, because the Fisher information matrix degenerates, that the model selection criteria such as AIC, BIC, and MDL fail to hold in these models, that a smooth Bayesian prior becomes singular in such models, and that the trajectories of dynamics of learning are strongly affected by the singularity, causing plateaus or slow manifolds in the parameter space. The natural gradient method is shown to perform well because it takes the singular

  9. Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii

    USGS Publications Warehouse

    Shaw, H.R.; Chouet, B.

    1989-01-01

    Fractal singularity analysis (FSA) is used to study a 22-yr record of deep seismic tremor (30-60 km depth) for regions below Kilauea Volcano on the assumption that magma transport and fracture can be treated as a system of coupled nonlinear oscillators. Tremor episodes range from 1 to 100 min (cumulative duration = 1.60 ?? 104 min; yearly average - 727 min yr-1; mean gradient = 24.2 min yr-1km-1). Partitioning of probabilities, Pi, in the phase space of normalized durations, xi, are expressed in terms of a function f(??), where ?? is a variable exponent of a length scale, l. Plots of f(??) vs. ?? are called multifractal singularity spectra. The spectrum for deep tremor durations is bounded by ?? values of about 0.4 and 1.9 at f = O; fmax ???1.0 for ?? ??? 1. Results for tremor are similar to those found for systems transitional between complete mode locking and chaos. -Authors

  10. Approximate Orthogonal Sparse Embedding for Dimensionality Reduction.

    PubMed

    Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Yang, Jian; Zhang, David

    2016-04-01

    Locally linear embedding (LLE) is one of the most well-known manifold learning methods. As the representative linear extension of LLE, orthogonal neighborhood preserving projection (ONPP) has attracted widespread attention in the field of dimensionality reduction. In this paper, a unified sparse learning framework is proposed by introducing the sparsity or L1-norm learning, which further extends the LLE-based methods to sparse cases. Theoretical connections between the ONPP and the proposed sparse linear embedding are discovered. The optimal sparse embeddings derived from the proposed framework can be computed by iterating the modified elastic net and singular value decomposition. We also show that the proposed model can be viewed as a general model for sparse linear and nonlinear (kernel) subspace learning. Based on this general model, sparse kernel embedding is also proposed for nonlinear sparse feature extraction. Extensive experiments on five databases demonstrate that the proposed sparse learning framework performs better than the existing subspace learning algorithm, particularly in the cases of small sample sizes.

  11. Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

    NASA Technical Reports Server (NTRS)

    Sidi, A.; Israeli, M.

    1986-01-01

    High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

  12. Embedding DNA in surfactant mesophases: the phase diagram of the ternary system dodecyltrimethylammonium-DNA/monoolein/water in comparison to the DNA-free analogue.

    PubMed

    Bilalov, Azat; Elsing, Jonas; Haas, Eva; Schmidt, Claudia; Olsson, Ulf

    2013-03-15

    The self-assembly of a true ternary mixture comprising an electroneutral complex of DNA anions and surfactant cations (dodecyltrimethylammonium cations, DTA), water, and nonionic surfactant (monoolein, MO) has been studied. The phase diagrams of two systems, DTA-DNA/MO/water and, for comparison, dodecyltrimethylammonium bromide (DTAB)/MO/water, were obtained by visual inspection, microscopic examination under polarized light, small-angle X-ray scattering (SAXS) and deuterium NMR ((2)H NMR) at 298 K and normal pressure. The isothermal phase diagram of the DTA-DNA/MO/water system contains four liquid crystalline (LC) phase regions (reversed hexagonal, Pn3m, Ia3d, lamellar). The supramolecular assemblies evolve from a bicontinuous cubic structure of the reversed type to the two-dimensional hexagonal phase as the content of DTA-DNA is increased. While DTA-DNA tends to form a reversed hexagonal phase, DTAB is incorporated into the existing lamellar phase formed by MO and water giving rise to swelling and to significant extension of the lamellar phase region. There is only a small tendency of the cubic phases existing in the binary system MO/water to accommodate DTAB or DTA-DNA.

  13. The structure of the classical cosmological singularity

    NASA Astrophysics Data System (ADS)

    Tipler, Frank J.

    The existence of an all-encompassing initial classical cosmological singularity is established: it is shown that if: (1) global hyperbolicity, (2) the timelike convergence condition, and (3) all past-directed nonspacelike geodesics start to reconverge within a compact region in the causal past of the present-day earth, then all timelike curves in the past have a finite proper time length less than a universal constant L. It is argued that an analogue of this predicted cosmological singularity should exist even when quantum effects are taken into account. In particular, in a closed Friedmann radiation-filled universe quantized via the ADM method, the R = 0 singularity still exists and influences wave packet evolution at all times. Furthermore, quantum effects can in most cases eliminate curvature singularities only by introducing singularities in the universal action; most classical closed universes have finite action if and only if they begin and end in curvature singularities. Finally, the two basic ways of studying the structure of cosmological singularities are reviewed: completion methods (e.g., the c-boundary construction), and approach methods (e.g., analyzing metric behavior in a synchronous coordinate system).

  14. Three-dimensional singular points in aerodynamics

    NASA Technical Reports Server (NTRS)

    Unal, Aynur

    1988-01-01

    When three-dimensional separation occurs on a body immersed in a flow governed by the incompressible Navier-Stokes equations, the geometrical surfaces formed by the three vector fields (velocity, vorticity and the skin-friction) and a scalar field (pressure) become interrelated through topological maps containing their respective singular points and extremal points. A mathematically consistent description of these singular points becomes inevitable when we want to study the geometry of the separation. A separated stream surface requires, for example, the existence of a saddle-type singular point on the skin-friction surface. This singular point is actually, in the proper language of mathematics, a saddle of index two. The index is a measure of the dimension of the outset (set leaving the singular point). Hence, when a saddle of index two is specified, a two dimensional surface that becomes separated from the osculating plane of the saddle is implied. The three-dimensional singular point is interpreted mathematically and the most common aerodynamical singular points are discussed through this perspective.

  15. Potential singularity mechanism for the Euler equations

    NASA Astrophysics Data System (ADS)

    Brenner, Michael P.; Hormoz, Sahand; Pumir, Alain

    2016-12-01

    Singular solutions to the Euler equations could provide essential insight into the formation of very small scales in highly turbulent flows. Previous attempts to find singular flow structures have proven inconclusive. We reconsider the problem of interacting vortex tubes, for which it has long been observed that the flattening of the vortices inhibits sustained self-amplification of velocity gradients. Here we consider an iterative mechanism, based on the transformation of vortex filaments into sheets and their subsequent instability back into filaments. Elementary fluid mechanical arguments are provided to support the formation of a singular structure via this iterated mechanism, which we analyze based on a simplified model of filament interactions.

  16. Cosmological singularity theorems and black holes

    NASA Astrophysics Data System (ADS)

    Vilenkin, Alexander; Wall, Aron C.

    2014-03-01

    An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from nonsingular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface which lies outside of black hole horizons and is not completely surrounded by horizons, we show that the spacetime region outside (or on) the horizons must contain singularities. If the trapped surface is surrounded by horizons, we show that the horizons divide spacetime into causally disconnected pieces. Unlike the original Penrose theorem, our theorems provide some information about the location of singularities. We illustrate how they can be used to rule out some cosmological scenarios.

  17. Tunneling singularities in the open Hubbard chain

    NASA Astrophysics Data System (ADS)

    Bedürftig, Gerald; Frahm, Holger

    We study singularities in the I- V characteristics for sequential tunneling from resonant localized levels (e.g. a quantum dot) into a one-dimensional electron system described by a Hubbard model. Boundary conformal field theory together with the exact solution of the Hubbard model subject to boundary fields allow to compute the exponents describing the singularity arising when the energy of the local level is tuned through the Fermi energy of the wire as a function of electron density and magnetic field. For boundary potentials with bound states a sequence of such singularities can be observed.

  18. Deformation Theory of Periodic Monopoles (With Singularities)

    NASA Astrophysics Data System (ADS)

    Foscolo, Lorenzo

    2016-01-01

    Cherkis and Kapustin (Commun Math Phys 218(2): 333-371, 2001 and Commun Math Phys 234(1):1-35, 2003) introduced periodic monopoles (with singularities), i.e. monopoles on {R2 × S1} possibly singular at a finite collection of points. In this paper we show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities) with structure group {SO(3)} are either empty or smooth hyperkähler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.

  19. A singularity model for chemical reactivity.

    PubMed

    Menger, Fredric M; Karaman, Rafik

    2010-02-01

    This article proposes a model for chemical reactivity that involves singularities ("catastrophes") in the timing of bond-making and bond-breaking events. The common stapler is a good mechanical analogy: As hand-pressure is increased on the machine, the staple hardly changes its configuration until the staple suddenly bends. This is viewed as a singularity or catastrophe, defined classically as an abrupt change resulting from a smooth increase or decrease in external conditions (pressure in the case of a stapler, distance in the case of reactivity). Although experimental observations are provided to support the singularity effect, the model remains a heterodox notion at the present time.

  20. A cosmological model without singularity

    NASA Astrophysics Data System (ADS)

    Fischer, E.

    1993-09-01

    Based on the assumption, that potential energy of matter in a mass filled space contributes a negative term to the energy tensor, solutions of the Einstein field equations are possible that exhibit no singularities, since the action of gravity changes sign when the density of potential energy exceeds the density of mass-energy. The solution, in which potential energy and mass-energy are in balance, is identical with Einstein's static universe. It is shown that all the observational facts, that are usually considered as confirming the 'big bang' model, as the cosmological red shift, the abudances of light elements and the existence of the microwave background radiation, can be understood also in a static world model, when it is taken into account that due to the finite velocity of gravitational interaction all moving quanta lose momentum to the gravitational tensor potential. As in the static cosmological model the overwhelming fraction of the total mass exists in form of a hot intergalactic plasma. The model gives a simple explanation for the diffuse x-ray background and a solution to the missing mass problem without invoking any kind of new physics or of yet undiscovered particles. Also the causality problem and the curvature problem posed by the energy density of the quantum mechanical vacuum fields find a natural solution.

  1. From general laws to singularities.

    PubMed

    Elkaïm, M

    1985-06-01

    This article comprises several sections. The first is devoted to an explanation of a number of notions stemming from work by Ilya Prigogine and others on open systems far from equilibrium. As a result of this work, I have been able to stand back from the traditional approach employed in family therapy, that of open systems at equilibrium (the theory of Ludwig von Bertalanffy). The second section describes a clinical example based on elements close to Prigogine's theories. In the third part I develop an approach that--although continuing to draw on Prigogine's work--is much more closely linked to the research I have carried out with Félix Guattari over recent years. In this part I attempt to study a level that, in my view, has too often been left outside the field of inquiry: that of couplings between "singularities" of members of the family system and the therapist. A clinical case is presented in which this "semiotic" level, as Guattari terms it, is used together with that of the "intrinsic rules" of the system. Finally, I propose a few avenues of inquiry and research on the basis of the concepts presented.

  2. Fully stable cosmological solutions with a non-singular classical bounce

    NASA Astrophysics Data System (ADS)

    Ijjas, Anna; Steinhardt, Paul J.

    2017-01-01

    We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order L4 Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.

  3. Quantum singularities in the BTZ spacetime

    SciTech Connect

    Pitelli, Joao Paulo M.; Letelier, Patricio S.

    2008-06-15

    The spinless Banados-Teiltelboim-Zanelli spacetime is considered in the quantum theory context. Specifically, we study the case of a negative mass parameter using quantum test particles obeying the Klein-Gordon and Dirac equations. We study if this classical singular spacetime, with a naked singularity at the origin, remains singular when tested with quantum particles. The need for additional information near the origin is confirmed for massive scalar particles and all of the possible boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found. When tested by massless scalar particles or fermions, the singularity is ''healed'' and no extra boundary condition is needed. Near infinity, no boundary conditions are necessary.

  4. Gravitational radiation from a cylindrical naked singularity

    SciTech Connect

    Nakao, Ken-ichi; Morisawa, Yoshiyuki

    2005-06-15

    We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singularity. We find a boundary condition that all the metric and matter variables are everywhere finite at least up to the first order approximation. This implies that the spacetime singularity formed by this high-speed dust collapse is very similar to that formed by the null dust and the final singularity will be a conical one. Weyl curvature is completely released from the collapsed dust.

  5. Singular points of protein beta-sheets.

    PubMed Central

    Liu, W. M.; Chou, K. C.

    1998-01-01

    Protein beta-sheets can be regarded as surfaces. Two surfaces can be connected along a common edge to form a larger surface, or two edges of a surface can coalesce to form a closed sheet such as a beta-barrel. Singular points are locations where these connections are not perfect. In protein beta-sheets, a singular point is characterized by a residue separating two beta-ladders. In this paper, we study the singular points of protein beta-sheets from the surface topologic viewpoint, summarize our search results from the protein structural data in the Protein Data Bank, and present examples where singular points are near the active sites and may contribute to forming the proper relative positions of catalytic residues. PMID:9827998

  6. Observational constraints on finite scale factor singularities

    SciTech Connect

    Denkiewicz, Tomasz

    2012-07-01

    We discuss the combined constraints on a Finite Scale Factor Singularity (FSF) universe evolution scenario, which come from the shift parameter R, baryon acoustic oscillations (BAO) A, and from the type Ia supernovae. We show that observations allow existence of such singularities in the 2 × 10{sup 9} years in future (at 1σ CL) which is much farther than a Sudden Future Singularity (SFS), and that at the present moment of the cosmic evolution, one cannot differentiate between cosmological scenario which allow finite scale factor singularities and the standard ΛCDM dark energy models. We also show that there is an allowed value of m = 2/3 within 1σ CL, which corresponds to a dust-filled Einstein-de-Sitter universe limit of the early time evolution and so it is pasted into a standard early-time scenario.

  7. Three-qutrit entanglement and simple singularities

    NASA Astrophysics Data System (ADS)

    Holweck, Frédéric; Jaffali, Hamza

    2016-11-01

    In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. We first consider the algebraic variety X of separable three-qutrit states within the projective Hilbert space {{P}}({ H })={{{P}}}26. Given a quantum pure state | \\varphi > \\in {{P}}({ H }) we define the X φ -hypersuface by cutting X with a hyperplane H φ defined by the linear form < \\varphi | (the X φ -hypersurface of X is X\\cap {H}\\varphi \\subset X). We prove that when | \\varphi > ranges over the stochastic local operation and classical communication entanglement classes, the ‘worst’ possible singular X φ -hypersuface with isolated singularities, has a unique singular point of type D 4.

  8. Stable computation of generalized singular values

    SciTech Connect

    Drmac, Z.; Jessup, E.R.

    1996-12-31

    We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.

  9. Analysis of Acoustic Emission During the Melting of Embedded Indium Particles in an Aluminum Matrix: A Study of Plastic Strain Accommodation During Phase Transformation

    NASA Astrophysics Data System (ADS)

    Kuba, Michael M.; Van Aken, David C.

    2013-08-01

    Acoustic emission (AE) is used in this article to study melting and solidification of embedded indium particles in the size ranging from 0.2 to 3 μm in diameter and to show that dislocation generation occurs in the aluminum matrix to accommodate a 2.5 pct volume change. The volume-averaged acoustic energy produced by indium particle melting is similar to that reported for bainite formation upon continuous cooling. A mechanism of prismatic loop generation is proposed to accommodate the volume change, and an upper limit to the geometrically necessary increase in dislocation density is calculated as 4.1 × 109 cm-2 for the Al-17In alloy. Thermomechanical processing is also used to change the size and distribution of the indium particles within the aluminum matrix. Dislocation generation with accompanied AE occurs when the melting indium particles are associated with grain boundaries or upon solidification where the solid-liquid interfaces act as free surfaces to facilitate dislocation generation. AE is not observed for indium particles that require super heating and exhibit elevated melting temperatures. The AE work corroborates previously proposed relaxation mechanisms from prior internal friction studies and that the superheat observed for melting of these micron-sized particles is a result of matrix constraint.

  10. Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis

    NASA Astrophysics Data System (ADS)

    Portes, Leonardo L.; Aguirre, Luis A.

    2016-05-01

    Groth and Ghil [Phys. Rev. E 84, 036206 (2011), 10.1103/PhysRevE.84.036206] developed a modified varimax rotation aimed at enhancing the ability of the multivariate singular spectrum analysis (M-SSA) to characterize phase synchronization in systems of coupled chaotic oscillators. Due to the special structure of the M-SSA eigenvectors, the modification proposed by Groth and Ghil imposes a constraint in the rotation of blocks of components associated with the different subsystems. Accordingly, here we call it a structured varimax rotation (SVR). The SVR was presented as successive pairwise rotations of the eigenvectors. The aim of this paper is threefold. First, we develop a closed matrix formulation for the entire family of structured orthomax rotation criteria, for which the SVR is a special case. Second, this matrix approach is used to enable the use of known singular value algorithms for fast computation, allowing a simultaneous rotation of the M-SSA eigenvectors (a Python code is provided in the Appendix). This could be critical in the characterization of phase synchronization phenomena in large real systems of coupled oscillators. Furthermore, the closed algebraic matrix formulation could be used in theoretical studies of the (modified) M-SSA approach. Third, we illustrate the use of the proposed singular value algorithm for the SVR in the context of the two benchmark examples of Groth and Ghil: the Rössler system in the chaotic (i) phase-coherent and (ii) funnel regimes. Comparison with the results obtained with Kaiser's original (unstructured) varimax rotation (UVR) reveals that both SVR and UVR give the same result for the phase-coherent scenario, but for the more complex behavior (ii) only the SVR improves on the M-SSA.

  11. Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis.

    PubMed

    Portes, Leonardo L; Aguirre, Luis A

    2016-05-01

    Groth and Ghil [Phys. Rev. E 84, 036206 (2011)PLEEE81539-375510.1103/PhysRevE.84.036206] developed a modified varimax rotation aimed at enhancing the ability of the multivariate singular spectrum analysis (M-SSA) to characterize phase synchronization in systems of coupled chaotic oscillators. Due to the special structure of the M-SSA eigenvectors, the modification proposed by Groth and Ghil imposes a constraint in the rotation of blocks of components associated with the different subsystems. Accordingly, here we call it a structured varimax rotation (SVR). The SVR was presented as successive pairwise rotations of the eigenvectors. The aim of this paper is threefold. First, we develop a closed matrix formulation for the entire family of structured orthomax rotation criteria, for which the SVR is a special case. Second, this matrix approach is used to enable the use of known singular value algorithms for fast computation, allowing a simultaneous rotation of the M-SSA eigenvectors (a Python code is provided in the Appendix). This could be critical in the characterization of phase synchronization phenomena in large real systems of coupled oscillators. Furthermore, the closed algebraic matrix formulation could be used in theoretical studies of the (modified) M-SSA approach. Third, we illustrate the use of the proposed singular value algorithm for the SVR in the context of the two benchmark examples of Groth and Ghil: the Rössler system in the chaotic (i) phase-coherent and (ii) funnel regimes. Comparison with the results obtained with Kaiser's original (unstructured) varimax rotation (UVR) reveals that both SVR and UVR give the same result for the phase-coherent scenario, but for the more complex behavior (ii) only the SVR improves on the M-SSA.

  12. Singularity avoidance and time in quantum gravity

    SciTech Connect

    Kreienbuehl, Andreas

    2009-06-15

    We consider the quantization of a Friedmann-Robertson-Walker universe. We derive a reduced square root Hamiltonian by choosing the scale factor as time variable and quantize the theory using Pauli matrices a la Dirac. From the resulting spinor equation we show that there is no semiclassical wave packet that avoids the big bang singularity. Our work raises the question concerning the relationship between the choice of time and singularity avoidance.

  13. Dynamic Singularity Spectrum Distribution of Sea Clutter

    NASA Astrophysics Data System (ADS)

    Xiong, Gang; Yu, Wenxian; Zhang, Shuning

    2015-12-01

    The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.

  14. Weyl anomaly and initial singularity crossing

    NASA Astrophysics Data System (ADS)

    Awad, Adel

    2016-04-01

    We consider the role of quantum effects, mainly, Weyl anomaly in modifying Friedmann-Lemaitre-Robertson-Walker (FLRW) model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections change the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a C1 extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in matter sources which keeps the equation of state unchanged.

  15. Frame Field Singularity Correction for Automatic Hexahedralization.

    PubMed

    Jiang, Tengfei; Huang, Jin; Wang, Yuanzhen; Tong, Yiying; Bao, Hujun

    2014-08-01

    We present an automatic hexahedralization tool, based on a systematic treatment that removes some of the singularities that would lead to degenerate volumetric parameterization. Such singularities could be abundant in automatically generated frame fields guiding the interior and boundary layouts of the hexahedra in an all hexahedral mesh. We first give the mathematical definitions of the inadmissible singularities prevalent in frame fields, including newly introduced surface singularity types. We then give a practical framework for adjusting singularity graphs by automatically modifying the rotational transition of frames between charts (cells of a tetrahedral mesh for the volume) to resolve the issues detected in the internal and boundary singularity graph. After applying an additional re-smoothing of the frame field with the modified transition conditions, we cut the volume into a topologically trivial domain, with the original topology encoded by the self-intersections of the boundary of the domain, and solve a mixed integer problem on this domain for a global parameterization. Finally, a properly connected hexahedral mesh is constructed from the integer isosurfaces of (u,v,w) in the parameterization. We demonstrate the applicability of the method on complex shapes, and discuss its limitations.

  16. Observational constraints on cosmological future singularities

    NASA Astrophysics Data System (ADS)

    Beltrán Jiménez, Jose; Lazkoz, Ruth; Sáez-Gómez, Diego; Salzano, Vincenzo

    2016-11-01

    In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H( z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means {˜ }2.8 Gyrs from the present time.

  17. Complete fluid equations for low-n singular modes in axisymmetric toroidal plasmas

    SciTech Connect

    Glasser, A.H.

    1990-01-01

    The goal of this work is to develop a complete linear theory of the singular region, including all important dynamical effects. The present phase of the work treats the more collision fluid regime. A later phase will treat the less collisional gyrokinetic regime. This paper concerns the derivation and form of the fluid equations for the singular region of low-n modes. Later work will treat high-n ballooning modes. In addition, the ordering in the present work must be amended before it is applicable to the neighborhood of the field reversal surface of the RFP.

  18. Minimal Solution of Singular LR Fuzzy Linear Systems

    PubMed Central

    Nikuie, M.; Ahmad, M. Z.

    2014-01-01

    In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated. PMID:24737977

  19. Minimal solution of singular LR fuzzy linear systems.

    PubMed

    Nikuie, M; Ahmad, M Z

    2014-01-01

    In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.

  20. The data embedding method

    SciTech Connect

    Sandford, M.T. II; Bradley, J.N.; Handel, T.G.

    1996-06-01

    Data embedding is a new steganographic method for combining digital information sets. This paper describes the data embedding method and gives examples of its application using software written in the C-programming language. Sandford and Handel produced a computer program (BMPEMBED, Ver. 1.51 written for IBM PC/AT or compatible, MS/DOS Ver. 3.3 or later) that implements data embedding in an application for digital imagery. Information is embedded into, and extracted from, Truecolor or color-pallet images in Microsoft{reg_sign} bitmap (.BMP) format. Hiding data in the noise component of a host, by means of an algorithm that modifies or replaces the noise bits, is termed {open_quote}steganography.{close_quote} Data embedding differs markedly from conventional steganography, because it uses the noise component of the host to insert information with few or no modifications to the host data values or their statistical properties. Consequently, the entropy of the host data is affected little by using data embedding to add information. The data embedding method applies to host data compressed with transform, or {open_quote}lossy{close_quote} compression algorithms, as for example ones based on discrete cosine transform and wavelet functions. Analysis of the host noise generates a key required for embedding and extracting the auxiliary data from the combined data. The key is stored easily in the combined data. Images without the key cannot be processed to extract the embedded information. To provide security for the embedded data, one can remove the key from the combined data and manage it separately. The image key can be encrypted and stored in the combined data or transmitted separately as a ciphertext much smaller in size than the embedded data. The key size is typically ten to one-hundred bytes, and it is in data an analysis algorithm.

  1. Paradox of soft singularity crossing and its resolution by distributional cosmological quantities

    NASA Astrophysics Data System (ADS)

    Keresztes, Zoltán; Gergely, László Á.; Kamenshchik, Alexander Yu.

    2012-09-01

    A cosmological model of a flat Friedmann universe filled with a mixture of anti-Chaplygin gas and dustlike matter exhibits a future soft singularity, where the pressure of the anti-Chaplygin gas diverges (while its energy density is finite). Despite infinite tidal forces the geodesics pass through the singularity. Because of the dust component, the Hubble parameter has a nonzero value at the encounter with the singularity, therefore the dust implies further expansion. With continued expansion however, the energy density and the pressure of the anti-Chaplygin gas would become ill-defined hence from the point of view of the anti-Chaplygin gas only a contraction is allowed. Paradoxically, the universe in this cosmological model would have to expand and contract simultaneously. This obviously could not happen. We solve the paradox by redefining the anti-Chaplygin gas in a distributional sense. Then a contraction could follow the expansion phase at the singularity at the price of a jump in the Hubble parameter. Although such an abrupt change is not common in any cosmological evolution, we explicitly show that the set of Friedmann, Raychaudhuri and continuity equations are all obeyed both at the singularity and in its vicinity. We also prove that the Israel junction conditions are obeyed through the singular spatial hypersurface. In particular we enounce and prove a more general form of the Lanczos equation.

  2. Dynamical singularity resolution in spherically symmetric black hole formation

    SciTech Connect

    Ziprick, Jonathan; Kunstatter, Gabor

    2009-07-15

    We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painleve-Gullstrand coordinates. Near criticality the system exhibits Choptuik scaling with a mass gap and a new scaling relationship dependant upon the quantum length scale. Classical singularities are resolved by a radiationlike phase in the quantum collapse: the black hole consists of a compact region of spacetime bounded by a single, smooth trapping horizon. The 'evaporation' is not complete but leaves behind a small expanding shell that disperses to infinity.

  3. Mapping of all polarization-singularity C-point morphologies

    NASA Astrophysics Data System (ADS)

    Galvez, E. J.; Rojec, B. L.; Beach, K.

    2014-02-01

    We present theoretical descriptions and measurements of optical beams carrying isolated polarization-singularity C-points. Our analysis covers all types of C-points, including asymmetric lemons, stars and monstars. They are formed by the superposition of a circularly polarized mode carrying an optical vortex and a fundamental Gaussian mode in the opposite state of polarization. The type of C-point can be controlled experimentally by varying two parameters controlling the asymmetry of the optical vortex. This was implemented via a superposition of modes with singly charged optical vortices of opposite sign, and varying the relative amplitude and phase. The results are in excellent agreement with the predictions.

  4. Quantum Embedding Theories.

    PubMed

    Sun, Qiming; Chan, Garnet Kin-Lic

    2016-12-20

    In complex systems, it is often the case that the region of interest forms only one part of a much larger system. The idea of joining two different quantum simulations-a high level calculation on the active region of interest, and a low level calculation on its environment-formally defines a quantum embedding. While any combination of techniques constitutes an embedding, several rigorous formalisms have emerged that provide for exact feedback between the embedded system and its environment. These three formulations: density functional embedding, Green's function embedding, and density matrix embedding, respectively, use the single-particle density, single-particle Green's function, and single-particle density matrix as the quantum variables of interest. Many excellent reviews exist covering these methods individually. However, a unified presentation of the different formalisms is so far lacking. Indeed, the various languages commonly used, functional equations for density functional embedding, diagrammatics for Green's function embedding, and entanglement arguments for density matrix embedding, make the three formulations appear vastly different. In this Account, we introduce the basic equations of all three formulations in such a way as to highlight their many common intellectual strands. While we focus primarily on a straightforward theoretical perspective, we also give a brief overview of recent applications and possible future developments. The first section starts with density functional embedding, where we introduce the key embedding potential via the Euler equation. We then discuss recent work concerning the treatment of the nonadditive kinetic potential, before describing mean-field density functional embedding and wave function in density functional embedding. We finish the section with extensions to time-dependence and excited states. The second section is devoted to Green's function embedding. Here, we use the Dyson equation to obtain equations that

  5. Singular Lagrangians. Classical dynamics and quantization. Lectures for young scientists

    NASA Astrophysics Data System (ADS)

    Nesterenko, V. V.; Chervyakov, A. M.

    The lectures are devoted to the classical and quantum dynamics of the systems described by singular (or degenerate) Lagrangians. The complete set of the Hamiltonian constraints is constructed in the framework of the Lagrangian formalism. The equations of motion in the phase space are derived by taking into account all the constraints in the theory. It is proved that the dynamic on the physical submanifold of the phase space has the Hamiltonian form. On lectures the second Noether theorem is widely used. On its basis the properties of the Poisson brackets of the primary constraints are investigated and the invariance of the Lagrangian constraints during evolution is proved. The setting of the Cauchy problem in the theories with singular Lagrangians is discussed. The quantization of the systems with constraints is carried out by the functional integration in the phase space. There is considered the most general case of the first class and the second class constraints with an explicit time dependence. The gauge conditions may be noninvoluntary and time dependent. The material is illustrated by some examples (relativistic point particle, relativistic string, electromagnetic field, and Yang-Mills fields).

  6. A novel image watermarking method based on singular value decomposition and digital holography

    NASA Astrophysics Data System (ADS)

    Cai, Zhishan

    2016-10-01

    According to the information optics theory, a novel watermarking method based on Fourier-transformed digital holography and singular value decomposition (SVD) is proposed in this paper. First of all, a watermark image is converted to a digital hologram using the Fourier transform. After that, the original image is divided into many non-overlapping blocks. All the blocks and the hologram are decomposed using SVD. The singular value components of the hologram are then embedded into the singular value components of each block using an addition principle. Finally, SVD inverse transformation is carried out on the blocks and hologram to generate the watermarked image. The watermark information embedded in each block is extracted at first when the watermark is extracted. After that, an averaging operation is carried out on the extracted information to generate the final watermark information. Finally, the algorithm is simulated. Furthermore, to test the encrypted image's resistance performance against attacks, various attack tests are carried out. The results show that the proposed algorithm has very good robustness against noise interference, image cut, compression, brightness stretching, etc. In particular, when the image is rotated by a large angle, the watermark information can still be extracted correctly.

  7. Effect of the acidic strength on the vapor phase Beckmann rearrangement of cyclohexanone oxime over the MFI zeolite: an embedded ONIOM study.

    PubMed

    Sirijaraensre, Jakkapan; Limtrakul, Jumras

    2009-01-21

    The mechanism and energetic profile of the Beckmann rearrangement reaction of cyclohexanone oxime to epsilon-caprolactam catalyzed by the H-[Al]-MFI and H-[B]-MFI zeolites were investigated by both the bare cluster and the ONIOM models at the B3LYP/6-31G(d,p) and the B3LYP/6-31G(d,p):MNDO levels of theory, respectively. In order to improve the energetic properties and take into account the whole zeolite framework effect, single point calculations are undertaken at the embedded ONIOM2 schemes; MP2/6-311G(d,p):HF/6-31G(d) with an additional long-range electrostatic potential from the extended zeolite framework. The reaction mechanism of the Beckmann rearrangement over the acid site of zeolites consists of three steps: the 1,2 H shift, the rearrangement and the tautomerization. The activation energies for the Beckmann rearrangement of cyclohexanone oxime on the H-[Al]-MFI zeolite are calculated to be 31.46, 16.15 and 18.95 kcal mol(-1), for the first, second and third steps, respectively, whereas in the H-[B]-MFI zeolite, the energy barriers for each step of the reaction are 24.33, 7.46 and 20.43 kcal mol(-1), respectively. The rate-determining step of the reaction is the first step, which is the transformation from the N-ended cyclohexanone oxime adsorption complex and the O-ended one. These results signify the important role that the acid strength of zeolites plays in altering the energy profile of the reaction. The results further indicate that the weak Brønsted acid sites in the [B]-MFI zeolite could better catalyze the Beckmann rearrangement of cyclohexanone oxime than the strong acid sites in the [Al]-MFI zeolite, as compared with the quantitatively low activation energy of most steps. However, the turnover reaction of the H-[B]-MFI zeolite might be delayed by the quantitatively high desorption energy of the product as compared to the adsorption energy of the reactant.

  8. Naked singularities as particle accelerators. II

    SciTech Connect

    Patil, Mandar; Joshi, Pankaj S.; Malafarina, Daniele

    2011-03-15

    We generalize here our earlier results on particle acceleration by naked singularities. We showed recently [M. Patil and P. S. Joshi, Phys. Rev. D 82, 104049 (2010).] that the naked singularities that form due to the gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center-of-mass energies. However, we focused there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as the final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that, when the particles interact and collide near the Cauchy horizon, the energy of collision in the center-of-mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high-energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative, but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore, the nature of naked singularities, both at the classical and quantum level, could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of the Cauchy horizon that participate in extreme high-energy collisions.

  9. Treatment of singularities in cracked bodies

    NASA Technical Reports Server (NTRS)

    Shivakumar, K. N.; Raju, I. S.

    1989-01-01

    Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.

  10. Treatment of singularities in cracked bodies

    NASA Technical Reports Server (NTRS)

    Shivakumar, K. N.; Raju, I. S.

    1990-01-01

    Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.

  11. Northern Hemisphere Summer Monsoon Singularities and Climatological Intraseasonal Oscillation.

    NASA Astrophysics Data System (ADS)

    Wang, Bin; Xu, Xihua

    1997-05-01

    Using climatological pentad mean outgoing longwave radiation (OLR) and European Centre for Medium-Range Weather Forecasts analysis winds, the authors show that the Northern Hemisphere summer monsoon displays statistically significant climatological intraseasonal oscillations (CISOs). The extreme phases of CISO characterize monsoon singularities-monsoon events that occur on a fixed pentad with usual regularity, whereas the transitional phases of CISO represent the largest year-to-year monsoon variations.The CISO results from a phase-locking of transient intraseasonal oscillation to annual cycle. It exhibits a dynamically coherent structure between enhanced convection and low-level convergent (upper-level divergent) cyclonic (anticyclonic) circulation. Its phase propagates primarily northward from the equator to the northern Philippines during early summer (May-July), and westward along 15°N from 170°E to the Bay of Bengal during August and September.The propagation of CISO links monsoon singularities occurring in different regions. Four CISO cycles are identified from May to October. The first cycle has a peak wet phase in mid-May that starts the monsoon over the South China Sea and Philippines. Its dry phase in late May and early June brings the premonsoon dry weather over the regions of western North Pacific summer monsoon (WNPSM), Meiyu/Baiu, and Indian summer monsoon (ISM). The wet phase of Cycle II peaking in mid-June marks the onsets of WNPSM, continental ISM, and Meiyu, whereas the dry phase in early to mid-July corresponds to the first major breaks in WNPSM and ISM, and the end of Meiyu. The wet phase of Cycle III peaking in mid-August benchmarks the height of WNPSM, which was followed by a conspicuous dry phase propagating westward and causing the second breaks of WNPSM (in early September) and ISM (in mid-September). The wet phase of Cycle IV represents the last active WNPSM and withdrawal of ISM in mid-October.The relationships among ISM, WNPSM, and

  12. Classical and quantum analysis of repulsive singularities in four-dimensional extended supergravity

    NASA Astrophysics Data System (ADS)

    Gaida, I.; Hollmann, H. R.; Stewart, J. M.

    1999-07-01

    Non-minimal repulsive singularities (`repulsons') in extended supergravity theories are investigated. The short-distance antigravity properties of the repulsons are tested at the classical and the quantum level by a scalar test-particle. Using a partial wave expansion it is shown that the particle is totally reflected at the origin. A high-frequency incoming particle undergoes a phase shift of icons/Journals/Common/pi" ALT="pi" ALIGN="TOP"/>/2. However, the phase shift for a low-frequency particle depends upon the physical data of the repulson. The curvature singularity at a finite distance rh turns out to be transparent for the scalar test-particle and the coordinate singularity at the origin serves as the repulsive barrier to bounce back the particles.

  13. Quantum Griffiths singularity of superconductor-metal transition in Ga thin films.

    PubMed

    Xing, Ying; Zhang, Hui-Min; Fu, Hai-Long; Liu, Haiwen; Sun, Yi; Peng, Jun-Ping; Wang, Fa; Lin, Xi; Ma, Xu-Cun; Xue, Qi-Kun; Wang, Jian; Xie, X C

    2015-10-30

    The Griffiths singularity in a phase transition, caused by disorder effects, was predicted more than 40 years ago. Its signature, the divergence of the dynamical critical exponent, is challenging to observe experimentally. We report the experimental observation of the quantum Griffiths singularity in a two-dimensional superconducting system. We measured the transport properties of atomically thin gallium films and found that the films undergo superconductor-metal transitions with increasing magnetic field. Approaching the zero-temperature quantum critical point, we observed divergence of the dynamical critical exponent, which is consistent with the Griffiths singularity behavior. We interpret the observed superconductor-metal quantum phase transition as the infinite-randomness critical point, where the properties of the system are controlled by rare large superconducting regions.

  14. Hamiltonian Description of Singular Lagrangian Systems with Spontaneously Broken Time Translation Symmetry

    NASA Astrophysics Data System (ADS)

    Zhao, Liu; Yu, Pengfei; Xu, Wei

    2013-02-01

    Shapere and Wilczek recently found some singular Lagrangian systems which spontaneously breaks time translation symmetry. The common feature of their models is that the energy functions are multi-valued in terms of the canonical phase space variables and the symmetry breaking ground states are all located at the brunching point singularities. By enlarging the phase space and making use of Dirac's theory on constrained Hamiltonian systems, we present the Hamiltonian description of some of the models discussed by Shapere and Wilczek and found that both the multi-valuedness and the brunching point singularities can be avoided, while the spontaneous breaking of time translation becomes more transparent. It is also shown that the breaking of time translation is always accompanied by the breaking of time reversal.

  15. Mapping Upper Mantle Seismic Discontinuities Using Singular Spectrum Analysis

    NASA Astrophysics Data System (ADS)

    Gu, Y. J.; Dokht, R.; Sacchi, M. D.

    2015-12-01

    Seismic discontinuities are fundamental to the understanding of mantle composition and dynamics. Their depth and impedance are generally determined using secondary seismic phases, most commonly SS precursors and P-to-S converted waves. However, the analysis and interpretation using these approaches often suffer from incomplete data coverage, high noise levels and interfering seismic phases, especially near tectonically complex regions such as subduction zones and continental margins. To overcome these pitfalls, we apply Singular Spectrum Analysis (SSA) to remove random noise, reconstruct missing traces and enhance the robustness of SS precursors and P-to-S conversions from seismic discontinuities. Our method takes advantage of the predictability of time series in frequency-space domain and performs a rank reduction using a singular value decomposition of the trajectory matrix. We apply SSA to synthetic record sections as well as observations of 1) SS precursors beneath the northwestern Pacific subduction zones, and 2) P-to-S converted waves from the Western Canada Sedimentary Basin (WCSB). In comparison with raw or interpolated data, the SSA enhanced reflectivity maps show a greater resolution and a stronger negative correlation between the depths of the 410 and 660 km discontinuities. These effects can be attributed to the suppression of incoherent noise, which tends to reduce the signal amplitude during normal averaging procedures, through rank reduction and the emphasis of principle singular values. Our new results suggest a more laterally coherent 520 km reflection in the western Pacific regions. Similar improvements in data imaging are achieved in western Canada, where strong lateral variations in discontinuity topography are observed in the craton-Cordillera boundary zone. Improvements from SSA relative to conventional approaches are most notable in under-sampled regions.

  16. Finite time singularities in the quasigeostrophic model

    NASA Astrophysics Data System (ADS)

    Scott, Richard

    2016-11-01

    A finite-time singularity in the evolution of a patch of surface temperature in the quasi-geostrophic equations via two distinct evolution routes is investigated with a grid-free, adaptive numerical scheme. In one case, the singularity proceeds through the formation of a corner, developing infinite curvature in the patch boundary in finite time. The corner is self-similar and the growth of curvature appears to be independent of initial patch shape. In the other case, the singularity proceeds through a self-similar cascade of filament instabilities with geometrically shrinking spatial and temporal scales, and the filament width approaches zero in a finite time. The spatially and temporally adaptive numerical scheme permits the accurate simulation of both corner and cascade singularities over a range of spatial scales spanning ten orders of magnitude. Some aspects of both singularity types exhibit universality, being independent of the initial patch shape and large-scale evolution; however, a simple extension of the initial temperature structure provides evidence that only the instability cascade persists in the case of a continuous initial temperature distribution.

  17. Unified approach for singularly perturbed control systems

    NASA Astrophysics Data System (ADS)

    Singh, Hardev

    2001-07-01

    The theory of singular perturbation has been a highly recognized and rapidly developing area of control systems in the last thirty years. Results now exists for both the continuous-time and discrete-time systems. However, in the way that these results are normally presented, the solutions to the discrete-time and continuous-time cases evolve from different starting points and seem to bear no relationship to each other. The aim of this dissertation is to develop a unified framework for discrete-time and continuous-time singularly perturbed systems. The discrete-time singularly perturbed control systems results are reorganized so that they are compatible in a way that the continuous-time singularly perturbed control system results are normally presented. This is, in part, achieved by using a newly developed "Unified Approach" to digital system theory, first proposed by Middleton and Goodwin. We first formulate the problem by modeling the singular perturbation parameter from the standpoint of the state space formulation and the second order unified equation. Building upon these results, we further apply this technique to state-feedback, robust state-feedback, Linear Quadratic Regulator (LQR) and Hinfinity optimization control problems. The unified results developed in this Dissertation are valid for both the continuous-time case (sampling interval T = 0) and the discrete-time (sampling interval T > 0).

  18. Construction of embedding for empirical prognostic models of climate

    NASA Astrophysics Data System (ADS)

    Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Loskutov, E. M.

    2015-12-01

    Empirical approach to modeling and forecasting complex dynamical systems becomes more and more popular in climate science because of two reasons: (i) not confidence reproducing and forecasting some of key climate modes by existing global climate models, and (ii) increasing number and duration of climatic time series which can be considered as a source of information about dynamical laws underlying observational variability. Such an approach is aimed to construction of prognostic models by way of direct analysis of data without involving any detailed physical equations. We developed a method for empirical modeling basing on reconstruction of prognostic evolution operator in a form of random dynamical system [1] - stochastic mapping the current state of the system to the next one. The most crucial point in application of the method to the analysis of real climatic data is the construction of proper embedding: the optimal set of variables - "principal modes" - determining the phase space the model works in. This task is non-trivial due to huge dimension of time series of typical space-distributed climatic fields. We outline two main features these modes should have to capture the main dynamical properties of the system: (i) capturing teleconnections in the atmosphere-ocean system by taking into account time-lagged couplings in data and (ii) reflecting the nonlinear interactions between the time series at different grid points. In this report we present the methodology of empirical forecasting which includes the construction of an embedding on the basis of the above principals: multichannel singular spectrum analysis (MSSA) together with nonlinear principal component analysis (NPCA) are used for phase space construction from data. The proposed methodology is applied to the analysis of sea surface temperature and atmospheric pressure fields. Capabilities to predict various indices of climate (such as SOI, PDO, NAO, NTA, etc.) is demonstrated. This research was supported

  19. Silica Embedded Metal Hydrides

    SciTech Connect

    Heung, L.K.; Wicks, G.G.

    1998-08-01

    A method to produce silica embedded metal hydride was developed. The product is a composite in which metal hydride particles are embedded in a matrix of silica. The silica matrix is highly porous. Hydrogen gas can easily reach the embedded metal hydride particles. The pores are small so that the metal hydride particles cannot leave the matrix. The porous matrix also protects the metal hydride particles from larger and reactive molecules such as oxygen, since the larger gas molecules cannot pass through the small pores easily. Tests show that granules of this composite can absorb hydrogen readily and withstand many cycles without making fines.

  20. Secure Embedded Systems

    DTIC Science & Technology

    2015-08-24

    embedded  12   systems ,  which   consists  of   an  architecture   that  decouples   secure  and   functional   design ...confidentiality   and  14   integrity  of  an   embedded   system  being   designed .    The  development  of  a  hypothetical...secure   embedded  15   system  for  an  unmanned

  1. Anisotropic singularities in modified gravity models

    NASA Astrophysics Data System (ADS)

    Figueiró, Michele Ferraz; Saa, Alberto

    2009-09-01

    We show that the common singularities present in generic modified gravity models governed by actions of the type S=∫d4x-gf(R,ϕ,X), with X=-(1)/(2)gab∂aϕ∂bϕ, are essentially the same anisotropic instabilities associated to the hypersurface F(ϕ)=0 in the case of a nonminimal coupling of the type F(ϕ)R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface (∂f)/(∂R)=0 is attained. Some examples are explicitly discussed.

  2. Singularities in a scalar field quantum cosmology

    NASA Astrophysics Data System (ADS)

    Lemos, Nivaldo A.

    1996-04-01

    The quantum theory of a spatially flat Friedmann-Robertson-Walker universe with a massless scalar field as the source is further investigated. The classical model is singular and in the framework of a genuine canonical quantization (Arnowitt-Deser-Misner formalism) a discussion is made of the cosmic evolution, particularly of the quantum gravitational collapse problem. It is shown that in a matter-time gauge such that time is identified with the scalar field the classical model is singular either at t=-∞ or at t=+∞, but the quantum model is nonsingular. The latter behavior disproves a conjecture according to which quantum cosmological singularities are predetermined on the classical level by the choice of time.

  3. Discrete variable representation for singular Hamiltonians

    NASA Astrophysics Data System (ADS)

    Schneider, Barry I.; Nygaard, Nicolai

    2004-11-01

    We discuss the application of the discrete variable representation (DVR) to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved, the boundary conditions are satisfied, and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.

  4. Removing singular refractive indices with sculpted surfaces

    PubMed Central

    Horsley, S. A. R.; Hooper, I. R.; Mitchell–Thomas, R. C.; Quevedo–Teruel, O.

    2014-01-01

    The advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity — that is, the requirement of an infinite refractive index — can be realised for waves confined to an appropriately sculpted surface. In particular, we redesign three singular omnidirectional devices: the Eaton lens, the generalized Maxwell Fish–Eye, and the invisible sphere. Our designs perfectly reproduce the behaviour of these singular devices, and can be achieved with simple isotropic media of low refractive index contrast. PMID:24786649

  5. Discrete variable representation for singular Hamiltonians.

    PubMed

    Schneider, Barry I; Nygaard, Nicolai

    2004-11-01

    We discuss the application of the discrete variable representation (DVR) to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved, the boundary conditions are satisfied, and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.

  6. Isotropic cosmological singularities: other matter models

    NASA Astrophysics Data System (ADS)

    Tod, K. P.

    2003-02-01

    Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied, the existence and uniqueness of cosmological models with data at the singularity has been established (Anguige K and Tod K P 1999 Ann. Phys., NY 276 257-93, 294-320, Anguige K 2000 Ann. Phys., NY 285 395-419). These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this paper, we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang-Mills plasma given by Choquet-Bruhat (Choquet-Bruhat Y 1996 Yang-Mills plasmas Global Structure and Evolution in General Relativity (Springer Lecture Notes in Physics vol 460) ed S Cotsakis and G W Gibbons (Berlin: Springer)) and matter satisfying the Einstein-Boltzmann equation.

  7. Solitons supported by singular modulation of the cubic nonlinearity.

    PubMed

    Lutsky, Vitaly; Malomed, Boris A

    2017-05-29

    A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a repulsive or attractive linear potential too. We find that a pair of mutually symmetric peaks readily gives rise to the spontaneous symmetry breaking (SSB) of modes pinned to individual peaks, while antisymmetric pinned modes are always unstable, transforming into robust spatially odd breathers. Three- and five-peak structures support symmetric modes, with in-phase or twisted profiles, and do not give rise to asymmetric states. A stability area is found for the twisted states pinned to the triple peaks, while the corresponding in-phase modes are unstable, unless the three modulation peaks are set very close to each other, covered by a single-peak pinned mode. All patterns pinned to five peaks are unstable too. Collisions of moving solitons with the singular-modulation peak are studied too. Slowly moving solitons bounce back from the peak, while the collisions are quasi-elastic for fast solitons. In the intermediate case, the soliton is destroyed by the collision. In a special case, the condition of a resonance of the incident soliton with a trapped mode supported by the peak leads to capture of the soliton.

  8. Stationary equilibrium singularity distributions in the plane

    NASA Astrophysics Data System (ADS)

    Newton, P. K.; Ostrovskyi, V.

    2012-02-01

    We characterize all stationary equilibrium point singularity distributions in the plane of logarithmic type, allowing for real, imaginary or complex singularity strengths. The dynamical system follows from the assumption that each of the N singularities moves according to the flow field generated by all the others at that point. For strength vector \\vec{\\Gamma} \\in {\\Bbb R}^N , the dynamical system is the classical point vortex system obtained from a singular discrete representation of the vorticity field from ideal, incompressible fluid flow. When \\vec{\\Gamma} \\in \\Im , it corresponds to a system of sources and sinks, whereas when \\vec{\\Gamma} \\in {\\Bbb C}^N the system consists of spiral sources and sinks discussed in Kochin et al (1964 Theoretical Hydromechanics 1 (London: Interscience)). We formulate the equilibrium problem as one in linear algebra, A \\vec{\\Gamma} = 0 , A \\in {\\Bbb C}^{N \\times N} , \\vec{\\Gamma} \\in {\\Bbb C}^N , where A is a N × N complex skew-symmetric configuration matrix which encodes the geometry of the system of interacting singularities. For an equilibrium to exist, A must have a kernel and \\vec{\\Gamma} must be an element of the nullspace of A. We prove that when N is odd, A always has a kernel, hence there is a choice of \\vec{\\Gamma} for which the system is a stationary equilibrium. When N is even, there may or may not be a non-trivial nullspace of A, depending on the relative position of the points in the plane. We provide examples of evenly and randomly distributed points on curves such as circles, figure eights, flower-petal configurations and spirals. We then show how to classify the stationary equilibria in terms of the singular spectrum of A.

  9. Induced ferromagnetism in Mn{sub 3}N{sub 2} phase embedded in Mn/Si{sub 3}N{sub 4} multilayers

    SciTech Connect

    Cespedes, E.; Roman, E.; Huttel, Y.; Andres, A. de; Prieto, C.; Chaboy, J.; Garcia-Lopez, J.

    2009-08-15

    Room temperature ferromagnetism has been obtained for different sets of Mn/Si{sub 3}N{sub 4} multilayers prepared by sputtering. In order to find the most suitable conditions to stabilize the ferromagnetic ordering in this system, the evolution of the magnetic properties has been studied for films in which the Si{sub 3}N{sub 4} layer thickness was maintained constant while that of the Mn layer was varied, [Mn(t{sub m})/Si{sub 3}N{sub 4}(3.4 nm)]{sub n}, and conversely, in [Mn(0.7 nm)/Si{sub 3}N{sub 4}(t{sub sn})]{sub 43} samples, in which the Mn layer thickness was kept constant while varying the Si{sub 3}N{sub 4} layer thickness. Structural, compositional, electronic and magnetic characterizations have been performed by means of x-ray reflectometry, Rutherford backscattering spectrometry, x-ray photoemission spectroscopy, x-ray absorption, and superconducting quantum interference device for further knowledge of the magnetic-structural relationship in this system. Our results show that the peculiar magnetic behavior of these films is mainly related to the stabilization of a slightly distorted Mn{sub 3}N{sub 2} phase that is induced by the Si{sub 3}N{sub 4} at the interfaces. For samples with larger Mn layer thickness, metallic Mn and Mn{sub 3}N{sub 2} phases coexist, which leads to a reduction of the total magnetization per Mn atom due to the presence of metallic Mn. For small Mn layer thickness (t{sub m}<0.86 nm), where noncontinuous Mn{sub 3}N{sub 2} layers are formed, the magnetization decreases noticeably due to the superparamagnetic size limit. It has been found that the best conditions for the stabilization of the ferromagnetism in this system occur when both, the manganese-rich and the silicon nitride layers, are continuous and with similar thickness, close to 3.5 nm.

  10. Asymmetrical singularities in real-world signals

    NASA Astrophysics Data System (ADS)

    Ohashi, Kyoko; Amaral, Luís A.; Natelson, Benjamin H.; Yamamoto, Yoshiharu

    2003-12-01

    We generalize the wavelet transform modulus maxima approach in order to analyze positive and negative changes separately and show different singularity spectra depending on the direction of changes in (i) human heartbeat interval data during sympathetic blockade, (ii) time series of daytime human physical activity of healthy individuals (but not of patients with debilitating fatigue), and (iii) daily stock price records of the Nikkei 225 in the period 1990 2002—but not of the S&P 500. We conclude that the analysis of asymmetrical singularities provides deeper insights into the underlying complexity of real-world signals that can greatly enhance our understanding of the mechanisms determining the systems’ dynamics.

  11. Quantum singularity of Levi-Civita spacetimes

    NASA Astrophysics Data System (ADS)

    Konkowski, D. A.; Helliwell, T. M.; Wieland, C.

    2004-01-01

    Quantum singularities in general relativistic spacetimes are determined by the behaviour of quantum test particles. A static spacetime is quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint. Here Weyl's limit point limit circle criterion is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes to help elucidate the physical properties of the spacetimes in terms of their metric parameters.

  12. Asymptotic stability of singularly perturbed differential equations

    NASA Astrophysics Data System (ADS)

    Artstein, Zvi

    2017-02-01

    Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.

  13. Dissipative universe-inflation with soft singularity

    NASA Astrophysics Data System (ADS)

    Brevik, Iver; Timoshkin, Alexander V.

    We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann-Robertson-Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data, while for the scalar-to-tensor ratio, there are minor deviations.

  14. The Singularity Problem in Brane Cosmology

    NASA Astrophysics Data System (ADS)

    Antoniadis, Ignatios; Cotsakis, Spiros

    2017-02-01

    We review results about the development and asymptotic nature of singularities in `brane-bulk' systems. These arise for warped metrics obeying the 5-dimensional Einstein equations with fluid-like sources, and including a brane 4-metric that is either Minkowski or de Sitter or Anti-de Sitter. We characterize all singular Minkowski brane solutions, and look for regular solutions with nonzero curvature. We briefly comment on matching solutions, energy conditions and finite Planck mass criteria for admissibility, and we briefly discuss the connection of these results to ambient theory.

  15. A dynamical system approach to the construction of singular solutions of some degenerate elliptic equations

    NASA Astrophysics Data System (ADS)

    Huentutripay, Jorge; Jazar, Mustapha; Véron, Laurent

    We study the existence of singular separable solutions to the 2-dimensional quasilinear equation -∇·(|∇ u| p-2 ∇ u)+| u| q-1 u=0 under the form u( r, θ)= r- βω( θ). We obtain the full description of the set of such solutions by combining a 2-dimensional shooting method with a phase plane analysis approach.

  16. Kohn singularity and Kohn anomaly in conventional superconductors--role of pairing mechanism.

    PubMed

    Chaudhury, Ranjan; Das, Mukunda P

    2013-03-27

    We present a theoretical analysis of the Kohn singularity and Kohn anomaly in the superconducting phase of a three-dimensional metallic system. We show that a phonon mechanism-based Cooper pairing in a Fermi liquid metal can lead to these phenomena quite naturally. The results are discussed against the background of some recent experimental findings.

  17. Impulse elimination for positive singular systems using derivative output feedback

    NASA Astrophysics Data System (ADS)

    Muhafzan; Zulakmal

    2017-09-01

    Nowadays the singular system constitute an interesting study considering it can become a mathematical model of variety of real problems. It is well known that the solutions of singular system can contain impulse. In some applications, this impulse constitutes some unwanted behaviour because it may cause degradation in the performance or even destroy the system. The positive singular system constitute a singular system in which its solution belong to some nonnegative octant. In this paper we propose a new technique to eliminate the impulses of the positive singular system using a derivative output feedback. Some new theorem that ensures the freedom of impulse of the positive singular system is established.

  18. Propagation of the Lissajous singularity dipole through an astigmatic lens

    NASA Astrophysics Data System (ADS)

    Chen, Haitao; Gao, Zenghui; Zou, Xuefang; Huang, Weigang; Wang, Fanhou

    2013-11-01

    The propagation was investigated of a pair of Lissajous singularities of opposite singularity index called the Lissajous singularity dipole (LSD) through an astigmatic lens. It is shown that after passing through the lens the positions of the singularities are inverted and more than two LSDs occur. Changes in the degree of polarization of the LSDs as well as in the shape of the Lissajous figures also occur. In addition, Lissajous singularities may take place at the focal plane, and a single Lissajous singularity may appear and vanish under certain conditions. The results are compared with those of previous work.

  19. Embedded Data Representations.

    PubMed

    Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre

    2017-01-01

    We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles are making it increasingly easier to display data in-context. While researchers and artists have already begun to create embedded data representations, the benefits, trade-offs, and even the language necessary to describe and compare these approaches remain unexplored. In this paper, we formalize the notion of physical data referents - the real-world entities and spaces to which data corresponds - and examine the relationship between referents and the visual and physical representations of their data. We differentiate situated representations, which display data in proximity to data referents, and embedded representations, which display data so that it spatially coincides with data referents. Drawing on examples from visualization, ubiquitous computing, and art, we explore the role of spatial indirection, scale, and interaction for embedded representations. We also examine the tradeoffs between non-situated, situated, and embedded data displays, including both visualizations and physicalizations. Based on our observations, we identify a variety of design challenges for embedded data representation, and suggest opportunities for future research and applications.

  20. Symmetry breaking in smectics and surface models of their singularities.

    PubMed

    Chen, Bryan Gin-ge; Alexander, Gareth P; Kamien, Randall D

    2009-09-15

    The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, whereas disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need to add compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.

  1. Asymmetric color image encryption based on singular value decomposition

    NASA Astrophysics Data System (ADS)

    Yao, Lili; Yuan, Caojin; Qiang, Junjie; Feng, Shaotong; Nie, Shouping

    2017-02-01

    A novel asymmetric color image encryption approach by using singular value decomposition (SVD) is proposed. The original color image is encrypted into a ciphertext shown as an indexed image by using the proposed method. The red, green and blue components of the color image are subsequently encoded into a complex function which is then separated into U, S and V parts by SVD. The data matrix of the ciphertext is obtained by multiplying orthogonal matrices U and V while implementing phase-truncation. Diagonal entries of the three diagonal matrices of the SVD results are abstracted and scrambling combined to construct the colormap of the ciphertext. Thus, the encrypted indexed image covers less space than the original image. For decryption, the original color image cannot be recovered without private keys which are obtained from phase-truncation and the orthogonality of V. Computer simulations are presented to evaluate the performance of the proposed algorithm. We also analyze the security of the proposed system.

  2. Singular Lyapunov spectra and conservation laws.

    PubMed

    Bohr, T.; Grinstein, G.; Jayaprakash, C.

    1995-06-01

    We give analytic arguments and numerical evidence to show that the presence of conservation laws can produce a singularity in the spectrum of Lyapunov exponents for extended dynamical systems of low spatial dimensionality. This phenomenon can be used, e.g., for finding hidden conservation laws. (c) 1995 American Institute of Physics.

  3. Singularity and Community: Levinas and Democracy

    ERIC Educational Resources Information Center

    Zhao, Guoping

    2016-01-01

    This article explores and extends Levinas's ideas of singularity and community as multiplicity and argues that his identification of language and discourse as the means to create ethical communities provides tangible possibilities for rebuilding genuine democracy in a humane world. These ideas help us reimagine school and classroom as communities…

  4. SINGULAR INTEGRALS AND THE PRINCIPAL SERIES

    PubMed Central

    Knapp, A. W.; Stein, E. M.

    1969-01-01

    The L2 theory of singular integral operators on nilpotent Lie groups is studied, extending known results for IRn. The intertwining operators for the representations of the simple Lie groups of real rank one turn out to be of this type. As a result we determine which representations of the principal series of these groups are irreducible. PMID:16591758

  5. Gravitational lensing by rotating naked singularities

    SciTech Connect

    Gyulchev, Galin N.; Yazadjiev, Stoytcho S.

    2008-10-15

    We model massive compact objects in galactic nuclei as stationary, axially symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are functions of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The pointlike caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation, we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis-Newman-Winicour naked singularities.

  6. Singularity and Community: Levinas and Democracy

    ERIC Educational Resources Information Center

    Zhao, Guoping

    2016-01-01

    This article explores and extends Levinas's ideas of singularity and community as multiplicity and argues that his identification of language and discourse as the means to create ethical communities provides tangible possibilities for rebuilding genuine democracy in a humane world. These ideas help us reimagine school and classroom as communities…

  7. Strong curvature singularities and causal simplicity

    SciTech Connect

    Krolak, A. )

    1992-02-01

    Techniques of differential topology in Lorentzian manifolds developed by Geroch, Hawking, and Penrose are used to rule out a class of locally naked strong curvature singularities in strongly causal space-times. This result yields some support to the validity of Penrose's strong cosmic censorship hypothesis.

  8. Configuration-Control Scheme Copes With Singularities

    NASA Technical Reports Server (NTRS)

    Seraji, Homayoun; Colbaugh, Richard D.

    1993-01-01

    Improved configuration-control scheme for robotic manipulator having redundant degrees of freedom suppresses large joint velocities near singularities, at expense of small trajectory errors. Provides means to enforce order of priority of tasks assigned to robot. Basic concept of configuration control of redundant robot described in "Increasing The Dexterity Of Redundant Robots" (NPO-17801).

  9. A numerical method of detecting singularity

    NASA Technical Reports Server (NTRS)

    Laporte, M.; Vignes, J.

    1978-01-01

    A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.

  10. 'Footballs', conical singularities, and the Liouville equation

    SciTech Connect

    Redi, Michele

    2005-02-15

    We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.

  11. Dynamics of learning near singularities in layered networks.

    PubMed

    Wei, Haikun; Zhang, Jun; Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi

    2008-03-01

    We explicitly analyze the trajectories of learning near singularities in hierarchical networks, such as multilayer perceptrons and radial basis function networks, which include permutation symmetry of hidden nodes, and show their general properties. Such symmetry induces singularities in their parameter space, where the Fisher information matrix degenerates and odd learning behaviors, especially the existence of plateaus in gradient descent learning, arise due to the geometric structure of singularity. We plot dynamic vector fields to demonstrate the universal trajectories of learning near singularities. The singularity induces two types of plateaus, the on-singularity plateau and the near-singularity plateau, depending on the stability of the singularity and the initial parameters of learning. The results presented in this letter are universally applicable to a wide class of hierarchical models. Detailed stability analysis of the dynamics of learning in radial basis function networks and multilayer perceptrons will be presented in separate work.

  12. Numerical solution of the Kolmogorov-Feller equation with singularities

    NASA Astrophysics Data System (ADS)

    Baranov, N. A.; Turchak, L. I.

    2010-02-01

    A method is proposed for solving the Kolmogorov-Feller integro-differential equation with kernels containing delta function singularities. The method is based on a decomposition of the solution into regular and singular parts.

  13. On (non)elementary singularities in Liénard systems

    NASA Astrophysics Data System (ADS)

    Ferčec, Brigita

    2017-07-01

    Liénard systems originate from ordinary differential equation (ODE) of the form x ¨+f (x )x ˙+g (x )=0 , which is well-known in (electro)mechanics and for example in radio and vacuum tube technology. The Van der Pol oscillator, which is a textbook example of a system with a limit cycle, is governed by the Liénard equation. There are two types of phase system representations in the literature: x' = y - F(x), y' = - g(x) and x' = y, y ' = -f(x)y - g(x), where F'(x) = f(x). In our case f(0)= f'(0) = g(0) = 0, g'(0) = c1, which makes (0,0) possibly nonelementary nonhyperbolic singular point of the system. Liénard showed that under some conditions on f(x) and g(x) in the system auto-oscillations arise. In this paper we consider a five-parameter family of Liénard systems with a possibly nonhyperbolic singular point. In the case of hyperbolic singularity according to the Hartman-Grobman theorem the stability of the singularity is preserved. In the case of nonhyperbolic singularity we resolve the so called center-focus problem and provide the numerical simulation of the corresponding oscillations. Recently, some generalizations of Liénard systems are studied for cyclicity, which is a part of famous Hilbert's sixteenth problem.

  14. Non-deformed singular and non-singular exponential-type potentials.

    PubMed

    Pe Na, J J; Ovando, G; Morales, J; García-Ravelo, J

    2017-08-18

    The canonical transformation method applied to the Schrödinger equation to transform it into a second-order differential equation of hypergeometric-type is presented. Starting from there, those exactly solvable multiparameter exponential-type (ME-T) potentials with hypergeometric wavefunctions that belong to the families of radial (singular) and one-dimensional (non-singular) potentials, are obtained. Furthermore, we show how the choice of the involved parameters leads, as particular cases, to different deformed or non-deformed potential models already used in the study of electronic properties of diatomic molecules. Also, the analysis of parameters lets us identify the couple of potential partners (singular/non-singular) that correspond to each choice of the parameters appearing in the ME-T potential. As a useful application of the proposal, the most important non-deformed exponential potential models are considered for which it can be viewed as a unified treatment with the following advantages: (1) It is not necessary to use a special method to solve the Schrödinger equation for a specific potential model because solution is obtained as particular case by the simple choice of the involved parameters; (2) The families of singular and non-singular potentials are straightforward identified; (3) The corresponding associated partners, between radial and one-dimensional non-deformed potentials, are found; (4) New potentials, as interesting alternatives for quantum applications, are obtained. In addition, from the conditions that parameters must meet to have physically acceptable solutions, we establish the requirements for the existence or not of singular/non-singular potential partners.

  15. Spectral singularities and Bragg scattering in complex crystals

    SciTech Connect

    Longhi, S.

    2010-02-15

    Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.

  16. 7 CFR 61.1 - Words in singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 3 2010-01-01 2010-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall be...

  17. 7 CFR 900.20 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

  18. 7 CFR 900.36 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall be...

  19. 7 CFR 900.1 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

  20. 7 CFR 900.100 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

  1. 7 CFR 46.1 - Words in singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the plural...

  2. 7 CFR 1200.50 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  3. 7 CFR 900.50 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

  4. Singular perturbation and time scale approaches in discrete control systems

    NASA Technical Reports Server (NTRS)

    Naidu, D. S.; Price, D. B.

    1988-01-01

    After considering a singularly perturbed discrete control system, a singular perturbation approach is used to obtain outer and correction subsystems. A time scale approach is then applied via block diagonalization transformations to decouple the system into slow and fast subsystems. To a zeroth-order approximation, the singular perturbation and time-scale approaches are found to yield equivalent results.

  5. Fold, Transcritical and Pitchfork Singularities for Time-Reversible Systems

    NASA Astrophysics Data System (ADS)

    Buzzi, C. A.; Silva, P. R.; Teixeira, M. A.

    This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

  6. 7 CFR 61.1 - Words in singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 3 2012-01-01 2012-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...

  7. 7 CFR 1200.50 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 10 2013-01-01 2013-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

  8. 7 CFR 46.1 - Words in singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 2 2013-01-01 2013-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...

  9. 7 CFR 900.36 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...

  10. 7 CFR 900.50 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  11. 7 CFR 900.20 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...

  12. 7 CFR 900.100 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  13. 7 CFR 900.50 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  14. 7 CFR 900.1 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  15. 7 CFR 900.1 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  16. 7 CFR 900.100 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  17. 7 CFR 900.36 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...

  18. 7 CFR 900.50 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  19. 7 CFR 900.1 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  20. 7 CFR 61.1 - Words in singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 3 2013-01-01 2013-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...

  1. 7 CFR 61.1 - Words in singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 3 2014-01-01 2014-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...

  2. 7 CFR 1200.50 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 10 2012-01-01 2012-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

  3. 7 CFR 900.36 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...

  4. 7 CFR 900.36 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...

  5. 7 CFR 1200.50 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 10 2014-01-01 2014-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

  6. 7 CFR 46.1 - Words in singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 2 2014-01-01 2014-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...

  7. 7 CFR 900.1 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  8. 7 CFR 900.100 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  9. 7 CFR 900.20 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...

  10. 7 CFR 900.20 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...

  11. 7 CFR 900.50 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  12. 7 CFR 1200.50 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 10 2011-01-01 2011-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

  13. 7 CFR 61.1 - Words in singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 3 2011-01-01 2011-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...

  14. 7 CFR 900.20 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...

  15. 7 CFR 46.1 - Words in singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 2 2012-01-01 2012-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...

  16. 7 CFR 46.1 - Words in singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 2 2011-01-01 2011-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...

  17. 7 CFR 900.100 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

  18. 32 CFR 1602.22 - Singular and plural.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 32 National Defense 6 2010-07-01 2010-07-01 false Singular and plural. 1602.22 Section 1602.22 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.22 Singular and plural. Words importing the singular number shall include the plural number,...

  19. Singularity analysis of frequency density of isotop age data

    NASA Astrophysics Data System (ADS)

    Cheng, Qiuming

    2017-04-01

    Frequency distribution (histogram) calculated on the basis of igneous and detrital zircon U-Pb ages has been commonly utilized to interpret the age (range) of magmatic events. The temporal properties of this type of data have also been integrated with other types of isotope data (e.g., neodymium, hafnium, and oxygen) to describe the high magmatic addition rate (MAR) caused by plate subduction. Major peaks are identified to determine pulses of high-volume magmatic flare-ups related to subduction. In this paper, power-law models are applied to analyze these age peaks. The strong singularities of these models indicate that magmatic flare ups might be related to nonlinear phenomena of plate subduction including but being not limited to phase transition, self-organized criticality and multiplicative cascade processes. The case studies chosen for methodology validation include an igneous zircon U-Pb datasets from Gangdese arc, a orogen related to the India-Asia collision and from the Coastal Batholith related to east pacific plate subduction. It was found that the age density around peaks ca 51-50 Ma in both datasets can be fitted by power-law functions with the age interval about 30 - 40 Myr. The positive singularities of the age peaks estimated by these power-law models suggest that these age peaks might be related to magmatic flare-ups caused by multiplicative cascade and self-organized criticality tectonic processes.

  20. Raman q-plates for Singular Atom Optics

    NASA Astrophysics Data System (ADS)

    Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.

    2016-05-01

    We use a coherent two-photon Raman interaction as the atom-optic equivalent of a birefringent optical q-plate to facilitate spin-to-orbital angular momentum conversion in a pseudo-spin-1/2 BEC. A q-plate is a waveplate with a fixed retardance but a spatially varying fast axis orientation angle. We derive the time evolution operator for the system and compare it to a Jones matrix for an optical waveplate to show that in our Raman q-plate, the equivalent orientation of the fast axis is described by the relative phase of the Raman beams and the retardance is determined by the pulse area. The charge of the Raman q-plate is determined by the orbital angular momentum of the Raman beams, and the beams contain umbilic C-point polarization singularities which are imprinted into the condensate as spin singularities: lemons, stars, spirals, and saddles. By tuning the optical beam parameters, we can create a full-Bloch BEC, which is a coreless vortex that contains every possible superposition of two spin states, that is, it covers the Bloch sphere.

  1. Topological phase transition in the Scheidegger model of river networks

    NASA Astrophysics Data System (ADS)

    Oppenheim, Jacob N.; Magnasco, Marcelo O.

    2012-08-01

    Transport networks are found at the heart of myriad natural systems, yet are poorly understood, except for the case of river networks. The Scheidegger model, in which rivers are convergent random walks, has been studied only in the case of flat topography, ignoring the variety of curved geometries found in nature. Embedding this model on a cone, we find a convergent and a divergent phase, corresponding to few, long basins and many, short basins, respectively, separated by a singularity, indicating a phase transition. Quantifying basin shape using Hacks law l˜ah gives distinct values for h, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular, differing number and shapes of arterial and venous trees.

  2. Modular error embedding

    DOEpatents

    Sandford, II, Maxwell T.; Handel, Theodore G.; Ettinger, J. Mark

    1999-01-01

    A method of embedding auxiliary information into the digital representation of host data containing noise in the low-order bits. The method applies to digital data representing analog signals, for example digital images. The method reduces the error introduced by other methods that replace the low-order bits with auxiliary information. By a substantially reverse process, the embedded auxiliary data can be retrieved easily by an authorized user through use of a digital key. The modular error embedding method includes a process to permute the order in which the host data values are processed. The method doubles the amount of auxiliary information that can be added to host data values, in comparison with bit-replacement methods for high bit-rate coding. The invention preserves human perception of the meaning and content of the host data, permitting the addition of auxiliary data in the amount of 50% or greater of the original host data.

  3. Embedded Sensor Networks

    NASA Astrophysics Data System (ADS)

    Iyengar, Sitharama S.

    Embedded sensor networks are distributed systems for sensing and in situ processing of spatially and temporally dense data from resource-limited and harsh environments such as seismic zones, ecological contamination sites are battle fields. From an application point of view, many interesting questions arise from sensor network technology that go far beyond the networking/computing aspects of the embedded system. This talk presents an overview of various open problems that are both of mathematical and engineering interests. These problems include sensor-centric quality of routing/energy optimization among other graph theoretic problems.

  4. Metric Description of Singular Defects in Isotropic Materials

    NASA Astrophysics Data System (ADS)

    Kupferman, Raz; Moshe, Michael; Solomon, Jake P.

    2015-06-01

    Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with the configuration of a body in classical elasticity is the sum of local contributions that arise from a discrepancy between the actual metric and the reference metric. In contrast, the modeling of defects in solids has traditionally involved extra structure on the material manifold, notably torsion to quantify the density of dislocations and non-metricity to represent the density of point defects. We show that all the classical defects can be described within the framework of classical elasticity using tensor fields that only assume a metric structure. Specifically, bodies with singular defects can be viewed as affine manifolds; both disclinations and dislocations are captured by the monodromy that maps curves that surround the loci of the defects into affine transformations. Finally, we showthat two dimensional defectswith trivial monodromy are purely local in the sense that if we remove from the manifold a compact set that contains the locus of the defect, the punctured manifold can be isometrically embedded in a Euclidean space.

  5. An Improved Transformation and Optimized Sampling Scheme for the Numerical Evaluation of Singular and Near-Singular Potentials

    NASA Technical Reports Server (NTRS)

    Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.

    2007-01-01

    Simple and efficient numerical procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration scheme.

  6. Midplane Ices in the Embedded Phase

    NASA Astrophysics Data System (ADS)

    Drozdovskaya, Maria; Walsh, Catherine; van Dishoeck, Ewine

    2015-08-01

    Icy grains in the midplanes of the youngest protoplanetary disks are the building blocks of protoplanets and protocometary bodies. Our Solar System shows significant chemical diversity. The chemical content is thought to be either inherited from the initial prestellar cloud, out of which our Solar System formed, or formed in-situ during the subsequent evolution of the protoplanetary disk. In this poster, the chemical analysis of midplanes in the context of globally evolving and collapsing star-forming systems will be presented. Previous studies compared various solid species relative to water ice in comets and towards young protostars [e.g., 1, 2, 3]. It remains unclear whether the overlap in abundances is just a coincidence or whether the origins of cometary ices are that of a prestellar cloud. For this work, an axisymmentric 2D semi-analytic collapse model [4], wavelength-dependent radiative transfer calculations with RADMC3D [5] and a comprehensive gas-grain chemical network [6] are used to pin down ice abundances in a midplane. The methanol content of protoplanetary disks will be presented [7], but also that of other main ice components, such as water, carbon monoxide and carbon dioxide [8]. Our models can be used to probe the validity of theories on the origin of chemical complexity and also to access the degree of processing upon inheritance into the forming disk.[1] Öberg K. I., Boogert A. C. A., Pontoppidan K. M., van den Broek S., van Dishoeck E. F., Bottinelli S., Blake G. A., Evans, II N. J., 2011, ApJ, 740, 109[2] Mumma M. J., Charnley S. B., 2011, ARA&A, 49, 471[3] Bockelée-Morvan D. et al., 2000, A&A, 353, 1101[4] Visser R., van Dishoeck E. F., Doty S. D., Dullemond C. P., 2009, A&A, 495, 881[5] Dullemond C. P., Dominik C., 2004, A&A, 417, 159[6] Walsh C., Millar T. J., Nomura H., Herbst E., Widicus Weaver S., Aikawa Y., Laas J. C., Vasyunin A. I., 2014, A&A, 563, A33[7] Drozdovskaya M. N., Walsh C., Visser R., Harsono D., van Dishoeck E. F., 2014, MNRAS, 445, 913[8] Drozdovskaya et al., in prep.

  7. Singularity theory of fitness functions under dimorphism equivalence.

    PubMed

    Wang, Xiaohui; Golubitsky, Martin

    2016-09-01

    We apply singularity theory to classify monomorphic singular points as they occur in adaptive dynamics. Our approach is based on a new equivalence relation called dimorphism equivalence, which is the largest equivalence relation on strategy functions that preserves ESS singularities, CvSS singularities, and dimorphisms. Specifically, we classify singularities up to topological codimension two and compute their normal forms and universal unfoldings. These calculations lead to the classification of local mutual invasibility plots that can be seen generically in systems with two parameters.

  8. Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

    SciTech Connect

    Haro, Jaume de

    2012-11-01

    It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent way to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.

  9. Singular Points of the Polarization Tensor

    NASA Astrophysics Data System (ADS)

    Molodensky, M. M.; Starkova, L. I.

    1996-03-01

    The problem to compute the magnetic field above the chromosphere using data of the vector τ = B t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors τ is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation tensor, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation tensor define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of Hα chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.

  10. Singular electrostatic energy of nanoparticle clusters

    NASA Astrophysics Data System (ADS)

    Qin, Jian; Krapf, Nathan W.; Witten, Thomas A.

    2016-02-01

    The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation h has a singular logarithmic dependence on h . We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact c (h ) , together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.

  11. Singular Function Integration in Computational Physics

    NASA Astrophysics Data System (ADS)

    Hasbun, Javier

    2009-03-01

    In teaching computational methods in the undergraduate physics curriculum, standard integration approaches taught include the rectangular, trapezoidal, Simpson, Romberg, and others. Over time, these techniques have proven to be invaluable and students are encouraged to employ the most efficient method that is expected to perform best when applied to a given problem. However, some physics research applications require techniques that can handle singularities. While decreasing the step size in traditional approaches is an alternative, this may not always work and repetitive processes make this route even more inefficient. Here, I present two existing integration rules designed to handle singular integrals. I compare them to traditional rules as well as to the exact analytic results. I suggest that it is perhaps time to include such approaches in the undergraduate computational physics course.

  12. Beyond singular values and loop shapes

    NASA Technical Reports Server (NTRS)

    Stein, G.

    1985-01-01

    The status of singular value loop-shaping as a design paradigm for multivariable feedback systems is reviewed. It shows that this paradigm is an effective design tool whenever the problem specifications are spacially round. The tool can be arbitrarily conservative, however, when they are not. This happens because singular value conditions for robust performance are not tight (necessary and sufficient) and can severely overstate actual requirements. An alternate paradign is discussed which overcomes these limitations. The alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The state of the art currently permits analysis of feedback systems within this new paradigm. Synthesis remains a subject of research.

  13. Embedded-monolith armor

    DOEpatents

    McElfresh, Michael W.; Groves, Scott E; Moffet, Mitchell L.; Martin, Louis P.

    2016-07-19

    A lightweight armor system utilizing a face section having a multiplicity of monoliths embedded in a matrix supported on low density foam. The face section is supported with a strong stiff backing plate. The backing plate is mounted on a spall plate.

  14. Embedded foveation image coding.

    PubMed

    Wang, Z; Bovik, A C

    2001-01-01

    The human visual system (HVS) is highly space-variant in sampling, coding, processing, and understanding. The spatial resolution of the HVS is highest around the point of fixation (foveation point) and decreases rapidly with increasing eccentricity. By taking advantage of this fact, it is possible to remove considerable high-frequency information redundancy from the peripheral regions and still reconstruct a perceptually good quality image. Great success has been obtained previously by a class of embedded wavelet image coding algorithms, such as the embedded zerotree wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT) algorithms. Embedded wavelet coding not only provides very good compression performance, but also has the property that the bitstream can be truncated at any point and still be decoded to recreate a reasonably good quality image. In this paper, we propose an embedded foveation image coding (EFIC) algorithm, which orders the encoded bitstream to optimize foveated visual quality at arbitrary bit-rates. A foveation-based image quality metric, namely, foveated wavelet image quality index (FWQI), plays an important role in the EFIC system. We also developed a modified SPIHT algorithm to improve the coding efficiency. Experiments show that EFIC integrates foveation filtering with foveated image coding and demonstrates very good coding performance and scalability in terms of foveated image quality measurement.

  15. Radiation Tolerant Embedded Memory

    DTIC Science & Technology

    2007-11-02

    REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 ...currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1 . REPORT DATE (DD-MM-YYYY) 27-06-2003 2. REPORT TYPE SBIR...Tolerant Embedded Memory 1 Table of Contents: Table of Contents

  16. Community-Embedded Learning

    ERIC Educational Resources Information Center

    Kazmer, Michelle M.

    2005-01-01

    Online learners often stay located in, and tied to, their communities, kinship networks, households, and workplaces. Institutions providing online education can thus create ties to communities as students draw their learning into networks in which they are already embedded. Frequent interactions across multiple media that are afforded by…

  17. Embedding Quantum Simulator

    NASA Astrophysics Data System (ADS)

    di Candia, Roberto; Mejia, Bernabé; Castillo, Hernan; Simon Pedernales, Julen; Casanova, Jorge; Solano, Enrique

    2014-03-01

    We introduce the concept of embedding quantum simulator, a paradigm allowing efficient computation of dynamical quantities requiring full quantum tomography in a standard quantum simulator (one-to-one quantum simulator). The concept consists in the suitable encoding of a simulated quantum dynamics in the enlarged Hilbert space of an embedding quantum simulator. In this manner, non-trivial quantities are mapped onto physical observables, overcoming the necessity of full tomography, and reducing drastically the experimental requirements. As examples, we discuss how to evaluate entanglement monotones and time correlation functions, each in a suitable embedding quantum simulator. Finally, we expect that the proposed embedding framework paves the way for a general theory of enhanced one-to-one quantum simulators. This work is supported by Spanish MINECO FIS2012-36673-C03-02; UPV/EHU UFI 11/55; UPV/EHU PhD fellowship; Basque Government IT472-10; SOLID, CCQED, PROMISCE, SCALEQIT EU projects; and Marco Polo PUCP grant.

  18. Modified Embedded Atom Method

    SciTech Connect

    Rudd, R. E.

    2012-08-01

    Interatomic force and energy calculation subroutine to be used with the molecular dynamics simulation code LAMMPS (Ref a.). The code evaluated the total energy and atomic forces (energy gradient) according to a cubic spline-based variant (Ref b.) of the Modified Embedded Atom Method (MEAM) with a additional Stillinger-Weber (SW) contribution.

  19. Testing framework for embedded languages

    NASA Astrophysics Data System (ADS)

    Leskó, Dániel; Tejfel, Máté

    2012-09-01

    Embedding a new programming language into an existing one is a widely used technique, because it fastens the development process and gives a part of a language infrastructure for free (e.g. lexical, syntactical analyzers). In this paper we are presenting a new advantage of this development approach regarding to adding testing support for these new languages. Tool support for testing is a crucial point for a newly designed programming language. It could be done in the hard way by creating a testing tool from scratch, or we could try to reuse existing testing tools by extending them with an interface to our new language. The second approach requires less work, and also it fits very well for the embedded approach. The problem is that the creation of such interfaces is not straightforward at all, because the existing testing tools were mostly not designed to be extendable and to be able to deal with new languages. This paper presents an extendable and modular model of a testing framework, in which the most basic design decision was to keep the - previously mentioned - interface creation simple and straightforward. Other important aspects of our model are the test data generation, the oracle problem and the customizability of the whole testing phase.

  20. Hardware Implementation of Singular Value Decomposition

    NASA Astrophysics Data System (ADS)

    Majumder, Swanirbhar; Shaw, Anil Kumar; Sarkar, Subir Kumar

    2016-06-01

    Singular value decomposition (SVD) is a useful decomposition technique which has important role in various engineering fields such as image compression, watermarking, signal processing, and numerous others. SVD does not involve convolution operation, which make it more suitable for hardware implementation, unlike the most popular transforms. This paper reviews the various methods of hardware implementation for SVD computation. This paper also studies the time complexity and hardware complexity in various methods of SVD computation.

  1. Symmetries and singularities of the Szekeres system

    NASA Astrophysics Data System (ADS)

    Paliathanasis, Andronikos; Leach, P. G. L.

    2017-04-01

    The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noether's theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the Left or Right Painlevé Series which describes the expansions.

  2. Acquisition of Singular-Plural Morphology

    ERIC Educational Resources Information Center

    Wood, Justin N.; Kouider, Sid; Carey, Susan

    2009-01-01

    A manual search paradigm explored the development of English singular-plural comprehension. After being shown a box into which they could reach but not see, infants heard verbal descriptions about the contents of the box (e.g., "There are some cars in the box" vs. "There is a car in the box)" and were then allowed to reach into the box. At 24…

  3. Invariant measures for singular hyperbolic attractors

    SciTech Connect

    Sataev, Evgueni A

    2010-05-11

    This paper continues the author's previous paper, where strong unstable spaces were constructed for a singular hyperbolic attractor. In this paper the existence of local strongly unstable manifolds and invariant measures of Sinai-Bowen-Ruelle type is established. The properties of such measures are studied. It is proved that the number of ergodic components is finite and the set of periodic trajectories is dense. Bibliography: 34 titles.

  4. Acquisition of Singular-Plural Morphology

    ERIC Educational Resources Information Center

    Wood, Justin N.; Kouider, Sid; Carey, Susan

    2009-01-01

    A manual search paradigm explored the development of English singular-plural comprehension. After being shown a box into which they could reach but not see, infants heard verbal descriptions about the contents of the box (e.g., "There are some cars in the box" vs. "There is a car in the box)" and were then allowed to reach into the box. At 24…

  5. Singularities in big-bang cosmology

    NASA Astrophysics Data System (ADS)

    Penrose, R.

    1988-03-01

    A review of the history of the development of the big bang theory is presented, including the nature of singularities in black holes and their contribution to the study of the origin of the universe. Various models of the origin of the universe, the question of cosmic censorship, and the possible effects of gravitational collapse are examined. The relationship between considerations of quantum gravity and the structure of quantum theory is discussed.

  6. Bergman kernel and complex singularity exponent

    NASA Astrophysics Data System (ADS)

    Chen, Boyong; Lee, Hanjin

    2009-12-01

    We give a precise estimate of the Bergman kernel for the model domain defined by $\\Omega_F=\\{(z,w)\\in \\mathbb{C}^{n+1}:{\\rm Im}w-|F(z)|^2>0\\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\\mathbb{C}^n$ to $\\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.

  7. Formation of turbulence around flow singularities

    NASA Technical Reports Server (NTRS)

    Zak, M.

    1983-01-01

    The formation of turbulence around singular points of a flow such as stagnation points, tangential jumps of velocity, are analyzed. It is proved that turbulence is inevitably generated by the rear stagnation point, but cannot be generated by the nose stagnation point of a streamlined body. Special attention is paid to an evolution of turbulence induced by a tangential jump of velocity. A qualitative analysis of a turbulent flow between two rotating concentric cylinders and around a streamlined cylinder is given.

  8. Isometric embeddings of polyhedra

    NASA Astrophysics Data System (ADS)

    Minemyer, Barry

    An indefinite metric polyhedron is a triple (X, T, g) where X is a topological space, T is a simplicial triangulation of X with edge set E, and g is a function from E to the reals. g assigns to each k-dimensional simplex S a unique quadratic form on Rk, denoted by G(S). An indefinite metric polyhedron is called a Euclidean polyhedron if the form G(S) is positive definite for every simplex S. Rpq denotes R p + q endowed with the inner product of signature (p, q). Our first result is that every compact n-dimensional indefinite metric polyhedron with vertex set V admits a simplicial isometric embedding into Rqq where q = max{d, 2n + 1} and d = max{deg(v) | v is in V}. We can use the compact case to extend to the non-compact case, but only if we assume that d = max{deg(v) | v is in V} is less than infinity. Specifically, every (non-compact) indefinite metric polyhedron admits a simplicial isometric embedding into Rpp where p = 2q(d3 - d2 + d + 1) and q and d are defined as above. Finally we use results of Akopyan and Greene to prove that every n-dimensional indefinite metric polyhedron admits a piecewise linear isometric embedding into Rn2n. In Chapter 2 we prove that every short (1-Lipschitz) map from an n-dimensional Euclidean polyhedron into EN is epsilon close to a pl isometric embedding (for anyepsilon > 0) provided N ≥ 3n. We can relax the dimensionality of the Euclidean space to 2n + 1 if we allow our map to be continuous instead of pl. These results are extensions of a result due to Akopyan. We provide a detailed proof of Akopyan's Theorem, as the only currently available proof is in Russian. The remaining results in this work are applications of our continuous isometric embedding theorem above. This result is used to prove that every Pro-Euclidean space of rank at most n admits an isometric embedding into E2n + 1. The result, as well as a theorem due to Bridson, also allows for an approximate isometric embedding theorem for geodesic metric spaces with

  9. H(infinity) filtering for fuzzy singularly perturbed systems.

    PubMed

    Yang, Guang-Hong; Dong, Jiuxiang

    2008-10-01

    This paper considers the problem of designing H(infinity) filters for fuzzy singularly perturbed systems with the consideration of improving the bound of singular-perturbation parameter epsilon. First, a linear-matrix-inequality (LMI)-based approach is presented for simultaneously designing the bound of the singularly perturbed parameter epsilon, and H(infinity) filters for a fuzzy singularly perturbed system. When the bound of singularly perturbed parameter epsilon is not under consideration, the result reduces to an LMI-based design method for H(infinity) filtering of fuzzy singularly perturbed systems. Furthermore, a method is given for evaluating the upper bound of singularly perturbed parameter subject to the constraint that the considered system is to be with a prescribed H(infinity) performance bound, and the upper bound can be obtained by solving a generalized eigenvalue problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

  10. Wheeler-DeWitt quantization and singularities

    NASA Astrophysics Data System (ADS)

    Falciano, F. T.; Pinto-Neto, N.; Struyve, W.

    2015-02-01

    We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaître-Robertson-Walker model and investigate the question of whether or not there are singularities, in the sense that the Universe reaches zero volume. We find that for generic wave functions (i.e., nonclassical wave functions), there is a nonzero probability for a trajectory to be nonsingular. This should be contrasted to the consistent histories approach for which it was recently shown by Craig and Singh that there is always a singularity. This result illustrates that the question of singularities depends much on which version of quantum theory one adopts. This was already pointed out by Pinto-Neto et al., albeit with a different Bohmian approach. Our current Bohmian approach agrees with the consistent histories approach by Craig and Singh for single-time histories, unlike the one studied earlier by Pinto-Neto et al. Although the trajectories are usually different in the two Bohmian approaches, their qualitative behavior is the same for generic wave functions.

  11. Singularity Classes of Special 2-Flags

    NASA Astrophysics Data System (ADS)

    Mormul, Piotr

    2009-11-01

    In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp). The classical Cartan prolongations deal with rank-2 distributions and are responsible for the appearance of the Goursat distributions. Similarly, the so-called special multi-flags are generated in the result of successive applications of gCp's. Singularities of such distributions turn out to be very rich, although without functional moduli of the local classification. The paper focuses on special 2-flags, obtained by sequences of gCp's applied to rank-3 distributions. A stratification of germs of special 2-flags of all lengths into singularity classes is constructed. This stratification provides invariant geometric significance to the vast family of local polynomial pseudo-normal forms for special 2-flags introduced earlier in [Mormul P., Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157-178]. This is the main contribution of the present paper. The singularity classes endow those multi-parameter normal forms, which were obtained just as a by-product of sequences of gCp's, with a geometrical meaning.

  12. Junction point on partially singular trajectories

    NASA Astrophysics Data System (ADS)

    Odia, Ameze; Bell, David J.

    2012-12-01

    In recent times, several works have been performed on the design of fuel optimal trajectories for space navigation. These works show the possibility of the existence of partially singular trajectories for systems that are linear analytic (Park et al. 2010). Linear analytic systems may show the existence of partially singular subarcs, and the point where these subarcs meet is called a junction point. Thus, knowledge about junction conditions became necessary when solving the optimal control problem for such systems. This led to the development of two 'theorems' on junction conditions, given by McDanell and Powers (McDanell, J.P. and Powers W.F. (1971), 'Necessary Conditions for Joining Optimal Singular and Nonsingular Sub Arcs', SIAM Journal of Control, 9, 161-173). However, the second 'theorem', which is now known as a conjecture, could not satisfy all classes of linear analytic system. Therefore, the aim of this study was to detect and correct the errors in the derivation of the McDanell and Powers conjecture. The error in their derivations was corrected and then tested on two newly mathematically constructed systems. The results of these tests were found to be satisfactory. This implies that by making the necessary corrections, the conjecture can still be useful in generating a general theorem for all classes of systems.

  13. Aerodynamic influence coefficient method using singularity splines

    NASA Technical Reports Server (NTRS)

    Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

    1974-01-01

    A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

  14. Equilibrium stellar systems with spindle singularities

    NASA Technical Reports Server (NTRS)

    Shapiro, Stuart L.; Teukolsky, Saul A.

    1992-01-01

    Equilibrium sequences of axisymmetric Newtonian clusters that tend toward singular states are constructed. The distribution functions are chosen to be of the form f = f(E, Jz). The numerical method then determines the density and gravitational potential self-consistently to satisfy Poisson's equation. For the prolate models, spindle singularities arise from the depletion of angular momentum near the symmetry axis. While the resulting density enhancement is confined to the region near the axis, the influence of the spindle extends much further out through its tidal gravitational field. Centrally condensed prolate clusters may contain strong-field regions even though the spindle mass is small and the mean cluster eccentricity is not extreme. While the calculations performed here are entirely Newtonian, the issue of singularities is an important topic in general relativity. Equilibrium solutions for relativistic star clusters can provide a testing ground for exploring this issue. The methods used in this paper for building nonspherical clusters can be extended to relativistic systems.

  15. Singular value decomposition for collaborative filtering on a GPU

    NASA Astrophysics Data System (ADS)

    Kato, Kimikazu; Hosino, Tikara

    2010-06-01

    A collaborative filtering predicts customers' unknown preferences from known preferences. In a computation of the collaborative filtering, a singular value decomposition (SVD) is needed to reduce the size of a large scale matrix so that the burden for the next phase computation will be decreased. In this application, SVD means a roughly approximated factorization of a given matrix into smaller sized matrices. Webb (a.k.a. Simon Funk) showed an effective algorithm to compute SVD toward a solution of an open competition called "Netflix Prize". The algorithm utilizes an iterative method so that the error of approximation improves in each step of the iteration. We give a GPU version of Webb's algorithm. Our algorithm is implemented in the CUDA and it is shown to be efficient by an experiment.

  16. A wavefront interpretation of the singularity expansion method

    NASA Astrophysics Data System (ADS)

    Heyman, E.; Felsen, L. B.

    1985-07-01

    Felsen (1984) has shown that transient fields scattered by an object may be synthesized in terms of progressing waves (wavefronts) or oscillatory waves (resonances). The present paper is concerned with multiple interaction and resonance phenomena in a broad sense, taking into account the employment of ray terminology to identify wave transport and interaction trajectories. Along those trajectories, the time harmonic field may be expressed by the ray approximation and is then subject to the rules and constraints of the geometrical theory of diffraction (GTD). However, the field may be expressed more generally by a 'better' wave function, for example a ray integral spanning a spectrum of local plane waves whose stationary phase approximation yields GTD but which, when kept intact, is uniformly valid in transition regions where GTD fails. Attention is given to the singularity expansion method (SEM) formulation, the ray formulation, the flow graph representation, and the illustration of the presented concepts with the aid of an example.

  17. Visualizing singularities of a groundstate landscape using superconducting circuits

    NASA Astrophysics Data System (ADS)

    Lucero, Erik; Dunsworth, A.; Roushan, P.; Megrant, A.; Neill, C.; Souza, T.; Tomka, M.; Kolodrubetz, M.; Chen, Y.; Barends, R.; Campbell, B.; Chen, Z.; Chiaro, B.; Jeffrey, E.; Kelly, J.; Mutus, J.; O'Malley, P.; Quintana, C.; Sank, D.; Wenner, J.; White, T.; Polkovnikov, A.; Martinis, J.

    The defining properties of condensed matter phases are set by their groundstate wavefunctions. The adiabatic theorem provides an experimental approach for realizing such states. However, a general protocol for applying this theorem is experimentally unexplored, in particular when the energy gap is small. Using two superconducting qubits, we adiabatically prepare the entire groundstate manifold in a region of the parameter-space where degeneracies are present. We prepare these states by varying the Hamiltonian along 'geodesics' in parameter-space, obtained by minimizing the local non-adiabatic error. From the measured total magnetization of the final state, we compute the Berry curvature, where degeneracies appear as singular points, allowing us to directly visualize the degeneracies in the groundstate landscape.

  18. Kasner solutions, climbing scalars and big-bang singularity

    SciTech Connect

    Condeescu, Cezar; Dudas, Emilian E-mail: emilian.dudas@cpht.polytechnique.fr

    2013-08-01

    We elaborate on a recently discovered phenomenon where a scalar field close to big-bang is forced to climb a steep potential by its dynamics. We analyze the phenomenon in more general terms by writing the leading order equations of motion near the singularity. We formulate the conditions for climbing to exist in the case of several scalars and after inclusion of higher-derivative corrections and we apply our results to some models of moduli stabilization. We analyze an example with steep stabilizing potential and notice again a related critical behavior: for a potential steepness above a critical value, going backwards towards big-bang, the scalar undergoes wilder oscillations, with the steep potential pushing it back at every passage and not allowing the scalar to escape to infinity. Whereas it was pointed out earlier that there are possible implications of the climbing phase to CMB, we point out here another potential application, to the issue of initial conditions in inflation.

  19. Manifestation of a Fermi edge singularity in the cotunneling regime

    NASA Astrophysics Data System (ADS)

    Borin, Artem; Sukhorukov, Eugene

    2017-08-01

    The Fermi edge singularity (FES) is a prominent manifestation of the Coulomb interaction. It can be observed in a controllable way by studying the transport through a quantum dot (QD), which is electrostatically coupled to the leads. In this paper, we study how FES affects higher-order tunneling processes (cotunneling). To address this problem we use the bosonic description of the electrons in the leads, which naturally accounts for the Coulomb interaction. We report the multiscale dependence of the current through the QD on the energy of the QD level and on the bias between the leads obtained for the limit of large and small bias. The new universal powers are determined by the scattering phases due to the interaction of electrons in the leads with the charge on the QD.

  20. A randomized controlled phase II trial of a novel composition of paclitaxel embedded into neutral and cationic lipids targeting tumor endothelial cells in advanced triple-negative breast cancer (TNBC).

    PubMed

    Awada, A; Bondarenko, I N; Bonneterre, J; Nowara, E; Ferrero, J M; Bakshi, A V; Wilke, C; Piccart, M

    2014-04-01

    EndoTAG-1, composed of paclitaxel embedded in liposomal membranes targeting tumor endothelial cells, was evaluated for safety and efficacy in advanced triple-negative breast cancer (TNBC). One hundred and forty patients were treated with weekly EndoTAG-1 (22 mg/m(2)) plus paclitaxel (70 mg/m(2)), twice weekly EndoTAG-1 (2× 44 mg/m(2)), or weekly paclitaxel (90 mg/m(2)) for greater than or equal to four cycles (3-week treatment + 1-week rest) or until progression/toxicity. Primary end point was progression-free survival (PFS) rate evaluated centrally after four cycles of therapy (week 16). The study was not powered for intergroup comparisons. The PFS rate at week 16 was 59.1% [one-sided 95% CI: 45.6, ∞] on combination treatment, 34.2% [21.6, ∞] on EndoTAG-1, and 48.0% [30.5, ∞] on paclitaxel. Median PFS reached 4.2, 3.4, and 3.7 months, respectively. After complete treatment (week 41 analysis), median overall survival (OS) was 13.0, 11.9, and 13.1 months for the modified Intention-to-Treat (ITT) population and 15.1, 12.5, and 8.9 months for the per-protocol population, respectively. The clinical benefit rate was 53%, 31%, and 36% for the treatment groups. Safety analysis revealed known toxicities of the drugs with slight increases of grade 3/4 neutropenia on combination therapy. Treatment of advanced TNBC with a combination of EndoTAG-1 and standard paclitaxel [Taxol® (Bristol-Myers Squibb GmbH), or equivalent generic formulation] was well tolerated and showed antitumor efficacy. The positive trend needs to be confirmed in a randomized phase III trial. European Clinical Trials Database: EudraCT number 2006-002221-23. ClinicalTrials.gov identifier: NCT00448305.

  1. An indirect watermark hiding in discrete cosine transform–singular value decomposition domain for copyright protection

    PubMed Central

    Pal, Arup Kumar

    2017-01-01

    Digital image watermarking has emerged as a promising solution for copyright protection. In this paper, a discrete cosine transform (DCT) and singular value decomposition (SVD) based hybrid robust image watermarking method using Arnold scrambling is proposed and simulated to protect the copyright of natural images. In this proposed scheme, before embedding, watermark is scrambled with Arnold scrambling. Then, the greyscale cover image and encrypted watermark logo are decomposed into non-overlapping blocks and subsequently some selected image blocks are transformed into the DCT domain for inserting the watermark blocks permanently. For better imperceptibility and effectiveness, in this proposed algorithm, watermark image blocks are embedded into singular values of selected blocks by multiplying with a feasible scaling factor. Simulation result demonstrates that robustness is achieved by recovering satisfactory watermark data from the reconstructed cover image after applying common geometric transformation attacks (such as rotation, flip operation, cropping, scaling, shearing and deletion of lines or columns operation), common enhancement technique attacks (such as low-pass filtering, histogram equalization, sharpening, gamma correction, noise addition) and jpeg compression attacks. PMID:28680684

  2. An indirect watermark hiding in discrete cosine transform-singular value decomposition domain for copyright protection.

    PubMed

    Roy, Soumitra; Pal, Arup Kumar

    2017-06-01

    Digital image watermarking has emerged as a promising solution for copyright protection. In this paper, a discrete cosine transform (DCT) and singular value decomposition (SVD) based hybrid robust image watermarking method using Arnold scrambling is proposed and simulated to protect the copyright of natural images. In this proposed scheme, before embedding, watermark is scrambled with Arnold scrambling. Then, the greyscale cover image and encrypted watermark logo are decomposed into non-overlapping blocks and subsequently some selected image blocks are transformed into the DCT domain for inserting the watermark blocks permanently. For better imperceptibility and effectiveness, in this proposed algorithm, watermark image blocks are embedded into singular values of selected blocks by multiplying with a feasible scaling factor. Simulation result demonstrates that robustness is achieved by recovering satisfactory watermark data from the reconstructed cover image after applying common geometric transformation attacks (such as rotation, flip operation, cropping, scaling, shearing and deletion of lines or columns operation), common enhancement technique attacks (such as low-pass filtering, histogram equalization, sharpening, gamma correction, noise addition) and jpeg compression attacks.

  3. Analytical solution for multi-singular vortex Gaussian beams: the mathematical theory of scattering modes

    NASA Astrophysics Data System (ADS)

    Ferrando, A.; García-March, M. A.

    2016-06-01

    We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre-Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.

  4. Connector For Embedded Optical Fiber

    NASA Technical Reports Server (NTRS)

    Wilkerson, Charles; Hiles, Steven; Houghton, J. Richard; Holland, Brent W.

    1994-01-01

    Partly embedded fixture is simpler and sturdier than other types of outlets for optical fibers embedded in solid structures. No need to align coupling prism and lenses. Fixture includes base, tube bent at 45 degree angle, and ceramic ferrule.

  5. Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations.

    PubMed

    Czakó, Gábor; Furtenbacher, Tibor; Barletta, Paolo; Császár, Attila G; Szalay, Viktor; Sutcliffe, Brian T

    2007-07-14

    A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R(1), with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H(3)(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.

  6. Effects of finite-time singularities on gravitational waves

    NASA Astrophysics Data System (ADS)

    Kleidis, K.; Oikonomou, V. K.

    2016-10-01

    We analyze the impact of finite-time singularities on gravitational waves, in the context of F(R) gravity. We investigate which singularities are allowed to occur during the inflationary era, when gravitational waves are considered, and we discuss the quantitative implications of each allowed singularity. As we show, only a pressure singularity, the so-called Type II and also a Type IV singularity are allowed to occur during the inflationary era. In the case of a Type II, the resulting amplitude of the gravitational wave is zero or almost zero, hence this pressure singularity has a significant impact on the primordial gravitational waves. The case of a Type IV singularity is more interesting since as we show, the singularity has no effect on the amplitude of the gravitational waves. Therefore, this result combined with the fact that the Type IV singularity affects only the dynamics of inflation, leads to the conclusion that the Universe passes smoothly through a Type IV singularity.

  7. Cosmological singularity resolution from quantum gravity: The emergent-bouncing universe

    NASA Astrophysics Data System (ADS)

    Alesci, Emanuele; Botta, Gioele; Cianfrani, Francesco; Liberati, Stefano

    2017-08-01

    Alternative scenarios to the big bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so-called quantum reduced loop gravity) the Friedmann equations for cosmology are modified in such a way to replace the big bang singularity with a short bounce preceded by a metastable quantum phase in which the volume of the universe oscillates between a series of local maxima and minima. We call this hybrid scenario an "emergent-bouncing universe" since after a pure oscillating quantum phase the classical Friedmann spacetime emerges. Perspective developments and possible tests of this scenario are discussed in the end.

  8. Absence of singularity along the wet solidus of carbonated peridotite

    NASA Astrophysics Data System (ADS)

    Keshav, S.; Gudfinnsson, G. H.

    2009-12-01

    For decades, there has been interest in the physical and chemical nature of petrological systems that undergo supercritical behavior. Such behavior is witnessed when a univariant reaction gets terminated because of its intersection with a critical curve (imposed by the condition, liquid=vapor or liquid X=liquid Y), resulting in the loss of a phase, which further turns the system divariant in pressure-temperature (P-T) space. The singularities that result from these terminations are commonly referred to as second critical end-points. In petrology, such behavior is observed in hydrous, silicate melt-aqueous vapor/fluid systems. At these terminations, the solute concentrations in the aqueous vapor become high enough that it can no longer be physically distinguished from silicate melt, as seen for example in albite, quartz, and granitic systems at 10-20 kbar. However, in mantle-relevant, basaltic or ultramafic systems (e.g., MgO-SiO2-H2O; MSH), the conditions where such singularities develop have been subject to vigorous and interesting debate. For instance, in MSH peridotite analog, supercriticality is claimed either at 40 or 110-130 kbar, translating to a difference of 80-90 kbar, which further affects our understanding of chemical transport in a variety of tectonic settings. Along with water, CO2 is the most important volatile component in magmatic systems. So far, barring studies in the systems CaO-SiO2-CO2-H2O (10-32 kbar), SiO2-H2O-CO2 (7-28 kbar) and albite-H2O-CO2 (3-20 kbar), experimental/theoretical studies of the influence of mixed volatiles on melting phase relations and critical phenomena are non-existent. In an effort to clarify some of these pending issues, and to systematically add chemical complexity to MSH, here we report melting phase relations of hydrous, carbonated garnet peridotite at 22 to 70 kbar in the system CMAS-CO2-H2O. With fo+opx+cpx+garnet+carbonate+melt present, the phase relations are divariant. In this divariant region, all the water

  9. Integrated Design and Implementation of Embedded Control Systems with Scilab.

    PubMed

    Ma, Longhua; Xia, Feng; Peng, Zhe

    2008-09-05

    Embedded systems are playing an increasingly important role in control engineering. Despite their popularity, embedded systems are generally subject to resource constraints and it is therefore difficult to build complex control systems on embedded platforms. Traditionally, the design and implementation of control systems are often separated, which causes the development of embedded control systems to be highly timeconsuming and costly. To address these problems, this paper presents a low-cost, reusable, reconfigurable platform that enables integrated design and implementation of embedded control systems. To minimize the cost, free and open source software packages such as Linux and Scilab are used. Scilab is ported to the embedded ARM-Linux system. The drivers for interfacing Scilab with several communication protocols including serial, Ethernet, and Modbus are developed. Experiments are conducted to test the developed embedded platform. The use of Scilab enables implementation of complex control algorithms on embedded platforms. With the developed platform, it is possible to perform all phases of the development cycle of embedded control systems in a unified environment, thus facilitating the reduction of development time and cost.

  10. Integrated Design and Implementation of Embedded Control Systems with Scilab

    PubMed Central

    Ma, Longhua; Xia, Feng; Peng, Zhe

    2008-01-01

    Embedded systems are playing an increasingly important role in control engineering. Despite their popularity, embedded systems are generally subject to resource constraints and it is therefore difficult to build complex control systems on embedded platforms. Traditionally, the design and implementation of control systems are often separated, which causes the development of embedded control systems to be highly time-consuming and costly. To address these problems, this paper presents a low-cost, reusable, reconfigurable platform that enables integrated design and implementation of embedded control systems. To minimize the cost, free and open source software packages such as Linux and Scilab are used. Scilab is ported to the embedded ARM-Linux system. The drivers for interfacing Scilab with several communication protocols including serial, Ethernet, and Modbus are developed. Experiments are conducted to test the developed embedded platform. The use of Scilab enables implementation of complex control algorithms on embedded platforms. With the developed platform, it is possible to perform all phases of the development cycle of embedded control systems in a unified environment, thus facilitating the reduction of development time and cost. PMID:27873827

  11. Penrose's singularity theorem in a Finsler spacetime

    NASA Astrophysics Data System (ADS)

    Babak Aazami, Amir; Javaloyes, Miguel Angel

    2016-01-01

    We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.

  12. Motion of a linear vortex singularity

    SciTech Connect

    Kiknadze, L.V.; Mamaladze, Y.G.

    1980-10-01

    A formula is obtained for the velocity of a certain element of a linear vortex in a Bose gas and in helium II in terms of the contribution made to the wave function by the remaining elements of the same wave vortex and of other perturbations of the ground state of the medium. It is shown that, besides the Magnus force, the vortex is acted upon by a force proportional to the condensate-density gradient and directed opposite to the gradient. A generalization is possible to linear vortex singularities of relativistic fields that do not describe any condensed medium at all.

  13. Enumeration of curves with one singular point

    NASA Astrophysics Data System (ADS)

    Basu, Somnath; Mukherjee, Ritwik

    2016-06-01

    In this paper we obtain an explicit formula for the number of curves in P2, of degree d, passing through (d(d + 3) / 2 - k) generic points and having a singularity X, where X is of type Ak≤7 ,Dk≤7 or Ek≤7. Our method comprises of expressing the enumerative problem as the Euler class of an appropriate bundle and using a purely topological method to compute the degenerate contribution to the Euler class. These numbers have also been computed by M. Kazarian using the existence of universal formulas for Thom polynomials.

  14. Light-Front Perturbation Without Spurious Singularities

    NASA Astrophysics Data System (ADS)

    Przeszowski, Jerzy A.; Dzimida-Chmielewska, Elżbieta; Żochowski, Jan

    2016-07-01

    A new form of the light front Feynman propagators is proposed. It contains no energy denominators. Instead the dependence on the longitudinal subinterval x^2_L = 2 x+ x- is explicit and a new formalism for doing the perturbative calculations is invented. These novel propagators are implemented for the one-loop effective potential and various 1-loop 2-point functions for a massive scalar field. The consistency with results for the standard covariant Feynman diagrams is obtained and no spurious singularities are encountered at all. Some remarks on the calculations with fermion and gauge fields in QED and QCD are added.

  15. Singularity formations for a surface wave model

    NASA Astrophysics Data System (ADS)

    Castro, Angel; Córdoba, Diego; Gancedo, Francisco

    2010-11-01

    In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

  16. Disturbance Decoupling of Singular Boolean Control Networks.

    PubMed

    Liu, Yang; Li, Bowen; Lou, Jungang

    2016-01-01

    This paper investigates the controller designing for disturbance decoupling problem (DDP) of singular Boolean control networks (SBCNs). Using semi-tensor product (STP) of matrices and the Implicit Function Theorem, a SBCN is converted into the standard BCN. Based on the redundant variable separation technique, both state feedback and output feedback controllers are designed to solve the DDP of the SBCN. Sufficient conditions are also given to analyze the invariance of controllers concerning the DDP of the SBCN with function perturbation. Two illustrative examples are presented to support the effectiveness of these obtained results.

  17. Singularity structure of maximally supersymmetric scattering amplitudes.

    PubMed

    Arkani-Hamed, Nima; Bourjaily, Jacob L; Cachazo, Freddy; Trnka, Jaroslav

    2014-12-31

    We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic singularities and is free of any poles at infinity--properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA).

  18. Heating of the corona by magnetic singularities

    NASA Technical Reports Server (NTRS)

    Antiochos, Spiro K.

    1990-01-01

    Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.

  19. Steering electromagnetic beams with conical curvature singularities.

    PubMed

    Zhang, Yong-Liang; Dong, Xian-Zi; Zheng, Mei-Ling; Zhao, Zhen-Sheng; Duan, Xuan-Ming

    2015-10-15

    We describe how the transformation-optics technique can be used to design an effective medium mimicking the conical curvature singularity. Anholonomic coordinate transformation gives rise to linear topological defects that break the rotational symmetry. The bending and splitting of the optical beams are found analytically and numerically, depending on the incident direction and the topological charge. Beyond their practical applications to omnidirectional beam steering for photonics, our findings set forth an attractive realm to simulate the relevant physical phenomena in the optical laboratory.

  20. Are Singularities Integral to General Theory of Relativity?

    NASA Astrophysics Data System (ADS)

    Krori, K.; Dutta, S.

    2011-11-01

    Since the 1960s the general relativists have been deeply obsessed with the possibilities of GTR singularities - blackhole as well as cosmological singularities. Senovilla, for the first time, followed by others, showed that there are cylindrically symmetric cosmological space-times which are free of singularities. On the other hand, Krori et al. have presently shown that spherically symmetric cosmological space-times - which later reduce to FRW space-times may also be free of singularities. Besides, Mitra has in the mean-time come forward with some realistic calculations which seem to rule out the possibility of a blackhole singularity. So whether singularities are integral to GTR seems to come under a shadow.

  1. Singularities in water waves and Rayleigh-Taylor instability

    NASA Technical Reports Server (NTRS)

    Tanveer, S.

    1991-01-01

    Singularities in inviscid two-dimensional finite-amplitude water waves and inviscid Rayleigh-Taylor instability are discussed. For the deep water gravity waves of permanent form, through a combination of analytical and numerical methods, results describing the precise form, number, and location of singularities in the unphysical domain as the wave height is increased are presented. It is shown how the information on the singularity in the unphysical region has the same form as for deep water waves. However, associated with such a singularity is a series of image singularities at increasing distances from the physical plane with possibly different behavior. Furthermore, for the Rayleigh-Taylor problem of motion of fluid over a vacuum and for the unsteady water wave problem, integro-differential equations valid in the unphysical region are derived, and how these equations can give information on the nature of singularities for arbitrary initial conditions is shown.

  2. Exploring Numerical (Naked) Singularity Formation with Collisionless Matter

    NASA Astrophysics Data System (ADS)

    Okounkova, Maria; Hemberger, Daniel; Scheel, Mark

    2017-01-01

    A proposed channel for the formation of naked singularities (singularities without event horizons) is the collapse of collisionless matter. In 1991, Shapiro and Teukolsky numerically investigated the collapse of prolate spheroids of collisionless matter in axisymmetry, and found that for certain initial configurations, a singularity formed on the domain without the appearance of an apparent horizon. While this may be a candidate for naked singularity formation, the role of the axisymmetry of the configuration and the termination of the simulation at singularity formation leave the question of generically forming an event horizon open. We have implemented (fully backreacting, fully 3-dimensional) collisionless matter evolution in SpEC, the Spectral Einstein Code, and present our results for the collapse of various configurations of collisionless matter. We expand on previous results by excising singularities, giving more time for the appearance of an apparent horizon, and by considering a variety of initial configurations.

  3. Quantum fields near phantom-energy ''sudden'' singularities

    SciTech Connect

    Calderon, Hector H.

    2008-08-15

    This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized stress tensors of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to quantum vacuum contributions. This dynamical analysis is then compared to results from thermodynamical considerations. In both cases, the vacuum states of quantized scalar and spinor fields strengthen the accelerating expansion near the singularity whereas the vacuum states of vector fields weaken it.

  4. Towards generic resolution of strong singularities in loop quantum cosmology

    NASA Astrophysics Data System (ADS)

    Singh, Parampreet

    2010-10-01

    Singularities are the boundaries of classical spacetime in General Relativity. It has been always hoped that quantum gravitational effects may resolve these singularities. In recent years, progress in loop quantum cosmology has provided insights on the resolution of big bang, big crunch and other spacelike singularities. In this talk we will give an update on the recent status of the generic resolution of strong spacelike singularities in loop quantum cosmology. We will show that for flat and curved Roberston-Walker backgrounds and also for Bianchi-I models, loop quantum gravity effects resolve all strong curvature singularities. However, weak curvature singularities, that is those beyond which geodesics can be continued, may not be resolved.

  5. Finite element techniques applied to cracks interacting with selected singularities

    NASA Technical Reports Server (NTRS)

    Conway, J. C.

    1975-01-01

    The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

  6. Polarisation singularities in photonic crystals for an on-chip spin-photon interface

    NASA Astrophysics Data System (ADS)

    Beggs, Daryl M.; Young, Andrew B.; Thijssen, Arthur C. T.; Oulton, Ruth

    2015-03-01

    Integrated quantum photonic chips are a leading contender for future quantum technologies, which aim to use the entanglement and superposition properties of quantum physics to speed up the manipulation of data. Quantum information may be stored and transmitted in photons, which make excellent flying qubits. Photons suffer little from decoherence, and single qubit gates performed by changing photon phase, are straightforward. Less straightforward is the ability to create two qubit gates, where one photon is used to switch another's state; inherently difficult due to the extremely small interaction cross-section between photons. The required deterministic two-qubit interactions will likely need a hybrid scheme with the ``flying'' photonic qubit interacting with a ``static'' matter qubit. Here we present the design of a photonic crystal waveguide structure that can couple electron-spin to photon path, thus providing an interface between a static and a flying qubit. We will show that the complex polarization properties inherent in the photonic crystal eigenmodes supports polarization singularities - positions in the electric field vector where one of the parameters describing the local polarization ellipse is singular - and that these singularities are ideal for a range of quantum information applications. In particular, we will show that by placing a quantum dot at one of these singularities, the electron-spin becomes correlated with the photon emission direction, creating an in-plane spin-photon interface that can transfer quantum information from static to flying qubits.

  7. 7 CFR 900.80 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice versa...

  8. 7 CFR 900.80 - Words in the singular form.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...

  9. 7 CFR 900.80 - Words in the singular form.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...

  10. 7 CFR 900.80 - Words in the singular form.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...

  11. 7 CFR 900.80 - Words in the singular form.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...

  12. Singularity-consistent parameterization of robot motion and control

    SciTech Connect

    Nenchev, D.N.; Tsumaki, Yuichi; Uchiyama, Masaru

    2000-02-01

    The inverse kinematics problem is formulated as a parameterized autonomous dynamical system problem, and respective analysis is carried out. It is shown that a singular point of work space can be mapped either as a critical or a noncritical point of the autonomous system, depending on the direction of approach to the singular point. Making use of the noncritical mapping, a closed-loop kinematic controller with asymptotic stability and velocity limits along degenerate singular or near-singular paths is designed. The authors introduce a specific type of motion along the reference path, the so-called natural motion. This type of motion is obtained in a straightforward manner from the autonomous dynamical system and always satisfies the motion constraint at a singular point. In the vicinity of the singular point, natural motion slows down the end-effector speed and keeps the joint velocity bounded. Thus, no special trajectory replanning will be required. In addition, the singular manifold can be crossed, if necessary. Further on, it is shown that natural motion constitutes an integrable motion component. The remaining, nonintegrable motion component is shown to be helpful in solving a problem related to the critical point mapping of the autonomous system. The authors design a singularity-consistent resolved acceleration controller, which they then apply to singular or near-singular trajectory tracking under torque limits. Finally, the authors compare the main features of the singularity-consistent method and the damped-least-squares method. It is shown that both methods introduce a so-called algorithmic error in the vicinity of a singular point. The direction of this error is, however, different in each method. This is shown to play an important role for system stability.

  13. Transmutation of planar media singularities in a conformal cloak.

    PubMed

    Liu, Yichao; Mukhtar, Musawwadah; Ma, Yungui; Ong, C K

    2013-11-01

    Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes.

  14. Two-dimensional gauge dynamics and the topology of singular determinantal varieties

    NASA Astrophysics Data System (ADS)

    Wong, Kenny

    2017-03-01

    We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices are related to the Euler characteristics of the singular skew-symmetric or symmetric determinantal varieties featuring in the analysis of their opposite phases, and we discuss the extent to which these relationships can be reconciled with standard Born-Oppenheimer arguments.

  15. Leadership in the Era of the Human Singularity: New Demands, New Skills, New Response

    DTIC Science & Technology

    2008-10-01

    of human inclinations. Like the few initial bacteria required to poison a pool of water, these forces carry with them an outsized set of consequences...morning wrestled naked at the gym . The balanced personality is often the best Phase 4 leader, which runs counter to the singularity’s focus on one or...distinctive means of asserting imperial aims in the Singularity Era will be: Use of ESI soldiers, equipped with ultra-tech weapons, to take • over

  16. Singular perturbation analysis of AOTV-related trajectory optimization problems

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Bae, Gyoung H.

    1990-01-01

    The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality

  17. Phases of unstable conifolds

    SciTech Connect

    Narayan, K.

    2007-03-15

    We explore the phase structure induced by closed string tachyon condensation of toric nonsupersymmetric conifold-like singularities described by an integral charge matrix Q=(n{sub 1}n{sub 2}-n{sub 3}-n{sub 4}), n{sub i}>0, iQ{sub i}{ne}0, initiated by Narayan [J. High Energy Phys. 03 (2006) 036]. Using gauged linear sigma model renormalization group flows and toric geometry techniques, we see a cascadelike phase structure containing decays to lower order conifold-like singularities, including, in particular, the supersymmetric conifold and the Y{sup pq} spaces. This structure is consistent with the Type II GSO projection obtained previously for these singularities. Transitions between the various phases of these geometries include flips and flops.

  18. Identify Foot of Continental Slope by singular spectrum and fractal singularity analysis

    NASA Astrophysics Data System (ADS)

    Li, Q.; Dehler, S.

    2012-04-01

    Identifying the Foot of Continental Slope (FOCS) plays a critical role in the determination of exclusive economic zone (EEZ) for coastal nations. The FOCS is defined by the Law of the Sea as the point of maximum change of the slope and it is mathematically equivalent to the point which has the maximum curvature value in its vicinity. However, curvature is the second derivative and the calculation of second derivative is a high pass and noise-prone filtering procedure. Therefore, identification of FOCS with curvature analysis methods is often uncertain and erroneous because observed bathymetry profiles or interpolated raster maps commonly include high frequency noises and artifacts, observation errors, and local sharp changes. Effective low-pass filtering methods and robust FOCS indicator algorithms are highly desirable. In this approach, nonlinear singular spectral filtering and singularity FOCS-indicator methods and software tools are developed to address this requirement. The normally used Fourier domain filtering methods decompose signals into Fourier space, composed of a fixed base that depends only on the acquisition interval of the signal; the signal is required to be stationary or at least weak stationary. In contrast to that requirement, the developed singular spectral filtering method constructs orthogonal basis functions dynamically according to different signals, and it does not require the signal to be stationary or weak stationary. Furthermore, singular spectrum analysis (SSA) can assist in designing suitable filters to carefully remove high-frequency local or noise components while reserving useful global and local components according to energy distribution. Geoscientific signals, including morphological ocean bathymetry data, often demonstrate fractal or multifractal properties. With proper definition of scales in the vicinity of a certain point and related measures, it is found that 1-dimensional bathymetry profiles and 2-dimensional raster maps

  19. Plane wave gravitons, curvature singularities and string physics

    SciTech Connect

    Brooks, R. . Center for Theoretical Physics)

    1991-03-21

    This paper discusses bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates. So are string propagation and supersymmetry in spacetimes with curvature singularities.

  20. Metric dimensional reduction at singularities with implications to Quantum Gravity

    NASA Astrophysics Data System (ADS)

    Stoica, Ovidiu Cristinel

    2014-08-01

    A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity.

  1. Propagation of the Lissajous singularity dipole in free space

    NASA Astrophysics Data System (ADS)

    Chen, Haitao; Gao, Zenghui; Zou, Xuefang; Xiao, Xi; Wang, Fanhou; Yang, Huajun

    2014-01-01

    The propagation properties of a pair of Lissajous singularities with opposite singularity indexes called the Lissajous singularity dipole (LSD) in free space are studied analytically and illustrated numerically. It is shown that the motion, creation, annihilation and change in the degree of polarization of the LSD, and change in the shape of Lissajous figures take place by suitably varying the waist width, off-axis distance or propagation distance. In particular, the creation and shift to infinity of a single Lissajous singularity may appear. A comparison with the free-space propagation of an optical vortex dipole and a C-dipole is also made.

  2. Fate of bound systems through sudden future singularities

    NASA Astrophysics Data System (ADS)

    Perivolaropoulos, L.

    2016-12-01

    Sudden singularities occur in Friedmann-Robertson-Walker (FRW) spacetimes when the scale factor remains finite and different from zero while some of its derivatives diverge. After proper rescaling, the scale factor close to such a singularity at t =0 takes the form a (t )=1 +c |t |η (where c and η are parameters and η ≥0 ). We investigate analytically and numerically the geodesics of free and gravitationally bound particles through such sudden singularities. We find that even though free particle geodesics go through sudden singularities for all η ≥0 , bound systems get dissociated (destroyed) for a wide range of the parameter c . For η <1 bound particles receive a diverging impulse at the singularity and get dissociated for all positive values of the parameter c . For η >1 [sudden future singularities (SFS)] bound systems get a finite impulse that depends on the value of c and get dissociated for values of c larger than a critical value ccr(η ,ω0)>0 that increases with the value of η and the rescaled angular velocity ω0 of the bound system. We obtain an approximate equation for the analytical estimate of ccr(η ,ω0). We also obtain its accurate form by numerical derivation of the bound system orbits through the singularities. Bound system orbits through big brake singularities (c <0 , 1 <η <2 ) are also derived numerically and are found to get disrupted (deformed) at the singularity. However, they remain bound for all values of the parameter c considered.

  3. Spectral singularity in confined PT symmetric optical potential

    SciTech Connect

    Sinha, Anjana; Roychoudhury, R.

    2013-11-15

    We present an analytical study for the scattering amplitudes (Reflection ‖R‖ and Transmission ‖T‖), of the periodic PT symmetric optical potential V(x)=W{sub 0}cos{sup 2}x+iV{sub 0}sin2x confined within the region 0 ⩽x⩽L, embedded in a homogeneous medium having uniform potential W{sub 0}. The confining length L is considered to be some integral multiple of the period π. We give some new and interesting results. Scattering is observed to be normal (‖T‖{sup 2}⩽ 1, ‖R‖{sup 2}⩽ 1) for V{sub 0}⩽ 0.5, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point (V{sub 0} > 0.5) scattering is found to be anomalous (‖T‖{sup 2}, ‖R‖{sup 2} not necessarily ⩽1). Additionally, in this parameter regime of V{sub 0}, one observes infinite number of spectral singularities E{sub SS} at different values of V{sub 0}. Furthermore, for L= 2nπ, the transition point V{sub 0}= 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] < 0) but with finite reflection when the beam is incident from the emissive side (Im[V(x)] > 0), transmission being identically unity in both cases. Finally, the scattering coefficients ‖R‖{sup 2} and ‖T‖{sup 2} always obey the generalized unitarity relation : ‖T|{sup 2}−1|=√(|R{sub R}|{sup 2}|R{sub L}|{sup 2}), where subscripts R and L stand for right and left incidence, respectively.

  4. On singular fibres in F-theory

    NASA Astrophysics Data System (ADS)

    Braun, Andreas P.; Watari, Taizan

    2013-07-01

    In this paper, we propose a connection between the field theory local model (Katz-Vafa field theory) and the type of singular fibre in flat crepant resolutions of elliptic Calabi-Yau fourfolds, a class of fourfolds considered by Esole and Yau. We review the analysis of degenerate fibres for models with gauge groups SU(5) and SO(10) in detail, and observe that the naively expected fibre type is realized if and only if the Higgs vev in the field theory local model is unramified. To test this idea, we implement a linear (unramified) Higgs vev for the " E 6" Yukawa point in a model with gauge group SU(5) and verify that this indeed leads to a fibre of Kodaira type IV*. Based on this observation, we argue i) that the singular fibre types appearing in the fourfolds studied by Esole-Yau are not puzzling at all, (so that this class of fourfolds does not have to be excluded from the candidate of input data of some yet-unknown formulation of F-theory) and ii) that such fourfold geometries also contain more information than just the eigenvalues of the Higgs field vev configuration in the field theory local models.

  5. Nonlinear spectral singularities and laser output intensity

    NASA Astrophysics Data System (ADS)

    Ghaemi-Dizicheh, Hamed; Mostafazadeh, Ali; Sarısaman, Mustafa

    2017-10-01

    The mathematical notion of spectral singularity admits a description in terms of purely outgoing solutions of a corresponding linear wave equation. This leads to a nonlinear generalization of this notion for nonlinearities that are confined in space. We examine the nonlinear spectral singularities in arbitrary transverse electric (TE) and transverse magnetic (TM) modes of a mirrorless slab laser that involves a weak Kerr nonlinearity. This provides a computational scheme for the determination of the laser output intensity I for these modes. In particular, we offer an essentially mathematical derivation of the linear-dependence of I on the gain coefficient g and obtain an explicit analytic expression for its slope. This shows that if the real part η of the refractive index of the slab does not exceed 3, there is a lower bound on the incidence angle θ below which lasing in both its TE and TM modes requires η to be shifted by a small amount as g surpasses the threshold gain. Our results suggest that lasing in the oblique TM modes of the slab is forbidden if the incidence (emission) angle of the TM mode exceeds the Brewster’s angle.

  6. Anisotropic singularities in chiral modified gravity

    NASA Astrophysics Data System (ADS)

    Herfray, Yannick; Krasnov, Kirill; Shtanov, Yuri

    2016-12-01

    In four spacetime dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. All these theories describe just two propagating polarisations of the graviton. General relativity (GR) with an arbitrary cosmological constant is the only parity-invariant member of this family. We review how these modified gravity theories arise within the framework of pure-connection formulation. We introduce a new convenient parametrisation of this family of theories by using a certain set of auxiliary fields. Modifications of GR can be arranged so as to become important in regions with large Weyl curvature, while the behaviour is indistinguishable from GR where Weyl curvature is small. We show how the Kasner singularity of GR is resolved in a particular class of modified gravity theories of this type, leading to solutions in which the fundamental connection field is regular all through the spacetime. There arises a new asymptotically De Sitter region ‘behind’ the would-be singularity, the complete solution thus being of a bounce type.

  7. Finite-time singularity signature of hyperinflation

    NASA Astrophysics Data System (ADS)

    Sornette, D.; Takayasu, H.; Zhou, W.-X.

    2003-07-01

    We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.

  8. Aircraft Range Optimization Using Singular Perturbations

    NASA Technical Reports Server (NTRS)

    Oconnor, Joseph Taffe

    1973-01-01

    An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

  9. Synthesis and characterization of embedded germanium nanocrystals

    NASA Astrophysics Data System (ADS)

    Xu, Qing

    Isotopically pure Ge nanocrystals have been synthesized by ion implantation followed by thermal annealing in amorphous silica and crystalline sapphire matrix. The structure, and the mechanical and thermal properties of the two systems are studied and compared. Ge cluster nucleation during implantation is observed in as-implanted silica samples. It results in the wide size distribution observed after thermal annealing. Theoretical calculations predict that if the nucleation during implantation can be suppressed, a much narrower size distribution is achievable. As-grown Ge nanocrystals are under large compressive stress, 1.2GPa for nanocrystals embedded in silica, and 4GPa for those embedded in sapphire. The stress can be gradually relieved by vapor etching, liberating the nanocrystals from the matrix as well as post-growth thermal treatments. One of the main sources of the stress observed in the sapphire system is the volume expansion of Ge clusters in the liquid/solid phase transformation which occurs during the cooling process from annealing temperature to room temperature, as the density of liquid Ge is larger by 4.6% than that of solid Ge. The large stress and damage in the sapphire matrix lead to a unique double-peak size distribution of the Ge nanocrystals. However, the in situ transmission electron microscopy (TEM) experiments indicate that the Ge nanocrystals embedded in silica are already in their solid phase at the annealing temperature. Therefore, the stress originates from other sources. Vapor etching with HF solutions enables a gradual exposure of embedded Ge nanocrystals in SiO2, while the liquid etching in HF solution leaves fully liberated Ge nanocrystals loosely packed on the Si substrate. Transfer of liberated Ge nanocrystals to other surfaces is achieved by solution dispersion and subsequent evaporation. The patterning of nanocrystals has been achieved by a combination of lithography, coimplantation and electron irradiation. The latter one will

  10. Adaptive Embedded Digital System for Plasma Diagnostics

    NASA Astrophysics Data System (ADS)

    González, Angel; Rodríguez, Othoniel; Mangual, Osvaldo; Ponce, Eduardo; Vélez, Xavier

    2014-05-01

    An Adaptive Embedded Digital System to perform plasma diagnostics using electrostatic probes was developed at the Plasma Engineering Laboratory at Polytechnic University of Puerto Rico. The system will replace the existing instrumentation at the Laboratory, using reconfigurable hardware to minimize the equipment and software needed to perform diagnostics. The adaptability of the design resides on the possibility of replacing the computational algorithm on the fly, allowing to use the same hardware for different probes. The system was prototyped using Very High Speed Integrated Circuits Hardware Description Language (VHDL) into an Field Programmable Gate Array (FPGA) board. The design of the Embedded Digital System includes a Zero Phase Digital Filter, a Derivative Unit, and a Computational Unit designed using the VHDL-2008 Support Library. The prototype is able to compute the Plasma Electron Temperature and Density from a Single Langmuir probe. The system was tested using real data previously acquired from a single Langmuir probe. The plasma parameters obtained from the embedded system were compared with results computed using matlab yielding excellent matching. The new embedded system operates on 4096 samples versus 500 on the previous system, and completes its computations in 26 milliseconds compared with about 15 seconds on the previous system.

  11. Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side

    NASA Astrophysics Data System (ADS)

    Amirjanyan, A. A.; Sahakyan, A. V.

    2017-08-01

    A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.

  12. Hybrid manifold embedding.

    PubMed

    Liu, Yang; Liu, Yan; Chan, Keith C C; Hua, Kien A

    2014-12-01

    In this brief, we present a novel supervised manifold learning framework dubbed hybrid manifold embedding (HyME). Unlike most of the existing supervised manifold learning algorithms that give linear explicit mapping functions, the HyME aims to provide a more general nonlinear explicit mapping function by performing a two-layer learning procedure. In the first layer, a new clustering strategy called geodesic clustering is proposed to divide the original data set into several subsets with minimum nonlinearity. In the second layer, a supervised dimensionality reduction scheme called locally conjugate discriminant projection is performed on each subset for maximizing the discriminant information and minimizing the dimension redundancy simultaneously in the reduced low-dimensional space. By integrating these two layers in a unified mapping function, a supervised manifold embedding framework is established to describe both global and local manifold structure as well as to preserve the discriminative ability in the learned subspace. Experiments on various data sets validate the effectiveness of the proposed method.

  13. Moving embedded lattice solitons.

    PubMed

    Malomed, B A; Fujioka, J; Espinosa-Cerón, A; Rodríguez, R F; González, S

    2006-03-01

    It was recently proved that solitons embedded in the spectrum of linear waves may exist in discrete systems, and explicit solutions for isolated unstable embedded lattice solitons (ELS) of a differential-difference version of a higher-order nonlinear Schrodinger equation were found [Gonzalez-Perez-Sandi, Fujioka, and Malomed, Physica D 197, 86 (2004)]. The discovery of these ELS gives rise to relevant questions such as the following: (1) Are there continuous families of ELS? (2) Can ELS be stable? (3) Is it possible for ELS to move along the lattice? (4) How do ELS interact? The present work addresses these questions by showing that a novel equation (a discrete version of a complex modified Korteweg-de Vries equation that includes next-nearest-neighbor couplings) has a two-parameter continuous family of exact ELS. These solitons can move with arbitrary velocities across the lattice, and the numerical simulations demonstrate that these ELS are completely stable. Moreover, the numerical tests show that these ELS are robust enough to withstand collisions, and the result of a collision is only a shift in the positions of the solitons. The model may apply to the description of a Bose-Einstein condensate with dipole-dipole interactions between the atoms, trapped in a deep optical-lattice potential.

  14. Differential embedding - From theory to application in palaeoclimatology

    NASA Astrophysics Data System (ADS)

    Lekscha, Jaqueline; Donner, Reik V.

    2017-04-01

    Analysing data from palaeoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's higher dimensional phase space can be crucial for further analyses. In this study, we revisit the concept of differential embedding as an alternative approach to time-delay embedding and aim at bringing it closer to application. Differential embedding relates the system's higher dimensional coordinates to the derivatives of the measured time series. For implementation, this requires robust and efficient algorithms to estimate derivatives from possibly irregularly sampled data. For this purpose, we consider several approaches: (i) central differences adapted to irregular sampling, (ii) a generalised version of discrete Legendre coordinates [1] and (iii) the concept of Moving Taylor Bayesian Regression [2]. We then systematically evaluate the performance of differential and time-delay embedding by comparing geometrical properties of the embedded attractors to those of the original attractor for two paradigmatic model systems - the Rössler and the Lorenz system. The quality of the phase space reconstruction is quantified using recurrence network analysis. Our results suggest that differential embedding can indeed be an alternative to time-delay embedding for unequally spaced time series. Hence, using differential embedding and recurrence network methods to analyse palaeoclimate data sets opens up good prospects of gaining new insights into past climate variability. We demonstrate the potential of this approach for real-world applications by applying derivative embedding in combination with recurrence network analysis to some well-studied palaeoclimate data sets from South America. [1] J. F. Gibson, J. D. Farmer, M. Casdagli, and S. Eubank. An analytic approach to practical phase space reconstruction. Physica, 57D(1), 1992. [2] J

  15. Metric dimensional reduction at singularities with implications to Quantum Gravity

    SciTech Connect

    Stoica, Ovidiu Cristinel

    2014-08-15

    A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained

  16. Imperfections, impacts, and the singularity of Euler's disk

    NASA Astrophysics Data System (ADS)

    Baranyai, Tamás; Várkonyi, Péter L.

    2017-09-01

    The motion of a rigid, spinning disk on a flat surface ends with a dissipation-induced finite-time singularity. The problem of finding the dominant energy absorption mechanism during the last phase of the motion generated a lively debate during the past two decades. Various candidates including air drag and different types of friction have been considered, nevertheless impacts have not been examined until now. We investigate the effect of impacts caused by geometric imperfections of the disk and of the underlying flat surface, through analyzing the dynamics of polygonal disks with unilateral point contacts. Similarly to earlier works, we determine the rate of energy absorption under the assumption of a regular pattern of motion analogous to precession-free motion of a rolling disk. In addition, we demonstrate that the asymptotic stability of this motion depends on parameters of the impact model. In the case of instability, the emerging irregular motion is investigated numerically. We conclude that there exists a range of model parameters (small radii of gyration or small restitution coefficients) in which absorption by impacts dominates all previously investigated mechanisms during the last phase of motion. Nevertheless the parameter values associated with a homogeneous disk on a hard surface are typically not in this range, hence the effect of impacts is in that case not dominant.

  17. Singular inflation from Born-Infeld-f(R) gravity

    NASA Astrophysics Data System (ADS)

    Elizalde, Emilio; Makarenko, Andrey N.

    2016-07-01

    Accelerating dynamics from Born-Infeld-f(R) gravity are studied in a simplified conformal approach without matter. Explicit unification of inflation with late-time acceleration is realized within this singular inflation approach, which is similar to Odintsov-Oikonomou singular f(R) inflation. Our model turns out to be consistent with the latest release of Planck data.

  18. Patterns of singularity in Dalaimiao district, Inner Mongolia, China.

    NASA Astrophysics Data System (ADS)

    Yang, Jie; Cheng, Qiuming

    2015-04-01

    The local singularity analysis (LSA) method is applied to Dalaimiao district, Inner Mongolia, China and some characteristics of singularity have been revealed and discussed. A sub-area of quaternary sediments, strata and intrusions are analysis with principle component analysis and scatter plots. The results show that different geo-object have clear and well-organized patterns in the space of singularity. Different lithologies shows a fixed order in the spaces of singularity for different element associations. Moreover, the differences among lithologies in the space of singularity are smaller than those in the space of concentrations. In addition, this pattern of singularity can be found in either whole map or a section. Therefore, it's reasonable to apply PCA on singularity maps to integrate geochemical information. So that, PCA is applied on both singularities of six pathfinder elements and their concentrations. The AUCs (Area under receiver operating characteristic curve) of PC1s of those two ways show that the former is superior to the later in indicating Mo deposits. This is important to how the LSA and PCA can be combined and applied to process geochemical data to assist mineral exploration.

  19. 7 CFR 1200.1 - Words in the singular form.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in this...

  20. Horizonless, singularity-free, compact shells satisfying NEC

    NASA Astrophysics Data System (ADS)

    Shankar, Karthik H.

    2017-02-01

    Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose's singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity.