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Sample records for embedded phase singularity

  1. Transformation of the optical vortex light beams in holographic elements with embedded phase singularities

    NASA Astrophysics Data System (ADS)

    Sviridova, S. V.; Bekshaev, A. Y.

    2012-01-01

    Transformations of spatial characteristics of optical vortex (OV) light beams at passing through a computer-generated hologram (CGH) that imparts an additional phase singularity ("fork" hologram) are investigated. The spatial structure of the diffracted beam is studied for different combinations of the incident OV order m, embedded topological charge of the CGH q and the diffraction order n. Variations of the intensity distribution are investigated experimentally. Due to the incident beam displacement with respect to the CGH optical axis, the diffracted beam profile is deformed, rotates in the azimuthal direction in agreement with the internal energy circulation and its 'center of gravity' is displaced orthogonally to the incident beam displacement. The results are compared with theoretical predictions based on two models of the incident OV beam. As, in experiment, the incident beam was created from the Gaussian beam passed another fork hologram, the Kummer beam model seems presumably more relevant but the standard Laguerre-Gaussian model in some cases fits the experimental data quite well.

  2. Transformation of the optical vortex light beams in holographic elements with embedded phase singularities

    NASA Astrophysics Data System (ADS)

    Sviridova, S. V.; Bekshaev, A. Y.

    2011-09-01

    Transformations of spatial characteristics of optical vortex (OV) light beams at passing through a computer-generated hologram (CGH) that imparts an additional phase singularity ("fork" hologram) are investigated. The spatial structure of the diffracted beam is studied for different combinations of the incident OV order m, embedded topological charge of the CGH q and the diffraction order n. Variations of the intensity distribution are investigated experimentally. Due to the incident beam displacement with respect to the CGH optical axis, the diffracted beam profile is deformed, rotates in the azimuthal direction in agreement with the internal energy circulation and its 'center of gravity' is displaced orthogonally to the incident beam displacement. The results are compared with theoretical predictions based on two models of the incident OV beam. As, in experiment, the incident beam was created from the Gaussian beam passed another fork hologram, the Kummer beam model seems presumably more relevant but the standard Laguerre-Gaussian model in some cases fits the experimental data quite well.

  3. Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

    NASA Astrophysics Data System (ADS)

    Bekshaev, A. Ya.; Sviridova, S. V.

    2010-12-01

    Spatial characteristics of diffracted beams produced by a "fork" hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the "proper" topological charge m of the incident vortex beam and the topological charge l of the singularity "imparted" by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.

  4. 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.

  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. Spatial Distribution of Phase Singularities in Optical Random Vector Waves.

    PubMed

    De Angelis, L; Alpeggiani, F; Di Falco, A; Kuipers, L

    2016-08-26

    Phase singularities are dislocations widely studied in optical fields as well as in other areas of physics. With experiment and theory we show that the vectorial nature of light affects the spatial distribution of phase singularities in random light fields. While in scalar random waves phase singularities exhibit spatial distributions reminiscent of particles in isotropic liquids, in vector fields their distribution for the different vector components becomes anisotropic due to the direct relation between propagation and field direction. By incorporating this relation in the theory for scalar fields by Berry and Dennis [Proc. R. Soc. A 456, 2059 (2000)], we quantitatively describe our experiments. PMID:27610854

  7. 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. PMID:21847236

  8. 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.

  9. 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. PMID:27607491

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

    PubMed

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

    2001-09-01

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

  11. Failure of the method of slowly varying amplitude and phase for non-linear, singular oscillators

    NASA Technical Reports Server (NTRS)

    Mickens, R. E.; Ramadhani, I.

    1992-01-01

    It is shown that the method of slowly varying amplitude and phase yields erroneous results in the study of the mathematical properties of nonlinear singular oscillator systems. The analytical solution is described in which the phase function is constant and for which a special limiting behavior exists when the wavelength is zero. The previous method based on the condition of boundedness cannot be satisfied for nonlinear singular characteristics, and the erroneous designation of the expansion parameter is identified.

  12. Projection of phase singularities in moiré fringe onto a light field

    NASA Astrophysics Data System (ADS)

    Ohno, Seigo

    2016-06-01

    A moiré pattern, which is a kind of spatial interference between two periodic patterns, is regarded as a spatial modulation of a "field." By defining the displacement field, we reveal that moiré patterns can have a topological phase singularity, similar to a disclination in liquid crystal and, more generally, a vector field treated in the singular optics. We propose that topological singularities in the moiré displacement field can be projected by passing an electromagnetic field through a metasurface. We designed a metasurface constructed from two layers of a metal disk array operating in the terahertz band; then we numerically estimated the spatial distribution of its transmission properties. The phase singularities in the electromagnetic fields coincided with the singularities appearing in the moiré pattern. We found two kinds of singularities, and the phase of the electromagnetic field changed by 2π or 4π around them. These phase changes were independent of the light frequency, implying that the topological properties of the moiré fields were projected onto the electromagnetic field. This feature of moiré metasurfaces can potentially be exploited in spiral phase plate arrays with no frequency dispersion of the phase change.

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

    PubMed

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

    2015-05-01

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

  14. 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.

  15. Singularity-free Green's function for EM sources embedded in a stratified medium

    NASA Astrophysics Data System (ADS)

    Weng, Ai-Hua; Liu, Yun-He; Yin, Chang-Chun; Jia, Ding-Yu

    2016-03-01

    We present a method to unify the calculation of Green's functions for an electromagnetic (EM) transmitting source embedded in a homogeneous stratified medium. A virtual interface parallel to layer interfaces is introduced through the source location. The potentials for Green's function are derived by decomposing the partial wave solutions to Helmholtz's equations into upward and downward within boundaries. The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level. The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface. Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters, whereas the kernel connected with the stratified media stays unchanged. Hence, the present method can be easily applied to EM transmitting sources with little modification. The application of the proposed method to the marine controlled-source electromagnetic method (MCSEM) demonstrates its simplicity and flexibility.

  16. Viscous singular shock profiles for a system of conservation laws modeling two-phase flow

    NASA Astrophysics Data System (ADS)

    Hsu, Ting-Hao

    2016-08-01

    This paper is concerned with singular shocks for a system of conservation laws via the Dafermos regularization ut + f(u)x = ɛtuxx. For a system modeling incompressible two-phase fluid flow, the existence of viscous profiles is proved using Geometric Singular Perturbation Theory. The weak convergence and the growth rate of the viscous solution are also derived; the weak limit is the sum of a piecewise constant function and a δ-measure supported on a shock line, and the maximum value of the viscous solution is of order exp ⁡ (1 / ɛ).

  17. 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

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

    NASA Astrophysics Data System (ADS)

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

    2012-12-01

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

  19. Laser-Directed Hierarchical Assembly of Liquid Crystal Defects and Control of Optical Phase Singularities

    SciTech Connect

    Ackerman, P. J.; Qi, Z. Y.; Lin, Y. H.; Twombly, C. W.; Laviada, M. J.; Lansac, Y.; Smalyukh, I. I.

    2012-06-07

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

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

    PubMed Central

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

    2012-01-01

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

  1. 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.

  2. 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.

  3. Phase correction-based singularity function analysis for partial k-space reconstruction.

    PubMed

    Luo, Jianhua; Zhu, Yuemin; Magnin, Isabelle

    2008-07-01

    Partial k-space acquisition is a conventional method in magnetic resonance imaging (MRI) for reducing imaging time while maintaining image quality. In this field, image reconstruction from partial k-space is a key issue. This paper proposes an approach fundamentally different from traditional techniques for reconstructing magnetic resonance (MR) images from partial k-space. It uses a so-called singularity function analysis (SFA) model based on phase correction. With such a reconstruction approach, some nonacquired negative spatial frequencies are first recovered by means of phase correction and Hermitian symmetry property, and then the other nonacquired negative and/or positive spatial frequencies are estimated using the mathematical SFA model. The method is particularly suitable for asymmetrical partial k-space acquisition owing to its ability of overcoming reconstruction limitations due to k-space truncations. The performance of this approach is evaluated using both simulated and real MR brain images, and compared with existing techniques. The results demonstrate that the proposed SFA based on phase correction achieves higher image quality than the initial SFA or the projection-onto-convex sets (POCS) method.

  4. 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.

  5. 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

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

    SciTech Connect

    B. NEWMAN; C. DUFFY; D. HICKMOTT

    2001-04-01

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

  7. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

    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 neigbouring 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 non-zero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.

  9. 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.

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

    PubMed

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

    2015-04-01

    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. PMID:25725953

  11. The force on a singularity in a two-phase layer

    NASA Astrophysics Data System (ADS)

    Aderogba, K.

    T HE FORCE acting on a centre of dilatation in the interior of one of two dissimilar layers of infinite extent but of different thicknesses is determined within the limits of the linear theory of elasticity. A remarkable feature of this force is that it is expressible in terms of the distances of the infinite series of images of the singularity from the interface and the plane boundaries. Owing to the dissimilarity in the elastic parameters and the presence of the plane boundaries, the influence of the force can be more drastic than that predicted by the case of a centre of dilatation in the interior of one of two bonded semi-infinite solids. The solution covers many interesting limiting cases, such as the effect of a thick elastic coating on an elastic half-space. As a pilot study on the effect of close boundaries on the force acting on singularities, a formula is first established for the force acting on an infinitesimal prismatic dislocation loop at an arbitrary site inside a free homogeneous layer.

  12. Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

    SciTech Connect

    Pogorelov, A. A.; Suslov, I. M.

    2007-08-15

    According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.

  13. An Open Source Embedding Code for the Condensed Phase

    NASA Astrophysics Data System (ADS)

    Genova, Alessandro; Ceresoli, Davide; Krishtal, Alisa; Andreussi, Oliviero; Distasio, Robert; Pavanello, Michele

    Work from our group as well as others has shown that for many systems such as molecular aggregates, liquids, and complex layered materials, subsystem Density-Functional Theory (DFT) is capable of immensely reducing the computational cost while providing a better and more intuitive insight into the underlying physics. We developed a massively parallel implementation of Subsystem DFT for the condensed phase into the open-source Quantum ESPRESSO software package. In this talk, we will discuss how we: (1) implemented such a flexible parallel framework aiming at the optimal load balancing; (2) simplified the solution of the electronic structure problem by allowing a fragment specific sampling of the first Brillouin Zone; (3) achieve enormous speedups by solving the electronic structure of each fragment in a unit cell smaller than the supersystem simulation cell, effectively introducing a fragment specific basis set, with no deterioration of the fully periodic simulation. As of March 14, 2016, the code has been released and is available to the public.

  14. Well-posedness and long-time behaviour for a singular phase field system of conserved type

    NASA Astrophysics Data System (ADS)

    Gilardi, Gianni; Rocca, Elisabetta

    2007-08-01

    In this paper, we study the well-posedness of a singular non-linear partial differential equation system and the long-time behaviour of its solutions. Namely, an equation ruling the evolution of the absolute temperature{theta} of the system (recently introduced in BONETTI, E., COLLI, P., FABRIZIO, M. & GILARDI, G. (2006) Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete Contin. Dyn. Syst. Ser. B, 6, 1001-1026 (electronic) and BONETTI, E., COLLI, P., FABRIZIO, M. & GILARDI, G. (2007) Global solution to a singular integrodifferential system related to the entropy balance. Nonlinear Anal., 66, 1949-1979) is coupled with a generalization of the well-known Cahn-Hilliard equation for the order parameter{chi} . In particular, under suitable assumptions on the non-linearities involved, we prove that the elements of the{omega} -limit set (i.e. the cluster points) of the trajectories solve the steady-state system that is naturally associated to the evolution problem.

  15. 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.

  16. The conversion of phase structure of singular beams spreading in uniaxial crystal

    NASA Astrophysics Data System (ADS)

    Sokolenko, B.; Poletaev, D.; Rubass, A.; Volyar, A.

    2016-08-01

    The transformation of the intensity and phase of paraxial optical beams passed uniaxial crystal strictly orthogonal to the optical axis is analysed. Imbedded optical vortex in such case imputes structural disturbance to the phase and intensity distribution after anisotropic media. Considering Left and Right circular polarized components of light, we theoretically and numerically shown the dynamics of phase shaping within the rotating birefringent crystal due to anisotropic diffraction effect. Off-axial vortex experienced tangential shift at the beam component and stimulates appearance of topological pairs in vicinity of beam axis.

  17. 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

  18. Singular Values for Products of Complex Ginibre Matrices with a Source: Hard Edge Limit and Phase Transition

    NASA Astrophysics Data System (ADS)

    Forrester, Peter J.; Liu, Dang-Zheng

    2016-05-01

    The singular values squared of the random matrix product {Y = {Gr G_{r-1}} ldots G1 (G0 + A)}, where each {Gj} is a rectangular standard complex Gaussian matrix while A is non-random, are shown to be a determinantal point process with the correlation kernel given by a double contour integral. When all but finitely many eigenvalues of A* A are equal to bN, the kernel is shown to admit a well-defined hard edge scaling, in which case a critical value is established and a phase transition phenomenon is observed. More specifically, the limiting kernel in the subcritical regime of {0 < b < 1} is independent of b, and is in fact the same as that known for the case b = 0 due to Kuijlaars and Zhang. The critical regime of b = 1 allows for a double scaling limit by choosing {{b = (1 - τ/√{N})^{-1}}}, and for this the critical kernel and outlier phenomenon are established. In the simplest case r = 0, which is closely related to non-intersecting squared Bessel paths, a distribution corresponding to the finite shifted mean LUE is proven to be the scaling limit in the supercritical regime of {b > 1} with two distinct scaling rates. Similar results also hold true for the random matrix product {Tr T_{r-1} ldots T1 (G0 + A)}, with each {Tj} being a truncated unitary matrix.

  19. 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.

  20. The Hamiltonian property of the flow of singular trajectories

    NASA Astrophysics Data System (ADS)

    Lokutsievskiy, L. V.

    2014-03-01

    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.

  1. The singular gas-phase structure of 1-aminocyclopropanecarboxylic acid (Ac3c).

    PubMed

    Jiménez, Ana I; Vaquero, Vanesa; Cabezas, Carlos; López, Juan C; Cativiela, Carlos; Alonso, José L

    2011-07-13

    The natural nonproteinogenic α-amino acid 1-aminocyclopropanecarboxylic acid (Ac(3)c) has been vaporized by laser ablation and studied in the gas phase by molecular-beam Fourier transform microwave spectroscopy. Comparison of the experimental rotational and (14)N nuclear quadrupole coupling constants with the values predicted ab initio for these parameters has allowed the unambiguous identification of three Ac(3)c conformers differing in the hydrogen bonding pattern. Two of them resemble those characterized before for the coded aliphatic α-amino acids. Remarkably, a third conformer predicted to be energetically accessible for all of these amino acids but never observed (the so-called "missing conformer") has been found for Ac(3)c, close in energy to the global minimum. This is the first time that such a conformer, stabilized by an N-H···O(H) hydrogen bond, is detected in the rotational spectrum of a gaseous α-amino acid with a nonpolar side chain. The conjugative interaction established between the cyclopropane ring and the adjacent carbonyl group seems to be responsible for the unique conformational properties exhibited by Ac(3)c.

  2. Matter and singularities

    NASA Astrophysics Data System (ADS)

    Morrison, David R.; Taylor, Washington

    2012-01-01

    We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU( N). We give a detailed local description of the geometry associated with several types of singularities and the associated matter representations. We also construct global F-theory models for 6D and 4D theories containing these matter representations. The codimension two singularities encountered include examples where the apparent Kodaira singularity type does not need to be completely resolved to produce a smooth Calabi-Yau, examples with rank enhancement by more than one, and examples where the 7-brane configuration is singular. We identify novel phase transitions, in some of which the gauge group remains fixed but the singularity type and associated matter content change along a continuous family of theories. Global analysis of 6D theories on ℙ2 with 7-branes wrapped on curves of small degree reproduces the range of 6D supergravity theories identified through anomaly cancellation and other consistency conditions. Analogous 4D models are constructed through global F-theory compactifications on ℙ3, and have a similar pattern of SU( N) matter content. This leads to a constraint on the matter content of a limited class of 4D supergravity theories containing SU( N) as a local factor of the gauge group.

  3. [Novel imidazolium-embedded amine stationary phase: preparation and its performance for hydrophilic interaction chromatography].

    PubMed

    Liu, Shijia; Qiao, Xiaoqiang; Yang, Yanjun; Yan, Hongyuan

    2014-10-01

    The development of the novel and highly efficient hydrophilic interaction chromatography stationary phase is important for the separation of polar compounds. In the present work, a novel imidazolium-embedded amine stationary phase (Sil-IEASP) was designed and prepared for hydrophilic interaction chromatographic separation. The prepared material was respectively characterized by Fourier transform infrared spectrometer, thermogravimetric analyzer and organic element analyzer. The results indicated that the novel stationary phase was successfully prepared with the present used method. The effects of the contents of water, salt concentration and pH on the retention of nucleosides and nucleic acid bases were respectively investigated, and the results indicated that Sil-IEASP is of hydrophilic interaction chromatographic nature. Furthermore, no obvious effect of buffer pH and salt concentration on the retention of these compounds were found. The developed material was further used for the separation of uracil, adenine, cytosine, uridine and positional isomers (o-terphenyl, m-terphenyl and triphenylene). Compared with the commonly used amino stationary phase, improved separation efficiency was achieved with the developed material, indicating the potential merit of the developed stationary phase for highly efficient hydrophilic interaction chromatographic separation. We anticipate that the novel stationary phase is promising for the hydrophilic interaction chromatography of polar compounds in the future research. PMID:25739268

  4. Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity

    PubMed Central

    Hwang, Minki; Song, Jun-Seop; Lee, Young-Seon; Li, Changyong; Shim, Eun Bo; Pak, Hui-Nam

    2016-01-01

    Background Although rotors have been considered among the drivers of atrial fibrillation (AF), the rotor definition is inconsistent. We evaluated the nature of rotors in 2D and 3D in- silico models of persistent AF (PeAF) by analyzing phase singularity (PS), dominant frequency (DF), Shannon entropy (ShEn), and complex fractionated atrial electrogram cycle length (CFAE-CL) and their ablation. Methods Mother rotor was spatiotemporally defined as stationary reentries with a meandering tip remaining within half the wavelength and lasting longer than 5 s. We generated 2D- and 3D-maps of the PS, DF, ShEn, and CFAE-CL during AF. The spatial correlations and ablation outcomes targeting each parameter were analyzed. Results 1. In the 2D PeAF model, we observed a mother rotor that matched relatively well with DF (>9 Hz, 71.0%, p<0.001), ShEn (upper 2.5%, 33.2%, p<0.001), and CFAE-CL (lower 2.5%, 23.7%, p<0.001). 2. The 3D-PeAF model also showed mother rotors that had spatial correlations with DF (>5.5 Hz, 39.7%, p<0.001), ShEn (upper 8.5%, 15.1%, p <0.001), and CFAE (lower 8.5%, 8.0%, p = 0.002). 3. In both the 2D and 3D models, virtual ablation targeting the upper 5% of the DF terminated AF within 20 s, but not the ablations based on long-lasting PS, high ShEn area, or lower CFAE-CL area. Conclusion Mother rotors were observed in both 2D and 3D human AF models. Rotor locations were well represented by DF, and their virtual ablation altered wave dynamics and terminated AF. PMID:26909492

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

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

    PubMed

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

    2015-02-14

    Nanostructured, responsive hydrogels formed due to electrostatic interactions have promise for applications such as drug delivery and tissue mimics. These physically cross-linked hydrogels are composed of an aqueous solution of oppositely charged triblocks with charged end-blocks and neutral, hydrophilic mid-blocks. Due to their electrostatic interactions, the end-blocks microphase separate and form physical cross-links that are bridged by the mid-blocks. The structure of this system was determined using a new, efficient embedded fluctuation (EF) model in conjunction with self-consistent field theory. The calculations using the EF model were validated against unapproximated field-theoretic simulations with complex Langevin sampling and were found consistent with small angle X-ray scattering (SAXS) measurements on an experimental system. Using both the EF model and SAXS, phase diagrams were generated as a function of end-block fraction and polymer concentration. Several structures were observed including a body-centered cubic sphere phase, a hexagonally packed cylinder phase, and a lamellar phase. Finally, the EF model was used to explore how parameters that directly relate to polymer chemistry can be tuned to modify the resulting phase diagram, which is of practical interest for the development of new hydrogels. PMID:25567551

  7. Phase transitions in KNO3 embedded in MCM-41 films with regular nanopores

    NASA Astrophysics Data System (ADS)

    Baryshnikov, S. V.; Charnaya, E. V.; Milinskiy, A. Yu.; Patrushev, Yu. V.

    2013-12-01

    This paper reports on a comparative study of phase transitions in nanocomposites made up of KNO3 embedded in 10-μm-thick MCM-41 films with unidirectional pores 4.0 nm in size on an aluminum substrate and of nanocomposites prepared in the form of potassium-nitrate-filled pressed MCM-41 powders with 3.7-nm pores. The temperature dependences of linear permittivity and the amplitude of third harmonic generation have been measured under heating and cooling. The structural transition from phase II to phase I shifts under heating relative to that occurring in bulk KNO3 toward lower temperatures for potassium nitrate in the film and toward higher temperatures for the pressed MCM-41-based nanocomposite. A significant difference has been observed also within the region of existence of ferroelectric phase III. The data obtained suggest that the shifts of phase transition temperatures observed in the conditions of nanoconfinement are influenced markedly not only by pore size and geometry but also by other factors.

  8. Relativistic solitary waves with phase modulation embedded in long laser pulses in plasmas

    SciTech Connect

    Sanchez-Arriaga, G.; Siminos, E.; Lefebvre, E.

    2011-08-15

    We investigate the existence of nonlinear phase-modulated relativistic solitary waves embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. These states are exact nonlinear solutions of the 1-dimensional Maxwell-fluid model for a cold plasma composed of electrons and ions. The solitary wave, which consists of an electromagnetic wave trapped in a self-generated Langmuir wave, presents a phase modulation when the group velocity V and the phase velocity V{sub ph} of the long circularly polarized electromagnetic wave do not match the condition VV{sub ph} = c{sup 2}. The main properties of the waves as a function of their group velocities, wavevectors, and frequencies are studied, as well as bifurcations of the dynamical system that describes the waves when the parameter controlling the phase modulation changes from zero to a finite value. Such a transition is illustrated in the limit of small amplitude waves where an analytical solution for a grey solitary wave exists. The solutions are interpreted as the stationary state after the collision of a long laser pulse with an isolated solitary wave.

  9. 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

  10. Identification of Impact Damage in Composite Laminates through Integrated Pulsed Phase Thermography and Embedded Thermal Sensors

    NASA Astrophysics Data System (ADS)

    Pawar, Sachin Sampatrao

    This dissertation develops a methodology to identify impact damage in aerospace composite laminates using integrated pulsed phase thermography and fiber Bragg grating (FBG) sensors. Initially, a two-dimensional woven, carbon fiber epoxy laminate is used to calibrate the defect depth with blind frequency for the particular material system using pulsed phase thermography (PPT). The calibration specimen contains simulated defects in the form of polymer foam inclusions. The calibrated depth vs. blind frequency relation is then applied to specimens with barely visible impact damage due to low velocity impacts. The results demonstrate that the use of the polymer insert simulated defects, in contrast to drilled holes or inserts with higher thermal contrast, provides thermal phase shifts similar to that observed in the impacted specimens. Despite the differences between the simulated and impact damage (e.g. the irregular boundaries and thin nature of the delaminations), the minimum depth of delamination from the impacted surface and the extent of damage on the rear surface of the specimen calculated from the PPT images are shown to correspond well with those of visual observations. The next group of laminated composite specimens are fabricated with embedded FBG sensors to test the ability of the combined inspection method using pulsed phase thermography and FBG sensors to identify impact damage severity. Initially three sets of specimens containing a single FBG sensor at the mid-plane, along with data from previous studies, are used to optimize the distance of low velocity impact damage from the FBG sensor and also to optimize the FBG interrogator data acquisition rate. The results from these specimens show a wide scatter in the FBG sensor temperature measurements during cooling. Also, due to its low conductivity, specimen took long time to cool, increasing the inspection time. Therefore for the final specimen the FBG sensor data acquisition is performed in the heating

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

    PubMed

    Kim, Se-Jin; Lim, Young-Cheol

    2014-01-01

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

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

    PubMed Central

    Kim, Se-Jin; Lim, Young-Cheol

    2014-01-01

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

  13. 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. PMID:25133241

  14. 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.

  15. Solar thermal charging properties of graphene oxide embedded myristic acid composites phase change material

    NASA Astrophysics Data System (ADS)

    Yadav, Apurv; Barman, Bidyut; Kumar, Vivek; Kardam, Abhishek; Narayanan, S. Shankara; Verma, Abhishek; Madhwal, Devinder; Shukla, Prashant; Jain, V. K.

    2016-05-01

    The present paper reports the heat transfer characteristics of graphene oxide (GO) embedded myristic acid based phase change material (GO-PCM) composites. By varying concentrations of GO (0.1-0.5 wt%), different GO-PCM composites were preapred. Two different experimental setups were used for investigating the heat transfer characteristics of the prepared GO-PCM composites during the melting and solidification processes: (i) conventional heating and (ii) solar illumination. The experimental observations indicated a higher heat transfer rate in the GO-PCM composites as compared to pristine PCM for both experimental setups. From the experimental results of conventional heating setup, it was observed that the melting and solidification rate for GO-PCM composites, at 0.5 wt% of GO, increased by 48% and 70%, respectively in comparison to pristine PCM. The experimental results using solar illumination setup demonstrated an ultrafast heating rate for GO-PCM composites than the conventional heating based approach.

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

    NASA Astrophysics Data System (ADS)

    Tamura, Yoshinobu; Yamada, Shigeru

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

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

    SciTech Connect

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

    2010-08-15

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

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

    SciTech Connect

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

    2013-10-15

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

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

    PubMed

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

    2015-11-01

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

  20. Magnetism and electronic phase transitions in monoclinic transition metal dichalcogenides with transition metal atoms embedded

    NASA Astrophysics Data System (ADS)

    Lin, Xianqing; Ni, Jun

    2016-08-01

    First-principles calculations have been performed to study the energetic, electronic, and magnetic properties of substitutional 3d transition metal dopants in monoclinic transition metal dichalcogenides (TMDs) as topological insulators ( 1 T ' - MX 2 with M = (Mo, W) and X = (S, Se)). We find various favorite features in these doped systems to introduce magnetism and other desirable electronic properties: (i) The Mn embedded monoclinic TMDs are magnetic, and the doped 1 T ' - MoS 2 still maintains the semiconducting character with high concentration of Mn, while an electronic phase transition occurs in other Mn doped monoclinic TMDs with an increasing concentration of Mn. Two Mn dopants prefer the ferromagnetic coupling except for substitution of the nearest Mo atoms in 1 T ' - MoS 2 , and the strength of exchange interaction shows anisotropic behavior with dopants along one Mo zigzag chain having much stronger coupling. (ii) The substitutional V is a promising hole dopant, which causes little change to the energy dispersion around the conduction and valence band edges in most systems. In contrast, parts of the conduction band drop for the electron dopants Co and Ni due to the large structural distortion. Moreover, closing band gaps of the host materials are observed with increasing carrier concentration. (iii) Single Fe dopant has a magnetic moment, but it also dopes electrons. When two Fe dopants have a small distance, the systems turn into nonmagnetic semiconductors. (iv) The formation energies of all dopants are much lower than those in hexagonal TMDs and are all negative in certain growth conditions, suggesting possible realization of the predicted magnetism, electronic phase transitions as well as carrier doping in 1 T ' - MX 2 based topological devices.

  1. Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film

    NASA Astrophysics Data System (ADS)

    Azzam, R. M. A.

    2006-04-01

    Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission Δr,Δt are found to be identical, and the associated ellipsometric parameters ψr,ψt are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the p and s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film thickness. In the limit of zero film thickness (i.e., for an ultrathin embedded layer), the reflection phase shifts are also quarter-wave independent of polarization (p or s) or angle of incidence (except at grazing incidence). Finally, variable-angle FTIR ellipsometry is shown to be a sensitive technique for measuring the thickness of thin uniform air gaps between transparent bulk media.

  2. Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film.

    PubMed

    Azzam, R M A

    2006-04-01

    Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission deltar, deltat are found to be identical, and the associated ellipsometric parameters psir, psit are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the p and s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film thickness. In the limit of zero film thickness (i.e., for an ultrathin embedded layer), the reflection phase shifts are also quarter-wave independent of polarization (p or s) or angle of incidence (except at grazing incidence). Finally, variable-angle FTIR ellipsometry is shown to be a sensitive technique for measuring the thickness of thin uniform air gaps between transparent bulk media.

  3. 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.

  4. Understanding Singular Vectors

    ERIC Educational Resources Information Center

    James, David; Botteron, Cynthia

    2013-01-01

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

  5. Imidazolium-embedded iodoacetamide-functionalized silica-based stationary phase for hydrophilic interaction/reversed-phase mixed-mode chromatography.

    PubMed

    Wang, Huizhen; Zhang, Lu; Ma, Teng; Zhang, Liyuan; Qiao, Xiaoqiang

    2016-09-01

    A novel imidazolium-embedded iodoacetamide-functionalized silica-based stationary phase has been prepared by surface radical chain-transfer polymerization. The stationary phase was characterized by Fourier transform infrared spectrometry, thermogravimetric analysis, and element analysis. Fast and efficient separations of polar analytes, such as nucleosides and nucleic acid bases, water-soluble vitamins and saponins, were well achieved in hydrophilic interaction chromatography mode. Additionally, a mixed mode of hydrophilic interaction and reversed-phase could be also obtained in the analysis of polar and nonpolar compounds, including weak acidic phenols, basic anilines and positional isomers, with high resolution and molecular-planarity selectivity, outperforming the commercially available amino column. Moreover, simultaneous separation of polar and nonpolar compounds was also achieved. In conclusion, the multimodal retention capabilities of the imidazolium-embedded iodoacetamide-functionalized silica-based column could offer a wide range of retention behavior and flexible selectivity toward hydrophilic and hydrophobic compounds. PMID:27470879

  6. Einstein equation at singularities

    NASA Astrophysics Data System (ADS)

    Stoica, Ovidiu-Cristinel

    2014-02-01

    Einstein's equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein's equation and the metric tensor).

  7. 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. PMID:26988475

  8. 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.

  9. Phase decomposition of AuFe alloy nanoparticles embedded in silica matrix under swift heavy ion irradiation

    NASA Astrophysics Data System (ADS)

    Pannu, Compesh; Bala, Manju; Singh, U. B.; Srivastava, S. K.; Kabiraj, D.; Avasthi, D. K.

    2016-07-01

    AuFe alloy nanoparticles embedded in silica matrix are synthesized using atom beam sputtering technique and subsequently irradiated with 100 MeV Au ions at various fluences ranging from 1 × 1013 to 6 × 1013 ions/cm2. The X-ray diffraction, absorption spectroscopy, X-ray photo electron spectroscopy and transmission electron microscopy results show that swift heavy ion irradiation leads to decomposition of AuFe alloy nanoparticles from surface region and subsequent reprecipitation of Au and Fe nanoparticles occur. The process of phase decomposition and reprecipitation of individual element nanoparticles is explained on the basis of inelastic thermal spike model.

  10. 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.

  11. Cosmological applications of singular hypersurfaces in general relativity

    NASA Astrophysics Data System (ADS)

    Laguna-Castillo, Pablo

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

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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…

  17. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

    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.

  19. Compact submanifolds supporting singular interactions

    SciTech Connect

    Kaynak, Burak Tevfik Teoman Turgut, O.

    2013-12-15

    A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound-state is perhaps the most important aspect. Such systems can be introduced as quadratic forms and generically they do not require renormalization. Yet an alternative path through the resolvent is also beneficial to study various properties. In the present work, we address these issues for compact surfaces embedded in a class of ambient manifolds. We discover that there is an exact bound state solution written in terms of the heat kernel of the ambient manifold for a range of coupling strengths. Moreover, we develop techniques to estimate bounds on the ground state energy when several surfaces, each of which admits a bound state solution, coexist. -- Highlights: •Schrödinger operator with singular interactions supported on compact submanifolds. •Exact bound-state solution in terms of the heat kernel of the ambient manifold. •Generalization of the variational approach to a collection of submanifolds. •Existence of a lower bound for a unique ground state energy.

  20. 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

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

    NASA Astrophysics Data System (ADS)

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

    2014-02-01

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

  2. 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.

  3. Singularities and Quantum Gravity

    NASA Astrophysics Data System (ADS)

    Bojowald, Martin

    2007-06-01

    Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria for non-singular behavior are often unclear or controversial. Often, only special types of singularities such as the curvature singularities found in isotropic cosmological models are discussed and it is far from clear what this implies for the very general singularities that arise according to the singularity theorems of general relativity. In these lectures we present an overview of the current status of singularities in classical and quantum gravity, starting with a review and interpretation of the classical singularity theorems. This suggests possible routes for quantum gravity to evade the devastating conclusion of the theorems by different means, including modified dynamics or modified geometrical structures underlying quantum gravity. The latter is most clearly present in canonical quantizations which are discussed in more detail. Finally, the results are used to propose a general scheme of singularity removal, quantum hyperbolicity, to show cases where it is realized and to derive intuitive semiclassical pictures of cosmological bounces.

  4. 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.

  5. Wave Geometry: a Plurality of Singularities

    NASA Astrophysics Data System (ADS)

    Berry, M. V.

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

  6. 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.

  7. Singular finite element methods

    NASA Technical Reports Server (NTRS)

    Fix, George J.

    1987-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

    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.

  9. 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.

  10. A well-based reverse-phase protein array of formalin-fixed paraffin-embedded tissue.

    PubMed

    Chung, Joon-Yong; Hewitt, Stephen M

    2015-01-01

    Biomarkers from tissue-based proteomic studies directly contribute to defining disease states as well as promise to improve early detection or provide for further targeted therapeutics. In the clinical setting, tissue samples are preserved as formalin-fixed paraffin-embedded (FFPE) tissue blocks for histological examination. However, proteomic analysis of FFPE tissue is complicated due to the high level of covalently cross-linked proteins arising from formalin fixation. To address these challenges, we developed well-based reverse-phase protein array (RPPA). This approach is a robust protein isolation methodology (29.44 ± 7.8 μg per 1 mm(3) of FFPE tissue) paired with a novel on electrochemiluminescence detection system. Protein samples derived from FFPE tissue by means of laser capture dissection, with as few as 500 shots, demonstrate measurable signal differences for different proteins. The lysates coated to the array plate, dried up and vacuum-sealed, remain stable up to 2 months at room temperature. This methodology is directly applicable to FFPE tissue and presents the direct opportunity of addressing hypothesis within clinical trials and well-annotated clinical tissue repositories.

  11. A well-based reverse-phase protein array of formalin-fixed paraffin-embedded tissue.

    PubMed

    Chung, Joon-Yong; Hewitt, Stephen M

    2015-01-01

    Biomarkers from tissue-based proteomic studies directly contribute to defining disease states as well as promise to improve early detection or provide for further targeted therapeutics. In the clinical setting, tissue samples are preserved as formalin-fixed paraffin-embedded (FFPE) tissue blocks for histological examination. However, proteomic analysis of FFPE tissue is complicated due to the high level of covalently cross-linked proteins arising from formalin fixation. To address these challenges, we developed well-based reverse-phase protein array (RPPA). This approach is a robust protein isolation methodology (29.44 ± 7.8 μg per 1 mm(3) of FFPE tissue) paired with a novel on electrochemiluminescence detection system. Protein samples derived from FFPE tissue by means of laser capture dissection, with as few as 500 shots, demonstrate measurable signal differences for different proteins. The lysates coated to the array plate, dried up and vacuum-sealed, remain stable up to 2 months at room temperature. This methodology is directly applicable to FFPE tissue and presents the direct opportunity of addressing hypothesis within clinical trials and well-annotated clinical tissue repositories. PMID:26043998

  12. Box graphs and singular fibers

    NASA Astrophysics Data System (ADS)

    Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schafer-Nameki, Sakura

    2014-05-01

    We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as "flopping" of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6, E7 and E 8.

  13. 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.

  14. 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.

  15. Spacetime Singularities: Recent Developments

    NASA Astrophysics Data System (ADS)

    Uggla, Claes

    2013-03-01

    Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second deals with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case, focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topics in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.

  16. 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.

  17. Dimensional Mutation and Spacelike Singularities

    SciTech Connect

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

    2005-10-28

    I argue that critical string theory on a Riemann surface of genus h >> 1 crosses over, when the surface approaches the string scale in size, to a background of supercritical string theory with effective central charge as large as 2h. Concrete evidence for this proposal is provided by the high energy density of states (realized on the Riemann surface side by strings wrapping nontrivial elements of the fundamental group) and by a linear sigma model which at large h approximates the time evolution through the initial transition. This suggests that cosmological singularities arising in negatively curved FRW backgrounds may be replaced by a phase of supercritical string theory.

  18. Singular Mueller matrices.

    PubMed

    Gil, José J; Ossikovski, Razvigor; José, Ignacio San

    2016-04-01

    Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance or because its associated canonical depolarizer has the property of fully randomizing the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed, and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, which are of potential usefulness to experimentalists dealing with such media. PMID:27140769

  19. Singular Mueller matrices.

    PubMed

    Gil, José J; Ossikovski, Razvigor; José, Ignacio San

    2016-04-01

    Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance or because its associated canonical depolarizer has the property of fully randomizing the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed, and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, which are of potential usefulness to experimentalists dealing with such media.

  20. Identifying conical singularities

    SciTech Connect

    Oliveira-Neto, G. |

    1996-09-01

    A method based upon the concept of holonomy of a metric space{endash}time ({ital M},{ital g}), in order to identify the presence of conical singularities in {ital M} is proposed. The validity and usefulness of this so-called holonomy method is proven by applying it to a set of four-dimensional space{endash}times and one three-dimensional space{endash}time. The holonomy method predictions are confirmed by the comparison with the predictions obtained after coordinate transformations which take the metrics {ital g}, to a new basis where the global properties of conical singularities are explicitly seen. {copyright} {ital 1996 American Institute of Physics.}

  1. 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.

  2. 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.

  3. Neural Excitability and Singular Bifurcations.

    PubMed

    De Maesschalck, Peter; Wechselberger, Martin

    2015-12-01

    We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov-Hopf bifurcation. In both cases, canards play an important role in the understanding of the unfolding of these singular bifurcation structures. We also explain the transition between the two excitability types and highlight all bifurcations involved, thus providing a complete analysis of excitability based on geometric singular perturbation theory.

  4. Cosmic Initial Singularities in a Single Repeating Universe as Opposed to Their Behavior in a Multiverse

    NASA Astrophysics Data System (ADS)

    Beckwith, Andrew

    When initial radius of the universe in four dimensions and there is only ONE repeating universe then the initial radius goes to zero or gets very close to zero if Stoica actually derived Einstein equations are used in a formalism which remove in four dimensions the big bang singularity pathology. So then the reason for Planck length no longer holds. This assumes a repeating single universe. We present a given entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto , and show that there are consequences due to initial entanged entropy for a time dependent horizon radius in cosmology, with (flat space conditions) horizon radius as equal to conformal time Even if the 3 dimensional spatial length goes to zero. This construction preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if in four dimensions we have the initial radii going to zero We also find that in the case of a multiverse, that such considerations will not hold and that cosmic singularities have a different characteristic in the multiverse setting than in the single universe repeated over and over again. i.e. using an argument borrowed and modified from Kauffman, the multiverse will not mandate ‘perfect’ singularities. The existence of a multiverse may allow for non zero singularities in lieu with the Kauffman argument cited at the end of the document, plus the lower pre big bang temperatures which may allow for the survivial of gravitons just before the onset of the cosmological expansion phase, if a multiverse exists embedding our present universe

  5. Singular behavior of jet substructure observables

    DOE PAGESBeta

    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. 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.

  7. 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.

  8. 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. PMID:27135808

  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. 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

  11. 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.

  12. Nonlinear singularly perturbed optimal control problems with singular arcs

    NASA Technical Reports Server (NTRS)

    Ardema, M. D.

    1977-01-01

    A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.

  13. Isolated singularities of graphs in warped products and Monge-Ampère equations

    NASA Astrophysics Data System (ADS)

    Gálvez, José A.; Jiménez, Asun; Mira, Pablo

    2016-02-01

    We study graphs of positive extrinsic curvature with a non-removable isolated singularity in 3-dimensional warped product spaces, and describe their behavior at the singularity in several natural situations. We use Monge-Ampère equations to give a classification of the surfaces in 3-dimensional space forms which are embedded around a non-removable isolated singularity and have a prescribed, real analytic, positive extrinsic curvature function at every point. Specifically, we prove that this space is in one-to-one correspondence with the space of regular, analytic, strictly convex Jordan curves in the 2-dimensional sphere S2.

  14. Holographic signatures of cosmological singularities.

    PubMed

    Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T

    2014-09-19

    To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves N=4 super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.

  15. Singularity Resolution in Quantum Gravity

    NASA Astrophysics Data System (ADS)

    Singh, Parampreet

    2014-03-01

    In recent years, progress in understanding of the quantization of cosmological spacetimes using techniques of loop quantum gravity, has led to important insights on the resolution of singularities. With a rigorous loop quantization of isotropic and anisotropic spacetimes and development of sophisticated numerical techniques, it is now possible to explore in detail the structure of spacetime in the Planck regime and extract new physics of the very early universe. Investigations of quantization of various spacetimes indicates that classical singularities such as the big bang are avoided, and quantum evolution results in a bounce of the scale factor. The resolution of singularities seems to occur without any assumption on the initial state for quantum evolution or the equation of state of matter. In this talk, we will review some of the main developments in this direction and provide an up to date summary of the novel results obtained on the resolution of singularities in various models in loop quantum gravity.

  16. 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.

  17. 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.

  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. 3D structures of liquid-phase GaIn alloy embedded in PDMS with freeze casting.

    PubMed

    Fassler, Andrew; Majidi, Carmel

    2013-11-21

    Liquid phase electronic circuits are created by freeze casting gallium-indium (GaIn) alloys, such as eutectic gallium-indium (EGaIn), and encapsulating these frozen components within an elastomer. These metal alloys are liquid at room temperature, and can be cast using either injection or a vacuum to fill a PDMS mold and placing the mold in a freezer. Once solidified, a GaIn alloy segment can be manipulated, altered, or bonded to other circuit elements. A stretchable circuit can be fabricated by placing frozen components onto an elastomer substrate, which can be either patterned or flat, and sealing with an additional layer of elastomer. Circuits produced in this fashion are soft, stretchable, and can have complex 3D channel geometries. In contrast, current fabrication techniques, including needle injection, mask deposition, and microcontact printing, are limited to 2D planar designs. Additionally, freeze casting fabrication can create closed loops, multi-terminal circuits with branching features, and large area geometries. PMID:24067934

  20. 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.

  1. Feedback control of singular systems with applications to incompressible flows

    NASA Astrophysics Data System (ADS)

    Gandikota, Ramakrishna V.

    2000-10-01

    Singular systems of differential equations, also referred to as differential algebraic equation (DAE) systems, arise as models in a variety of engineering applications. In chemical engineering, they typically arise under the quasi-steady state assumptions of phase, reaction or thermal equilibrium in the modeling of processes with fast mass transfer, reaction or heat transfer. They also arise in incompressible fluid flow systems. The control of singular systems has attracted considerable attention in the last two decades. The majority of the developed methods are on the state feedback control of linear and nonlinear singular systems in continuous-time, and they rely on the derivation of standard state space realizations (i.e. ODE descriptions) that can be used as the basis for the controller design. This thesis addresses (i) the derivation of state space realizations for the output feedback control of linear singular systems in continuous time, (ii) the derivation of state space realizations of singular systems of difference equations, which can be used for the state feedback control of nonlinear discrete time singular systems, (iii) a parallel analysis of the continuous in space and discretized in space incompressible Navier Stokes equations, with emphasis on the derivation of standard PDE and ODE descriptions respectively, and (iv) a case study on the numerical simulation and feedback control of the flow pattern in a lid-driven cavity. The performance of the developed controllers is illustrated via numerical simulation studies.

  2. 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.

  3. Singular values, nematic disclinations, and emergent biaxiality.

    PubMed

    Čopar, Simon; Dennis, Mark R; Kamien, Randall D; Žumer, Slobodan

    2013-05-01

    Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame that can be extracted from the tensorial description of the nematic order vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. The degrees of freedom are unveiled in the form of quasidefects and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase. PMID:23767474

  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. 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%.

  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. 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.

  8. 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.

  9. Singularities of quantum control landscapes

    NASA Astrophysics Data System (ADS)

    Wu, Re-Bing; Long, Ruixing; Dominy, Jason; Ho, Tak-San; Rabitz, Herschel

    2012-07-01

    Quantum control landscape theory was formulated to assess the ease of finding optimal control fields in simulations and in the laboratory. The landscape is the observable as a function of the controls, and a primary goal of the theory is the analysis of landscape features. In what is referred to as the kinematic picture of the landscape, prior work showed that the landscapes are generally free of traps that could halt the search for an optimal control at a suboptimal observable value. The present paper considers the dynamical picture of the landscape, seeking the existence of singular controls, especially of a nonkinematic nature along with an assessment of whether they correspond to traps. We analyze the necessary and sufficient conditions for singular controls to be kinematic or nonkinematic critical solutions and the likelihood of their being encountered while maximizing an observable. An algorithm is introduced to seek singular controls on the landscape in simulations along with an associated Hessian landscape analysis. Simulations are performed for a large number of model finite-level quantum systems, showing that all the numerically identified kinematic and nonkinematic singular critical controls are not traps, in support of the prior empirical observations on the ease of finding high-quality optimal control fields.

  10. 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.

  11. Singular Casimir Elements of the Euler Equation and Equilibrium Points

    NASA Astrophysics Data System (ADS)

    Yoshida, Zensho; Morrison, Philip J.; Dobarro, Fernando

    2013-04-01

    The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of singularities of the Poisson operator defining the Poisson bracket. The kernel of the Poisson operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the Poisson operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the Poisson operator (the "dimension" of the center) changes. The problem is an infinite-dimension generalization of the theory of singular differential equations. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket.

  12. Singular Casimir Elements of the Euler Equation and Equilibrium Points

    NASA Astrophysics Data System (ADS)

    Yoshida, Zensho; Morrison, Philip J.; Dobarro, Fernando

    2014-03-01

    The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of singularities of the Poisson operator defining the Poisson bracket. The kernel of the Poisson operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the Poisson operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the Poisson operator (the "dimension" of the center) changes. The problem is an infinite-dimension generalization of the theory of singular differential equations. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket.

  13. Frozen singularities in M and F theory

    NASA Astrophysics Data System (ADS)

    Tachikawa, Yuji

    2016-06-01

    We revisit the duality between ALE singularities in M-theory and 7-branes on a circle in F-theory. We see that a frozen M-theory singularity maps to a circle compactification involving a rotation of the plane transverse to the 7-brane, showing an interesting correspondence between commuting triples in simply-laced groups and Kodaira's classification of singular elliptic fibrations. Our analysis strongly suggests that the O7+ plane is the only completely frozen F-theory singularity.

  14. Properties of a Two-Sphere Singularity

    NASA Astrophysics Data System (ADS)

    Konkowski, Deborah A.; Helliwell, Thomas M.

    2015-01-01

    Recently Böhmer and Lobo have shown that a metric due to Florides can be extended to reveal a classical singularity that has the form of a two-sphere. Here we discuss and expand on the classical singularity properties and then show the classical singularity is not healed by a quantum analysis.

  15. Some aspects of singular interactions in condensed Fermi systems

    NASA Astrophysics Data System (ADS)

    Stamp, P. C. E.

    1993-02-01

    This article gives a fairly detailed survey of some of the problems raised when the interaction energy f^{σ σ'}_{k k'} between 2 fermionic quasiparticles (in 2 dimensions) is singular when |k-k'|to 0. Before dealing with singular interactions, it is shown how a non-singular f^{σ σ'}_{k k'} leads to a 2-dimensional Fermi liquid theory, which is internally consistent, at least as far as its infrared properties are concerned. The quasiparticle properties are calculated in detail. The question of whether singular interactions arise for the dilute Fermi gas, with short-range repulsive interactions, is investigated perturbatively. One finds a weak singularity in f^{σ σ'}_{k k'}, when the dimensionality D = 2, but it does not destabilize the Fermi liquid. A more sophisticated analysis is then given, to all orders in the interaction, using the Lippman-Schwinger equation as well as a phase shift analysis for a finite box. The conclusion is that any breakdown of Fermi liquid theory must come from non-perturbative effects. An examination is then made of some of the consequences arising if a singular interaction is introduced — the form proposed by Anderson is used as an example. A hierarchy of singular terms arise in all quantities — this is shown for the self-energy, and also the 3 point and 4 point scattering functions. These may be summed in a perfectly consistent manner. Most attention is given to the particle-hole channel, since it appears to lead to results different from those of Anderson. Nevertheless it appears that it is possible to derive a sensible theory starting from a singular effective Hamiltonian — although Fermi Liquid theory breaks down, all fermionic quantities may be calculated consistently. Finally, the effect of a magnetic field (which cuts off the infrared divergences) is investigated, and the de Haas-van Alphen amplitude calculated, for such a singular Fermionic system.

  16. G 2-Monopoles with Singularities (Examples)

    NASA Astrophysics Data System (ADS)

    Oliveira, Goncalo

    2016-08-01

    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.

  17. Cancellation of singularities for synthetic aperture radar

    NASA Astrophysics Data System (ADS)

    Caday, Peter

    2015-01-01

    In a basic model for synthetic aperture radar (SAR) imaging, one wishes to recover a function or distribution f from line integrals over circles whose centers lie on a given curve γ. In this paper, we consider the problem of recovering the singularities (wavefront set) of f given its SAR data, and specifically whether it is possible to choose a singular f whose singularities are hidden from γ, meaning that its SAR data is smooth. We show that f 's singularities can be hidden to leading order if a certain discrete reflection map is the identity, and give examples where this is the case. Finally, numerical experiments illustrate the hiding of singularities.

  18. Naked singularity and a thunderbolt

    NASA Astrophysics Data System (ADS)

    Ishibashi, Akihiro; Hosoya, Akio

    2002-11-01

    We consider the quantum theoretical effects of a sudden change of boundary conditions which mimics the occurrence of naked singularities. For a simple demonstration, we study a massless scalar field in (1+1)-dimensional Minkowski spacetime with a finite spatial interval. We calculate the vacuum expectation value of the energy-momentum tensor and explicitly show that singular wave or thunderbolt appears along the Cauchy horizon. The thunderbolt possibly destroys the Cauchy horizon if its back reaction on the geometry is taken into account, leading to quantum restoration of the global hyperbolicity. The result of the present work may also apply to the situation where a closed string freely oscillating is traveling to a brane and changes itself to an open string pinned down by the ends, satisfying the Dirichlet boundary conditions on the brane.

  19. Shadow of a naked singularity

    NASA Astrophysics Data System (ADS)

    Ortiz, Néstor; Sarbach, Olivier; Zannias, Thomas

    2015-08-01

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

  20. Singular perturbation of absolute stability.

    NASA Technical Reports Server (NTRS)

    Siljak, D. D.

    1972-01-01

    It was previously shown (author, 1969) that the regions of absolute stability in the parameter space can be determined when the parameters appear on the right-hand side of the system equations, i.e., the regular case. Here, the effect on absolute stability of a small parameter attached to higher derivatives in the equations (the singular case) is studied. The Lur'e-Postnikov class of nonlinear systems is considered.

  1. Splash singularity for water waves

    PubMed Central

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

    2012-01-01

    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. PMID:22219372

  2. Initial directional singularity in inflationary models

    NASA Astrophysics Data System (ADS)

    Fernández-Jambrina, L.

    2016-07-01

    In Haro, Amorós, and Pan [Phys. Rev. D 93, 084018 (2016)] a new cosmological model is proposed with no big bang singularity in the past, though past geodesically incomplete. This model starts with an inflationary era, follows with a stiff matter dominated period and evolves to accelerated expansion in an asymptotically de Sitter regime in a realistic fashion. The big bang singularity is replaced by a directional singularity. This singularity cannot be reached by comoving observers, since it would take them an infinite proper time lapse to go back to it. On the contrary, observers with nonzero linear momentum have the singularity at finite proper time in their past, though arbitrarily large. Hence, the time lapse from the initial singularity can be as long as desired, even infinity, depending on the linear momentum of the observer. This conclusion applies to similar inflationary models. Due to the interest of these models, we address here the properties of such singularities.

  3. Dual Vector Spaces and Physical Singularities

    NASA Astrophysics Data System (ADS)

    Rowlands, Peter

    Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

  4. F-theory duals of singular heterotic K3 models

    NASA Astrophysics Data System (ADS)

    Lüdeling, Christoph; Ruehle, Fabian

    2015-01-01

    We study F-theory duals of singular heterotic K3 models that correspond to Abelian toroidal orbifolds T4/ZN . While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type I0* , IV * , II I * , and II * . This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram. The results from the Weierstrass description are then used to restrict the complex structure of the F-theory Calabi-Yau threefold such that the gauge group and the matter spectrum of the heterotic theories are reproduced. We also comment on previous approaches that have been employed to construct the duality and point out the differences and limitations in our case. Our results show explicitly how the various orbifold models are connected and described in F-theory.

  5. Experimental verification of free-space singular boundary conditions in an invisibility cloak

    NASA Astrophysics Data System (ADS)

    Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

    2016-04-01

    A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

  6. Singular inflationary universe from F (R ) gravity

    NASA Astrophysics Data System (ADS)

    Odintsov, S. D.; Oikonomou, V. K.

    2015-12-01

    Unlike crushing singularities, the so-called type IV finite time singularity offers the possibility that the Universe passes smoothly it, without any catastrophic effects. Then the question is if the effects of a type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of F (R ) gravity. As we demonstrate, the effects of a type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a type IV singularity, with the singularity occurring at the end of inflation. Particularly we study a toy model and a singular version of the R2 gravity Hubble rate. As we evince, some of the Hubble flow parameters become singular at the singularity, an effect which indicates that at that point a dynamical instability occurs. This dynamical instability eventually indicates the graceful exit from inflation. We demonstrate that the toy model has an unstable de Sitter point at the singularity, so indeed graceful exit could be triggered. In the case of the singular inflation model, graceful exit proceeds in the standard way. In addition, we investigate how the form of the F (R ) gravity affects the singularity structure of the Hubble flow parameters. In the case of the singular inflation model, we found various scenarios for singular evolution, most of which are compatible with observations, and only one leads to severe instabilities. In addition, in one of these scenarios, the presence of the type IV singularity slightly modifies the spectral index of primordial curvature perturbations. We also compare the ordinary Starobinsky with the singular inflation model, and we point out the qualitative and quantitative differences. Finally, we study the late-time dynamics of the toy model and of the singular inflation model and we demonstrate that the unification of early and late-time acceleration can be achieved

  7. The complex structured singular value

    NASA Technical Reports Server (NTRS)

    Packard, A.; Doyle, J.

    1993-01-01

    A tutorial introduction to the complex structured singular value (mu) is presented, with an emphasis on the mathematical aspects of mu. The mu-based methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared, and a simple synthesis problem is studied. Uncertain systems are represented using linear fractional transformations which naturally unify the frequency-domain and state space methods.

  8. Wentzel-Bardeen singularity in coupled Luttinger liquids: Transport properties

    SciTech Connect

    Martin, T.

    1994-08-26

    The recent progress on 1 D interacting electrons systems and their applications to study the transport properties of quasi one dimensional wires is reviewed. We focus on strongly correlated elections coupled to low energy acoustic phonons in one dimension. The exponents of various response functions are calculated, and their striking sensitivity to the Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons the equivalent of a phase diagram is established. By increasing the filling factor towards half filling the WB singularity is approached. This in turn suppresses antiferromagnetic fluctuations and drives the system towards the superconducting regime, via a new intermediate (metallic) phase. The implications of this phenomenon on the transport properties of an ideal wire as well as the properties of a wire with weak or strong scattering are analyzed in a perturbative renormalization group calculation. This allows to recover the three regimes predicted from the divergence criteria of the response functions.

  9. String spectra near some null cosmological singularities

    SciTech Connect

    Madhu, Kallingalthodi; Narayan, K.

    2009-06-15

    We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyze string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near-singularity string spectrum, (time-dependent) oscillator masses, and wave functions. We find that for low-lying string modes (finite oscillation number), the classical near-singularity string mode functions are nondivergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultrahigh oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.

  10. 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.

  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. Precursory singularities in spherical gravitational collapse

    NASA Astrophysics Data System (ADS)

    Lake, Kayll

    1992-05-01

    General conditions are developed for the formation of naked precursory ('shell-focusing') singularities in spherical gravitational collapse. These singularities owe their nakedness to the fact that the gravitational potential fails to be single valued prior to the onset of a true gravitational singularity. It is argued that they do not violate the spirit of cosmic censorship. Rather, they may well be an essentially generic feature of relativistic gravitational collapse.

  13. 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.

  14. 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.

  15. 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.

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

    PubMed

    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.

  17. 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.

  18. 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.

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

    PubMed

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

    2014-01-01

    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. PMID:24784778

  20. 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.

  1. Entanglement in a second-order quantum phase transition

    SciTech Connect

    Vidal, Julien; Palacios, Guillaume; Mosseri, Remy

    2004-02-01

    We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point {lambda}{sub c} in the thermodynamical limit. We also show that there exists a value {lambda}{sub 0}{>=}{lambda}{sub c} above which the ground state is not spin squeezed despite a nonvanishing concurrence.

  2. The web of D-branes at singularities in compact Calabi-Yau manifolds

    NASA Astrophysics Data System (ADS)

    Cicoli, Michele; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto

    2013-05-01

    We present novel continuous supersymmetric transitions which take place among different chiral configurations of D3/D7 branes at singularities in the context of type IIB Calabi-Yau compactifications. We find that distinct local models which admit a consistent global embedding can actually be connected to each other along flat directions by means of transitions of bulk-to-flavour branes. This has interesting interpretations in terms of brane recombination/splitting and brane/anti-brane creation/annihilation. These transitions give rise to a large web of quiver gauge theories parametrised by splitting/recombination modes of bulk branes which are not present in the non-compact case. We illustrate our results in concrete global embeddings of chiral models at a dP0 singularity.

  3. 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. PMID:25187409

  4. 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.

  5. Ramond singular vectors and Jack superpolynomials

    NASA Astrophysics Data System (ADS)

    Alarie-Vézina, Ludovic; Desrosiers, Patrick; Mathieu, Pierre

    2014-01-01

    The explicit formula for the superconformal singular vectors in the Neveu-Schwarz sector has been obtained recently, via its symmetric polynomial representation, as a sum of Jack superpolynomials. Here we present the analogous, but slightly more complicated, closed-form expression for the Ramond singular vectors.

  6. Varying constant cosmologies and cosmic singularities

    NASA Astrophysics Data System (ADS)

    Dabrowski, Mariusz P.; Marosek, Konrad

    2013-02-01

    We review standard and non-standard cosmological singularities paying special attention onto those which are of a weak type and do not necessarily exhibit geodesic incompletness. Then, we discuss how these singularities can be weakened, strengthened, or avoided due to the time-variation of the physical constants such as the speed of light c and the gravitational constant G.

  7. Quadrature rules for weakly singular, strongly singular, and hypersingular integrals in boundary integral equation methods

    NASA Astrophysics Data System (ADS)

    Tsalamengas, John L.

    2015-12-01

    We present n-point Gauss-Gegenbauer quadrature rules for weakly singular, strongly singular, and hypersingular integrals that arise in integral equation formulations of potential problems in domains with edges and corners. The rules are tailored to weight functions with algebraic endpoint singularities related to the geometrical singularities of the domain. Each rule has two different expressions involving Legendre functions and hypergeometric functions, respectively. Numerical examples amply demonstrate the accuracy and stability of the proposed algorithms. Application to the solution of a singular integral equation is exemplified.

  8. 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.

  9. Singular perturbations and the sounding rocket problem

    NASA Technical Reports Server (NTRS)

    Ardema, M. D.

    1979-01-01

    In this paper, Goddard's problem of maximizing the final altitude of a sounding rocket (a singular problem of optimal control) is analyzed using singular perturbation methods. The problem is first cast in singular perturbation form and then solved to zero order by adding boundary-layer corrections to the reduced solution. For a quadratic drag law, a closed-form solution is obtained, although consideration of a numerical example indicates that this solution is not useful for practical sounding rockets. However, use of state variable transformations allows a very accurate numerical approximation to be constructed. It is concluded that application of singular perturbation methods to the well-known sounding rocket problem indicates that these methods may have utility in dealing with singular problems of optimal control.

  10. Topological regularizations of the triple collision singularity in the 3-vortex problem

    NASA Astrophysics Data System (ADS)

    Hiraoka, Yasuaki

    2008-02-01

    The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k_1^{-1}+k_2^{-1}+k_3^{-1}=0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k1 = k2, the triple collision singularity is topologically regularizable. (ii) For 0 < |k1 - k2| < epsilon with a sufficiently small epsilon, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191-227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92-9), topological regularizations of the triple collision singularity are studied in detail.

  11. Gevrey properties of real planar singularly perturbed systems

    NASA Astrophysics Data System (ADS)

    De Maesschalck, P.

    By applying geometric techniques to real analytic singularly perturbed vector fields on the plane, we develop a way to give a bound on the Gevrey type of the Taylor development of canard manifolds at degenerate planar turning points. By blowing up the phase space at the turning point, we find asymptotic estimates even when such expansions w.r.t. traditional phase space variables do not exist. The asymptotic estimates are then used to give a sufficient and necessary condition on the existence of (local) canard solutions.

  12. Energy circulations in singular beams diffracted through an isosceles right triangular aperture

    NASA Astrophysics Data System (ADS)

    Bahl, Monika; Senthilkumaran, P.

    2015-07-01

    The Poynting vector in a singular optical field follows a helical path. Hence, it is the presence of a phase singularity that provides the circulating energy flow component to an optical field. These circulations in turn are responsible for the orbital angular momentum of light. This field when diffracted through an isosceles right triangular aperture generates straight line fringes in the far-field diffraction. We have addressed the modifications that happen to the energy circulations and the orbital angular momentum of light due to diffraction. Transverse components of the energy circulations in the diffracted field are studied by the Helmholtz-Hodge decomposition method. Interference experiments are presented to reveal the presence of phase singularities in the diffraction. This paper presents a complete analysis of the phase, phase gradient, and the intensity distributions in the diffraction pattern.

  13. 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

  14. 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.

  15. 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.

  16. On the Impossibility of Finite-Time Splash Singularities for Vortex Sheets

    NASA Astrophysics Data System (ADS)

    Coutand, Daniel; Shkoller, Steve

    2016-08-01

    In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. By means of elementary arguments, we prove that such a singularity cannot occur in finite time for vortex sheet evolution, that is for the two-phase incompressible Euler equations. We prove this by contradiction; we assume that a splash singularity does indeed occur in finite time. Based on this assumption, we find precise blow-up rates for the components of the velocity gradient which, in turn, allow us to characterize the geometry of the evolving interface just prior to self-intersection. The constraints on the geometry then lead to an impossible outcome, showing that our assumption of a finite-time splash singularity was false.

  17. Generalizations of the abstract boundary singularity theorem

    NASA Astrophysics Data System (ADS)

    Whale, Ben E.; Ashley, Michael J. S. L.; Scott, Susan M.

    2015-07-01

    The abstract boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of abstract boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from C1 curves to locally Lipschitz curves.

  18. Singular plastic element: NASTRAN implementation and application

    NASA Technical Reports Server (NTRS)

    Hussain, M. A.; Pu, S. L.; Lorensen, W. E.

    1977-01-01

    The elastic and plastic singularities near a crack tip are obtained from higher order isoparametric elements. This is simply accomplished by collapsing the quadrilateral element into the triangular element and by judicious choice of adjacent mid-side nodes. Specifically for the cubic element the elastic singularity is obtained by placing the mid-side nodes adjacent to the crack tip at 1/9th and 4/9th locations. The plastic singularity is constructed using the sliding node concept. These elements have been implemented in NASTRAN as user dummy elements.

  19. Multichannel framework for singular quantum mechanics

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

    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.

  20. Quasi-transverse optical phonon mode in self-generated semipolar AlN grains embedded in c-oriented AlN matrix grown on sapphire using hydride vapor phase epitaxy

    NASA Astrophysics Data System (ADS)

    Hu, Y. Y.; Zhou, T. F.; Zheng, S. N.; Liu, X. H.; Zhao, J. J.; Su, X. J.; Huang, J.; Qiu, Y. X.; Zhang, J. C.; Xu, K.

    2016-05-01

    In this study, we present a microspectroscopic investigation on the quasi-transverse optical phonon modes Q(TO) in some self-generated aluminum nitride (AlN) grains grown on sapphire using hydride vapor phase epitaxy. Using X-ray diffraction and transmission electron microscope, these grains were confirmed to be embedded in (0001)-AlN (c-AlN) epitaxial matrix with an appearance plane of (10 1 ¯ 1 ) (s-plane). Two beam bright field images further showed that the AlN grains were free of dislocation. In-plane phonon anisotropy of the AlN grains was discussed in detail using angular-dependent polarized Raman spectroscopy. The dependence of pure Raman phonons intensity on rotation angle agrees well with the calculation. The Q(TO) phonon intensity exhibited similar behavior to that of A1(TO) phonon, which can be explained by Loudon's formula. However, the observed frequency fluctuation for the Q(TO) phonon differs from that of the pure phonon modes, which cannot be directly understood from the classic Loudon's formula. A modified Loudon's formula appropriate to non-normal incidence was presented to explain the observed Q(TO) phonon frequency fluctuation. Combining with the angular-dependent Raman spectra, we proposed that a small inclination of s-plane along with the various in-plane orientations in c-AlN matrix lead to the frequency fluctuation of Q(TO) in these embedded semipolar AlN grains.

  1. 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.

  2. 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.

  3. Constraints on singular evolution from gravitational baryogenesis

    NASA Astrophysics Data System (ADS)

    Oikonomou, V. K.

    2016-02-01

    We investigate how the gravitational baryogenesis mechanism can potentially constrain the form of a Type IV singularity. Specifically, we study two different models with interesting phenomenology, that realize two distinct Type IV singularities, one occurring at the end of inflation and one during the radiation domination era or during the matter domination era. As we demonstrate, the Type IV singularities occurring at the matter domination era or during the radiation domination era are constrained by the gravitational baryogenesis, in such a way so that these do not render the baryon to entropy ratio singular. Both the cosmological models we study cannot be realized in the context of ordinary Einstein-Hilbert gravity, and hence our work can only be realized in the context of F(R) gravity and more generally in the context of modified gravity only.

  4. 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}.

  5. Singular control in minimum time spacecraft reorientation

    NASA Technical Reports Server (NTRS)

    Seywald, Hans; Kumar, Renjith R.

    1991-01-01

    Spacecraft reorientation is investigated numerically for an inertially symmetric rigid spacecraft with three bounded independent control torques aligned with the principal axes. The dynamical system of the spacecraft and the framework of the optimal-control problem are established in order to identify all of the potential strategies. The investigation lists bang-bang solutions and finite-order and infinite-order singular arcs, and the conditions for the finite-order singular arcs are given. Numerical examples are developed for all of the control-logic systems, and the suboptimality of the rest-to-rest maneuvers is proven for principal-axis rotations. The most efficient control technique is the singular control of infinite order, and the vector-valued singular control can be utilized in a derivative of the switching function.

  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. PMID:27300889

  8. 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.

  9. 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.

  10. Cosmological tests of sudden future singularities

    NASA Astrophysics Data System (ADS)

    Denkiewicz, Tomasz; Dąbrowski, Mariusz P.; Ghodsi, Hoda; Hendry, Martin A.

    2012-04-01

    We discuss combined constraints, coming from the cosmic microwave background shift parameter R, the baryon acoustic oscillations distance parameter A, and from the latest type Ia supernovae data, imposed on cosmological models which allow sudden future singularities of pressure. We show that due to their weakness such sudden singularities may happen in the very near future and that at present they can mimic standard dark energy models.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  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. Naked singularities as particle accelerators. II.

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

    We generalize here our earlier results on particle acceleration by naked singularities. We showed recently [M. Patil and P. S. Joshi, Phys. Rev. DPRVDAQ1550-7998 82, 104049 (2010).10.1103/PhysRevD.82.104049] 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Singular Value Decomposition of Pinhole SPECT Systems.

    PubMed

    Palit, Robin; Kupinski, Matthew A; Barrett, Harrison H; Clarkson, Eric W; Aarsvold, John N; Volokh, Lana; Grobshtein, Yariv

    2009-03-12

    A single photon emission computed tomography (SPECT) imaging system can be modeled by a linear operator H that maps from object space to detector pixels in image space. The singular vectors and singular-value spectra of H provide useful tools for assessing system performance. The number of voxels used to discretize object space and the number of collection angles and pixels used to measure image space make the matrix dimensions H large. As a result, H must be stored sparsely which renders several conventional singular value decomposition (SVD) methods impractical. We used an iterative power methods SVD algorithm (Lanczos) designed to operate on very large sparsely stored matrices to calculate the singular vectors and singular-value spectra for two small animal pinhole SPECT imaging systems: FastSPECT II and M(3)R. The FastSPECT II system consisted of two rings of eight scintillation cameras each. The resulting dimensions of H were 68921 voxels by 97344 detector pixels. The M(3)R system is a four camera system that was reconfigured to measure image space using a single scintillation camera. The resulting dimensions of H were 50864 voxels by 6241 detector pixels. In this paper we present results of the SVD of each system and discuss calculation of the measurement and null space for each system.

  2. 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.

  3. Silica Embedded Metal Hydrides

    SciTech Connect

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

    1998-08-01

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

  4. Removing singular refractive indices with sculpted surfaces

    PubMed Central

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

    2014-01-01

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

  5. Incorporation of perceptually adaptive QIM with singular value decomposition for blind audio watermarking

    NASA Astrophysics Data System (ADS)

    Hu, Hwai-Tsu; Chou, Hsien-Hsin; Yu, Chu; Hsu, Ling-Yuan

    2014-12-01

    This paper presents a novel approach for blind audio watermarking. The proposed scheme utilizes the flexibility of discrete wavelet packet transformation (DWPT) to approximate the critical bands and adaptively determines suitable embedding strengths for carrying out quantization index modulation (QIM). The singular value decomposition (SVD) is employed to analyze the matrix formed by the DWPT coefficients and embed watermark bits by manipulating singular values subject to perceptual criteria. To achieve even better performance, two auxiliary enhancement measures are attached to the developed scheme. Performance evaluation and comparison are demonstrated with the presence of common digital signal processing attacks. Experimental results confirm that the combination of the DWPT, SVD, and adaptive QIM achieves imperceptible data hiding with satisfying robustness and payload capacity. Moreover, the inclusion of self-synchronization capability allows the developed watermarking system to withstand time-shifting and cropping attacks.

  6. Luttinger Liquid, Singular Interaction and Quantum Criticality in Cuprate Materials

    NASA Astrophysics Data System (ADS)

    di Castro, C.; Caprara, S.

    2014-10-01

    With particular reference to the role of the renormalization group (RG) approach and Ward identities (WI's), we start by recalling some old features of the one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior. Its dimensional crossover to the Landau normal Fermi liquid implies that a non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature superconductors, can be maintained in d > 1 only in the presence of a sufficiently singular effective interaction among the charge carriers. This is the case when, nearby an instability, the interaction is mediated by critical fluctuations. We are then led to introduce the specific case of superconductivity in cuprates as an example of avoided quantum criticality. We will disentangle the fluctuations which act as mediators of singular electron-electron interaction, enlightening the possible order competing with superconductivity and a mechanism for the non-Fermi-liquid behavior of the metallic phase. This paper is not meant to be a comprehensive review. Many important contributions will not be considered. We will also avoid using extensive technicalities and making full calculations for which we refer to the original papers and to the many good available reviews. We will here only follow one line of reasoning which guided our research activity in this field.

  7. Class of supersymmetric solitons with naked singularities

    SciTech Connect

    Cvetic, M.; Youm, D. )

    1995-02-15

    We study vacuum domain walls in a class of four-dimensional [ital N]=1 supergravity theories where along with the matter field, forming the wall, there is more than one dilaton,'' each respecting SU(1,1) symmetry in their subsector. We find [ital supersymmetric] (planar, static) walls, interpolating between a Minkowski vacuum and a new class of supersymmetric vacua which have a naked (planar) singularity. Although such walls correspond to idealized configurations, i.e., they correspond to planar configurations of infinite extent, they provide the first example of supersymmetric classical solitons with naked singularities.

  8. Timelike singularities and Hamiltonian cosmological billiards

    NASA Astrophysics Data System (ADS)

    Klinger, Paul

    2016-06-01

    We construct a large class of vacuum solutions of the Einstein equations without any symmetries and with controlled asymptotics near a timelike singularity. The solutions are obtained by a Fuchs analysis of the equations which evolve the metric in a spacelike direction. We further observe that the change of sign of some of the terms (walls) in the associated Hamiltonian invalidate the ‘cosmological billards’ heuristic arguments for the existence of singularities of the mixmaster type in the current context. UWThPh-2015-33

  9. Quantum singularity of Levi-Civita spacetimes

    NASA Astrophysics Data System (ADS)

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

    2004-01-01

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

  10. 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.

  11. Quadrature methods for periodic singular and weakly singular Fredholm integral equations

    NASA Technical Reports Server (NTRS)

    Sidi, Avram; Israeli, Moshe

    1988-01-01

    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 subsequently used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Throughout the development the periodic nature of the problem plays a crucial role. Such periodic equations are used in the solution of planar elliptic boundary value problems such as those that arise in elasticity, potential theory, conformal mapping, and free surface flows. The use of the quadrature methods is demonstrated with numerical examples.

  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. '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.

  14. 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.

  15. Modulated solitons at a singular Hopf bifurcation

    SciTech Connect

    Pismen, L.M.

    1987-02-15

    Dynamics near a singular Hopf bifurcation under conditions of nonlinear self-focusing is dominated by intermediate-scale solitons with amplitudes and speeds evolving on a slower time scale. The long-scale evolution can result in selection of either standing or propagating solitons with either stationary or oscillating amplitude and speed.

  16. Strong curvature singularities and causal simplicity

    SciTech Connect

    Krolak, A. )

    1992-02-01

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

  17. A survey on the structured singular value

    NASA Technical Reports Server (NTRS)

    Packard, Andy; Fan, Michael

    1989-01-01

    The structured singular value, U, is an important linear algebra tool to study a class of matrix perturbation problems. It is useful for analyzing the robustness of stability and performance of uncertain, (nominally) linear systems. Computation of (M) is difficult, and usually, upper and lower bounds are all that can be reliably computed. Upper bounds give conservative estimates of the sizes of allowable perturbations. The maximum singular value of a matrix M is an upper bound for (M). As an upper bound, it can be improved by finding a transformations to the data (i.e. M) which do not change the structured singular value, but do reduce the maximum singular value. Typically, upper bound algorithms involve searches over sets of transformations to yield the tightest bound. Lower bound algorithms are intelligent searches for minimum-norm solutions to multivariable polynomial equations, and are based on various optimality conditions that hold at the global (and, unfortunately, some local) minima. The current methods to compute both of these types of bounds are reviewed. Theoretical justification and extensive numerical experience with the various algorithms are covered.

  18. The Singular, The Plural, and the Numberless.

    ERIC Educational Resources Information Center

    Gilsdorf, Jeanette

    1986-01-01

    Outlines major publishing houses' solutions to the common-gender singular pronoun problem. Maintains that the American English-speaking world employs different standards for speaking and writing, even in educated ranks. Argues that changing spoken language is probably hopeless. Proposes seven tactics through which to counter written grammar and…

  19. 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.

  20. Null cosmological singularities and free strings: II

    NASA Astrophysics Data System (ADS)

    Narayan, K.

    2011-01-01

    In arXiv:0909:4731 , we argued that the free string lightcone Schrodinger wavefunctional in the vicinity of null Kasner-like cosmological singularities has nonsingular time-dependence if the Kasner exponents satisfy certain relations. These backgrounds are anisotropic plane waves with singularities. We first show here that only certain singularities admit a Rosen-Kasner frame with exponents satisfying relations leading to a wavefunctional with nonsingular time-dependence. Then we build on the (Rosen) description further and study various physical observables for a time-dependent harmonic oscillator toy model and then the free string, reconciling this with the corresponding description in the conventional plane wave variables. We find that observables containing no time derivatives are identical in these variables while those with time derivatives are different. Various free string observables are still divergent, perhaps consistent with string oscillator states becoming light in the vicinity of the singularity.

  1. 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…

  2. 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).

  3. Application of an ensemble technique based on singular spectrum analysis to daily rainfall forecasting.

    PubMed

    Baratta, Daniela; Cicioni, Giovambattista; Masulli, Francesco; Studer, Léonard

    2003-01-01

    In previous work, we have proposed a constructive methodology for temporal data learning supported by results and prescriptions related to the embedding theorem, and using the singular spectrum analysis both in order to reduce the effects of the possible discontinuity of the signal and to implement an efficient ensemble method. In this paper we present new results concerning the application of this approach to the forecasting of the individual rain-fall intensities series collected by 135 stations distributed in the Tiber basin. The average RMS error of the obtained forecasting is less than 3mm of rain. PMID:12672433

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

    PubMed

    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. PMID:27661688

  5. 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.

  6. Generalized Parton Distributions and their Singularities

    SciTech Connect

    Anatoly Radyushkin

    2011-04-01

    A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function $f(\\beta)/\\beta$ rather than with the usual parton density $f(\\beta)$. This results in a non-integrable singularity at $\\beta=0$ exaggerated by the fact that $f(\\beta)$'s, on their own, have a singular $\\beta^{-a}$ Regge behavior for small $\\beta$. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs $H(x,\\xi)$ that are finite and continuous at the "border point'' $x=\\xi$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $\\beta=0$ singularities is proposed that is based on the separation of the initial single DD $f(\\beta, \\alpha)$ into the "plus'' part $[f(\\beta,\\alpha)]_{+}$ and the $D$-term. It is demonstrated that the "DD+D'' separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution $f(x)=H(x,0)$ and the border function $H(x,x)$ with the $D$-term function $D(\\alpha)$.

  7. Generalized parton distributions and their singularities

    SciTech Connect

    Radyushkin, A. V.

    2011-04-01

    A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function f({beta})/{beta} rather than with the usual parton density f({beta}). This results in a nonintegrable singularity at {beta}=0 exaggerated by the fact that f({beta})'s, on their own, have a singular {beta}{sup -a} Regge behavior for small {beta}. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs H(x,{xi}) that are finite and continuous at the 'border point' x={xi}. Using a simple input forward distribution, we illustrate implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the {beta}=0 singularities is proposed that is based on the separation of the initial single DD f({beta},{alpha}) into the 'plus' part [f({beta},{alpha})]{sub +} and the D term. It is demonstrated that the ''DD+D'' separation method allows one to (re)derive GPD sum rules that relate the difference between the forward distribution f(x)=H(x,0) and the border function H(x,x) with the D-term function D({alpha}).

  8. Resolution of SU (2) monopole singularities by oxidation

    NASA Astrophysics Data System (ADS)

    Bueno, Pablo; Meessen, Patrick; Ortín, Tomás; Ramírez, Pedro F.

    2015-06-01

    We show how colored SU (2) BPS monopoles (that is: SU (2) monopoles satisfying the Bogomol'nyi equation whose Higgs field and magnetic charge vanish at infinity and which are singular at the origin) can be obtained from the BPST instanton by a singular dimensional reduction, explaining the origin of the singularity and implying that the singularity can be cured by the oxidation of the solution. We study the oxidation of other monopole solutions in this scheme.

  9. Persistence of the Hopf bifurcation under singular perturbations

    SciTech Connect

    Abed, E.H.

    1984-05-01

    The purpose of this paper is to study persistence of the Hopf bifurcation under singular perturbations of the associated vector field. Both single parameter and multiparameter singular perturbation problems are considered. In each case, hyperbolicity of an associated fast time system is shown to imply persistence. For single parameter singular perturbation problems, we employ Fenichel's center manifold theorem for singularly perturbed systems (1) to prove regular degeneration of the bifurcated periodic solutions and to study their stability.

  10. Spatially embedded random networks.

    PubMed

    Barnett, L; Di Paolo, E; Bullock, S

    2007-11-01

    Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples. PMID:18233726

  11. Spatially embedded random networks

    NASA Astrophysics Data System (ADS)

    Barnett, L.; di Paolo, E.; Bullock, S.

    2007-11-01

    Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples.

  12. 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.

  13. 32 CFR 1602.22 - Singular and plural.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 32 National Defense 6 2012-07-01 2012-07-01 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,...

  14. 32 CFR 1602.22 - Singular and plural.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 32 National Defense 6 2011-07-01 2011-07-01 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,...

  15. 32 CFR 1602.22 - Singular and plural.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 32 National Defense 6 2014-07-01 2014-07-01 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,...

  16. 32 CFR 1602.22 - Singular and plural.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 32 National Defense 6 2013-07-01 2013-07-01 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,...

  17. 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,...

  18. Behavior of Friedmann-Lemaître-Robertson-Walker Singularities

    NASA Astrophysics Data System (ADS)

    Fernández-Jambrina, L.

    2016-08-01

    In Stoica (Int. J. Theor. Phys. 55, 71-80, 2016) a regularization procedure is suggested for regularizing Big Bang singularities in Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.

  19. 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.

  20. 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...

  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. 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...

  3. 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...

  4. 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...

  5. 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...

  6. 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...

  7. 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...

  8. Diffraction by polyhedral angle: Field in vicinity of singular ray

    NASA Astrophysics Data System (ADS)

    Borovikov, Vladimir A.

    2002-11-01

    If the plane acoustic wave hits a polyhedral angle, the scattered field consists of an incident wave, of its reflections from the angle's facets, of primary edge waves excited at angle's edges, and of a spherical wave excited at the angle's vertex. It is supposed for simplicity that the geometry of the problem is such that there is no secondary and subsequent edge waves. There are two types of light-shadow boundaries: first for incident and reflected waves and second for edge waves. As is well known, the field in penumbras is expressed via a Fresnel integral. The incident wave's ray passing through the vertex and its reflections from facets are singular rays belonging to the light-shadow boundaries of both types. It will be shown that the field in the vicinity of a singular ray is expressed via a Fresnel intergal and via a generalized Fresnel integral G(p,q) which was introduced in [P. S. Clemmov and T. B. A. Senior, Proc. Cambridge Philos. Soc. 9, 570-572 (1953); see also V. A. Borovikov, Uniform Stationary Phase Method, IEE Electromagnetic Series 40, London, 1994]. This result is valid for an elastic incident wave as well.

  9. 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.

  10. 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

  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. Analysis of local ionospheric time varying characteristics with singular value decomposition

    NASA Astrophysics Data System (ADS)

    Jakobsen, Jakob; Knudsen, Per; Jensen, Anna B. O.

    2010-07-01

    In this paper, a time series from 1999 to 2007 of absolute total electron content (TEC) values has been computed and analyzed using singular value decomposition (SVD). The data set has been computed using a Kalman Filter and is based on dual frequency GPS data from three reference stations in Denmark located in the midlatitude region. The station separation between the three stations is 132-208 km (the time series of the TEC can be freely downloaded at http://www.heisesgade.dk ). For each year, a SVD has been performed on the TEC time series in order to identify the three time varying (daily, yearly, and 11 yearly) characteristics of the ionosphere. The applied SVD analysis provides a new method for separating the daily from the yearly components. The first singular value is very dominant (approximately six times larger than the second singular value), and this singular value corresponds clearly to the variation of the daily cycle over the year. The second singular value corresponds to variations of the width of the daily peak over the year, and the third singular value shows a clear yearly variation of the daily signal with peaks around the equinoxes. The singular values for each year show a very strong correlation with the sunspot number for all the singular values. The correlation coefficients for the first 5 sets of singular values are all above 0.96. Based on the SVD analysis yearly models of the TEC in the ionosphere can be recomposed and illustrate the three time varying characteristics of the ionosphere very clearly. By prediction of the yearly mean sunspot number, future yearly models can also be predicted. These can serve as a priori information for a real time space weather service providing information of the current status of the ionosphere. They will improve the Kalman filter processing making it more robust, but can also be used as

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

    NASA Technical Reports Server (NTRS)

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

    2007-01-01

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

  14. 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.

  15. 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.

  16. 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.

  17. Singularity resolution from polymer quantum matter

    NASA Astrophysics Data System (ADS)

    Kreienbuehl, Andreas; Pawłowski, Tomasz

    2013-08-01

    We study the polymeric nature of quantum matter fields using the example of a Friedmann-Lemaître-Robertson-Walker universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via deparametrization techniques, with the scale factor playing the role of time. Subsequently, the remaining dynamic degrees of freedom corresponding to the matter are polymer quantized. The analysis of the resulting genuine quantum dynamic shows that the big bang singularity is resolved, although with the form of the resolution differing significantly from that in the models with matter clocks: dynamically, the singularity is made passable rather than avoided. Furthermore, this analysis exposes crucial limitations to the so-called effective dynamic in loop quantum cosmology when applied outside of the most basic isotropic settings.

  18. Singular Jets and Bubbles in Drop Impact

    NASA Astrophysics Data System (ADS)

    Bartolo, Denis; Josserand, Christophe; Bonn, Daniel

    2006-03-01

    We show that when water droplets gently impact on a hydrophobic surface, the droplet shoots out a violent jet, the velocity of which can be up to 40 times the drop impact speed. As a function of the impact velocity, two different hydrodynamic singularities are found that correspond to the collapse of the air cavity formed by the deformation of the drop at impact. It is the collapse that subsequently leads to the jet formation. We show that the divergence of the jet velocity can be understood using simple scaling arguments. In addition, we find that very large air bubbles can remain trapped in the drops. The surprising occurrence of the bubbles for low-speed impact is connected with the nature of the singularities, and can have important consequences for drop deposition, e.g., in ink-jet printing.

  19. Global dynamics in the singular logarithmic potential

    NASA Astrophysics Data System (ADS)

    Stoica, Cristina; Font, Andreea

    2003-07-01

    We present an analytical description of the motion in the singular logarithmic potential of the form Phi = ln surdx21/b2 + x22, a potential which plays an important role in the modelling of triaxial systems (such as elliptical galaxies) or bars in the centres of galaxy discs. In order to obtain information about the motion near the singularity, we resort to McGehee-type transformations and regularize the vector field. In the axis-symmetric case (b = 1), we offer a complete description of the global dynamics. In the non-axis-symmetric case (b < 1), we prove that all orbits, with the exception of a negligible set, are centrophobic and retrieve numerically partial aspects of the orbital structure.

  20. Stability of the nakedness of Weyl singularities

    NASA Technical Reports Server (NTRS)

    Haugan, M. P.; Liang, E. P. T.

    1979-01-01

    The stability of the nakedness of the Weyl singularities against matter perturbations is investigated. Consideration is given to the effects of infalling test matter on the convergence of outgoing null rays. It is shown that the additional convergence induced by infalling test matter does not blow up sufficiently fast to reconverge diverging outgoing rays, at least in the equator, and that the nakedness seems to be stable in this limited sense.

  1. 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.

  2. Space-time singularities in Weyl manifolds

    NASA Astrophysics Data System (ADS)

    Lobo, I. P.; Barreto, A. B.; Romero, C.

    2015-09-01

    We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame.

  3. Modified Embedded Atom Method

    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.

  4. 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.

  5. Flexible embedding of networks

    NASA Astrophysics Data System (ADS)

    Fernandez-Gracia, Juan; Buckee, Caroline; Onnela, Jukka-Pekka

    We introduce a model for embedding one network into another, focusing on the case where network A is much bigger than network B. Nodes from network A are assigned to the nodes in network B using an algorithm where we control the extent of localization of node placement in network B using a single parameter. Starting from an unassigned node in network A, called the source node, we first map this node to a randomly chosen node in network B, called the target node. We then assign the neighbors of the source node to the neighborhood of the target node using a random walk based approach. To assign each neighbor of the source node to one of the nodes in network B, we perform a random walk starting from the target node with stopping probability α. We repeat this process until all nodes in network A have been mapped to the nodes of network B. The simplicity of the model allows us to calculate key quantities of interest in closed form. By varying the parameter α, we are able to produce embeddings from very local (α = 1) to very global (α --> 0). We show how our calculations fit the simulated results, and we apply the model to study how social networks are embedded in geography and how the neurons of C. Elegans are embedded in the surrounding volume.

  6. Twin kernel embedding.

    PubMed

    Guo, Yi; Gao, Junbin; Kwan, Paul W

    2008-08-01

    In most existing dimensionality reduction algorithms, the main objective is to preserve relational structure among objects of the input space in a low dimensional embedding space. This is achieved by minimizing the inconsistency between two similarity/dissimilarity measures, one for the input data and the other for the embedded data, via a separate matching objective function. Based on this idea, a new dimensionality reduction method called Twin Kernel Embedding (TKE) is proposed. TKE addresses the problem of visualizing non-vectorial data that is difficult for conventional methods in practice due to the lack of efficient vectorial representation. TKE solves this problem by minimizing the inconsistency between the similarity measures captured respectively by their kernel Gram matrices in the two spaces. In the implementation, by optimizing a nonlinear objective function using the gradient descent algorithm, a local minimum can be reached. The results obtained include both the optimal similarity preserving embedding and the appropriate values for the hyperparameters of the kernel. Experimental evaluation on real non-vectorial datasets confirmed the effectiveness of TKE. TKE can be applied to other types of data beyond those mentioned in this paper whenever suitable measures of similarity/dissimilarity can be defined on the input data. PMID:18566501

  7. Media Embedded Interactions.

    ERIC Educational Resources Information Center

    Johnson, J. David

    A review of literature and two surveys, one of college students and one of a random sample of adults, were used to examine four aspects of media embedded interactions (social behavior in front of a TV or radio): their functions, their environment, their effects, and the reactions of the interactants to them. Television is seen as performing a…

  8. 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.

  9. Testing framework for embedded languages

    NASA Astrophysics Data System (ADS)

    Leskó, Dániel; Tejfel, Máté

    2012-09-01

    Embedding a new programming language into an existing one is a widely used technique, because it fastens the development process and gives a part of a language infrastructure for free (e.g. lexical, syntactical analyzers). In this paper we are presenting a new advantage of this development approach regarding to adding testing support for these new languages. Tool support for testing is a crucial point for a newly designed programming language. It could be done in the hard way by creating a testing tool from scratch, or we could try to reuse existing testing tools by extending them with an interface to our new language. The second approach requires less work, and also it fits very well for the embedded approach. The problem is that the creation of such interfaces is not straightforward at all, because the existing testing tools were mostly not designed to be extendable and to be able to deal with new languages. This paper presents an extendable and modular model of a testing framework, in which the most basic design decision was to keep the - previously mentioned - interface creation simple and straightforward. Other important aspects of our model are the test data generation, the oracle problem and the customizability of the whole testing phase.

  10. Evaluation of Protein Profiles From Treated Xenograft Tumor Models Identifies an Antibody Panel for Formalin-fixed and Paraffin-embedded (FFPE) Tissue Analysis by Reverse Phase Protein Arrays (RPPA)*

    PubMed Central

    Bader, Sabine; Zajac, Magdalena; Friess, Thomas; Ruge, Elisabeth; Rieder, Natascha; Gierke, Berthold; Heubach, Yvonne; Thomas, Marlene; Pawlak, Michael

    2015-01-01

    Reverse phase protein arrays (RPPA) are an established tool for measuring the expression and activation status of multiple proteins in parallel using only very small amounts of tissue. Several studies have demonstrated the value of this technique for signaling pathway analysis using proteins extracted from fresh frozen (FF) tissue in line with validated antibodies for this tissue type; however, formalin fixation and paraffin embedding (FFPE) is the standard method for tissue preservation in the clinical setting. Hence, we performed RPPA to measure profiles for a set of 300 protein markers using matched FF and FFPE tissue specimens to identify which markers performed similarly using the RPPA technique in fixed and unfixed tissues. Protein lysates were prepared from matched FF and FFPE tissue specimens of individual tumors taken from three different xenograft models of human cancer. Materials from both untreated mice and mice treated with either anti-HER3 or bispecific anti-IGF-1R/EGFR monoclonal antibodies were analyzed. Correlations between signals from FF and FFPE tissue samples were investigated. Overall, 60 markers were identified that produced comparable profiles between FF and FFPE tissues, demonstrating significant correlation between the two sample types. The top 25 markers also showed significance after correction for multiple testing. The panel of markers covered several clinically relevant tumor signaling pathways and both phosphorylated and nonphosphorylated proteins were represented. Biologically relevant changes in marker expression were noted when RPPA profiles from treated and untreated xenografts were compared. These data demonstrate that, using appropriately selected antibodies, RPPA analysis from FFPE tissue is well feasible and generates biologically meaningful information. The identified panel of markers that generate similar profiles in matched fixed and unfixed tissue samples may be clinically useful for pharmacodynamic studies of drug effect

  11. Evaluation of Protein Profiles From Treated Xenograft Tumor Models Identifies an Antibody Panel for Formalin-fixed and Paraffin-embedded (FFPE) Tissue Analysis by Reverse Phase Protein Arrays (RPPA).

    PubMed

    Bader, Sabine; Zajac, Magdalena; Friess, Thomas; Ruge, Elisabeth; Rieder, Natascha; Gierke, Berthold; Heubach, Yvonne; Thomas, Marlene; Pawlak, Michael

    2015-10-01

    Reverse phase protein arrays (RPPA) are an established tool for measuring the expression and activation status of multiple proteins in parallel using only very small amounts of tissue. Several studies have demonstrated the value of this technique for signaling pathway analysis using proteins extracted from fresh frozen (FF) tissue in line with validated antibodies for this tissue type; however, formalin fixation and paraffin embedding (FFPE) is the standard method for tissue preservation in the clinical setting. Hence, we performed RPPA to measure profiles for a set of 300 protein markers using matched FF and FFPE tissue specimens to identify which markers performed similarly using the RPPA technique in fixed and unfixed tissues. Protein lysates were prepared from matched FF and FFPE tissue specimens of individual tumors taken from three different xenograft models of human cancer. Materials from both untreated mice and mice treated with either anti-HER3 or bispecific anti-IGF-1R/EGFR monoclonal antibodies were analyzed. Correlations between signals from FF and FFPE tissue samples were investigated. Overall, 60 markers were identified that produced comparable profiles between FF and FFPE tissues, demonstrating significant correlation between the two sample types. The top 25 markers also showed significance after correction for multiple testing. The panel of markers covered several clinically relevant tumor signaling pathways and both phosphorylated and nonphosphorylated proteins were represented. Biologically relevant changes in marker expression were noted when RPPA profiles from treated and untreated xenografts were compared. These data demonstrate that, using appropriately selected antibodies, RPPA analysis from FFPE tissue is well feasible and generates biologically meaningful information. The identified panel of markers that generate similar profiles in matched fixed and unfixed tissue samples may be clinically useful for pharmacodynamic studies of drug effect

  12. 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.

  13. 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.

  14. 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.

  15. Nonlinear singularly perturbed optimal control problems with singular arcs. [flight mechanics application

    NASA Technical Reports Server (NTRS)

    Ardema, M. D.

    1979-01-01

    Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.

  16. 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.

  17. ARCnet for embedded control

    SciTech Connect

    McEntee, M.

    1996-11-01

    ARCnet began life in the late 1970s as a distributed data processing network. When demand for office networks shifted to Ethernet in the late 80s, the token-passing protocol found a new home in real-time, embedded control applications. It has proven its reliability in the seven million nodes currently installed worldwide. ARCnet is used in hundreds of embedded applications that affect everyday lives. ARCnet is used in planes, trains, boats, and cars. It`s used in elevators, fast-food restaurants, stores, buildings` climate control and security systems, and even bank ATMs. ARCnet also has become an important part of factory automation systems. The protocol`s advantages in real-time control systems include determinism, reliable message delivery, peer-to-peer communication, automatic reconfiguration, high node count, long distance, variable baud rates, and variable message sizes. 2 figs.

  18. 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

  19. 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.

  20. 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.

  1. Multigrid applied to singular perturbation problems

    NASA Technical Reports Server (NTRS)

    Kamowitz, David

    1987-01-01

    The solution of the singular perturbation problem by a multigrid algorithm is considered. Theoretical and experimental results for a number of different discretizations are presented. The theoretical and observed rates agree with the results developed in an earlier work of Kamowitz and Parter. In addition, the rate of convergence of the algorithm when the coarse grid operator is the natural finite difference analog of the fine grid operator is presented. This is in contrast to the case in the previous work where the Galerkin choice (I sup H sub h L sub h,I sup h sub H) was used for the coarse grid operators.

  2. 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.

  3. 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.

  4. Internal energy flows of coma-affected singular beams in low-numerical-aperture systems.

    PubMed

    Bahl, Monika; Singh, Brijesh Kumar; Singh, Rakesh Kumar; Senthilkumaran, P

    2015-04-01

    The circulating phase gradient component of a singular beam gets modified when focused by a low-numerical-aperature system suffering from coma aberration. The gradient due to this coma aberration splits the higher charge vortex into elementary vortices and distributes them spatially. This splitting depends on the charge and polarity of the incident singular beam as well as the sign and magnitude of the aberration coefficient. The transverse component of the Poynting vector field distribution at the focal plane is decomposed into the curl or solenoidal component and divergence or irrotational component using the Helmholtz-Hodge decomposition technique. The solenoidal component that relates to the orbital angular momentum carries the circulating energy, while the irrotational component shows the sources and sinks of the energy. Intriguing results of the study of energy flow around the edge dislocations apart from the point phase defects in the irrotational components are also presented.

  5. 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.

  6. 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.

  7. 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.

  8. Observer-dependent sign inversions of polarization singularities.

    PubMed

    Freund, Isaac

    2014-10-15

    We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

  9. Naked singularities in self-similar spherical gravitational collapse

    SciTech Connect

    Ori, A.; Piran, T.

    1987-11-09

    We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (GAMMA-1<<1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold.

  10. 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...

  11. 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

  12. Identify Foot of Continental Slope by singular spectrum and fractal singularity analysis

    NASA Astrophysics Data System (ADS)

    Li, Q.; Dehler, S.

    2012-04-01

    Identifying the Foot of Continental Slope (FOCS) plays a critical role in the determination of exclusive economic zone (EEZ) for coastal nations. The FOCS is defined by the Law of the Sea as the point of maximum change of the slope and it is mathematically equivalent to the point which has the maximum curvature value in its vicinity. However, curvature is the second derivative and the calculation of second derivative is a high pass and noise-prone filtering procedure. Therefore, identification of FOCS with curvature analysis methods is often uncertain and erroneous because observed bathymetry profiles or interpolated raster maps commonly include high frequency noises and artifacts, observation errors, and local sharp changes. Effective low-pass filtering methods and robust FOCS indicator algorithms are highly desirable. In this approach, nonlinear singular spectral filtering and singularity FOCS-indicator methods and software tools are developed to address this requirement. The normally used Fourier domain filtering methods decompose signals into Fourier space, composed of a fixed base that depends only on the acquisition interval of the signal; the signal is required to be stationary or at least weak stationary. In contrast to that requirement, the developed singular spectral filtering method constructs orthogonal basis functions dynamically according to different signals, and it does not require the signal to be stationary or weak stationary. Furthermore, singular spectrum analysis (SSA) can assist in designing suitable filters to carefully remove high-frequency local or noise components while reserving useful global and local components according to energy distribution. Geoscientific signals, including morphological ocean bathymetry data, often demonstrate fractal or multifractal properties. With proper definition of scales in the vicinity of a certain point and related measures, it is found that 1-dimensional bathymetry profiles and 2-dimensional raster maps

  13. Timelike BKL singularities and chaos in AdS/CFT

    NASA Astrophysics Data System (ADS)

    Shaghoulian, Edgar; Wang, Huajia

    2016-06-01

    We study the nature of a family of curvature singularities which are precisely the timelike cousins of the spacelike singularities studied by Belinski, Khalatnikov, and Lifshitz (BKL). We show that the approach to the singularity can be modeled by a billiard ball problem on hyperbolic space, just as in the case of BKL. For pure gravity, generic chaotic behavior is retained in (3 + 1) dimensions, and we provide evidence that it disappears in higher dimensions. We speculate that such singularities, if occurring in AdS/CFT and of the chaotic variety, may be interpreted as (transient) chaotic renormalization group flows which exhibit features reminiscent of chaotic duality cascades.

  14. LETTER TO THE EDITOR: Penrose limits and spacetime singularities

    NASA Astrophysics Data System (ADS)

    Blau, M.; Borunda, M.; O'Loughlin, M.; Papadopoulos, G.

    2004-04-01

    We give a covariant characterization of the Penrose plane wave limit: the plane wave profile matrix A(u) is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres Iyer 'power-law type'), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile A(u) ~ u-2, the scale invariance of the latter reflecting the power-law behaviour of the singularities.

  15. 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.

  16. 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.

  17. Singular Isotropic Cosmologies and Bel-Robinson Energy

    NASA Astrophysics Data System (ADS)

    Cotsakis, Spiros; Klaoudatou, Ifigeneia

    2006-11-01

    We consider the problem of the nature and possible types of spacetime singularities that can form during the evolution of FRW universes in general relativity. We show that by using, in addition to the Hubble expansion rate and the scale factor, the Bel-Robinson energy of these universes we can consistently distinguish between the possible different types of singularities and arrive at a complete classification of the singularities that can occur in the isotropic case. We also use the Bel-Robinson energy to prove that known behaviours of exact flat isotropic universes with given singularities are generic in the sense that they hold true in every type of spatial geometry.

  18. Discrete and Embedded Eigenvalues for One-Dimensional Schrödinger Operators

    NASA Astrophysics Data System (ADS)

    Remling, Christian

    2007-04-01

    I present an example of a discrete Schrödinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously identified borderline situation.

  19. 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.

  20. Quantum singularities in the FRW universe revisited

    SciTech Connect

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

    2010-08-15

    The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state p=(1/3){rho} in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied, and it is shown that the energy conditions are violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the nonsingular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of nonnormalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.

  1. 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.

  2. 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.

  3. Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs

    NASA Astrophysics Data System (ADS)

    Lou, Yu-Qing; Zou, Yue

    2004-06-01

    We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. This study extends recent analyses on (magnetized) SIDs by Shu et al., Lou and Lou & Shen. By this model, we intend to provide a conceptual framework to gain insights for multiwavelength large-scale structural observations of disc galaxies. Both SIDs are approximated to be razor thin and are in a self-consistent axisymmetric background equilibrium with power-law surface mass densities and flat rotation curves. The gaseous SID is embedded with a coplanar azimuthal magnetic field Bθ(r) of a radial scaling r-1/2 that is not force-free. In comparison with the SID problems studied earlier, there are three possible classes of stationary solutions allowed by more dynamic freedoms. To identify physical solutions, we explore parameter space involving three dimensionless parameters: ratio λ of Alfvén speed to sound speed in the magnetized gaseous SID; ratio β of the square of the stellar velocity dispersion to the gas sound speed; and ratio δ of the surface mass densities of the two SIDs. For both aligned and unaligned spiral cases with azimuthal periodicities |m| >= 2, one of the three solution branches is always physical, while the other two branches might become invalid when β exceeds certain critical values. For the onset criteria from an axisymmetric equilibrium to aligned secular bar-like instabilities, the corresponding ratio, which varies with λ, β and δ, may be considerably lower than the oft-quoted value of , where is the total kinetic energy, is the total gravitational potential energy and is the total magnetic energy. For unaligned spiral cases, we examine marginal instabilities for axisymmetric (|m| = 0) and non-axisymmetric (|m| > 0) disturbances. The resulting marginal stability curves differ from the previous ones. The case of a composite partial magnetized

  4. Shutters with embedded microprocessors

    NASA Astrophysics Data System (ADS)

    Stephenson, S.

    2015-06-01

    Shutters are used to periodically provide a non-uniformity correction (NUC) calibration surface to micro bolometers. Many bolometer applications, such as TWS and DVE, require compact, power efficient actuators. Actuators in these applications, such as bistable solenoids and stepper motors, benefit from complex drive schemes. Consumer electronics products have generated compact, low-cost drive components that can be used to embed complex drives into these shutters. Shutter drives using these components maintain compactness and power efficiency while simplifying interfaces at minimal cost. Recently, several commercially available shutter systems have been created that incorporate embedded microprocessors into shutters usable for NUC correction of micro bolometers.

  5. Embeddings of Causal Sets

    SciTech Connect

    Reid, David D.

    2009-07-06

    A key postulate of the causal set program is that this discrete partial order offers a sufficiently rich structure to make it a viable model of spacetime for quantum gravity. If the deep structure of spacetime is that of a causal set, then the correspondence principle (with the spacetimes of general relativity) must be obeyed. Therefore, one of the requirements of this program is to establish that the causal set structure is in fact, not just in principle, fully consistent with our macroscopic notion of spacetime as a Lorentzian manifold. An important component of any such 'manifold test' is the ability to find embeddings of causal sets into Lorentzian manifolds.

  6. 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.

  7. 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

  8. Quantum mechanical embedding theory based on a unique embedding potential

    SciTech Connect

    Chen Huang; Pavone, Michele; Carter, Emily A.

    2011-04-21

    We remove the nonuniqueness of the embedding potential that exists in most previous quantum mechanical embedding schemes by letting the environment and embedded region share a common embedding (interaction) potential. To efficiently solve for the embedding potential, an optimized effective potential method is derived. This embedding potential, which eschews use of approximate kinetic energy density functionals, is then used to describe the environment while a correlated wavefunction (CW) treatment of the embedded region is employed. We first demonstrate the accuracy of this new embedded CW (ECW) method by calculating the van der Waals binding energy curve between a hydrogen molecule and a hydrogen chain. We then examine the prototypical adsorption of CO on a metal surface, here the Cu(111) surface. In addition to obtaining proper site ordering (top site most stable) and binding energies within this theory, the ECW exhibits dramatic changes in the p-character of the CO 4{sigma} and 5{sigma} orbitals upon adsorption that agree very well with x-ray emission spectra, providing further validation of the theory. Finally, we generalize our embedding theory to spin-polarized quantum systems and discuss the connection between our theory and partition density functional theory.

  9. 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.

  10. 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…

  11. Singularities in the Origin and Evolution of Life

    SciTech Connect

    Duve, Christian de

    2003-11-19

    The history of life is landmarked by a large number of remarkable singularities. The single ancestry of all living beings, the universal genetic code, and the monophyletic origin of eukaryotes are typical examples, but there are many others. The mechanisms responsible for these singularities will be discussed.

  12. 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.

  13. Singular accelerated evolution in massive F (R ) bigravity

    NASA Astrophysics Data System (ADS)

    Nojiri, S.; Odintsov, S. D.; Oikonomou, V. K.

    2015-12-01

    The possibility to have singular accelerated evolution in the context of F (R ) bimetric gravity is investigated. Particularly, we study two singular models of cosmological evolution, one of which is a singular modified version of the Starobinsky R2 inflation model. As we demonstrate, for both models in some cases, the slow-roll parameters become singular at the Type IV singularity, a fact that we interpret as a dynamical instability of the theory under study. This dynamical instability may be an indicator of a graceful exit from inflation, and we thoroughly discuss this scenario and the interpretation of the singular slow-roll parameters. Furthermore, it is demonstrated that for some versions of F (R ) bigravity, singular inflation is realized in a consistent way so that inflationary indices are compatible with Planck data. Moreover, we study the late-time behavior of the two singular models, and we show that the unified description of early- and late-time acceleration can be achieved in the context of bimetric F (R ) gravity.

  14. Generalised hyperbolicity in spacetimes with string-like singularities

    NASA Astrophysics Data System (ADS)

    Sanchez Sanchez, Yafet; Vickers, James A.

    2016-10-01

    In this paper we present well-posedness results for H 1 solutions of the wave equation for spacetimes that contain string-like singularities. These results extend a framework in which one characterises gravitational singularities as obstruction to the dynamics of test fields rather than point particles. In particular, we discuss spacetimes with cosmic strings.

  15. 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.

  16. 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...

  17. 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.

  18. 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

  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. 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.

  1. 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

  2. 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.

  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. 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.

  5. 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.

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

    SciTech Connect

    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.

  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. 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.

  9. Analysis of stress singularities at singular points of elastic solids made of functionally graded materials

    NASA Astrophysics Data System (ADS)

    Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

    2016-01-01

    The results of analytical and numerical investigations on estimating the character of the singularity of stresses in a vicinity of different variants of special points of the 2D elastic solids made of functionally graded materials (FGMs) are presented. The variant of construction by analytical methods in the polar system of coordinates is considered for eigensolutions in the flat wedges made of the FGM, the elastic properties of which are represented as power series in terms of the radial coordinate.

  10. 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.

  11. An Analytical Singularity-Free Solution to the J2 Perturbation Problem

    NASA Technical Reports Server (NTRS)

    Bond, V. R.

    1979-01-01

    The development of a singularity-free solution of the J2 problem in satellite theory is presented. The procedure resembles that of Lyndane who rederives Brouwer's satellite theory using Poincare elements. A comparable procedure is used in this report in which the satellite theory of Scheifele, who used elements similar to the Delaunay elements but in the extended phase space, is rederived using Poincare elements also in the extended phase space. Only the short-period effects due to J2 are included.

  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. Structure properties of evolutionary spatially embedded networks

    NASA Astrophysics Data System (ADS)

    Hui, Z.; Li, W.; Cai, X.; Greneche, J. M.; Wang, Q. A.

    2013-04-01

    This work is a modeling of evolutionary networks embedded in one or two dimensional configuration space. The evolution is based on two attachments depending on degree and spatial distance. The probability for a new node n to connect with a previous node i at distance r follows aki∑jkj+(1-a)rni-α∑jrnj-α, where ki is the degree of node i, α and a are tunable parameters. In spatial driven model (a=0), the spatial distance distribution follows the power-law feature. The mean topological distance l and the clustering coefficient C exhibit phase transitions at same critical values of α which change with the dimensionality d of the embedding space. When a≠0, the degree distribution follows the "shifted power law" (SPL) which interpolates between exponential and scale-free distributions depending on the value of a.

  14. Stylistic Embedding in Yoruba Literature.

    ERIC Educational Resources Information Center

    Olabode, Afolabi

    The process of embedding, a term used in generative grammar to refer to a construction in which a sentence is included within another sentence, is examined as it occurs in Yoruba literature. Examples are drawn from Yoruba praise poetry, in both written and oral form and within Yoruba novels. Forms of embedding identified include those to draw…

  15. 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.

  16. 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.

  17. Chapter 4 embedded metal fragments.

    PubMed

    Kalinich, John F; Vane, Elizabeth A; Centeno, Jose A; Gaitens, Joanna M; Squibb, Katherine S; McDiarmid, Melissa A; Kasper, Christine E

    2014-01-01

    The continued evolution of military munitions and armor on the battlefield, as well as the insurgent use of improvised explosive devices, has led to embedded fragment wounds containing metal and metal mixtures whose long-term toxicologic and carcinogenic properties are not as yet known. Advances in medical care have greatly increased the survival from these types of injuries. Standard surgical guidelines suggest leaving embedded fragments in place, thus individuals may carry these retained metal fragments for the rest of their lives. Nursing professionals will be at the forefront in caring for these wounded individuals, both immediately after the trauma and during the healing and rehabilitation process. Therefore, an understanding of the potential health effects of embedded metal fragment wounds is essential. This review will explore the history of embedded fragment wounds, current research in the field, and Department of Defense and Department of Veterans Affairs guidelines for the identification and long-term monitoring of individuals with embedded fragments.

  18. 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.

  19. 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).

  20. Generating Hyperbolic Singularities in Semitoric Systems Via Hopf Bifurcations

    NASA Astrophysics Data System (ADS)

    Dullin, Holger R.; Pelayo, Álvaro

    2016-06-01

    Let (M,Ω ) be a connected symplectic 4-manifold and let F=(J,H) :M→ {R}^2 be a completely integrable system on M with only non-degenerate singularities. Assume that F does not have singularities with hyperbolic blocks and that p_1,ldots ,p_n are the focus-focus singularities of F. For each subset S={i_1,ldots ,i_j}, we will show how to modify F locally around any p_i, i in S, in order to create a new integrable system widetilde{F}=(J, widetilde{H}) :M → {R}^2 such that its classical spectrum widetilde{F}(M) contains j smooth curves of singular values corresponding to non-degenerate transversally hyperbolic singularities of widetilde{F}. Moreover the focus-focus singularities of widetilde{F} are precisely p_i, i in {1,ldots ,n} setminus S. The proof is based on Eliasson's linearization theorem for non-degenerate singularities, and properties of the Hamiltonian Hopf bifurcation.

  1. 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.

  2. Threshold singularities, dispersion relations and fixed-order perturbative calculations

    NASA Astrophysics Data System (ADS)

    Beneke, M.; Ruiz-Femenía, P.

    2016-08-01

    We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the "non-perturbative", resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order cal-culation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual corrections over phase space at a given order in the expansion in the strong coupling, an additional contribution has to be added at N3LO.

  3. 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.

  4. Embedded gage impact study

    NASA Technical Reports Server (NTRS)

    Schramm, S. W.; Daniel, I. M.

    1984-01-01

    Impact damage in graphite/epoxy laminates was characterized and transient strain history during impact was correlated. The material investigated was AS-4/3501-6 graphite/epoxy. Eight-ply and sixteen-ply quasi-isotropic laminates of 45/0/-45/90 sub s and 45/0/-45/90 sub 2s layups were fabricated with strain gages embedded between plies during the strain gages and leads from the highly conductive graphite fibers. The specimens were circular plates 12.7 cm (5 in.) in diameter and clamped along their circumference. The specimens were impacted with a 185 gm impactor, dropped from heights of 1.20 m and 1.65 m. An accelerometer was attached to the back surface of the specimen opposite the impact point and was used to trigger the recording instrumentation. The transient strain data were recorded with an eight channel waveform digitizer capable of sampling data at 0.5 microsec intervals. The data were stored, processed, and plotted by means of a microcomputer. Transient strain data were correlated with results from ultrasonic inspection of the specimens.

  5. 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

  6. 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.

  7. Ordinary polarization singularities in three-dimensional optical fields.

    PubMed

    Freund, Isaac

    2012-06-15

    In generic three-dimensional optical fields the canonical point polarization singularities are points of circular polarization, C points on C lines, and points of linear polarization, L points on L lines. These special points are surrounded by a sea of ordinary points. In planes oriented normal to the principle axes of the polarization ellipse at the point, every ordinary point is also a singularity, here an ordinary polarization singularity, or O point. Interactions between O points, between O points and C points, and between O points and L points are described that highlight the fact that a consistent description of optical fields containing C and L lines must include O points.

  8. 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.

  9. Spontaneous generation of singularities in paraxial optical fields.

    PubMed

    Aiello, Andrea

    2016-04-01

    In nonrelativistic quantum mechanics, the spontaneous generation of singularities in smooth and finite wave functions is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schrödinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields that develop a spatial singularity in the focal point of a weakly focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful research for diverse technological and scientific applications. PMID:27192314

  10. On the Singular Perturbations for Fractional Differential Equation

    PubMed Central

    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. PMID:24683357

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. Particle Production and Big Rip Singularities

    NASA Astrophysics Data System (ADS)

    Bates, Jason

    2010-02-01

    In 1929, Edwin Hubble found that objects in our Universe generally recede from us at a rate proportional to their distance, suggesting that the Universe as a whole is expanding. More recently, astronomers have observed that this expansion is accelerating. According to Einstein's theory of gravity, all normal matter in the Universe should act to slow the rate of expansion, so there must be something new which is causing this acceleration. Cosmologists call this ``Dark Energy.'' One of the possibilities for dark energy leads to a Universe which expands to an infinite size in a finite amount of time. This scenario is called a ``Big Rip,'' because near the end of time this expansion overcomes all other forces in the Universe - even atoms are ripped apart. However, Quantum Mechanics predicts that as the Universe expands particles will be created. If enough particles are created, this process could slow or even halt the expansion, and the ``Big Rip'' might be avoided. Using numerical methods, we considered the quantum effects for massive and massless scalar fields, and found that while at late times quantum effects do grow large, they do not become comparable to the dark energy until very near the singularity when the curvature of the Universe approaches the Planck scale. )

  17. Extreme value theory for singular measures.

    PubMed

    Lucarini, Valerio; Faranda, Davide; Turchetti, Giorgio; Vaienti, Sandro

    2012-06-01

    In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor. Using the block maxima approach, we show that the extremes are distributed according to the generalised extreme value distribution, where the parameters can be written as functions of the information dimension of the attractor. The numerical analysis is performed on a few low dimensional maps. For the Cantor ternary set and the Sierpinskij triangle, which can be constructed as iterated function systems, the inferred parameters show a very good agreement with the theoretical values. For strange attractors like those corresponding to the Lozi and Hènon maps, a slower convergence to the generalised extreme value distribution is observed. Nevertheless, the results are in good statistical agreement with the theoretical estimates. It is apparent that the analysis of extremes allows for capturing fundamental information of the geometrical structure of the attractor of the underlying dynamical system, the basic reason being that the chosen observables act as magnifying glass in the neighborhood of the point from which the distance is computed.

  18. Accessing singular antecedents in conjoined phrases.

    PubMed

    Albrecht, J E; Clifton, C

    1998-05-01

    Two experiments examined processing of singular pronouns when the antecedent (e.g., Mary) was a noun phrase (NP) in a conjoined phrase (e.g., Mary and John). Whole-sentence reading times showed an increase in processing time associated with splitting the conjoined phrase to access a single NP antecedent. The increase in processing occurred both when the antecedent was in the subject position and when it was in a nonsubject position. The source of the disruption was further investigated using eyetracking methods. Summing over regions of the text, the magnitude of the processing cost incurred by having to split a conjoined NP was closely comparable when there was and when there was not a gender-appropriate distracting potential antecedent. When there was no such potential antecedent, the increase in processing time occurred immediately in the pronoun region when eye movements were measured. In contrast, when there was a second discourse entity that matched the gender and number of the pronoun (but was not a plausible antecedent for the pronoun), eyetracking measures suggested that the processing difficulty was delayed until additional information was read that forced the antecedent to be one of the conjoined NPs. The results are interpreted in terms of Sanford and Garrod's (1981) scenario-based model of text comprehension.

  19. Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamics

    NASA Astrophysics Data System (ADS)

    Duplij, Steven

    2015-09-01

    A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number of velocities) is proposed. The equations of motion become first-order differential equations, and they coincide with those of multi-time dynamics, if a certain condition is imposed. In a singular theory, this condition is fulfilled in the case of the coincidence of the number of generalized momenta with the rank of the Hessian matrix. The noncanonical generalized velocities satisfy a system of linear algebraic equations, which allows an appropriate classification of singular theories (gauge and nongauge). A new antisymmetric bracket (similar to the Poisson bracket) is introduced, which describes the time evolution of physical quantities in a singular theory. The origin of constraints is shown to be a consequence of the (unneeded in our formulation) extension of the phase space, when the new bracket transforms into the Dirac bracket. Quantization is briefly discussed.

  20. 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.

  1. Singular perturbation margin and generalised gain margin for nonlinear time-invariant systems

    NASA Astrophysics Data System (ADS)

    Yang, Xiaojing; Zhu, J. Jim

    2016-03-01

    In this paper, singular perturbation margin (SPM) and generalised gain margin (GGM) are proposed as the classical phase margin and gain margin like stability metrics for nonlinear systems established from the view of the singular perturbation and the regular perturbation, respectively. The problem of SPM and GGM assessment of a nonlinear nominal system is formulated. The SPM and GGM formulations are provided as the functions of radius of attraction (ROA), which is introduced as a conservative measure of the domain of attraction (DOA). Furthermore, the ROA constrained SPM and GGM analysis are processed through two stages: (1) the SPM and GGM assessment for nonlinear systems at the equilibrium point, based on the SPM and GGM equilibrium theorems, including time-invariant and time-varying cases (Theorem 5.3, Theorem 5.2, Theorem 5.4 and Theorem 5.5); (2) the establishment of the relationship between the SPM or GGM and the ROA for nonlinear time-invariant systems through the construction of the Lyapunov function for the singularly perturbed model (Theorem 6.1 and Section 6.2.3).

  2. 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. PMID:26821277

  3. 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

  4. 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.

  5. 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.

  6. Singularity avoidance in the hybrid quantization of the Gowdy model

    NASA Astrophysics Data System (ADS)

    Tarrío, Paula; Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.

    2013-10-01

    One of the most remarkable phenomena in loop quantum cosmology is that, at least for homogeneous cosmological models, the big bang is replaced with a big bounce that connects our Universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in loop quantum cosmology, including inhomogeneities, and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case.

  7. 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.

  8. The Cauchy horizon singularity inside Kerr black holes

    NASA Astrophysics Data System (ADS)

    Burko, Lior M.; Khanna, Gaurav

    2016-03-01

    The numerical technology that allows for the careful evolution of linearized fields inside Kerr black holes and the study of their behavior approaching the Cauchy horizon singularity includes a number of interesting aspects. The latter include compactified hyperboloidal coordinates and foliation, mixed type hyperbolic-elliptic PDE, and initial data evolution where all equal-coordinate hypersurfaces are spacelike. We review the need for the numerical technology that allows for the solution of the spin-2 Teukolsky equation inside Kerr black holes, and discuss the main features thereof. We present new results about the numerical properties of the Cauchy horizon singularity and their correspondence with the predictions of perturbative analysis. We then discuss present directions of study, which include the sub-dominant azimuthal modes, approaching the Cauchy horizon singularity along timelike directions, approaching the Marolf-Ori (``outflying'') singularity and the studying the fields along the Cauchy horizon.

  9. 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.

  10. Grand rip and grand bang/crunch cosmological singularities

    NASA Astrophysics Data System (ADS)

    Fernández-Jambrina, L.

    2014-09-01

    The present accelerated expansion of the Universe has enriched the list of possible scenarios for its fate, singular or not. In this paper a unifying framework for analyzing such behaviors is proposed, based on generalized power and asymptotic expansions of the barotropic index w, or equivalently of the deceleration parameter q, in terms of the time coordinate. Besides well-known singular and nonsingular future behaviors, other types of strong singularities appear around the phantom divide in flat models, with features similar to those of big rip or big bang/crunch, which we have dubbed "grand rip" and "grand bang/crunch," respectively, since energy density and pressure diverge faster than t-2 in coordinate time. In addition to this, the scale factor does not admit convergent generalized power series around these singularities with a finite number of terms with negative powers.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. Ghost free massive gravity with singular reference metrics

    NASA Astrophysics Data System (ADS)

    Zhang, Hongsheng; Li, Xin-Zhou

    2016-06-01

    An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of the gauge/gravity duality, massive gravity with a singular reference metric is used to study momentum dissipation, which describes the electric and heat conductivity for normal conductors. We demonstrate in detail that the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric is ghost free.

  16. 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.

  17. Local analysis near a folded saddle-node singularity

    NASA Astrophysics Data System (ADS)

    Krupa, Martin; Wechselberger, Martin

    Folded saddle-nodes occur generically in one parameter families of singularly perturbed systems with two slow variables. We show that these folded singularities are the organizing centers for two main delay phenomena in singular perturbation problems: canards and delayed Hopf bifurcations. We combine techniques from geometric singular perturbation theory—the blow-up technique—and from delayed Hopf bifurcation theory—complex time path analysis—to analyze the flow near such folded saddle-nodes. In particular, we show the existence of canards as intersections of stable and unstable slow manifolds. To derive these canard results, we extend the singularly perturbed vector field into the complex domain and study it along elliptic paths. This enables us to extend the invariant slow manifolds beyond points where normal hyperbolicity is lost. Furthermore, we define a way-in/way-out function describing the maximal delay expected for generic solutions passing through a folded saddle-node singularity. Branch points associated with the change from a complex to a real eigenvalue structure in the variational equation along the critical (slow) manifold make our analysis significantly different from the classical delayed Hopf bifurcation analysis where these eigenvalues are complex only.

  18. Germanium Nanocrystals Embedded in Sapphire

    SciTech Connect

    Xu, Q.; Sharp, I.D.; Liao, C.Y.; Yi, D.O.; Ager III, J.W.; Beeman, J.W.; Yu, K.M.; Chrzan, D.C.; Haller, E.E.

    2005-04-15

    {sup 74}Ge nanocrystals are formed in a sapphire matrix by ion implantation followed by damage. Embedded nanocrystals experience large compressive stress relative to bulk, as embedded in sapphire melt very close to the bulk melting point (Tm = 936 C) whereas experience considerably lower stresses. Also, in situ TEM reveals that nanocrystals ion-beam-synthesized nanocrystals embedded in silica are observed to be spherical and measured by Raman spectroscopy of the zone center optical phonon. In contrast, reveals that the nanocrystals are faceted and have a bi-modal size distribution. Notably, the matrix remains crystalline despite the large implantation dose and corresponding thermal annealing. Transmission electron microscopy (TEM) of as-grown samples those embedded in silica exhibit a significant melting point hysteresis around T{sub m}.

  19. Singular Spectrum Analysis With Missing Data

    NASA Astrophysics Data System (ADS)

    Kondrashov, D.; Feliks, Y.; Ghil, M.

    2004-12-01

    A Singular Spectrum Analysis (SSA) with gaps of missing data is presented. SSA is a data-adaptive, non-parametric spectral method based on diagonalizing the lag-covariance matrix of a time series. Using leading oscillatory SSA modes, we iteratively produce estimates of missing data, which are then used to compute a self-consistent lag-covariance matrix. For a univariate record, SSA imputation utilizes only temporal correlations in the data to fill up missing points. For a multivariate record, multi-channel SSA imputation takes advantage of both spatial and temporal correlations. Analyzing the whole available record with the missing points filled, allows for greater accuracy and better significance testing in the spectral analysis. It also provides information on the evolution of the oscillatory modes in the gaps. We use cross-validation to optimize the SSA window width and number of SSA modes to fill the gaps. The algorithm is applied to the extended (A.D. 622--1922) historical records of the low- and high-water levels of the Nile River at Cairo. We fill in the large gaps in the later part of the records (A.D. 1471--1922), and identify statistically significant interannual and interdecadal periodicities. Our analysis suggests that the 7-year periodicity in the records, possibly related to the biblical "Joseph" cycle, is due to North-Atlantic influences. We find that the climate shifts at the beginning and the end of the Medieval Warm Period were fairly abrupt and affected several climatic modes of variability.

  20. 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

  1. A toy MCT model for multiple glass transitions: Double swallow tail singularity

    NASA Astrophysics Data System (ADS)

    Ryzhov, V. N.; Tareyeva, E. E.

    2014-11-01

    We propose a toy model to describe in the frame of Mode Coupling Theory multiple glass transitions. The model is based on the postulated simple form for static structure factor as a sum of two delta-functions. This form makes it possible to solve the MCT equations in almost analytical way. The phase diagram is governed by two swallow tails resulting from two A4 singularities and includes liquid-glass transition and multiple glasses. The diagram has much in common with those of binary and quasibinary systems.

  2. 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.

  3. On the limit cycles of a class of planar singular perturbed differential equations.

    PubMed

    Wu, Yuhai; Zhou, Jingjing

    2014-01-01

    Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. PMID:25143973

  4. On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations

    PubMed Central

    Zhou, Jingjing

    2014-01-01

    Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. PMID:25143973

  5. Singularities and symmetries of nonlinear ordinary and partial differential equations. Final technical report

    SciTech Connect

    Chu, C.K.

    1993-09-01

    Real singularities govern self-focusing singularities and current sheet formation. Complex singularities govern integrable properties, nonintegrable properties, intermittency, and from propagation. This project has studied singularities as both fundamental mathematical objects and as the determining mechanism of crucial physical processes. During the past year, progress was made on: Painleve property and geometry of solvable groups, singularity clustering and psi-lambda series, and current sheet formation in MHD.

  6. 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

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

    PubMed

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

    2016-01-01

    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

  8. 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...

  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. 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. PMID:24843162

  11. Preprocessing and parameterizing bioimpedance spectroscopy measurements by singular value decomposition.

    PubMed

    Nejadgholi, Isar; Caytak, Herschel; Bolic, Miodrag; Batkin, Izmail; Shirmohammadi, Shervin

    2015-05-01

    In several applications of bioimpedance spectroscopy, the measured spectrum is parameterized by being fitted into the Cole equation. However, the extracted Cole parameters seem to be inconsistent from one measurement session to another, which leads to a high standard deviation of extracted parameters. This inconsistency is modeled with a source of random variations added to the voltage measurement carried out in the time domain. These random variations may originate from biological variations that are irrelevant to the evidence that we are investigating. Yet, they affect the voltage measured by using a bioimpedance device based on which magnitude and phase of impedance are calculated.By means of simulated data, we showed that Cole parameters are highly affected by this type of variation. We further showed that singular value decomposition (SVD) is an effective tool for parameterizing bioimpedance measurements, which results in more consistent parameters than Cole parameters. We propose to apply SVD as a preprocessing method to reconstruct denoised bioimpedance measurements. In order to evaluate the method, we calculated the relative difference between parameters extracted from noisy and clean simulated bioimpedance spectra. Both mean and standard deviation of this relative difference are shown to effectively decrease when Cole parameters are extracted from preprocessed data in comparison to being extracted from raw measurements.We evaluated the performance of the proposed method in distinguishing three arm positions, for a set of experiments including eight subjects. It is shown that Cole parameters of different positions are not distinguishable when extracted from raw measurements. However, one arm position can be distinguished based on SVD scores. Moreover, all three positions are shown to be distinguished by two parameters, R0/R∞ and Fc, when Cole parameters are extracted from preprocessed measurements. These results suggest that SVD could be considered as an

  12. An Expression Refinement Process Ensures Singular Odorant Receptor Gene Choice.

    PubMed

    Abdus-Saboor, Ishmail; Al Nufal, Mohammed J; Agha, Maha V; Ruinart de Brimont, Marion; Fleischmann, Alexander; Shykind, Benjamin M

    2016-04-25

    Odorant receptor (OR) gene choice in mammals is a paradigmatic example of monogenic and monoallelic transcriptional selection, in which each olfactory sensory neuron (OSN) chooses to express one OR allele from over 1,000 encoded in the genome [1-3]. This process, critical for generation of the circuit from nose to brain [4-6], is thought to occur in two steps: a slow initial phase that randomly activates a single OR allele, followed by a rapid feedback that halts subsequent expression [7-14]. Inherent in this model is a finite failure rate wherein multiple OR alleles may be activated prior to feedback suppression [15, 16]. Confronted with more than one receptor, the neuron would need to activate a refinement mechanism to eliminate multigenic OR expression and resolve unique neuronal identity [16], critical to the generation of the circuit from nose to olfactory bulb. Here we used a genetic approach in mice to reveal a new facet of OR regulation that corrects adventitious activation of multiple OR alleles, restoring monogenic OR expression and unique neuronal identity. Using the tetM71tg model system, in which the M71 OR is expressed in >95% of mature OSNs and potently suppresses the expression of the endogenous OR repertoire [10], we provide clear evidence of a post-selection refinement (PSR) process that winnows down the number of ORs. We further demonstrate that PSR efficiency is linked to OR expression level, suggesting an underlying competitive process and shedding light on OR gene switching and the fundamental mechanism of singular OR choice. PMID:27040780

  13. Focal plane internal energy flows of singular beams in astigmatically aberrated low numerical aperture systems.

    PubMed

    Bahl, Monika; Senthilkumaran, P

    2014-09-01

    Singular beams have circulating energy components. When such beams are focused by low numerical aperture systems suffering from astigmatic aberration, these circulating energy components get modified. The phase gradient introduced by this type of aberration splits the higher charge vortices. The dependence of the charge, the aberration coefficient, and the size of the aperture on the nature of the splitting process are reported in this paper. The transverse components of the Poynting vector fields that can be derived from the phase gradient vector field distributions are further decomposed into solenoidal and irrotational components using the Helmholtz-Hodge decomposition method. The solenoidal components relate to the orbital angular momentum of the beams, and the irrotational components are useful in the transport of intensity equations for phase retrieval.

  14. Reprint of : Regular and singular Fermi liquid in triple quantum dots: Coherent transport studies

    NASA Astrophysics Data System (ADS)

    Tooski, S. B.; Ramšak, A.; Bułka, B. R.

    2016-08-01

    A system of three coupled quantum dots in a triangular geometry (TQD) with electron-electron interaction and symmetrically coupled to two leads is analyzed with respect to the electron transport by means of the numerical renormalization group. Varying gate potentials this system exhibits extremely rich range of regimes with different many-electron states with various local spin orderings. It is demonstrated how the Luttinger phase changes in a controlled manner which then via the Friedel sum rule formula exactly reproduces the conductance through the TQD system. The analysis of the uncoupled TQD molecule from the leads gives a reliable qualitative understanding of various relevant regimes and an insight into the phase diagram with the regular Fermi liquid and singular-Fermi liquid phases.

  15. 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.

  16. 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).

  17. Codimension-3 singularities and Yukawa couplings in F-theory

    NASA Astrophysics Data System (ADS)

    Hayashi, Hirotaka; Kawano, Teruhiko; Tatar, Radu; Watari, Taizan

    2009-12-01

    F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic-F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.

  18. On the Backward Stability of the Schwarzschild Black Hole Singularity

    NASA Astrophysics Data System (ADS)

    Fournodavlos, Grigorios

    2016-08-01

    We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface {Σ_0} in the interior of the black hole region, tangent to the singular hypersurface {{r = 0}} at a single sphere, we study the problem of perturbing the Schwarzschild data on {Σ_0} and solving the Einstein vacuum equations backwards in time. We obtain a local backwards well-posedness result for small perturbations lying in certain weighted Sobolev spaces. No symmetry assumptions are imposed. The perturbed spacetimes all have a singularity at a "collapsed" sphere on {Σ_0}, where the leading asymptotics of the curvature and the metric match those of their Schwarzschild counterparts to a suitably high order. As in the Schwarzschild backward evolution, the pinched initial hypersurface {Σ_0} `opens up' instantly, becoming a regular spacelike (cylindrical) hypersurface. This result thus yields classes of examples of non-symmetric vacuum spacetimes, evolving forward-in-time from regular initial data, which form a Schwarzschild type singularity at a collapsed sphere. We rely on a precise asymptotic analysis of the Schwarzschild geometry near the singularity which turns out to be at the threshold that our energy methods can handle.

  19. 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.

  20. Dynamics of learning near singularities in radial basis function networks.

    PubMed

    Wei, Haikun; Amari, Shun-Ichi

    2008-09-01

    The radial basis function (RBF) networks are one of the most widely used models for function approximation in the regression problem. In the learning paradigm, the best approximation is recursively or iteratively searched for based on observed data (teacher signals). One encounters difficulties in such a process when two component basis functions become identical, or when the magnitude of one component becomes null. In this case, the number of the components reduces by one, and then the reduced component recovers as the learning process proceeds further, provided such a component is necessary for the best approximation. Strange behaviors, especially the plateau phenomena, have been observed in dynamics of learning when such reduction occurs. There exist singularities in the space of parameters, and the above reduction takes place at the singular regions. This paper focuses on a detailed analysis of the dynamical behaviors of learning near the overlap and elimination singularities in RBF networks, based on the averaged learning equation that is applicable to both on-line and batch mode learning. We analyze the stability on the overlap singularity by solving the eigenvalues of the Hessian explicitly. Based on the stability analysis, we plot the analytical dynamic vector fields near the singularity, which are then compared to those real trajectories obtained by a numeric method. We also confirm the existence of the plateaus in both batch and on-line learning by simulation.

  1. Singularity detection by wavelet approach: application to electrocardiogram signal

    NASA Astrophysics Data System (ADS)

    Jalil, Bushra; Beya, Ouadi; Fauvet, Eric; Laligant, Olivier

    2010-01-01

    In signal processing, the region of abrupt changes contains the most of the useful information about the nature of the signal. The region or the points where these changes occurred are often termed as singular point or singular region. The singularity is considered to be an important character of the signal, as it refers to the discontinuity and interruption present in the signal and the main purpose of the detection of such singular point is to identify the existence, location and size of those singularities. Electrocardiogram (ECG) signal is used to analyze the cardiovascular activity in the human body. However the presence of noise due to several reasons limits the doctor's decision and prevents accurate identification of different pathologies. In this work we attempt to analyze the ECG signal with energy based approach and some heuristic methods to segment and identify different signatures inside the signal. ECG signal has been initially denoised by empirical wavelet shrinkage approach based on Steins Unbiased Risk Estimate (SURE). At the second stage, the ECG signal has been analyzed by Mallat approach based on modulus maximas and Lipschitz exponent computation. The results from both approaches has been discussed and important aspects has been highlighted. In order to evaluate the algorithm, the analysis has been done on MIT-BIH Arrhythmia database; a set of ECG data records sampled at a rate of 360 Hz with 11 bit resolution over a 10mv range. The results have been examined and approved by medical doctors.

  2. Volatile snowlines in embedded disks around low-mass protostars

    NASA Astrophysics Data System (ADS)

    Harsono, D.; Bruderer, S.; van Dishoeck, E. F.

    2015-10-01

    Context. Models of the young solar nebula assume a hot initial disk in which most volatiles are in the gas phase. Water emission arising from within 50 AU radius has been detected around low-mass embedded young stellar objects. The question remains whether an actively accreting disk is warm enough to have gas-phase water up to 50 AU radius. No detailed studies have yet been performed on the extent of snowlines in an accreting disk embedded in a dense envelope (stage 0). Aims: We aim to quantify the location of gas-phase volatiles in the inner envelope and disk system for an actively accreting embedded disk. Methods: Two-dimensional physical and radiative transfer models were used to calculate the temperature structure of embedded protostellar systems. Heating due to viscous accretion was added through the diffusion approximation. Gas and ice abundances of H2O, CO2, and CO were calculated using the density-dependent thermal desorption formulation. Results: The midplane water snowline increases from 3 to ~55 AU for accretion rates through the disk onto the star between 10-9-10-4M⊙ yr-1. CO2 can remain in the solid phase within the disk for Ṁ ≤ 10-5M⊙ yr-1 down to ~20 AU. Most of the CO is in the gas phase within an actively accreting disk independent of disk properties and accretion rate. The predicted optically thin water isotopolog emission is consistent with the detected H218O emission toward the stage 0 embedded young stellar objects, originating from both the disk and the warm inner envelope (hot core). An accreting embedded disk can only account for water emission arising from R< 50 AU, however, and the extent rapidly decreases for Ṁ ≤ 10-5M⊙ yr-1. Thus, the radial extent of the emission can be measured with future ALMA observations and compared to this 50 AU limit. Conclusions: Volatiles such as H2O, CO2, CO, and the associated complex organics sublimate out to 50 AU in the midplane of young disks and, thus, can reset the chemical content

  3. Consequences of embedding Ti4+ 3d0 centers in Pr0.50Ca0.50MnO3 : Phase competition in Pr0.50Ca0.50Mn1-xTixO3

    NASA Astrophysics Data System (ADS)

    García-Muñoz, J. L.; Frontera, C.; Beran, P.; Bellido, N.; Hernández-Velasco, J.; Ritter, C.

    2010-01-01

    We have studied the structural and magnetic phase coexistence/competition derived from the partial random substitution of 3d0 nonmagnetic Ti4+ ions for Mn in Pr0.50Ca0.50MnO3 , and their evolution with the doping level in Pr0.50Ca0.50Mn1-xTixO3 ( x=0 , 0.01, 0.03, and 0.05) manganites. Combining high-resolution synchrotron, neutron powder-diffraction, and muon techniques we describe with great detail the coexistence of two different structural phases below ≈240K (charge-order transition temperature, TCO ) with different cell distortion, antiferromagnetic order, and strain characteristics. The evolution of all these features with Ti substitution level is thoroughly described. Ti4+ (3d0) ions do not favor the stabilization of ferromagnetic/metallic (FM/M) islands/regions in the antiferromagnetic/insulating (AFM/I) orbital-ordered matrix. The absence of short- and long-range ferromagnetism in zero field has been confirmed by different techniques. The proportion of microdomains exhibiting pseudo-(CE)-type magnetic order (CE: charge exchange) increases with the Ti content at expenses of the CE-type regions. Differences in the stability of competing phases against magnetic field have been found by neutron-diffraction measurements under application of external fields. The phase coexistence exhibits strong anisotropic strain effects that have been thoroughly analyzed as a function of the Ti content x . We have found very remarkable changes in the strain characteristics of the AFM segregated phases on going from 1% to 5% Ti. Large anisotropic strains develop mainly in the minority phase of the material. The magnitude of strains is discussed in comparison with anisotropic strain values recently determined in the case of substitutions (such as Co) that favor FM/M domains.

  4. Perturbative analysis of spectral singularities and their optical realizations

    NASA Astrophysics Data System (ADS)

    Mostafazadeh, Ali; Rostamzadeh, Saber

    2012-08-01

    We develop a perturbative method of computing spectral singularities of a Schrödinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as antilasing. We use our general results to establish the exactness of the nth-order perturbation theory for an arbitrary complex potential consisting of n delta functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.

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

    PubMed

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

    2015-01-01

    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.

  6. Cosmological singularities in Born-Infeld determinantal gravity

    NASA Astrophysics Data System (ADS)

    Bouhmadi-López, Mariam; Chen, Che-Yu; Chen, Pisin

    2014-12-01

    The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the big bang singularity. This theory is formulated on the Weitzenböck space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity free for a certain region of the parameter space in which the divergence of the Hubble rate in the high-energy regime is substituted by a de Sitter stage or a bounce in a Friedmann-Lemaître-Robertson-Walker universe, cosmological singularities—such as a big rip, big bang, big freeze, and sudden singularities—can emerge in other regions of the configuration space of the theory. We also show that all these singular events exist even though the universe is filled with a perfect fluid with a constant equation of state.

  7. Singularity resolution in cosmologies using AdS/CFT

    NASA Astrophysics Data System (ADS)

    Ghosh, A.

    2014-03-01

    Singularities in general relativity are expected to be cured by a quantum theory of gravity. String theory is a prospective candidate for quantum gravity and holographic correspondences like AdS/CFT, that arise from string theory, might shed some light into the nature of singularities. While the theory of gravity might not be tractable near the singularity, the corresponding field theory might be well-behaved. We have come up with a model of cosmology, where curvatures become large at some time, thus, resembling a big crunch, but whose field theory dual remains well-behaved. Our analysis in the field theory indicates that we have a bouncing cosmology with a thermal distribution of radiation, and a possible formation of a small black hole after the bounce.

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

    PubMed

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

    2015-01-01

    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

  9. Analytic evolution of singular distribution amplitudes in QCD

    NASA Astrophysics Data System (ADS)

    Radyushkin, A. V.; Tandogan, A.

    2014-04-01

    We describe a method of analytic evolution of distribution amplitudes (DAs) that have singularities, such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA and antisymmetric flat DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.

  10. Analytic Evolution of Singular Distribution Amplitudes in QCD

    SciTech Connect

    Radyushkin, Anatoly V.; Tandogan Kunkel, Asli

    2014-03-01

    We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, anti-symmetric at DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.

  11. 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.

  12. 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

  13. On the regularizability of the big bang singularity

    NASA Astrophysics Data System (ADS)

    Belbruno, Edward

    2013-01-01

    The singularity for the big bang state can be represented using the generalized anisotropic Friedmann equation, resulting in a system of differential equations in a central force field. We study the regularizability of this singularity as a function of a parameter, the equation of state, w. We prove that for w > 1 it is regularizable only for w satisfying relative prime number conditions, and for w ≤ 1 it can always be regularized. This is done by using a McGehee transformation, usually applied in the three and four-body problems. This transformation blows up the singularity into an invariant manifold. The relationship of this result to other cosmological models is briefly discussed.

  14. Statistical Analysis of the Ionosphere based on Singular Value Decomposition

    NASA Astrophysics Data System (ADS)

    Demir, Uygar; Arikan, Feza; Necat Deviren, M.; Toker, Cenk

    2016-07-01

    Ionosphere is made up of a spatio-temporally varying trend structure and secondary variations due to solar, geomagnetic, gravitational and seismic activities. Hence, it is important to monitor the ionosphere and acquire up-to-date information about its state in order both to better understand the physical phenomena that cause the variability and also to predict the effect of the ionosphere on HF and satellite communications, and satellite-based positioning systems. To charaterise the behaviour of the ionosphere, we propose to apply Singular Value Decomposition (SVD) to Total Electron Content (TEC) maps obtained from the TNPGN-Active (Turkish National Permanent GPS Network) CORS network. TNPGN-Active network consists of 146 GNSS receivers spread over Turkey. IONOLAB-TEC values estimated from each station are spatio-temporally interpolated using a Universal Kriging based algorithm with linear trend, namely IONOLAB-MAP, with very high spatial resolution. It is observed that the dominant singular value of TEC maps is an indicator of the trend structure of the ionosphere. The diurnal, seasonal and annual variability of the most dominant value is the representation of solar effect on ionosphere in midlatitude range. Secondary and smaller singular values are indicators of secondary variation which can have significance especially during geomagnetic storms or seismic disturbances. The dominant singular values are related to the physical basis vectors where ionosphere can be fully reconstructed using these vectors. Therefore, the proposed method can be used both for the monitoring of the current state of a region and also for the prediction and tracking of future states of ionosphere using singular values and singular basis vectors. This study is supported by by TUBITAK 115E915 and Joint TUBITAK 114E092 and AS CR14/001 projects.

  15. A new analytic solution representing anisotropic stellar objects in embedding class I

    NASA Astrophysics Data System (ADS)

    Singh, Ksh. Newton; Pant, Neeraj

    2016-05-01

    A new type of embedding class-I representing anisotropic fluid distribution is presented. The new solution is free from singularity and also satisfies all physical criteria. It also satisfies all energy conditions such as SEC, WEC, NEC and DEC. The solution so obtained is used to optimize mass and radius of some well compact stars candidates like, Her X-1, SAX J1808.4-3658, RX J1856.5-3754, PSR J1614-2230 and PSR J0348+0432.

  16. The Force Singularity for Partially Immersed Parallel Plates

    NASA Astrophysics Data System (ADS)

    Bhatnagar, Rajat; Finn, Robert

    2016-05-01

    In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine some unusual details of the exotic behavior that can occur at the singular configuration separating infinite rise from infinite descent of the fluid between the plates, as the plates approach each other. In connection with this singular behavior, we present also some new estimates on meniscus height details.

  17. Asymptotics of action variables near semi-toric singularities

    NASA Astrophysics Data System (ADS)

    Wacheux, Christophe

    2015-12-01

    The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does not apply. In particular, the affine structure of the image of the moment map around has non-trivial monodromy. In this article, we establish that the singular behavior and the multi-valuedness of the Action integrals is given by a complex logarithm. This extends a previous result by San Vũ Ngọc to any dimension. We also calculate the monodromy matrix for these systems.

  18. 18. Simulations of Generic Singularities in Harmonic Coordinates

    NASA Astrophysics Data System (ADS)

    Garfinkle, David

    This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such coordinates, the terms in Einstein's equations with the highest number of derivatives take a form similar to that of the wave equation. The application is an exploration of the generic approach to the singularity for this type of matter. The preliminary results indicate that the dynamics as one approaches the singularity is locally the dynamics of the Kasner spacetimes.

  19. Velocity Dominated Singularities in the Cheese Slice Universe

    NASA Astrophysics Data System (ADS)

    Giang, Dan; Dyer, Charles C.

    We investigate the properties of space-times resulting from matching together exact solutions using the Darmois matching conditions. In particular, we focus on the asymptotically velocity-term dominated property (AVTD). We propose a criterion that can be used to test if a space-time constructed from a matching can be considered AVTD. Using the "cheese slice" universe as an example, we show that a space-time constructed from a such a matching can inherit the AVTD property from the original space-times. Furthermore the singularity resulting from this particular matching is an AVTD singularity.

  20. The effect of singular potentials on the harmonic oscillator

    SciTech Connect

    Filgueiras, C.; Silva, E.O.; Oliveira, W.; Moraes, F.

    2010-11-15

    We address the problem of a quantum particle moving under interactions presenting singularities. The self-adjoint extension approach is used to guarantee that the Hamiltonian is self-adjoint and to fix the choice of boundary conditions. We specifically look at the harmonic oscillator added of either a {delta}-function potential or a Coulomb potential (which is singular at the origin). The results are applied to Landau levels in the presence of a topological defect, the Calogero model and to the quantum motion on the noncommutative plane.

  1. Photonic analog of a van Hove singularity in metamaterials

    NASA Astrophysics Data System (ADS)

    Cortes, Cristian L.; Jacob, Zubin

    2013-07-01

    We introduce the photonic analog of electronic van Hove singularities (VHS) in artificial media (metamaterials) with hyperbolic dispersion. Unlike photonic and electronic crystals, the VHS in metamaterials are unrelated to the underlying periodicity and occur due to slow-light modes in the structure. We show that the VHS characteristics are manifested in the near-field local density of optical states in spite of the losses, dispersion, and finite unit-cell size of the hyperbolic metamaterial. Finally, we show that this work should lead to quantum, thermal, nanolasing, and biosensing applications of van Hove singularities in hyperbolic metamaterials achievable by current fabrication technology.

  2. Approximate analytic solutions for singular non-linear oscillators

    NASA Technical Reports Server (NTRS)

    Bota, K. B.; Mickens, R. E.

    1984-01-01

    Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.

  3. Design of a singularity-free articulated arm subassembly

    SciTech Connect

    Remis, S.J.; Stanisic, M.M. . Aerospace and Mechanical Engineering Dept.)

    1993-12-01

    Adding a redundant degree of freedom to the shoulder pointing system complex of an articulated arm subassembly makes it possible to achieve a maximal workspace that is free of singularities. This paper derives a functional constraint between three of the four joints of this new type of arm, achieving a singularity-free workspace encompassing the entire reachable volume between the maximal- and minimal-reach surfaces. The large volume of dexterous workspace is verified by animation of the resulting arm design. Graphical results from the animation are presented comparing the dexterous workspace of this new arm to that of the standard nonredundant articulated arm subassembly such as found in the Puma manipulator.

  4. Surface singularities in Eddington-inspired Born-Infeld gravity.

    PubMed

    Pani, Paolo; Sotiriou, Thomas P

    2012-12-21

    Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubt on its viability.

  5. Surface singularities in Eddington-inspired Born-Infeld gravity.

    PubMed

    Pani, Paolo; Sotiriou, Thomas P

    2012-12-21

    Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubt on its viability. PMID:23368444

  6. 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

  7. A Connection between Singular Stochastic Control and Optimal Stopping

    SciTech Connect

    Espen Benth, Fred Reikvam, Kristin

    2003-12-15

    We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.

  8. Lidar signal de-noising by singular value decomposition

    NASA Astrophysics Data System (ADS)

    Wang, Huanxue; Liu, Jianguo; Zhang, Tianshu

    2014-11-01

    Signal de-noising remains an important problem in lidar signal processing. This paper presents a de-noising method based on singular value decomposition. Experimental results on lidar simulated signal and real signal show that the proposed algorithm not only improves the signal-to-noise ratio effectively, but also preserves more detail information.

  9. Wigner Measure Propagation and Conical Singularity for General Initial Data

    NASA Astrophysics Data System (ADS)

    Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline

    2013-07-01

    We study the evolution of Wigner measures of a family of solutions of a Schrödinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.

  10. On Resolutions of Cosmological Singularities in Higher-Spin Gravity

    NASA Astrophysics Data System (ADS)

    Burrington, Benjamin; Pando Zayas, Leopoldo; Rombes, Nicholas

    2014-03-01

    Gravity in three dimensions is simpler than in four, due to the lack of gravitational waves, and can be recast as a Chern-Simons theory. In this context, it is straightforward to generalize Einstein's gravity, with or without cosmological constant, by changing the gauge group. Using this, we study the resolution of certain cosmological singularities, and extend the singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the case of gravity coupled to a spin-4 field realized as Chern-Simons theory with gauge group SL (4 , C) . We show the existence of gauge transformations that do not change the holonomy of the Chern-Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-N field when described by Chern-Simons with gauge group SL (N , C) . This work was supported by the DOE under grant DE-FG02-95ER40899, a research grant from Troy University, and the Honors Summer Fellowship at the University of Michigan.

  11. Faddeev-Jackiw quantization of non-autonomous singular systems

    NASA Astrophysics Data System (ADS)

    Belhadi, Zahir; Bérard, Alain; Mohrbach, Hervé

    2016-10-01

    We extend the quantization à la Faddeev-Jackiw for non-autonomous singular systems. This leads to a generalization of the Schrödinger equation for those systems. The method is exemplified by the quantization of the damped harmonic oscillator and the relativistic particle in an external electromagnetic field.

  12. Non-singular dislocation loops in gradient elasticity

    NASA Astrophysics Data System (ADS)

    Lazar, Markus

    2012-04-01

    Using gradient elasticity, we give in this Letter the non-singular fields produced by arbitrary dislocation loops in isotropic media. We present the ‘modified’ Mura, Peach-Koehler and Burgers formulae in the framework of gradient elasticity theory.

  13. The singularity of being: Lacan and the immortal within.

    PubMed

    Ruti, Mari

    2010-12-01

    Drawing on the work of Eric Santner, Slavoj Žižek, and Alenka Zupančič, this paper constructs a theory of subjective singularity from a Lacanian perspective. It argues that, unlike the "subject" (who comes into existence as a result of symbolic prohibition), or the "person" (who is aligned with the narcissistic conceits of the imaginary), the singular self emerges in response to a galvanizing directive arising from the real. This directive summons the individual to a "character" beyond his or her social and intersubjective investments. Consequently, singularity expresses the individual's nonnegotiable distinctiveness, eccentricity, or idiosyncrasy at the same time as it prevents both symbolic and imaginary closure. It opens to layers of rebelliousness that indicate that there are components of human life that exceed the realm of normative sociality. Indeed, insofar as singularity articulates something about the "undead" pulse of jouissance, it connects the individual to a paradoxical kind of immortality. This does not mean that the individual will not die, but rather that he or she is capable of "transcendent" experiences, such as heightened states of creativity, that (always momentarily) reach "outside" the parameters of mortal life. Such experiences allow the individual to feel "real" in ways that fend off symbolic abduction and psychic death.

  14. Pulsar Magnetospheres: Variation Principle, Singularities, and Estimate of Power

    NASA Astrophysics Data System (ADS)

    Gruzinov, Andrei

    2006-08-01

    We formulate a variation principle for the force-free magnetosphere of an inclined pulsar: E+Ω b.dot M (where E and M are electromagnetic energy and angular momentum and Ω is the angular velocity of the star) is stationary under isotopological variations of the magnetic field and arbitrary variations of the electric field. The variation principle gives the reason for the existence and proves the local stability of singular current layers along magnetic separatrices. Magnetic field lines of inclined pulsar magnetospheres lie on magnetic surfaces and do have magnetic separatrices. In the framework of the isotopological variation principle, inclined magnetospheres are expected to be simple deformations of the axisymmetric pulsar magnetosphere. A singular line should exist on the light cylinder, where the inner separatrix terminates and the outer separatrix emanates. The electromagnetic field should have an inverse square root singularity near the singular line inside the inner magnetic separatrix. The large-distance asymptotic solution is calculated and used to estimate the pulsar power, L~c-3μ2Ω4 for spin-dipole inclinations <~30°.

  15. Optimal singular control with applications to trajectory optimization

    NASA Technical Reports Server (NTRS)

    Vinh, N. X.

    1979-01-01

    The switching conditions are expressed explicitly in terms of the derivatives of the Hamiltonians at the two ends of the switching. A new expression of the Kelley-Contensou necessary condition for the optimality of a singular arc is given. Some examples illustrating the application of the theory are presented.

  16. Quantum jump from singularity to outside of black hole

    NASA Astrophysics Data System (ADS)

    Dündar, Furkan Semih; Hajian, Kamal

    2016-02-01

    Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

  17. Singular perturbations in shape optimization for the Dirichlet Laplacian

    NASA Astrophysics Data System (ADS)

    Nazarov, Serguei A.; Sokolowski, Jan

    2005-04-01

    A shape optimization problem is considered for the Dirichlet Laplacian. Asymptotic analysis is used in order to characterise the optimal shapes which are finally given by a singular perturbation of the smooth initial domain. To cite this article: S.A. Nazarov, J. Sokolowski, C. R. Mecanique 333 (2005).

  18. Print to Paint: Breaking Away from Singular Images

    ERIC Educational Resources Information Center

    Alexander, Kristi

    2010-01-01

    Each fall, the author presents a printmaking unit, starting with simple techniques such as rubbings, stamping and stenciling. In this article, the author describes a linoleum printmaking lesson wherein students are challenged to break away from singular images of peace signs and initials, and create illustrative plates that could communicate a…

  19. Formation and morphological transformation of polarization singularities: hunting the monstar

    NASA Astrophysics Data System (ADS)

    Kumar, Vijay; Philip, Geo M.; Viswanathan, Nirmal K.

    2013-04-01

    The theoretical formalism and experimental measurements to form and transform between the three morphologies of the polarization singular patterns—star, lemon and monstar—are presented here. The monstar is statistically rare in isotropic random fields but its controllable realization is achieved by tuning the field anisotropy in three-beam interference.

  20. Singular Behaviour of the Electrodynamic Fields of an Oscillating Dipole

    ERIC Educational Resources Information Center

    Leung, P. T.

    2008-01-01

    The singularity of the exact electromagnetic fields is derived to include the "source terms" for harmonically oscillating electric (and magnetic) dipoles, so that the fields will be consistent with the full Maxwell equations with a source. It is shown explicitly, as somewhat expected, that the same [delta]-function terms for the case of static…

  1. Helical-mode magnetostatic resonances in small ferrite particles and singular metamaterials.

    PubMed

    Kamenetskii, E O

    2010-12-01

    Small ferrite-disk particles with magnetostatic (magneto-dipole) oscillations are characterized by the topological-phase states-the vortex states. In a recently published paper (Kamenetskii et al 2010 Phys. Rev. A 81 053823), it was shown that such magnetic vortices act as traps, providing purely subwavelength confinement of electromagnetic fields. The symmetry properties of magnetostatic-vortex ferrite disks allow one to propose new-type subwavelength microwave structures. In this paper it is demonstrated that the unique topological properties of the fields in a ferrite disk are intimately related to the symmetry breaking effects of magnetostatic oscillations. This analysis is based on postulates about a physical meaning of the magnetostatic-potential function ψ(r, t) as a complex scalar wavefunction, which presumes a long-range phase coherence in magnetic dipole-dipole interactions. The proper solutions are found based on an analysis of magnetostatic-wave propagation in a helical coordinate system. It is shown that while a composition of two helical waves may acquire a geometrical phase over-running of 2π during a period, every separate helical wave has a dynamical phase over-running of π and so behaves as a double-valued function. This results in the appearance of helical-mode magnetostatic resonances in quasi-2D ferrite disks. The solutions give magnetostatic-wave power-flow-density vortices with cores at the disk center and azimuthally running waves of magnetization. The near fields of magnetostatic-vortex ferrite-disk particles are characterized by space-time symmetry violation. For incident electromagnetic waves, such particles, with sizes much less than the free-space electromagnetic wavelength, appear as local singular regions. From the properties of a composition of magnetostatic-vortex ferrite-disk particles, one may propose novel metamaterials-singular metamaterials. PMID:21406763

  2. Characterization of peak flow events with local singularity method

    NASA Astrophysics Data System (ADS)

    Cheng, Q.; Li, L.; Wang, L.

    2009-07-01

    Three methods, return period, power-law frequency plot (concentration-area) and local singularity index, are introduced in the paper for characterizing peak flow events from river flow data for the past 100 years from 1900 to 2000 recorded at 25 selected gauging stations on rivers in the Oak Ridges Moraine (ORM) area, Canada. First a traditional method, return period, was applied to the maximum annual river flow data. Whereas the Pearson III distribution generally fits the values, a power-law frequency plot (C-A) on the basis of self-similarity principle provides an effective mean for distinguishing "extremely" large flow events from the regular flow events. While the latter show a power-law distribution, about 10 large flow events manifest departure from the power-law distribution and these flow events can be classified into a separate group most of which are related to flood events. It is shown that the relation between the average water releases over a time period after flow peak and the time duration may follow a power-law distribution. The exponent of the power-law or singularity index estimated from this power-law relation may be used to characterize non-linearity of peak flow recessions. Viewing large peak flow events or floods as singular processes can anticipate the application of power-law models not only for characterizing the frequency distribution of peak flow events, for example, power-law relation between the number and size of floods, but also for describing local singularity of processes such as power-law relation between the amount of water released versus releasing time. With the introduction and validation of singularity of peak flow events, alternative power-law models can be used to depict the recession property as well as other types of non-linear properties.

  3. Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

    NASA Astrophysics Data System (ADS)

    Stuchlík, Z.; Pugliese, D.; Schee, J.; Kučáková, H.

    2015-09-01

    We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.

  4. An Embedded Reconfigurable Logic Module

    NASA Technical Reports Server (NTRS)

    Tucker, Jerry H.; Klenke, Robert H.; Shams, Qamar A. (Technical Monitor)

    2002-01-01

    A Miniature Embedded Reconfigurable Computer and Logic (MERCAL) module has been developed and verified. MERCAL was designed to be a general-purpose, universal module that that can provide significant hardware and software resources to meet the requirements of many of today's complex embedded applications. This is accomplished in the MERCAL module by combining a sub credit card size PC in a DIMM form factor with a XILINX Spartan I1 FPGA. The PC has the ability to download program files to the FPGA to configure it for different hardware functions and to transfer data to and from the FPGA via the PC's ISA bus during run time. The MERCAL module combines, in a compact package, the computational power of a 133 MHz PC with up to 150,000 gate equivalents of digital logic that can be reconfigured by software. The general architecture and functionality of the MERCAL hardware and system software are described.

  5. The embedded operating system project

    NASA Technical Reports Server (NTRS)

    Campbell, R. H.

    1984-01-01

    This progress report describes research towards the design and construction of embedded operating systems for real-time advanced aerospace applications. The applications concerned require reliable operating system support that must accommodate networks of computers. The report addresses the problems of constructing such operating systems, the communications media, reconfiguration, consistency and recovery in a distributed system, and the issues of realtime processing. A discussion is included on suitable theoretical foundations for the use of atomic actions to support fault tolerance and data consistency in real-time object-based systems. In particular, this report addresses: atomic actions, fault tolerance, operating system structure, program development, reliability and availability, and networking issues. This document reports the status of various experiments designed and conducted to investigate embedded operating system design issues.

  6. The Friedmann-Lemaître-Robertson-Walker Big Bang Singularities are Well Behaved

    NASA Astrophysics Data System (ADS)

    Stoica, Ovidiu Cristinel

    2016-01-01

    We show that the Big Bang singularity of the Friedmann-Lemaître-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.

  7. Singularities, trapped sets, and cosmic censorship in asymptotically flat space-times

    SciTech Connect

    Krolak, A. ); Rudnicki, W. )

    1993-01-01

    We show that space-time is future asymptotically predictable from a regular partial Cauchy provided that singularities are causally preceded by trapped sets. Future asymptotic predictability is a formal statement of cosmic censorship in asymptotically flat space-times. A regular partial Cauchy surface means that singularities in gravitational collapse can arise only from regular initial data. Our result confirms a supposition by Hawking that singularities forced by singularity theorems cannot be naked.

  8. COMB: Compact embedded object simulations

    NASA Astrophysics Data System (ADS)

    McEwen, Jason D.

    2016-06-01

    COMB supports the simulation on the sphere of compact objects embedded in a stochastic background process of specified power spectrum. Support is provided to add additional white noise and convolve with beam functions. Functionality to support functions defined on the sphere is provided by the S2 code (ascl:1606.008); HEALPix (ascl:1107.018) and CFITSIO (ascl:1010.001) are also required.

  9. Zero-distortion lossless data embedding

    NASA Astrophysics Data System (ADS)

    Nagaraj, Nithin; Mullick, Rakesh

    2004-05-01

    All known methods of lossless or reversible data embedding that exist today suffer from two major disadvantages: 1) The embedded image suffers from distortion, however small it may be by the very process of embedding and 2) The requirement of a special parser (decoder), which is necessary for the client to remove the embedded data in order to obtain the original image (lossless). We propose a novel lossless data embedding method where both these disadvantages are circumvented. Zero-distortion lossless data embedding (ZeroD-LDE) claims 'zero-distortion' of the embedded image for all viewing purposes and further maintaining that clients without any specialized parser can still recover the original image losslessly but would not have direct access to the embedded data. The fact that not all gray levels are used by most images is exploited to embed data by selective lossless compression of run-lengths of zeros (or any compressible pattern). Contiguous runs of zeros are changed such that the leading zero is made equal to the maximum original intensity plus the run-length and the succeeding zeros are converted to the embedded data (plus maximum original intensity) thus achieving extremely high embedding capacities. This way, the histograms of the host-data and the embedded data do not overlap and hence we can obtain zero-distortion by using the window-level setting of standard DICOM viewers. The embedded image is thus not only DICOM compatible but also zero-distortion visually and requires no clinical validation.

  10. Embedded Services in Chinese Academic Libraries

    ERIC Educational Resources Information Center

    Si, Li; Xing, Wenming; Zhou, Limei; Liu, Sha

    2012-01-01

    Embedded librarianship service describes the practice of librarians integrating actively into the user's environment, rather than remaining in the library to await requests for service. This paper examines the concept of embedded service in the recent literature, within the past 5 years. It reports on a survey of embedded service in Chinese…

  11. Density-orbital embedding theory

    SciTech Connect

    Gritsenko, O. V.; Visscher, L.

    2010-09-15

    In the article density-orbital embedding (DOE) theory is proposed. DOE is based on the concept of density orbital (DO), which is a generalization of the square root of the density for real functions and fractional electron numbers. The basic feature of DOE is the representation of the total supermolecular density {rho}{sub s} as the square of the sum of the DO {phi}{sub a}, which represents the active subsystem A and the square root of the frozen density {rho}{sub f} of the environment F. The correct {rho}{sub s} is obtained with {phi}{sub a} being negative in the regions in which {rho}{sub f} might exceed {rho}{sub s}. This makes it possible to obtain the correct {rho}{sub s} with a broad range of the input frozen densities {rho}{sub f} so that DOE resolves the problem of the frozen-density admissibility of the current frozen-density embedding theory. The DOE Euler equation for the DO {phi}{sub a} is derived with the characteristic embedding potential representing the effect of the environment. The DO square {phi}{sub a}{sup 2} is determined from the orbitals of the effective Kohn-Sham (KS) system. Self-consistent solution of the corresponding one-electron KS equations yields not only {phi}{sub a}{sup 2}, but also the DO {phi}{sub a} itself.

  12. Liquid-Embedded Elastomer Electronics

    NASA Astrophysics Data System (ADS)

    Kramer, Rebecca; Majidi, Carmel; Park, Yong-Lae; Paik, Jamie; Wood, Robert

    2012-02-01

    Hyperelastic sensors are fabricated by embedding a silicone rubber film with microchannels of conductive liquid. In the case of soft tactile sensors, pressing the surface of the elastomer will deform the cross-section of underlying channels and change their electrical resistance. Soft pressure sensors may be employed in a variety of applications. For example, a network of pressure sensors can serve as artificial skin by yielding detailed information about contact pressures. This concept was demonstrated in a hyperelastic keypad, where perpendicular conductive channels form a quasi-planar network within an elastomeric matrix that registers the location, intensity and duration of applied pressure. In a second demonstration, soft curvature sensors were used for joint angle proprioception. Because the sensors are soft and stretchable, they conform to the host without interfering with the natural mechanics of motion. This marked the first use of liquid-embedded elastomer electronics to monitor human or robotic motion. Finally, liquid-embedded elastomers may be implemented as conductors in applications that call for flexible or stretchable circuitry, such as robotic origami.

  13. Embedding parameters for Quantum Annealing

    NASA Astrophysics Data System (ADS)

    Venturelli, Davide

    Many optimization problems are defined on highly connected graphs and many interesting physical spin-glass systems are featuring long-range interactions. One method to solve for the optimum/ground state is quantum annealing (QA). Most architectures for QA devices, manufactured or proposed, are based on optimizing Hamiltonians having spins connected in a non-complete graph, with nodes with a small maximum degree, compared to the requirements. To overcome this limitation 'embedding' is employed: the native graph is 'tiled' with ferromagnetic chains of spins that now are meant to represent the logical binary variables. While it is known how the strength of the ferromagnetic bonds can ensure that the classical Ising ground state of the embedded system can be univocally mapped to the ground state of the original system, there is very little study on the impact of these parameters on QA. Programmers have taken conservative choices for the parameters and the common practices can be improved. Starting from the physics of connected ferromagnetic Ising chains, we will review several parameter choices and discuss previous and new results obtained on the D-Wave 2X machine, on carefully designed problems that allow to isolate and evaluate the role of connectivity in embedded systems.

  14. The analysis of optimal singular controls for SEIR model of tuberculosis

    NASA Astrophysics Data System (ADS)

    Marpaung, Faridawaty; Rangkuti, Yulita M.; Sinaga, Marlina S.

    2014-12-01

    The optimally of singular control for SEIR model of Tuberculosis is analyzed. There are controls that correspond to time of the vaccination and treatment schedule. The optimally of singular control is obtained by differentiate a switching function of the model. The result shows that vaccination and treatment control are singular.

  15. Naked singularities in non-self-similar gravitational collapse of radiation shells

    SciTech Connect

    Joshi, P.S.; Dwivedi, I.H. )

    1992-03-15

    Non-self-similar gravitational collapse of imploding radiation is shown to give rise to a strong curvature naked singularity. The conditions are specified for the singularity to be globally naked and the strength of the same is examined along nonspacelike curves and along all the families of nonspacelike geodesics terminating at the singularity in the past.

  16. A Generalized Method of Image Analysis from an Intercorrelation Matrix which May Be Singular.

    ERIC Educational Resources Information Center

    Yanai, Haruo; Mukherjee, Bishwa Nath

    1987-01-01

    This generalized image analysis method is applicable to singular and non-singular correlation matrices (CMs). Using the orthogonal projector and a weaker generalized inverse matrix, image and anti-image covariance matrices can be derived from a singular CM. (SLD)

  17. Fractional charge and inter-Landau-level states at points of singular curvature

    NASA Astrophysics Data System (ADS)

    Biswas, Rudro R.; Thanh Son, Dam

    2016-08-01

    The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

  18. Fractional charge and inter-Landau-level states at points of singular curvature.

    PubMed

    Biswas, Rudro R; Son, Dam Thanh

    2016-08-01

    The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

  19. Fractional charge and inter-Landau–level states at points of singular curvature

    NASA Astrophysics Data System (ADS)

    Biswas, Rudro R.; Thanh Son, Dam

    2016-08-01

    The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau–level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau–level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

  20. Fractional charge and inter-Landau-level states at points of singular curvature.

    PubMed

    Biswas, Rudro R; Son, Dam Thanh

    2016-08-01

    The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation. PMID:27436906

  1. A singular thermodynamically consistent temperature at the origin of the anomalous behavior of liquid water

    PubMed Central

    Mallamace, Francesco; Corsaro, Carmelo; Stanley, H. Eugene

    2012-01-01

    The density maximum of water dominates the thermodynamics of the system under ambient conditions, is strongly P-dependent, and disappears at a crossover pressure Pcross ~ 1.8 kbar. We study this variable across a wide area of the T–P phase diagram. We consider old and new data of both the isothermal compressibility KT(T, P) and the coefficient of thermal expansion αP(T, P). We observe that KT(T) shows a minimum at T* ~ 315±5 K for all the studied pressures. We find the behavior of αP to also be surprising: all the αP(T) curves measured at different P cross at T*. The experimental data show a “singular and universal expansivity point” at T* ~ 315 K and αP(T*) ≃ 0.44 10−3 K−1. Unlike other water singularities, we find this temperature to be thermodynamically consistent in the relationship connecting the two response functions. PMID:23251779

  2. Self-similar cosmological solutions with dark energy. II. Black holes, naked singularities, and wormholes

    SciTech Connect

    Maeda, Hideki; Harada, Tomohiro; Carr, B. J.

    2008-01-15

    We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=({gamma}-1){mu} with 0<{gamma}<2/3. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all nontraversable because of the absence of a past null infinity.

  3. Higher order singular value decomposition of tensors for fusion of registered images

    NASA Astrophysics Data System (ADS)

    Thomason, Michael G.; Gregor, Jens

    2011-01-01

    This paper describes a computational method using tensor math for higher order singular value decomposition (HOSVD) of registered images. Tensor decomposition is a rigorous way to expose structure embedded in multidimensional datasets. Given a dataset of registered 2-D images, the dataset is represented in tensor format and HOSVD of the tensor is computed to obtain a set of 2-D basis images. The basis images constitute a linear decomposition of the original dataset. HOSVD is data-driven and does not require the user to select parameters or assign thresholds. A specific application uses the basis images for pixel-level fusion of registered images into a single image for visualization. The fusion is optimized with respect to a measure of mean squared error. HOSVD and image fusion are illustrated empirically with four real datasets: (1) visible and infrared data of a natural scene, (2) MRI and x ray CT brain images, and in nondestructive testing (3) x ray, ultrasound, and eddy current images, and (4) x ray, ultrasound, and shearography images.

  4. [Study of analysis of the singularity of R-wave by using wavelet transform].

    PubMed

    Wang, Weidong; Wang, Buqing; Liu, Guangrong

    2011-08-01

    Singularity is a basic feature of biological signals. Based on the variations of wavelet transform modulus maxima in multi-scales, we studied the basic theorem for analyzing the singularity and proposed an algorithm for calculating lipschitz exponent. Then we applied the algorithm to calculate the singularity of R-wave in ECG. Our study found that the level of singularity of R-waves in ECG between the 10 arrhythm patients randomly chosen and the healthy persons was significantly different, with the level of singularity of R-wave of normal persons remarkably higher than that of arrhythmia patients.

  5. The singularities, forces transmission index and mechanism selfblocking

    NASA Astrophysics Data System (ADS)

    Duca, C.; Buium, F.

    2016-08-01

    The paper represents a synthesis of the most representative results obtained by authors, along their researches in the field of mechanism singularities, forces transmission quality in mechanisms and self-blocking phenomenon. Our research is based on the idea that mechanism critical positions are a consequence of critical configurations in the component structural groups. At its turn, the critical configurations are noticed when the mathematical model of the kinematics and statics without friction, is affected by singularities. Thus, we have presented in the paper, the case of the principal structural groups, and we have established the critical configuration, the calculus formula of the configuration parameter and the existence conditions of the configuration (real solutions in the position problem).

  6. Asymptotically AdS spacetimes with a timelike Kasner singularity

    NASA Astrophysics Data System (ADS)

    Ren, Jie

    2016-07-01

    Exact solutions to Einstein's equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution's appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.

  7. Potentially singular solutions of the 3D axisymmetric Euler equations

    PubMed Central

    Luo, Guo; Hou, Thomas Y.

    2014-01-01

    The question of finite-time blowup of the 3D incompressible Euler equations is numerically investigated in a periodic cylinder with solid boundaries. Using rotational symmetry, the equations are discretized in the (2D) meridian plane on an adaptive (moving) mesh and is integrated in time with adaptively chosen time steps. The vorticity is observed to develop a ring-singularity on the solid boundary with a growth proportional to ∼(ts − t)−2.46, where ts ∼ 0.0035056 is the estimated singularity time. A local analysis also suggests the existence of a self-similar blowup. The simulations stop at τ2 = 0.003505 at which time the vorticity amplifies by more than (3 × 108)-fold and the maximum mesh resolution exceeds (3 × 1012)2. The vorticity vector is observed to maintain four significant digits throughout the computations. PMID:25157172

  8. Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

    NASA Technical Reports Server (NTRS)

    Bossel, H. H.

    1972-01-01

    A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

  9. Two-time-scale population evolution on a singular landscape

    NASA Astrophysics Data System (ADS)

    Xu, Song; Jiao, Shuyun; Jiang, Pengyao; Ao, Ping

    2014-01-01

    Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by singular peaks on a potential landscape. The genetic drift-induced noise gives rise to two-time-scale diffusion dynamics on the bipeaked landscape. We find that the logarithmically divergent (singular) peaks do not necessarily imply infinite escape times or biological fixations by iterating the Wright-Fisher model and approximating the average escape time. Our analytical results under weak mutation and weak selection extend Kramers's escape time formula to models with B (Beta) function-like equilibrium distributions and overcome constraints in previous methods. The constructed landscape provides a coherent description for the bistable system, supports the quantitative analysis of bipeaked dynamics, and generates mathematical insights for understanding the boundary behaviors of the diffusion model.

  10. Formation of current singularity in a topologically constrained plasma.

    PubMed

    Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A

    2016-02-01

    Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies. PMID:26986430

  11. Multiple unfoldings of orbifold singularities: Engineering geometric analogies to unification

    SciTech Connect

    Bourjaily, Jacob L.

    2009-02-15

    Katz and Vafa [Nucl. Phys. B497, 146 (1997)] showed how charged matter can arise geometrically by the deformation of ADE-type orbifold singularities in type IIa, M-theory, and F-theory compactifications. In this paper we use those same basic ingredients, used there to geometrically engineer specific matter representations, here to deform the compactification manifold itself in a way which naturally compliments many features of unified model building. We realize this idea explicitly by deforming a manifold engineered to give rise to an SU{sub 5} grand unified model into a one giving rise to the standard model. In this framework, the relative local positions of the singularities giving rise to standard model fields are specified in terms of the values of a small number of complex structure moduli which deform the original manifold, greatly reducing the arbitrariness of their relative positions.

  12. A Constrained Multibody System Dynamics Avoiding Kinematic Singularities

    NASA Astrophysics Data System (ADS)

    Huang, Chih-Fang; Yan, Chang-Dau; Jeng, Shyr-Long; Cheing, Wei-Hua

    In the analysis of constrained multibody systems, the constraint reaction forces are normally expressed in terms of the constraint equations and a vector of Lagrange multipliers. Because it fails to incorporate conservation of momentum, the Lagrange multiplier method is deficient when the constraint Jacobian matrix is singular. This paper presents an improved dynamic formulation for the constrained multibody system. In our formulation, the kinematic constraints are still formulated in terms of the joint constraint reaction forces and moments; however, the formulations are based on a second-order Taylor expansion so as to incorporate the rigid body velocities. Conservation of momentum is included explicitly in this method; hence the problems caused by kinematic singularities can be avoided. In addition, the dynamic formulation is general and applicable to most dynamic analyses. Finally the 3-leg Stewart platform is used for the example of analysis.

  13. Formation of current singularity in a topologically constrained plasma

    NASA Astrophysics Data System (ADS)

    Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.

    2016-02-01

    Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.

  14. Potentially singular solutions of the 3D axisymmetric Euler equations.

    PubMed

    Luo, Guo; Hou, Thomas Y

    2014-09-01

    The question of finite-time blowup of the 3D incompressible Euler equations is numerically investigated in a periodic cylinder with solid boundaries. Using rotational symmetry, the equations are discretized in the (2D) meridian plane on an adaptive (moving) mesh and is integrated in time with adaptively chosen time steps. The vorticity is observed to develop a ring-singularity on the solid boundary with a growth proportional to ∼(ts - t)(-2.46), where ts ∼ 0.0035056 is the estimated singularity time. A local analysis also suggests the existence of a self-similar blowup. The simulations stop at τ(2) = 0.003505 at which time the vorticity amplifies by more than (3 × 10(8))-fold and the maximum mesh resolution exceeds (3 × 10(12))(2). The vorticity vector is observed to maintain four significant digits throughout the computations.

  15. A Schwarz alternating procedure for singular perturbation problems

    SciTech Connect

    Garbey, M.; Kaper, H.G.

    1994-12-31

    The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.

  16. The multivariate Hahn polynomials and the singular oscillator

    NASA Astrophysics Data System (ADS)

    Genest, Vincent X.; Vinet, Luc

    2014-11-01

    Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated with the separation of variables in Cartesian and hyperspherical coordinates. These polynomials in d discrete variables depend on d+1 real parameters and are orthogonal with respect to the multidimensional hypergeometric distribution. The focus is put on the d = 2 case for which the connection with the three-dimensional singular oscillator is used to derive the main properties of the polynomials: forward/backward shift operators, orthogonality relation, generating function, recurrence relations, bispectrality (difference equations) and explicit expression in terms of the univariate Hahn polynomials. The extension of these results to an arbitrary number of variables is presented at the end of the paper.

  17. Realization of deep subwavelength resolution with singular media

    PubMed Central

    Xu, Su; Jiang, Yuyu; Xu, Hongyi; Wang, Junxia; Lin, Shisheng; Chen, Hongsheng; Zhang, Baile

    2014-01-01

    The record of imaging resolution has kept being refreshed in the past decades and the best resolution of hyperlenses and superlenses so far is about one out of tens in terms of wavelength. In this paper, by adopting a hybrid concept of transformation optics and singular media, we report a broadband meta-lens design methodology with ultra-high resolution. The meta-lens is made of subwavelength metal/air layers, which exhibit singular medium property over a broad band. As a proof of concept, the subwavelength imaging ability is demonstrated over a broad frequency band from 1.5–10 GHz with the resolution varying from 1/117 to 1/17 wavelength experimentally. PMID:24909738

  18. Black holes and Thunderbolt singularities with Lifshitz scaling terms

    NASA Astrophysics Data System (ADS)

    Misonoh, Yosuke; Maeda, Kei-ichi

    2015-10-01

    We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Hořava-Lifshitz theory, which is composed of the z =2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. Whereas, if a three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns out to be a spacelike singularity.

  19. Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.

    PubMed

    Nagarale, Ravindrakumar M; Patre, B M

    2014-05-01

    This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.

  20. Promise of a low power mobile CPU based embedded system in artificial leg control.

    PubMed

    Hernandez, Robert; Zhang, Fan; Zhang, Xiaorong; Huang, He; Yang, Qing

    2012-01-01

    This paper presents the design and implementation of a low power embedded system using mobile processor technology (Intel Atom™ Z530 Processor) specifically tailored for a neural-machine interface (NMI) for artificial limbs. This embedded system effectively performs our previously developed NMI algorithm based on neuromuscular-mechanical fusion and phase-dependent pattern classification. The analysis shows that NMI embedded system can meet real-time constraints with high accuracies for recognizing the user's locomotion mode. Our implementation utilizes the mobile processor efficiently to allow a power consumption of 2.2 watts and low CPU utilization (less than 4.3%) while executing the complex NMI algorithm. Our experiments have shown that the highly optimized C program implementation on the embedded system has superb advantages over existing PC implementations on MATLAB. The study results suggest that mobile-CPU-based embedded system is promising for implementing advanced control for powered lower limb prostheses.

  1. A rapid local singularity analysis algorithm with applications

    NASA Astrophysics Data System (ADS)

    Chen, Zhijun; Cheng, Qiuming; Agterberg, Frits

    2015-04-01

    The local singularity model developed by Cheng is fast gaining popularity in characterizing mineralization and detecting anomalies of geochemical, geophysical and remote sensing data. However in one of the conventional algorithms involving the moving average values with different scales is time-consuming especially while analyzing a large dataset. Summed area table (SAT), also called as integral image, is a fast algorithm used within the Viola-Jones object detection framework in computer vision area. Historically, the principle of SAT is well-known in the study of multi-dimensional probability distribution functions, namely in computing 2D (or ND) probabilities (area under the probability distribution) from the respective cumulative distribution functions. We introduce SAT and it's variation Rotated Summed Area Table in the isotropic, anisotropic or directional local singularity mapping in this study. Once computed using SAT, any one of the rectangular sum can be computed at any scale or location in constant time. The area for any rectangular region in the image can be computed by using only 4 array accesses in constant time independently of the size of the region; effectively reducing the time complexity from O(n) to O(1). New programs using Python, Julia, matlab and C++ are implemented respectively to satisfy different applications, especially to the big data analysis. Several large geochemical and remote sensing datasets are tested. A wide variety of scale changes (linear spacing or log spacing) for non-iterative or iterative approach are adopted to calculate the singularity index values and compare the results. The results indicate that the local singularity analysis with SAT is more robust and superior to traditional approach in identifying anomalies.

  2. Singularity confinement for matrix discrete Painlevé equations

    NASA Astrophysics Data System (ADS)

    Cassatella-Contra, Giovanni A.; Mañas, Manuel; Tempesta, Piergiulio

    2014-09-01

    We study the analytic properties of a matrix discrete system introduced by Cassatella and Mañas (2012 Stud. Appl. Math. 128 252-74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This paves the way to a generalization of Painlevé analysis to discrete matrix models.

  3. Singularity-free interaction in dilaton-Maxwell electrodynamics

    NASA Astrophysics Data System (ADS)

    Kechkin, O. V.; Mosharev, P. A.

    2016-09-01

    An effective potential is created for the dynamics of a test particle, which preserves dilatation symmetry for nonlinear static dilaton-Maxwell background. It is found that the central interaction in this theory is singularity-free everywhere; it vanishes at short distances and demonstrates Coulomb behavior far from the source. It is shown that static and spherically symmetric source behaves like a soliton: it has the finite energy characteristics that are inversely proportional to the dilaton-Maxwell coupling constant.

  4. Solution of coupled and singular perturbation methods using duality theory.

    NASA Technical Reports Server (NTRS)

    Chan, W. L.; Leininger, G. G.

    1973-01-01

    Dual variational techniques developed by Chan and Leininger (1972) are summarized, and duality theory in the form of the Complementary Variational Principle is employed to provide a suboptimal measure for the singular and epsilon-coupled perturbation methods proposed by Kokotovic and Cruz. The suboptimal measure is independent of any a priori knowledge of the optimal solution, thereby providing an absolute estimate of the performance loss rather than an estimate relative to the unknown optimal solution.

  5. Feynman method for disentangling operators and a singular oscillator

    SciTech Connect

    Popov, V. S.; Trusov, M. A.

    2012-02-15

    The problem of the evolution of a singular quantum oscillator with a frequency exhibiting an arbitrary time dependence has been solved. The probabilities w{sub mn} of transitions in the oscillator spectrum and generating functions have been calculated, and the sum rules for w{sub mn} have been derived. The calculations are based on the Feynman disentangling method and the theory of representations of the SU(1, 1) group.

  6. Sensor Authentication: Embedded Processor Code

    SciTech Connect

    Svoboda, John

    2012-09-25

    Described is the c code running on the embedded Microchip 32bit PIC32MX575F256H located on the INL developed noise analysis circuit board. The code performs the following functions: Controls the noise analysis circuit board preamplifier voltage gains of 1, 10, 100, 000 Initializes the analog to digital conversion hardware, input channel selection, Fast Fourier Transform (FFT) function, USB communications interface, and internal memory allocations Initiates high resolution 4096 point 200 kHz data acquisition Computes complex 2048 point FFT and FFT magnitude. Services Host command set Transfers raw data to Host Transfers FFT result to host Communication error checking

  7. Transmutations between singular and subsingular vectors of the N = 2 superconformal algebras

    NASA Astrophysics Data System (ADS)

    Dörrzapf, Matthias; Gato-Rivera, Beatriz

    1999-09-01

    We present subsingular vectors of the N = 2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the topological algebra become subsingular vectors of the antiperiodic NS algebra under the topological untwistings. These classes consist of BRST-invariant singular vectors with relative charges q = -2, -1 and zero conformal weight, and nolabel singular vectors with q = 0, -1. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2.

  8. Singularity and Nonnormality in the Classification of Compositional Data

    USGS Publications Warehouse

    Bohling, G.C.; Davis, J.C.; Olea, R.A.; Harff, Jan

    1998-01-01

    Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore-Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.

  9. Geometric and algebraic properties of minimal bases of singular systems

    NASA Astrophysics Data System (ADS)

    Karcanias, Nicos

    2013-11-01

    For a general singular system ? with an associated pencil T(S), a complete classification of the right polynomial vector pairs ?, connected with the ? rational vector space, is given according to the proper-nonproper property, characterising the relationship of the degrees of those two vectors. An integral part of the classification of right pairs is the development of the notions of canonical and normal minimal bases for ? and ? rational vector spaces, where R(s) is the state restriction pencil of ?. It is shown that the notions of canonical and normal minimal bases are equivalent; the first notion characterises the pure algebraic aspect of the classification, whereas the second is intimately connected to the real geometry properties and the underlying generation mechanism of the proper and nonproper state vectors ?. The results describe the algebraic and geometric dimensions of the invariant partitioning of the set of reachability indices of singular systems. The classification of all proper and nonproper polynomial vectors ? induces a corresponding classification for the reachability spaces to proper-nonproper and results related to the possible dimensions feedback-spectra assignment properties of them are also given. The classification of minimal bases introduces new feedback invariants for singular systems, based on the real geometry of polynomial minimal bases, and provides an extension of the standard theory for proper systems (Warren, M.E., & Eckenberg, A.E. (1975).

  10. An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

    NASA Astrophysics Data System (ADS)

    Ceniceros, Hector D.; Hou, Thomas Y.

    2001-09-01

    We develop an efficient dynamically adaptive mesh generator for time-dependent problems in two or more dimensions. The mesh generator is motivated by the variational approach and is based on solving a new set of nonlinear elliptic PDEs for the mesh map. When coupled to a physical problem, the mesh map evolves with the underlying solution and maintains high adaptivity as the solution develops complicated structures and even singular behavior. The overall mesh strategy is simple to implement, avoids interpolation, and can be easily incorporated into a broad range of applications. The efficacy of the mesh is first demonstrated by two examples of blowing-up solutions to the 2-D semilinear heat equation. These examples show that the mesh can follow with high adaptivity a finite-time singularity process. The focus of applications presented here is however the baroclinic generation of vorticity in a strongly layered 2-D Boussinesq fluid, a challenging problem. The moving mesh follows effectively the flow resolving both its global features and the almost singular shear layers developed dynamically. The numerical results show the fast collapse to small scales and an exponential vorticity growth.

  11. Analytic evolution of singular distribution amplitudes in QCD

    NASA Astrophysics Data System (ADS)

    Tandogan, Asli

    Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, antisymmetric flat DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standard method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.

  12. The fractal energy measurement and the singularity energy spectrum analysis

    NASA Astrophysics Data System (ADS)

    Xiong, Gang; Zhang, Shuning; Yang, Xiaoniu

    2012-12-01

    The singularity exponent (SE) is the characteristic parameter of fractal and multifractal signals. Based on SE, the fractal dimension reflecting the global self-similar character, the instantaneous SE reflecting the local self-similar character, the multifractal spectrum (MFS) reflecting the distribution of SE, and the time-varying MFS reflecting pointwise multifractal spectrum were proposed. However, all the studies were based on the depiction of spatial or differentiability characters of fractal signals. Taking the SE as the independent dimension, this paper investigates the fractal energy measurement (FEM) and the singularity energy spectrum (SES) theory. Firstly, we study the energy measurement and the energy spectrum of a fractal signal in the singularity domain, propose the conception of FEM and SES of multifractal signals, and investigate the Hausdorff measure and the local direction angle of the fractal energy element. Then, we prove the compatibility between FEM and traditional energy, and point out that SES can be measured in the fractal space. Finally, we study the algorithm of SES under the condition of a continuous signal and a discrete signal, and give the approximation algorithm of the latter, and the estimations of FEM and SES of the Gaussian white noise, Fractal Brownian motion and the multifractal Brownian motion show the theoretical significance and application value of FEM and SES.

  13. Naked singularity explosion in higher-dimensional dust collapse

    NASA Astrophysics Data System (ADS)

    Shimano, Masahiro; Miyamoto, Umpei

    2014-02-01

    In the context of the large extra dimensions or TeV-scale gravity, it has been argued that an effective naked singularity, called the visible border of spacetime, would be generated by high-energy particle collisions. Motivated by this interesting possibility, we investigate a particle creation by a naked singularity in general dimensions, adopting a spherically symmetric self-similar dust collapse as the simple model of a naked singularity formation. The power and energy of the particle emission behave in two distinct ways depending on a parameter in the model. In a generic case, the emission power is proportional to the quadratic inverse of the remaining time to the Cauchy horizon, which has been known for the four-dimensional case in the literature. On the other hand, in a degenerate case the emission power is proportional to the quartic inverse of the remaining time to the Cauchy horizon, and depends on the total mass of a dust fluid in spite that the central region of the collapse is scale-free due to the self-similarity. In the both cases, within a test-field approximation the energy radiated before any quantum gravitational effect dominates amounts to TeV. This suggests that a backreaction is not ignorable in the TeV-scale gravity context, in contrast to the similar phenomena in stellar collapse.

  14. Analysis on singular spaces: Lie manifolds and operator algebras

    NASA Astrophysics Data System (ADS)

    Nistor, Victor

    2016-07-01

    We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called "Lie manifolds" -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

  15. Observation of van Hove Singularities in Twisted Silicene Multilayers.

    PubMed

    Li, Zhi; Zhuang, Jincheng; Chen, Lan; Ni, Zhenyi; Liu, Chen; Wang, Li; Xu, Xun; Wang, Jiaou; Pi, Xiaodong; Wang, Xiaolin; Du, Yi; Wu, Kehui; Dou, Shi Xue

    2016-08-24

    Interlayer interactions perturb the electronic structure of two-dimensional materials and lead to new physical phenomena, such as van Hove singularities and Hofstadter's butterfly pattern. Silicene, the recently discovered two-dimensional form of silicon, is quite unique, in that silicon atoms adopt competing sp(2) and sp(3) hybridization states leading to a low-buckled structure promising relatively strong interlayer interaction. In multilayer silicene, the stacking order provides an important yet rarely explored degree of freedom for tuning its electronic structures through manipulating interlayer coupling. Here, we report the emergence of van Hove singularities in the multilayer silicene created by an interlayer rotation. We demonstrate that even a large-angle rotation (>20°) between stacked silicene layers can generate a Moiré pattern and van Hove singularities due to the strong interlayer coupling in multilayer silicene. Our study suggests an intriguing method for expanding the tunability of the electronic structure for electronic applications in this two-dimensional material. PMID:27610412

  16. Non-singular bounce transitions in the multiverse

    NASA Astrophysics Data System (ADS)

    Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun

    2013-11-01

    According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρc. This is combined with a simple scalar field `landscape', where the energy barriers between different vacua are small compared to ρc. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δphi ~ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.

  17. Non-singular bounce transitions in the multiverse

    SciTech Connect

    Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun E-mail: vilenkin@cosmos.phy.tufts.edu

    2013-11-01

    According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.

  18. Schrodinger formalism, black hole horizons, and singularity behavior

    SciTech Connect

    Wang, John E.; Greenwood, Eric; Stojkovic, Dejan

    2009-12-15

    The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstroem domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schroedinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schroedinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schroedinger equation becomes nonlocal, but the wave function describing the system is nonsingular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.

  19. Dynamical mechanism of circadian singularity behavior in Neurospora

    NASA Astrophysics Data System (ADS)

    Sun, Maorong; Wang, Yi; Xu, Xin; Yang, Ling

    2016-09-01

    Many organisms have oscillators with a period of about 24 hours, called "circadian clocks". They employ negative biochemical feedback loops that are self-contained within a single cell (requiring no cell-to-cell interaction). Circadian singularity behavior is a phenomenon of the abolishment of circadian rhythmicities by a critical stimulus. These behaviors have been found experimentally in Neurospora, human and hamster, by temperature step-up or light pulse. Two alternative models have been proposed to explain this phenomenon: desynchronization of cell populations, and loss of oscillations in all cells by resetting each cell close to a steady state. In this work, we use a mathematical model to investigate the dynamical mechanism of circadian singularity behavior in Neurospora. Our findings suggest that the arrhythmic behavior after the critical stimulus is caused by the collaboration of the desynchronization and the loss of oscillation amplitude. More importantly, we found that the stable manifold of the unstable equilibrium point, instead of the steady state itself, plays a crucial role in circadian singularity behavior.

  20. Observation of van Hove Singularities in Twisted Silicene Multilayers

    PubMed Central

    2016-01-01

    Interlayer interactions perturb the electronic structure of two-dimensional materials and lead to new physical phenomena, such as van Hove singularities and Hofstadter’s butterfly pattern. Silicene, the recently discovered two-dimensional form of silicon, is quite unique, in that silicon atoms adopt competing sp2 and sp3 hybridization states leading to a low-buckled structure promising relatively strong interlayer interaction. In multilayer silicene, the stacking order provides an important yet rarely explored degree of freedom for tuning its electronic structures through manipulating interlayer coupling. Here, we report the emergence of van Hove singularities in the multilayer silicene created by an interlayer rotation. We demonstrate that even a large-angle rotation (>20°) between stacked silicene layers can generate a Moiré pattern and van Hove singularities due to the strong interlayer coupling in multilayer silicene. Our study suggests an intriguing method for expanding the tunability of the electronic structure for electronic applications in this two-dimensional material. PMID:27610412