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.
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.
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.
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.
Singular Shell Embedded into a Cosmological Model
NASA Astrophysics Data System (ADS)
Grøn, Øyvind; Rippis, Peter D.
2003-12-01
We generalize Israel's formalism to cover singular shells embedded in a non-vacuum Universe. That is, we deduce the relativistic equation of motion for a thin shell embedded in a Schwarzschild/Friedmann-Lemaître-Robertson-Walker spacetime. Also, we review the embedding of a Schwarzschild mass into a cosmological model using ``curvature'' coordinates and give solutions with (Sch/FLRW) and without the embedded mass (FLRW).
Singularity embedding method in potential flow calculations
NASA Technical Reports Server (NTRS)
Jou, W. H.; Huynh, H.
1982-01-01
The so-called H-type mesh is used in a finite-element (or finite-volume) calculation of the potential flow past an airfoil. Due to coordinate singularity at the leading edge, a special singular trial function is used for the elements neighboring the leading edge. The results using the special singular elements are compared to those using the regular elements. It is found that the unreasonable pressure distribution obtained by the latter is removed by the embedding of the singular element. Suggestions to extend the present method to transonic cases are given.
Singular interactions supported by embedded curves
NASA Astrophysics Data System (ADS)
Tevfik Kaynak, Burak; Teoman Turgut, O.
2012-07-01
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed. Dedicated to the memory of Professor Yavuz Nutku.
Global embeddings for branes at toric singularities
NASA Astrophysics Data System (ADS)
Balasubramanian, Vijay; Berglund, Per; Braun, Volker; García-Etxebarria, Iñaki
2012-10-01
We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) ( dP 0)3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.
Characteristic classes, singular embeddings, and intersection homology.
Cappell, S E; Shaneson, J L
1987-06-01
This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper. PMID:16593842
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.
Incoherent averaging of phase singularities in speckle-shearing interferometry.
Mantel, Klaus; Nercissian, Vanusch; Lindlein, Norbert
2014-08-01
Interferometric speckle techniques are plagued by the omnipresence of phase singularities, impairing the phase unwrapping process. To reduce the number of phase singularities by physical means, an incoherent averaging of multiple speckle fields may be applied. It turns out, however, that the results may strongly deviate from the expected √N behavior. Using speckle-shearing interferometry as an example, we investigate the mechanism behind the reduction of phase singularities, both by calculations and by computer simulations. Key to an understanding of the reduction mechanism during incoherent averaging is the representation of the physical averaging process in terms of certain vector fields associated with each speckle field. PMID:25078215
Spatial Distribution of Phase Singularities in Optical Random Vector Waves.
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
D-branes at del Pezzo singularities: global embedding and moduli stabilisation
NASA Astrophysics Data System (ADS)
Cicoli, Michele; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto
2012-09-01
In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification. By means of toric geometry, we classify all the Calabi-Yau manifolds with 3 < h 1,1 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kähler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors. We present concrete models where the visible sector, containing the Standard Model, gauge and matter content, is built via fractional D3-branes at del Pezzo singularities and all the Kähler moduli are fixed providing an explicit realisation of both KKLT and LARGE volume scenarios, the latter with D-term uplifting to de Sitter minima. We perform the consistency checks for global embedding such as tadpole, K-theory charges and Freed-Witten anomaly cancellation. We briefly discuss phenomenological and cosmological implications of our models.
Recurrent noise-induced phase singularities in drifting patterns
NASA Astrophysics Data System (ADS)
Clerc, M. G.; Coulibaly, S.; del Campo, F.; Garcia-Nustes, M. A.; Louvergneaux, E.; Wilson, M.
2015-11-01
We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.
Observation of Vortex Phase Singularities in Bose-Einstein Condensates
Inouye, S.; Gupta, S.; Rosenband, T.; Chikkatur, A. P.; Goerlitz, A.; Gustavson, T. L.; Leanhardt, A. E.; Pritchard, D. E.; Ketterle, W.
2001-08-20
We have observed phase singularities due to vortex excitation in Bose-Einstein condensates. Vortices were created by moving a laser beam through a condensate. They were observed as dislocations in the interference fringes formed by the stirred condensate and a second unperturbed condensate. The velocity dependence for vortex excitation and the time scale for re-establishing a uniform phase across the condensate were determined.
Singular-value demodulation of phase-shifted holograms.
Lopes, Fernando; Atlan, Michael
2015-06-01
We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts. PMID:26030552
Optical Vortex Metrology: Displacement and Flow Measurements with Phase Singularities
NASA Astrophysics Data System (ADS)
Takeda, Mitsuo; Wang, Wei; Hanson, Steen G.; Miyamoto, Yoko
2007-10-01
We review the principle and the applications of a new technique which we recently proposed for displacement and flow measurements. The technique is called optical vortex metrology because it makes use of phase singularities in the complex signal as markers or tracers, which are generated by a vortex filer that performs a Riesz or Laguerre-Gauss transform operation to a speckle-like random pattern.
Cycle of phase, coherence and polarization singularities in Young's three-pinhole experiment.
Pang, Xiaoyan; Gbur, Greg; Visser, Taco D
2015-12-28
It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to create a continuous cycle of transformations between classes of singularities, often accompanied by topological reactions in which different singularities are created and annihilated. This arrangement serves to clarify the relationships between the different singularity types, and provides a simple tool for further exploration. PMID:26832065
Turbulent diffusion phase transition is due to singular energy spectrum.
Wallstrom, T C
1995-01-01
The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion. Images Fig. 2 PMID:11607590
Phase singularity of surface plasmon polaritons generated by optical vortices.
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
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.
Numerical generation of a polarization singularity array with modulated amplitude and phase.
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
Near-field phase singularity in subwavelength metallic microstructures
Kang Ming; Guo Qinghua; Chen Jing; Gu Bing; Li Yongnan; Wang Huitian
2011-10-15
A near-field phase singularity (NFPS) depending on the spin state of the incident electromagnetic (EM) radiation is very fascinating because it can enrich the functionality of the EM radiation in metamaterials. Here we present a microscopic dipole model to describe the NFPS effect under the time-harmonic quasistatic limit. The results reveal that NFPS exists for the longitudinal components of both electric and magnetic fields as well as the transverse component of time-averaged Poynting vector. The localized surface plasmon polariton in the subwavelength metallic structure contributes to enhance the generation efficiency of NFPS by introducing the resonance of the electric dipole. This effect not only is promising for microtrapping and manipulation but also enriches the functionality of the existing metamaterials.
Multivariate singular spectrum analysis and the road to phase synchronization
NASA Astrophysics Data System (ADS)
Groth, Andreas; Ghil, Michael
2010-05-01
Singular spectrum analysis (SSA) and multivariate SSA (M-SSA) are based on the classical work of Kosambi (1943), Loeve (1945) and Karhunen (1946) and are closely related to principal component analysis. They have been introduced into information theory by Bertero, Pike and co-workers (1982, 1984) and into dynamical systems analysis by Broomhead and King (1986a,b). Ghil, Vautard and associates have applied SSA and M-SSA to the temporal and spatio-temporal analysis of short and noisy time series in climate dynamics and other fields in the geosciences since the late 1980s. M-SSA provides insight into the unknown or partially known dynamics of the underlying system by decomposing the delay-coordinate phase space of a given multivariate time series into a set of data-adaptive orthonormal components. These components can be classified essentially into trends, oscillatory patterns and noise, and allow one to reconstruct a robust "skeleton" of the dynamical system's structure. For an overview we refer to Ghil et al. (Rev. Geophys., 2002). In this talk, we present M-SSA in the context of synchronization analysis and illustrate its ability to unveil information about the mechanisms behind the adjustment of rhythms in coupled dynamical systems. The focus of the talk is on the special case of phase synchronization between coupled chaotic oscillators (Rosenblum et al., PRL, 1996). Several ways of measuring phase synchronization are in use, and the robust definition of a reasonable phase for each oscillator is critical in each of them. We illustrate here the advantages of M-SSA in the automatic identification of oscillatory modes and in drawing conclusions about the transition to phase synchronization. Without using any a priori definition of a suitable phase, we show that M-SSA is able to detect phase synchronization in a chain of coupled chaotic oscillators (Osipov et al., PRE, 1996). Recently, Muller et al. (PRE, 2005) and Allefeld et al. (Intl. J. Bif. Chaos, 2007) have
Observation of photonic spin Hall effect with phase singularity at dielectric metasurfaces.
Li, Ying; Liu, Yachao; Ling, Xiaohui; Yi, Xunong; Zhou, Xinxing; Ke, Yougang; Luo, Hailu; Wen, Shuangchun; Fan, Dianyuan
2015-01-26
Observation of photonic spin Hall effect (SHE) near the phase singularity at dielectric metasurfaces is presented. The structured metasurface works as a space-variant Pancharatnam-Berry phase element and produces a vortex beam with phase singularity. The dynamical vortex phase is introduced to eliminate or enhance the phase singularity, thus realizing the manipulation of spin-dependent Pancharatnam-Berry phase. The spin-orbit coupling near the singularity of the Pancharatnam-Berry phase leads to the observation of the photonic SHE which manifests itself as spin-dependent splitting. The underlying mechanism is significantly different from previously reported cases. It thereby provides an alternative way to manipulate the spin states of photons. PMID:25835932
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.
The Embedded Phase of Massive Star Formation
NASA Astrophysics Data System (ADS)
van der Tak, Floris
2000-11-01
evolutionary order of phenomena associated with massive star formation appears to be: embedded infrared source to hot core to (ultra-) compact H II region. In the first two stages, CH3OH and H2O masers occur, which are replaced by OH masers in the third. Chemically, the low deuterium fractionation and total abundances of H2CO and CH3OH argue for a short duration of the cold (≅ 10 K) pre-stellar phase. The fractional ionization of the envelopes of massive young stars is consistent with cosmic-ray ionization at an average rate of ζCR = (2.6 +/- 1.8) × 10-17 s-1. Variations in ζCR are a factor ≅ 2 on a ~kpc scale, in good agreement with γ-ray data. Ionization by local X-rays and shielding against cosmic rays appear unimportant. The differences in ζCR for a given source derived using H3+ or H13CO+, and the correlation of the H3+ column density with distance suggest that significant H3+ absorption occurs in intervening translucent clouds. The abundances of several molecules are found to increase with increasing temperature. Four types of species can be distinguished: (i) `passive' molecules, which are formed in the gas phase, freeze out onto grains during the cold collapse phase and are released during warm-up without chemical modification (e.g. CO); (ii) molecules which form by reactions on or inside the ice layer, and subsequently evaporate (e.g. CH3OH); (iii) molecules formed by gas-phase reactions with evaporated species (e.g. CH3OCH3); (iv) molecules which are formed in the hot gas by high-temperature reactions (e.g. HCN). In 5 out of 5 sources, compact (radius < 300 AU) dust emission is detected with the OVRO interferometer, which resides in a dense shell or in a disk. The mass of this component is not well constrained because of optical depth effects, but it may be as high as 10 Modot, which is comparable to the stellar mass.
Singularity problem and phase-space noncanonical noncommutativity
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2010-08-01
The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the Heisenberg-Weyl algebra. An integral of motion is used to factorize the wave function into an oscillatory part and a function of a configuration space variable. The latter is shown to be normalizable using asymptotic arguments. It is then shown that on the hypersurfaces of constant value of the argument of the wave function’s oscillatory piece, the probability vanishes in the vicinity of the black hole singularity.
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.
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.
Absence of Squirt Singularities for the Multi-Phase Muskat Problem
NASA Astrophysics Data System (ADS)
Córdoba, Diego; Gancedo, Francisco
2010-10-01
In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that the fluids do not develop squirt singularities.
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).
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
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
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
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
Aristov, Andrey I.; Kabashin, Andrei V.; Zywietz, Urs; Evlyukhin, Andrey B.; Reinhardt, Carsten; Chichkov, Boris N.
2014-02-17
By using methods of laser-induced transfer combined with nanoparticle lithography, we design and fabricate large-area gold nanoparticle-based metamaterial arrays exhibiting extreme Heaviside-like phase jumps in reflected light due to a strong diffractive coupling of localized plasmons. When employed in sensing schemes, these phase singularities provide the sensitivity of 5 × 10{sup 4} deg. of phase shift per refractive index unit change that is comparable with best values reported for plasmonic biosensors. The implementation of sensor platforms on the basis of such metamaterial arrays promises a drastic improvement of sensitivity and cost efficiency of plasmonic biosensing devices.
Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity
Chen, Y. F.; Liang, H. C.; Lin, Y. C.; Tzeng, Y. S.; Su, K. W.; Huang, K. F.
2011-05-15
We explore the feasibility of the generation of pseudonondiffracting optical beams related to crystal and quasicrystal structures. It is experimentally confirmed that optical crystal and quasicrystal beams can be remarkably generated with a collimated light to illuminate a high-precision mask with multiple apertures regularly distributed on a ring. We also found that exotic kaleidoscopic patterns can be exhibited with the high-order quasicrystal beams. More importantly, the structures of phase singularities in optical quasicrystal beams are manifested.
Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection.
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. PMID:23314104
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.
High-multipole excitations of hydrogen-like atoms by twisted photons near a phase singularity
NASA Astrophysics Data System (ADS)
Afanasev, Andrei; Carlson, Carl E.; Mukherjee, Asmita
2016-07-01
We calculate transition amplitudes and cross sections for excitation of hydrogen-like atoms by the twisted photon states, or photon states with angular momentum projection on the direction of propagation exceeding ℏ. If the target atom is located at distances of the order of atomic size near the phase singularity in the vortex center, the transition rates into the states with orbital angular momentum {l}f\\gt 1 become comparable with the rates for electric dipole transitions. It is shown that when the transition rates are normalized to the local photon flux, the resulting cross sections for {l}f\\gt 1 are singular near the optical vortex center. The relation to the ‘quantum core’ concept introduced by Berry and Dennis is discussed.
NASA Astrophysics Data System (ADS)
Yulmetyev, R. M.; Hänggi, P.; Yulmetyeva, D. G.; Shimojo, S.; Khusaenova, E. V.; Watanabe, K.; Bhattacharya, J.
2007-09-01
To analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses (magnetoencephalogram, MEG). The signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy (PSE). We found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of PSE.
ALIGNMENT OF PROTOSTARS AND CIRCUMSTELLAR DISKS DURING THE EMBEDDED PHASE
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.
High-resolution phase imaging of phase singularities in the focal region of a lens
NASA Astrophysics Data System (ADS)
Walford, J. N.; Nugent, K. A.; Roberts, A.; Scholten, R. E.
2002-03-01
Subwavelength-resolution phase images of phase dislocations at the focal region of a 20×, 0.4-N.A. lens have been obtained by use of an optical fiber interferometer with a tapered probe in one arm. A phase-stepping algorithm is used to determine a quantitative value of the phase at each point in the scan, clearly showing the presence of edge dislocations between the Airy rings of the diffraction pattern near the lens focus, as well as four isolated screw-type singularties caused by astigmatism in the lens.
Singularities and Closed String Tachyons
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.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
NASA Astrophysics Data System (ADS)
Suzuki, Akio; Konno, Hidetoshi
2011-09-01
The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
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.
Kim, Youngwook; Herlinger, Patrick; Moon, Pilkyung; Koshino, Mikito; Taniguchi, Takashi; Watanabe, Kenji; Smet, Jurgen H
2016-08-10
van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity. PMID:27387484
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.
Nagel, Sidney
2007-01-17
The exhilarating spray from waves crashing into the shore, the distressing sound of a faucet leaking in the night, and the indispensable role of bubbles dissolving gas into the oceans are but a few examples of the ubiquitous presence and profound importance of drop formation and splashing in our lives. During fission, a fluid forms a neck that becomes vanishingly thin at the point of breakup. This topological transition is accompanied by a dynamic singularity in which physical properties such as pressure diverge. Singularities of this sort often organize the overall dynamical evolution of nonlinear systems. I will first discuss the role of singularities in the breakup of droplets. I will then present a second experiment, selective withdrawal, in which we study the steady-state shape of a liquid as it is withdrawn by a nozzle through a surrounding fluid. Here, a change in topology may again be accompanied by a singularity. Applications of this geometry that rely on singular dynamical behavior are relevant for the coating of biological particles that may be of particular use in medical transplantation technologies.
Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2011-07-01
We consider a cosmological model based upon a noncanonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of black holes whose interior are described by the Kantowski-Sachs metric and modeled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of these black holes and compare the results with the Hawking values. We observe that it is actually the noncommutativity in the momentum sector that allows for the existence of a minimum in the potential, which is the key to apply the Feynman-Hibbs procedure. It is shown that this noncommutative model generates a nonunitary dynamics that predicts a vanishing probability in the neighborhood of the singularity. This result effectively regularizes the Kantowski-Sachs singularity and generalizes a similar result, previously obtained for the case of Schwarzschild black holes.
Behavior of embedded phase in shock-driven two-phase flow
NASA Astrophysics Data System (ADS)
Kuehner, Garrett; Wayne, Patrick; Olmstead, Dell; Corbin, Clint; Bernard, Tennille; Vorobieff, Peter; Truman, C. Randall
2013-11-01
We present an experimental study of droplet acceleration in a shock-driven two-phase flow (air with embedded liquid droplets). The droplets (propylene glycol, diameter 0.5-3 μm) were pre-mixed with the air in the test section of a shock tube, then impulsively accelerated with planar shock wave with a Mach number of 1.7. A cross-section of the flow is illuminated with multiple pulses from Nd:YAG lasers, producing time-resolved visualizations of the seeded volume. The images are then analyzed to quantify droplet velocity and acceleration from the shock passage to about 1.5 ms after the shock. Based on the velocity measurements, we can resolve the droplet lag after the shock, when the massive droplets ``catch up'' with the flow of the surrounding air, as well as validate our earlier estimates of boundary layer growth. This research is supported by NNSA (US National Nuclear Security Agency).
NASA Astrophysics Data System (ADS)
A, Savelyev D.; N, Khonina S.
2014-03-01
We analyze the diffraction of the laser beam with a vortex phase singularity on the basis of the finite-difference time-domain method (FDTD). It is shown that, when incident beam has phase singularity, increase of the micro-axicon radius leads to extension of the light needle consisting of longitudinal electric field component. The numerical investigations held of the near-field diffraction for the most common and easily implemented types of polarization of the incident beam - linear and circular.
A polar-embedded C30 stationary phase: preparation and evaluation.
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
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.
Formation of nanometer embedded phases during high-energy Ti-implanted and annealed steel
NASA Astrophysics Data System (ADS)
Zhang, Tonghe; Wu, Yuguang; Deng, Zhiwei; Cui, Ping; Wang, Ping
2000-06-01
Observation by transmission electron microscope (TEM) indicated the formation of FeTi 2 phase of 3.5-20 nm in diameter embedded in a high-energy Ti-implanted layer. The nanometer phases were embedded among dislocations and grain boundaries in Ti-implanted steel at 400°C. It has good wear resistance. The embedded structure changes after annealing. The structure changed slightly after annealing at temperature ranging from 350°C to 500°C, while the hardness of the implanted layer increased greatly. The maximum of hardness is obtained when the sample was annealed at 500°C for 20 min and the Ti phases had an average diameter of 8 nm. Dislocations disappeared and the diameter of nanometer phases increased to 10 and 16 nm after annealing at temperature of 750°C and 1000°C, respectively. The average densities of the nanometer phases are 8.8×10 10 and 6.5×10 10 cm-2, respectively for both annealing temperatures.
Restoration of singularities in reconstructed phase of crystal image in electron holography.
Li, Wei; Tanji, Takayoshi
2014-12-01
Off-axis electron holography can be used to measure the inner potential of a specimen from its reconstructed phase image and is thus a powerful technique for materials scientists. However, abrupt reversals of contrast from white to black may sometimes occur in a digitally reconstructed phase image, which results in inaccurate information. Such phase distortion is mainly due to the digital reconstruction process and weak electron wave amplitude in some areas of the specimen. Therefore, digital image processing can be applied to the reconstruction and restoration of phase images. In this paper, fringe reconnection processing is applied to phase image restoration of a crystal structure image. The disconnection and wrong connection of interference fringes in the hologram that directly cause a 2π phase jump imperfection are correctly reconnected. Experimental results show that the phase distortion is significantly reduced after the processing. The quality of the reconstructed phase image was improved by the removal of imperfections in the final phase. PMID:25272997
Phase changes in nickel clusters from an embedded-atom potential
Guevenc, Z.B.; Jellinek, J. ); Voter, A.F. )
1991-01-01
The meltinglike behavior of Ni{sub n}, n=12,13,14,19 clusters is studied using molecular dynamics simulations. The cohesion in clusters is modelled by an embedded-atom potential incorporating many-body effects. The features of the phase change transition derived are compared to those obtained earlier from pairwise interactions and a different many-body (Gupta-like) potential. 7 refs., 3 figs.
3D imaging of amplitude objects embedded in phase objects using transport of intensity
NASA Astrophysics Data System (ADS)
Banerjee, Partha; Basunia, Mahmudunnabi
2015-09-01
The amplitude and phase of the complex optical field in the Helmholtz equation obey a pair of coupled equations, arising from equating the real and imaginary parts. The imaginary part yields the transport of intensity equation (TIE), which can be used to derive the phase distribution at the observation plane. If a phase object is approximately imaged on the recording plane(s), TIE yields the phase without the need for phase unwrapping. In our experiment, the 3D image of a phase object and an amplitude object embedded in a phase object is recovered. The phase object is created by heating a liquid, comprising a solution of red dye in alcohol, using a focused 514 nm laser beam to the point where self-phase modulation of the beam is observed. The optical intensities are recorded at various planes during propagation of a low power 633 nm laser beam through the liquid. In the process of applying TIE to derive the phase at the observation plane, the real part of the complex equation is also examined as a cross-check of our calculations. For pure phase objects, it is shown that the real part of the complex equation is best satisfied around the image plane. Alternatively, it is proposed that this information can be used to determine the optimum image plane.
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.
NASA Astrophysics Data System (ADS)
Bunsen, Masatoshi; Umetsu, Shuhei; Takabayashi, Masanori; Okamoto, Atsushi
2013-09-01
A technique for the phase and amplitude detection of object beams with multivalued phase and amplitude modulation is proposed for holographic storage systems. Generally, the spatial distribution of the complex amplitude of the object beam can be precisely detected by phase-shifting interferometric measurements in which the phase of the reference wave for interferometry is temporally or spatially changed in the datapage retrieval process. On the other hand, our technique allows fast, accurate, and feasible phase and amplitude demodulations by preliminary embedding phase shift into the phase signal of the datapage during recording. This technique will significantly improve the data transfer rate and vibration tolerance of the holographic storage system because the complex amplitudes of the object beam carrying datapages can be detected by single-shot image capturing. The optical system for datapage replay will also be simplified because there is no need to use any phase-shifting device during data retrieval. The single-shot detection of the phase-modulated datapage is experimentally demonstrated.
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.
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.
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.
Zou, Renqiang; Kneller, James; Leon, L. Joshua; Nattel, Stanley
2002-09-01
Atrial fibrillation (AF) is a common cardiac arrhythmia, but its mechanisms are incompletely understood. The identification of phase singularities (PSs) has been used to define spiral waves involved in maintaining the arrhythmia, as well as daughter wavelets. In the past, PSs have often been identified manually. Automated PS detection algorithms have been described previously, but when we attempted to apply a previously developed algorithm we experienced problems with false positives that made the results difficult to use directly. We therefore developed a tool for PS identification that uses multiple strategies incorporating both image analysis and mathematical convolution for automated detection with optimized sensitivity and specificity, followed by manual verification. The tool was then applied to analyze PS behavior in simulations of AF maintained in the presence of spatially distributed acetylcholine effects in cell grids of varying size. These analyses indicated that in almost all cases, a single PS lasted throughout the simulation, corresponding to the central-core tip of a single spiral wave that maintained AF. The sustained PS always localized to an area of low acetylcholine concentration. When the grid became very small and no area of low acetylcholine concentration was surrounded by zones of higher concentration, AF could not be sustained. The behavior of PSs and the mechanisms of AF were qualitatively constant over an 11.1-fold range of atrial grid size, suggesting that the classical emphasis on tissue size as a primary determinant of fibrillatory behavior may be overstated. (c) 2002 American Institute of Physics. PMID:12779605
At wavelength observation of phase defect embedded in EUV mask using microscope technique
NASA Astrophysics Data System (ADS)
Terasawa, Tsuneo; Amano, Tsuyoshi; Yamane, Takeshi; Watanabe, Hidehiro; Toyoda, Mitsunori; Harada, Tetsuo; Watanabe, Takeo; Kinoshita, Hiroo
2014-04-01
The effect of phase defect on extreme ultraviolet (EUV) lithography was examined using an EUV microscope. A test mask containing periodic absorber line patterns and programmed pit phase defects embedded in a multilayer-coated mask blank was prepared, and the mask patterns were observed by the EUV microscope developed by Tohoku University and constructed at the site of a beam line of the New SUBARU of the University of Hyogo. The half pitches of the absorber patterns were 64 nm and 44 nm at mask which corresponded to 16 nm and 11 nm device generations. The programmed defects included not only square-shape defects but also rectangular-shape defects with different orientations. When a phase defect was located between two adjacent absorber patterns, then the observation image intensity of the absorber lines and spaces (L/S) patterns varied, and the impact of a phase defect was predicted as an intensity variation of bright space image. Phase defect location dependency and defect shape dependency of the observation image intensity were examined. The effectiveness of the EUV microscope to predict the phase defect impacts was confirmed.
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.
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
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.
A single-phase embedded Z-source DC-AC inverter.
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
A Single-Phase Embedded Z-Source DC-AC Inverter
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
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
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.
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.
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)
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.
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. PMID:26356599
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.
NASA Technical Reports Server (NTRS)
Reddy, C. P.; Gupta, S. C.
1973-01-01
An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.
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.
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…
NASA Astrophysics Data System (ADS)
Li, Dong; Tian, Jindong
2010-11-01
An embedded three-dimensional (3-D) profilometry system based on a combination of gray-code and phase shifting (GCPS) method is proposed. This system consists of a digital-micromirror-device (DMD) based video projector, a high-speed CCD camera and an embedded digital signal processing hardware system based on DSP. In this technique, seven gray-code patterns and three sinusoidal fringe patterns with 120-deg phase shift are integrated in red, green and blue channels to form four color fringe patterns. When the four color fringe patterns are sent to the DMD based projector without color filter, the previous gray-code patterns and three sinusoidal fringe patterns are repeatedly projected to an object surface in gray-scale sequentially. These fringe patterns deformed by the object surface are captured by a high-speed CCD camera synchronized with the projector. An embedded hardware system is developed for synchronization between the camera and the projector and taking full advantage of DSP parallel processing capability for real-time phase retrieve and 3-D reconstruction. Since the number of projected images of GCPS is reduced from 11 to 4, the measurement speed is enhanced dramatically. Experimental results demonstrated the feasibility of the proposed technique for high-speed 3-D shape measurement.
Mallik, Abul K; Qiu, Hongdeng; Oishi, Tomohiro; Kuwahara, Yutaka; Takafuji, Makoto; Ihara, Hirotaka
2015-07-01
For the first time, we synthesized multiple embedded polar groups (EPGs) containing linear C18 organic phases. The new materials were characterized by elemental analysis, IR spectroscopy, (1)H NMR, diffuse reflectance infrared Fourier transform (DRIFT), solid-state (13)C cross-polarization magic angle spinning (CP/MAS) NMR, suspended-state (1)H NMR, and differential scanning calorimetry (DSC). (29)Si CP/MAS NMR was carried out to investigate the degree of cross-linking of the silane and silane functionality of the modified silica. Solid-state (13)C CP/MAS NMR and suspended-state (1)H NMR spectroscopy indicated a higher alkyl chain order for the phase containing four EPGs than for the phase with three EPGs. To correlate the NMR results with temperature-dependent chromatographic studies, standard reference materials (SRM 869b and SRM 1647e), a column selectivity test mixture for liquid chromatography was employed. A single EPG containing the C18 phase was also prepared in a similar manner to be used as a reference column especially for the separation of basic and polar compounds in reversed-phase liquid chromatography (RPLC) and hydrophilic interaction liquid chromatography (HILIC), respectively. Detailed chromatographic characterization of the new phases was performed in terms of their surface coverage, hydrophobic selectivity, shape selectivity, hydrogen bonding capacity, and ion-exchange capacity at pH 2.7 and 7.6 for RPLC as well as their hydrophilicity, the selectivity for hydrophilic-hydrophobic substituents, the selectivity for the region and configurational differences in hydrophilic substituents, the evaluation of electrostatic interactions, and the evaluation of the acidic-basic nature for HILIC-mode separation. Furthermore, peak shapes for the basic analytes propranolol and amitriptyline were studied as a function of the number of EPGs on the C18 phases in the RPLC. The chromatographic performance of multiple EPGs containing C18 HILIC phases is illustrated
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
NASA Astrophysics Data System (ADS)
Ponevchinsky, V. V.; Goncharuk, A. I.; Vasil'Ev, V. I.; Lebovka, N. I.; Soskin, M. S.
2010-03-01
The structural features, as well as the optical and electrophysical properties of a 5CB nematic liquid crystal with additions of multilayer carbon nanotubes, have been investigated in the concentration range C = 0.0025-0.1 wt %. The self-aggregation of nanotubes into clusters with a fractal structure occurs in the liquid crystal. At 0.025 wt %, the clusters are merged, initiating the percolation transition of the composite to a state with a high electric conductivity. The strong interaction of 5CB molecules with the surface of nanotube clusters is responsible for the formation of micron surface liquid crystal layers with an irregular field of elastic stresses and a complex structure of birefringence. They are easily observed in a polarization microscope and visualize directly invisible submicron nanotube aggregates. Their transverse size increases when an electric field is applied to the liquid crystal cell. Two mechanisms of the generation of optical singularities in the passing laser beam have been revealed. Optical vortices appear in the speckle fields of laser radiation scattered at the indented boundaries of the nanotube clusters, whereas the birefringence of the beam in surface liquid-crystal layers is accompanied by the appearance of polarization C points.
Singularity in structural optimization
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Guptill, J. D.; Berke, L.
1993-01-01
The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.
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).
NASA Astrophysics Data System (ADS)
Kovalevsky, Valery O.; Lobachev, Vitaly V.
2002-02-01
Detail analysis of active medium flow structure is presented. Schlieren method photography of flow is processed to reconstruct parameters both stochastic and order phase components. Properties of random part including correlation function, spectrum of spatial frequency, scale of turbulence, are determined by digital filtering. It was possible to compare influence of random and regular phase distortions on radiation divergence structure.
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.
Defect reduction of SiNx embedded m-plane GaN grown by hydride vapor phase epitaxy
NASA Astrophysics Data System (ADS)
Woo, Seohwi; Kim, Minho; So, Byeongchan; Yoo, Geunho; Jang, Jongjin; Lee, Kyuseung; Nam, Okhyun
2014-12-01
Nonpolar (1 0 -1 0) m-plane GaN has been grown on m-plane sapphire substrates by hydride vapor phase epitaxy (HVPE). We studied the defect reduction of m-GaN with embedded SiNx interlayers deposited by ex-situ metal organic chemical vapor deposition (MOCVD). The full-width at half-maximum values of the X-ray rocking curves for m-GaN with embedded SiNx along [1 1 -2 0]GaN and [0 0 0 1]GaN were reduced to 528 and 1427 arcs, respectively, as compared with the respective values of 947 and 3170 arcs, of m-GaN without SiNx. Cross-section transmission electron microscopy revealed that the basal stacking fault density was decreased by approximately one order to 5×104 cm-1 due to the defect blocking of the embedded SiNx. As a result, the near band edge emission intensities of the room-temperature and low-temperature photoluminescence showed approximately two-fold and four-fold improvement, respectively.
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.
Shen, H Z; Shao, X Q; Wang, G C; Zhao, X L; Yi, X X
2016-01-01
The quantum phase transition (QPT) describes a sudden qualitative change of the macroscopic properties mapped from the eigenspectrum of a quantum many-body system. It has been studied intensively in quantum systems with the spin-boson model, but it has barely been explored for systems in coupled spin-boson models. In this paper, we study the QPT with coupled spin-boson models consisting of coupled two-level atoms embedded in three-dimensional anisotropic photonic crystals. The dynamics of the system is derived exactly by means of the Laplace transform method, which has been proven to be equivalent to the dissipationless non-Markovian dynamics. Drawing on methods for analyzing the ground state, we obtain the phase diagrams through two exact critical equations and two QPTs are found: one QPT is that from the phase without one bound state to the phase with one bound state and another is that from one phase with the bound state having one eigenvalue to another phase where the bound state has two eigenvalues. Our analytical results also suggest a way of control to overcome the effect of decoherence by engineering the spectrum of the reservoirs to approach the non-Markovian regime and to form the bound state of the whole system for quantum devices and quantum statistics. PMID:26871024
Liu, Shijia; Xu, Hongxin; Yu, Jiaojiao; Li, Danyang; Li, Mingyan; Qiao, Xiaoqiang; Qin, Xinying; Yan, Hongyuan
2015-12-01
A novel imidazolium-embedded N,N-dimethylaminopropyl-functionalized silica-based stationary phase (Sil-ImCl) was prepared and further used for hydrophilic interaction/reversed-phase mixed-mode chromatography. The Sil-ImCl stationary phase was respectively characterized by Fourier transform infrared spectrometry, thermogravimetric analysis, and element analysis. A variety of hydrophilic or hydrophobic compounds were used to evaluate the retention mechanisms of the developed stationary phase, and the effects of buffer salt concentration and pH of mobile phase on the retention of these compounds were also investigated. The developed stationary phase was successfully applied for separation of nucleosides and nucleic acid bases, water-soluble vitamins, phenols, and positional isomers. Moreover, simultaneous separation of polar and nonpolar compounds was also achieved with high resolution, outperforming the commercially available C8 column and amino column. Furthermore, the Sil-ImCl stationary phase has been successfully applied for separation of secondary metabolites of Hansfordia sinuosae. All these results demonstrate that the Sil-ImCl stationary phase might be promising for separation of complex polar and nonpolar compounds with high efficiency, especially in biological industry. PMID:26427503
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.
The Hamiltonian property of the flow of singular trajectories
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.
NASA Astrophysics Data System (ADS)
Bray, Joey R.
Phased array antennas, capable of forming multiple agile beams of radiation, are ever-increasing operating frequencies. Systems operating at being deployed at frequencies of 30 GHz and above, a range known as millimetre-waves, include military radar, commercial collision-avoidance radar, inter-satellite communication links, and future wideband mobile internet satellite communications services. Millimetre-wave phase shifters, the topic of this thesis, are key components of many phased array antennas. A phase shifter refers to any device that can dynamically alter the phase, or the timing, of a signal. Although a number of concurrent millimetre-wave phase shifter designs presently exist, none simultaneously satisfies all of the desired requirements, including: light weight, small size, low cost, and good electrical performance. Phase shifters may be broadly categorised based on the material they use, either semiconductor or ferrite. Semiconductor shifters satisfy the former two requirements but suffer from high electrical losses. Conversely, traditional ferrite phase shifters have excellent electrical performance but are bulky and difficult to integrate with other components. Given the superior electrical performance of ferrite phase shifters, a more compact means of fabricating these is proposed in this thesis. In addition, new types of ferrite phase shifters are devised, and these are subsequently made from a chip-packaging technology called low temperature cofired ceramic. The resulting phase shifters are easily fabricated, are simple to interconnect to other integrated circuits, are more compact and lightweight than their predecessors, and have excellent electrical performance at millimetre-wave frequencies. Prototype phase shifters have been successfully manufactured using an experimental ferrite ceramic material and have yielded a maximum phase shift of 53° at 36 GHz for bias currents of -500 to +500 mA. Phased array antennas, capable of forming multiple agile
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.
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…
Bocian, Szymon; Krzemińska, Katarzyna; Buszewski, Bogusław
2016-07-01
A new type of stationary bonded phase for liquid chromatography with various functional groups bonded to diol-modified silica via ester bond was synthesized. The structures of the proposed stationary phases contain: alkyl chains (C10, C18), phenyl, and cholesterol groups. The structures of the synthesized materials were confirmed by different physico-chemical techniques such as elemental analysis, infrared spectroscopy (FTIR), (13)C CP/MAS NMR and liquid chromatography under reversed phase conditions (RP) and with hydrophilic interaction liquid chromatography (HILIC). Depending on the type of functionalities bonded to the Diol-Ester, the stationary phases are capable of separating various groups of compounds in RP and HILC, even using pure water as a mobile phase. PMID:27170946
Corrosion behavior of the embedded layer with nanometer phase in Ti and /Ti+C-implanted steel
NASA Astrophysics Data System (ADS)
Zhang, Tonghe; Wu, Yuguang; Zhang, Huixing; Deng, Zhiwei; Zhou, Gu; Liang, Hong; Ma, Furong; Zhang, Xiaoji; Wang, Xiaoyan
2000-06-01
Ti and Ti + C ions were implanted into H13 steel, the cross-sections of the samples were observed by transmission electron microscope (TEM). The results show that the structure of the implanted layer has greatly changed. The layer, embedded with nanometer phase of FeTi 2, TiC and Fe-C compound, is formed in Ti and Ti + C ion-implanted layer. The thickness of the embedded layer is greater than that of the corresponding ion range. The structure of the double ion-implanted layers is obviously different. The wear resistance and hardness of Ti or Ti + C-implanted H13 steel increased, and the friction coefficient decreased. This indicates that unique resistance for wear and corrosion can be obtained. An even higher corrosion resistance has been found, as the layer with an embedded structure was formed in Ti or Ti + C-implanted H13 steel. The results of electrochemical measurement show that the corrosion current density decreases obviously with increase of ion dose. The corrosion current density of Ti-implanted steel with a dose 1.3×10 18 cm -2 is 5-13% of that of unimplanted steel. The corrosion behavior of Ti + C dual implantation could be further improved; the corrosion current density is 1.2% of that of non-implanted samples. The corrosion trace could not be observed on the annealing sample by scanning electron microscope (SEM), after multi-sweep cyclic voltammetry (CV) of 40 cycles were performed on it. Finally, the modification mechanism of Ti or Ti + C-implanted H13 steel is discussed.
CD and profile metrology of embedded phase shift masks using scatterometry
NASA Astrophysics Data System (ADS)
Lee, Kyung man; Yedur, Sanjay; Hetzer, Dave; Tavassoli, Malahat; Baik, Kiho
2006-06-01
Linewidth and etch depth control on the photomask is rapidly becoming a major concern in mask processing. In this paper, we report on a Scatterometry based metrology system that provides line width and etch profile measurements on Embedded PSMs on Intel's 65nm and 45nm node test masks. Measurements were made with Nanometric's Atlas-M reticle measurement system. Spectrum data obtained from plates were analyzed using Timbre Technologies' ODP analysis software. We characterized the CD uniformity, linearity, sidewall angle and thickness uniformity. Significant reduction in time per measurement is achieved when compared to CD-SEM. ODP Scatterometry reported a 2x reduction in the CD Uniformity compared to that reported from the SEM. This reduction is typically due to outliers reported by the CD-SEM that is averaged out in ODP Scatterometry. Good correlation to top-down CD-SEM and cross-sectional SEM is reported. R-squared correlation of >0.99 (ODP scatterometry to top down CD-SEM) is reported. Profile measurements from ODP show excellent match to cross-section SEM. The data show that Scatterometry provides a nondestructive way to monitor basic etch profile combined with relatively little CD metrology lag.
Dimensional mutation and spacelike singularities
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.
NASA Astrophysics Data System (ADS)
Tolstik, A. L.
2016-02-01
Basic patterns of interaction of Gaussian and singular light beams (optical vortices) in media with resonant and thermal nonlinearity are experimentally investigated. It is demonstrated that interference of the Gaussian and singular beams in a nonlinear medium leads to the formation of dynamic volume holograms characterized by a singular structure. Under conditions of nonlinear holographic recording and Bragg diffraction on singular volume holograms, multiplexing of a topological charge and frequency conversion of optical vortices (transition from the IR to the visible range of the spectrum) is observed. Polarization recording of singular holograms that allows dynamic control to be performed over polarization of singular light beams including rotation of the polarization plane and conversion of linearly polarized radiation into circularly or elliptically polarized radiation.
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.
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.
ERIC Educational Resources Information Center
Sangueza, Cheryl Ramirez
2010-01-01
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…
Noncommutative Black Holes and the Singularity Problem
NASA Astrophysics Data System (ADS)
Bastos, C.; Bertolami, O.; Dias, N. C.; Prata, J. N.
2011-09-01
A phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model is considered to study the interior of a Schwarzschild black hole. Due to the divergence of the probability of finding the black hole at the singularity from a canonical noncommutativity, one considers a non-canonical noncommutativity. It is shown that this more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole.
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.
NASA Astrophysics Data System (ADS)
Hawking, Stephen
2005-01-01
The last chapter of my PhD thesis, contained my first singularity theorem. This showed that under certain reasonable conditions, any cosmological solution of the field equations, would have a big bang singularity. At this singularity, classical general relativity would break down, so one could not use it to predict how the universe began. It was therefore necessary to develop a quantum theory of gravity, in order to understand the origin of the universe. In this talk, I explore if the origin of the universe can be semi classical, and non singular. This is possible despite the singularity theorems, because like so many other no go theorems, they have a get out clause. In this case, the get out is the strong energy condition.
A well-based reverse-phase protein array of formalin-fixed paraffin-embedded tissue.
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
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.
Singular Atom Optics with Spinor BECs
NASA Astrophysics Data System (ADS)
Schultz, Justin T.; Hansen, Azure; Bigelow, Nicholas P.
2015-05-01
We create and study singular spin textures in pseudo-spin-1/2 BECs. A series of two-photon Raman interactions allows us to not only engineer the spinor wavefunction but also perform the equivalent of atomic polarimetry on the BEC. Adapting techniques from optical polarimetry, we can image two-dimensional maps of the atomic Stokes parameters, thereby fully reconstructing the atomic wavefunction. In a spin-1/2 system, we can represent the local spin superposition with ellipses in a Cartesian basis. The patterns that emerge from the major axes of the ellipses provide fingerprints of the singularities that enable us to classify them as lemons, stars, saddles, or spirals similar to classification schemes for singularities in singular optics, condensed matter, and liquid crystals. These techniques may facilitate the study of geometric Gouy phases in matter waves as well as provide an avenue for utilizing topological structures as quantum gates.
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.
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.
Singularities for PRANDTL'S Equations
NASA Astrophysics Data System (ADS)
Lo Bosco, G.; Sammartino, M.; Sciacca, V.
2006-03-01
We use a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our tool is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformly bounded in H1.
Dimensional Mutation and Spacelike Singularities
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.
Anatomy of malicious singularities
NASA Astrophysics Data System (ADS)
Heller, Michael; Odrzygóźdź, Zdzisław; Pysiak, Leszek; Sasin, Wiesław
2007-09-01
As well known, the b boundaries of the closed Friedman world model and of Schwarzschild solution consist of a single point. We study this phenomenon in a broader context of differential and structured spaces. We show that it is an equivalence relation ρ, defined on the Cauchy completed total space E¯ of the frame bundle over a given space-time, that is responsible for this pathology. A singularity is called malicious if the equivalence class [p0] related to the singularity remains in close contact with all other equivalence classes, i.e., if p0ɛcl[p] for every p ɛE. We formulate conditions for which such a situation occurs. The differential structure of any space-time with malicious singularities consists only of constant functions which means that, from the topological point of view, everything collapses to a single point. It was noncommutative geometry that was especially devised to deal with such situations. A noncommutative algebra on E¯, which turns out to be a von Neumann algebra of random operators, allows us to study probabilistic properties (in a generalized sense) of malicious singularities. Our main result is that, in the noncommutative regime, even the strongest singularities are probabilistically irrelevant.
Singular Continuations of Attractors
NASA Astrophysics Data System (ADS)
Giraldo, A.; Sanjurjo, J. M. R.
2009-01-01
We study dynamical and topological properties of the singularities of continuations of attractors of flows on manifolds. Despite the fact that these singularities are not isolated invariant sets, they share many of the properties of attractors; in particular, they have finitely generated Čech homology and cohomology, and they have the Čech homotopy type of attractors. This means that, from a global point of view, the singularities of continuations are topological objects closely related to finite polyhedra. The global structure is preserved even for weaker forms of continuation. An interesting case occurs with the Lorenz system for parameter values close to the situation of preturbulence. A general result, motivated by this particular case, is presented.
NASA Astrophysics Data System (ADS)
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, of potential usefulness to experimentalists dealing with such media.
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
Liu, Hai-Yan; Li, Zhi-Yong; Liu, Dan; Xue, Ying-Wen; Shi, Zhi-Guo
2016-04-22
Octadecyl bonded silica (ODS) is the most popular packing for reversed-phase chromatography. However, it generally demonstrates bad resolution for polar analytes because of the residue silanols and its poor stability in aqueous mobile phase. To address the problem, a new reversed-phase packing containing both polar-embedded and polar-endcapped moieties was proposed. It was prepared by a very simple method, in which the epoxide addition reaction of 3-glycidoxypropyltrimethoxysilane with 1-octadecanethiol proceeded simultaneously with the reaction of silane coupling onto silica particles. By controlling the molecular ratio of 3-glycidoxypropyltrimethoxysilane to 1-octadecanethiol higher than 1.0 (1.56 for the present study), both polar-embedded and polar-endcapped moieties were achieved onto the packing. The performance of the packing was evaluated in detail. The results demonstrated that neutral, acidic and basic analytes were well separated on the packing. The column efficiency for phenanthrene was 34,200 theoretical plates per meter. In addition, four nucleotides can be separated in 100% phosphate buffered saline solution with good reproducibility, which indicates the packing has good stability in aqueous mobile phase. Amitriptyline, a typical basic analytes, was eluted out with relatively symmetric peak shape (asymmetry factor of 1.36), which implies that the packing has not suffered from the negative effect of residue silanols significantly. Good stability in buffer solution of pH ranging from 2.0 to 10.0 was also documented for the packing. PMID:27033982
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
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.
New singularities in unexpected places
NASA Astrophysics Data System (ADS)
Barrow, John D.; Graham, Alexander A. H.
2015-09-01
Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe.
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.
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.
NASA Astrophysics Data System (ADS)
Pavelko, A. A.; Shilkina, L. A.; Reznichenko, L. A.; Dudkina, S. I.; Andryushina, I. N.; Yurasov, Yu. I.; Andryushin, K. P.; Razumovskaya, O. N.
2015-12-01
The boundaries of the phase states of solid solutions in the rhombohedral region of the Pb(Zr1‒ x Ti x )O3 (0 ≤ x ≤ 1.00) system and the curve of the R3 c → R3 m phase transition have been refined on the basis of detailed (with a small concentration step) high-temperature (25°C ≤ T ≤ 700°C) studies of the structural characteristics and frequencies of the piezoelectric resonance of the radial oscillation mode of polarized ceramic samples. It has been shown that, in the range 0.07 ≤ x ≤ 0.20, the transition curve practically coincides with the generally accepted one and, in the interval 0.20 ≤ x ≤ 0.36, it differs from the latter by a nonmonotonic behavior and agrees in the boundaries and regions of the phase states. The curve of the transition from the region of coexistence of the R- and Rh 1-phases in the clusterized state to a region with single Rh 1-phase in the interval of concentrations 0.08 ≤ x ≤ 0.12 and temperatures 200-250°C has been constructed. The full x- T phase diagram of the Pb(Zr1- x Ti x )O3 system has been presented. Dispersion spectra of solid solutions on variation in the frequency of the measuring electric field in the interval of 25-106 Hz have been studied, and their correlation with singularities of the phase portrait has been established.
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
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
Singularities in Optimal Structural Design
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Guptill, J. D.; Berke, L.
1992-01-01
Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.
Singularities in optimal structural design
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Guptill, J. D.; Berke, L.
1992-01-01
Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.
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
Singular parabolic equations of second order on manifolds with singularities
NASA Astrophysics Data System (ADS)
Shao, Yuanzhen
2016-01-01
The main aim of this article is to establish an Lp-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the singular ends of the manifolds. Such a theory is of importance for the study of elliptic and parabolic equations on non-compact, or even incomplete manifolds, with or without boundary.
One Model of Singular Relativistic Lagrangian
NASA Astrophysics Data System (ADS)
Laserra, E.; Strianese, M.; Pavlotsky, I. P.
The so-called no-interaction theorem of D.G. Currie, T.F. Jordan, E.C. Sudarshan, H. Leutwyler, G. Marmo and N. Mukunda makes it possible to construct relativistic quasiclassical particle dynamics in the post-Galilean approximation only. It is obtained that in this approximation the Lagrangians are singular on some surfaces of the phase space. These peculiarities have different physical and mathematical nature from the ones studied by P.M.A. Dirac, where Hessians vanish in the whole phase-space. The dynamical properties are essentially peculiar on the studied singular surfaces. These properties, in our opinion, can be related with some physical phenomena. In the present paper the general situation is first described. As the whole problem is large and difficult we examined in detail just typical one- and two-dimensional models in the second part of the paper.
Singular eigenfunctions for shearing fluids I
Balmforth, N.J.; Morrison, P.J.
1995-02-01
The authors construct singular eigenfunctions corresponding to the continuous spectrum of eigenvalues for shear flow in a channel. These modes are irregular as a result of a singularity in the eigenvalue problem at the critical layer of each mode. They consider flows with monotonic shear, so there is only a single critical layer for each mode. They then solve the initial-value problem to establish that these continuum modes, together with any discrete, growing/decaying pairs of modes, comprise a complete basis. They also view the problem within the framework of Hamiltonian theory. In that context, the singular solutions can be viewed as the kernel of an integral, canonical transformation that allows us to write the fluid system, an infinite-dimensional Hamiltonian system, in action-angle form. This yields an expression for the energy in terms of the continuum modes and provides a means for attaching a characteristic signature (sign) to the energy associate with each eigenfunction. They follow on to consider shear-flow stability within the Hamiltonian framework. Next, the authors show the equivalence of integral superpositions of the singular eigenfunctions with the solution derived with Laplace transform techniques. In the long-time limit, such superpositions have decaying integral averages across the channel, revealing phase mixing or continuum damping. Under some conditions, this decay is exponential and is then the fluid analogue of Landau damping. Finally, the authors discuss the energetics of continuum damping.
Singular behavior of jet substructure observables
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
Kallioniemi, O P; Visakorpi, T; Holli, K; Heikkinen, A; Isola, J; Koivula, T
1991-01-01
Nuclear debris may significantly interfere with the analysis of S-phase fraction (SPF) from paraffin-embedded tumors. We used a background subtraction algorithm to compensate for the effects of slicing of tumor cell nuclei during preparation of paraffin-embedded specimens. DNA histograms were analyzed from 88 node-negative breast and from 78 prostatic carcinomas. Median SPFs corrected for nuclear slicing were lower than uncorrected ones in both breast cancer (7.6% vs. 5.7%) and prostate cancer (6.7% vs. 4.2%). The median SPF value in each group was used as a cut-off point in survival studies. As compared with the uncorrected SPFs, corrected SPF levels resulted in a more significant survival difference between breast cancer patients with above and below median SPF (p = 0.0014 vs. p = 0.014) and in a higher relative risk (RR) of death (4.5 vs. 3.1). The same was true for prostate cancer survival (p less than 0.0001 vs. p = 0.002) and RR (5.3 vs. 3.1). Compared with the exponential background subtraction method, the sliced nuclei correction was more reproducible and could be applied in all evaluable histograms without the risk of overcompensation. In conclusion, our results support the use of background correction with the sliced nuclei model in DNA flow cytometric studies of archival tissues. PMID:1935457
Naked singularities in initial surfaces
Wojtkiewicz, J. )
1990-03-15
We consider a singular hypersurface {Sigma}, carrying time-symmetric initial data for the Einstein equations. We assume that the area of the arbitrary two-sphere, enclosing the singularity, is bounded from below by some positive constant. A conformally flat ring,'' or pancake'' singularities having sufficiently large Euclidean radius, can serve as examples. We prove that if the Arnowitt-Deser-Misner mass associated with such a hypersurface is small enough, then this singularity is naked (i.e., it is not entirely surrounded by an apparent horizon). We suggest that a similar effect appears also for general (i.e., non-time-symmetric) hypersurfaces.
Updating the singular value decomposition
NASA Astrophysics Data System (ADS)
Davies, Philip I.; Smith, M. I. Matthew I.
2004-09-01
The spectral decomposition of a symmetric matrix A with small off-diagonal and distinct diagonal elements can be approximated using a direct scheme of R. Davies and Modi (Linear Algebra Appl. 77 (1986) 61). In this paper a generalization of this method for computing the singular value decomposition of close-to-diagonal is presented. When A has repeated or "close" singular values it is possible to apply the direct method to split the problem in two with one part containing the well-separated singular values and one requiring the computation of the "close" singular values.
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.
NASA Astrophysics Data System (ADS)
Sreesattabud, Tharathip; Gibbons, Brady J.; Watcharapasorn, Anucha; Jiansirisomboon, Sukanda
2013-07-01
Pb(Zr0.52Ti0.48)O3 or PZT thin films embedded with CuO nano-particles were successfully prepared by a hybrid sol-gel process. In this process, CuO (0, 0.1, 0.2, 0.3, 0.4, 0.5 and 1 wt. %) nanopowder was suspended in an organometallic solution of PZT, and then coated on platinised silicon substrate using a spin-coating technique. The influence of CuO nano-particles' dispersion on the phase of PZT thin films was investigated. XRD results showed a perovskite phase in all films. At the CuO concentration of 0.4-1 wt. %, a second phase was observed. The addition of CuO nano-particles affected the orientation of PZT thin films. The addition was also found to reduce the ferroelectric properties of PZT thin films. However, at 0.2 wt. % CuO concentration, the film exhibited good ferroelectric properties similar to those of PZT films. In addition, the fatigue retention properties of the PZT/CuO system was observed, and it showed 14% fatigue at 108 switching bipolar pulse cycles while the fatigue in PZT thin films was found to be 17% at the same switching bipolar pulse cycles.
ERIC Educational Resources Information Center
Avital, Doron
2007-01-01
This paper will examine an unresolved tension inherent in the question of art and argue for the idea of a singular rule as a natural resolution. In so doing, the structure of a singular rule will be fully outlined and its paradoxical constitution will be resolved. The tension I mention above unfolds both as a matter of history and as a product of…
Computing singularities of perturbation series
Kvaal, Simen; Jarlebring, Elias; Michiels, Wim
2011-03-15
Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schroedinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be useful for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with {delta}-function interactions for which Moeller-Plesset perturbation theory is considered and the radius of convergence found.
Staus, Chad; Kuech, Thomas; McCaughan, Leon
2008-08-18
We demonstrate an all-single mode structure which enables continuous phase matching of difference frequency generated THz light from the near-IR. This structure provides a long interaction length by way of well-confined collinear propagation of pumps and product without diffraction, resulting in high conversion efficiency. A LiNbO(3) version of this structure achieved a power-normalized conversion efficiency of 1.3 x 10(-7) W(-1)--some 23 times larger than the largest previously reported results. PMID:18711566
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.
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.
Wave-front singularities for two-dimensional anisotropic elastic waves.
NASA Technical Reports Server (NTRS)
Payton, R. G.
1972-01-01
Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.
Five-dimensional null-cone structure of big bang singularity
Lauro, S.; Schucking, E.L.
1985-04-01
The Friedmann model PHI of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five-dimensional Minkowski space MV is globally rigid: if F(PHI) and F'(PHI) are isometric embeddings in MV there is a motion of MV such that F'= F. The big bang singularity is the vertex of a null half-cone in MV. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.
Singularity spectrum of fractal signals from wavelet analysis: Exact results
Bacry, E.; Muzy, J.F.; Arneodo, A. )
1993-02-01
The multifractal formalism for singular measures is revisited using the wave transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimension D(h) of the set of singularities of Hoelder exponent h can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of order n, provided one uses an analyzing wavelet that possesses at least N > n vanishing moments. However, it is shown that a C[infinity] behavior generally induces a phase transition in the D(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the number N of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.
3D structures of liquid-phase GaIn alloy embedded in PDMS with freeze casting.
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
Mogaddam, N. A. P.; Turan, R.; Alagoz, A. S.; Yerci, S.; Foss, S.; Finstad, T. G.
2008-12-15
SiGe nanocrystals have been formed in SiO{sub 2} matrix by cosputtering Si, Ge, and SiO{sub 2} independently on Si substrate. Effects of the annealing time and temperature on structural and compositional properties are studied by transmission electron microscopy, x-ray diffraction (XRD), and Raman spectroscopy measurements. It is observed that Ge-rich Si{sub (1-x)}Ge{sub x} nanocrystals do not hold their compositional uniformity when annealed at high temperatures for enough long time. A segregation process leading to separation of Ge and Si atoms from each other takes place. This process has been evidenced by a double peak formation in the XRD and Raman spectra. We attributed this phase separation to the differences in atomic size, surface energy, and surface diffusion disparity between Si and Ge atoms leading to the formation of nonhomogenous structure consist of a Si-rich SiGe core covered by a Ge-rich SiGe shell. This experimental observation is consistent with the result of reported theoretical and simulation methods.
Singular field response and singular screening of vacancies in antiferromagnets.
Wollny, Alexander; Andrade, Eric C; Vojta, Matthias
2012-10-26
For isolated vacancies in ordered local-moment antiferromagnets we show that the magnetic-field linear-response limit is generically singular: The magnetic moment associated with a vacancy in zero field is different from that in a finite field h in the limit h→0(+). The origin is a universal and singular screening cloud, which moreover leads to perfect screening as h→0(+) for magnets which display spin-flop bulk states in the weak-field limit. PMID:23215218
NASA Astrophysics Data System (ADS)
Riggs, Lloyd Stephen
In this work the transient currents induced on an arbitrary system of thin linear scatterers by an electromagnetic plane wave are solved by using an electric field integral equation (EFIE) formulation. The transient analysis is carried out using the singularity expansion method (SEM). The general analysis developed here is useful for assessing the vulnerability of military aircraft to a nuclear generated electromagnetic pulse (EMP). It is also useful as a modal synthesis tool in the analysis and design of frequency selective surfaces (FSS). SEM parameters for a variety of thin cylindrical geometries have been computed. Specifically, SEM poles, modes, coupling coefficients, and transient currents are given for the two and three element planar array. Poles and modes for planar arrays with a larger number (as many as eight) of identical equally spaced elements are also considered. SEM pole-mode results are given for identical parallel elements with ends located at the vertices of a regular N-agon. Pole-mode patterns are found for symmetric (and slightly perturbed) single junction N-arm elements and for the five junction Jerusalem cross. The Jerusalem cross element has been used extensively in FSS.
Singular behavior of jet substructure observables
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Moult, Ian
2016-01-01
Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the limit in which hard substructure is resolved, as well as the limit of a jet with a single hard core. In this paper we study in detail the perturbative structure of two prominent jet substructure observables, N -subjettiness and the energy correlation functions, as measured on background QCD jets. In particular, we focus on the distinction between the limits in which two-prong structure is resolved or unresolved. Depending on the choice of subjet axes, we demonstrate that at fixed order, N -subjettiness can manifest myriad behaviors in the unresolved region: smooth tails, end point singularities, or singularities in the physical region. The energy correlation functions, by contrast, only have nonsingular 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 nonperturbative shape functions is highly dependent on the N -subjettiness axes definitions. 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.
Visibility of a spacetime singularity
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.
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.
Holographic signatures of cosmological singularities.
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. PMID:25279620
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%.
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.
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.
New singularities for Stokes waves
NASA Astrophysics Data System (ADS)
Crew, Samuel C.; Trinh, Philippe H.
2016-07-01
In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of $120^\\circ$. Here, the complex velocity scales like $f^{1/3}$ where $f$ is the complex potential. Later in 1973, Grant showed that for any wave away from the steepest configuration, the singularity $f = f^*$ moves into the complex plane, and is of order $(f-f^*)^{1/2}$ (J. Fluid Mech., vol. 59, 1973, pp. 257-262). Grant conjectured that as the highest wave is approached, other singularities must coalesce at the crest so as to cancel the square-root behaviour. Despite recent advances, the complete singularity structure of the Stokes wave is still not well understood. In this work, we develop numerical methods for constructing the Riemann surface that represents the extension of the water wave into the complex plane. We show that a countably infinite number of distinct singularities exists on other branches of the solution, and that these singularities coalesce as Stokes' highest wave is approached.
Monkhouse, W S
1985-08-01
Following an intraperitoneal injection of tritiated thymidine to neonatal mice, livers and spleens were removed and their labelling indices were derived autoradiographically. This was done in a number of ways: (1) from tissue imprints on gelatinised glass slides; (2) from tissue embedded in JB4 plastic sectioned at thicknesses of 2, 5 and 7 micron; and (3) from tissue embedded in paraffin wax and sectioned at 7 micron. The results show that the indices from the JB4 embedded sections increase as the section thickness decreases, and that this relationship persists down to the notional section thickness of zero in the tissue imprints (in which all the cells are in contact with the autoradiographic emulsion). Indices from the 7 micron paraffin wax embedded sections are surprisingly close to the values from the imprints, are higher than indices from the 5 and 7 micron JB4 embedded sections, and are not significantly different (at the 2% level) from those from 2 micron JB4 embedded sections. Possible reasons for these results are discussed in respect of the autoradiographic process and in relationship to various mathematical correction factors which have been proposed to take account of beta-particle self-absorption in thick sections. It is concluded that none of these correction factors is of value and that the embedding medium has an important effect on the observed labelling indices. Comparisons between labelling indices, therefore, should be made only when they are derived from similarly embedded material at the same section thickness. PMID:3908424
Naked singularity resolution in cylindrical collapse
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.
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.
Singular values, nematic disclinations, and emergent biaxiality.
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
LaBonte, Melissa J; Yang, Dongyun; Zhang, Wu; Wilson, Peter M; Nagarwala, Yasir M; Koch, Kevin M; Briner, Colleen; Kaneko, Tomomi; Rha, Sun-Young; Gladkov, Oleg; Urba, Susan G; Sakaeva, Dina; Pishvaian, Michael J; Hsieh, Ruey-Kuen; Lee, Wei-Ping; Lenz, Heinz-Josef
2016-09-01
An exploratory phase II biomarker-embedded trial (LPT109747; NCT00526669) designed to determine the association of lapatinib-induced fluoropyrimidine gene changes with efficacy of lapatinib plus capecitabine as first-line treatment for advanced gastric cancer or gastroesophageal junction adenocarcinoma independent of tumor HER2 status. Tumor biopsies obtained before and after 7-day lapatinib (1,250 mg) to analyze changes in gene expression, followed by a 14-day course of capecitabine (1,000 mg/m(2) twice daily, 14/21 days) plus lapatinib 1,250 mg daily. Blood samples were acquired for pharmacokinetic analysis. Primary clinical objectives were response rate (RR) and 5-month progression-free survival (PFS). Secondary objectives were overall survival (OS), PFS, time to response, duration of response, toxicity, and identification of associations between lapatinib pharmacokinetics and biomarker endpoints. Primary biomarker objectives were modulation of 5-FU-pathway genes by lapatinib, effects of germline SNPs on treatment outcome, and trough steady-state plasma lapatinib concentrations. Sixty-eight patients were enrolled; (75% gastric cancer, 25% gastroesophageal junction). Twelve patients (17.9%) had confirmed partial response, 31 (46.3%) had stable disease, and 16 (23.9%) had progressive disease. Median PFS and OS were 3.3 and 6.3 months, respectively. Frequent adverse events included diarrhea (45%), decreased appetite (39%), nausea (36%), and fatigue (36%). Lapatinib induced no changes in gene expression from baseline and no significant associations were found for SNPs analyzed. Elevated baseline HER3 mRNA expression was associated with a higher RR (33% vs. 0%; P = 0.008). Lapatinib plus capecitabine was well tolerated, demonstrating modest antitumor activity in patients with advanced gastric cancer. The association of elevated HER3 and RR warrants further investigation as an important player for HER-targeted regimens in combination with capecitabine. Mol Cancer Ther
Naked singularities as particle accelerators
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.
Recent Results on Singularity Strengths
NASA Astrophysics Data System (ADS)
Nolan, Brien
2002-12-01
In this contribution, we review some recent results on strengths of singularities. In a space-time (M,g), let γ[τ0, 0) → M be an incomplete, inextendible causal geodesic, affinely parametrised by τ, tangent ěc k. Let Jτ1 :=set of Jacobi fields along γ, orthogonal to γ and vanishing at time τ1 ≥ τ0 i.e. ěc ξ ∈ J{τ 1 } iff D2ξa = -Rbcdakbkdξc, gabξakb = 0, and ěc ξ (τ 1 ) = 0. Vτ1(τ) := volume element defined by full set of independent elements of Jτ1 (2-dim for null geodesies, 3-dim for time-like); Vτ1 := ∥Vτ1∥. Definition (Tipler 1977): γ terminates in a gravitationally strong singularity if for all 0 > τ1 ≥ τ0, lim inf
Algebraic Singularity Method for Mass Measurements with Missing Energy
Kim, Ian-Woo
2010-02-26
We propose a novel generalized method for mass measurements based on phase space singularity structures that can be applied to any event topology with missing energy. Our method subsumes the well-known end point and transverse mass methods and yields new techniques for studying 'missing particle' events, such as the double chain production of stable neutral particles at the LHC.
SINGULARITIES OF GENERALIZED PARTON DISTRIBUTIONS
Anatoly Radyushkin
2012-12-01
We discuss recent developments in building models for generalized parton distributions (GPDs) that are based on the formalism of double distributions (DDs). A special attention is given to a careful analysis of the singularity structure of DDs. The DD formalism is applied to construction of a model GPDs with a singular Regge behavior. Within the developed DD-based approach, we discuss the structure of GPD sum rules. It is shown that separation of DDs into the so-called ``plus'' part and the D-term part may be treated as a renormalization procedure for the GPD sum rules. This approach is compared with an alternative prescription based on analytic regularization.
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.
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.
Barotropic index w-singularities in cosmology
DaPbrowski, Mariusz P.; Denkiewicz, Tomasz
2009-03-15
We find an explicit cosmological model which allows a special type of cosmological singularity which we call a w-singularity. This singularity has the scale factor finite, the energy density and pressure vanishing, and the only singular behavior appears in a time-dependent barotropic index w(t). It is different from the type IV cosmological singularity in that it does not exhibit the divergence of the higher derivatives of the Hubble parameter and from the big brake since it does not fulfill the anti-Chaplygin gas equation of state. We also find an interesting duality between the w-singularities and the big-bang singularities. Physical examples of w-singularities appear in f(R), scalar field and brane cosmologies.
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.
Continuations of the nonlinear Schrödinger equation beyond the singularity
NASA Astrophysics Data System (ADS)
Fibich, G.; Klein, M.
2011-07-01
We present four continuations of the critical nonlinear Schrödinger equation (NLS) beyond the singularity: (1) a sub-threshold power continuation, (2) a shrinking-hole continuation for ring-type solutions, (3) a vanishing nonlinear-damping continuation and (4) a complex Ginzburg-Landau (CGL) continuation. Using asymptotic analysis, we explicitly calculate the limiting solutions beyond the singularity. These calculations show that for generic initial data that lead to a loglog collapse, the sub-threshold power limit is a Bourgain-Wang solution, both before and after the singularity, and the vanishing nonlinear-damping and CGL limits are a loglog solution before the singularity, and have an infinite-velocity expanding core after the singularity. Our results suggest that all NLS continuations share the universal feature that after the singularity time Tc, the phase of the singular core is only determined up to multiplication by eiθ. As a result, interactions between post-collapse beams (filaments) become chaotic. We also show that when the continuation model leads to a point singularity and preserves the NLS invariance under the transformation t → -t and ψ → ψ*, the singular core of the weak solution is symmetric with respect to Tc. Therefore, the sub-threshold power and the shrinking-hole continuations are symmetric with respect to Tc, but continuations which are based on perturbations of the NLS equation are generically asymmetric.
Emerging singularities in the bouncing loop cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Szydłowski, Marek
2008-06-01
In this paper we calculate O(μ4) corrections from holonomies in the loop quantum gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the loop quantum cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat Friedmann-Robertson-Walker cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard O(μ2) quantization scheme and is shifted to the higher energies ρbounce=3ρc. Also, a pole in the Hubble parameter appears for ρpole=(3)/(2)ρc corresponding to hyperinflation/deflation phases. This pole represents a curvature singularity at which the scale factor is finite. In this scenario the singularity and bounce coexist. Moreover, we find that an ordinary bouncing solution appears only when quantum corrections in the lowest order are considered. Higher order corrections can lead to nonperturbative effects.
Singularities in the Andreev spectrum of a multiterminal Josephson junction
NASA Astrophysics Data System (ADS)
Yokoyama, Tomohiro; Nazarov, Yuli V.
2015-10-01
The energies of Andreev bound states (ABS) forming in an N -terminal junction are affected by N -1 independent macroscopic phase differences between superconducting leads and can be regarded as energy bands in (N -1 )-periodic solids owing to the 2 π periodicity in all phases. We investigate the singularities and peculiarities of the resulting ABS spectrum combining phenomenological and analytical methods and illustrating with the numerical results. We pay special attention to spin-orbit (SO) effects. We consider Weyl singularities with a conical spectrum that are situated at zero energy in the absence of SO interaction. We show that the SO interaction splits the spectrum in spin like a Zeeman field would do. The singularity is preserved while departing from zero energy. With SO interaction, points of zero energy form an (N -2 )-dimensional manifold in an (N -1 )-dimensional space of phases, while this dimension is N -3 in the absence of SO interaction. Singularities of other types are situated near the superconducting gap edge. In the absence (presence) of SO interaction, the ABS spectrum at the gap edge is mathematically analogous to that at zero energy in the presence (absence) of SO interaction. We demonstrate that the gap edge touching (GET) points of the spectrum in principle form an N -2 (N -3 ) dimensional manifold when the SO interaction is absent (present). Certain symmetry lines in the Brillouin zone of the phases are exceptions from this rule, and GET there should be considered separately. We derive and study the effective Hamiltonians for all the singularities under consideration.
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.
Singularities of noncompact charged objects
NASA Astrophysics Data System (ADS)
Sharif, M.; G., Abbas
2013-03-01
We formulate a model for noncompact spherical charged objects in the framework of noncommutative field theory. The Einstein—Maxwell field equations are solved with charged anisotropic fluid. We choose matter and charge densities as functions of the two parameters, instead of defining these quantities in terms of the Gaussian distribution function. It is found that the corresponding densities and the Ricci scalar are singular in origin, whereas the metric is nonsingular, indicating a spacelike singularity. The numerical solution of the horizon equation implies that there are two or one or no horizon(s), depending on the mass. We also evaluate the Hawking temperature and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.
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.
Splash singularity for water waves.
Castro, Angel; Córdoba, Diego; Fefferman, Charles L; Gancedo, Francisco; Gómez-Serrano, Javier
2012-01-17
We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time. PMID:22219372
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.
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.
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.
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.
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.
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
Wentzel-Bardeen singularity in coupled Luttinger liquids: Transport properties
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.
String spectra near some null cosmological singularities
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.
Multichannel framework for singular quantum mechanics
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.
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.
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.
Singularities in Dromo formulation. Analysis of deep flybys
NASA Astrophysics Data System (ADS)
Roa, Javier; Sanjurjo-Rivo, Manuel; Peláez, Jesús
2015-08-01
The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very specific situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric flybys. The performance of Dromo is evaluated in different scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical flybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the flyby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity.
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.
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.
Exact solutions and singularities in string theory
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.
Overcoming Robot-Arm Joint Singularities
NASA Technical Reports Server (NTRS)
Barker, L. K.; Houck, J. A.
1986-01-01
Kinematic equations allow arm to pass smoothly through singular region. Report discusses mathematical singularities in equations of robotarm control. Operator commands robot arm to move in direction relative to its own axis system by specifying velocity in that direction. Velocity command then resolved into individual-joint rotational velocities in robot arm to effect motion. However, usual resolved-rate equations become singular when robot arm is straightened.
Optical spectral singularities as threshold resonances
Mostafazadeh, Ali
2011-04-15
Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral singularity appears whenever the gain coefficient coincides with its threshold value and other parameters of the system are selected properly. We explore a concrete realization of spectral singularities for a typical semiconductor gain medium and propose a method of constructing a tunable laser that operates at threshold gain.
Singularity analysis: theory and further developments
NASA Astrophysics Data System (ADS)
Cheng, Qiuming
2015-04-01
Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.
Entanglement in a second-order quantum phase transition
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.
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.
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
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
Naked singularities and quantum gravity
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.
Unfolding the singularities in superspace
NASA Astrophysics Data System (ADS)
Fischer, Arthur E.
1983-12-01
A method is described for unfolding the singularities in superspace,mathcal{G} = mathfrak{M}/mathfrak{D}, the space of Riemannian geometries of a manifoldM. This unfolded superspace is described by the projection mathcal{G}_{Fleft( M right)} = {mathfrak{M} × Fleft( M right)}/mathfrak{D} to mathfrak{M}/mathfrak{D} = mathcal{G} whereF(M) is the frame bundle ofM. The unfolded spacemathcal{G}_{Fleft( M right)} is infinite-dimensional manifold without singularities. Moreover, as expected, the unfolding ofmathcal{G}_{Fleft( M right)} at each geometry [g o] ∈mathcal{G} is parameterized by the isometry groupIg o (M) of g0. Our construction is natural, is generally covariant with respect to all coordinate transformations, and gives the necessary information at each geometry to makemathcal{G} a manifold. This construction is a canonical and geometric model of a nonrelativistic construction that unfolds superspace by restricting to those coordinate transformations that fix a frame at a point. These particular unfoldings are tied together by an infinite-dimensional fiber bundleE overM, associated with the frame bundleF(M), with standard fibermathcal{G}_{Fleft( M right)}, and with fiber at a point inM being the particular noncanonical unfolding ofmathcal{G} based at that point. ThusE is the totality of all the particular unfoldings, and so is a grand unfolding ofmathcal{G}.
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.
Approximate Orthogonal Sparse Embedding for Dimensionality Reduction.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Yang, Jian; Zhang, David
2016-04-01
Locally linear embedding (LLE) is one of the most well-known manifold learning methods. As the representative linear extension of LLE, orthogonal neighborhood preserving projection (ONPP) has attracted widespread attention in the field of dimensionality reduction. In this paper, a unified sparse learning framework is proposed by introducing the sparsity or L1-norm learning, which further extends the LLE-based methods to sparse cases. Theoretical connections between the ONPP and the proposed sparse linear embedding are discovered. The optimal sparse embeddings derived from the proposed framework can be computed by iterating the modified elastic net and singular value decomposition. We also show that the proposed model can be viewed as a general model for sparse linear and nonlinear (kernel) subspace learning. Based on this general model, sparse kernel embedding is also proposed for nonlinear sparse feature extraction. Extensive experiments on five databases demonstrate that the proposed sparse learning framework performs better than the existing subspace learning algorithm, particularly in the cases of small sample sizes. PMID:25955995
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
NASA Astrophysics Data System (ADS)
Yamamoto, Takafumi D.; Kotani, Atsuhiro; Nakajima, Hiroshi; Okazaki, Ryuji; Taniguchi, Hiroki; Mori, Shigeo; Terasaki, Ichiro
2016-03-01
We have investigated both static and dynamic magnetic properties of polycrystalline CaRu1-xScxO3 system in order to clarify the role of Sc ions as a disorder for magnetic ordering. We have observed typical features of a ferromagnetic cluster glass state below around 40 K: (i) a broad, frequency-dependent peak in the ac magnetic susceptibility, (ii) a slow relaxation of the magnetization, and (iii) a continuous increase in the dc magnetic susceptibility in field cooling process. The composition dependence of characteristic parameters for the cluster glass state suggests that chemical segregation can hardly explain the clustering mechanism. We propose a possible picture that the ferromagnetic clusters are distributed uniformly and form the glassy state embedded in the paramagnetic and metallic host of CaRuO3.
Singularity formation for Prandtl’s equations
NASA Astrophysics Data System (ADS)
Gargano, F.; Sammartino, M.; Sciacca, V.
2009-10-01
We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen’s singularity as a cubic root singularity. We introduce a class of initial data, uniformly bounded in H1, which have a dipole singularity in the complex plane. These data lead to a solution blow-up whose time can be made arbitrarily short within the class. This is numerical evidence of the ill-posedness of the Prandtl equations in H1. The presence of a small viscosity in the streamwise direction changes the behavior of the singularities. They stabilize at a distance from the real axis which depends on the amount of viscosity. We show that the Van Dommelen and Shen singularity and the singularity predicted by E and Engquist in [W. E, B. Engquist, Blowup of the solutions to the unsteady Prandtl’s equations, Comm. Pure Appl. Math. 50 (1997) 1287-1293.] have different complex structures.
An extension theorem for conformal gauge singularities
Luebbe, Christian; Tod, Paul
2009-11-15
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
Regularizing cosmological singularities by varying physical constants
Dąbrowski, Mariusz P.; Marosek, Konrad E-mail: k.marosek@wmf.univ.szczecin.pl
2013-02-01
Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the Λ-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.
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.
Singularities in fully developed turbulence
NASA Astrophysics Data System (ADS)
Shivamoggi, Bhimsen K.
2015-09-01
Phenomenological arguments are used to explore finite-time singularity (FTS) development in different physical fully-developed turbulence (FDT) situations. Effects of spatial intermittency and fluid compressibility in three-dimensional (3D) FDT and the role of the divorticity amplification mechanism in two-dimensional (2D) FDT and quasi-geostrophic FDT and the advection-diffusion mechanism in magnetohydrodynamic turbulence are considered to provide physical insights into the FTS development in variant cascade physics situations. The quasi-geostrophic FDT results connect with the 2D FDT results in the barotropic limit while they connect with 3D FDT results in the baroclinic limit and hence apparently provide a bridge between 2D and 3D.
Naked shell singularities on the brane
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.
Singular value decomposition with systolic arrays
NASA Technical Reports Server (NTRS)
Ipsen, I. C. F.
1984-01-01
Systolic arrays for determining the singular value decomposition of a mxn, m n, matrix A of bandwidth w are presented. After A has been reduced to bidiagonal form B by means of Givens plane rotations, the singular values of B are computed by the Golub-Reinsch iteration. The products of plane rotations form the matrices of left and right singular vectors. Assuming each processor can compute or supply a plane rotation, O(wn) processors accomplish the reduction to bidiagonal form in O(np) steps, where p is the number of superdiagonals. A constant number of processors then determines each singular value in about 6n steps. The singular vectors are computed by rerouting the rotations through the arrays used for the reduction to bidiagonal form, or else along the way by employing another rectangular array of O(wm) processors.
NASA Astrophysics Data System (ADS)
Beggs, Daryl; Lang, Ben; Young, Andrew; Oulton, Ruth
A polarisation singularity occurs at a position in a vector field where one of the parameters of the local polarisation ellipse (handedness, eccentricity or orientation) becomes singular. With the vector nature of electromagnetic fields, optics is an obvious place for the study of polarisation singularities, and they can be found in systems ranging from tightly focused beams to speckle fields. Here we demonstrate that photonic crystal waveguides support on-chip polarisation singularities. As Bloch waves, the eigenmodes of photonic crystal waveguides possess a strong longitudinal, as well as transverse, component of their electric field. The spatial dependence of both these components and the phase between them ensures a rich and complex polarisation landscape in the waveguide. Recently, the use of polarisation singularities found in photonic crystal waveguides is generating much interest for integrated quantum information applications, as they can couple the spin-states of electrons confined to quantum dots to the optical modes of the waveguide. For example, at a circular-point (C-point), the sign of the local helicity is governed by the propagation direction of the optical mode, which allows for spin-photon coupling to one direction only. However, any real system will inevitably contain imperfections, and it is not obvious that the polarisation singularities will persist in the disordered waveguides. Here, we use calculations of the eigenmodes of disordered waveguides to demonstrate that the polarisation singularities persist far beyond realistically expected levels of disorder.
Singularities affect dynamics of learning in neuromanifolds.
Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko
2006-05-01
The parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units. A parameter space forms a geometrical manifold, called the neuromanifold in the case of neural networks. Such a model is identified with a statistical model, and a Riemannian metric is given by the Fisher information matrix. However, the matrix degenerates at singularities. Such a singular structure is ubiquitous not only in multilayer perceptrons but also in the gaussian mixture probability densities, ARMA time-series model, and many other cases. The standard statistical paradigm of the Cramér-Rao theorem does not hold, and the singularity gives rise to strange behaviors in parameter estimation, hypothesis testing, Bayesian inference, model selection, and in particular, the dynamics of learning from examples. Prevailing theories so far have not paid much attention to the problem caused by singularity, relying only on ordinary statistical theories developed for regular (nonsingular) models. Only recently have researchers remarked on the effects of singularity, and theories are now being developed. This article gives an overview of the phenomena caused by the singularities of statistical manifolds related to multilayer perceptrons and gaussian mixtures. We demonstrate our recent results on these problems. Simple toy models are also used to show explicit solutions. We explain that the maximum likelihood estimator is no longer subject to the gaussian distribution even asymptotically, because the Fisher information matrix degenerates, that the model selection criteria such as AIC, BIC, and MDL fail to hold in these models, that a smooth Bayesian prior becomes singular in such models, and that the trajectories of dynamics of learning are strongly affected by the singularity, causing plateaus or slow manifolds in the parameter space. The natural gradient method is shown to perform well because it takes the singular
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.
Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii
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
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.
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.
Singularity analysis and elimination of CMA in multistage PMD channel model
NASA Astrophysics Data System (ADS)
Nie, Xinhui; Li, Yan; Du, Wentao; Cheng, Haiquan; Wu, Jian; Li, Wei; Lin, Jintong; Lu, Jianxin; Xu, Jian; Zhang, Guoyi; Luo, Huihong
2015-08-01
Polarization-division-multiplexed(PDM) optical coherent systems is considered a promising technique for next generation optical networks. With coherent detection, various impairments in the optical transmission system can be compensated by using digital signal processing (DSP) in the electrical domain. Constant modulus algorithm (CMA), due to its simplicity and immunity to phase noise, has been widely used to demultiplex polarizations and compensate received signals. On the other hand, CMA suffers from the singularity problem which results from Polarization- Dependent-Loss (PDL) and the less sensitivity in phase of CMA. Although many people have researched the singularity problem of CMA both in theory and experiments (modify CMA to avoid singularity problem), their theoretical channel model only contains fiber birefringence and does not consider the situation of multistage channel model which is used in long distance transmission system. Then we analyse the performance of CMA in the channel with multistage channel model through simulation. We change the initial tap of the traditional CMA which can achieve correct polarization demultiplexing without singularity in one stage channel model. But it is not very suitable in multistage channel model. We analysed singularity ratio in long distance transmission system. The simulation results play an active role in following research on singularity problem and the performance of CMA.
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.
Three-dimensional singular points in aerodynamics
NASA Technical Reports Server (NTRS)
Unal, Aynur
1988-01-01
When three-dimensional separation occurs on a body immersed in a flow governed by the incompressible Navier-Stokes equations, the geometrical surfaces formed by the three vector fields (velocity, vorticity and the skin-friction) and a scalar field (pressure) become interrelated through topological maps containing their respective singular points and extremal points. A mathematically consistent description of these singular points becomes inevitable when we want to study the geometry of the separation. A separated stream surface requires, for example, the existence of a saddle-type singular point on the skin-friction surface. This singular point is actually, in the proper language of mathematics, a saddle of index two. The index is a measure of the dimension of the outset (set leaving the singular point). Hence, when a saddle of index two is specified, a two dimensional surface that becomes separated from the osculating plane of the saddle is implied. The three-dimensional singular point is interpreted mathematically and the most common aerodynamical singular points are discussed through this perspective.
Mathematical Singularity Behaviour of Turbulent Transition
NASA Astrophysics Data System (ADS)
Dou, Hua-Shu; Cheong Khoo, Boo
2008-11-01
In our previous work, a criterion for turbulent transition has been proposed which is expressed by an energy gradient function which is the ratio of the transverse energy gradient and the streamwise energy loss of unit volumetric fluid in the base flow. Further, the threshold of the disturbance amplitude obtained is scaled with the Reynolds number by an exponent of -1, which is in agreement with the experimental results for pipe flow. In the present study, we show that turbulent transition can be excited via a singularity of the energy gradient function. This singularity of the energy gradient function corresponds to the case of infinite Re. When a laminar flow is stable (at low Re), the energy gradient function is located remotely from the mentioned singularity. It is found that the role of disturbance introduced to a laminar flow is to promote the energy gradient function to approach the singularity. When the Reynolds number is sufficiently large, a large disturbance may trigger the energy gradient function to enter the singularity. Once this function is trapped into this singularity, the fluid flow becomes increasingly ``chaotic'' tending towards the turbulent state. For the occurrence of the singularity, the amplitude of disturbance needs to reach a certain threshold for a given Reynolds number. These findings are in agreement with those in the literature.
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.
Singularity-free decaying-vacuum cosmologies
Abdel-Rahman, A.M. )
1992-05-15
Decaying-vacuum singularity-free cosmological models based on the Chen-Wu ansatz of a cosmological term varying as {ital R}{sup {minus}2} where {ital R} is the scale factor of the Universe are introduced. They describe a closed ever-expanding universe of density parameter {Omega}{ge}1 and with no entropy, horizon, or monopole problems. They include and extend the critical density cosmology of Oezer and Taha. The Oezer-Taha period of phase transition during part of which the pressure is negative occurs in these models. In its wake and throughout the radiation-dominated era the Universe is Einstein--de Sitter--like with {Omega} then and subsequently near unity. Nucleosynthesis proceeds as in the standard model. Consistency with the observed helium abundance and baryon asymmetry allows a maximum vacuum energy close to the radiation energy today. The presence of this vacuum energy could be detrimental to certain theories of galaxy formation. A specific model with initial conditions approaching the hot big bang is studied in detail, particularly as regards the entropy and flatness of the very early Universe.
Singularity-free decaying-vacuum cosmologies
NASA Astrophysics Data System (ADS)
Abdel-Rahman, A.-M. M.
1992-05-01
Decaying-vacuum singularity-free cosmological models based on the Chen-Wu ansatz of a cosmological term varying as R-2 where R is the scale factor of the Universe are introduced. They describe a closed ever-expanding universe of density parameter Ω>=1 and with no entropy, horizon, or monopole problems. They include and extend the critical density cosmology of Özer and Taha. The Özer-Taha period of phase transition during part of which the pressure is negative occurs in these models. In its wake and throughout the radiation-dominated era the Universe is Einstein-de Sitter-like with Ω then and subsequently near unity. Nucleosynthesis proceeds as in the standard model. Consistency with the observed helium abundance and baryon asymmetry allows a maximum vacuum energy close to the radiation energy today. The presence of this vacuum energy could be detrimental to certain theories of galaxy formation. A specific model with initial conditions approaching the hot big bang is studied in detail, particularly as regards the entropy and flatness of the very early Universe.
Nationale Roadmap Embedded Systems
NASA Astrophysics Data System (ADS)
Damm, Werner; Achatz, Reinhold; Beetz, Klaus; Broy, Manfred; Daembkes, Heinrich; Grimm, Klaus; Liggesmeyer, Peter
Eingebettete Systeme" sind in ihrem Softwareanteil nicht sichtbar und doch hoch relevant für den Wirtschaftsstandort Deutschland. Ihre Bedeutung fasst die vorliegende Nationale Roadmap Embedded Systems in den folgenden 10 Thesen zusammen: These 1 Die zentralen ökonomischen und gesellschaftlichen Herausforderungen in Deutschland lassen sich ohne die Querschnittstechnologie Embedded Systems nicht lösen1.
Schubert calculus and singularity theory
NASA Astrophysics Data System (ADS)
Gorbounov, Vassily; Petrov, Victor
2012-02-01
Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces, it has to be redesigned when applied to other generalized cohomology theories such as the equivariant, the quantum cohomology, K-theory, and cobordism. All this cohomology theories are different deformations of the ordinary cohomology. In this note, we show that there is, in some sense, the universal deformation of Schubert calculus which produces the above mentioned by specialization of the appropriate parameters. We build on the work of Lerche Vafa and Warner. The main conjecture these authors made was that the classical cohomology of a Hermitian symmetric homogeneous manifold is a Jacobi ring of an appropriate potential. We extend this conjecture and provide a simple proof. Namely, we show that the cohomology of the Hermitian symmetric space is a Jacobi ring of a certain potential and the equivariant and the quantum cohomology and the K-theory is a Jacobi ring of a particular deformation of this potential. This suggests to study the most general deformations of the Frobenius algebra of cohomology of these manifolds by considering the versal deformation of the appropriate potential. The structure of the Jacobi ring of such potential is a subject of well developed singularity theory. This gives a potentially new way to look at the classical, the equivariant, the quantum and other flavors of Schubert calculus.
Structural singularities in GexTe100-x films
NASA Astrophysics Data System (ADS)
Piarristeguy, A. A.; Micoulaut, M.; Escalier, R.; Jóvári, P.; Kaban, I.; van Eijk, J.; Luckas, J.; Ravindren, S.; Boolchand, P.; Pradel, A.
2015-08-01
Structural and calorimetric investigation of GexTe100-x films over wide range of concentration 10 < x < 50 led to evidence two structural singularities at x ˜ 22 at. % and x ˜ 33-35 at. %. Analysis of bond distribution, bond variability, and glass thermal stability led to conclude to the origin of the first singularity being the flexible/rigid transition proposed in the framework of rigidity model and the origin of the second one being the disappearance of the undercooled region resulting in amorphous materials with statistical distributions of bonds. While the first singularity signs the onset of the Ge-Ge homopolar bonds, the second is related to compositions where enhanced Ge-Ge correlations at intermediate lengthscales (7.7 Å) are observed. These two threshold compositions correspond to recently reported resistance drift threshold compositions, an important support for models pointing the breaking of homopolar Ge-Ge bonds as the main phenomenon behind the ageing of phase change materials.
Structural singularities in Ge(x)Te(100-x) films.
Piarristeguy, A A; Micoulaut, M; Escalier, R; Jóvári, P; Kaban, I; van Eijk, J; Luckas, J; Ravindren, S; Boolchand, P; Pradel, A
2015-08-21
Structural and calorimetric investigation of Ge(x)Te(100-x) films over wide range of concentration 10 < x < 50 led to evidence two structural singularities at x ∼ 22 at. % and x ∼ 33-35 at. %. Analysis of bond distribution, bond variability, and glass thermal stability led to conclude to the origin of the first singularity being the flexible/rigid transition proposed in the framework of rigidity model and the origin of the second one being the disappearance of the undercooled region resulting in amorphous materials with statistical distributions of bonds. While the first singularity signs the onset of the Ge-Ge homopolar bonds, the second is related to compositions where enhanced Ge-Ge correlations at intermediate lengthscales (7.7 Å) are observed. These two threshold compositions correspond to recently reported resistance drift threshold compositions, an important support for models pointing the breaking of homopolar Ge-Ge bonds as the main phenomenon behind the ageing of phase change materials. PMID:26298140
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.
Quantum singularities in the BTZ spacetime
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.
Gravitational radiation from a cylindrical naked singularity
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.
Observational constraints on finite scale factor singularities
Denkiewicz, Tomasz
2012-07-01
We discuss the combined constraints on a Finite Scale Factor Singularity (FSF) universe evolution scenario, which come from the shift parameter R, baryon acoustic oscillations (BAO) A, and from the type Ia supernovae. We show that observations allow existence of such singularities in the 2 × 10{sup 9} years in future (at 1σ CL) which is much farther than a Sudden Future Singularity (SFS), and that at the present moment of the cosmic evolution, one cannot differentiate between cosmological scenario which allow finite scale factor singularities and the standard ΛCDM dark energy models. We also show that there is an allowed value of m = 2/3 within 1σ CL, which corresponds to a dust-filled Einstein-de-Sitter universe limit of the early time evolution and so it is pasted into a standard early-time scenario.
Stable computation of generalized singular values
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}.
Quantum Hall State on Singular Surfaces
NASA Astrophysics Data System (ADS)
Chiu, Yu Hung; Can, Tankut; Laskin, Michael; Wiegmann, Paul B.
We propose a framework to study the response towards geometry with FQHE state on singular surfaces. Such study on singular surface provides a path to measure the gravitational anomaly, the third universal transport coefficient of FQHE, in leading order. The large N expansion of generating functional is computed via two independent methods: a Ward Identity and a field theory approach. Meanwhile the second moment of the density is also obtained via Ward Identity. We observe that the generating functional on singular surfaces can be viewed as vertex operators at the cone tips. Divergence in the Liouville functional due to singularities is, as expected, a source for the modification, but not the sole source. From both methods, we are able to obtain the charge and conformal dimension hα of such a vertex operator. The talk will concentrate on the one cone result obtained via both approaches.
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.
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
Singularity avoidance and time in quantum gravity
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.
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.
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.
Complete fluid equations for low-n singular modes in axisymmetric toroidal plasmas
Glasser, A.H.
1990-01-01
The goal of this work is to develop a complete linear theory of the singular region, including all important dynamical effects. The present phase of the work treats the more collision fluid regime. A later phase will treat the less collisional gyrokinetic regime. This paper concerns the derivation and form of the fluid equations for the singular region of low-n modes. Later work will treat high-n ballooning modes. In addition, the ordering in the present work must be amended before it is applicable to the neighborhood of the field reversal surface of the RFP.
Silica Embedded Metal Hydrides
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.
Hussain, Shah; Güzel, Yüksel; Schönbichler, Stefan A; Rainer, Matthias; Huck, Christian W; Bonn, Günther K
2013-09-01
Thionins are cysteine-rich, biologically active small (∼5 kDa) and basic proteins occurring ubiquitously in the plant kingdom. This study describes an efficient solid-phase extraction (SPE) method for the selective isolation of these pharmacologically active proteins. Hollow-monolithic extraction tips based on poly(styrene-co-divinylbenzene) with embedded zirconium silicate nano-powder were designed, which showed an excellent selectivity for sulphur-rich proteins owing to strong co-ordination between zirconium and the sulphur atoms from the thiol-group of cysteine. The sorbent provides a combination of strong hydrophobic and electrostatic interactions which may help in targeted separation of certain classes of proteins in a complex mixture based upon the binding strength of different proteins. European mistletoe, wheat and barley samples were used for selective isolation of viscotoxins, purothionins and hordothionins, respectively. The enriched fractions were subjected to analysis by matrix-assisted laser desorption/ionisation-time-of-flight mass spectrometer to prove the selectivity of the SPE method towards thionins. For peptide mass-fingerprint analysis, tryptic digests of SPE eluates were examined. Reversed-phase high-performance liquid chromatography hyphenated to diode-array detection was employed for the purification of individual isoforms. The developed method was found to be highly specific for the isolation and purification of thionins. PMID:23861184
Dynamical singularities in adaptive delayed-feedback control.
Saito, Asaki; Konishi, Keiji
2011-09-01
We demonstrate the dynamical characteristics of adaptive delayed-feedback control systems, exploiting a discrete-time adaptive control method derived for carrying out detailed analysis. In particular, the systems exhibit singularities such as power-law decay of the distribution of transient times and almost zero finite-time Lyapunov exponents. We can explain these results by characterizing such systems as having (1) a Jacobian matrix with unity eigenvalue in the whole phase space, and (2) parameters approaching a stability boundary proven to be identical with that of (nonadaptive) delayed-feedback control. PMID:22060398
Construction of embedding for empirical prognostic models of climate
NASA Astrophysics Data System (ADS)
Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Loskutov, E. M.
2015-12-01
Empirical approach to modeling and forecasting complex dynamical systems becomes more and more popular in climate science because of two reasons: (i) not confidence reproducing and forecasting some of key climate modes by existing global climate models, and (ii) increasing number and duration of climatic time series which can be considered as a source of information about dynamical laws underlying observational variability. Such an approach is aimed to construction of prognostic models by way of direct analysis of data without involving any detailed physical equations. We developed a method for empirical modeling basing on reconstruction of prognostic evolution operator in a form of random dynamical system [1] - stochastic mapping the current state of the system to the next one. The most crucial point in application of the method to the analysis of real climatic data is the construction of proper embedding: the optimal set of variables - "principal modes" - determining the phase space the model works in. This task is non-trivial due to huge dimension of time series of typical space-distributed climatic fields. We outline two main features these modes should have to capture the main dynamical properties of the system: (i) capturing teleconnections in the atmosphere-ocean system by taking into account time-lagged couplings in data and (ii) reflecting the nonlinear interactions between the time series at different grid points. In this report we present the methodology of empirical forecasting which includes the construction of an embedding on the basis of the above principals: multichannel singular spectrum analysis (MSSA) together with nonlinear principal component analysis (NPCA) are used for phase space construction from data. The proposed methodology is applied to the analysis of sea surface temperature and atmospheric pressure fields. Capabilities to predict various indices of climate (such as SOI, PDO, NAO, NTA, etc.) is demonstrated. This research was supported
Resolution of curvature singularities from quantum mechanical and loop perspective
NASA Astrophysics Data System (ADS)
Tahamtan, T.; Svítek, O.
2014-08-01
We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein-Gordon and Chandrasekhar-Dirac equation are used to probe the classical timelike naked singularity. We show that the classical singularity is felt even by our quantum probes. Next, we use loop quantization to resolve a singularity hidden beneath the horizon. The singularity is resolved in this case.
Singular Lagrangians. Classical dynamics and quantization. Lectures for young scientists
NASA Astrophysics Data System (ADS)
Nesterenko, V. V.; Chervyakov, A. M.
The lectures are devoted to the classical and quantum dynamics of the systems described by singular (or degenerate) Lagrangians. The complete set of the Hamiltonian constraints is constructed in the framework of the Lagrangian formalism. The equations of motion in the phase space are derived by taking into account all the constraints in the theory. It is proved that the dynamic on the physical submanifold of the phase space has the Hamiltonian form. On lectures the second Noether theorem is widely used. On its basis the properties of the Poisson brackets of the primary constraints are investigated and the invariance of the Lagrangian constraints during evolution is proved. The setting of the Cauchy problem in the theories with singular Lagrangians is discussed. The quantization of the systems with constraints is carried out by the functional integration in the phase space. There is considered the most general case of the first class and the second class constraints with an explicit time dependence. The gauge conditions may be noninvoluntary and time dependent. The material is illustrated by some examples (relativistic point particle, relativistic string, electromagnetic field, and Yang-Mills fields).
Naked singularities as particle accelerators. II
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.
Cosmologies with quasiregular singularities. II. Stability considerations
Konkowski, D.A.; Helliwell, T.M.
1985-03-15
The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R/sup 1/ x T/sup 3/ and R/sup 3/ x S/sup 1/ flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added.
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.
Treatment of singularities in cracked bodies
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Raju, I. S.
1990-01-01
Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.
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.
Quantum Griffiths singularity of superconductor-metal transition in Ga thin films.
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. PMID:26472763
Jo, Wan-Kuen; Kang, Hyun-Jung; Chun, Ho-Hwan
2014-01-01
In this study, one-dimensional rod-shaped titania (RST) and nitrogen-doped RST (N-RST) with different ratios of N to Ti were prepared using a hydrothermal method and their applications for purification of indoor toxic organic contaminants in a plug-flow reactor were examined under visible or ultraviolet (UV) irradiation. The surface characteristics of as-prepared photocatalysts were investigated by transmission electron microscopy (TEM), X-ray diffraction (XRD), and UV-visible spectroscopy. The TEM images revealed that both pure RSTs and N-RSTs displayed uniform and nanorod-shaped structures. XRD revealed that the photocatalysts had crystalline TiO2. The UV-visible spectra demonstrated that the N-RSTs could be activated in the visible region. In most cases, N-RSTs showed higher degradation efficiencies than pure RSTs under visible-light and UV irradiation. N-RSTs with a N-to-Ti ratio of 0.5 exhibited the highest degradation efficiencies of benzene, toluene, ethyl benzene, and o-xylene (BTEX), suggesting the presence of an optimal N-to-Ti ratio for preparation of N-RSTs. In addition, the average degradation efficiencies of BTEX determined for the N-RSTs with a N-to-Ti ratio of 0.5 under visible-light irradiation for the lowest initial concentration (IC, 0.1 ppm) were 19%, 53%, 85%, and 92%, respectively, while the degradation efficiencies for the highest IC (2.0 ppm) were 2%, 8%, 17%, and 33%. These values decreased as the stream flow rate increased. Overall, the as-prepared N-RSTs could be effectively applied for degradation of toxic gas-phase organic contaminants under visible-light as well as UV irradiation. PMID:25145164
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.
Thermally-induced interlaminar crack-tip singularities in laminated anisotropic composites
NASA Astrophysics Data System (ADS)
Choi, Hyung J.; Thangjitham, S.
1993-04-01
Thermally-induced stress singularities of an interlaminar crack in a fiber-reinforced composite laminate under a state of generalized plane deformation are examined within the framework of steady-state anisotropic thermoelasticity. The crack is assumed to be embedded within a matrix-rich interlaminar region of the composite. The Fourier integral transform technique and the flexibility/stiffness matrix method are introduced to formulate the current mixed boundary value problem. As a result, two sets of simultaneous Cauchy-type singular integral equations of the first kind are derived for the heat conduction and thermoelasticity. Within the context of linear elastic fracture mechanics, the mixed-mode thermal stress intensity factors are defined in terms of the solutions of the corresponding integral equations. Numerical results are presented, addressing the effects of laminate stacking sequence, crack 1ocation, and crack surface partial insulation on the values of thermal stress intensity factors.
Autonomy and singularity in dynamic fracture.
Bouchbinder, Eran
2010-07-01
The recently developed weakly nonlinear theory of dynamic fracture predicts 1/r corrections to the standard asymptotic linear elastic 1/(square root of r) displacement gradients, where r is measured from the tip of a tensile crack. We show that the 1/r singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic 1/(square root of r) fields) and that it does not automatically satisfy the resultant Newton's equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton's equation is satisfied, autonomy of the 1/r singular solution is retained. We further show that the resultant linear momentum carried by the 1/r singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the solution, are in favorable agreement with recent near-tip measurements. PMID:20866674
Removing singular refractive indices with sculpted surfaces
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
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.
Class of supersymmetric solitons with naked singularities
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.
Singular perturbation applications in neutron transport
Losey, D.C.; Lee, J.C.
1996-09-01
This is a paper on singular perturbation applications in neutron transport for submission at the next ANS conference. A singular perturbation technique was developed for neutron transport analysis by postulating expansion in terms of a small ordering parameter {eta}. Our perturbation analysis is carried, without approximation, through {Omicron}({eta}{sup 2}) to derive a material interface correction for diffusion theory. Here we present results from an analytical application of the perturbation technique to a fixed source problem and then describe and implementation of the technique in a computational scheme.
The singular coagulation equation with multiple fragmentation
NASA Astrophysics Data System (ADS)
Saha, Jitraj; Kumar, Jitendra
2015-06-01
In this paper, we prove the global existence and uniqueness of the solutions to the initial-value problem for the coagulation-fragmentation equation with singular coagulation kernel and multiple fragmentation kernel. The solution obtained in this case also satisfies the mass conservation law. The proof is based on strong convergence methods applied to suitably chosen unbounded coagulation kernels having singularities in both the coordinate axes and satisfying certain growth conditions, which can possibly reach up to a quadratic growth at infinity, and the fragmentation kernel covers a very large class of unbounded functions.
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
Mirror Symmetry for Quasi-Homogeneous Singularities
NASA Astrophysics Data System (ADS)
Rathnakumara, Himal; Jarvis, Tyler
2008-10-01
I will present an introduction to mirror symmetry in the context of string theory. Then I will describe an instance of mirror symmetry for singularties defined by quasi-homogeneous polynomials in weighted projective spaces. Milnor rings and the FJRW (Fan-Jarvis-Ruan-Witten) rings associated with these singularities and their relation to the Landua-Ginzburg A model and the Landua-Ginzburg B model will be explained. Results of the calculations for certain singularities for which the mirror symmetry conjecture has been verified will be presented.
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.
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.
Embedded GPS solves the installation dilemma
NASA Astrophysics Data System (ADS)
Sturza, Mark A.; Richards, Charles C.
The authors describe a proposed embedded GPS/INS (Global Positioning System/Inertial Navigation System) architecture. The architecture provides full Phase III (jammed) GPS performance and supports all GPS/inertial integration approaches. The GPS unique interfaces are minimized by taking advantage of existing INS interfaces. Single-point failures are minimized by use of a partitioned power supply. It is concluded that the embedded GPS receiver offers equal or better performance, increased reliability, and significantly reduced weight and volume when compared to a standalone Receiver 3A.
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
Painleve singularity analysis applied to charged particle dynamics during reconnection
Larson, J.W.
1992-01-01
For a plasma in the collisionless regime, test-particle modelling can lend some insight into the macroscopic behavior of the plasma, e.g. conductivity and heating. A common example for which this technique is used is a system with electric and magnetic fields given by B = [delta]yx + zy + yz and E = [epsilon]z, where [delta], [gamma], and [epsilon] are constant parameters. This model can be used to model plasma behavior near neutral lines, ([gamma] = 0), as well as current sheets ([gamma] = 0, [delta] = 0). The integrability properties of the particle motion in such fields might affect the plasma's macroscopic behavior, and the author has asked the question [open quotes]For what values of [delta], [gamma], and [epsilon] is the system integrable [close quotes] To answer this question, the author has employed Painleve singularity analysis, which is an examination of the singularity properties of a test particle's equations of motion in the complex time plane. This analysis has identified two field geometries for which the system's particle dynamics are integrable in terms of the second Painleve transcendent: the circular O-line case and the case of the neutral sheet configuration. These geometries yield particle dynamics that are integrable in the Liouville sense (i.e., there exist the proper number of integrals in involution) in an extended phase space which includes the time as a canonical coordinate, and this property is also true for nonzero [gamma]. The singularity property tests also identified a large, dense set of X-line and O-line field geometries that yield dynamics that may possess the weak Painleve property. In the case of the X-line geometries, this result shows little relevance to the physical nature of the system, but the existence of a dense set of elliptical O-line geometries with this property may be related to the fact that for [epsilon] positive, one can construct asymptotic solutions in the limit t [yields] [infinity].
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…
Gravitational lensing by rotating naked singularities
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.
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.
'Footballs', conical singularities, and the Liouville equation
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.
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).
Inverting dedevelopment: geometric singularity theory in embryology
NASA Astrophysics Data System (ADS)
Bookstein, Fred L.; Smith, Bradley R.
2000-10-01
The diffeomorphism model so useful in the biomathematics of normal morphological variability and disease is inappropriate for applications in embryogenesis, where whole coordinate patches are created out of single points. For this application we need a suitable algebra for the creation of something from nothing in a carefully organized geometry: a formalism for parameterizing discrete nondifferentiabilities of invertible functions on Rk, k $GTR 1. One easy way to begin is via the inverse of the development map - call it the dedevelopment map, the deformation backwards in time. Extrapolated, this map will inevitably have singularities at which its derivative is zero. When the dedevelopment map is inverted to face forward in time, the singularities become appropriately isolated infinities of derivative. We have recently introduced growth visualizations via extrapolations to the isolated singularities at which only one directional derivative is zero. Maps inverse to these create new coordinate patches directionally rather than radically. The most generic singularity that suits this purpose is the crease f(x,y) equals (x,x2y+y3), which has already been applied in morphometrics for the description of focal morphogenetic phenomena. We apply it to embryogenesis in the form of its analytic inverse, and demonstrate its power using a priceless new data set of mouse embryos imaged in 3D by micro-MR with voxels smaller than 100micrometers 3.
Normal forms of Hopf-zero singularity
NASA Astrophysics Data System (ADS)
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.
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.
ERIC Educational Resources Information Center
Kazmer, Michelle M.
2005-01-01
Online learners often stay located in, and tied to, their communities, kinship networks, households, and workplaces. Institutions providing online education can thus create ties to communities as students draw their learning into networks in which they are already embedded. Frequent interactions across multiple media that are afforded by…
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.
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.
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…
Isometric embeddings of polyhedra
NASA Astrophysics Data System (ADS)
Minemyer, Barry
An indefinite metric polyhedron is a triple (X, T, g) where X is a topological space, T is a simplicial triangulation of X with edge set E, and g is a function from E to the reals. g assigns to each k-dimensional simplex S a unique quadratic form on Rk, denoted by G(S). An indefinite metric polyhedron is called a Euclidean polyhedron if the form G(S) is positive definite for every simplex S. Rpq denotes R p + q endowed with the inner product of signature (p, q). Our first result is that every compact n-dimensional indefinite metric polyhedron with vertex set V admits a simplicial isometric embedding into Rqq where q = max{d, 2n + 1} and d = max{deg(v) | v is in V}. We can use the compact case to extend to the non-compact case, but only if we assume that d = max{deg(v) | v is in V} is less than infinity. Specifically, every (non-compact) indefinite metric polyhedron admits a simplicial isometric embedding into Rpp where p = 2q(d3 - d2 + d + 1) and q and d are defined as above. Finally we use results of Akopyan and Greene to prove that every n-dimensional indefinite metric polyhedron admits a piecewise linear isometric embedding into Rn2n. In Chapter 2 we prove that every short (1-Lipschitz) map from an n-dimensional Euclidean polyhedron into EN is epsilon close to a pl isometric embedding (for anyepsilon > 0) provided N ≥ 3n. We can relax the dimensionality of the Euclidean space to 2n + 1 if we allow our map to be continuous instead of pl. These results are extensions of a result due to Akopyan. We provide a detailed proof of Akopyan's Theorem, as the only currently available proof is in Russian. The remaining results in this work are applications of our continuous isometric embedding theorem above. This result is used to prove that every Pro-Euclidean space of rank at most n admits an isometric embedding into E2n + 1. The result, as well as a theorem due to Bridson, also allows for an approximate isometric embedding theorem for geodesic metric spaces with
The geometry of singularities and the black hole information paradox
NASA Astrophysics Data System (ADS)
Stoica, O. C.
2015-07-01
The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have nonsingular electromagnetic field. As a bonus, if particles are such black holes, spacetime undergoes dimensional reduction effects like those required by some approaches to perturbative Quantum Gravity.
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.
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.
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.
Generalized Parton Distributions and their Singularities
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 $D(\\alpha)$.
Generalized parton distributions and their singularities
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}).
Nonlinear Growth of Singular Vector Based Perturbations
NASA Astrophysics Data System (ADS)
Reynolds, C. A.
2002-12-01
The nonlinearity of singular vector-based perturbation growth is examined within the context of a global atmospheric forecast model. The characteristics of these nonlinearities and their impact on the utility of SV-based diagnostics are assessed both qualitatively and quantitatively. Nonlinearities are quantified by examining the symmetry of evolving positive and negative "twin" perturbations. Perturbations initially scaled to be consistent with estimates of analysis uncertainty become significantly nonlinear by 12 hours. However, the relative magnitude of the nonlinearities is a strong function of scale and metric. Small scales become nonlinear very quickly while synoptic scales can remain significantly linear out to three day. Small shifts between positive and negative perturbations can result in significant nonlinearities even when the basic anomaly patterns are quite similar. Thus, singular vectors may be qualitatively useful even when nonlinearities are large. Post-time pseudo-inverse experiments show that despite significant nonlinear perturbation growth, the nonlinear forecast corrections are similar to the expected linear corrections, even at 72 hours. When the nonlinear correction does differ significantly from the expected linear correction, the nonlinear correction is usually better, indicating that in some cases the pseudo-inverse correction effectively suppresses error growth outside the subspace defined by the leading (dry) singular vectors. Because a significant portion of the nonlinear growth occurs outside of the dry singular vector subspace, an a priori nonlinearity index based on the full perturbations is not a good predictor of when pseudo-inverse based corrections will be ineffective. However, one can construct a reasonable predictor of pseudo-inverse ineffectiveness by focusing on nonlinearities in the synoptic scales or in the singular vector subspace only.
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.
7 CFR 900.36 - Words in the singular form.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...
7 CFR 900.20 - Words in the singular form.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...
7 CFR 900.50 - Words in the singular form.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.100 - Words in the singular form.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.1 - Words in the singular form.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.100 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
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...
7 CFR 900.1 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 1200.50 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 10 2011-01-01 2011-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...
7 CFR 61.1 - Words in singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 3 2011-01-01 2011-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...
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 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...
7 CFR 46.1 - Words in singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...
7 CFR 900.20 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...
7 CFR 900.36 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...
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...
7 CFR 46.1 - Words in singular form.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...
7 CFR 900.50 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 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...
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...
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...
Behavior of Friedmann-Lemaître-Robertson-Walker Singularities
NASA Astrophysics Data System (ADS)
Fernández-Jambrina, L.
2016-03-01
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.
7 CFR 900.1 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 61.1 - Words in singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 3 2014-01-01 2014-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...
7 CFR 1200.50 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 10 2014-01-01 2014-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...
7 CFR 900.1 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.36 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...
7 CFR 46.1 - Words in singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...
7 CFR 1200.50 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 10 2013-01-01 2013-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to...
7 CFR 900.100 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.20 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...
7 CFR 900.50 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.100 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 61.1 - Words in singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 3 2013-01-01 2013-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall...
7 CFR 900.20 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed...
7 CFR 46.1 - Words in singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the...
7 CFR 900.50 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.36 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall...
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.
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
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
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
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.
Singularity theory of fitness functions under dimorphism equivalence.
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. PMID:26733311
Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?
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.
Integrated Design and Implementation of Embedded Control Systems with Scilab
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.
Cosmological singularities encoded in IR boundary correlations
NASA Astrophysics Data System (ADS)
Bzowski, Adam; Hertog, Thomas; Schillo, Marjorie
2016-05-01
We study the dynamics near big crunch singularities produced in asymptotic AdS cosmologies using gauge/gravity duality. The dual description consists of a constant mass deformation of ABJM theory on de Sitter space and is well-defined and stable for small deformations. We identify the critical deformation where the theory becomes unstable at weak and at strong coupling. Using spacelike geodesics anchored on the boundary we compute two-point correlators of ABJM operators of large dimensions. Near the critical deformation a second saddle point contribution enters, in which the spacelike geodesics probe the high curvature region near the singularity. Its contribution strongly enhances the long-distance correlations. This has a natural interpretation in the weakly coupled boundary theory where the critical point corresponds to a massless limit.
Singular electrostatic energy of nanoparticle clusters
NASA Astrophysics Data System (ADS)
Qin, Jian; Krapf, Nathan W.; Witten, Thomas A.
2016-02-01
The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation h has a singular logarithmic dependence on h . We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact c (h ) , together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.
Coordinate singularities in harmonically sliced cosmologies
NASA Astrophysics Data System (ADS)
Hern, Simon D.
2000-08-01
Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre [Phys. Rev. D 55, 5981 (1997)], numerical solutions generated using this slicing condition can show pathological behavior. In this paper, analytic and numerical methods are used to examine harmonic slicings of Kasner and Gowdy cosmological spacetimes. It is shown that in general the slicings are prevented from covering the whole of the spacetimes by the appearance of coordinate singularities. As well as limiting the maximum running times of numerical simulations, the coordinate singularities can lead to features being produced in numerically evolved solutions which must be distinguished from genuine physical effects.
Singular Function Integration in Computational Physics
NASA Astrophysics Data System (ADS)
Hasbun, Javier
2009-03-01
In teaching computational methods in the undergraduate physics curriculum, standard integration approaches taught include the rectangular, trapezoidal, Simpson, Romberg, and others. Over time, these techniques have proven to be invaluable and students are encouraged to employ the most efficient method that is expected to perform best when applied to a given problem. However, some physics research applications require techniques that can handle singularities. While decreasing the step size in traditional approaches is an alternative, this may not always work and repetitive processes make this route even more inefficient. Here, I present two existing integration rules designed to handle singular integrals. I compare them to traditional rules as well as to the exact analytic results. I suggest that it is perhaps time to include such approaches in the undergraduate computational physics course.
Singularities in soft-impacting systems
NASA Astrophysics Data System (ADS)
Kundu, Soumya; Banerjee, Soumitro; Ing, James; Pavlovskaia, Ekaterina; Wiercigroch, Marian
2012-03-01
In this paper, the character of the normal form map in the neighbourhood of a grazing orbit is investigated for four possible configurations of soft impacting systems. It is shown that, if the spring in the impacting surface is relaxed, the impacting side of the map has a power of 3/2, but if the spring is pre-stressed the map has a square root singularity. The singularity appears only in the trace of the Jacobian matrix and not in the determinant. Under all conditions, the determinant of the Jacobian matrix varies continuously across the grazing condition. However, if the impacting surface has a damper, the determinant decreases exponentially with increasing penetration. It is found that the system behaviour is greatly dependent upon a parameter m, given by 2ω0/ω, and that the singularity disappears for integer values of m. Thus, if the parameters are chosen to obtain an integer value of m, one can expect no abrupt change in behaviour as the system passes through the grazing condition from a non-impacting mode to an impacting mode with increasing excitation amplitude. The above result has been tested on an experimental rig, which showed a persistence of a period-1 orbit across the grazing condition for integer values of m, but an abrupt transition to a chaotic orbit or a high-period orbit for non-integer values of m. Finally, through simulation, it is shown that the condition for vanishing singularity is not a discrete point in the parameter space. This property is valid over a neighbourhood in the parameter space, which shrinks for larger values of the stiffness ratio k2/k1.
Formation of turbulence around flow singularities
NASA Technical Reports Server (NTRS)
Zak, M.
1983-01-01
The formation of turbulence around singular points of a flow such as stagnation points, tangential jumps of velocity, are analyzed. It is proved that turbulence is inevitably generated by the rear stagnation point, but cannot be generated by the nose stagnation point of a streamlined body. Special attention is paid to an evolution of turbulence induced by a tangential jump of velocity. A qualitative analysis of a turbulent flow between two rotating concentric cylinders and around a streamlined cylinder is given.
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.
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.
Aerodynamic influence coefficient method using singularity splines
NASA Technical Reports Server (NTRS)
Mercer, J. E.; Weber, J. A.; Lesferd, E. P.
1974-01-01
A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.
Singularities and symmetry breaking in swarms.
Li, Wei; Zhang, Hai-Tao; Chen, Michael Zhi Qiang; Zhou, Tao
2008-02-01
A large-scale system consisting of self-propelled particles, moving under the directional alignment rule (DAR), can often self-organize to an ordered state that emerges from an initially rotationally symmetric configuration. It is commonly accepted that the DAR, which leads to effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this paper, we demonstrate that a swarm under the DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce an unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights into the fundamental issue of collective dynamics: What is the underlying mechanism causing the spontaneous symmetry breaking and leading to eventual coherent motion? PMID:18352064
Equilibrium stellar systems with spindle singularities
NASA Technical Reports Server (NTRS)
Shapiro, Stuart L.; Teukolsky, Saul A.
1992-01-01
Equilibrium sequences of axisymmetric Newtonian clusters that tend toward singular states are constructed. The distribution functions are chosen to be of the form f = f(E, Jz). The numerical method then determines the density and gravitational potential self-consistently to satisfy Poisson's equation. For the prolate models, spindle singularities arise from the depletion of angular momentum near the symmetry axis. While the resulting density enhancement is confined to the region near the axis, the influence of the spindle extends much further out through its tidal gravitational field. Centrally condensed prolate clusters may contain strong-field regions even though the spindle mass is small and the mean cluster eccentricity is not extreme. While the calculations performed here are entirely Newtonian, the issue of singularities is an important topic in general relativity. Equilibrium solutions for relativistic star clusters can provide a testing ground for exploring this issue. The methods used in this paper for building nonspherical clusters can be extended to relativistic systems.
Kasner solutions, climbing scalars and big-bang singularity
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.
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.
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.
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.
Embedded instrumentation systems architecture
NASA Astrophysics Data System (ADS)
Visnevski, Nikita A.
2007-04-01
This paper describes the operational concept of the Embedded Instrumentation Systems Architecture (EISA) that is being developed for Test and Evaluation (T&E) applications. The architecture addresses such future T&E requirements as interoperability, flexibility, and non-intrusiveness. These are the ultimate requirements that support continuous T&E objectives. In this paper, we demonstrate that these objectives can be met by decoupling the Embedded Instrumentation (EI) system into an on-board and an off-board component. An on-board component is responsible for sampling, pre-processing, buffering, and transmitting data to the off-board component. The latter is responsible for aggregating, post-processing, and storing test data as well as providing access to the data via a clearly defined interface including such aspects as security, user authentication and access control. The power of the EISA architecture approach is in its inherent ability to support virtual instrumentation as well as enabling interoperability with such important T&E systems as Integrated Network-Enhanced Telemetry (iNET), Test and Training Enabling Architecture (TENA) and other relevant Department of Defense initiatives.
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.
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
Internal energy flows of coma-affected singular beams in low-numerical-aperture systems.
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. PMID:26366760
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.
Finite element techniques applied to cracks interacting with selected singularities
NASA Technical Reports Server (NTRS)
Conway, J. C.
1975-01-01
The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.
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.
Quantum fields near phantom-energy ''sudden'' singularities
Calderon, Hector H.
2008-08-15
This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized stress tensors of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to quantum vacuum contributions. This dynamical analysis is then compared to results from thermodynamical considerations. In both cases, the vacuum states of quantized scalar and spinor fields strengthen the accelerating expansion near the singularity whereas the vacuum states of vector fields weaken it.
Tomographic resolution without singular value decomposition
Berryman, J.G.
1994-06-01
An explicit procedure is presented for computing both model and data resolution matrices within a Paige-Saunders LSQR algorithm for iterative inversion in seismic tomography. These methods are designed to avoid the need for an additional singular value decomposition of the ray-path matrix. The techniques discussed are completely general since they are based on the multiplicity of equivalent exact formulas that may be used to define the resolution matrices. Thus, resolution matrices may also be computed for a wide variety of iterative inversion algorithms using the same ideas.
Aerodynamic influence coefficient method using singularity splines.
NASA Technical Reports Server (NTRS)
Mercer, J. E.; Weber, J. A.; Lesferd, E. P.
1973-01-01
A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.
Inflation, singular instantons, and eleven dimensional cosmology
NASA Astrophysics Data System (ADS)
Hawking, S. W.; Reall, Harvey S.
1999-01-01
We investigate cosmological solutions of eleven dimensional supergravity compactified on a squashed seven manifold. The effective action for the four dimensional theory contains scalar fields describing the size and squashing of the compactifying space. The potential for these fields consists of a sum of exponential terms. At early times only one such term is expected to dominate. The condition for an exponential potential to admit inflationary solutions is derived and it is shown that inflation is not possible in our model. The criterion for an exponential potential to admit a Hawking-Turok instanton is also derived. It is shown that the instanton remains singular in eleven dimensions.
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.
Heating of the corona by magnetic singularities
NASA Technical Reports Server (NTRS)
Antiochos, Spiro K.
1990-01-01
Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.
Light-Front Perturbation Without Spurious Singularities
NASA Astrophysics Data System (ADS)
Przeszowski, Jerzy A.; Dzimida-Chmielewska, Elżbieta; Żochowski, Jan
2016-03-01
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.
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.
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.
Steering electromagnetic beams with conical curvature singularities.
Zhang, Yong-Liang; Dong, Xian-Zi; Zheng, Mei-Ling; Zhao, Zhen-Sheng; Duan, Xuan-Ming
2015-10-15
We describe how the transformation-optics technique can be used to design an effective medium mimicking the conical curvature singularity. Anholonomic coordinate transformation gives rise to linear topological defects that break the rotational symmetry. The bending and splitting of the optical beams are found analytically and numerically, depending on the incident direction and the topological charge. Beyond their practical applications to omnidirectional beam steering for photonics, our findings set forth an attractive realm to simulate the relevant physical phenomena in the optical laboratory. PMID:26469619
The Hubbard model description of the TCNQ related singular features in photoemission of TTF-TCNQ
NASA Astrophysics Data System (ADS)
Carmelo, J. M. P.; Penc, K.; Sacramento, P. D.; Sing, M.; Claessen, R.
2006-06-01
In this paper we use the pseudofermion dynamical theory (PDT) to study the singular spectral features due to one-electron removal within the one-dimensional Hubbard model. The PDT reveals that in the whole (k, ω)-plane such features are of the power-law type and correspond to well defined lines of three types: charge singular branch lines, spin singular branch lines and border lines. One of our goals is the study of the momentum and energy dependence of the distribution of the spectral weight in the vicinity of such lines. We find that the charge and spin branch lines correspond to the main tetracyanoquinodimethane (TCNQ) peak dispersions observed with angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ). Our expressions refer to all values of the electronic density and on-site repulsion U. The weight distribution in the vicinity of the singular spectral lines is fully controlled by the overall pseudofermion phase shifts. Moreover, the shape of these lines is determined by the bare-momentum dependence of the pseudofermion energy dispersions.
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.
Singularity computations. [finite element methods for elastoplastic flow
NASA Technical Reports Server (NTRS)
Swedlow, J. L.
1978-01-01
Direct descriptions of the structure of a singularity would describe the radial and angular distributions of the field quantities as explicitly as practicable along with some measure of the intensity of the singularity. This paper discusses such an approach based on recent development of numerical methods for elastoplastic flow. Attention is restricted to problems where one variable or set of variables is finite at the origin of the singularity but a second set is not.
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...
7 CFR 900.80 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...
Teleman localization of Hochschild homology in a singular setting
NASA Astrophysics Data System (ADS)
Brasselet, J.-P.; Legrand, A.
2009-09-01
The aim of this paper is to generalize the Hochschild-Kostant-Rosenberg theorem to the case of singular varieties, more precisely, to manifolds with boundary and to varieties with isolated singularities. In these situations, we define suitable algebras of functions and study the localization of the corresponding Hochschild homology. The tool we use is the Teleman localization process. In the case of isolated singularities, the closed Hochschild homology corresponds to the intersection complex which relates the objects defined here to intersection homology.
Transmutation of planar media singularities in a conformal cloak.
Liu, Yichao; Mukhtar, Musawwadah; Ma, Yungui; Ong, C K
2013-11-01
Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes. PMID:24322926
7 CFR 900.80 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...
7 CFR 900.80 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...
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
Spectral singularity in confined PT symmetric optical potential
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.
NASA Astrophysics Data System (ADS)
Sakagami, Takahide; Kubo, Shiro
A new thermographic NDT technique was proposed, in which singular electrothermal field near crack tips under the application of periodically modulated electric current was measured using an infrared thermography combined with lock-in data processing technique. Experimental investigations were made on the resolution and the applicability in the identification of through-thickness artificial cracks and fatigue cracks embedded in steel and aluminum alloy plate samples. Modulated electric current was applied to the cracked sample by an induction coli. Lock-in thermal images synchronized to the reference current modulation signal were taken by the lock-in thermography. Significant singular electrothermal field was observed at the crack tip in the lock-in thermal image. The fatigue cracks as well as artificial cracks were found to be sensitively identified by the proposed technique in good resolution compared with the singular method using a conventional thermographic temperature measurement.
Embedding potentials for excited states of embedded species
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.
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.
Plane wave gravitons, curvature singularities and string physics
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.
Quantum singularities in a model of f( R) gravity
NASA Astrophysics Data System (ADS)
Gurtug, O.; Tahamtan, T.
2012-07-01
The formation of a naked singularity in a model of f( R) gravity having as source a linear electromagnetic field is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r=0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity remains quantum mechanically singular when it is probed with quantum fields having different spin structures.
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.
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.
Enhanced Singular Wave Reactor for Surface Power
NASA Astrophysics Data System (ADS)
Popa-Simil, L.
The "CANDLE" (Constant Axial shape of Neutron flux, nuclide densities and power shape During Life of Energy producing reactor) also known as singular wave reactor has many significant advantages related to elimination of the need for enrichment. The use of micro-hetero structured fuel, generically called "cer-liq-mesh" will further improve burnup up to 90%. In spite it has typically large dimensions, being heavy to be transported in space, in a single piece, but because it will deliver energy in hundreds MW level for about 100 years per charge using natural Uranium or Thorium as fuel available on the planet's surface, and because it can be assembled locally becomes a very attractive option for self sustainable power cycles. The "cer-liq-mesh" fuel based singular wave reactor is smaller, less than ¼ from the size of "Candle" reactor, and has a very high burnup reducing the fuel cycle drastically. It can be transported by parts, with extremely small probability of over-unity criticality accident and be assembled to run on the surface. This represents a better option for extraterrestrial applications; in spite it requires a more complicated fuel fabrication that pays back in a simplified fuel cycle and minimum waste.
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.
Finite-time singularity signature of hyperinflation
NASA Astrophysics Data System (ADS)
Sornette, D.; Takayasu, H.; Zhou, W.-X.
2003-07-01
We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.
Embedded Clusters in Molecular Clouds
NASA Astrophysics Data System (ADS)
Lada, Charles J.; Lada, Elizabeth A.
Stellar clusters are born embedded within giant molecular clouds (GMCs) and during their formation and early evolution are often only visible at infrared wavelengths, being heavily obscured by dust. Over the past 15 years advances in infrared detection capabilities have enabled the first systematic studies of embedded clusters in galactic molecular clouds. In this article we review the current state of empirical knowledge concerning these extremely young protocluster systems. From a survey of the literature we compile the first extensive catalog of galactic embedded clusters. We use the catalog to construct the mass function and estimate the birthrate for embedded clusters within 2 kpc of the sun. We find that the embedded cluster birthrate exceeds that of visible open clusters by an order of magnitude or more indicating a high infant mortality rate for protocluster systems. Less than 4-7% of embedded clusters survive emergence from molecular clouds to become bound clusters of Pleiades age. The vast majority (90%) of stars that form in embedded clusters form in rich clusters of 100 or more members with masses in excess of 50 M⊙. Moreover, observations of nearby cloud complexes indicate that embedded clusters account for a significant (70-90%) fraction of all stars formed in GMCs. We review the role of embedded clusters in investigating the nature of the initial mass function (IMF) that, in one nearby example, has been measured over the entire range of stellar and substellar mass, from OB stars to substellar objects near the deuterium burning limit. We also review the role embedded clusters play in the investigation of circumstellar disk evolution and the important constraints they provide for understanding the origin of planetary systems. Finally, we discuss current ideas concerning the origin and dynamical evolution of embedded clusters and the implications for the formation of bound open clusters.
Metric dimensional reduction at singularities with implications to Quantum Gravity
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
Chapter 4 embedded metal fragments.
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. PMID:25222538
Embodied, Embedded Language Use
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
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.
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…
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.
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.
7 CFR 900.80 - Words in the singular form.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Words in the singular form. 900.80 Section 900.80 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... form. Words in this subpart in the singular form shall be deemed to import the plural, and vice...
Singularities in the Origin and Evolution of Life
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.
7 CFR 1200.1 - Words in the singular form.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 10 2011-01-01 2011-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in...
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...
Classification of almost toric singularities of Lagrangian foliations
Izosimov, Anton M
2011-07-31
The topological classification is given of almost toric singularities of integrable Hamiltonian systems with a large number of degrees of freedom, that is, of nondegenerate singularities without hyperbolic components. A descriptive geometric model is constructed, which makes it possible to perform effective calculations. Bibliography: 10 titles.
A numerical method for solving singular De`s
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.
Exotic singularities and spatially curved loop quantum cosmology
Singh, Parampreet; Vidotto, Francesca
2011-03-15
We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of k={+-}1 Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the nontrivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities, are ignored by quantum gravity when spatial curvature is negative, as was previously found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with nonzero spatial curvature.
7 CFR 1200.1 - Words in the singular form.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 10 2013-01-01 2013-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in...
7 CFR 1200.1 - Words in the singular form.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 10 2014-01-01 2014-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in...
String wave function across a Kasner singularity
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.
Similarity and singularity in adhesive elastohydrodynamic touchdown
NASA Astrophysics Data System (ADS)
Carlson, Andreas; Mahadevan, L.
2016-01-01
We consider the dynamics of an elastic sheet as it starts to adhere to a wall, a process that is limited by the viscous squeeze flow of the intervening liquid. Elastohydrodynamic lubrication theory allows us to derive a partial differential equation coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion, and viscous thin film flow. We use a combination of numerical simulations of the governing equation and a scaling analysis to describe the self-similar touchdown of the sheet as it approaches the wall. An analysis of the equation in terms of similarity variables in the vicinity of the touchdown event shows that only the fundamental similarity solution is observed in the time-dependent numerical simulations, consistent with the fact that it alone is stable. Our analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics, and adhesion.
Helicity and singular structures in fluid dynamics
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
Infinitely many singular interactions on noncompact manifolds
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.
ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS
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.
Particle creation by naked singularities in higher dimensions
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.
Slow Dynamics Due to Singularities of Hierarchical Learning Machines
NASA Astrophysics Data System (ADS)
Inoue, H. P. M.; Okada, M.
Recently, slow dynamics in learning ofneural networks has been known to be closely related to singularities, which exist in parameter spaces of hierarchical learning models. To show the influence of singular structure on learning dynamics, we take statistical mechanical approaches and investigate online-learning dynamics under various learning scenario with different relationship between optimum and singularities. From the investigation, we found a quasi-plateau phenomenon which differs from the well known plateau. The quasi-plateau and plateau become extremely serious when an optimal point is in a neighborhood of a singularity. The quasi-plateau and plateau disappear in the natural gradient learning, which takes singular structures into account and uses Riemannian measure for the parameter space.
Treatment of singularities in a middle-crack tension specimen
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Raju, I. S.
1990-01-01
A three-dimensional finite-element analysis of a middle-crack tension specimen subjected to mode I loading was performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed nonsingular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities, by a log-log regression analysis, along the crack front. Analyses showed that finite-sized cracked bodies have two singular stress fields. Because of two singular stress fields near the free surface and the classical square root singularity elsewhere, the strain energy release rate appears to be an appropriate parameter all along the crack front.
Stress singularities at the vertex of a cylindrically anisotropic wedge
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.; Boduroglu, H.
1980-01-01
The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.
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.
Quantum naked singularities in 2D dilaton gravity
NASA Astrophysics Data System (ADS)
Vaz, Cenalo; Witten, Louis
1997-02-01
Roughly speaking, naked singularities are singularities that may be seen by timelike observers. The Cosmic Censorship conjecture forbids their existence by stating that a reasonable system of energy will not, under reasonable conditions, collapse into a naked singularity. There are however many (classical) counter-examples to this conjecture in the literature. We propose a defense of the conjecture through the quantum theory. We will show that the Hawking effect and the accompanying back reaction, when consistently applied to naked singularities in two-dimensional models of dilaton gravity with matter and a cosmological constant, prevent their formation by causing them to explode or to emit radiation catastrophically. This contrasts with black holes which radiate slowly. If this phenomenon is reproduced in the four-dimensional world, the radiation accompanying the formation of naked singularities should have observable consequences.
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.
Structural monitoring of filamentary composites using embedded fiber optics
NASA Technical Reports Server (NTRS)
Cashon, John L.; Lehner, David L.; Bower, Mark V.; Gilbert, John A.
1990-01-01
The feasibility of monitoring overall integrity of structural components made of filamentary composites, by embedding optical fibers between lamina of a composite beam, is investigated using a beam constructed of Kevlar/epoxy cloth with embedded optical fibers aligned with the longitudinal axis of the beam. Phase changes were monitored in three different optical fibers as the composite beam was subjected to pure bending, and the strain response of the fibers was compared to the strain gage readings taken at the surface, showing a strong correlation between the phase change and the applied deformation.
On the moving contact line singularity: asymptotics of a diffuse-interface model.
Sibley, David N; Nold, Andreas; Savva, Nikos; Kalliadasis, Serafim
2013-03-01
The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall. PMID:23515762
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.
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.
Structural properties of spatially embedded networks
NASA Astrophysics Data System (ADS)
Kosmidis, K.; Havlin, S.; Bunde, A.
2008-05-01
We study the effects of spatial constraints on the structural properties of networks embedded in one- or two-dimensional space. When nodes are embedded in space, they have a well-defined Euclidean distance r between any pair. We assume that nodes at distance r have a link with probability p(r)~r-δ. We study the mean topological distance l and the clustering coefficient C of these networks and find that they both exhibit phase transitions for some critical value of the control parameter δ depending on the dimensionality d of the embedding space. We have identified three regimes. When δ
Embedded sensors in layered manufacturing
NASA Astrophysics Data System (ADS)
Li, Xiaochun
Layered Manufacturing can be applied to build ``smart'' parts with sensors, integrated circuits, and actuators placed within the component. Embedded sensors can be used to gain data for validating or improving designs during the prototype stage or to obtain information on the performance and structural integrity of components in service. Techniques for embedding fiber optic sensors in metals, polymers, and ceramics have been investigated. Embedding optical fibers into metals is especially challenging because engineering alloys tend to exhibit high melting temperatures. In the present research an embedding sequence was developed capable of embedding fiber sensors into parts made of metal alloys with high melting temperatures. Fiber Bragg Grating (FBG) sensors were selected as the most promising sensor candidate. The embedded FBG sensors were characterized for temperature and strain measurements. The embedded FBG sensors in nickel and stainless steel provided high sensitivity, good accuracy, and high temperature capacity for temperature measurements. Temperature sensitivity approximately 100% higher than that of bare FBGs was demonstrated. For strain measurements, the sensors embedded in metal and polyurethane yielded high sensitivity, accuracy, and linearity. The sensitivity of the embedded FBGs was in good agreement with that of bare FBGs. Moreover, a decoupling technique for embedded FBG sensors was developed to separate temperature and strain effects. The embedded FBG sensors were used to monitor the accumulation of residual stresses during the laser- assisted Layered Manufacturing, to measure the strain field in layered materials, to measure pressure, and to monitor temperature and strain simultaneously. New techniques have been developed for temperature and strain measurements of rotating components with FBG sensors embedded or attached to the surface. Tunable laser diodes were incorporated into the sensing system for monitoring the Bragg grating wavelength
Embedded fiducials in optical surfaces
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.
Embedded fiducials in optical surfaces
Sommargren, G.E.
2000-01-11
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.
NASA Astrophysics Data System (ADS)
Boyd, John P.
1985-02-01
Calculations of inviscid, linearized waves in fluids are very difficult when a mean wind or current U( y) is included because the differential equation is singular wherever U( y)= c, the phase speed. These "critical latitude," "critical level," or "critical point" singularities are particularly severe for Chebyshev methods since these global expansion algorithms are very sensitive to the analytic properties of the solution. A simple remedy is described: by making a change of coordinates y= f( x) where y is the original variable and x is the new coordinate with f( x) a complex function, one can solve the problem on an arc in the complex plane that makes a wide detour around the singularity. Specific guidelines for choosing f( x) for different problems are given in the text. Results are impressive: for an eigenvalue problem with a pole in the middle of the original real interval (a "Sturm-Liouville problem of the fourth kind"), just six basis functions suffice to calculate the real and imaginary parts of the lowest eigenvalue to within 1.4%. For strong instability, i.e., modes whose phase speeds have large imaginary parts, the complex mapping is unnecessary because the critical latitudes are complex and distant from the real axis. Even so, the mapping is useful for instability problems because it can be used to make calculations for very slowly growing modes to follow the changes in c right up to the "neutral curve" where the imaginary part of c=0. Although especially valuable for spectral algorithms, the same trick can be applied with finite difference methods also. The main disadvantage of the algorithm is that the eigenfunction must be calculated in a second, separate step, but this is usually a minor flaw in comparison to the complex mapping's virtues for coping with singular eigenvalue problems.
Exact string theory model of closed timelike curves and cosmological singularities
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.
NASA Astrophysics Data System (ADS)
Hatefi, Ehsan
2015-12-01
We evaluate five point world-sheet string theory amplitudes of one transverse scalar field, two world volume gauge fields (and two transverse scalars, a gauge field) in the presence of a closed string Ramond-Ramond vertex operator in its symmetric picture. We carry out all the entire S-matrix elements of five point mixed RR-scalars/gauge fields < C -1 ϕ 0 A -1 A 0>, < C -1 ϕ -1 A 0 A 0>, < C -1 A 0 ϕ -1 ϕ 0> and < C -1 A -1 ϕ 0 ϕ 0> in detail and start comparing all order α' contact interactions and singularities in both transverse and world volume directions. We explore the presence of various new couplings in string theory effective actions and find out their all order α' higher derivative corrections in both type IIA and IIB. Ultimately we make various remarks for the singularities and contact terms whose RR momenta are embedded in transverse directions. α' corrections to some of Myers terms are also addressed.
Charged anisotropic Buchdahl solution as an embedding class I spacetime
NASA Astrophysics Data System (ADS)
Singh, Ksh. Newton; Pant, Neeraj; Pradhan, N.
2016-05-01
We present a new solution of embedding class I describing the interior of a spherically symmetric charged anisotropic stellar configuration. The exact analytic solution has been explored by considering Buchdahl type metric potential g_{rr}. Using this analytic solution, we have discussed various physical aspects of a compact star. The solution is free from central singularities. The solution also satisfies WEC, SEC, NEC and DEC. The compactness parameter 2M/rb as obtained from the solution satisfies the Buchdahl-Andreasson condition. Finally we have compared the calculated masses and radii of well-known compact star candidates like RX J1856.5-3754, XTE J1739-285, PSR B0943+10 and SAX J1808.4-3658 with their observational values.
Germanium Nanocrystals Embedded in Sapphire
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}.
Conservation laws in embedding theory
NASA Astrophysics Data System (ADS)
Murillo, Oscar; Mustafaev, Alexander
2015-09-01
In this work is considered embedding theory, a theory in which independent variables which describe gravity are functions of the space-time embedding into a ten-dimensional pseudo-Euclidean space. Neother's theorem is used to find conservation laws for energy and angular momentum as a result from the action's invariance in relation to the rotation and translation of the system. The form of these conservation laws and their consequences depending on the different formulations of embedding theory is discussed. It is also analyzed a transition from embedding theory to a field theory in a flat space-time with a number of dimensions greater than four. The same procedure is followed in this case to find conservation laws, resulting in the solution of the problem of time present in Einstein's theory of general relativity.
Conformal bootstrap in embedding space
NASA Astrophysics Data System (ADS)
Fortin, Jean-François; Skiba, Witold
2016-05-01
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation function of four scalars. All remaining conformal blocks are simple derivatives of the minimal conformal block. With the help of the orthogonality properties of the conformal blocks, the analytic conformal bootstrap can be implemented directly in embedding space, leading to a Jacobi-like definition of conformal field theories.
Future singularity avoidance in phantom dark energy models
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.
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.
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).
Singularity-free dislocation dynamics with strain gradient elasticity
NASA Astrophysics Data System (ADS)
Po, Giacomo; Lazar, Markus; Seif, Dariush; Ghoniem, Nasr
2014-08-01
The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and non-singular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the non-singular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop self-energy non-divergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of Lome-Cottrell junctions in Al show that the strength of the
Naked singularities in higher dimensional Vaidya space-times
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.
On the problem of stress singularities in bonded orthotropic materials
NASA Technical Reports Server (NTRS)
Erdogan, F.; Delale, F.
1976-01-01
The problem of stress singularities at the leading edge of a crack lying in the neighborhood of a bimaterial interface in bonded orthotropic materials is considered. The main objective is to study the effect of material orthotropy on the singular behavior of the stress state when the crack touches or intersects the interface. The results indicate that, due to the large number of material constants involved, in orthotropic materials, the power of stress singularity as well as the stress intensity factor can be considerably different than that found in the isotropic materials with the same stiffness ratio perpendicular to the crack.
Dalitz plot distributions in presence of triangle singularities
NASA Astrophysics Data System (ADS)
Szczepaniak, Adam P.
2016-06-01
We discuss properties of three-particle Dalitz distributions in coupled channel systems in presence of triangle singularities. The single channel case was discussed long ago [1] where it was found that as a consequence of unitarity, effects of a triangle singularity seen in the Dalitz plot are not seen in Dalitz plot projections. In the coupled channel case we find the same is true for the sum of intensities of all interacting channels. Unlike the single channel case, however, triangle singularities do remain visible in Dalitz plot projections of individual channels.
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.
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.
Configuration of singular optical cones in gyrotropic crystals with dichroism
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.
Singularities of the Euler equation and hydrodynamic stability
NASA Technical Reports Server (NTRS)
Tanveer, S.; Speziale, Charles G.
1993-01-01
Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.
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.
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.
Quantum singularities in spherically symmetric, conformally static spacetimes
NASA Astrophysics Data System (ADS)
Helliwell, T. M.; Konkowski, D. A.
2013-05-01
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed and then applied to a class of spherically symmetric, conformally static spacetimes, including as special cases those studied by Roberts, by Fonarev, and by Husain et al. We use solutions of the generally coupled, massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are healed quantum mechanically.
Spontaneous generation of singularities in paraxial optical fields.
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
On the singular perturbations for fractional differential equation.
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
Spacelike Singularities and Hidden Symmetries of Gravity
NASA Astrophysics Data System (ADS)
Henneaux, Marc; Persson, Daniel; Spindel, Philippe
2008-04-01
We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E_10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.
Fully developed turbulence and complex time singularities
NASA Astrophysics Data System (ADS)
Dombre, T.; Gagne, Y.; Hopfinger, E.
The hypothesis of Frisch and Morf (1981), relating intermittent bursts observed in high-pass-filtered turbulent-flow data to complex time singularities in the solution of the Navier-Stokes equations, is tested experimentally. Velocity signals filtered at high-pass frequency 1 kHz and low-pass frequency 6 kHz are recorded for 7 min at sampling frequency 20 kHz in a flow of mean velocity 6.1 m/s, with mesh length d = 7.5 cm, observation point x/d = 40, R sub lambda = 67, dissipation length eta = 0.5 mm, and Kolmogorov frequency fK = about 2 kHz. The results are presented in graphs, and it is shown that the exponential behavior of the energy spectrum settles well before fK, the spectra of individual bursts having exponential behavior and delta(asterisk) values consistent with the Frisch-Morf hypothesis, at least for high-amplitude events.
Fermi edge singularity in a tunnel junction
NASA Astrophysics Data System (ADS)
Zhang, Jin; Sherkunov, Yury; D'Ambrumenil, Nicholas; Muzykantskii, Boris
2010-03-01
We present results on the non-equilibrium Fermi edge singularity (FES) problem in tunnel junctions. The FES, which is present in a Fermi gas subject to any sudden change of potential, manifests itself in the final state many body interaction between the electrons in the leads [1]. We establish a connection between the FES problem in a tunnel junction and the Full Counting Statistics (FCS) for the device [2]. We find that the exact profile of the changing potential (or the profile for the barrier opening and closing in the tunnel junction case) strongly affects the overlap between the initial and final state of the Fermi gas. We factorize the contribution to the FES into two approximately independent terms: one is connected with the short time opening process while the other is concerned with the long time asymptotic effect, namely the Anderson orthogonality catastrophe. We consider applications to a localized level coupled through a tunnel barrier to a 1D lead driven out of equilibrium [3]. References: [1] G. Mahan, Phys. Rev. 163, 1612 (1967); P. Nozieres and C. T. De Dominicis, Phys. Rev. 178, 1079 (1969); P. Anderson, Phys. Rev. Lett. 18, 1049 (1967) [2] J. Zhang, Y. Sherkunov, N. d'Ambrumenil, and B. Muzykantskii, ArXiv:0909.3427 [3] D. Abanin and L. Levitov, Phys. Rev. Lett. 94, 186803 (2005)
NASA Astrophysics Data System (ADS)
Sarkar, Sanjay
2016-01-01
The present work deals with the accretion of two interacting fluids: dark matter and a hypothetical fluid as the holographic dark energy components onto wormhole in a non-flat FRW universe. First of all, following Cruz et al. (Phys. Lett. B 669, 271 2008), we obtained an exact solution of the Einstein's field equations. Solution describes effectively the actual acceleration and indicates a big rip type future singularity of the universe. After that we have studied the evolution of the mass of wormhole embedded in this FRW universe in order to reproduce a stable universe protected against future-time singularity. We found that the accretion of these dark components leads to a gradual increase of wormhole mass. It is also observed that contrary to the case as shown by Cruz et al. (Phys. Lett. B 669, 271 2008), the big rip singularity of the universe with a divergent Hubble parameter of this dark energy model may be avoided by a big trip. We have established a correspondence between the holographic dark energy with the polytropic gas dark energy model and obtained the potential as well as dynamics of the scalar field which describes the polytropic cosmology.
Modelling Molecular Emission from Young Embedded Disks
NASA Astrophysics Data System (ADS)
Harsono, D.; Visser, R.; van Dishoeck, E. F.; Kristensen, L.; Bruderer, S.; Brinch, C. Hogerheijde, M.
2011-05-01
Circumstellar disks play an important role in the formation of stars and planets. Recent observations and models have placed strong constraints on the later stages of their evolution (the T Tauri or Herbig Ae/Be phase), when an envelope is no longer present. However, little is known of the disk structure and evolution during the embedded phase of star formation. With Herschel and the VLT, and soon ALMA, we will be able to detect and characterize the early stages of disk formation. Sophisticated modeling including both physical and chemical structure of the system would be needed to interpret the high quality of data. We present a two-dimensional, semi-analytical model of disk formation as also used in Visser et al. (2009) and Visser and Dullemond (2010). The dust temperature is determined using a three-dimensional dust continuum radiative transfer code (RADMC-3D). Molecular abundances are calculated by following freeze-out and evaporation from the pre-stellar core up to the formation of the circumstellar disk. Synthetic spectra of CO and H2O within the wavelength ranges observable with Herschel and VLT-CRIRES are then produced at a series of time steps, tracing the different stages of disk formation. We also present simulated ALMA images. We discuss the evolution of the molecular emission and the possibility of identifying the presence of embedded disks.
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.
On Singularities and Black Holes in Combination-Driven Models of Technological Innovation Networks
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
Non-singular bounce scenarios in loop quantum cosmology and the effective field description
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.
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).
On Singularities and Black Holes in Combination-Driven Models of Technological Innovation Networks.
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
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...
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...
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.
Statistical analysis of effective singular values in matrix rank determination
NASA Technical Reports Server (NTRS)
Konstantinides, Konstantinos; Yao, Kung
1988-01-01
A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.
Singularity of the Velocity Distribution Function in Molecular Velocity Space
NASA Astrophysics Data System (ADS)
Chen, I.-Kun; Funagane, Hitoshi; Liu, Tai-Ping; Takata, Shigeru
2016-01-01
We study the boundary singularity of the solutions to the Boltzmann equation in the kinetic theory. The solution has a jump discontinuity in the microscopic velocity {ζ} on the boundary and a secondary singularity of logarithmic type around the velocity tangential to the boundary, {ζn ˜ 0-}, where {ζn} is the component of molecular velocity normal to the boundary, pointing to the gas. We demonstrate this secondary singularity by obtaining an asymptotic formula for the derivative of the solution on the boundary with respect to {ζn} that diverges logarithmically when {ζn ˜ 0-}. Our study is for the thermal transpiration problem between two plates for the hard sphere gases with sufficiently large Knudsen number and with the diffuse reflection boundary condition. The solution is constructed and its singularity is studied by an iteration procedure.
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.
A singularity-free WEC-respecting time machine
NASA Astrophysics Data System (ADS)
Krasnikov, S. V.
1998-04-01
A time machine (TM) is constructed whose creation, in contrast to all TMs known so far, requires neither singularities, nor violation of the weak energy condition (WEC). The spacetime exterior to the TM closely resembles the Friedmann universe.
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.
Molecular dynamics study of the stress singularity at a corner
NASA Astrophysics Data System (ADS)
Vafek, Oskar; Robbins, Mark O.
1999-11-01
Linear elasticity theory predicts a power-law singularity in the internal stress at the corner between dissimilar materials under a wide range of conditions. We have studied this singular region using molecular dynamics simulations with harmonic and Lennard-Jones interactions. For the harmonic potential the singularity is cut off by the discreteness of the lattice at a distance of one or two lattice constants from the corner. Anharmonicity leads to much longer range deviations for the Lennard-Jones potential, and plastic flow is observed in some cases. The prefactor of the singularity shows a power-law divergence with increasing system size. This implies that yield will always occur if the system is sufficiently large.
Object detection with a multistatic array using singular value decomposition
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.
Nonlinear ordinary differential equations: A discussion on symmetries and singularities
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Leach, P. G. L.
2016-06-01
Two essential methods, the symmetry analysis and the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations is the purpose of this work. The main similarities and the differences of these two different methods are discussed.
Open and closed universes, initial singularities, and inflation
NASA Astrophysics Data System (ADS)
Borde, Arvind
1994-09-01
The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a) previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b) the timelike convergence condition is known to be violated in inflationary spaceitmes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may not be extended to include many closed universes. Also, as a fringe benefit, the time reverse of the theorem may be applied to gravitational collapse.
Why do naked singularities form in gravitational collapse? II
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.
Automatic recording of direct current singularity amplitudes in Josephson junctions
Costabile, G.; Gambardella, U.; Pagano, S.
1985-08-01
We have designed and tested an electronic circuit to record the amplitude of any current singularity in the current-voltage characteristic of a Josephson tunnel junction. The detection of the peak current occurs only when the junction voltage is within a range that can be centered and narrowed conveniently. We describe the circuit in detail and illustrate its operation in the recording of some typical dc singularities.
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.
Singular and nonlinear processes in applied mathematics. Final technical report
Tabor, M.
1998-08-05
A wide range of research topics were supported under this grant. These included: (1) complex space time singularities in nonlinear differential equations; (2) singularities in magneto-hydrodynamics; (3) the dynamics of knots and curves; and (4) the structure and dynamics of foams and grain boundaries. A brief summary of results achieved in each of these four areas is given below along with the associated publications acknowledging DOE support.
Cooperative Output Regulation of Singular Heterogeneous Multiagent Systems.
Ma, Qian; Xu, Shengyuan; Lewis, Frank L; Zhang, Baoyong; Zou, Yun
2016-06-01
This paper investigates the cooperative output regulation problem of singular heterogeneous multiagent systems. General distributed observers are proposed for every agent obtaining the estimated state of the exosystem. The feedforward control technique and reduced-order approach are used to design distributed singular output feedback controllers and distributed normal output feedback controllers. The proposed cooperative dynamic controller is dependent on the plant parameters and the interaction topologies. A simulation example is provided to demonstrate the effectiveness of the proposed design method. PMID:26173224
Higher order matrix differential equations with singular coefficient matrices
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.
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.
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.
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.
On the Construction of Property Based Diabatizations: Diabolical Singular Points.
Zhu, Xiaolei; Yarkony, David R
2015-12-17
Diabatizations achieved by diagonalization of a property operator or as the extremum of a molecular property are numerous and widely used, although for a particular system a given property method may have limited accuracy or even fail catastrophically. These failures are usually analyzed in terms of limitations of the chosen property or method. Here we introduce an alternative perspective, failure attributable to singularities in the defining equations. The singular subspace is analogous to the conical intersection seam in potential energy surfaces. Using the archetypical NH3 nonadiabatic photodissociation, it is shown that for two states the diabatization condition has singularities on a subspace of dimension N - 2, where N = 3N(atom) - 6, is the number of internal coordinates. This singular subspace is distinct from the N - 2-dimensional seam of conical intersections of the electronic Hamiltonian and results incorrectly, in singular derivative couplings between diabatic states in unexpected regions of nuclear coordinate space. Simple indicators are developed that provide ways to anticipate and avoid these singularities. PMID:26444643
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.
On the singular values decoupling in the Singular Spectrum Analysis of volcanic tremor at Stromboli
NASA Astrophysics Data System (ADS)
Carniel, R.; Barazza, F.; Tárraga, M.; Ortiz, R.
2006-10-01
The well known strombolian activity at Stromboli volcano is occasionally interrupted by rarer episodes of paroxysmal activity which can lead to considerable hazard for Stromboli inhabitants and tourists. On 5 April 2003 a powerful explosion, which can be compared in size with the latest one of 1930, covered with bombs a good part of the normally tourist-accessible summit area. This explosion was not forecasted, although the island was by then effectively monitored by a dense deployment of instruments. After having tackled in a previous paper the problem of highlighting the timescale of preparation of this event, we investigate here the possibility of highlighting precursors in the volcanic tremor continuously recorded by a short period summit seismic station. We show that a promising candidate is found by examining the degree of coupling between successive singular values that result from the Singular Spectrum Analysis of the raw seismic data. We suggest therefore that possible anomalies in the time evolution of this parameter could be indicators of volcano instability to be taken into account e.g. in a bayesian eruptive scenario evaluator. Obviously, further (and possibly forward) testing on other cases is needed to confirm the usefulness of this parameter.
Texture Representations Using Subspace Embeddings
Yang, Xiaodong; Tian, YingLi
2013-01-01
In this paper, we propose a texture representation framework to map local texture patches into a low-dimensional texture subspace. In natural texture images, textons are entangled with multiple factors, such as rotation, scaling, viewpoint variation, illumination change, and non-rigid surface deformation. Mapping local texture patches into a low-dimensional subspace can alleviate or eliminate these undesired variation factors resulting from both geometric and photometric transformations. We observe that texture representations based on subspace embeddings have strong resistance to image deformations, meanwhile, are more distinctive and more compact than traditional representations. We investigate both linear and non-linear embedding methods including Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projections (LPP) to compute the essential texture subspace. The experiments in the context of texture classification on benchmark datasets demonstrate that the proposed subspace embedding representations achieve the state-of-the-art results while with much fewer feature dimensions. PMID:23710105
Texture Representations Using Subspace Embeddings.
Yang, Xiaodong; Tian, Yingli
2013-07-15
In this paper, we propose a texture representation framework to map local texture patches into a low-dimensional texture subspace. In natural texture images, textons are entangled with multiple factors, such as rotation, scaling, viewpoint variation, illumination change, and non-rigid surface deformation. Mapping local texture patches into a low-dimensional subspace can alleviate or eliminate these undesired variation factors resulting from both geometric and photometric transformations. We observe that texture representations based on subspace embeddings have strong resistance to image deformations, meanwhile, are more distinctive and more compact than traditional representations. We investigate both linear and non-linear embedding methods including Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projections (LPP) to compute the essential texture subspace. The experiments in the context of texture classification on benchmark datasets demonstrate that the proposed subspace embedding representations achieve the state-of-the-art results while with much fewer feature dimensions. PMID:23710105
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
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.
Singularities in Axisymmetric Free Boundaries for ElectroHydroDynamic Equations
NASA Astrophysics Data System (ADS)
Garcia, Mariana Smit Vega; Vărvărucă, Eugen; Weiss, Georg S.
2016-06-01
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.
On the limit cycles of a class of planar singular perturbed differential equations.
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
On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
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
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.
Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere.
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
Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere
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
Embedded Temperature-Change Sensors
NASA Technical Reports Server (NTRS)
Thakoor, Sarita; Thakoor, Anil; Karmon, Dan
1995-01-01
Transducers sensitive to rates of change of temperature embedded in integrated circuits and discrete electronic components damaged by overheating, according to proposal. Used to detect onset of rapid heating and to trigger shutoffs of power or other corrective actions before temperatures rise beyond safe limits. Sensors respond fast and reliably to incipient overheating because they are in direct thermal contact with vulnerable circuit elements.
Embedding Sensors During Additive Manufacturing
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
Boundary singularities produced by the motion of soap films
Goldstein, Raymond E.; McTavish, James; Moffatt, H. Keith; Pesci, Adriana I.
2014-01-01
Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a “neck-pinching” boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck’s geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures. PMID:24843162