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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. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  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. 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

  20. 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

  1. 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.

  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. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  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. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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)

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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…

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

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

    PubMed

    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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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

  7. 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…

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  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. 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.

  11. 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…

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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%.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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).

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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}.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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).

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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).

  15. 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…

  16. 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.

  17. '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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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...

  3. 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...

  4. 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...

  5. 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...

  6. 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...

  7. 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...

  8. 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...

  9. 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...

  10. 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...

  11. 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...

  12. 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...

  13. 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...

  14. 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...

  15. 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...

  16. 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...

  17. 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...

  18. 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...

  19. 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...

  20. 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...

  1. 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...

  2. 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...

  3. 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...

  4. 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...

  5. 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...

  6. 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...

  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 900.100 - 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...

  12. 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...

  13. 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...

  14. 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...

  15. 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...

  16. 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...

  17. 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...

  18. 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...

  19. 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...

  20. 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...

  1. 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...

  2. 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.

  3. 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,...

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. Singularities and the geometry of spacetime

    NASA Astrophysics Data System (ADS)

    Hawking, Stephen

    2014-11-01

    The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

  12. 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.

  13. 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.

  14. Cosmological future singularities in interacting dark energy models

    NASA Astrophysics Data System (ADS)

    Jiménez, Jose Beltrán; Rubiera-Garcia, Diego; Sáez-Gómez, Diego; Salzano, Vincenzo

    2016-12-01

    The existence of interactions between dark matter and dark energy has been widely studied, since they can fit well the observational data and may provide new physics through such an interaction. In this work, we analyze these models and investigate their potential relation with future cosmological singularities. We find that every future singularity found in the literature can be mapped into a singularity of the interaction term, that we call the Q singularity, where the energy flow between the dark components diverges. Furthermore, this framework allows us to identify a new type of future singularity induced by the divergence of the first derivative of the dark energy equation of state parameter.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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…

  2. 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.

  3. 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.

  4. 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 $F$.

  5. 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.

  6. 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.

  7. Coupled singular value decomposition of a cross-covariance matrix.

    PubMed

    Kaiser, Alexander; Schenck, Wolfram; Möller, Ralf

    2010-08-01

    We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as decorrelation method for the estimation of multiple singular vectors and singular values. Experiments on synthetic data show that coupled learning rules converge faster than Hebbian learning rules and that the first-order approximation of Gram-Schmidt orthonormalization produces more precise estimates and better orthonormality than the standard deflation method.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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).

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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...

  2. 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...

  3. 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...

  4. 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...

  5. 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...

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. Embedded SIC-POVMs

    NASA Astrophysics Data System (ADS)

    Dang, Hoan; Blanchfield, Kate; Bengtsson, Ingemar; Appleby, Marcus

    2013-03-01

    Symmetric informationally complete (SIC) sets of quantum states have applications in foundational studies of quantum mechanics, quantum tomography, quantum communication, quantum cryptography, and classical signal processing. However, their existence in every dimension has not been proven, and no general construction has been known. During our study of linear dependencies in Weyl-Heisenberg orbits, we discovered 2-dimensional SICs embedded in a 6-dimensional Hilbert space. This offers a robust construction for 2-dimensional SICs, and may potentially impact the SIC existence problem. In this talk, I will explain how this construction works, and present numerical results for some other dimensions. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and by the U. S. Office of Naval Research (Grant No. N00014-09-1-0247).

  17. Embedding potentials for excited states of embedded species

    SciTech Connect

    Wesolowski, Tomasz A.

    2014-05-14

    Frozen-Density-Embedding Theory (FDET) is a formalism to obtain the upper bound of the ground-state energy of the total system and the corresponding embedded wavefunction by means of Euler-Lagrange equations [T. A. Wesolowski, Phys. Rev. A 77(1), 012504 (2008)]. FDET provides the expression for the embedding potential as a functional of the electron density of the embedded species, electron density of the environment, and the field generated by other charges in the environment. Under certain conditions, FDET leads to the exact ground-state energy and density of the whole system. Following Perdew-Levy theorem on stationary states of the ground-state energy functional, the other-than-ground-state stationary states of the FDET energy functional correspond to excited states. In the present work, we analyze such use of other-than-ground-state embedded wavefunctions obtained in practical calculations, i.e., when the FDET embedding potential is approximated. Three computational approaches based on FDET, that assure self-consistent excitation energy and embedded wavefunction dealing with the issue of orthogonality of embedded wavefunctions for different states in a different manner, are proposed and discussed.

  18. Embedding potentials for excited states of embedded species.

    PubMed

    Wesolowski, Tomasz A

    2014-05-14

    Frozen-Density-Embedding Theory (FDET) is a formalism to obtain the upper bound of the ground-state energy of the total system and the corresponding embedded wavefunction by means of Euler-Lagrange equations [T. A. Wesolowski, Phys. Rev. A 77(1), 012504 (2008)]. FDET provides the expression for the embedding potential as a functional of the electron density of the embedded species, electron density of the environment, and the field generated by other charges in the environment. Under certain conditions, FDET leads to the exact ground-state energy and density of the whole system. Following Perdew-Levy theorem on stationary states of the ground-state energy functional, the other-than-ground-state stationary states of the FDET energy functional correspond to excited states. In the present work, we analyze such use of other-than-ground-state embedded wavefunctions obtained in practical calculations, i.e., when the FDET embedding potential is approximated. Three computational approaches based on FDET, that assure self-consistent excitation energy and embedded wavefunction dealing with the issue of orthogonality of embedded wavefunctions for different states in a different manner, are proposed and discussed.

  19. 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

  20. Density perturbations in a finite scale factor singularity universe

    NASA Astrophysics Data System (ADS)

    Balcerzak, Adam; Denkiewicz, Tomasz

    2012-07-01

    We discuss evolution of density perturbations in cosmological models which admit finite scale factor singularities. After solving the matter perturbations equations we find that there exists a set of parameters which admits a finite scale factor singularity in future and instantaneously recover matter density evolution history which is indistinguishable from the standard ΛCDM scenario.

  1. Twisting singular solutions of Betheʼs equations

    NASA Astrophysics Data System (ADS)

    Nepomechie, Rafael I.; Wang, Chunguang

    2014-12-01

    The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.

  2. Two Approaches of Studying Singularity of Projective Conics

    ERIC Educational Resources Information Center

    Broyles, Chris; Muller, Lars; Tikoo, Mohan; Wang, Haohao

    2010-01-01

    The singularity of a projective conic can be determined via the associated matrix to the implicit equation of the projective conic. In this expository article, we will first derive a known result for determining the singularity of a projective conic via the associated matrix. Then we will introduce the concepts of [mu]-basis of the parametric…

  3. Detection of finger gesture using singular spectrum transformation

    NASA Astrophysics Data System (ADS)

    Tamura, Y.; Umetani, T.; Nakamura, H.

    2015-01-01

    The purpose of this study is to detect finger movement using a singular spectrum transformation method. Human gesture recognition is essential for realizing natural user interfaces. However, constructing a robust, easily installable interface is extremely difficult. Our proposed method uses singular spectrum transformation to classify finger movements. This method robustly classifies gestures and behavior.

  4. A numerical method for solving singular De`s

    SciTech Connect

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  5. Classification of almost toric singularities of Lagrangian foliations

    SciTech Connect

    Izosimov, Anton M

    2011-07-31

    The topological classification is given of almost toric singularities of integrable Hamiltonian systems with a large number of degrees of freedom, that is, of nondegenerate singularities without hyperbolic components. A descriptive geometric model is constructed, which makes it possible to perform effective calculations. Bibliography: 10 titles.

  6. 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...

  7. 7 CFR 1200.1 - 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. 1200.1 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...

  8. 7 CFR 1200.1 - 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. 1200.1 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...

  9. 7 CFR 1200.1 - 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. 1200.1 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...

  10. 7 CFR 1200.1 - 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. 1200.1 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...

  11. 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.

  12. 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.

  13. 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.

  14. Infinitely many singular interactions on noncompact manifolds

    SciTech Connect

    Kaynak, Burak Tevfik Turgut, O. Teoman

    2015-05-15

    We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004). - Highlights: • Schrödinger-operator for infinitely many singular interactions on noncompact manifolds. • Proof of the finiteness of the ground-state energy.

  15. Helicity and singular structures in fluid dynamics

    PubMed Central

    Moffatt, H. Keith

    2014-01-01

    Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described. PMID:24520175

  16. Stress Singularities in Swelling Soft Solids

    NASA Astrophysics Data System (ADS)

    Goriely, Alain; Weickenmeier, Johannes; Kuhl, Ellen

    2016-09-01

    When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening. At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. We also consider the possibility of damage triggered by zones of either high shear stresses or high fiber stretches.

  17. Singularity-Driven Pattern Formation by Bacteria

    NASA Astrophysics Data System (ADS)

    Brenner, Michael P.; Betterton, M. D.

    2000-03-01

    Under special conditions bacteria excrete an attractant and aggregate. The patterns formation is driven by the formation of singularities. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process. Cylindrical collapse is marginal, which leads to corrections to the collapse laws expected from dimensional analysis. The instability of a collapsing cylinder is composed of two stages: Initially, slow modulations to the cylinder develop, which correspond to a variation of the collapse time along the cylinder axis. Ultimately, one point on the cylinder pinches off. At this final stage of the instability, a front propagates from the pinch into the remainder of the cylinder. The spacing of the resulting spherical aggregates is determined by the front propagation.

  18. Efficient load measurements using singular value decomposition

    NASA Technical Reports Server (NTRS)

    Yao, Kung; Balakrishnan, A. V.

    1988-01-01

    Various basic research was performed on efficient load measurement estimation techniques for aircraft structure analysis. An overview is presented of the load measurement problem. Two basic equivalent approaches to load measurement evaluations were considered. Under approach 1, the load values are modeled as depending linearly on the measured values. Under approach 2, the measured values depend linearly on the load values. By using the modern Singular Value Decomposition method, it was shown that under all conditions of the number of loads and number of gages, approach 1 is equivalent to approach 2. By using the conventional normal equation (linear regression) approach, approach 1 is only valid when the number of loads is equal to or greater than the number of gages, while approach 2 is the reverse. Furthermore, except for the case of the number of loads equals the number of gages, the load prediction formulas under the two approaches are not equivalent.

  19. Singular perturbations in the state regulator problem

    NASA Technical Reports Server (NTRS)

    Ardema, M. D.

    1972-01-01

    Most of the results of singular perturbation theory have been concerned with initial value problems whereas optimal control problems are of two-point boundary value type. The portions of this theory applicable to the open loop state regulator problem are reviewed. For obtaining approximate solutions to the state regulator problem the method of matched asymptotic expansions is employed. This method has been developed in connection with certain fluid mechanics problems and is applicable to nonlinear as well as linear problems. It has been found in the past to be advantageous not to formulate this method generally but to apply it to each individual problem and this approach is adopted here. A general recipe for the method is given and its application is illustrated by using the method to obtain an approximate solution to a simple, specific state regulator problem.

  20. Singular Instantons and Painlevé VI

    NASA Astrophysics Data System (ADS)

    Muñiz Manasliski, Richard

    2016-06-01

    We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU_2 on S^4, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (P_VI}) and we will give an explicit expression of the map between instantons and solutions to P_{VI}. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S^4. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.

  1. String wave function across a Kasner singularity

    SciTech Connect

    Copeland, Edmund J.; Niz, Gustavo; Turok, Neil

    2010-06-15

    A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a 1+1-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.

  2. Autoregressive models of singular spectral matrices☆

    PubMed Central

    Anderson, Brian D.O.; Deistler, Manfred; Chen, Weitian; Filler, Alexander

    2012-01-01

    This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description D−1(q)B with B a tall constant matrix of full column rank and with the determinantal zeros of D(q) all stable, i.e. in |q|>1,q∈C. To obtain a parsimonious AR model, a canonical form is derived and a number of advantageous properties are demonstrated. First, the maximum lag of the canonical AR model is shown to be minimal in the equivalence class of AR models of the same transfer function matrix. Second, the canonical form model is shown to display a nesting property under natural conditions. Finally, an upper bound is provided for the total number of real parameters in the obtained canonical AR model, which demonstrates that the total number of real parameters grows linearly with the number of rows in W(q). PMID:23483210

  3. ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS

    SciTech Connect

    Chu Zhe; Lin, W. P.; Yang Xiaofeng E-mail: linwp@shao.ac.cn

    2013-06-20

    Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.

  4. Polarization singularities in Young's two-slit experiment

    NASA Astrophysics Data System (ADS)

    Lian, Xiaoxu; Lü, Baida

    2011-10-01

    Young's interference experiment is regarded as a two-slit diffraction phenomenon, the polarization singularities in Young's two-slit configuration illuminated with two linearly, orthogonally polarized Gaussian vortex beams are studied. It is shown that generally, there exist L-lines (linearly polarization) and polarization singularities including C-points (circular polarization), S23 and S31 singularities even though the parameters of two beams are the same. The pair creation-annihilation and motion of polarization singularities take place upon propagation, or by varying a control parameter, such as the amplitude ratio of two beams or obscure ratio of slits etc. For a special case of the illumination with two linearly, orthogonally polarized Gaussian vortex-free beams, polarization singularities, in particular, C-points may occur if a parameter of two beams is not equal.

  5. Treatment of singularities in a middle-crack tension specimen

    NASA Technical Reports Server (NTRS)

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

    1990-01-01

    A three-dimensional finite-element analysis of a middle-crack tension specimen subjected to mode I loading was performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed nonsingular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities, by a log-log regression analysis, along the crack front. Analyses showed that finite-sized cracked bodies have two singular stress fields. Because of two singular stress fields near the free surface and the classical square root singularity elsewhere, the strain energy release rate appears to be an appropriate parameter all along the crack front.

  6. Spacetime singularities in (2 + 1)-dimensional quantum gravity

    NASA Astrophysics Data System (ADS)

    Minassian, Eric

    2002-12-01

    The effects of spacetime quantization on black-hole and big-bang/big-crunch singularities can be studied using new tools from (2 + 1)-dimensional quantum gravity. I investigate effects of spacetime quantization on the 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 singularity. Using generic Gaussian wavefunctions, I show that both the BTZ black hole and the torus universe contain families of paths that still reach the singularities with finite QGAPs, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular-invariant wavefunctions of Carlip and Nelson for the torus universe, further support this conclusion.

  7. Sharp bounds for singular values of fractional integral operators

    NASA Astrophysics Data System (ADS)

    Burman, Prabir

    2007-03-01

    From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and Vu and Gorenflo [Kim Tuan Vu, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order [alpha]>0 is approximately ([pi]j)-[alpha] for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is ([pi]j)-[alpha][1+O(j-1)].

  8. Particle creation by naked singularities in higher dimensions

    SciTech Connect

    Miyamoto, Umpei; Nemoto, Hiroya; Shimano, Masahiro

    2011-04-15

    Recently, the possibility was pointed out by one of the present authors and his collaborators that an effective naked singularity referred to as ''a visible border of spacetime'' is generated by high-energy particle collision in the context of large extra dimensions or TeV-scale gravity. In this paper, we investigate the particle creation by a naked singularity in general dimensions, while adopting a model in which a marginally naked singularity forms in the collapse of a homothetic lightlike pressureless fluid. We find that the spectrum deviates from that of Hawking radiation due to scattering near the singularity but can be recast in quasithermal form. The temperature is always higher than that of Hawking radiation of a same-mass black hole, and can be arbitrarily high depending on a parameter in the model. This implies that, in principle, the naked singularity may be distinguished from a black hole in collider experiments.

  9. Singular Lorentz-violating Lagrangians and associated Finsler structures

    NASA Astrophysics Data System (ADS)

    Colladay, Don; McDonald, Patrick

    2015-10-01

    Several Lagrangians associated with classical limits of Lorentz-violating fermions in the standard model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin couplings are present, the Lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive-definite quadratic form defined on a desingularized variety.

  10. Three-dimensional isolated quotient singularities in odd characteristic

    NASA Astrophysics Data System (ADS)

    Stepanov, D. A.

    2016-06-01

    Let a finite group G act linearly on a finite-dimensional vector space V over an algebraically closed field k of characteristic p>2. Suppose that the quotient space V/G has an isolated singularity only. The isolated singularities of the form V/G are completely classified in the case when p does not divide the order of G, and their classification reduces to Vincent's classification of isolated quotient singularities over C. In the present paper we show that, if \\dim V=3, then the classification of isolated quotient singularities reduces to Vincent's classification in the modular case as well (when p divides \\vert G\\vert). Some remarks on quotient singularities in other dimensions and in even characteristic are also given. Bibliography: 14 titles.

  11. Cusp singularities in f(R) gravity: pros and cons

    NASA Astrophysics Data System (ADS)

    Chen, Pisin; Yeom, Dong-han

    2015-10-01

    We investigate cusp singularities in f(R) gravity, especially for Starobinsky and Hu-Sawicki dark energy models. We illustrate that, by using double-null numerical simulations, a cusp singularity can be triggered by gravitational collapses. This singularity can be cured by adding a quadratic term, but this causes a Ricci scalar bump that can be observed by an observer outside the event horizon. Comparing with cosmological parameters, it seems that it would be difficult to see super-Planckian effects by astrophysical experiments. On the other hand, at once there exists a cusp singularity, it can be a mechanism to realize a horizon scale curvature singularity that can be interpreted by a firewall.

  12. Stability robustness improvement of direct eigenspace assignment based feedback systems using singular value sensitivities

    NASA Technical Reports Server (NTRS)

    Garg, Sanjay

    1989-01-01

    A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.

  13. Relation between observability and differential embeddings for nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Letellier, Christophe; Aguirre, Luis A.; Maquet, Jean

    2005-06-01

    In the analysis of a scalar time series, which lies on an m -dimensional object, a great number of techniques will start by embedding such a time series in a d -dimensional space, with d>m . Therefore there is a coordinate transformation Φs from the original phase space to the embedded one. The embedding space depends on the observable s(t) . In theory, the main results reached are valid regardless of s(t) . In a number of practical situations, however, the choice of the observable does influence our ability to extract dynamical information from the embedded attractor. This may arise in problems in nonlinear dynamics such as model building, control and synchronization. To some degree, ease of success will depend on the choice of the observable simply because it is related to the observability of the dynamics. In this paper the observability matrix for nonlinear systems, which uses Lie derivatives, is revisited. It is shown that such a matrix can be interpreted as the Jacobian matrix of Φs —the map between the original phase space and the differential embedding induced by the observable—thus establishing a link between observability and embedding theory.

  14. Embedding of Semantic Predications.

    PubMed

    Cohen, Trevor; Widdows, Dominic

    2017-03-08

    This paper concerns the generation of distributed vector representations of biomedical concepts from structured knowledge, in the form of subject-relation-object triplets known as semantic predications. Specifically, we evaluate the extent to which a representational approach we have developed for this purpose previously, known as Predication-based Semantic Indexing (PSI), might benefit from insights gleaned from neural-probabilistic language models, which have enjoyed a surge in popularity in recent years as a means to generate distributed vector representations of terms from free text. To do so, we develop a novel neural-probabilistic approach to encoding predications, called Embedding of Semantic Predications (ESP), by adapting aspects of the Skipgram with Negative Sampling (SGNS) algorithm to this purpose. We compare ESP and PSI across a number of tasks including recovery of encoded information, estimation of semantic similarity and relatedness, and identification of potentially therapeutic and harmful relationships using both analogical retrieval and supervised learning. We find advantages for ESP in some, but not all of these tasks, revealing the contexts in which the additional computational work of neural-probabilistic modeling is justified.

  15. Embodied, Embedded Language Use

    PubMed Central

    Fowler, Carol A.

    2011-01-01

    Language use has a public face that is as important to study as the private faces under intensive psycholinguistic study. In the domain of phonology, public use of speech must meet an interpersonal “parity” constraint if it is to serve to communicate. That is, spoken language forms must reliably be identified by listeners. To that end, language forms are embodied, at the lowest level of description, as phonetic gestures of the vocal tract that lawfully structure informational media such as air and light. Over time, under the parity constraint, sound inventories emerge over communicative exchanges that have the property of sufficient identifiability. Communicative activities involve more than vocal tract actions. Talkers gesture and use facial expressions and eye gaze to communicate. Listeners embody their language understandings, exhibiting dispositions to behave in ways related to language understanding. Moreover, linguistic interchanges are embedded in the larger context of language use. Talkers recruit the environment in their communicative activities, for example, in using deictic points. Moreover, in using language as a “coordination device,” interlocutors mutually entrain. PMID:21243080

  16. A higher order accurate solution decomposition scheme for a singularly perturbed parabolic reaction-diffusion equation

    NASA Astrophysics Data System (ADS)

    Shishkin, G. I.; Shishkina, L. P.

    2015-03-01

    An initial-boundary value problem is considered for a singularly perturbed parabolic reaction-diffusion equation. For this problem, a technique is developed for constructing higher order accurate difference schemes that converge ɛ-uniformly in the maximum norm (where ɛ is the perturbation parameter multiplying the highest order derivative, ɛ ∈ (0, 1]). A solution decomposition scheme is described in which the grid subproblems for the regular and singular solution components are considered on uniform meshes. The Richardson technique is used to construct a higher order accurate solution decomposition scheme whose solution converges ɛ-uniformly in the maximum norm at a rate of [InlineMediaObject not available: see fulltext.], where N + 1 and N 0 + 1 are the numbers of nodes in uniform meshes in x and t, respectively. Also, a new numerical-analytical Richardson scheme for the solution decomposition method is developed. Relying on the approach proposed, improved difference schemes can be constructed by applying the solution decomposition method and the Richardson extrapolation method when the number of embedded grids is more than two. These schemes converge ɛ-uniformly with an order close to the sixth in x and equal to the third in t.

  17. Spectral singularity in composite systems and simulation of laser resonant chamber

    NASA Astrophysics Data System (ADS)

    Zhang, Xizheng

    A non-Hermitian system with spectral singularity (SS) exhibits fascinating phenomena which never appear in a Hermitian system. We investigate the existence of SS for a composite system which is consisted of two separated scattering centers A and B embedded in a one-dimensional free space, one of which is non-Hermitian at last. We show that the composite system has a SS at kc if the reflection amplitudes rAkc and rBkc of two scattering centers satisfy the condition rRAkcrLBkce i 2kcxB -xA = 1 , based on the theorem proposed by Ali (PRL 102, 220402 (2009). Multi-scattering-centers generalization of the theorem is also obtained. As an application, we construct a simple system to simulate the resonant chamber for generating laser light. Spectral singularity in composite systems and simulation of laser resonant chamber.

  18. Exact string theory model of closed timelike curves and cosmological singularities

    NASA Astrophysics Data System (ADS)

    Johnson, Clifford V.; Svendsen, Harald G.

    2004-12-01

    We study an exact model of string theory propagating in a space-time containing regions with closed timelike curves (CTCs) separated from a finite cosmological region bounded by a big bang and a big crunch. The model is an nontrivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of α' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by timelike curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in general relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-big bang cosmological scenarios.

  19. Exact string theory model of closed timelike curves and cosmological singularities

    SciTech Connect

    Johnson, Clifford V.; Svendsen, Harald G.

    2004-12-15

    We study an exact model of string theory propagating in a space-time containing regions with closed timelike curves (CTCs) separated from a finite cosmological region bounded by a big bang and a big crunch. The model is an nontrivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of {alpha}{sup '} corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by timelike curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in general relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-big bang cosmological scenarios.

  20. Embedded I&C for Extreme Environments

    SciTech Connect

    Kisner, Roger A.

    2016-04-01

    This project uses embedded instrumentation and control (I&C) technologies to demonstrate potential performance gains of nuclear power plant components in extreme environments. Extreme environments include high temperature, radiation, high pressure, high vibration, and high EMI conditions. For extreme environments, performance gains arise from moment-to-moment sensing of local variables and immediate application of local feedback control. Planning for embedding I&C during early system design phases contrasts with the traditional, serial design approach that incorporates minimal I&C after mechanical and electrical design is complete. The demonstration application involves the development and control of a novel, proof-of-concept motor/pump design. The motor and pump combination operate within the fluid environment, eliminating the need for rotating seals. Actively controlled magnetic bearings also replace failure-prone mechanical contact bearings that typically suspend rotating components. Such as design has the potential to significantly enhance the reliability and life of the pumping system and would not be possible without embedded I&C.

  1. Phylogenetic trees and Euclidean embeddings.

    PubMed

    Layer, Mark; Rhodes, John A

    2017-01-01

    It was recently observed by de Vienne et al. (Syst Biol 60(6):826-832, 2011) that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on a diffusion model of continuous character evolution along the tree, here we give a direct and elementary explanation for it that provides substantial additional insight. We use this embedding to reinterpret the differences between the NJ and BIONJ tree building algorithms, providing one illustration of how this embedding reflects tree structures in data.

  2. Embedded fiducials in optical surfaces

    DOEpatents

    Sommargren, Gary E.

    2000-01-01

    Embedded fiducials are provided in optical surfaces and a method for embedding the fiducials. Fiducials, or marks on a surface, are important for optical fabrication and alignment, particularly when individual optical elements are aspheres. Fiducials are used during the course of the polishing process to connect interferometric data, and the equation describing the asphere, to physical points on the optic. By embedding fiducials below the surface of the optic and slightly outside the clear aperture of the optic, the fiducials are not removed by polishing, do not interfere with the polishing process, and do not affect the performance of the finished optic.

  3. Future singularity avoidance in phantom dark energy models

    SciTech Connect

    Haro, Jaume de

    2012-07-01

    Different approaches to quantum cosmology are studied in order to deal with the future singularity avoidance problem. Our results show that these future singularities will persist but could take different forms. As an example we have studied the big rip which appear when one considers the state equation P = ωρ with ω < −1, showing that it does not disappear in modified gravity. On the other hand, it is well-known that quantum geometric effects (holonomy corrections) in loop quantum cosmology introduce a quadratic modification, namely proportional to ρ{sup 2}, in Friedmann's equation that replace the big rip by a non-singular bounce. However this modified Friedmann equation could have been obtained in an inconsistent way, what means that the obtained results from this equation, in particular singularity avoidance, would be incorrect. In fact, we will show that instead of a non-singular bounce, the big rip singularity would be replaced, in loop quantum cosmology, by other kind of singularity.

  4. Singular Dimensions of theN= 2 Superconformal Algebras. I

    NASA Astrophysics Data System (ADS)

    Dörrzapf, Matthias; Gato-Rivera, Beatriz

    Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3).

  5. Boundary singularities produced by the motion of soap films.

    PubMed

    Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I

    2014-06-10

    Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

  6. Non-singular and cyclic universe from the modified GUP

    NASA Astrophysics Data System (ADS)

    Salah, Maha; Hammad, Fayçal; Faizal, Mir; Farag Ali, Ahmed

    2017-02-01

    In this paper, we investigate the effects of a new version of the generalized uncertainty principle (modified GUP) on the dynamics of the Universe. As the modified GUP will modify the relation between the entropy and area of the apparent horizon, it will also deform the Friedmann equations within Jacobson's approach. We explicitly find these deformed Friedmann equations governing the modified GUP-corrected dynamics of such a Universe. It is shown that the modified GUP-deformed Jacobson's approach implies an upper bound for the density of such a Universe. The Big Bang singularity can therefore also be avoided using the modified GUP-corrections to horizons' thermodynamics. In fact, we are able to analyze the pre Big Bang state of the Universe. Furthermore, the equations imply that the expansion of the Universe will come to a halt and then will immediately be followed by a contracting phase. When the equations are extrapolated beyond the maximum rate of contraction, a cyclic Universe scenario emerges.

  7. Tangled nonlinear driven chain reactions of all optical singularities

    NASA Astrophysics Data System (ADS)

    Vasil'ev, V. I.; Soskin, M. S.

    2012-03-01

    Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.

  8. Singularities of the Euler equation and hydrodynamic stability

    NASA Technical Reports Server (NTRS)

    Tanveer, S.; Speziale, Charles G.

    1993-01-01

    Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

  9. Singularities of the Euler equation and hydrodynamic stability

    NASA Technical Reports Server (NTRS)

    Tanveer, S.; Speziale, Charles G.

    1992-01-01

    Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

  10. On the solution of integral equations with strongly singular kernels

    NASA Technical Reports Server (NTRS)

    Kaya, A. C.; Erdogan, F.

    1987-01-01

    Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

  11. On the solution of integral equations with strongly singular kernels

    NASA Technical Reports Server (NTRS)

    Kaya, A. C.; Erdogan, F.

    1986-01-01

    Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

  12. Nondimensional forms for singular perturbation analyses of aircraft energy climbs

    NASA Technical Reports Server (NTRS)

    Calise, A. J.; Markopoulos, N.; Corban, J. E.

    1991-01-01

    This paper proposes a systematic approach for identifying the perturbation parameter in singular perturbation analysis of aircraft optimal guidance, and in particular considers a family of problems related to aircraft energy climbs. The approach, which is based on a nondimensionalization of the equations of motion, is used to evaluatae the appropriateness of forced singular perturbation formulations used in the past for transport and fighter aircraft, and to assess the applicability of energy state approximations and singular perturbation analysis for airbreathing transatmospheric vehicles with hypersonic cruise and orbital capabilities.

  13. Evolution of coherence singularities of Schell-model beams.

    PubMed

    Rodrigo, José A; Alieva, Tatiana

    2015-08-01

    We show that the propagation of the widely used Schell-model partially coherent light can be easily understood using the ambiguity function. This approach is especially beneficial for the analysis of the mutual intensity of Schell-model beams (SMBs), which are associated with stable coherent beams such as Laguerre-, Hermite-, and Ince-Gaussian. We study the evolution of the coherence singularities during the SMB propagation. It is demonstrated that the distance of singularity formation depends on the coherence degree of the input beam. Moreover, it is proved that the shape, position, and number of singularity curves in far field are defined by the associated coherent beam.

  14. On the singular perturbations for fractional differential equation.

    PubMed

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  15. Vortex collapse from a viewpoint of complex-time singularity

    SciTech Connect

    Kimura, Yoshifumi.

    1990-01-01

    When collisions of point vortices occur under certain initial and parametrical conditions, a singularity appears on the real time axis. If some of the conditions are deviated from the collapse ones, the singularity splits to a (or some) complex-conjugate pair(s). Recently a scaling law between a deviation of an initial conditions and a resulted shift of the position of singularity from the real point was proposed for a system of point vortices. This scaling law is verified using the collisions of three and four point vortices. 17 refs., 7 figs.

  16. Absence of a singularity in loop quantum cosmology.

    PubMed

    Bojowald, M

    2001-06-04

    It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstration comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.

  17. Singularity Preserving Numerical Methods for Boundary Integral Equations

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki (Principal Investigator)

    1996-01-01

    In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

  18. Naked singularities in higher dimensional Vaidya space-times

    SciTech Connect

    Ghosh, S. G.; Dadhich, Naresh

    2001-08-15

    We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension.

  19. Configuration of singular optical cones in gyrotropic crystals with dichroism

    SciTech Connect

    Merkulov, V. S.

    2015-02-15

    Optical conic singularities in crystals with linear dichroism and natural optical activity at the point of intersection of dispersion curves for the main refractive indices are considered. The possible existence of singularities like a nodal point, tangency point, triple point, and cusps of the first and second order is demonstrated. Forty-nine different types of irreducible fourth-order optical cones obtained by sequential bifurcations of eight main singular cones are established. The classification is based on the concept of roughness of systems depending on parameters.

  20. Singular Solutions of Fully Nonlinear Elliptic Equations and Applications

    NASA Astrophysics Data System (ADS)

    Armstrong, Scott N.; Sirakov, Boyan; Smart, Charles K.

    2012-08-01

    We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of {R^n} , and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragmén-Lindelöf result as well as a principle of positive singularities in certain Lipschitz domains.

  1. Holographic dark energy with linearly varying deceleration parameter and escaping big rip singularity of the Bianchi type-V universe

    NASA Astrophysics Data System (ADS)

    Sarkar, Sanjay

    2014-08-01

    The present work deals with the accretion of two minimally interacting fluids: dark matter and a hypothetical isotropic fluid as the holographic dark energy components onto black hole and wormhole in a spatially homogeneous and anisotropic Bianchi type-V universe. To obtain an exact solution of the Einstein's field equations, we use the assumption of linearly varying deceleration parameter. Solution describes effectively the actual acceleration and indicates a big rip type future singularity of the universe. We have studied the evolution of the mass of black hole and the wormhole embedded in this anisotropic universe in order to reproduce a stable universe protected against future-time singularity. It is observed that the accretion of these dark components leads to a gradual decrease and increase of black hole and wormhole mass respectively. Finally, we have found that contrary to our previous case (Sarkar in Astrophys. Space. Sci. 341:651, 2014a), the big rip singularity of the universe with a divergent Hubble parameter of this dark energy model may be avoided by a big trip.

  2. Cosmological constant, near brane behavior and singularities

    NASA Astrophysics Data System (ADS)

    Gautason, Fridrik Freyr; Junghans, Daniel; Zagermann, Marco

    2013-09-01

    We show that the classical cosmological constant in type II flux compactifications can be written as a sum of terms from the action of localized sources plus a specific contribution from non-trivial background fluxes. Exploiting two global scaling symmetries of the classical supergravity action, we find that the flux contribution can in many interesting cases be set to zero such that the cosmological constant is fully determined by the boundary conditions of the fields in the near-source region. This generalizes and makes more explicit previous arguments in the literature. We then discuss the problem of putting -branes at the tip of the Klebanov-Strassler throat glued to a compact space in type IIB string theory so as to engineer a de Sitter solution. Our result for the cosmological constant and a simple global argument indicate that inserting a fully localized and backreacting -brane into such a background yields a singular energy density for the NSNS and RR 3-form field strengths at the -brane. This argument does not rely on partial smearing of the -brane or a linearization of field equations, but on a few general assumptions that we also discuss carefully.

  3. Singularity-free anisotropic strange quintessence star

    NASA Astrophysics Data System (ADS)

    Bhar, Piyali

    2015-04-01

    Present paper provides a new model of anisotropic strange star corresponding to the exterior Schwarzschild metric. The Einstein field equations have been solved by utilizing the Krori-Barua (KB) ansatz (Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975) in presence of quintessence field characterized by a parameter ω q with . The obtained solutions are free from central singularity. Our model is potentially stable. The numerical values of mass of the different strange stars SAXJ1808.4-3658(SS1) (radius=7.07 km), 4U1820-30 (radius=10 km), Vela X-12 (radius=9.99 km), PSR J 1614-2230 (radius=10.3 km) obtained from our model is very close to the observational data that confirms the validity of our proposed model. The interior solution is also matched to the exterior Schwarzschild spacetime in presence of thin shell where negative surface pressure is required to hold the thin shell against collapsing.

  4. Interior Tomography With Continuous Singular Value Decomposition

    PubMed Central

    Jin, Xin; Katsevich, Alexander; Yu, Hengyong; Wang, Ge; Li, Liang; Chen, Zhiqiang

    2013-01-01

    The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known subregion in the region of interest (ROI). In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known subregion. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior subregion knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the projection onto convex set type interior reconstructions. PMID:22907966

  5. On Singularities and Black Holes in Combination-Driven Models of Technological Innovation Networks.

    PubMed

    Solé, Ricard; Amor, Daniel R; Valverde, Sergi

    2016-01-01

    It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under which combinatorial technology should become explosive. Here we present a generalised model of technological evolution that takes into account two major properties: the number of previous technologies needed to create a novel one and how rapidly technology ages. Two different models of combinatorial growth are considered, involving different forms of ageing. When long-range memory is used and thus old inventions are available for novel innovations, singularities can emerge under some conditions with two phases separated by a critical boundary. If the ageing has a characteristic time scale, it is shown that no singularities will be observed. Instead, a "black hole" of old innovations appears and expands in time, making the rate of invention creation slow down into a linear regime.

  6. Acceleration toward polarization singularity inspired by relativistic E×B drift.

    PubMed

    Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

    2016-11-24

    The relativistic trajectory of a charged particle driven by the Lorentz force is different from the classical one, by velocity-dependent relativistic acceleration term. Here we show that the evolution of optical polarization states near the polarization singularity can be described in analogy to the relativistic dynamics of charged particles. A phase transition in parity-time symmetric potentials is then interpreted in terms of the competition between electric and magnetic 'pseudo'-fields applied to polarization states. Based on this Lorentz pseudo-force representation, we reveal that zero Lorentz pseudo-force is the origin of recently reported strong polarization convergence to the singular state at the exceptional point. We also demonstrate the deterministic design of achiral and directional eigenstates at the exceptional point, allowing an anomalous linear polarizer which operates orthogonal to forward and backward waves. Our results linking parity-time symmetry and relativistic electrodynamics show that previous PT-symmetric potentials for the polarization singularity with a chiral eigenstate are the subset of optical potentials for the E×B "polarization" drift.

  7. Acceleration toward polarization singularity inspired by relativistic E×B drift

    PubMed Central

    Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

    2016-01-01

    The relativistic trajectory of a charged particle driven by the Lorentz force is different from the classical one, by velocity-dependent relativistic acceleration term. Here we show that the evolution of optical polarization states near the polarization singularity can be described in analogy to the relativistic dynamics of charged particles. A phase transition in parity-time symmetric potentials is then interpreted in terms of the competition between electric and magnetic ‘pseudo’-fields applied to polarization states. Based on this Lorentz pseudo-force representation, we reveal that zero Lorentz pseudo-force is the origin of recently reported strong polarization convergence to the singular state at the exceptional point. We also demonstrate the deterministic design of achiral and directional eigenstates at the exceptional point, allowing an anomalous linear polarizer which operates orthogonal to forward and backward waves. Our results linking parity-time symmetry and relativistic electrodynamics show that previous PT-symmetric potentials for the polarization singularity with a chiral eigenstate are the subset of optical potentials for the E×B “polarization” drift. PMID:27883043

  8. On Singularities and Black Holes in Combination-Driven Models of Technological Innovation Networks

    PubMed Central

    Solé, Ricard; Amor, Daniel R.; Valverde, Sergi

    2016-01-01

    It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under which combinatorial technology should become explosive. Here we present a generalised model of technological evolution that takes into account two major properties: the number of previous technologies needed to create a novel one and how rapidly technology ages. Two different models of combinatorial growth are considered, involving different forms of ageing. When long-range memory is used and thus old inventions are available for novel innovations, singularities can emerge under some conditions with two phases separated by a critical boundary. If the ageing has a characteristic time scale, it is shown that no singularities will be observed. Instead, a “black hole” of old innovations appears and expands in time, making the rate of invention creation slow down into a linear regime. PMID:26821277

  9. Non-singular bounce scenarios in loop quantum cosmology and the effective field description

    SciTech Connect

    Cai, Yi-Fu; Wilson-Ewing, Edward E-mail: wilson-ewing@phys.lsu.edu

    2014-03-01

    A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmology and in a non-singular bouncing effective field model with a non-standard kinetic term at both the background and perturbative levels. We find that these two settings share many important properties, including the result that they both generate scale-invariant scalar perturbations. This shows that some quantum gravity effects of the very early universe may be mimicked by effective field models.

  10. Thermogeometric phase transition in a unified framework

    NASA Astrophysics Data System (ADS)

    Banerjee, Rabin; Majhi, Bibhas Ranjan; Samanta, Saurav

    2017-04-01

    Using geomterothermodynamics (GTD), we investigate the phase transition of black hole in a metric independent way. We show that for any black hole, curvature scalar (of equilibrium state space geometry) is singular at the point where specific heat diverges. Previously such a result could only be shown by taking specific examples on a case by case basis. A different type of phase transition, where inverse specific heat diverges, is also studied within this framework. We show that in the latter case, metric (of equilibrium state space geometry) is singular instead of curvature scalar. Since a metric singularity may be a coordinate artifact, we propose that GTD indicates that it is the singularity of specific heat and not inverse specific heat which indicates a phase transition of black holes.

  11. Singularity-free backstepping controller for model helicopters.

    PubMed

    Zou, Yao; Huo, Wei

    2016-11-01

    This paper develops a backstepping controller for model helicopters to achieve trajectory tracking without singularity, which occurs in the attitude representation when the roll or pitch reaches ±π2. Based on a simplified model with unmodeled dynamics, backstepping technique is introduced to exploit the controller and hyperbolic tangent functions are utilized to compensate the unmodeled dynamics. Firstly, a position loop controller is designed for the position tracking, where an auxiliary dynamic system with suitable parameters is introduced to warrant the singularity-free requirement for the extracted command attitude. Then, a novel attitude loop controller is proposed to obviate singularity. It is demonstrated that, based on the established criteria for selecting controller parameters and desired trajectories, the proposed controller realizes the singularity-free trajectory tracking of the model helicopter. Simulations confirm the theoretical results.

  12. Redundant single gimbal control moment gyroscope singularity analysis

    NASA Technical Reports Server (NTRS)

    Bedrossian, Nazareth S.; Paradiso, Joseph; Bergmann, Edward V.; Rowell, Derek

    1990-01-01

    The robotic manipulator is proposed as the mechanical analog to single gimbal control moment gyroscope systems, and it is shown that both systems share similar difficulties with singular configurations. This analogy is used to group gimbal angles corresponding to any momentum state into different families. The singularity problem associated with these systems is examined in detail. In particular, a method is presented to test for the possibility of nontorque-producing gimbal motion at a singular configuration, as well as to determine the admissible motions in the case when this is possible. Sufficient conditions are derived for instances where the singular system can be reconfigured into a nonsingular state by these nontorque-producing motions.

  13. Singularity in polarization: rewiring yeast cells to make two buds.

    PubMed

    Howell, Audrey S; Savage, Natasha S; Johnson, Sam A; Bose, Indrani; Wagner, Allison W; Zyla, Trevin R; Nijhout, H Frederik; Reed, Michael C; Goryachev, Andrew B; Lew, Daniel J

    2009-11-13

    For budding yeast to ensure formation of only one bud, cells must polarize toward one, and only one, site. Polarity establishment involves the Rho family GTPase Cdc42, which concentrates at polarization sites via a positive feedback loop. To assess whether singularity is linked to the specific Cdc42 feedback loop, we disabled the yeast cell's endogenous amplification mechanism and synthetically rewired the cells to employ a different positive feedback loop. Rewired cells violated singularity, occasionally making two buds. Even cells that made only one bud sometimes initiated two clusters of Cdc42, but then one cluster became dominant. Mathematical modeling indicated that, given sufficient time, competition between clusters would promote singularity. In rewired cells, competition occurred slowly and sometimes failed to develop a single "winning" cluster before budding. Slowing competition in normal cells also allowed occasional formation of two buds, suggesting that singularity is enforced by rapid competition between Cdc42 clusters.

  14. Stationary solutions for conservation laws with singular nonlocal sources

    NASA Astrophysics Data System (ADS)

    Coclite, Giuseppe Maria; Coclite, Mario Michele

    The existence of an a.e. positive stationary solution with bounded variation in [0,1] for an integro-differential conservation law with source depending on a function singular in the origin is proved.

  15. A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints

    SciTech Connect

    de Leon, M.; de Diego, D.M.

    1997-06-01

    We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}

  16. Object detection with a multistatic array using singular value decomposition

    DOEpatents

    Hallquist, Aaron T.; Chambers, David H.

    2014-07-01

    A method and system for detecting the presence of subsurface objects within a medium is provided. In some embodiments, the detection system operates in a multistatic mode to collect radar return signals generated by an array of transceiver antenna pairs that is positioned across a surface and that travels down the surface. The detection system converts the return signals from a time domain to a frequency domain, resulting in frequency return signals. The detection system then performs a singular value decomposition for each frequency to identify singular values for each frequency. The detection system then detects the presence of a subsurface object based on a comparison of the identified singular values to expected singular values when no subsurface object is present.

  17. Statistical analysis of effective singular values in matrix rank determination

    NASA Technical Reports Server (NTRS)

    Konstantinides, Konstantinos; Yao, Kung

    1988-01-01

    A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

  18. Quantum particle probe of the Kerr naked singularity

    NASA Astrophysics Data System (ADS)

    Gurtug, O.; Halilsoy, M.

    2017-01-01

    We investigate Kerr's timelike naked singularity within the framework of quantum mechanics. A quantum particle in the form of a massive boson is sent in the plane θ = π/2 to the naked ring singularity of Kerr which develops for the overspinning case (a>M) to test it from a quantum picture. This singularity is analysed in two different coordinate systems. We show that the spatial operator of the Klein-Gordon equation both in Boyer-Lindquist and in the dragging coordinate systems has a unique self-adjoint extension. As a result, the classical Kerr's ring singularity becomes quantum regular, if it is probed with massive bosonic particles obeying the Klein-Gordon equation.

  19. Dark energy and dark matter perturbations in singular universes

    SciTech Connect

    Denkiewicz, Tomasz

    2015-03-01

    We discuss the evolution of density perturbations of dark matter and dark energy in cosmological models which admit future singularities in a finite time. Up to now geometrical tests of the evolution of the universe do not differentiate between singular universes and ΛCDM scenario. We solve perturbation equations using the gauge invariant formalism. The analysis shows that the detailed reconstruction of the evolution of perturbations within singular cosmologies, in the dark sector, can exhibit important differences between the singular universes models and the ΛCDM cosmology. This is encouraging for further examination and gives hope for discriminating between those models with future galaxy weak lensing experiments like the Dark Energy Survey (DES) and Euclid or CMB observations like PRISM and CoRE.

  20. Higher order matrix differential equations with singular coefficient matrices

    SciTech Connect

    Fragkoulis, V. C.; Kougioumtzoglou, I. A.; Pantelous, A. A.; Pirrotta, A.

    2015-03-10

    In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

  1. Analysis and design of nonlinear resonances via singularity theory

    NASA Astrophysics Data System (ADS)

    Cirillo, G. I.; Habib, G.; Kerschen, G.; Sepulchre, R.

    2017-03-01

    Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.

  2. Classical resolution of black hole singularities via wormholes

    NASA Astrophysics Data System (ADS)

    Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.

    2016-03-01

    In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature.

  3. Switched impulsive control of the endocrine disruptor diethylstilbestrol singular model

    NASA Astrophysics Data System (ADS)

    Zamani, Iman; Shafiee, Masoud; Ibeas, Asier; de la Sen, M.

    2014-12-01

    In this work, a switched and impulsive controller is designed to control the Endocrine Disruptor Diethylstilbestrol mechanism which is usually modeled as a singular system. Then the exponential stabilization property of the proposed switched and impulsive singular model is discussed under matrix inequalities. A design algorithm is given and applied for the physiological process of endocrine disruptor diethylstilbestrol model to illustrate the effectiveness of the results.

  4. Singular optical manipulation of birefringent elastic media using nonsingular beams.

    PubMed

    Brasselet, Etienne

    2009-10-15

    It is shown that nonsingular light beams can generate singular birefringent patterns in homogeneous birefringent elastic media. These orientational defects of the optical-axis spatial distribution originate from an optical torque driven by a nonzero longitudinal field component. Singular radial and spin-dependent azimuthal light-induced elastic distortion patterns are described and experimentally observed in a uniform liquid-crystal film in the course of a focused circularly polarized Gaussian beam.

  5. Kurzweil's Singularity as a part of Evo-SETI Theory

    NASA Astrophysics Data System (ADS)

    Maccone, Claudio

    2017-03-01

    Ray Kurzweil's famous 2006 book "The Singularity Is Near" predicted that the Singularity (i.e. computers taking over humans) would occur around the year 2045. In this paper we prove that Kurzweil's prediction is in agreement with the "Evo-SETI" (Evolution and SETI)" mathematical model that this author has developed over the last five years in a series of mathematical papers published in both Acta Astronautica and the International Journal of Astrobiology.

  6. Why do naked singularities form in gravitational collapse? II

    SciTech Connect

    Joshi, Pankaj S.; Goswami, Rituparno; Dadhich, Naresh

    2004-10-15

    We examine physical features that could lead to formation of a naked singularity rather than black hole, as end state of spherical collapse. Generalizing earlier results on dust collapse to general type I matter fields, it is shown that collapse always creates black hole if shear vanishes or density is homogeneous. It follows that nonzero shear is a necessary condition for singularity to be visible to external observers, when trapped surface formation is delayed by shearing forces or inhomogeneity within the collapsing cloud.

  7. Bifurcations and Singularities for Coupled Oscillators with Inertia and Frustration

    NASA Astrophysics Data System (ADS)

    Barré, J.; Métivier, D.

    2016-11-01

    We prove that any nonzero inertia, however small, is able to change the nature of the synchronization transition in Kuramoto-like models, either from continuous to discontinuous or from discontinuous to continuous. This result is obtained through an unstable manifold expansion in the spirit of Crawford, which features singularities in the vicinity of the bifurcation. Far from being unwanted artifacts, these singularities actually control the qualitative behavior of the system. Our numerical tests fully support this picture.

  8. Evidence of singularities for a family of contour dynamics equations

    PubMed Central

    Córdoba, Diego; Fontelos, Marco A.; Mancho, Ana M.; Rodrigo, Jose L.

    2005-01-01

    In this work, we show evidence of the existence of singularities developing in finite time for a class of contour dynamics equations depending on a parameter 0 < α ≤ 1. The limiting case α → 0 corresponds to 2D Euler equations, and α = 1 corresponds to the surface quasi-geostrophic equation. The singularity is point-like, and it is approached in a self-similar manner. PMID:15837929

  9. Integrating an embedded system in a microwave moisture meter

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The conversion of a PC- or laptop-controlled microwave moisture meter to a stand-alone meter hosting its own embedded system is discussed. The moisture meter measures the attenuation and phase shift of low power microwaves traversing the sample, from which the dielectric properties are calculated. T...

  10. Integrating an Embedded System within a Microwave Moisture Meter

    Technology Transfer Automated Retrieval System (TEKTRAN)

    In this paper, the conversion of a PC or laptop-controlled microwave moisture meter to a stand-alone meter hosting its own embedded system is discussed. The moisture meter uses low-power microwaves to measure the attenuation and phase shift of the sample, from which the dielectric properties are cal...

  11. On the Construction of Property Based Diabatizations: Diabolical Singular Points.

    PubMed

    Zhu, Xiaolei; Yarkony, David R

    2015-12-17

    Diabatizations achieved by diagonalization of a property operator or as the extremum of a molecular property are numerous and widely used, although for a particular system a given property method may have limited accuracy or even fail catastrophically. These failures are usually analyzed in terms of limitations of the chosen property or method. Here we introduce an alternative perspective, failure attributable to singularities in the defining equations. The singular subspace is analogous to the conical intersection seam in potential energy surfaces. Using the archetypical NH3 nonadiabatic photodissociation, it is shown that for two states the diabatization condition has singularities on a subspace of dimension N - 2, where N = 3N(atom) - 6, is the number of internal coordinates. This singular subspace is distinct from the N - 2-dimensional seam of conical intersections of the electronic Hamiltonian and results incorrectly, in singular derivative couplings between diabatic states in unexpected regions of nuclear coordinate space. Simple indicators are developed that provide ways to anticipate and avoid these singularities.

  12. Symmetry breaking and singularity structure in Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Commeford, K. A.; Garcia-March, M. A.; Ferrando, A.; Carr, Lincoln D.

    2012-08-01

    We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005.

  13. Relative perturbation theory: (II) Eigenspace and singular subspace variations

    SciTech Connect

    Li, R.-C.

    1996-01-20

    The classical perturbation theory for Hermitian matrix enigenvalue and singular value problems provides bounds on invariant subspace variations that are proportional to the reciporcals of absolute gaps between subsets of spectra or subsets of singular values. These bounds may be bad news for invariant subspaces corresponding to clustered eigenvalues or clustered singular values of much smaller magnitudes than the norms of matrices under considerations when some of these clustered eigenvalues ro clustered singular values are perfectly relatively distinguishable from the rest. This paper considers how eigenvalues of a Hermitian matrix A change when it is perturbed to {tilde A}= D{sup {asterisk}}AD and how singular values of a (nonsquare) matrix B change whenit is perturbed to {tilde B}=D{sub 1}{sup {asterisk}}BD{sub 2}, where D, D{sub 1}, and D{sub 2} are assumed to be close to identity matrices of suitable dimensions, or either D{sub 1} or D{sub 2} close to some unitary matrix. It is proved that under these kinds of perturbations, the change of invarient subspaces are proportional to reciprocals of relative gaps between subsets of spectra or subsets of singular values. We have been able to extend well-known Davis-Kahan sin {theta} theorems and Wedin sin {theta} theorems. As applications, we obtained bounds for perturbations of graded matrices.

  14. Singularity of Navier-Stokes Equations Leading to Turbulent Transition

    NASA Astrophysics Data System (ADS)

    Dou, Hua-Shu; Fluid Mechanics Research Team

    2014-11-01

    As is well known, there is discontinuity during the transition from laminar flow to turbulence in the time-averaged Navier-Stokes equations. In other words, singularity may implicitly exist in the Navier-Stokes equations. Transition of a laminar flow to turbulence must be implemented via the singularity. However, how the singularity of Navier-Stokes equations is related to the turbulent transition is not understood. In this study, the singularity possibly hidden in the Navier-Stokes equation is exactly derived by mathematical treatment. Then, it is found that for pressure driven flows, the singularity of Navier-Stokes equations corresponds to the inflection point on the velocity profile. Since the rate of amplification to a disturbance at the inflection point is infinite, the laminar flow is able to involve into turbulence at this point firstly at a sufficient high Reynolds number. This is the reason why turbulent spot is formed at the location of inflection point. It is further demonstrated that the existence of the singularity in the time-averaged Navier-Stokes equations is the necessary and sufficient condition for the turbulent transition in pressure driven flows. These results agrees well with the findings from the recent proposed energy gradient method. Professor in Fluid Mechanics; AIAA Associate Fellow.

  15. On the singular values decoupling in the Singular Spectrum Analysis of volcanic tremor at Stromboli

    NASA Astrophysics Data System (ADS)

    Carniel, R.; Barazza, F.; Tárraga, M.; Ortiz, R.

    2006-10-01

    The well known strombolian activity at Stromboli volcano is occasionally interrupted by rarer episodes of paroxysmal activity which can lead to considerable hazard for Stromboli inhabitants and tourists. On 5 April 2003 a powerful explosion, which can be compared in size with the latest one of 1930, covered with bombs a good part of the normally tourist-accessible summit area. This explosion was not forecasted, although the island was by then effectively monitored by a dense deployment of instruments. After having tackled in a previous paper the problem of highlighting the timescale of preparation of this event, we investigate here the possibility of highlighting precursors in the volcanic tremor continuously recorded by a short period summit seismic station. We show that a promising candidate is found by examining the degree of coupling between successive singular values that result from the Singular Spectrum Analysis of the raw seismic data. We suggest therefore that possible anomalies in the time evolution of this parameter could be indicators of volcano instability to be taken into account e.g. in a bayesian eruptive scenario evaluator. Obviously, further (and possibly forward) testing on other cases is needed to confirm the usefulness of this parameter.

  16. Singularities in Axisymmetric Free Boundaries for ElectroHydroDynamic Equations

    NASA Astrophysics Data System (ADS)

    Garcia, Mariana Smit Vega; Vărvărucă, Eugen; Weiss, Georg S.

    2016-11-01

    We consider singularities in the ElectroHydroDynamic equations. In a regime where we are allowed to neglect surface tension, and assuming that the free surface is given by an injective curve and that either the fluid velocity or the electric field satisfies a certain non-degeneracy condition, we prove that either the fluid region or the gas region is asymptotically a cusp. Our proofs depend on a combination of monotonicity formulas and a non-vanishing result by Caffarelli and Friedman. As a by-product of our analysis we also obtain a special solution with convex conical air-phase which we believe to be new.

  17. Segmentation of singularity maps in the context of soil porosity

    NASA Astrophysics Data System (ADS)

    Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.

    2016-04-01

    Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in

  18. Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere.

    PubMed

    Oh, Sangchul; Hu, Xuedong; Nori, Franco; Kais, Sabre

    2016-02-26

    Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov-Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs.

  19. Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere

    PubMed Central

    Oh, Sangchul; Hu, Xuedong; Nori, Franco; Kais, Sabre

    2016-01-01

    Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov- Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs. PMID:26916031

  20. Rare regions and Griffiths singularities at a clean critical point: the five-dimensional disordered contact process.

    PubMed

    Vojta, Thomas; Igo, John; Hoyos, José A

    2014-07-01

    We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.

  1. Boundary singularities produced by the motion of soap films

    PubMed Central

    Goldstein, Raymond E.; McTavish, James; Moffatt, H. Keith; Pesci, Adriana I.

    2014-01-01

    Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a “neck-pinching” boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck’s geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures. PMID:24843162

  2. Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings

    NASA Astrophysics Data System (ADS)

    Engle, J.

    2007-12-01

    In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of Engle (2006 Quantum field theory and its symmetry reduction Class. Quantum Gravity 23 2861 94). We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions.

  3. Hermitian hat wavelet design for singularity detection in the Paraguay river-level data analyses

    NASA Astrophysics Data System (ADS)

    Szu, Harold H.; Hsu, Charles C.; Sa, Leonardo D.; Li, Weigang

    1997-04-01

    The direct differentiation of a noisy signal ds/dt is known to be inaccurate. Differentiation can be improved by employing the Dirac (delta) -function introduced into a convolution product denoted by (direct product) and then integrated by parts: ds/dt equals ds/dt (direct product) (delta) equals - s (direct product) d(delta) /dt. The Schwartz Gaussian representation of the delta function is then explicitly used in the differentiation. It turns out that such a convolution approach to the first and the second derivatives produces a pair of mother wavelets the combination of which is the complex generalization of the Mexican hat called a Hermitian hat wavelet. It is shown that the Hermitian filter is a single oscillation wavelet having much lower frequency bandwidth than the Mortlet or Gabor wavelet. As a result of Nyquist theorem, a fewer number of grid points would be needed for the discrete convolution operation. Therefore, the singularity characteristic will not be overly smeared and the noise can be smoothed away. The phase plot of the Hermitian wavelet transform in terms of the time scale and frequency domains reveal a bifurcation discontinuity of a noisy cusp singularity at the precise location of the singularity as well as the scale nature of the underlying dynamics. This phase plot is defined as (theta) (t/a) equals tan-1 [(ds/dt)/(-d2s/dt2] equals tan-1 [((d(delta) (t/a)dt) (direct product) s)/((d2(delta) (t/a)/dt2) (direct product) s)] applied to a real world data of the Paraguay river levels.

  4. Dynamics of learning in multilayer perceptrons near singularities.

    PubMed

    Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi

    2008-08-01

    The dynamical behavior of learning is known to be very slow for the multilayer perceptron, being often trapped in the "plateau." It has been recently understood that this is due to the singularity in the parameter space of perceptrons, in which trajectories of learning are drawn. The space is Riemannian from the point of view of information geometry and contains singular regions where the Riemannian metric or the Fisher information matrix degenerates. This paper analyzes the dynamics of learning in a neighborhood of the singular regions when the true teacher machine lies at the singularity. We give explicit asymptotic analytical solutions (trajectories) both for the standard gradient (SGD) and natural gradient (NGD) methods. It is clearly shown, in the case of the SGD method, that the plateau phenomenon appears in a neighborhood of the critical regions, where the dynamical behavior is extremely slow. The analysis of the NGD method is much more difficult, because the inverse of the Fisher information matrix diverges. We conquer the difficulty by introducing the "blow-down" technique used in algebraic geometry. The NGD method works efficiently, and the state converges directly to the true parameters very quickly while it staggers in the case of the SGD method. The analytical results are compared with computer simulations, showing good agreement. The effects of singularities on learning are thus qualitatively clarified for both standard and NGD methods.

  5. On the initial singularity problem in rainbow cosmology

    SciTech Connect

    Santos, Grasiele; Gubitosi, Giulia; Amelino-Camelia, Giovanni E-mail: g.gubitosi@imperial.ac.uk

    2015-08-01

    It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ('rainbow') spacetime metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbow metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.

  6. Loop quantum cosmology and the fate of cosmological singularities

    NASA Astrophysics Data System (ADS)

    Singh, Parampreet

    2014-09-01

    Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and the breakdown of the geodesic evolution. Recent progress on implementing techniques of loop quantum gravity to cosmological models reveals that such singularities may be generically resolved because of the quantum gravitational effects. Due to the quantum geometry, which replaces the classical differential geometry at the Planck scale, the big bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. In this manuscript, we discuss some of the main features of this approach and the results on the generic resolution of singularities for the isotropic as well as anisotropic models. Using effective spacetime description of the quantum theory, we show the way quantum gravitational effects lead to the universal bounds on the energy density, the Hubble rate and the anisotropic shear. We discuss the geodesic completeness in the effective spacetime and the resolution of all of the strong singularities. It turns out that despite the bounds on energy density and the Hubble rate, there can be divergences in the curvature invariants. However such events are geodesically extendible, with tidal forces not strong enough to cause inevitable destruction of the in-falling objects.

  7. Railway ground vibrations induced by wheel and rail singular defects

    NASA Astrophysics Data System (ADS)

    Kouroussis, Georges; Connolly, David P.; Alexandrou, Georgios; Vogiatzis, Konstantinos

    2015-10-01

    Railway local irregularities are a growing source of ground-borne vibration and can cause negative environmental impacts, particularly in urban areas. Therefore, this paper analyses the effect of railway track singular defects (discontinuities) on ground vibration generation and propagation. A vehicle/track/soil numerical railway model is presented, capable of accurately predicting vibration levels. The prediction model is composed of a multibody vehicle model, a flexible track model and a finite/infinite element soil model. Firstly, analysis is undertaken to assess the ability of wheel/rail contact models to accurately simulate the force generation at the wheel/rail contact, in the presence of a singular defect. It is found that, although linear contact models are sufficient for modelling ground vibration on smooth tracks, when singular defects are present higher accuracy wheel/rail models are required. Furthermore, it is found that the variation in wheel/rail force during the singular defect contact depends on the track flexibility, and thus requires a fully coupled vehicle/track/foundation model. Next, a parametric study of ground vibrations generated by singular rail and wheel defects is undertaken. Six shapes of discontinuity are modelled, representing various defect types such as transition zones, switches, crossings, rail joints and wheel flats. The vehicle is modelled as an AM96 train set and it is found that ground vibration levels are highly sensitive to defect height, length and shape.

  8. The Maslov index and nondegenerate singularities of integrable systems

    NASA Astrophysics Data System (ADS)

    Foxman, J. A.; Robbins, J. M.

    2005-11-01

    We consider integrable Hamiltonian systems in {\\mathbb R}^{2n} with integrals of motion F = (F1, ..., Fn) in involution. Nondegenerate singularities of corank one are critical points of F where rank dF = n - 1 and which have definite linear stability. The set of corank-one nondegenerate singularities is a codimension-two symplectic submanifold invariant under the flow. We show that the Maslov index of a closed curve is a sum of contributions ± 2 from the nondegenerate singularities it encloses, the sign depending on the local orientation and stability at the singularities. For one-freedom systems this corresponds to the well-known formula for the Poincaré index of a closed curve as the oriented difference between the number of elliptic and hyperbolic fixed points enclosed. We also obtain a formula for the Liapunov exponent of invariant (n - 1)-dimensional tori in the nondegenerate singular set. Examples include rotationally symmetric n-freedom Hamiltonians, while an application to the periodic Toda chain is described in a companion paper (Foxman and Robbins 2005 Nonlinearity 18 2795-813).

  9. Inflationary cosmology leading to a soft type singularity

    NASA Astrophysics Data System (ADS)

    Brevik, I.; Obukhov, V. V.; Timoshkin, A. V.

    2016-06-01

    A remarkable property of modern cosmology is that it allows for a special case of symmetry, consisting in the possibility of describing the early-time acceleration (inflation) and the late-time acceleration using the same theoretical framework. In this paper, we consider various cosmological models corresponding to a generalized form for the equation of state for the fluid in a flat Friedmann-Robertson-Walker (FRW) universe, emphasizing cases where the so-called type IV singular inflation is encountered in the future. This is a soft (non-crushing) kind of singularity. Parameter values for an inhomogeneous equation of state leading to singular inflation are obtained. We present models for which there are two type IV singularities, the first corresponding to the end of the inflationary era and the second to a late-time event. We also study the correspondence between the theoretical slow-roll parameters leading to type IV singular inflation and the recent results observed by the Planck satellite.

  10. Embedding Sensors During Additive Manufacturing

    SciTech Connect

    Sbriglia, Lexey Raylene

    2015-08-10

    This PowerPoint presentation had the following headings: Fused deposition modeling (FDM); Open source 3D printing; Objectives; Vibration analysis; Equipment; Design; Material choices; Failure causes, such as tension, bubbling; Potential solutions; Simulations; Embedding the sensors; LabView programming; Alternate data acquisition; Problem and proposed solution; and, Conclusions

  11. Motif-based embedding for graph clustering

    NASA Astrophysics Data System (ADS)

    Lim, Sungsu; Lee, Jae-Gil

    2016-12-01

    Community detection in complex networks is a fundamental problem that has been extensively studied owing to its wide range of applications. However, because community detection methods typically rely on the relations between vertices in networks, they may fail to discover higher-order graph substructures, called the network motifs. In this paper, we propose a novel embedding method for graph clustering that considers higher-order relationships involving multiple vertices. We show that our embedding method, which we call motif-based embedding, is more effective in detecting communities than existing graph embedding methods, spectral embedding and force-directed embedding, both theoretically and experimentally.

  12. Singular spectrum analysis and its applications in mapping mantle seismic structure

    NASA Astrophysics Data System (ADS)

    Dokht, Ramin M. H.; Gu, Yu Jeffrey; Sacchi, Mauricio D.

    2017-03-01

    Seismic discontinuities are fundamental to the understanding of mantle composition and dynamics. Their depths and impedance contrasts are generally determined using secondary phases such as SS precursors and P-to-S converted waves. However, analysing and interpreting these weak signals often suffer from incomplete data coverage, high noise levels and interfering seismic arrivals, especially near tectonically complex regions such as subduction zones. To overcome these pitfalls, we adopt a singular spectrum analysis (SSA) method to remove random noise, reconstruct missing traces and enhance the robustness of SS precursors and P-to-S conversions from mantle seismic discontinuities. Our method takes advantage of the predictability of time series in the frequency-space domain and performs rank reduction using a singular value decomposition of the trajectory matrix. We apply SSA to synthetic record sections as well as the observations of (1) SS precursors beneath the northwestern Pacific subduction zones, and (2) P-to-S converted waves from southwestern Canada. In comparison with raw or interpolated data, the SSA enhanced seismic sections exhibit greater resolution due to the suppression of random noise (which reduces signal amplitude during standard averaging procedures) through rank reduction. SSA also enables an effective separation of the SS precursors from the postcursors of S-wave core diffractions. This method will greatly benefit future analyses of weak crustal and mantle seismic phases, especially when data coverages are less than ideal.

  13. Curved singular beams for three-dimensional particle manipulation

    PubMed Central

    Zhao, Juanying; Chremmos, Ioannis D.; Song, Daohong; Christodoulides, Demetrios N.; Efremidis, Nikolaos K.; Chen, Zhigang

    2015-01-01

    For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark “hole” in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications. PMID:26166011

  14. Medical image denoising using one-dimensional singularity function model.

    PubMed

    Luo, Jianhua; Zhu, Yuemin; Hiba, Bassem

    2010-03-01

    A novel denoising approach is proposed that is based on a spectral data substitution mechanism through using a mathematical model of one-dimensional singularity function analysis (1-D SFA). The method consists in dividing the complete spectral domain of the noisy signal into two subsets: the preserved set where the spectral data are kept unchanged, and the substitution set where the original spectral data having lower signal-to-noise ratio (SNR) are replaced by those reconstructed using the 1-D SFA model. The preserved set containing original spectral data is determined according to the SNR of the spectrum. The singular points and singularity degrees in the 1-D SFA model are obtained through calculating finite difference of the noisy signal. The theoretical formulation and experimental results demonstrated that the proposed method allows more efficient denoising while introducing less distortion, and presents significant improvement over conventional denoising methods.

  15. Singular cosmological evolution using canonical and ghost scalar fields

    SciTech Connect

    Nojiri, Shin'ichi; Odintsov, S.D.; Oikonomou, V.K.; Saridakis, Emmanuel N. E-mail: odintsov@ieec.uab.es E-mail: Emmanuel_Saridakis@baylor.edu

    2015-09-01

    We demonstrate that finite time singularities of Type IV can be consistently incorporated in the Universe's cosmological evolution, either appearing in the inflationary era, or in the late-time regime. While using only one scalar field instabilities can in principle occur at the time of the phantom-divide crossing, when two fields are involved we are able to avoid such instabilities. Additionally, the two-field scalar-tensor theories prove to be able to offer a plethora of possible viable cosmological scenarios, at which various types of cosmological singularities can be realized. Amongst others, it is possible to describe inflation with the appearance of a Type IV singularity, and phantom late-time acceleration which ends in a Big Rip. Finally, for completeness, we also present the Type IV realization in the context of suitably reconstructed F(R) gravity.

  16. Optimal singular control with applications to trajectory optimization

    NASA Technical Reports Server (NTRS)

    Vinh, N. X.

    1977-01-01

    A comprehensive discussion of the problem of singular control is presented. Singular control enters an optimal trajectory when the so called switching function vanishes identically over a finite time interval. Using the concept of domain of maneuverability, the problem of optical switching is analyzed. Criteria for the optimal direction of switching are presented. The switching, or junction, between nonsingular and singular subarcs is examined in detail. Several theorems concerning the necessary, and also sufficient conditions for smooth junction are presented. The concepts of quasi-linear control and linearized control are introduced. They are designed for the purpose of obtaining approximate solution for the difficult Euler-Lagrange type of optimal control in the case where the control is nonlinear.

  17. PT -symmetric spectral singularity and negative-frequency resonance

    NASA Astrophysics Data System (ADS)

    Pendharker, Sarang; Guo, Yu; Khosravi, Farhad; Jacob, Zubin

    2017-03-01

    Vacuum consists of a bath of balanced and symmetric positive- and negative-frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative-frequency modes as in quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative-frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT ) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation-related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive- and negative-frequency plasmonic fluctuations (negative-frequency resonance). Our work paves the way for understanding the role of PT -symmetric spectral singularities in amplifying fluctuations and motivates the search for PT symmetry in novel photonic systems.

  18. Curved singular beams for three-dimensional particle manipulation.

    PubMed

    Zhao, Juanying; Chremmos, Ioannis D; Song, Daohong; Christodoulides, Demetrios N; Efremidis, Nikolaos K; Chen, Zhigang

    2015-07-13

    For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark "hole" in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications.

  19. Conditions for the naked singularity formation in generalized Vaidya spacetime

    NASA Astrophysics Data System (ADS)

    Vertogradov, V. D.

    2016-11-01

    The gravitational collapse of generalised Vaidya spacetime is considered. It is known that the endstate of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M(v,r). Here we give conditions for the mass function which corresponds to the equation of the state P = αρ where α ∈ (0, ⅓] and according to these conditions we obtain either a black hole or a naked singularity at the endstate of gravitational collapse. Also we give conditions for the mass function when the singularity is gravitationally strong. Also we provide the metric which is the analogue of Vaidya metric in case of rotation.

  20. Singular Harmonic Maps and Applications to General Relativity

    NASA Astrophysics Data System (ADS)

    Nguyen, Luc

    2011-01-01

    The study of axially symmetric stationary multi-black-hole configurations and the force between co-axially rotating black holes involves, as a first step, an analysis on the "boundary regularity" of the so-called reduced singular harmonic maps. We carry out this analysis by considering those harmonic maps as solutions to some homogeneous divergence systems of partial differential equations with singular coefficients. Our results extend previous works by Weinstein (Comm Pure Appl Math 43:903-948, 1990; Comm Pure Appl Math 45:1183-1203, 1992) and by Li and Tian (Manu Math 73(1):83-89, 1991; Commun Math Phys 149:1-30, 1992; Differential geometry: PDE on manifolds, vol 54, pp. 317-326, 1993). This paper is based on the Ph.D. thesis of the author (Singular harmonic maps into hyperbolic spaces and applications to general relativity, PhD thesis, The State University of New Jersey, Rutgers, 2009).