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.
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.
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.
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.
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.
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.
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
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.
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
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.
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.
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
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.
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
Symmetries, Singularities and the De-Emergence of Space
NASA Astrophysics Data System (ADS)
Damour, Thibault; Nicolai, Hermann
Recent work has revealed intriguing connections between a Belinsky-Khalatnikov-Lifshitz-type analysis of spacelike singularities in general relativity and certain infinite-dimensional Lie algebras, particularly the "maximally extended" hyperbolic Kac-Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(-time) at the Planck scale, and hence — via an effective "de-emergence" of space near the singularity — to a novel mechanism for achieving background independence in quantum gravity.
Analysis on singular spaces: Lie manifolds and operator algebras
NASA Astrophysics Data System (ADS)
Nistor, Victor
2016-07-01
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called "Lie manifolds" -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.
The singular cubical set of a topological space
NASA Astrophysics Data System (ADS)
Antolini, Rosa; Wiest, Bert
1999-01-01
For any topological space X let C(X) be the realization of the singular cubical set of X; let * be the topological space consisting of one point. In [1] Antolini proves, as a corollary to a general theorem about cubical sets, that C(X) and X×C(*) are homotopy equivalent, provided X is a CW-complex. In this note we give a short geometric proof that for any topological space X there is a natural weak homotopy equivalence between C(X) and X×C(*).
The wave equation on static singular space-times
NASA Astrophysics Data System (ADS)
Mayerhofer, Eberhard
2008-02-01
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis evolved from the main topic, the wave equation on singular space-times. The second and main part of my thesis is devoted to establishing a local existence and uniqueness theorem for the wave equation on singular space-times. The singular Lorentz metric subject to our discussion is modeled within the special algebra on manifolds in the sense of Colombeau. Inspired by an approach to generalized hyperbolicity of conical-space times due to Vickers and Wilson, we succeed in establishing certain energy estimates, which by a further elaborated equivalence of energy integrals and Sobolev norms allow us to prove existence and uniqueness of local generalized solutions of the wave equation with respect to a wide class of generalized metrics. The third part of my thesis treats three different point value resp. uniqueness questions in algebras of generalized functions
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.
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
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
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
Horizons versus singularities in spherically symmetric space-times
Bronnikov, K. A.; Elizalde, E.; Odintsov, S. D.; Zaslavskii, O. B.
2008-09-15
We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as 'usual', 'naked', and 'truly naked' ones depending on the near-horizon behavior of transverse tidal forces acting on an extended body. We obtain the necessary conditions for the metric to be extensible beyond a horizon in terms of an arbitrary radial coordinate and show that all truly naked horizons, as well as many of those previously characterized as naked and even usual ones, do not admit an extension and therefore must be considered as singularities. Some examples are given, showing which kinds of matter are able to create specific space-times with different kinds of horizons, including truly naked ones. Among them are fluids with negative pressure and scalar fields with a particular behavior of the potential. We also discuss horizons and singularities in Kantowski-Sachs spherically symmetric cosmologies and present horizon regularity conditions in terms of an arbitrary time coordinate and proper (synchronous) time. It turns out that horizons of orders 2 and higher occur in infinite proper times in the past or future, but one-way communication with regions beyond such horizons is still possible.
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
Planning Paths Through Singularities in the Center of Mass Space
NASA Technical Reports Server (NTRS)
Doggett, William R.; Messner, William C.; Juang, Jer-Nan
1998-01-01
The center of mass space is a convenient space for planning motions that minimize reaction forces at the robot's base or optimize the stability of a mechanism. A unique problem associated with path planning in the center of mass space is the potential existence of multiple center of mass images for a single Cartesian obstacle, since a single center of mass location can correspond to multiple robot joint configurations. The existence of multiple images results in a need to either maintain multiple center of mass obstacle maps or to update obstacle locations when the robot passes through a singularity, such as when it moves from an elbow-up to an elbow-down configuration. To illustrate the concepts presented in this paper, a path is planned for an example task requiring motion through multiple center of mass space maps. The object of the path planning algorithm is to locate the bang- bang acceleration profile that minimizes the robot's base reactions in the presence of a single Cartesian obstacle. To simplify the presentation, only non-redundant robots are considered and joint non-linearities are neglected.
Black-and-white hole as a space-time with integrable singularity
NASA Astrophysics Data System (ADS)
Strokov, Vladimir N.; Lukash, Vladimir N.; Mikheeva, Elena V.
2016-01-01
We discuss the problem of singularities in general relativity and emphasize the distinction that should be made between what is understood to be mathematical and physical singularities. We revise examples of space-times that conventionally contain a singularity which, in a sense, does not manifest itself physically. A special attention is paid to the case of integrable singularities for which we propose a well-defined mathematical procedure used to extend the space-time beyond the singularity. We argue that this type of singularity may connect the interior of a black hole with a newly born universe (a space-time referred to as black-and-white hole) giving a resolution to the problem of initial high density and symmetry of the universe. We exemplify by presenting toy models of eternal and astrophysical black-and-white holes.
Chao, Alexander Wu; /SLAC
2012-03-01
As accelerator technology advances, the requirements on accelerator beam quality become increasingly demanding. Facing these new demands, the topic of phase space gymnastics is becoming a new focus of accelerator physics R&D. In a phase space gymnastics, the beam's phase space distribution is manipulated and precision tailored to meet the required beam qualities. On the other hand, all realization of such gymnastics will have to obey accelerator physics principles as well as technological limitations. Recent examples of phase space gymnastics include Emittance exchanges, Phase space exchanges, Emittance partitioning, Seeded FELs and Microbunched beams. The emittance related topics of this list are reviewed in this report. The accelerator physics basis, the optics design principles that provide these phase space manipulations, and the possible applications of these gymnastics, are discussed. This fascinating new field promises to be a powerful tool of the future.
Practical approaches to handle the singularities of a wrist-partitioned space manipulator
NASA Astrophysics Data System (ADS)
Xu, Wenfu; Liang, Bin; Xu, Yangsheng
2011-01-01
Space robotic systems are expected to play an increasingly important role in the future. However, the control methods based on the inverse kinematics are affected by singularities. In this paper, practical approaches are proposed to solve the problems of a wrist-partitioned space manipulator. For spacecraft-referenced end-point motion control, we presented the singularity separation plus damped reciprocal (SSPDR) method, which separates the singularity parameters from the inverse of the Jacobian, and replaces their reciprocals using the damped reciprocals. For another control strategy, i.e. inertially referenced end-point motion control, including spacecraft attitude-controlled mode and free-floating mode, the linear momentum equation is used to eliminate three independent variables. With modifying some expressions, the SSPDR method is utilized to solve the singularities of spacecraft attitude-controlled space robot. When the space robot is free-floating, the singularities, i.e. the so-called dynamic singularities, cannot be predicted according to its kinematic structure. Combining with the measured angular velocity of the base, the dynamic singularity handling problem is transformed into real-time kinematic singularity avoiding problem, which can be solved by the SSPDR method. Since the SVD decomposition, the estimation of the minimum singularity value, and the calculation of the generalized Jacobian matrix are not required, the algorithm has lower computation load. Another advantage is that, only the accuracy of part velocity components is reduced by adding the damped coefficients. Simulation results verify the proposed approaches.
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.
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.
On the dynamic singularities in the control of free-floating space manipulators
NASA Technical Reports Server (NTRS)
Papadopoulos, E.; Dubowsky, S.
1989-01-01
It is shown that free-floating space manipulator systems have configurations which are dynamically singular. At a dynamically singular position, the manipulator is unable to move its end effector in some direction. This problem appears in any free-floating space manipulator system that permits the vehicle to move in response to manipulator motion without correction from the vehicle's attitude control system. Dynamic singularities are functions of the dynamic properties of the system; their existence and locations cannot be predicted solely from the kinematic structure of the manipulator, unlike the singularities for fixed base manipulators. It is also shown that the location of these dynamic singularities in the workplace is dependent upon the path taken by the manipulator in reaching them. Dynamic singularities must be considered in the control, planning and design of free-floating space manipulator systems. A method for calculating these dynamic singularities is presented, and it is shown that the system parameters can be selected to reduce the effect of dynamic singularities on a system's performance.
Is the shell-focusing singularity of Szekeres space-time visible?
Nolan, Brien C; Debnath, Ujjal
2007-11-15
The visibility of the shell-focusing singularity in Szekeres space-time--which represents quasispherical dust collapse--has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaitre-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach.
Compactification on phase space
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin; Wheeler, James
2016-03-01
A major challenge for string theory is to understand the dimensional reduction required for comparison with the standard model. We propose reducing the dimension of the compactification by interpreting some of the extra dimensions as the energy-momentum portion of a phase-space. Such models naturally arise as generalized quotients of the conformal group called biconformal spaces. By combining the standard Kaluza-Klein approach with such a conformal gauge theory, we may start from the conformal group of an n-dimensional Euclidean space to form a 2n-dimensional quotient manifold with symplectic structure. A pair of involutions leads naturally to two n-dimensional Lorentzian manifolds. For n = 5, this leaves only two extra dimensions, with a countable family of possible compactifications and an SO(5) Yang-Mills field on the fibers. Starting with n=6 leads to 4-dimensional compactification of the phase space. In the latter case, if the two dimensions each from spacetime and momentum space are compactified onto spheres, then there is an SU(2)xSU(2) (left-right symmetric electroweak) field between phase and configuration space and an SO(6) field on the fibers. Such a theory, with minor additional symmetry breaking, could contain all parts of the standard model.
NASA Astrophysics Data System (ADS)
Błaszak, Maciej; Domański, Ziemowit
2012-02-01
This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic
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.
Scalar field probes of power-law space-time singularities
NASA Astrophysics Data System (ADS)
Blau, Matthias; Frank, Denis; Weiss, Sebastian
2006-08-01
We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x-2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x-2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
NASA Astrophysics Data System (ADS)
Sheehan, Daniel Peter
1987-09-01
Experimental measurements are presented of ion phase space evolution in a collisionless magnetoplasma utilizing nonperturbing laser induced fluorescence (LIF) diagnostics. Ion configuration space and velocity space transport, and ion thermodynamic information were derived from the phase space diagrams for the following beam-plasma and obstacle-plasma systems:(UNFORMATTED TABLE OR EQUATION FOLLOWS) OBSTACLE & PLASMA SPECIES qquad disc & quad Ba ^+/e^ qquad disc & quad Ba^+/SF _6^-/e^ BEAM SPECIES & PLASMA SPECIES} qquad Ba^+ & quad Cs^+/e^ qquad Cs^+ & quad Ba^+/e^ qquad Ba^+ & quad Cs^+/SF_6 ^-/e^ qquad e^- & quad Ba^+ /e^ TABLE/EQUATION ENDS The ions were roughly mass symmetric. Plasma systems were reconstructed from multiple discrete Ba(II) ion velocity distributions with spatial, temporal, and velocity resolution of 1 mm^3, 2 musec, and 3 times 1010 cm ^3/sec^3 respectively. Phase space reconstructions indicated resonant ion response to the current-driven electrostatic ion cyclotron wave (EICW) in the case of an electron beam and to the ion cyclotron-cyclotron wave in the case of ion beams. Ion energization was observed in both systems. Local particle kinetic energy densities increase far above thermal levels in the presence of the EICW and ICCW. Time-resolved measurements of the EICW identified phase space particle bunching. The nonlinear evolution of f_{rm i}(x,v,t) was investigated for both beam systems. The near wake of conducting electrically floating disc obstacle was studied. Anomalous cross field diffusion (D_bot > 10 ^4 cm^2/sec) and ion energization were correlated with strong, low-frequency turbulence generated by the obstacle. Ion perpendicular kinetic energy densities doubled over thermal levels in the near wake. Upstream of the obstacle, l ~ 50 lambda_ {rm D}, a collisionless shock was indicated; far downstream, an ion flux peak was observed. Three negative ion plasma (NIP) sources were developed and characterized in the course of research: two
Efficiently enclosing the compact binary parameter space by singular-value decomposition
Cannon, Kipp; Hanna, Chad; Keppel, Drew
2011-10-15
Gravitational-wave searches for the merger of compact binaries use matched filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high density. Previously it has been shown that singular-value decomposition can reduce the effective number of filters required to search the data. Here we study how the basis provided by the singular-value decomposition changes dimension as a function of template-bank density. We will demonstrate that it is sufficient to use the basis provided by the singular-value decomposition of a low-density bank to accurately reconstruct arbitrary points within the boundaries of the template bank. Since this technique is purely numerical, it may have applications to interpolating the space of numerical relativity waveforms.
Classical lattice spin models involving singular interactions isotropic in spin space.
Chamati, Hassan; Romano, Silvano
2015-07-01
We address here a few classical lattice spin models, involving n-component unit vectors (n=2,3), associated with a D-dimensional lattice Z(D),D=1,2, and interacting via a pair potential restricted to nearest neighbors and being isotropic in spin space, i.e., defined by a function of the scalar product between the interacting spins. When the potential involves a continuous function of the scalar product, the Mermin-Wagner theorem and its generalizations exclude orientational order at all finite temperatures in the thermodynamic limit, and exclude phase transitions at finite temperatures when D=1; on the other hand, we have considered here some comparatively simple functions of the scalar product which are bounded from below, diverge to +∞ for certain mutual orientations, and are continuous almost everywhere with integrable singularities. Exact solutions are presented for D=1, showing an absence of phase transitions and an absence of orientational order at all finite temperatures in the thermodynamic limit; for D=2, and in the absence of more stringent mathematical results, extensive simulations carried out on some of them point to the absence of orientational order at all finite temperatures and suggest the existence of a Berezinskiĭ-Kosterlitz-Thouless transition. PMID:26274152
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.
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).
Emittance and Phase Space Exchange
Xiang, Dao; Chao, Alex; /SLAC
2011-08-19
Alternative chicane-type beam lines are proposed for exact emittance exchange between horizontal phase space (x; x{prime}) and longitudinal phase space (z; {delta}). Methods to achieve exact phase space exchanges, i.e. mapping x to z, x{prime} to {delta}, z to x and {delta} to x{prime} are suggested. Methods to mitigate the thick-lens effect of the transverse cavity on emittance exchange are discussed. Some applications of the phase space exchanger and the feasibility of an emittance exchange experiment with the proposed chicane-type beam line at SLAC are discussed.
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
NASA Astrophysics Data System (ADS)
Xie, Guizhong; Zhang, Dehai; Zhang, Jianming; Meng, Fannian; Du, Wenliao; Wen, Xiaoyu
2016-07-01
As a widely used numerical method, boundary element method (BEM) is efficient for computer aided engineering (CAE). However, boundary integrals with near singularity need to be calculated accurately and efficiently to implement BEM for CAE analysis on thin bodies successfully. In this paper, the distance in the denominator of the fundamental solution is first designed as an equivalent form using approximate expansion and the original sinh method can be revised into a new form considering the minimum distance and the approximate expansion. Second, the acquisition of the projection point by Newton-Raphson method is introduced. We acquire the nearest point between the source point and element edge by solving a cubic equation if the location of the projection point is outside the element, where boundary integrals with near singularity appear. Finally, the subtriangles of the local coordinate space are mapped into the integration space and the sinh method is applied in the integration space. The revised sinh method can be directly performed in the integration element. Averification test of our method is proposed. Results demonstrate that our method is effective for regularizing the boundary integrals with near singularity.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F.
2006-09-15
Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
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.
Holographic curvature perturbations in a cosmology with a space-like singularity
NASA Astrophysics Data System (ADS)
Ferreira, Elisa G. M.; Brandenberger, Robert
2016-07-01
We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t = 0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in the bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.
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.
Phase microscope imaging in phase space
NASA Astrophysics Data System (ADS)
Sheppard, Colin J. R.; Mehta, Shalin B.
2016-03-01
Imaging in a bright field or phase contrast microscope is partially coherent. We have found that the image can be conveniently considered and modeled in terms of the Wigner distribution function (WDF) of the object transmission. The WDF of the object has a simple physical interpretation for the case of a slowly varying object. Basically, the image intensity is the spatial marginal of the spatial convolution of the object WDF with the phase space imager kernel (PSIkernel), a rotated version of the transmission cross-coefficient. The PSI-kernel can be regarded as a partially-coherent generalization of the point spread function. This approach can be extended to consider the partial coherence of the image itself. In particular, we can consider the mutual intensity, WDF or ambiguity function of the image. It is important to note that the spatial convolution of the object WDF with the PSI-kernel is not a WDF, and not the WDF of the image. The phase space representations of the image have relevance to phase reconstruction methods such as phase space tomography, or the transport of intensity equation approach, and to the three-dimensional image properties.
Quantum phase transition in space
Damski, Bogdan; Zurek, Wojciech H
2008-01-01
A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose-Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e., the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent {nu}.
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
Phase nucleation in curved space
NASA Astrophysics Data System (ADS)
Gómez, Leopoldo; García, Nicolás; Vitelli, Vincenzo; Lorenzana, José; Daniel, Vega
Nucleation and growth is the dominant relaxation mechanism driving first-order phase transitions. In two-dimensional flat systems, nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study nucleation and growth of two-dimensional phases lying on curved surfaces and show that curvature modifies both critical sizes of nuclei and paths towards the equilibrium phase. In curved space, nucleation and growth becomes inherently inhomogeneous and critical nuclei form faster on regions of positive Gaussian curvature. Substrates of varying shape display complex energy landscapes with several geometry-induced local minima, where initially propagating nuclei become stabilized and trapped by the underlying curvature (Gómez, L. R. et al. Phase nucleation in curved space. Nat. Commun. 6:6856 doi: 10.1038/ncomms7856 (2015).).
Formation of naked singularities in five-dimensional space-time
Yamada, Yuta; Shinkai, Hisa-aki
2011-03-15
We numerically investigate the gravitational collapse of collisionless particles in spheroidal configurations both in four- and five-dimensional (5D) space-time. We repeat the simulation performed by Shapiro and Teukolsky (1991) that announced an appearance of a naked singularity, and also find similar results in the 5D version. That is, in a collapse of a highly prolate spindle, the Kretschmann invariant blows up outside the matter and no apparent horizon forms. We also find that the collapses in 5D proceed more rapidly than in 4D, and the critical prolateness for the appearance of an apparent horizon in 5D is loosened, compared to 4D cases. We also show how collapses differ with spatial symmetries comparing 5D evolutions in single-axisymmetry, SO(3), and those in double-axisymmetry, U(1)xU(1).
Longitudinal phase space tomography with space charge
NASA Astrophysics Data System (ADS)
Hancock, S.; Lindroos, M.; Koscielniak, S.
2000-12-01
Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of the vacuum chamber parametrized by a single value of distributed reactive impedance and by a geometrical coupling coefficient. This is sufficient to model the dominant collective effects in machines of low to moderate energy. In contrast to simulation codes, binning is not an issue since the profiles to be differentiated are measured ones. The program is written in Fortran 90 with high-performance Fortran extensions for parallel processing. A major effort has been made to identify and remove execution bottlenecks, for example, by reducing floating-point calculations and recoding slow intrinsic functions. A pointerlike mechanism which avoids the problems associated with pointers and parallel processing has been implemented. This is required to handle the large, sparse matrices that the algorithm employs. Results obtained with and without the inclusion of space charge are presented and compared for proton beams in the CERN protron synchrotron booster. Comparisons
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
NASA Technical Reports Server (NTRS)
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
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.
Nonlinear bulk viscosity in FRW cosmology: a phase space analysis.
NASA Astrophysics Data System (ADS)
Acquaviva, G.; Beesham, A.
2015-11-01
We consider a Friedmann-Robertson-Walker spacetime filled with both viscous radiation and nonviscous dust. The former has a bulk viscosity that is proportional to an arbitrary power of the energy density, i.e. \\zeta \\propto {ρ }{{v}}ν , and viscous pressure satisfying a nonlinear evolution equation. The analysis is carried out in the context of dynamical systems and the properties of solutions corresponding to the fixed points are discussed. For some ranges of the relevant parameter ν we find that the trajectories in the phase space evolve from a FRW singularity towards an asymptotic de Sitter attractor, confirming and extending previous analysis in the literature.
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.
A general formalism for phase space calculations
NASA Technical Reports Server (NTRS)
Norbury, John W.; Deutchman, Philip A.; Townsend, Lawrence W.; Cucinotta, Francis A.
1988-01-01
General formulas for calculating the interactions of galactic cosmic rays with target nuclei are presented. Methods for calculating the appropriate normalization volume elements and phase space factors are presented. Particular emphasis is placed on obtaining correct phase space factors for 2-, and 3-body final states. Calculations for both Lorentz-invariant and noninvariant phase space are presented.
Quantum phase-space representation for curved configuration spaces
NASA Astrophysics Data System (ADS)
Gneiting, Clemens; Fischer, Timo; Hornberger, Klaus
2013-12-01
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The resulting Wigner function displays the axioms of a quasiprobability distribution, and any Weyl-ordered operator gets associated with the corresponding phase-space function, even in the absence of continuous symmetries. The corresponding quantum Liouville equation reduces to the classical curved space Liouville equation in the semiclassical limit. We demonstrate the formalism for a point particle moving on two-dimensional manifolds, such as a paraboloid or the surface of a sphere. The latter clarifies the treatment of compact coordinate spaces, as well as the relation of the presented phase-space representation to symmetry groups of the configuration space.
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)
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.
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.
Mining the Observational Phase Space
NASA Astrophysics Data System (ADS)
Norris, Ray
2012-09-01
Experience has shown that many great discoveries in astronomy have been made, not by testing a hypothesis, but by observing the sky in an innovative way. The necessary conditions for this to take place are (a) a telescope observing an unexplored part of the observational phase space (frequency, resolution, time-domain, area of sky, etc), (b) an intelligent observer who understands the instrument sufficiently well to distinguish between artefact and discovery, (c) a prepared and enthusiastic mind ready to accommodate and interpret a new discovery. Next generation survey telescopes will easily satisfy (a), if only in terms of the numbers of objects surveyed. However, their petabytes of data, and arms-length access, may prevent an observer from satisfying (b) and (c). We can only hope that someone will eventually stumble across any unexpected phenomena in the data. However the impenetrable size of the database implies dark corners that will never be fully explored. Discoveries may remain undiscovered, forever. What is the alternative? Can we harness data-mining techniques to help the intelligent observer search for the unexpected? I believe we can, and indeed we must if we are to reap the full scientific benefit of next-generation survey telescopes.
Quantum Phase Space from Schwinger's Measurement Algebra
NASA Astrophysics Data System (ADS)
Watson, P.; Bracken, A. J.
2014-07-01
Schwinger's algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking distinct values, where is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is thereby related to definite experimental configurations.
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
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
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.
Solving close-coupling equations in momentum space without singularities II
NASA Astrophysics Data System (ADS)
Bray, A. W.; Abdurakhmanov, I. B.; Kadyrov, A. S.; Fursa, D. V.; Bray, I.
2016-06-01
The implementation of the convergent close-coupling method, whereby the principal-value singularity is treated analytically (Bray et al., 2015), has been extended to non-zero angular momenta. Its utility is demonstrated through application to proton scattering on excited states of positronium at incident energies spanning six orders of magnitude. It is shown that the analytic treatment is necessary in the case of highly excited positronium states.
Singular dynamics of a q-difference Painlevé equation in its initial-value space
NASA Astrophysics Data System (ADS)
Joshi, N.; Lobb, S. B.
2016-01-01
We construct the initial-value space of a q-discrete first Painlevé equation explicitly and describe the behaviours of its solutions w(n) in this space as n\\to ∞ , with particular attention paid to neighbourhoods of exceptional lines and irreducible components of the anti-canonical divisor. These results show that trajectories starting in domains bounded away from the origin in initial value space are repelled away from such singular lines. However, the dynamical behaviours in neighbourhoods containing the origin are complicated by the merger of two simple base points at the origin in the limit. We show that these lead to a saddle-point-type behaviour in a punctured neighbourhood of the origin.
The Way to Phase Space Crystals
NASA Astrophysics Data System (ADS)
Guo, Lingzhen; Michael, Marthaler; Schön, Gerd
A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field. Under rotating wave approximation, the system can produce a periodic lattice structure in phase space. The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field. We propose explicit models to realize such a phase space crystal and analyze its band structure in the frame of a tightbinding approximation. The phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry. The phase space crystal opens new ways to engineer energy band structures, with the added advantage that its properties can be changed in situ by tuning the driving field's parameters. Carl-Zeiss Stiftung.
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.
Gravitational collapse of a homogeneous scalar field in deformed phase space
NASA Astrophysics Data System (ADS)
Rasouli, S. M. M.; Ziaie, A. H.; Marto, J.; Moniz, P. V.
2014-02-01
We study the gravitational collapse of a homogeneous scalar field, minimally coupled to gravity, in the presence of a particular type of dynamical deformation between the canonical momenta of the scale factor and of the scalar field. In the absence of such a deformation, a class of solutions can be found in the literature [R. Goswami and P. S. Joshi], whereby a curvature singularity occurs at the collapse end state, which can be either hidden behind a horizon or be visible to external observers. However, when the phase space is deformed, as implemented herein this paper, we find that the singularity may be either removed or instead, attained faster. More precisely, for negative values of the deformation parameter, we identify the emergence of a negative pressure term, which slows down the collapse so that the singularity is replaced with a bounce. In this respect, the formation of a dynamical horizon can be avoided depending on the suitable choice of the boundary surface of the star. Whereas for positive values, the pressure that originates from the deformation effects assists the collapse toward the singularity formation. In this case, since the collapse speed is unbounded, the condition on the horizon formation is always satisfied and furthermore the dynamical horizon develops earlier than when the phase-space deformations are absent. These results are obtained by means of a thoroughly numerical discussion.
Zhao, Hongya; Wang, Debby D; Chen, Long; Liu, Xinyu; Yan, Hong
2016-01-01
Co-clustering, often called biclustering for two-dimensional data, has found many applications, such as gene expression data analysis and text mining. Nowadays, a variety of multi-dimensional arrays (tensors) frequently occur in data analysis tasks, and co-clustering techniques play a key role in dealing with such datasets. Co-clusters represent coherent patterns and exhibit important properties along all the modes. Development of robust co-clustering techniques is important for the detection and analysis of these patterns. In this paper, a co-clustering method based on hyperplane detection in singular vector spaces (HDSVS) is proposed. Specifically in this method, higher-order singular value decomposition (HOSVD) transforms a tensor into a core part and a singular vector matrix along each mode, whose row vectors can be clustered by a linear grouping algorithm (LGA). Meanwhile, hyperplanar patterns are extracted and successfully supported the identification of multi-dimensional co-clusters. To validate HDSVS, a number of synthetic and biological tensors were adopted. The synthetic tensors attested a favorable performance of this algorithm on noisy or overlapped data. Experiments with gene expression data and lineage data of embryonic cells further verified the reliability of HDSVS to practical problems. Moreover, the detected co-clusters are well consistent with important genetic pathways and gene ontology annotations. Finally, a series of comparisons between HDSVS and state-of-the-art methods on synthetic tensors and a yeast gene expression tensor were implemented, verifying the robust and stable performance of our method. PMID:27598575
RADON reconstruction in longitudinal phase space
Mane, V.; Peggs, S.; Wei, J.
1997-07-01
Longitudinal particle motion in circular accelerators is typically monitoring by one dimensional (1-D) profiles. Adiabatic particle motion in two dimensional (2-D) phase space can be reconstructed with tomographic techniques, using 1-D profiles. A computer program RADON has been developed in C++ to process digitized mountain range data and perform the phase space reconstruction for the AGS, and later for Relativistic Heavy Ion Collider (RHIC).
NASA Astrophysics Data System (ADS)
Frey, Randy W.; Rawlins, Greg; Zepkin, Neil; Bohlin, John
1989-03-01
A pseudo-ranging laser radar (PRLADAR) concept is proposed to provide extended range capability to tracking LADAR systems meeting the long-range requirements of SDI mission scenarios such as the SIE midcourse program. The project will investigate the payoff of several transmitter modulation techniques and a feasibility demonstration using a breadboard implementation of a new receiver concept called the Phase Multiplexed Correlator (PMC) will be accomplished. The PRLADAR concept has specific application to spaceborne LADAR tracking missions where increased CNR/SNR performance gained by the proposed technique may reduce the laser power and/or optical aperture requirement for a given mission. The reduction in power/aperture has similar cost reduction advantages in commercial ranging applications. A successful Phase 1 program will lay the groundwork for a quick reaction upgrade to the AMOS/LASE system in support of near term SIE measurement objectives.
Liquid crystal phase shifters for space applications
NASA Astrophysics Data System (ADS)
Woehrle, Christopher D.
Space communication satellites have historically relied heavily on high gain gimbal dish antennas for performing communications. Reflector dish antennas lack flexibility in anti-jamming capabilities, and they tend to have a high risk associated to them given the need for mechanical mechanisms to beam steer. In recent years, a great amount of investment has been made into phased array antenna technologies. Phased arrays offer increased signal flexibility at reduced financial cost and in system risk. The problem with traditional phased arrays is the significant program cost and overall complexity added to the satellite by integrating antenna elements that require many dedicated components to properly perform adaptive beam steering. Several unique methods have been proposed to address the issues that plague traditional phase shifters slated for space applications. Proposed approaches range from complex mechanical switches (MEMS) and ferroelectric devices to more robust molecular changes. Nematic liquid crystals offer adaptive beam steering capabilities that traditional phased arrays have; however, with the added benefit of reduced system cost, complexity, and increased resilience to space environmental factors. The objective of the work presented is to investigate the feasibility of using nematic liquid crystals as a means of phase shifting individual phased array elements slated for space applications. Significant attention is paid to the survivability and performance of liquid crystal and associated materials in the space environment. Performance regarding thermal extremes and interactions with charged particles are the primary factors addressed.
Single phase space laundry development
NASA Technical Reports Server (NTRS)
Colombo, Gerald V.; Putnam, David F.; Lunsford, Teddie D.; Streech, Neil D.; Wheeler, Richard R., Jr.; Reimers, Harold
1993-01-01
This paper describes a newly designed, 2.7 Kg (6 pound) capacity, laundry machine called the Single Phase Laundry (SPSL). The machine was designed to wash and dry crew clothing in a micro-gravity environment. A prototype unit was fabricated for NASA-JSC under a Small Business Innovated Research (SBIR) contract extending from September 1990 to January 1993. The unit employs liquid jet agitation, microwave vacuum drying, and air jet tumbling, which was perfected by KC-135 zero-g flight testing. Operation is completely automated except for loading and unloading clothes. The unit uses about 20 percent less power than a conventional household appliance.
Quantum dynamics in phase space: Moyal trajectories 2
Braunss, G.
2013-01-15
Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010)] where we had calculated Planck-Constant-Over-Two-Pi {sup 2}-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of Planck-Constant-Over-Two-Pi {sup 2}-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an Planck-Constant-Over-Two-Pi {sup 2}-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r= 0) whereas the classical trajectories are singular at r= 0. In the third example, we show in particular that for an arbitrary function {gamma}(H, z) the expression {beta}{identical_to}p{sub z}+{gamma}(H, z) is classically ( Planck-Constant-Over-Two-Pi = 0) a constant of motion, whereas for Planck-Constant-Over-Two-Pi {ne} 0 this holds only if {gamma}(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Henon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.
Beam Tomography in Longitudinal Phase Space
NASA Astrophysics Data System (ADS)
Mane, V.; Wei, J.; Peggs, S.
1997-05-01
Longitudinal particle motion in circular accelerators is typically monitored by one dimensional (1-D) profiles. Adiabatic particle motion in 2-D phase space can be reconstructed with tomographic techniques, using 1-D profiles. In this paper, we discuss a filtered backprojection algorithm, with a high pass ramp or Hann filter, for phase space reconstruction. The algorithm uses several projections of the beam at equally spaced angles over half a synchrotron period. A computer program RADON has been developed to process digitized mountain range data and do the phase space reconstruction for the AGS, and later for Relativistic Heavy Ion Collider (RHIC). Analysis has been performed to determine the sensitivity to machine parameters and data acquisition errors. During the Sextant test of RHIC in early 1997, this program has been successfully employed to reconstruct the motion of Au^77+ beam in the AGS.
Space Phase III - The commercial era dawns
NASA Technical Reports Server (NTRS)
Allnutt, R. F.
1983-01-01
After the 'Phase I' of space activities, the period bounded by Sputnik and Apollo, 'Phase II', has been entered, a phase in which concerns over the use and the protection of space assets which support national security predominate. However, it is only when the commercial motive becomes prominent that human activity in new regions truly prospers and enters periods of exponential growth. It is believed that there are increasing signs that such a period, called 'Space Phase III', may be coming soon. A description is presented of developments and results upon which this conclusion is based. Since 1980, there have been three developments of great importance for the future of space activities. Six highly successful flights have demonstrated that the Space Shuttle concept works. A series of Soviet missions are related to the emergence of a capability to construct and service modular space stations. Successful tests of the European Ariane 1 indicate an end to U.S. monopoly with respect to the provision of launch services to the Western World.
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.
Neutral line chaos and phase space structure
NASA Technical Reports Server (NTRS)
Burkhart, Grant R.; Speiser, Theodore W.; Martin, Richard F., Jr.; Dusenbery, Paul B.
1991-01-01
Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.
Noether symmetries in the phase space
NASA Astrophysics Data System (ADS)
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Space Fence PDR Concept Development Phase
NASA Astrophysics Data System (ADS)
Haines, L.; Phu, P.
2011-09-01
The Space Fence, a major Air Force acquisition program, will become the dominant low-earth orbit uncued sensor in the space surveillance network (SSN). Its primary objective is to provide a 24/7 un-cued capability to find, fix, and track small objects in low earth orbit to include emerging and evolving threats, as well as the rapidly growing population of orbital debris. Composed of up to two geographically dispersed large-scale S-band phased array radars, this new system-of-systems concept will provide comprehensive Space Situational Awareness through net-centric operations and integrated decision support. Additionally, this program will facilitate cost saving force structure changes in the SSN, specifically including the decommissioning of very-high frequency VHF Air Force Space Surveillance System (AFSSS). The Space Fence Program Office entered a Preliminary Design Review (PDR) concept development phase in January 2011 to achieve the delivery of the Initial Operational Capability (IOC) expected in FY17. Two contractors were awarded to perform preliminary system design, conduct radar performance analyses and evaluations, and develop a functional PDR radar system prototype. The key objectives for the Phase A PDR effort are to reduce Space Fence total program technical, cost, schedule, and performance risk. The overall program objective is to achieve a preliminary design that demonstrates sufficient technical and manufacturing maturity and that represents a low risk, affordable approach to meet the Space Fence Technical Requirements Document (TRD) requirements for the final development and production phase to begin in 3QFY12. This paper provides an overview of the revised Space Fence program acquisition strategy for the Phase-A PDR phase to IOC, the overall program milestones and major technical efforts. In addition, the key system trade studies and modeling/simulation efforts undertaken during the System Design Requirement (SDR) phase to address and mitigate
Phase-space foundations of electron holography
NASA Astrophysics Data System (ADS)
Lubk, A.; Röder, F.
2015-09-01
We present a unified formalism for describing various forms of electron holography in quantum mechanical phase space including their extensions to quantum-state reconstructions. The phase-space perspective allows for taking into account partial coherence as well as the quantum mechanical detection process typically hampering the unique reconstruction of a wave function. We elaborate on the limitations imposed by the electron optical elements of the transmission electron microscope as well as the scattering at the target. The results provide the basis for vastly extending the scope of electron holographic techniques towards analyzing partially coherent signals such as inelastically scattered electrons or electron pulses used in ultrafast transmission electron microscopy.
Phase-space contraction and quantum operations
Garcia-Mata, Ignacio; Spina, Maria Elena; Saraceno, Marcos; Carlo, Gabriel
2005-12-15
We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as 'quantum phase space contraction rate' and which is related to a fundamental property of quantum channels: nonunitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attractor-like structures is displayed.
Positive phase space distributions and uncertainty relations
NASA Technical Reports Server (NTRS)
Kruger, Jan
1993-01-01
In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.
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
Particle emission from covariant phase space
Bambah, B.A. )
1992-12-01
Using Lorentz-covariant sources, we calculate the multiplicity distribution of {ital n} pair correlated particles emerging from a Lorentz-covariant phase-space volume. We use the Kim-Wigner formalism and identify these sources as the squeezed states of a relativistic harmonic oscillator. The applications of this to multiplicity distributions in particle physics is discussed.
A space-fed phased array for surveillance from space
NASA Astrophysics Data System (ADS)
Hightower, Charles H.; Wong, Sam H.; Perkons, Alfred R.; Igwe, Christian I.
1991-05-01
A space-fed radar antenna called a venetian blind is proposed for all-weather wide-area surveillance from space. Radar requirements for tasked and untasked operation are discussed, and the process of selecting the venetian blind concept, which can support both, is described. In its untasked form (essentially a space-fed passive lens), it achieves off-axis squint angles of many beamwidths with negligible performance degradation. It is inherently insensitive to mechanical distortion and is a first step in the evolution to the more complex tasked system antenna. The antenna lens consists of easily manufactured slats with microstrip dipole radiating elements and matching networks on a dielectric substrate. Phase control is achieved with low-loss delay lines in the passive lens or active transmit/receive modules if electronic scan is desired.
Space market model development project, phase 3
NASA Technical Reports Server (NTRS)
Bishop, Peter C.; Hamel, Gary P.
1989-01-01
The results of a research project investigating information needs for space commercialization is described. The Space Market Model Development Project (SMMDP) was designed to help NASA identify the information needs of the business community and to explore means to meet those needs. The activity of the SMMDP is reviewed and a report of its operation via three sections is presented. The first part contains a brief historical review of the project since inception. The next part reports results of Phase 3, the most recent stage of activity. Finally, overall conclusions and observations based on the SMMDP research results are presented.
Rockstar: Phase-space halo finder
NASA Astrophysics Data System (ADS)
Behroozi, Peter; Wechsler, Risa; Wu, Hao-Yi
2012-10-01
Rockstar (Robust Overdensity Calculation using K-Space Topologically Adaptive Refinement) identifies dark matter halos, substructure, and tidal features. The approach is based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension, which allows for robust (grid-independent, shape-independent, and noise-resilient) tracking of substructure. Our method is massively parallel (up to 10^5 CPUs) and runs on the largest current simulations (>10^10 particles) with high efficiency (10 CPU hours and 60 gigabytes of memory required per billion particles analyzed). Rockstar offers significant improvement in substructure recovery as compared to several other halo finders.
Stratakis, D.; Kishek, R. A.; Bernal, S.; Walter, M.; Haber, I.; Fiorito, R.; Thangaraj, J. C. T.; Quinn, B.; Reiser, M.; O'Shea, P. G.; Li, H.
2006-11-27
In order to understand the charged particle dynamics, e.g. the halo formation, emittance growth, x-y energy transfer and coupling, knowledge of the actual phase space is needed. Other the past decade there is an increasing number of articles who use tomography to map the beam phase space and measure the beam emittance. These studies where performed at high energy facilities where the effect of space charge was neglible and therefore not considered in the analysis. This work extends the tomography technique to beams with space charge. In order to simplify the analysis linear forces where assumed. By carefully modeling the tomography process using the particle-in-cell code WARP we test the validity of our assumptions and the accuracy of the reconstructed phase space. Finally, we report experimental results of phase space mapping at the University of Maryland Electron Ring (UMER) using tomography.
Generalizing the Boltzmann equation in complex phase space.
Zadehgol, Abed
2016-08-01
In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)JCTPAH0021-999110.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015)PLEEE81539-375510.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others. PMID:27627421
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.
Thermophotovoltaic space power system, phase 3
NASA Technical Reports Server (NTRS)
Horne, W. E.; Lancaster, C.
1987-01-01
Work performed on a research and development program to establish the feasibility of a solar thermophotovoltaic space power generation concept was summarized. The program was multiphased. The earlier work is summarized and the work on the current phase is detailed as it pertains to and extends the earlier work. Much of the experimental hardware and materials development was performed on the internal program. Experimental measurements and data evaluation were performed on the contracted effort. The objectives of the most recent phase were: to examine the thermal control design in order to optimize it for lightweight and low cost; to examine the concentrator optics in an attempt to relieve pointing accuracy requirements to + or - 2 degrees about the optical axis; and to use the results of the thermal and optical studies to synthesize a solar thermophotovoltaic (STPV) module design that is optimized for space application.
Noncanonical phase-space noncommutative black holes
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, Joa~o. Nuno
2012-07-01
In this contribution we present a noncanonical phase-space noncommutative (NC) extension of a Kantowski Sachs (KS) cosmological model to describe the interior of a Schwarzschild black hole (BH). We evaluate the thermodynamical quantities inside this NC Schwarzschild BH and compare with the well known quantities. We find that for a NCBH the temperature and entropy have the same mass dependence as the Hawking quantities for a Schwarzschild BH.
Analytical satellite theory in extended phase space
NASA Technical Reports Server (NTRS)
Bond, V.; Broucke, R.
1980-01-01
It is noted that a satellite theory, based on extended phase space and on the true anomaly, was introduced by Scheifele (1970). In the present paper a simple canonical transformation is shown that makes the transition from the classical Delaunay elements to the Scheifele variables. It is stressed that neither spherical coordinates nor Hamilton-Jacobi theory is used. Finally, attention is given to the meaning of the new variables, especially the use of the true anomaly as one of the variables.
Chirp-driven giant phase space vortices
NASA Astrophysics Data System (ADS)
Trivedi, Pallavi; Ganesh, Rajaraman
2016-06-01
In a collisionless, unbounded, one-dimensional plasma, modelled using periodic boundary conditions, formation of steady state phase space coherent structures or phase space vortices (PSV) is investigated. Using a high resolution one-dimensional Vlasov-Poisson solver based on piecewise-parabolic advection scheme, the formation of giant PSV is addressed numerically. For an infinitesimal external drive amplitude and wavenumber k, we demonstrate the existence of a window of chirped external drive frequency that leads to the formation of giant PSV. The linear, small amplitude, external drive, when chirped, is shown to couple effectively to the plasma and increase both streaming of "untrapped" and "trapped" particle fraction. The steady state attained after the external drive is turned off and is shown to lead to a giant PSV with multiple extrema and phase velocities, with excess density fraction, defined as the deviation from the Maxwellian background, Δ n / n 0 ≃ 20 % - 25 % . It is shown that the process depends on the chirp time duration Δt. The excess density fraction Δn/n0, which contains both trapped and untrapped particle contribution, is also seen to scale with Δt, only inhibited by the gradient of the distribution in velocity space. Both single step drive and multistep chirp processes are shown to lead to steady state giant PSV, with multiple extrema due to embedded holes and clumps, long after the external drive is turned off.
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.
Attosecond strong-field interferometry in graphene: Chirality, singularity, and Berry phase
NASA Astrophysics Data System (ADS)
Kelardeh, Hamed Koochaki; Apalkov, Vadym; Stockman, Mark I.
2016-04-01
We propose an interferometry in graphene's reciprocal space without a magnetic field, employing strong ultrafast circularly polarized optical pulses. The reciprocal space interferograms contain information on the electronic spectra and topological properties of graphene and on the waveform and circular polarization of the excitation optical pulses. These can be measured using angle-resolved photoemission spectroscopy (ARPES) with attosecond ultraviolet pulses. The predicted effects provide unique opportunities in fundamental studies of two-dimensional topological materials and in applications to future petahertz light-wave-driven electronics.
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.
Formation of phase space holes and clumps.
Lilley, M K; Nyqvist, R M
2014-04-18
It is shown that the formation of phase space holes and clumps in kinetically driven, dissipative systems is not restricted to the near threshold regime, as previously reported and widely believed. Specifically, we observe hole-clump generation from the edges of an unmodulated phase space plateau, created via excitation, phase mixing and subsequent dissipative decay of a linearly unstable bulk plasma mode in the electrostatic bump-on-tail model. This has now allowed us to elucidate the underlying physics of the hole-clump formation process for the first time. Holes and clumps develop from negative energy waves that arise due to the sharp gradients at the interface between the plateau and the nearly unperturbed, ambient distribution and destabilize in the presence of dissipation in the bulk plasma. We confirm this picture by demonstrating that the formation of such nonlinear structures in general does not rely on a "seed" wave, only on the ability of the system to generate a plateau. In addition, we observe repetitive cycles of plateau generation and erosion, the latter due to hole-clump formation and detachment, which appear to be insensitive to initial conditions and can persist for a long time. We present an intuitive discussion of why this continual regeneration occurs. PMID:24785043
Phase change water processing for Space Station
NASA Technical Reports Server (NTRS)
Zdankiewicz, E. M.; Price, D. F.
1985-01-01
The use of a vapor compression distillation subsystem (VCDS) for water recovery on the Space Station is analyzed. The self-contained automated system can process waste water at a rate of 32.6 kg/day and requires only 115 W of electric power. The improvements in the mechanical components of VCDS are studied. The operation of VCDS in the normal mode is examined. The VCDS preprototype is evaluated based on water quality, water production rate, and specific energy. The relation between water production rate and fluids pump speed is investigated; it is concluded that a variable speed fluids pump will optimize water production. Components development and testing currently being conducted are described. The properties and operation of the proposed phase change water processing system for the Space Station, based on vapor compression distillation, are examined.
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.
Weak values and the quantum phase space
Lobo, A. C.; Ribeiro, C. A.
2009-07-15
We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring process on the entire phase space of the measuring system. By using coherent states, we go a step further than Jozsa in a recent paper and we present an example where the result of the measurement is symmetrical in the position and momentum observables and seems to be much better suited for quantum optical implementation.
Optical image encryption in phase space
NASA Astrophysics Data System (ADS)
Liu, Jun; Xu, Xiaobin; Situ, Guohai; Wu, Quanying
2014-11-01
In the field of optical information security, the research of double random phase encoding is becoming deeper with each passing day, however the encryption system is linear, and the dependencies between plaintext and ciphertext is not complicated, with leaving a great hidden danger to the security of the encryption system. In this paper, we encrypted the higher dimensional Wigner distribution function of low dimensional plaintext by using the bilinear property of Wigner distribution function. Computer simulation results show that this method can not only enlarge the key space, but also break through the linear characteristic of the traditional optical encryption technology. So it can significantly improve the safety of the encryption system.
Space Transportation Engine Program (STEP), phase B
NASA Technical Reports Server (NTRS)
1990-01-01
The Space Transportation Engine Program (STEP) Phase 2 effort includes preliminary design and activities plan preparation that will allow smooth and time transition into a Prototype Phase and then into Phases 3, 4, and 5. A Concurrent Engineering approach using Total Quality Management (TQM) techniques, is being applied to define an oxygen-hydrogen engine. The baseline from Phase 1/1' studies was used as a point of departure for trade studies and analyses. Existing STME system models are being enhanced as more detailed module/component characteristics are determined. Preliminary designs for the open expander, closed expander, and gas generator cycles were prepared, and recommendations for cycle selection made at the Design Concept Review (DCR). As a result of July '90 DCR, and information subsequently supplied to the Technical Review Team, a gas generator cycle was selected. Results of the various Advanced Development Programs (ADP's) for the Advanced Launch Systems (ALS) were contributive to this effort. An active vehicle integration effort is supplying the NASA, Air Force, and vehicle contractors with engine parameters and data, and flowing down appropriate vehicle requirements. Engine design and analysis trade studies are being documented in a data base that was developed and is being used to organize information. To date, seventy four trade studies were input to the data base.
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
Phase space representation of quantum dynamics
Polkovnikov, Anatoli
2010-08-15
We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze expansions around three such limits: (i) corpuscular or Newtonian limit in the coordinate-momentum representation, (ii) wave or Gross-Pitaevskii limit for interacting bosons in the coherent state representation, and (iii) Bloch limit for the spin systems. We discuss both the semiclassical (truncated Wigner) approximation and further quantum corrections appearing in the form of either stochastic quantum jumps along the classical trajectories or the nonlinear response to such jumps. We also discuss how quantum jumps naturally emerge in the analysis of non-equal time correlation functions. This representation of quantum dynamics is closely related to the phase space methods based on the Wigner-Weyl quantization and to the Keldysh technique. We show how such concepts as the Wigner function, Weyl symbol, Moyal product, Bopp operators, and others automatically emerge from the Feynmann's path integral representation of the evolution in the Heisenberg representation. We illustrate the applicability of this expansion with various examples mostly in the context of cold atom systems including sine-Gordon model, one- and two-dimensional Bose-Hubbard model, Dicke model and others.
Quantum mechanics on phase space and teleportation
NASA Astrophysics Data System (ADS)
Messamah, Juba; Schroeck, Franklin E.; Hachemane, Mahmoud; Smida, Abdallah; Hamici, Amel H.
2015-03-01
The formalism of quantum mechanics on phase space is used to describe the standard protocol of quantum teleportation with continuous variables in order to partially investigate the interplay between this formalism and quantum information. Instead of the Wigner quasi-probability distributions used in the standard protocol, we use positive definite true probability densities which account for unsharp measurements through a proper wave function representing a non-ideal quantum measuring device. This is based on a result of Schroeck and may be taken on any relativistic or nonrelativistic phase space. The obtained formula is similar to a known formula in quantum optics, but contains the effect of the measuring device. It has been applied in three cases. In the first case, the two measuring devices, corresponding to the two entangled parts shared by Alice and Bob, are not entangled and described by two identical Gaussian wave functions with respect to the Heisenberg group. They lead to a probability density identical to the function which is analyzed and compared with the Wigner formalism. A new expression of the teleportation fidelity for a coherent state in terms of the quadrature variances is obtained. In the second case, these two measuring devices are entangled in a two-mode squeezed vacuum state. In the third case, two Gaussian states are combined in an entangled squeezed state. The overall observation is that the state of the measuring devices shared by Alice and Bob influences the fidelity of teleportation through their unsharpness and entanglement.
Uncertainty relations for general phase spaces
NASA Astrophysics Data System (ADS)
Werner, Reinhard F.
2016-04-01
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the equality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.
Reanalysis of relativistic electron phase space density
NASA Astrophysics Data System (ADS)
Shprits, Yuri; Chen, Yue; Kondrashov, Dmitri
In this study we perform a reanalysis of the sparse relativistic electron data using a relatively simple one-dimensional radial diffusion model and a Kalman filtering approach. The results of the reanalysis clearly show pronounced peaks in the electron phase space density (PSD), which can not be explained by the variations in the outer boundary, and can only be produced by a local acceleration processes. The location of the innovation vector shows that local acceleration is most efficient at L* = 5.5. To verify that our results are not affected by the limitations of the satellite orbit and coverage, we performed an "identical twin" experiments with synthetic data specified only at the locations for which CRRES observations are available. Our results indicate that the model with data assimilation can accurately reproduce the underlying structure of the PSD even when data is sparse.
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
Space-time geometry of topological phases
Burnell, F.J.; Simon, Steven H.
2010-11-15
The 2 + 1 dimensional lattice models of Levin and Wen (2005) provide the most general known microscopic construction of topological phases of matter. Based heavily on the mathematical structure of category theory, many of the special properties of these models are not obvious. In the current paper, we present a geometrical space-time picture of the partition function of the Levin-Wen models which can be described as doubles (two copies with opposite chiralities) of underlying anyon theories. Our space-time picture describes the partition function as a knot invariant of a complicated link, where both the lattice variables of the microscopic Levin-Wen model and the terms of the Hamiltonian are represented as labeled strings of this link. This complicated link, previously studied in the mathematical literature, and known as Chain-Mail, can be related directly to known topological invariants of 3-manifolds such as the so-called Turaev-Viro invariant and the Witten-Reshitikhin-Turaev invariant. We further consider quasi-particle excitations of the Levin-Wen models and we see how they can be understood by adding additional strings to the Chain-Mail link representing quasi-particle world-lines. Our construction gives particularly important new insight into how a doubled theory arises from these microscopic models.
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.
Space market model development project, phase 2
NASA Technical Reports Server (NTRS)
Bishop, Peter C.
1988-01-01
The results of the prototype operations of the Space Business Information Center are presented. A clearinghouse for space business information for members of the U.S. space industry composed of public, private, and academic sectors was conducted. Behavioral and evaluation statistics were recorded from the clearinghouse and the conclusions from these statistics are presented. Business guidebooks on major markets in space business are discussed. Proprietary research and briefings for firms and agencies in the space industry are also discussed.
Stabilizer information inequalities from phase space distributions
NASA Astrophysics Data System (ADS)
Gross, David; Walter, Michael
2013-08-01
The Shannon entropy of a collection of random variables is subject to a number of constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question to decide which of these "laws of information theory" are also respected by the von Neumann entropy of many-body quantum states. In this article, we consider a toy version of this difficult problem by analyzing the von Neumann entropy of stabilizer states. We find that the von Neumann entropy of stabilizer states satisfies all balanced information inequalities that hold in the classical case. Our argument is built on the fact that stabilizer states have a classical model, provided by the discrete Wigner function: The phase-space entropy of the Wigner function corresponds directly to the von Neumann entropy of the state, which allows us to reduce to the classical case. Our result has a natural counterpart for multi-mode Gaussian states, which sheds some light on the general properties of the construction. We also discuss the relation of our results to recent work by Linden, Ruskai, and Winter ["The quantum entropy cone of stabiliser states," e-print arXiv:1302.5453].
Constructing Phase Space Distributions within the Heliosheath
NASA Astrophysics Data System (ADS)
Roelof, E. C.
2014-12-01
The key function in the description of the dynamics of the heliosheath (HS) is the phase space distribution (PSD) of the protons, i.e., how the interaction between the thermal and non-thermal (heated pick-up) proton populations evolves from the termination shock to the heliopause (HP) in this high-beta plasma. Voyager 1 found the heliopause to be essentially a (compound) magnetic separatrix, because the intensity of the non-thermal particle population became undetectably small beyond the HP, whereas the anisotropy characteristics of the galactic cosmic rays were consistent with no re-entry of the magnetic field lines into the HS (at either end). This paper attempts to synthesize in situ observations from Voyagers 1 and 2 (thermal plasma, magnetic field, energetic ions, and cosmic rays) with global ENA images from IBEX and Cassini/INCA into a self-consistent representation of the PSD within the noseward HS from thermal energies to several MeV/nuc. The interpretation of the ENA images requires assumptions on the global behavior of the bulk plasma flow throughout the HS that are self-consistent with all the available data (e.g., the spatial and energy dependence of the IBEX ribbon), because the Compton-Getting effects produced by the flows strongly affect the intensities (and thereby the partial densities and pressures) inferred from the ENA images.
Overview of Phase Space Manipulations of Relativistic Electron Beams
Xiang, Dao; /SLAC
2012-08-31
Phase space manipulation is a process to rearrange beam's distribution in 6-D phase space. In this paper, we give an overview of the techniques for tailoring beam distribution in 2D, 4D, and 6D phase space to meet the requirements of various applications. These techniques become a new focus of accelerator physics R&D and very likely these advanced concepts will open up new opportunities in advanced accelerators and the science enabled by them.
NASA Astrophysics Data System (ADS)
Korf, Lisa A.; Schroeck, Franklin E.
2015-12-01
We consider an effect algebra of phase space localization operators for a quantum mechanical Hilbert space that contains no non-trivial projections, and the C*-algebra generated by it. This C∗-algebra forms an informationally complete set in the original Hilbert space. Its elements are shown to have singular-value-based decompositions that permit their characterization in terms of limits of linear combinations of products of pairs of the phase space fuzzy localization operators. Through these results, it is shown that the informational completeness of the C*-algebra can be greatly reduced to the informational completeness of the set of products of pairs formed from the elements of the effect algebra.
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
Arnol'd, V.I.
1986-02-10
The authors describe the critical values of the maps at time''t'' and their evolution as ''t'' changes for potential initial velocity fields in general position under the assumption that the force field is potential. The paper is concerned with the structure and evolution of caustics of a general one-parameter family of Lagrangian maps of manifolds of dimension not exceeding three. For each type of evolution, the authors give a detailed geometric description of the structure of the singularity. The investigation required new algebraic information about the manifold of polynomials with multiple roots; these are given in the paper.
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.
Space shuttle phase B study plan
NASA Technical Reports Server (NTRS)
Hello, B.
1971-01-01
Phase B emphasis was directed toward development of data which would facilitate selection of the booster concept, and main propulsion system for the orbiter. A shuttle system is also defined which will form the baseline for Phase C program activities.
Space Shuttle aerothermodynamic data report, phase C
NASA Technical Reports Server (NTRS)
1985-01-01
Space shuttle aerothermodynamic data, collected from a continuing series of wind tunnel tests, are permanently stored with the Data Management Services (DMS) system. Information pertaining to current baseline configuration definition is also stored. Documentation of DMS processed data arranged sequentially and by space shuttle configuration are included. An up-to-date record of all applicable aerothermodynamic data collected, processed, or summarized during the space shuttle program is provided. Tables are designed to provide suvery information to the various space shuttle managerial and technical levels.
Prediction of Indian Summer Monsoon Rainfall by Phase-Space Reconstruction Model
NASA Astrophysics Data System (ADS)
Sharma, A. S.; Krishnamurthy, V.
2015-12-01
The prediction of the Indian summer monsoon rainfall at intraseasonal time scale is investigated in this study. The summer monsoon exhibits intraseasonal oscillations (ISOs) with different periods. The leading ISO, with a period of 45 days, is presumably related to the Madden-Julian Oscillation. The ISOs have large-scale spatial structure and propagate northeastward and northwestward. A prediction model, based on some basic results of nonlinear dynamical systems theory, is constructed to predict the monsoon rainfall. An equivalent phase space of reduced dimension can be reconstructed from a long time-series of a single or a few variables of the dynamical system. In such a phase space, the trajectory of the dynamical system can be examined to search for nearest neighbors. An ensemble of such nearest neighbors and their subsequent evolution are used to construct the prediction model. In some respects, this method is similar to Lorenz's analog method. The reduced phase space is reconstructed by using a limited number of eigenmodes obtained from multi-channel singular spectrum analysis of the rainfall over the monsoon region. For this purpose, the daily gridded rainfall over India for the period 1901-2010 is used. These eigenmodes represent the ISOs and seasonally persistent modes. The prediction of the monsoon rainfall by this model is compared with the retrospective forecasts made by NCEP CFSv2 and other S2S models.
Quasi-Hermitian quantum mechanics in phase space
Curtright, Thomas; Veitia, Andrzej
2007-10-15
We investigate quasi-Hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.
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.
Space law information system design, phase 2
NASA Technical Reports Server (NTRS)
Morenoff, J.; Roth, D. L.; Singleton, J. W.
1973-01-01
Design alternatives were defined for the implementation of a Space Law Information System for the Office of the General Counsel, NASA. A thesaurus of space law terms was developed and a selected document sample indexed on the basis of that thesaurus. Abstracts were also prepared for the sample document set.
Phase partitioning in space and on earth
NASA Technical Reports Server (NTRS)
Van Alstine, James M.; Karr, Laurel J.; Snyder, Robert S.; Matsos, Helen C.; Curreri, Peter A.; Harris, J. Milton; Bamberger, Stephan B.; Boyce, John; Brooks, Donald E.
1987-01-01
The influence of gravity on the efficiency and quality of the impressive separations achievable by bioparticle partitioning is investigated by demixing polymer phase systems in microgravity. The study involves the neutral polymers dextran and polyethylene glycol, which form a two-phase system in aqueous solution at low concentrations. It is found that demixing in low-gravity occurs primarily by coalescence, whereas on earth the demixing occurs because of density differences between the phases.
Tracing the dark matter sheet in phase space
NASA Astrophysics Data System (ADS)
Abel, Tom; Hahn, Oliver; Kaehler, Ralf
2012-11-01
The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform, and it occupies an initial sheet in phase space that is single valued in velocity space. Because of gravitational forces, this 3D manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured 3D mesh moving in 6D phase space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics and count the number of streams as well as their individual contributions to any point in configuration space. We calculate the bulk velocity, local velocity dispersions and densities from the sheet - all without averaging over control volumes. This gives a wealth of new information about dark matter fluid flow which had previously been thought of as inaccessible to N-body simulations. We outline how this mapping may be used to create new accurate collisionless fluid simulation codes that may be able to overcome the sparse sampling and unphysical two-body effects that plague current N-body techniques.
Real-space Berry phases: Skyrmion soccer (invited)
Everschor-Sitte, Karin Sitte, Matthias
2014-05-07
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.
Real-space Berry phases: Skyrmion soccer (invited)
NASA Astrophysics Data System (ADS)
Everschor-Sitte, Karin; Sitte, Matthias
2014-05-01
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.
4D phase-space multiplexing for fluorescent microscopy
NASA Astrophysics Data System (ADS)
Liu, Hsiou-Yuan; Zhong, Jingshan; Waller, Laura
2016-03-01
Phase-space measurements enable characterization of second-order spatial coherence properties and can be used for digital aberration removal or 3D position reconstruction. Previous methods use a scanning aperture to measure the phase space spectrogram, which is slow and light inefficient, while also attenuating information about higher-order correlations. We demonstrate a significant improvement of speed and light throughput by incorporating multiplexing techniques into our phase-space imaging system. The scheme implements 2D coded aperture patterning in the Fourier (pupil) plane of a microscope using a Spatial Light Modulator (SLM), while capturing multiple intensity images in real space. We compare various multiplexing schemes to scanning apertures and show that our phase-space reconstructions are accurate for experimental data with biological samples containing many 3D fluorophores.
Selected tether applications in space: Phase 2
NASA Technical Reports Server (NTRS)
Thorsen, M. H.; Lippy, L. J.
1985-01-01
System characteristics and design requirements are assessed for tether deployment. Criteria are established for comparing alternate concepts for: (1) deployment of 220 klb space shuttle from the space station; (2) tether assisted launch of a 20,000 lb payload to geosynchronous orbit; (3) placement of the 20,000 lb AXAF into 320 nmi orbit via orbiter; (4) retrieval of 20,000 lb AXAF from 205 nmi circular orbit for maintenance and reboost to 320 nmi; and (5) tethered OMV rendezvous and retrieval of OTV returning from a geosynchronous mission. Tether deployment systems and technical issues are discussed.
Leptons, Quarks, and Their Antiparticles: A Phase-Space View
NASA Astrophysics Data System (ADS)
Żenczykowski, Piotr
2010-09-01
Recently, a correspondence has been shown to exist between the structure of a single Standard Model generation of elementary particles and the properties of the Clifford algebra of nonrelativistic phase space. Here, this correspondence is spelled out in terms of phase-space variables. Thus, a phase-space interpretation of the connections between leptons, quarks and their antiparticles is proposed, in particular providing a timeless alternative to the standard Stückelberg-Feynman interpretation. The issue of the additivity of canonical momenta is raised and argued to be intimately related to the unobservability of free quarks and the emergence of mesons and baryons.
Longitudinal phase space experiments on the ELSA photoinjector
Dowell, D.H.; Joly, S.; Brion, J.P. de
1995-12-31
The excellent beam quality produced by RF photocathode injectors is well established, andhas been verified by numerous measurements of the transverse emittance. However, there are few experimental determinations of the longitudinal phase space. This paper reports on experiments performed at the ELSA FEL facility to emasure the longitudinal phase space distribution at the exit of the 144 MHz photoinjector cavity. Phase spaces were determined by the analysis of beam energy spectra and pulse shapes at 17.5 MeV for micropulse charges between 0.5 and 5 nC.
Phase Space Distribution Near the Self-Excited Oscillation Threshold
NASA Astrophysics Data System (ADS)
Dhayalan, Yuvaraj; Baskin, Ilya; Shlomi, Keren; Buks, Eyal
2014-05-01
We study the phase space distribution of an optomechanical cavity near the threshold of self-excited oscillation. A fully on-fiber optomechanical cavity is fabricated by patterning a suspended metallic mirror on the tip of the fiber. Optically induced self-excited oscillation of the suspended mirror is observed above a threshold value of the injected laser power. A theoretical analysis based on the Fokker-Planck equation evaluates the expected phase space distribution near threshold. A tomography technique is employed for extracting phase space distribution from the measured reflected optical power vs time in steady state. Comparison between theory and experimental results allows the extraction of the device parameters.
A Simple, Low Cost Longitudinal Phase Space Diagnostic
Bertsche, Kirk; Emma, Paul; Shevchenko, Oleg; /Novosibirsk, IYF
2009-05-15
For proper operation of the LCLS [1] x-ray free-electron laser (FEL), and other similar machines, measurement and control of the electron bunch longitudinal phase space is critical. The LCLS accelerator includes two bunch compressor chicanes to magnify the peak current. These magnetic chicanes can generate significant coherent synchrotron radiation (CSR), which can distort the phase space distribution. We propose a diagnostic scheme by exciting a weak skew quadrupole at an energy-chirped, high dispersion point in the first LCLS bunch compressor (BC1) to reconstruct longitudinal phase space on an OTR screen after BC1, allowing a time-resolved characterization of CSR effects.
The space transportation main engine phase A' study
NASA Technical Reports Server (NTRS)
1987-01-01
The Space Transportation Main Engine Phase A prime study was conducted over a 7 month period as an extension to the Phase A study. The Phase A prime program was designed to expand the study effort completed in Phase A, focusing on the baseline engine configuration selected. Analysis and trade studies were conducted to further optimize some of the major engine subsystems. These changes resulted in improvements to the baseline engine. Several options were evaluated for consideration by vehicle contractors.
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…
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
Liquid phase sintered compacts in space
NASA Technical Reports Server (NTRS)
Mookherji, T. K.; Mcanelly, W. B.
1974-01-01
A model that will explain the effect of gravity on liquid phase sintering was developed. Wetting characteristics and density segregation which are the two important phenomena in liquid phase sintering are considered in the model development. Experiments were conducted on some selected material combinations to study the gravity effects on liquid phase sintering, and to verify the validity of the model. It is concluded that: (1) The surface tension forces acting on solid particles in a one-g environment are not appreciably different from those anticipated in a 0.00001g/g sub 0 (or lower) environment. (2) The capillary forces are dependent on the contact angle, the quantity of the liquid phase, and the distance between solid particles. (3) The pores (i.e., bubbles) do not appear to be driven to the surface by gravity-produced buoyancy forces. (4) The length of time to produce the same degree of settling in a low-gravity environment will be increased significantly. (5) A low gravity environment would appear to offer a unique means of satisfactorily infiltrating a larger and/or complex shaped compact.
Phase I Space Station power system development
Price, R.O.
1988-10-01
The development of the electric power system (EPS) for the Space Station is discussed. The EPS requirements related to station size, operational lifetime, operational autonomy, and technology evolution are considered. It is suggested that environmental control and life support will require 55 kWe of power. The possible use of solar photovoltaic, solar thermal dynamic, or a hybrid combination of the two are examined.
Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.
Mauguière, Frédéric A L; Collins, Peter; Kramer, Zeb C; Carpenter, Barry K; Ezra, Gregory S; Farantos, Stavros C; Wiggins, Stephen
2015-10-15
We re-examine the prototypical roaming reaction--hydrogen atom roaming in formaldehyde decomposition--from a phase space perspective. Specifically, we address the question "why do trajectories roam, rather than dissociate through the radical channel?" We describe and compute the phase space structures that define and control all possible reactive events for this reaction, as well as provide a dynamically exact description of the roaming region in phase space. Using these phase space constructs, we show that in the roaming region, there is an unstable periodic orbit whose stable and unstable manifolds define a conduit that both encompasses all roaming trajectories exiting the formaldehyde well and shepherds them toward the H2···CO well. PMID:26499774
An extensive phase space for the potential martian biosphere.
Jones, Eriita G; Lineweaver, Charles H; Clarke, Jonathan D
2011-12-01
We present a comprehensive model of martian pressure-temperature (P-T) phase space and compare it with that of Earth. Martian P-T conditions compatible with liquid water extend to a depth of ∼310 km. We use our phase space model of Mars and of terrestrial life to estimate the depths and extent of the water on Mars that is habitable for terrestrial life. We find an extensive overlap between inhabited terrestrial phase space and martian phase space. The lower martian surface temperatures and shallower martian geotherm suggest that, if there is a hot deep biosphere on Mars, it could extend 7 times deeper than the ∼5 km depth of the hot deep terrestrial biosphere in the crust inhabited by hyperthermophilic chemolithotrophs. This corresponds to ∼3.2% of the volume of present-day Mars being potentially habitable for terrestrial-like life. PMID:22149914
Wigner function and Schroedinger equation in phase-space representation
Chruscinski, Dariusz; Mlodawski, Krzysztof
2005-05-15
We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation.
Kac Moody theories for colored phase space (quantum Hall) droplets
NASA Astrophysics Data System (ADS)
Polychronakos, Alexios P.
2005-04-01
We derive the canonical structure and Hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza-Klein construction on the phase space. The emerging theory is a nonlinear higher-dimensional generalization of the gauged Kac-Moody algebra. To leading order in ℏ this reproduces the edge state chiral Wess-Zumino-Witten action of the droplets.
Group theoretical construction of planar noncommutative phase spaces
Ngendakumana, Ancille Todjihoundé, Leonard; Nzotungicimpaye, Joachim
2014-01-15
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.
Tracing, Analyzing and Visualizing Dark Matter in Phase Space
NASA Astrophysics Data System (ADS)
Hahn, Oliver; Abel, Tom; Kaehler, Ralf
2015-01-01
In a Universe dominated by cold dark matter, structure forms from foldings of a three-dimensional sheet permeating six-dimensional phase space. The dynamics of the sheet is governed by gravity alone, and it never tears or intersects itself in phase space. In position space, these foldings lead to the formation of pancakes, filaments and finally dark matter halos: the cosmic web. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, local velocity dispersion and detect caustics. We also discuss how information about the sheet can be used to create highly accurate volume visualizations and devise new simulation codes to evolve cold collisionless fluids under self-gravity.
Phase space variations of near equatorially mirroring ring current ions
NASA Technical Reports Server (NTRS)
Williams, D. J.
1981-01-01
Observations of near equatorially mirroring ring current ions before and after a magnetic storm are presented in the form of phase space densities with respect to the first adiabatic invariant. Particle densities were obtained from the medium energy particles instrument covering the energy range 24-2081 keV on ISEE 1 at L values between 3 and 8 earth radii and ratios of the magnetic field at the satellite position to the magnetic field at the magnetic equator less than 1.2. Analysis of the phase space densities through the magnetosphere reveals a well-defined high magnetic moment peak in the prestorm near-equatorial ring current ion phase space density distribution, with the magnetic storm resulting from an enhancement of phase space densities at magnetic moment values below the peak and phase space densities remaining constant above the peak. Results are found to be in good agreement with those obtained by Explorer 45 six years previously, indicating that the observed phase space density variations are characteristic of energetic ion behavior during magnetic storms.
Symmetry of quantum phase space in a degenerate Hamiltonian system
NASA Astrophysics Data System (ADS)
Berman, G. P.; Demikhovskii, V. Ya.; Kamenev, D. I.
2000-09-01
The structure of the global "quantum phase space" is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2μ (where μ is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior.
The diffusion of stars through phase space
NASA Technical Reports Server (NTRS)
Binney, James; Lacey, Cedric
1988-01-01
An orbit-averaged Fokker-Planck equation has been derived to study the secular evolution of stellar systems with regular orbits and the heating of stellar disks. It is shown that a population of stars with an initially Maxwellian peculiar-velocity distribution will remain Maxwellian as it diffuses through orbit space only if: (1) a second-order diffusion tensor is proportional to epicycle energy; and (2) the population's velocity dispersion grows as the square root of time. Scattering by ephemeral spiral waves is able to account for the observed kinematics of the solar neighborhood only if the waves have wavelengths in excess of 9 kpc and constantly drifting pattern speeds.
Space power demonstrator engine, phase 1
NASA Technical Reports Server (NTRS)
1987-01-01
The design, analysis, and preliminary test results for a 25 kWe Free-Piston Stirling engine with integral linear alternators are described. The project is conducted by Mechanical Technology under the direction of LeRC as part of the SP-100 Nuclear Space Power Systems Program. The engine/alternator system is designed to demonstrate the following performance: (1) 25 kWe output at a specific weight less than 8 kg/kW; (2) 25 percent efficiency at a temperature ratio of 2.0; (3) low vibration (amplitude less than .003 in); (4) internal gas bearings (no wear, no external pump); and (5) heater temperature/cooler temperature from 630 to 315 K. The design approach to minimize vibration is a two-module engine (12.5 kWe per module) in a linearly-opposed configuration with a common expansion space. The low specific weight is obtained at high helium pressure (150 bar) and high frequency (105 Hz) and by using high magnetic strength (samarium cobalt) alternator magnets. Engine tests began in June 1985; 16 months following initiation of engine and test cell design. Hydrotest and consequent engine testing to date has been intentionally limited to half pressure, and electrical power output is within 15 to 20 percent of design predictions.
Space transfer concepts and analyses for exploration missions, phase 3
NASA Technical Reports Server (NTRS)
Woodcock, Gordon R.
1993-01-01
This report covers the third phase of a broad-scoped and systematic study of space transfer concepts for human lunar and Mars missions. The study addressed issues that were raised during Phase 2, developed generic Mars missions profile analysis data, and conducted preliminary analysis of the Mars in-space transportation requirements and implementation from Stafford Committee Synthesis Report. The major effort of the study was the development of the first Lunar Outpost (FLO) baseline which evolved from the Space Station Freedom Hab Module. Modifications for the First Lunar Outpost were made to meet mission requirements and technology advancements.
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.
ERIC Educational Resources Information Center
Wissman, Kelly
2010-01-01
In this article, the author investigates the teaching and writing of poetry within public school spaces, illuminating how the work of poetry in an Academic Interventions classroom stirs new visions of who the students and the teacher can be. The study involves five teachers from a range of rural, urban, and suburban districts. These teachers…
Phase-Space Detection of Cyber Events
Hernandez Jimenez, Jarilyn M; Ferber, Aaron E; Prowell, Stacy J; Hively, Lee M
2015-01-01
Energy Delivery Systems (EDS) are a network of processes that produce, transfer and distribute energy. EDS are increasingly dependent on networked computing assets, as are many Industrial Control Systems. Consequently, cyber-attacks pose a real and pertinent threat, as evidenced by Stuxnet, Shamoon and Dragonfly. Hence, there is a critical need for novel methods to detect, prevent, and mitigate effects of such attacks. To detect cyber-attacks in EDS, we developed a framework for gathering and analyzing timing data that involves establishing a baseline execution profile and then capturing the effect of perturbations in the state from injecting various malware. The data analysis was based on nonlinear dynamics and graph theory to improve detection of anomalous events in cyber applications. The goal was the extraction of changing dynamics or anomalous activity in the underlying computer system. Takens' theorem in nonlinear dynamics allows reconstruction of topologically invariant, time-delay-embedding states from the computer data in a sufficiently high-dimensional space. The resultant dynamical states were nodes, and the state-to-state transitions were links in a mathematical graph. Alternatively, sequential tabulation of executing instructions provides the nodes with corresponding instruction-to-instruction links. Graph theorems guarantee graph-invariant measures to quantify the dynamical changes in the running applications. Results showed a successful detection of cyber events.
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-15
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form {sigma}{sup xn}. Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states)
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.
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)
Hoover, Wm. G.; Hoover, Carol G.; Grond, Florian
2008-08-01
We investigate and discuss the time-reversible nature of phase-space instabilities for several flows, x˙=f(x). The flows describe thermostated oscillator systems in from two through eight phase-space dimensions. We determine the local extremal phase-space growth rates, which bound the instantaneous comoving Lyapunov exponents. The extremal rates are point functions which vary continuously in phase space. The extremal rates can best be determined with a "singular-value decomposition" algorithm. In contrast to these precisely time-reversible local "point function" values, a time-reversibility analysis of the comoving Lyapunov spectra is more complex. The latter analysis is nonlocal and requires the additional storing and playback of relatively long (billion-step) trajectories. All the oscillator models studied here show the same time reversibility symmetry linking their time-reversed and time-averaged "global" Lyapunov spectra. Averaged over a long-time-reversed trajectory, each of the long-time-averaged Lyapunov exponents simply changes signs. The negative/positive sign of the summed-up and long-time-averaged spectra in the forward/backward time directions is the microscopic analog of the Second Law of Thermodynamics. This sign changing of the individual global exponents contrasts with typical more-complex instantaneous "local" behavior, where there is no simple relation between the forward and backward exponents other than the local (instantaneous) dissipative constraint on their sum. As the extremal rates are point functions, they too always satisfy the sum rule.
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.
Multivariable Hermite polynomials and phase-space dynamics
NASA Technical Reports Server (NTRS)
Dattoli, G.; Torre, Amalia; Lorenzutta, S.; Maino, G.; Chiccoli, C.
1994-01-01
The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.
Phase-space approach to continuous variable quantum teleportation
Ban, Masashi
2004-05-01
The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the s-parametrized phase-space function of an input state into the (s+{delta})-parametrized phase-space function, where the parameter {delta} is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for F{sub c}{<=}2/3 and the Glauber-Sudarshan P function non-negative for F{sub c}{<=}1/2, where F{sub c} is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.
Explicit methods in extended phase space for inseparable Hamiltonian problems
NASA Astrophysics Data System (ADS)
Pihajoki, Pauli
2015-03-01
We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.
κ-Deformed Phase Space, Hopf Algebroid and Twisting
NASA Astrophysics Data System (ADS)
Jurić; , Tajron; Kovačević, Domagoj; Meljanac, Stjepan
2014-11-01
Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for κ-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of κ-Poincaré algebra. Several examples of realizations are worked out in details.
MUB Entanglement Patterns by Transformations in Phase Space
NASA Astrophysics Data System (ADS)
Lawrence, Jay
2011-03-01
All possible MUB entanglement patterns for systems of N prime-state particles are obtained from standard ones by unitary transformations in the Hilbert space, thus preserving the relationships between the generalized Pauli operators, the phase point operators, and the MUB projectors. The transformations are described geometrically in discrete phase space. Illustrative examples show the invariance of the total entanglement content and the connection of entanglement with Galois fields. Different field representations for the same dimension may produce inequivalent MUB sets. This work provides alternative constructions and generalizes previous work on qubit systems [1,2].
The solidification of monotectic alloys - Microstructures and phase spacings
NASA Technical Reports Server (NTRS)
Grugel, R. N.; Hellawell, A.; Lograsso, T. A.
1984-01-01
The microstructures of directionally grown monotectic alloys in metallic and organic systems fall into two categories those which can form aligned fibrous composite structures with even phase spacings and fiber sections, and those in which the phase distribution is coarser and less regular. This division appears to relate to the form of the phase diagram and has been rationalized by Cahn (1977, 1979) in terms of the relative surface energies between solid and two liquids to give steady state or nonsteady state profiles. The transition in growth behavior occurs when the ratio of the monotectic temperature to that of the upper consolute temperature is approximately 0.9. Differences in phase spacings between a range of monotectic and eutectic systems are discussed in terms of the expected growth interface shapes and the factors which will influence them.
Adaptive optics and phase diversity imaging for responsive space applications.
Smith, Mark William; Wick, David Victor
2004-11-01
The combination of phase diversity and adaptive optics offers great flexibility. Phase diverse images can be used to diagnose aberrations and then provide feedback control to the optics to correct the aberrations. Alternatively, phase diversity can be used to partially compensate for aberrations during post-detection image processing. The adaptive optic can produce simple defocus or more complex types of phase diversity. This report presents an analysis, based on numerical simulations, of the efficiency of different modes of phase diversity with respect to compensating for specific aberrations during post-processing. It also comments on the efficiency of post-processing versus direct aberration correction. The construction of a bench top optical system that uses a membrane mirror as an active optic is described. The results of characterization tests performed on the bench top optical system are presented. The work described in this report was conducted to explore the use of adaptive optics and phase diversity imaging for responsive space applications.
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.
Phase-field study of spacing evolution during transient growth
NASA Astrophysics Data System (ADS)
Gurevich, Sebastian; Amoorezaei, Morteza; Provatas, Nikolas
2010-11-01
The primary spacing of a dendritic array grown under transient growth conditions displays a distribution of wavelengths. The average primary spacing is shown, both experimentally and numerically, to evolve between characteristic incubation periods during which the distribution of wavelengths remains essentially stable. Our primary spacing results display a gradual transition period from one spacing range to another, consistent with the fact that the abrupt doubling of spacing predicted by Warren and Langer for an idealized periodic array affects different wavelengths of the distribution at different times. This transition is shown to depend on the rate of change in growth speed using phase-field simulations of directional solidification where the pulling speed is ramped at different rates. In particular, for high rates of change of the pulling speed we observe temporary marginally stable array configurations separated by relatively short lived transitions, while for lower rates of change of the pulling speed the distinction between incubation and transition periods disappears.
Ogurtani, Tarik Omer
2006-04-14
A theory of irreversible thermodynamics of curved surfaces and interfaces with triple junction singularities is elaborated to give a full consideration of the effects of the specific surface Gibbs free energy anisotropy in addition to the diffusional anisotropy, on the morphological evolution of surfaces and interfaces in crystalline solids. To entangle this intricate problem, the internal entropy production associated with arbitrary virtual displacements of triple junction and ordinary points on the interfacial layers, embedded in a multicomponent, multiphase, anisotropic composite continuum system, is formulated by adapting a mesoscopic description of the orientation dependence of the chemical potentials in terms of the rotational degree of freedom of individual microelements. The rate of local internal entropy production resulted generalized forces and conjugated fluxes not only for the grain boundary triple junction transversal and longitudinal movements, but also for the ordinary points. The natural combination of the mesoscopic approach coupled with the rigorous theory of irreversible thermodynamics developed previously by the global entropy production hypothesis yields a well-posed, nonlinear, moving free-boundary value problem in two-dimensional (2D) space, as a unified theory. The results obtained for 2D space are generalized into the three-dimensional continuum by utilizing the invariant properties of the vector operators in connection with the descriptions of curved surfaces in differential geometry. This mathematical model after normalization and scaling procedures may be easily adapted for computer simulation studies without introducing any additional phenomenological system parameters (the generalized mobilities), other than the enlarged concept of the surface stiffness. PMID:16626230
Naval Space Surveillance Center uses of time, frequency, and phase
NASA Technical Reports Server (NTRS)
Hayden, Carroll C.; Knowles, Stephen H.
1992-01-01
The Naval Space Surveillance Center (NAVSPASUR) is an operational naval command that has the mission of determining the location of all manmade objects in space and transmitting information on objects of interest to the fleet. NAVSPASUR operates a 217 MHz radar fence that has 9 transmitting and receiving stations deployed in a line across southern Continental United States (CONUS). This surveillance fence provides unalerted detection of satellites overflying CONUS. NAVSPASUR also maintains a space catalog of all orbiting space objects. NAVSPASUR plays an important role as operational alternate to the primary national Space Surveillance Center (SSC) and Space Defence Operations Center (SPADOC). In executing these responsibilities, NAVSPASUR needs precise and/or standardized time and frequency in a number of applications. These include maintenance of the radar fence references to specification, and coordination with other commands and agencies for data receipt and dissemination. Precise time and frequency must be maintained within each site to enable proper operation of the interferometry phasing technique used. Precise time-of-day clocking must exist between sites for proper intersite coordination. Phase may be considered a derivative of time and frequency. Its control within each transmitter or receiver site is of great importance to NAVSPASUR because of the operation of the sensor as an interferometer system, with source direction angles as the primary observable. Determination of the angular position of a satellite is directly dependent on the accuracy with which the differential phase between spaced subarrays can be measured at each receiver site. Various aspects of the NAVSPASUR are discussed with respect to time, frequency, and phase.
Two Phase Flow and Space-Based Applications
NASA Technical Reports Server (NTRS)
McQuillen, John
1999-01-01
A reduced gravity environment offers the ability to remove the effect of buoyancy on two phase flows whereby density differences that normally would promote relative velocities between the phases and also alter the shape of the interface are removed. However, besides being a potent research tool, there are also many space-based technologies that will either utilize or encounter two-phase flow behavior, and as a consequence, several questions must be addressed. This paper presents some of these technologies missions. Finally, this paper gives a description of web-sites for some funding.
Quantum particles from coarse grained classical probabilities in phase space
Wetterich, C.
2010-07-15
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.
Strong Field Double Ionization: The Phase Space Perspective
Mauger, F.; Chandre, C.; Uzer, T.
2009-05-01
We identify the phase-space structures that regulate atomic double ionization in strong ultrashort laser pulses. The emerging dynamical picture complements the recollision scenario by clarifying the distinct roles played by the recolliding and core electrons, and leads to verifiable predictions on the characteristic features of the 'knee', a hallmark of the nonsequential process.
Phase space flow of particles in squeezed states
NASA Technical Reports Server (NTRS)
Ceperley, Peter H.
1994-01-01
The manipulation of noise and uncertainty in squeezed states is governed by the wave nature of the quantum mechanical particles in these states. This paper uses a deterministic model of quantum mechanics in which real guiding waves control the flow of localized particles. This model will be used to examine the phase space flow of particles in typical squeezed states.
Depositing spacing layers on magnetic film with liquid phase epitaxy
NASA Technical Reports Server (NTRS)
Moody, J. W.; Shaw, R. W.; Sanfort, R. M.
1975-01-01
Liquid phase epitaxy spacing layer is compatible with systems which are hard-bubble proofed by use of second magnetic garnet film as capping layer. Composite is superior in that: circuit fabrication time is reduced; adherence is superior; visibility is better; and, good match of thermal expansion coefficients is provided.
Dimension of quantum phase space measured by photon correlations
NASA Astrophysics Data System (ADS)
Leuchs, Gerd; Glauber, Roy J.; Schleich, Wolfgang P.
2015-06-01
We show that the different values 1, 2 and 3 of the normalized second-order correlation function {g}(2)(0) corresponding to a coherent state, a thermal state and a highly squeezed vacuum originate from the different dimensionality of these states in phase space. In particular, we derive an exact expression for {g}(2)(0) in terms of the ratio of the moments of the classical energy evaluated with the Wigner function of the quantum state of interest and corrections proportional to the reciprocal of powers of the average number of photons. In this way we establish a direct link between {g}(2)(0) and the shape of the state in phase space. Moreover, we illuminate this connection by demonstrating that in the semi-classical limit the familiar photon statistics of a thermal state arise from an area in phase space weighted by a two-dimensional Gaussian, whereas those of a highly squeezed state are governed by a line-integral of a one-dimensional Gaussian. We dedicate this article to Margarita and Vladimir Man’ko on the occasion of their birthdays. The topic of our contribution is deeply rooted in and motivated by their love for non-classical light, quantum mechanical phase space distribution functions and orthogonal polynomials. Indeed, through their articles, talks and most importantly by many stimulating discussions and intensive collaborations with us they have contributed much to our understanding of physics. Happy birthday to you both!
Geometrical Series and Phase Space in a Finite Oscillatory Motion
ERIC Educational Resources Information Center
Mareco, H. R. Olmedo
2006-01-01
This article discusses some interesting physical properties of oscillatory motion of a particle on two joined inclined planes. The geometrical series demonstrates that the particle will oscillate during a finite time. Another detail is the converging path to the origin of the phase space. Due to its simplicity, this motion may be used as a…
Phase-locked injection laser arrays with variable stripe spacing
NASA Technical Reports Server (NTRS)
Ackley, Donald E.; Butler, Jerome K.; Ettenberg, Michael
1986-01-01
A phase-locked injection laser array is described which utilizes variations in spacing of identical lasing elements to vary the coupling between them. A coupled-mode analysis indicates that excellent matching of fundamental array mode to a uniform gain distribution can be obtained. Observation of the array emission patterns confirms the results of the coupled-mode analysis.
Twisted geometries: A geometric parametrization of SU(2) phase space
Freidel, Laurent; Speziale, Simone
2010-10-15
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each face of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an Abelianization of the SU(2) connection. The results are relevant for the construction of coherent states and, as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries.
Painting the Phase Space Portrait of an Integrable Dynamical System
NASA Astrophysics Data System (ADS)
Coffey, Shannon; Deprit, Andre; Deprit, Etienne; Healy, Liam
1990-02-01
For an integrable dynamical system with one degree of freedom, "painting" the integral over the phase space proves to be very effective for uncovering the global flow down to minute details. Applied to the main problem in artificial satellite theory, for instance, the technique reveals an intricate configuration of equilibria and bifurcations when the polar component of the angular momentum approaches zero.
Phase-space reconstruction of focused x-ray fields
Tran, Chanh Q.; Mancuso, Adrian P.; Dhal, Bipin B.; Nugent, Keith A.; Peele, Andrew G.; Cai, Zhonghou; Paterson, David
2006-01-01
The phase-space tomography is used to reconstruct x-ray beams focused using a compound refractive lens, showing that it is possible to decouple the effect of aberrations in the optical system from the field and therefore measure both them and the original field. The complex coherence function is recovered and found to be consistent with expectations.
Vital phase of space science. [solar terrestrial interactions
NASA Technical Reports Server (NTRS)
Parker, E. N.
1994-01-01
Space science began with the indirect phase where the activity in space was inferred from such terrestrial phenomena as geomagnetic storms, ionospheric variations, and fluctuations in the cosmic ray intensity. The direct phase was initiated with spaceflight placing instruments directly in space and permitting the direct observation of UV and X rays, as well as precision observations of solar luminosity variations. The evidence from these many direct studies, together with the historical record of terrestrial conditions, shows that the variations of the luminosity of the Sun affect the terrestrial atmosphere at all levels, with devastating changes in climate tracking the major changes in the activity level and luminosity of the Sun. The quantification and understanding of this vital connection should be the first priority of space science and geophysics, from oceans and atmosphere through the ionosphere, magnetosphere, and all the way to the convective zone of the Sun. It becomes the vital phase of space science, focused on the basic science of the changing habitability of Earth.
Master space, Hilbert series and Seiberg duality
NASA Astrophysics Data System (ADS)
Forcella, Davide; Hanany, Amihay; Zaffaroni, Alberto
2009-07-01
We analyze the action of Toric (Seiberg) duality on the combined mesonic and baryonic moduli space of quiver gauge theories obtained from D3 branes at Calabi-Yau singularities. We analyze in particular the structure of the master space, the complete moduli space for one brane, for different toric phases of a given singularity. We show that the Hilbert Series for the largest component of the master space of different phases is the same, when refined with all the non anomalous charges. This reflects the fact that the quiver gauge theories associated with different phases are related by Seiberg duality when the number of branes is greater than one.
Phase-space exploration in nuclear giant resonance decay
Drozdz, S.; Nishizaki, S.; Wambach, J.; Speth, J. Institute of Nuclear Physics, PL-31-342 Krakow Department of Physics, University of Illinois at Urbana, Illinois 61801 College of Humanities and Social Sciences, Iwate University, Ueda 3-18-34, Morioka 020 )
1995-02-13
The rate of phase-space exploration in the decay of isovector and isoscalar giant quadrupole resonances in [sup 40]Ca is analyzed. The study is based on the time dependence of the survival probability and of the spectrum of generalized entropies evaluated in the space of one-particle--one-hole (1p-1h) and 2p-2h states. Three different cases for the level distribution of 2p-2h background states, corresponding to (a) high degeneracy, (b) classically regular motion, and (c) classically chaotic motion, are studied. In the latter case the isovector excitation evolves almost statistically while the isoscalar excitation remains largely localized, even though it penetrates the whole available phase space.
Extended phase space description of human-controlled systems dynamics
NASA Astrophysics Data System (ADS)
Zgonnikov, Arkady; Lubashevsky, Ihor
2014-03-01
Humans are often incapable of precisely identifying and implementing the desired control strategy in controlling unstable dynamical systems. That is, the operator of a dynamical system treats the current control effort as acceptable even if it deviates slightly from the desired value, and starts correcting the actions only when the deviation has become evident. We argue that the standard Newtonian approach does not allow such behavior to be modeled. Instead, the physical phase space of a controlled system should be extended with an independent phase variable characterizing the motivated actions of the operator. The proposed approach is illustrated via a simple non-Newtonian model capturing the operators' fuzzy perception of their own actions. The properties of the model are investigated analytically and numerically; the results confirm that the extended phase space may aid in capturing the intricate dynamical properties of human-controlled systems.
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
Phase-space Dynamics of Runaway Electrons In Tokamaks
Xiaoyin Guan, Hong Qin, and Nathaniel J. Fisch
2010-08-31
The phase-space dynamics of runaway electrons is studied, including the influence of loop voltage, radiation damping, and collisions. A theoretical model and a numerical algorithm for the runaway dynamics in phase space are developed. Instead of standard integrators, such as the Runge-Kutta method, a variational symplectic integrator is applied to simulate the long-term dynamics of a runaway electron. The variational symplectic integrator is able to globally bound the numerical error for arbitrary number of time-steps, and thus accurately track the runaway trajectory in phase space. Simulation results show that the circulating orbits of runaway electrons drift outward toward the wall, which is consistent with experimental observations. The physics of the outward drift is analyzed. It is found that the outward drift is caused by the imbalance between the increase of mechanical angular momentum and the input of toroidal angular momentum due to the parallel acceleration. An analytical expression of the outward drift velocity is derived. The knowledge of trajectory of runaway electrons in configuration space sheds light on how the electrons hit the first wall, and thus provides clues for possible remedies.
Kinetic solvers with adaptive mesh in phase space.
Arslanbekov, Robert R; Kolobov, Vladimir I; Frolova, Anna A
2013-12-01
An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a "tree of trees" (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems. PMID:24483578
Probabilistic Q-function distributions in fermionic phase-space
NASA Astrophysics Data System (ADS)
Rosales-Zárate, Laura E. C.; Drummond, P. D.
2015-03-01
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q-function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q-function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO(2M) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q-function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem.
Kinetic solvers with adaptive mesh in phase space
NASA Astrophysics Data System (ADS)
Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.
2013-12-01
An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.
Space transfer vehicle concepts and requirements study, phase 2
NASA Technical Reports Server (NTRS)
Cannon, Jeffrey H.; Vinopal, Tim; Andrews, Dana; Richards, Bill; Weber, Gary; Paddock, Greg; Maricich, Peter; Bouton, Bruce; Hagen, Jim; Kolesar, Richard
1992-01-01
This final report is a compilation of the Phase 1 and Phase 2 study findings and is intended as a Space Transfer Vehicle (STV) 'users guide' rather than an exhaustive explanation of STV design details. It provides a database for design choices in the general areas of basing, reusability, propulsion, and staging; with selection criteria based on cost, performance, available infrastructure, risk, and technology. The report is organized into the following three parts: (1) design guide; (2) STV Phase 1 Concepts and Requirements Study Summary; and (3) STV Phase 2 Concepts and Requirements Study Summary. The overall objectives of the STV study were to: (1) define preferred STV concepts capable of accommodating future exploration missions in a cost-effective manner; (2) determine the level of technology development required to perform these missions in the most cost effective manner; and (3) develop a decision database of programmatic approaches for the development of an STV concept.
Asteroid orbital inversion using uniform phase-space sampling
NASA Astrophysics Data System (ADS)
Muinonen, K.; Pentikäinen, H.; Granvik, M.; Oszkiewicz, D.; Virtanen, J.
2014-07-01
We review statistical inverse methods for asteroid orbit computation from a small number of astrometric observations and short time intervals of observations. With the help of Markov-chain Monte Carlo methods (MCMC), we present a novel inverse method that utilizes uniform sampling of the phase space for the orbital elements. The statistical orbital ranging method (Virtanen et al. 2001, Muinonen et al. 2001) was set out to resolve the long-lasting challenges in the initial computation of orbits for asteroids. The ranging method starts from the selection of a pair of astrometric observations. Thereafter, the topocentric ranges and angular deviations in R.A. and Decl. are randomly sampled. The two Cartesian positions allow for the computation of orbital elements and, subsequently, the computation of ephemerides for the observation dates. Candidate orbital elements are included in the sample of accepted elements if the χ^2-value between the observed and computed observations is within a pre-defined threshold. The sample orbital elements obtain weights based on a certain debiasing procedure. When the weights are available, the full sample of orbital elements allows the probabilistic assessments for, e.g., object classification and ephemeris computation as well as the computation of collision probabilities. The MCMC ranging method (Oszkiewicz et al. 2009; see also Granvik et al. 2009) replaces the original sampling algorithm described above with a proposal probability density function (p.d.f.), and a chain of sample orbital elements results in the phase space. MCMC ranging is based on a bivariate Gaussian p.d.f. for the topocentric ranges, and allows for the sampling to focus on the phase-space domain with most of the probability mass. In the virtual-observation MCMC method (Muinonen et al. 2012), the proposal p.d.f. for the orbital elements is chosen to mimic the a posteriori p.d.f. for the elements: first, random errors are simulated for each observation, resulting in
On the Landau system in noncommutative phase-space
NASA Astrophysics Data System (ADS)
Gangopadhyay, Sunandan; Saha, Anirban; Halder, Aslam
2015-12-01
We consider the Landau system in a canonically noncommutative phase-space. A set of generalized transformations containing scaling parameters is derived which maps the NC problem to an equivalent commutative problem. The energy spectrum admits NC corrections which are computed using the explicit NC variables as well as the commutative-equivalent variables. Their exact matching solidifies the evidence of the equivalence of the two approaches. We also obtain the magnetic length and level degeneracy, which admit NC corrections. We further study the Aharonov-Bohm effect where the phase-shift is found to alter due to noncommutativity and also depends on the scaling parameters.
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
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.
Nonclassicality phase-space functions: more insight with fewer detectors.
Luis, Alfredo; Sperling, Jan; Vogel, Werner
2015-03-13
Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click-counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, a small number of on-off diodes can yield more insight than perfect photon number resolution. Quantum signatures in the particle and wave domain of the quantized radiation field, as shown by photon number and squeezed states, respectively, will be uncovered in terms of negativities of the sampled phase-space functions. Application in the vast fields of quantum optics and quantum technology will benefit from our efficient nonclassicality characterization approach. PMID:25815932
On a quantum algebraic approach to a generalized phase space
NASA Astrophysics Data System (ADS)
Bohm, D.; Hiley, B. J.
1981-04-01
We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding the solutions of our equations as constants of the motion, rather than as statistical weight factors. We show a close relationship of our work to that of Prigogine and his group. We bring in a new nonnegative probability function, and we propose extensions of the theory to cover thermodynamic processes involving entropy changes, as well as the usual reversible processes.
Large space telescope, phase A. Volume 1: Executive summary
NASA Technical Reports Server (NTRS)
1972-01-01
The Phase A study of the Large Space Telescope (LST) is reported. The study defines an LST concept based on the broad mission guidelines provided by the Office of Space Science (OSS), the scientific requirements developed by OSS with the scientific community, and an understanding of long range NASA planning current at the time the study was performed. The LST is an unmanned astronomical observatory facility, consisting of an optical telescope assembly (OTA), scientific instrument package (SIP), and a support systems module (SSM). The report consists of five volumes. The report describes the constraints and trade off analyses that were performed to arrive at a reference design for each system and for the overall LST configuration. A low cost design approach was followed in the Phase A study. This resulted in the use of standard spacecraft hardware, the provision for maintenance at the black box level, growth potential in systems designs, and the sharing of shuttle maintenance flights with other payloads.
Order parameter aided phase space exploration under extreme conditions
NASA Astrophysics Data System (ADS)
Samanta, Amit; Hamel, Sebastian; Schwegler, Eric
Efficient exploration of configuration space and identification of metastable structures in condensed phase systems are challenging from both computational as well as algorithmic perspectives. In this talk I will illustrate how we can extend the recently proposed order-parameter aided temperature accelerated sampling schemes to efficiently and systematically explore free energy surfaces, and search for metastable states and reaction pathways within the framework of density functional theory based molecular dynamics. I will illustrate how this sampling scheme can be used to explore the relevant parts of configuration space in prototypical materials, like SiO2 and identify the different metastable structures, transition pathways and phase boundaries. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Communication: Phase space wavelets for solving Coulomb problems.
Shimshovitz, Asaf; Tannor, David J
2012-09-14
Recently we introduced a phase space approach for solving the time-independent Schrödinger equation using a periodic von Neumann basis with bi-orthogonal exchange (pvb) [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012)]. Here we extend the approach to allow a wavelet scaling of the phase space Gaussians. The new basis set, which we call the wavelet pvb basis, is simple to implement and provides an appealing alternative to other wavelet approaches. For the 1D Coulomb problems tested in this paper, the method reduces the size of the basis relative to the Fourier grid method by a factor of 13-60. The savings in basis set size is predicted to grow steeply as the dimensionality increases. PMID:22979843
Space shuttle phase B wind tunnel test database
NASA Technical Reports Server (NTRS)
Glynn, J. L.; Poucher, D. E.
1988-01-01
Archived wind tunnel test data are available for flyback booster or other alternate recoverable configurations as well as reusable orbiters studied during initial development (Phase B) of the Space Shuttle. Considerable wind tunnel data were acquired by competing contractors and NASA centers for an extensive variety of configurations with an array of wing and body planforms. This wind tunnel test data has been compiled into a database and are available for application to current winged flyback or recoverable booster aerodynamic studies. The Space Shuttle Phase B Wind Tunnel Database is structured by vehicle component and configuration type. Basic components include the booster, the orbiter and the launch vehicle. Booster configuration types include straight and delta wings, canard, cylindrical, retro-glide and twin body. Orbiter configuration types include straight and delta wings, lifting body, drop tanks and double delta wings.
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.
Visualizing the quantum interaction picture in phase space
NASA Astrophysics Data System (ADS)
Mehmani, Bahar; Aiello, Andrea
2012-09-01
We present a graphical example of the interaction picture-time evolution. Our aim is to help students understand in a didactic manner the simplicity that this picture provides. Visualizing the interaction picture unveils its advantages, which are hidden behind the involved mathematics. Specifically, we show that the time evolution of a driven harmonic oscillator in the interaction picture corresponds to a local transformation of a phase space-reference frame into the one that is co-rotating with the Wigner function.
Phase space representation of spatially partially coherent imaging.
Castaneda, Roman
2008-08-01
The phase space representation of imaging with optical fields in any state of spatial coherence is developed by using spatial coherence wavelets. It leads to new functions for describing the optical transfer and response of imaging systems when the field is represented by Wigner distribution functions. Specific imaging cases are analyzed in this context, and special attention is devoted to the imaging of two point sources. PMID:18670542
The ESA Virtual Space Weather Modelling Centre - Phase 1
NASA Astrophysics Data System (ADS)
Poedts, Stefaan
The ESA ITT project (AO/1-6738/11/NL/AT) to develop Phase 1 of a Virtual Space Weather Modelling Centre has the following objectives and scope: 1. The construction of a long term (~10 yrs) plan for the future development of a European virtual space weather modelling centre consisting of a new ‘open’ and distributed framework for the coupling of physics based models for space weather phenomena; 2. The assessment of model capabilities and the amount of work required to make them operational by integrating them in this framework and the identification of computing and networking requirements to do so. 3. The design of a system to enable models and other components to be installed locally or geographically distributed and the creation of a validation plan including a system of metrics for testing results. The consortium that took up this challenge involves: 1)the Katholieke Universiteit Leuven (Prime Contractor, coordinator: Prof. S. Poedts); 2) the Belgian Institute for Space Aeronomy (BIRA-IASB); 3) the Royal Observatory of Belgium (ROB); 4) the Von Karman Institute (VKI); 5) DH Consultancy (DHC); 6) Space Applications Services (SAS). The project started on May 14 2012, and will finish in May 2014. Thus, by the time of the meeting, both Phase 1A and Phase 1B (the development of the prototype) will be finished. The final report will be presented incl. the architecture decisions made, the framework, the current models integrated already as well as the model couplers installed. The prototype VSWMC will be demonstrated.
Prediction of Tropical Climate on Intraseasonal Timescale using Phase Space Reconstruction
NASA Astrophysics Data System (ADS)
Sharma, A. S.; Krishnamurthy, V.
2009-12-01
Although considerable success has been achieved in weather prediction on the order of about ten days lead time, the prediction of climate variability on intraseasonal and seasonal timescales is still in developmental stage. The optimism for climate prediction comes from the realization that climate variability, especially in the tropics, is influenced mainly by slowly varying components of the climate system. Applying multichannel singular spectrum analysis (MSSA) to daily values of climate variables, such as outgoing longwave radiation (OLR) and low-level winds, the tropical climate variability is found to consist of nonlinear oscillations on intraseasonal time scales and large-scale seasonally persisting patterns. The nonlinear oscillations are found to be manifestations of the South Asian monsoon’s active-break cycles and the well-known Madden Julian Oscillation over the Indian and Pacific Oceans. Exploiting the coherent and more regularly varying nature of these nonlinear MSSA modes, this study has constructed a dynamical model for the prediction of tropical climate on intraseasonal time scale. The prediction model is constructed from the time series of the MSSA modes using time-delay embedding technique for the reconstruction of phase space. The predictions are expressed in a probabilistic manner by providing ensemble forecasts.
Medical care capabilities for Space Station Freedom: A phase approach
NASA Technical Reports Server (NTRS)
Doarn, C. R.; Lloyd, C. W.
1992-01-01
As a result of Congressional mandate Space Station Freedom (SSF) was restructured. This restructuring activity has affected the capabilities for providing medical care on board the station. This presentation addresses the health care facility to be built and used on the orbiting space station. This unit, named the Health Maintenance Facility (HMF) is based on and modeled after remote, terrestrial medical facilities. It will provide a phased approach to health care for the crews of SSF. Beginning with a stabilization and transport phase, HMF will expand to provide the most advanced state of the art therapeutic and diagnostic capabilities. This presentation details the capabilities of such a phased HMF. As Freedom takes form over the next decade there will be ever-increasing engineering and scientific developmental activities. The HMF will evolve with this process until it eventually reaches a mature, complete stand-alone health care facility that provides a foundation to support interplanetary travel. As man's experience in space continues to grow so will the ability to provide advanced health care for Earth-orbital and exploratory missions as well.
Relativistic algebraic spinors and quantum motions in phase space
Holland, P.R.
1986-08-01
Following suggestions of Schonberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C/sub 4/, a Jordan-Wigner algebra G/sub 4/, and Wigner transformations. To do this we solve the problem of the conditions under which elements in C/sub 4/ generate minimal ideals, and extend this to G/sub 4/. This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations.
Calculation of a fluctuating entropic force by phase space sampling.
Waters, James T; Kim, Harold D
2015-07-01
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system. PMID:26274308
NASA Astrophysics Data System (ADS)
Wünsche, A.
2015-06-01
Starting from the characteristic function of an operator, we investigate cumulant expansions in quantum optics and apply them to two-dimensional distributions for the canonical variables of the phase space in the case of one degree of freedom (Wigner quasiprobability and its Fourier transform, uncertainty matrix) and to one-dimensional distributions (phase operator, time evolution operator to Hamiltonian). In the relations between cumulants and moments, we make emphasis on the central moments of an operator. It is shown that the determinant of the uncertainty matrix (modified uncertainty product) is invariant with respect to rotation and squeezing of the state in the phase space, whereas the uncertainty sum is only invariant with respect to rotations. We examine some problems for exponentials of the phase operator and show how mean values and variances are connected with the cumulants. The Hilbert-Schmidt distance of a state during time evolution to an initial state is discussed by cumulants.
Deep Space Habitat Team: HEFT Phase 2 Effects
NASA Technical Reports Server (NTRS)
Toups, Larry D.; Smitherman, David; Shyface, Hilary; Simon, Matt; Bobkill, Marianne; Komar, D. R.; Guirgis, Peggy; Bagdigian, Bob; Spexarth, Gary
2011-01-01
HEFT was a NASA-wide team that performed analyses of architectures for human exploration beyond LEO, evaluating technical, programmatic, and budgetary issues to support decisions at the highest level of the agency in HSF planning. HEFT Phase I (April - September, 2010) and Phase II (September - December, 2010) examined a broad set of Human Exploration of Near Earth Objects (NEOs) Design Reference Missions (DRMs), evaluating such factors as elements, performance, technologies, schedule, and cost. At end of HEFT Phase 1, an architecture concept known as DRM 4a represented the best available option for a full capability NEO mission. Within DRM4a, the habitation system was provided by Deep Space Habitat (DSH), Multi-Mission Space Exploration Vehicle (MMSEV), and Crew Transfer Vehicle (CTV) pressurized elements. HEFT Phase 2 extended DRM4a, resulting in DRM4b. Scrubbed element-level functionality assumptions and mission Concepts of Operations. Habitation Team developed more detailed concepts of the DSH and the DSH/MMSEV/CTV Conops, including functionality and accommodations, mass & volume estimates, technology requirements, and DDT&E costs. DRM 5 represented an effort to reduce cost by scaling back on technologies and eliminating the need for the development of an MMSEV.
Grassmann phase space methods for fermions. I. Mode theory
NASA Astrophysics Data System (ADS)
Dalton, B. J.; Jeffers, J.; Barnett, S. M.
2016-07-01
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. The theory of Grassmann phase space methods for fermions based on separate modes is developed, showing how the distribution function is defined and used to determine quantum correlation functions, Fock state populations and coherences via Grassmann phase space integrals, how the Fokker-Planck equations are obtained and then converted into equivalent Ito equations for stochastic Grassmann variables. The fermion distribution function is an even Grassmann function, and is unique. The number of c-number Wiener increments involved is 2n2, if there are n modes. The situation is somewhat different to the bosonic c-number case where only 2 n Wiener increments are involved, the sign of the drift term in the Ito equation is reversed and the diffusion matrix in the Fokker-Planck equation is anti-symmetric rather than symmetric. The un-normalised B distribution is of particular importance for determining Fock state populations and coherences, and as pointed out by Plimak, Collett and Olsen, the drift vector in its Fokker-Planck equation only depends linearly on the Grassmann variables. Using this key feature we show how the Ito stochastic equations can be solved numerically for finite times in terms of c-number stochastic
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)
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.
Phase space analysis of bulk viscous matter dominated universe
NASA Astrophysics Data System (ADS)
Sasidharan, Athira; Mathew, Titus K.
2016-06-01
We consider a Friedmann model of the universe with bulk viscous matter and radiation as the cosmic components. We study the asymptotic properties in the equivalent phase space by considering the three cases for the bulk viscous coefficient as (i) ζ = ζ 0, a constant (ii) ζ ={ζ}_0+{ζ}_1overset{\\cdot /a}{a} , depending on velocity of the expansion of the universe and (iii) ζ ={ζ}_0+{ζ}_1overset{\\cdot /a}{a}+{ζ}_2overset{\\cdot \\cdot /a}{overset{\\cdot }{a}} , depending both on velocity and acceleration of the expansion of the universe. It is found that all the three cases predicts the late acceleration of the universe. However, a conventional realistic behaviour of the universe, i.e., a universe having an initial radiation dominated phase, followed by decelerated matter dominated phase and then finally evolving to accelerated epoch, is shown only when ζ = ζ 0, a constant. For the other two cases, it does not show either a prior conventional radiation dominated phase or a matter dominated phase of the universe.
Linearization of the longitudinal phase space without higher harmonic field
NASA Astrophysics Data System (ADS)
Zeitler, Benno; Floettmann, Klaus; Grüner, Florian
2015-12-01
Accelerator applications like free-electron lasers, time-resolved electron diffraction, and advanced accelerator concepts like plasma acceleration desire bunches of ever shorter longitudinal extent. However, apart from space charge repulsion, the internal bunch structure and its development along the beam line can limit the achievable compression due to nonlinear phase space correlations. In order to improve such a limited longitudinal focus, a correction by properly linearizing the phase space is required. At large scale facilities like Flash at Desy or the European Xfel, a higher harmonic cavity is installed for this purpose. In this paper, another method is described and evaluated: Expanding the beam after the electron source enables a higher order correction of the longitudinal focus by a subsequent accelerating cavity which is operated at the same frequency as the electron gun. The elaboration of this idea presented here is based on a ballistic bunching scheme, but can be extended to bunch compression based on magnetic chicanes. The core of this article is an analytic model describing this approach, which is verified by simulations, predicting possible bunch length below 1 fs at low bunch charge. Minimizing the energy spread down to σE/E <1 0-5 while keeping the bunch long is another interesting possibility, which finds applications, e.g., in time resolved transmission electron microscopy concepts.
Tomographic measurement of the phase space distribution of a space-charge-dominated beam
NASA Astrophysics Data System (ADS)
Stratakis, Diktys
Many applications of accelerators, such as free electron lasers, pulsed neutron sources, and heavy ion fusion, require a good quality beam with high intensity. In practice, the achievable intensity is often limited by the dynamics at the low-energy, space-charge dominated end of the machine. Because low-energy beams can have complex distribution functions, a good understanding of their detailed evolution is needed. To address this issue, we have developed a simple and accurate tomographic method to map the beam phase using quadrupole magnets, which includes the effects from space charge. We extend this technique to use also solenoidal magnets which are commonly used at low energies, especially in photoinjectors, thus making the diagnostic applicable to most machines. We simulate our technique using a particle in cell code (PIC), to ascertain accuracy of the reconstruction. Using this diagnostic we report a number of experiments to study and optimize injection, transport and acceleration of intense space charge dominated beams. We examine phase mixing, by studying the phase-space evolution of an intense beam with a transversely nonuniform initial density distribution. Experimental measurements, theoretical predictions and PIC simulations are in good agreement each other. Finally, we generate a parabolic beam pulse to model those beams from photoinjectors, and combine tomography with fast imaging techniques to investigate the time-sliced parameters of beam current, size, energy spread and transverse emittance. We found significant differences between the slice emittance profiles and slice orientation as the beam propagates downstream. The combined effect of longitudinal nonuniform profiles and fast imaging of the transverse phase space provided us with information about correlations between longitudinal and transverse dynamics that we report within this dissertation.
Method of phase space beam dilution utilizing bounded chaos generated by rf phase modulation
NASA Astrophysics Data System (ADS)
Pham, Alfonse N.; Lee, S. Y.; Ng, K. Y.
2015-12-01
This paper explores the physics of chaos in a localized phase-space region produced by rf phase modulation applied to a double rf system. The study can be exploited to produce rapid particle bunch broadening exhibiting longitudinal particle distribution uniformity. Hamiltonian models and particle-tracking simulations are introduced to understand the mechanism and applicability of controlled particle diffusion. When phase modulation is applied to the double rf system, regions of localized chaos are produced through the disruption and overlapping of parametric resonant islands and configured to be bounded by well-behaved invariant tori to prevent particle loss. The condition of chaoticity and the degree of particle dilution can be controlled by the rf parameters. The method has applications in alleviating adverse space-charge effects in high-intensity beams, particle bunch distribution uniformization, and industrial radiation-effects experiments.
Multimegawatt space nuclear power supply, Phase 1 Final report
Not Available
1989-02-17
This Specification establishes the performance, design, development, and test requirements for the Boeing Multimegawatt Space Nuclear Power System (MSNPS). The Boeing Multimegawatt Space Power System is part of the DOE/SDIO Multimegawatt Space Nuclear Power Program. The purpose of this program is to provide a space-based nuclear power system to meet the needs of SDIO missions. The Boeing MSNPS is a category 1 concept which is capable of delivering 10's of MW(e) for 100's of seconds with effluent permitted. A design goal is for the system to have growth or downscale capability for other power system concepts. The growth objective is to meet the category 3 capability of 100's of MW(e) for 100's of seconds, also with effluent permitted. The purpose of this preliminary document is to guide the conceptual design effort throughout the Phase 1 study effort. This document will be updated through out the study. It will thus result in a record of the development of the design effort.
Phase space analysis of multipactor saturation in rectangular waveguide
NASA Astrophysics Data System (ADS)
Lingwood, C. J.; Burt, G.; Dexter, A. C.; Smith, J. D. A.; Goudket, P.; Stoltz, P. H.
2012-03-01
In certain high power RF systems multipactor cannot be avoided for all operating points, but its existence places limits on performance, efficiency, lifetime, and reliability. As an example multipactor in the input couplers of superconducting RF cavities can be a major limitation to the maximum RF power. Several studies have concentrated on rectangular waveguide input couplers which are used in many light sources. Most of these studies neglect space charge assuming that the effect of space charge is simply to defocus the electron bunches. Modelling multipactor to saturation is of interest in determining the performance of waveguide under a range of conditions. Particle-in-cell modelling including space charge has been performed for 500 MHz half-height rectangular waveguide. Phase plots of electron trajectories can aid understanding the processes taking place in the multipactor. Results strongly suggest that the multipacting trajectories are strongly perturbed by space charge causing the electrons to transition from two-surface to single-surface trajectories as the multipactor approaches saturation.
A gauge theory of gravity in curved phase-spaces
NASA Astrophysics Data System (ADS)
Castro, Carlos
2016-06-01
After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann-Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the 8D cotangent bundle T∗M of spacetime is explicitly constructed and based on the gauge group SO(6, 2) ×sR8 which acts on the tangent space to the cotangent bundle T(x,p)T∗M at each point (x,p). Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.
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).
Values of the phase space factors for double beta decay
Stoica, Sabin Mirea, Mihai
2015-10-28
We report an up-date list of the experimentally most interesting phase space factors for double beta decay (DBD). The electron/positron wave functions are obtained by solving the Dirac equations with a Coulomb potential derived from a realistic proton density distribution in nucleus and with inclusion of the finite nuclear size (FNS) and electron screening (ES) effects. We build up new numerical routines which allow us a good control of the accuracy of calculations. We found several notable differences as compared with previous results reported in literature and possible sources of these discrepancies are discussed.
Testing gravity with the stacked phase space around galaxy clusters.
Lam, Tsz Yan; Nishimichi, Takahiro; Schmidt, Fabian; Takada, Masahiro
2012-08-01
In general relativity, the average velocity field of dark matter around galaxy clusters is uniquely determined by the mass profile. The latter can be measured through weak lensing. We propose a new method of measuring the velocity field (phase space density) by stacking redshifts of surrounding galaxies from a spectroscopic sample. In combination with lensing, this yields a direct test of gravity on scales of 1-30 Mpc. Using N-body simulations, we show that this method can improve upon current constraints on f(R) and Dvali-Gabadadze-Porrati model parameters by several orders of magnitude when applied to upcoming imaging and redshift surveys. PMID:23006162
Space shuttle phase B. Volume 2: Technical summary, addendum A
NASA Technical Reports Server (NTRS)
1971-01-01
A study was conducted to analyze the characteristics and performance data for the booster vehicles to be used with the space shuttle operations. It was determined that the single pressure-fed booster offered the lowest program cost per flight of the pressure-fed booster arrangements studied. The fly back booster required the highest peak annual funding and highest program cost. It was recommended that the pressure-fed booster, series burn with liquid oxygen phase, be continued for further study. The flyback booster study was discontinued. Both solid and liquid propelled booster vehicles with 14 by 45 foot and 15 by 60 foot payload orbiters were considered.
Advanced microelectronics research for space applications, phase 2
NASA Technical Reports Server (NTRS)
Gaertner, W. W.
1971-01-01
Negative-resistance circuits with possible space flight applications are discussed. The basic design approach is to use impedance rotation, i.e., the conversion from capacitance to negative resistance, and from resistance to inductance by the phase shift of the transistor current gain at high frequencies. The subjects discussed in detail are the following: hybrid fabrication of VHF and UHF negative-resistance stages with lumped passive elements; formulation of measurement techniques to characterize transistors and to extend the frequency of negative-resistance transistor amplifiers to higher microwave frequencies; and derivation of transistor characteristics required to increase the frequency range of negative-resistance transistor stages.