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.
Efficient computations of quantum canonical Gibbs state in phase space
NASA Astrophysics Data System (ADS)
Bondar, Denys I.; Campos, Andre G.; Cabrera, Renan; Rabitz, Herschel A.
2016-06-01
The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.
The Simpsons program 6-D phase space tracking with acceleration
NASA Astrophysics Data System (ADS)
Machida, S.
1993-12-01
A particle tracking code, Simpsons, in 6-D phase space including energy ramping has been developed to model proton synchrotrons and storage rings. We take time as the independent variable to change machine parameters and diagnose beam quality in a quite similar way as real machines, unlike existing tracking codes for synchrotrons which advance a particle element by element. Arbitrary energy ramping and rf voltage curves as a function of time are read as an input file for defining a machine cycle. The code is used to study beam dynamics with time dependent parameters. Some of the examples from simulations of the Superconducting Super Collider (SSC) boosters are shown.
Spatial coherence wavelets and phase-space representation of diffraction.
Castañeda, Román; Carrasquilla, Juan
2008-08-01
The phase-space representation of the Fresnel-Fraunhofer diffraction of optical fields in any state of spatial coherence is based on the marginal power spectrum carried by the spatial coherence wavelets. Its structure is analyzed in terms of the classes of source pairs and the spot of the field, which is treated as the hologram of the map of classes. Negative values of the marginal power spectrum are interpreted as negative energies. The influence of the aperture edge on diffraction is stated in terms of the distortion of the supports of the complex degree of spatial coherence near it. Experimental results are presented. PMID:18670545
Phase space view of quantum mechanical systems and Fisher information
NASA Astrophysics Data System (ADS)
Nagy, Á.
2016-06-01
Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Phase-space rotations and orbital Stokes parameters.
Alieva, Tatiana; Bastiaans, Martin J
2009-02-15
We introduce the orbital Stokes parameters as a linear combination of a beam's second-order moments. Similar to the ones describing the field polarization and associated with beam energy and its spin angular momentum, the orbital Stokes parameters are related to the total beam width and its orbital angular momentum. We derive the transformation laws for these parameters during beam propagation through first-order optical systems associated with phase-space rotations. The values of the orbital Stokes parameters for Gaussian modes and arbitrary fields expressed as their linear superposition are obtained. PMID:19373324
The Helmholtz Hierarchy: phase space statistics of cold dark matter
Tassev, Svetlin V.
2011-10-01
We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the ''Helmholtz Hierarchy'') of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle trajectories.
Dynamical Evolution of Quintessence Cosmology in a Physical Phase Space
NASA Astrophysics Data System (ADS)
Qi, Jing-Zhao; Zhang, Ming-Jian; Liu, Wen-Biao
2016-04-01
The phase space analysis of cosmological parameters Ω ϕ and γ ϕ is given. Based on this, the well-known quintessence cosmology is studied with an exponential potential V(φ )=V0exp (-λ φ ). Given observational data, the current state of universe could be pinpointed in the phase diagrams, thus making the diagrams more informative. The scaling solution of quintessence usually is not supposed to give the cosmic accelerating expansion, but we prove it could educe the transient acceleration. We also find that the differential equations of system used widely in study of scalar field are incomplete, and then a numerical method is used to figure out the range of application.
Dynamical Evolution of Quintessence Cosmology in a Physical Phase Space
NASA Astrophysics Data System (ADS)
Qi, Jing-Zhao; Zhang, Ming-Jian; Liu, Wen-Biao
2016-08-01
The phase space analysis of cosmological parameters Ω ϕ and γ ϕ is given. Based on this, the well-known quintessence cosmology is studied with an exponential potential V(φ )=V0exp (-λ φ ). Given observational data, the current state of universe could be pinpointed in the phase diagrams, thus making the diagrams more informative. The scaling solution of quintessence usually is not supposed to give the cosmic accelerating expansion, but we prove it could educe the transient acceleration. We also find that the differential equations of system used widely in study of scalar field are incomplete, and then a numerical method is used to figure out the range of application.
Solution of phase space diffusion equations using interacting trajectory ensembles
NASA Astrophysics Data System (ADS)
Donoso, Arnaldo; Martens, Craig C.
2002-06-01
In this paper, we present a new method for simulating the evolution of the phase space distribution function describing a system coupled to a Markovian thermal bath. The approach is based on the propagation of ensembles of trajectories. Instead of incorporating environmental perturbations as stochastic forces, however, the present method includes these effects by additional deterministic interactions between the ensemble members. The general formalism is developed and tested on model systems describing one-dimensional diffusion, relaxation of a coherently excited harmonic oscillator coupled to a thermal bath, and activated barrier crossing in a bistable potential. Excellent agreement with exact results or approximate theories is obtained in all cases. The method provides an entirely deterministic trajectory-based approach to the solution of condensed phase dynamics and chemical reactions.
Are Singularities Integral to General Theory of Relativity?
NASA Astrophysics Data System (ADS)
Krori, K.; Dutta, S.
2011-11-01
Since the 1960s the general relativists have been deeply obsessed with the possibilities of GTR singularities - blackhole as well as cosmological singularities. Senovilla, for the first time, followed by others, showed that there are cylindrically symmetric cosmological space-times which are free of singularities. On the other hand, Krori et al. have presently shown that spherically symmetric cosmological space-times - which later reduce to FRW space-times may also be free of singularities. Besides, Mitra has in the mean-time come forward with some realistic calculations which seem to rule out the possibility of a blackhole singularity. So whether singularities are integral to GTR seems to come under a shadow.
Xia, J.; Xu, Y.; Miller, R.D.; Chen, C.
2006-01-01
A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and the Poisson's ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques. The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically, to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required. This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model. ?? Springer 2006.
The Hamiltonian property of the flow of singular trajectories
Lokutsievskiy, L V
2014-03-31
Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles.
The complex structured singular value
NASA Technical Reports Server (NTRS)
Packard, A.; Doyle, J.
1993-01-01
A tutorial introduction to the complex structured singular value (mu) is presented, with an emphasis on the mathematical aspects of mu. The mu-based methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared, and a simple synthesis problem is studied. Uncertain systems are represented using linear fractional transformations which naturally unify the frequency-domain and state space methods.
Phase space lattices and integrable nonlinear wave equations
NASA Astrophysics Data System (ADS)
Tracy, Eugene; Zobin, Nahum
2003-10-01
Nonlinear wave equations in fluids and plasmas that are integrable by Inverse Scattering Theory (IST), such as the Korteweg-deVries and nonlinear Schrodinger equations, are known to be infinite-dimensional Hamiltonian systems [1]. These are of interest physically because they predict new phenomena not present in linear wave theories, such as solitons and rogue waves. The IST method provides solutions of these equations in terms of a special class of functions called Riemann theta functions. The usual approach to the theory of theta functions tends to obscure the underlying phase space structure. A theory due to Mumford and Igusa [2], however shows that the theta functions arise naturally in the study of phase space lattices. We will describe this theory, as well as potential applications to nonlinear signal processing and the statistical theory of nonlinear waves. 1] , S. Novikov, S. V. Manakov, L. P. Pitaevskii and V. E. Zakharov, Theory of solitons: the inverse scattering method (Consultants Bureau, New York, 1984). 2] D. Mumford, Tata lectures on theta, Vols. I-III (Birkhauser); J. Igusa, Theta functions (Springer-Verlag, New York, 1972).
Fast-phase space computation of multiple arrivals
Fomel, S.; Sethian, J. A.
2002-01-01
We present a fast, general computational technique for computing the phase-space solution of static Hamilton–Jacobi equations. Starting with the Liouville formulation of the characteristic equations, we derive “Escape Equations” which are static, time-independent Eulerian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically constructed through a “one-pass” formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. To compute all possible trajectories corresponding to all possible boundary conditions, the technique is of computational order O(N log N), where N is the total number of points in the computational phase-space domain; any particular set of boundary conditions then is extracted through rapid post-processing. Suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance. As an application, we apply the technique to the problem of computing first, multiple, and most energetic arrivals to the Eikonal equation. PMID:12032282
An Absolute Phase Space for the Physicality of Matter
NASA Astrophysics Data System (ADS)
Valentine, John S.
2010-12-01
We define an abstract and absolute phase space ("APS") for sub-quantum intrinsic wave states, in three axes, each mapping directly to a duality having fundamental ontological basis. Many aspects of quantum physics emerge from the interaction algebra and a model deduced from principles of `unique solvability' and `identifiable entity', and we reconstruct previously abstract fundamental principles and phenomena from these new foundations. The physical model defines bosons as virtual continuous waves pairs in the APS, and fermions as real self-quantizing snapshots of those waves when simple conditions are met. The abstraction and physical model define a template for the constitution of all fermions, a template for all the standard fundamental bosons and their local interactions, in a common framework and compactified phase space for all forms of real matter and virtual vacuum energy, and a distinct algebra for observables and unobservables. To illustrate our scheme's potential, we provide examples of slit experiment variations (where the model finds theoretical basis for interference only occurring between two final sources), QCD (where we may model most attributes known to QCD, and a new view on entanglement), and we suggest approaches for other varied applications. We believe this is a viable candidate for further exploration as a foundational proposition for physics.
An Absolute Phase Space for the Physicality of Matter
Valentine, John S.
2010-12-22
We define an abstract and absolute phase space (''APS'') for sub-quantum intrinsic wave states, in three axes, each mapping directly to a duality having fundamental ontological basis. Many aspects of quantum physics emerge from the interaction algebra and a model deduced from principles of 'unique solvability' and 'identifiable entity', and we reconstruct previously abstract fundamental principles and phenomena from these new foundations. The physical model defines bosons as virtual continuous waves pairs in the APS, and fermions as real self-quantizing snapshots of those waves when simple conditions are met. The abstraction and physical model define a template for the constitution of all fermions, a template for all the standard fundamental bosons and their local interactions, in a common framework and compactified phase space for all forms of real matter and virtual vacuum energy, and a distinct algebra for observables and unobservables. To illustrate our scheme's potential, we provide examples of slit experiment variations (where the model finds theoretical basis for interference only occurring between two final sources), QCD (where we may model most attributes known to QCD, and a new view on entanglement), and we suggest approaches for other varied applications. We believe this is a viable candidate for further exploration as a foundational proposition for physics.
Coherent quantum squeezing due to the phase space noncommutativity
NASA Astrophysics Data System (ADS)
Bernardini, Alex E.; Mizrahi, Salomon S.
2015-06-01
The effects of general noncommutativity of operators on producing deformed coherent squeezed states is examined in phase space. A two-dimensional noncommutative (NC) quantum system supported by a deformed mathematical structure, similar to that of Hadamard billiard, is obtained and the components behaviour is monitored in time. It is assumed that the independent degrees of freedom are two free 1D harmonic oscillators (HOs), so the system Hamiltonian does not contain interaction terms. Through the NC deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained, new, Hamiltonian represents two interacting 1D HOs. By admitting that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed in terms of Wigner functions, which are essential to put in evidence the effects of the noncommutativity.
Fast-phase space computation of multiple arrivals.
Fomel, S; Sethian, J A
2002-05-28
We present a fast, general computational technique for computing the phase-space solution of static Hamilton-Jacobi equations. Starting with the Liouville formulation of the characteristic equations, we derive "Escape Equations" which are static, time-independent Eulerian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically constructed through a "one-pass" formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. To compute all possible trajectories corresponding to all possible boundary conditions, the technique is of computational order O(N log N), where N is the total number of points in the computational phase-space domain; any particular set of boundary conditions then is extracted through rapid post-processing. Suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance. As an application, we apply the technique to the problem of computing first, multiple, and most energetic arrivals to the Eikonal equation. PMID:12032282
Singular finite element methods
NASA Technical Reports Server (NTRS)
Fix, George J.
1987-01-01
Singularities which arise in the solution to elliptic systems are often of great technological importance. This is certainly the case in models of fracture of structures. A survey of the ways singularities are modeled is presented with special emphasis on the effects due to nonlinearities.
Laser Interferometer Space Antenna (LISA) Far Field Phase Patterns
NASA Technical Reports Server (NTRS)
Waluschka, Eugene; Obenschain, Arthur F. (Technical Monitor)
2000-01-01
The Laser Interferometer Space Antenna (LISA) consists of three spacecraft in orbit about the sun. The orbits are chosen such that the three spacecraft are always at (roughly) the vertices of a equilateral triangle with 5 million kilometer leg lengths. Even though the distances between the three spacecraft are 5 million kilometers, the expected phase shifts between any two beams, due to a gravitational wave, only correspond to a distance change of about 10 pico meters, which is about 10(exp -5) waves for a laser wavelength of 1064 nm. To obtain the best signal-to-noise ratio, noise sources such as changes in the apparent distances due to pointing jitter must be controlled carefully. This is the main reason for determining the far-field phase patterns of a LISA type telescope. Because of torque on the LISA spacecraft and other disturbances, continuous adjustments to the pointing of the telescopes are required. These pointing adjustments will be a "jitter" source. If the transmitted wave is perfectly spherical then rotations (Jitter) about its geometric center will not produce any effect at the receiving spacecraft. However, if the outgoing wave is not perfectly spherical, then pointing jitter will produce a phase variation at the receiving spacecraft. The following sections describe the "brute force" computational approach used to determine the scalar wave front as a function of exit pupil (Zernike) aberrations and to show the results (mostly graphically) of the computations. This approach is straightforward and produces believable phase variations to sub-pico meter accuracy over distances on the order of 5 million kilometers. As such this analyzes the far field phase sensitivity to exit pupil aberrations.
NASA Astrophysics Data System (ADS)
Hawking, Stephen
2005-01-01
The last chapter of my PhD thesis, contained my first singularity theorem. This showed that under certain reasonable conditions, any cosmological solution of the field equations, would have a big bang singularity. At this singularity, classical general relativity would break down, so one could not use it to predict how the universe began. It was therefore necessary to develop a quantum theory of gravity, in order to understand the origin of the universe. In this talk, I explore if the origin of the universe can be semi classical, and non singular. This is possible despite the singularity theorems, because like so many other no go theorems, they have a get out clause. In this case, the get out is the strong energy condition.
Volumic omit maps in ab initio dual-space phasing.
Oszlányi, Gábor; Sütő, András
2016-07-01
Alternating-projection-type dual-space algorithms have a clear construction, but are susceptible to stagnation and, thus, inefficient for solving the phase problem ab initio. To improve this behaviour new omit maps are introduced, which are real-space perturbations applied periodically during the iteration process. The omit maps are called volumic, because they delete some predetermined subvolume of the unit cell without searching for atomic regions or analysing the electron density in any other way. The basic algorithms of positivity, histogram matching and low-density elimination are tested by their solution statistics. It is concluded that, while all these algorithms based on weak constraints are practically useless in their pure forms, appropriate volumic omit maps can transform them to practically useful methods. In addition, the efficiency of the already useful reflector-type charge-flipping algorithm can be further improved. It is important that these results are obtained by using non-sharpened structure factors and without any weighting scheme or reciprocal-space perturbation. The mathematical background of volumic omit maps and their expected applications are also discussed. PMID:27357850
Dynamical singularities in adaptive delayed-feedback control.
Saito, Asaki; Konishi, Keiji
2011-09-01
We demonstrate the dynamical characteristics of adaptive delayed-feedback control systems, exploiting a discrete-time adaptive control method derived for carrying out detailed analysis. In particular, the systems exhibit singularities such as power-law decay of the distribution of transient times and almost zero finite-time Lyapunov exponents. We can explain these results by characterizing such systems as having (1) a Jacobian matrix with unity eigenvalue in the whole phase space, and (2) parameters approaching a stability boundary proven to be identical with that of (nonadaptive) delayed-feedback control. PMID:22060398
Constraining neutron guide optimizations with phase-space considerations
NASA Astrophysics Data System (ADS)
Bertelsen, Mads; Lefmann, Kim
2016-09-01
We introduce a method named the Minimalist Principle that serves to reduce the parameter space for neutron guide optimization when the required beam divergence is limited. The reduced parameter space will restrict the optimization to guides with a minimal neutron intake that are still theoretically able to deliver the maximal possible performance. The geometrical constraints are derived using phase-space propagation from moderator to guide and from guide to sample, while assuming that the optimized guides will achieve perfect transport of the limited neutron intake. Guide systems optimized using these constraints are shown to provide performance close to guides optimized without any constraints, however the divergence received at the sample is limited to the desired interval, even when the neutron transport is not limited by the supermirrors used in the guide. As the constraints strongly limit the parameter space for the optimizer, two control parameters are introduced that can be used to adjust the selected subspace, effectively balancing between maximizing neutron transport and avoiding background from unnecessary neutrons. One parameter is needed to describe the expected focusing abilities of the guide to be optimized, going from perfectly focusing to no correlation between position and velocity. The second parameter controls neutron intake into the guide, so that one can select exactly how aggressively the background should be limited. We show examples of guides optimized using these constraints which demonstrates the higher signal to noise than conventional optimizations. Furthermore the parameter controlling neutron intake is explored which shows that the simulated optimal neutron intake is close to the analytically predicted, when assuming that the guide is dominated by multiple scattering events.
NASA Astrophysics Data System (ADS)
Trahan, Corey J.; Wyatt, Robert E.
2003-10-01
Recently, Donoso and Martens described a method for evolving both classical and quantum phase-space distribution functions, W(q,p,t), that involves the propagation of an ensemble of correlated trajectories. The trajectories are linked into a unified whole by spatial and momentum derivatives of density dependent terms in the equations of motion. On each time step, these nonlocal terms were evaluated by fitting the density around each trajectory to an assumed functional form. In the present study, we develop a different trajectory method for propagating phase-space distribution functions. A hierarchy of coupled analytic equations of motion are derived for the q and p derivatives of the density and a truncated set of these are integrated along each trajectory concurrently with the equation of motion for the density. The advantage of this approach is that individual trajectories can be propagated, one at a time, and function fitting is not required to evaluate the nonlocal terms. Regional nonlocality can be incorporated at various levels of approximation to "dress" what would otherwise be "thin" locally propagating trajectories. This derivative propagation method is used to obtain trajectory solutions for the Klein-Kramers equation, the Husimi equation, and for a smoothed version of the Caldeira-Leggett equation derived by the Diosi. Trajectory solutions are obtained for the relaxation of an oscillator in contact with a thermal bath and for the decay of a metastable state.
NASA Astrophysics Data System (ADS)
Riggs, Lloyd Stephen
In this work the transient currents induced on an arbitrary system of thin linear scatterers by an electromagnetic plane wave are solved by using an electric field integral equation (EFIE) formulation. The transient analysis is carried out using the singularity expansion method (SEM). The general analysis developed here is useful for assessing the vulnerability of military aircraft to a nuclear generated electromagnetic pulse (EMP). It is also useful as a modal synthesis tool in the analysis and design of frequency selective surfaces (FSS). SEM parameters for a variety of thin cylindrical geometries have been computed. Specifically, SEM poles, modes, coupling coefficients, and transient currents are given for the two and three element planar array. Poles and modes for planar arrays with a larger number (as many as eight) of identical equally spaced elements are also considered. SEM pole-mode results are given for identical parallel elements with ends located at the vertices of a regular N-agon. Pole-mode patterns are found for symmetric (and slightly perturbed) single junction N-arm elements and for the five junction Jerusalem cross. The Jerusalem cross element has been used extensively in FSS.
A phase-space beam position monitor for synchrotron radiation
Samadi, Nazanin; Bassey, Bassey; Martinson, Mercedes; Belev, George; Dallin, Les; de Jong, Mark; Chapman, Dean
2015-01-01
The stability of the photon beam position on synchrotron beamlines is critical for most if not all synchrotron radiation experiments. The position of the beam at the experiment or optical element location is set by the position and angle of the electron beam source as it traverses the magnetic field of the bend-magnet or insertion device. Thus an ideal photon beam monitor would be able to simultaneously measure the photon beam’s position and angle, and thus infer the electron beam’s position in phase space. X-ray diffraction is commonly used to prepare monochromatic beams on X-ray beamlines usually in the form of a double-crystal monochromator. Diffraction couples the photon wavelength or energy to the incident angle on the lattice planes within the crystal. The beam from such a monochromator will contain a spread of energies due to the vertical divergence of the photon beam from the source. This range of energies can easily cover the absorption edge of a filter element such as iodine at 33.17 keV. A vertical profile measurement of the photon beam footprint with and without the filter can be used to determine the vertical centroid position and angle of the photon beam. In the measurements described here an imaging detector is used to measure these vertical profiles with an iodine filter that horizontally covers part of the monochromatic beam. The goal was to investigate the use of a combined monochromator, filter and detector as a phase-space beam position monitor. The system was tested for sensitivity to position and angle under a number of synchrotron operating conditions, such as normal operations and special operating modes where the photon beam is intentionally altered in position and angle at the source point. The results are comparable with other methods of beam position measurement and indicate that such a system is feasible in situations where part of the synchrotron beam can be used for the phase-space measurement. PMID:26134798
Singular Atom Optics with Spinor BECs
NASA Astrophysics Data System (ADS)
Schultz, Justin T.; Hansen, Azure; Bigelow, Nicholas P.
2015-05-01
We create and study singular spin textures in pseudo-spin-1/2 BECs. A series of two-photon Raman interactions allows us to not only engineer the spinor wavefunction but also perform the equivalent of atomic polarimetry on the BEC. Adapting techniques from optical polarimetry, we can image two-dimensional maps of the atomic Stokes parameters, thereby fully reconstructing the atomic wavefunction. In a spin-1/2 system, we can represent the local spin superposition with ellipses in a Cartesian basis. The patterns that emerge from the major axes of the ellipses provide fingerprints of the singularities that enable us to classify them as lemons, stars, saddles, or spirals similar to classification schemes for singularities in singular optics, condensed matter, and liquid crystals. These techniques may facilitate the study of geometric Gouy phases in matter waves as well as provide an avenue for utilizing topological structures as quantum gates.
Tailoring phase-space in neutron beam extraction
NASA Astrophysics Data System (ADS)
Weichselbaumer, S.; Brandl, G.; Georgii, R.; Stahn, J.; Panzner, T.; Böni, P.
2015-09-01
In view of the trend towards smaller samples and experiments under extreme conditions it is important to deliver small and homogeneous neutron beams to the sample area. For this purpose, elliptic and/or Montel mirrors are ideally suited as the phase space of the neutrons can be defined far away from the sample. Therefore, only the useful neutrons will arrive at the sample position leading to a very low background. We demonstrate the ease of designing neutron transport systems using simple numeric tools, which are verified using Monte-Carlo simulations that allow taking into account effects of gravity and finite beam size. It is shown that a significant part of the brilliance can be transferred from the moderator to the sample. Our results may have a serious impact on the design of instruments at spallation sources such as the European Spallation Source (ESS) in Lund, Sweden.
Capture into resonance and phase space dynamics in optical centrifuge
NASA Astrophysics Data System (ADS)
Armon, Tsafrir; Friedland, Lazar
2016-05-01
The process of capture of a molecular enesemble into rotational resonance in the optical centrifuge is investigated. The adiabaticity and phase space incompressibility are used to find the resonant capture probability in terms of two dimensionless parameters P1 , 2 characterising the driving strength and the nonlinearity, and related to three characteristic time scales in the problem. The analysis is based on the transformation to action-angle variables and the single resonance approximation, yielding reduction of the three-dimensional rotation problem to one degree of freedom. The analytic results for capture probability are in a good agreement with simulations. The existing experiments satisfy the validity conditions of the theory. This work was supported by the Israel Science Foundation Grant 30/14.
Nonclassicality indicator for the real phase-space distribution functions
Sadeghi, Parvin; Khademi, Siamak; Nasiri, Sadollah
2010-07-15
Benedict et al. and Kenfack et al. advocated nonclassicality indicators based on the measurement of negativity of the Wigner distribution functions. These indicators have some applications in quantum mechanics and quantum optics. In this paper we define a nonclassicality indicator in terms of the interference in phase space, which is applicable to some real distribution functions including those of Wigner. As a special case one may reproduce the previous results using our indicator for the Wigner distribution functions. This indicator is examined for cases of the Schroedinger cat state and the thermal states and the results are compared with those obtained by previous methods. It seems that the physical behavior of nonclassicality indicators originates in the uncertainty principle. This is shown by an onto correspondence between these indicators and the uncertainty principle.
Space shuttle electromagnetic environment experiment. Phase A: Definition study
NASA Technical Reports Server (NTRS)
Haber, F.; Showers, R. M.; Taheri, S. H.; Forrest, L. A., Jr.; Kocher, C.
1974-01-01
A program is discussed which develops a concept for measuring the electromagnetic environment on earth with equipment on board an orbiting space shuttle. Earlier work on spaceborne measuring experiments is reviewed, and emissions to be expected are estimated using, in part, previously gathered data. General relations among system parameters are presented, followed by a proposal on spatial and frequency scanning concepts. The methods proposed include a nadir looking measurement with small lateral scan and a circularly scanned measurement looking tangent to the earth's surface at the horizon. Antenna requirements are given, assuming frequency coverage from 400 MHz to 40 GHz. For the low frequency range, 400-1000 MHz, a processed, thinned array is proposed which will be more fully analyzed in the next phase of the program. Preliminary hardware and data processing requirements are presented.
Production of Coherent Phase Space Islands in Trapped Plasma
NASA Astrophysics Data System (ADS)
Hunter, Eric; Povilus, Alex; Belmore, Nathan; Lewis, Nicole; Shanman, Sabrina; Fajans, Joel
2015-11-01
Particles are coherently extracted from a cold Maxwellian distribution into phase space islands by applying a fixed-frequency RF drive while the plasma bounce frequency is swept downward by lowering the potential confining the plasma. These objects can appear spontaneously in pure electron and mixed ion plasma experiments during particle extraction when the noise power spectrum of the confining potential has peaks in the rf band, as is often the case in a laboratory environment. Interestingly, the particles in these islands have been observed to form tight energy distributions, making the mechanism potentially useful for low energy/monoenergetic plasma injection devices. In particular, these features would be useful for antimatter spectroscopy and mixing for antihydrogen formation. This work is supported by DoE, Grant DE-FG02-06ER54904.
Transverse - longitudinal phase-space manipulations and correlations.
Kim, K.-J.; Sessler, A.; Accelerator Systems Division; LBNL
2006-01-01
Manipulations on transverse and longitudinal phase-space distribution of an electron beam are discussed within the constraints imposed by symplectic conditions. A few examples are presented: transverse-longitudinal emittance exchange to improve performance of a high-gain free-electron laser (FEL) for hard x-rays, and the flat beam technique and its application to compact Terahertz devices and ultrashort-pulse generation. It is shown that emittance transfer to some degree would be advantageous for FELs and that introducing correlations would allow just such transfers. Also, it is shown that transverse-longitudinal correlations would be distinctly advantageous for FELs. Conventional and exotic methods of producing such correlations are described. Practical difficulties associated with each of the conventional methods are described, although the nonconventional methods appear to hold promise.
Transverse-Longitudinal Phase-Space Manipulations and Correlations
Kim, Kwang-Je; Sessler, Andrew
2006-03-20
Manipulations on transverse and longitudinal phase-space distribution of an electron beam are discussed within the constraints imposed by symplectic conditions. A few examples are presented: transverse-longitudinal emittance exchange to improve performance of a high-gain free-electron laser (FEL) for hard x-rays, and the flat beam technique and its application to compact Terahertz devices and ultrashort-pulse generation. It is shown that emittance transfer to some degree would be advantageous for FELs and that introducing correlations would allow just such transfers. Also, it is shown that transverse-longitudinal correlations would be distinctly advantageous for FELs. Conventional and exotic methods of producing such correlations are described. Practical difficulties associated with each of the conventional methods are described, although the nonconventional methods appear to hold promise.
Phase-space noncommutative formulation of Ozawa's uncertainty principle
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Costa Dias, Nuno; Prata, João Nuno
2014-08-01
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.
Wigner phase space distribution via classical adiabatic switching.
Bose, Amartya; Makri, Nancy
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations. PMID:26395694
Nonlinear instabilities driven by coherent phase-space structures
NASA Astrophysics Data System (ADS)
Lesur, Maxime
2012-10-01
Coherent phase-space (PS) structures are an important feature of plasma turbulence. They can drive nonlinear instabilities [1], intermittency in drift-wave turbulence [2], and transport [3]. We aim at a comprehensive understanding of turbulence, not just as an ensemble of waves, as quasilinear theory implies, but as a mixture of coupled waves and localized structures. This work, which focuses on isolated PS structures, is a fundamental advance in this direction. We analyze the effects of self-binding negative fluctuations (PS holes) on stability, intermittency and anomalous resistivity, both analytically and numerically. We present a new theory which describes the growth of a hole or clump [4]. We find that PS holes grow nonlinearly, independently of linear stability. Numerical simulations clarify the physics of nonlinear instabilities in both subcritical and supercritical conditions. When many resonances are unstable, several holes can coalesce into one main macro-scale structure, which survives much longer than a quasilinear diffusion time, suggesting that it may be crucial to resolve phase-space turbulence in analytical and numerical studies of transport. These findings are applied to two fundamental paradigms of plasma physics: bump-on-tail instabilities in 1D electronic plasma and current-driven ion-acoustic instabilities electron-ion plasma. Our results expose important limits of routinely-used linear and quasilinear theories.[4pt] [1] T.H. Dupree, Phys. Fluids 15, 334 (1972); R.H. Berman et al., Phys. Rev. Lett. 48, 1249 (1982).[0pt] [2] P.W. Terry, P.H. Diamond, and T.S. Hahm, Phys. Fluids B 2, 2048 (1990).[0pt] [3] H. Biglari et al., Phys. Fluids 31, 2644 (1988); Y. Kosuga et al., Phys. Plasmas 18, 122305 (2011).[0pt] [4] M. Lesur, P.H. Diamond, submitted to Phys. Rev. Lett.
Wigner phase space distribution via classical adiabatic switching
Bose, Amartya; Makri, Nancy
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
An analytical phase-space model for tidal caustics
NASA Astrophysics Data System (ADS)
Sanderson, Robyn E.; Helmi, Amina
2013-10-01
The class of tidal features around galaxies known as `shells' or `umbrellas' comprises debris that has arisen from high-mass-ratio mergers with low-impact parameter; the nearly radial orbits of the debris give rise to a unique morphology, a universal density profile and a tight correlation between positions and velocities of the material. As such they are accessible to analytical treatment, and can provide a relatively clean system for probing the gravitational potential of the host galaxy. In this work, we present a simple analytical model that describes the density profile, phase-space distribution, and geometry of a shell and whose parameters are directly related to physical characteristics of the interacting galaxies. The model makes three assumptions: the orbit of the interacting galaxies is radial, the potential of the host galaxy at the shell radius is spherical and the satellite galaxy's initial velocity distribution is Maxwellian. We quantify the error introduced by the first two assumptions and show that selecting shells by their appearance on the sky is a sufficient basis to assume that these simplifications are valid. We further demonstrate that (1) given only an image of a shell, the radial gravitational force at the shell edge and the phase-space density of the satellite are jointly constrained, (2) combining the image with measurements of either point line-of-sight velocities or integrated-light spectra will yield an independent estimate of the gravitational force at a shell and (3) an independent measurement of this force is obtained for each shell observed around a given galaxy, potentially enabling a determination of the galactic mass distribution.
Wigner phase space distribution via classical adiabatic switching
NASA Astrophysics Data System (ADS)
Bose, Amartya; Makri, Nancy
2015-09-01
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Dynamics of Structures in Configuration Space and Phase Space: An Introductory Tutorial
NASA Astrophysics Data System (ADS)
Diamond, P. H.; Kosuga, Y.; Lesur, M.
2015-12-01
Some basic ideas relevant to the dynamics of phase space and real space structures are presented in a pedagogical fashion. We focus on three paradigmatic examples, namely; G. I. Taylor's structure based re-formulation of Rayleigh's stability criterion and its implications for zonal flow momentum balance relations; Dupree's mechanism for nonlinear current driven ion acoustic instability and its implication for anomalous resistivity; and the dynamics of structures in drift and gyrokinetic turbulence and their relation to zonal flow physics. We briefly survey the extension of mean field theory to calculate evolution in the presence of localized structures for regimes where Kubo number K ≃ 1 rather than K ≪ 1, as is usual for quasilinear theory.
A varying polytropic gas universe and phase space analysis
NASA Astrophysics Data System (ADS)
Khurshudyan, M.
2016-05-01
In this paper, we will consider a phenomenological model of a dark fluid that is able to explain an accelerated expansion of our low redshift universe and the phase transition to this accelerated expanding universe. Recent developments in modern cosmology towards understanding of the accelerated expansion of the large scale universe involve various scenarios and approaches. Among these approaches, one of well-known and accepted practice is modeling of the content of our universe via dark fluid. There are various models of dark energy fluid actively studied in recent literature and polytropic gas is among them. In this work, we will consider a varying polytropic gas which is a phenomenological modification of polytropic gas. Our model of varying polytropic dark fluid has been constructed to analogue to a varying Chaplygin gas actively discussed in the literature. We will consider interacting models, where dark matter is a pressureless fluid, to have a comprehensive picture. Phase space analysis is an elegant mathematical tool to earn general understanding of large scale universe and easily see an existence of a solution to cosmological coincidence problem. Imposing some constraints on parameters of the models, we found late time attractors for each case analytically. Cosmological consequences for the obtained late time attractors are discussed.
Quantum trajectories in complex phase space: multidimensional barrier transmission.
Wyatt, Robert E; Rowland, Brad A
2007-07-28
The quantum Hamilton-Jacobi equation for the action function is approximately solved by propagating individual Lagrangian quantum trajectories in complex-valued phase space. Equations of motion for these trajectories are derived through use of the derivative propagation method (DPM), which leads to a hierarchy of coupled differential equations for the action function and its spatial derivatives along each trajectory. In this study, complex-valued classical trajectories (second order DPM), along which is transported quantum phase information, are used to study low energy barrier transmission for a model two-dimensional system involving either an Eckart or Gaussian barrier along the reaction coordinate coupled to a harmonic oscillator. The arrival time for trajectories to reach the transmitted (product) region is studied. Trajectories launched from an "equal arrival time surface," defined as an isochrone, all reach the real-valued subspace in the transmitted region at the same time. The Rutherford-type diffraction of trajectories around poles in the complex extended Eckart potential energy surface is described. For thin barriers, these poles are close to the real axis and present problems for computing the transmitted density. In contrast, for the Gaussian barrier or the thick Eckart barrier where the poles are further from the real axis, smooth transmitted densities are obtained. Results obtained using higher-order quantum trajectories (third order DPM) are described for both thick and thin barriers, and some issues that arise for thin barriers are examined. PMID:17672677
Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis
2004-10-15
We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture.
NASA Astrophysics Data System (ADS)
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
Singularities for PRANDTL'S Equations
NASA Astrophysics Data System (ADS)
Lo Bosco, G.; Sammartino, M.; Sciacca, V.
2006-03-01
We use a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our tool is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformly bounded in H1.
NASA Astrophysics Data System (ADS)
Rowlands, Peter
2013-09-01
Physics at the fundamental level can be effectively reduced to an explanation of the structures and interactions of fermions. Fermions appear to be singularities rather than extended objects, but there is no obvious way of creating such structures within the 3-dimensional space of observation. However, the algebra associated with the Dirac equation appears to suggest that the fermion requires a double, rather than a single, vector space, and this would seem to be confirmed by the double rotation required by spin 1/2 objects, and the associated effects of zitterberwegung and Berry phase shift. Further investigation of the second `space' reveals that it is, in effect, an `antispace', which contains the same information as real space but in a less accessible form. The two spaces effectively cancel to produce a norm 0 (nilpotent) object which has exactly the mathematical structure required to be a fermionic singularity.
Sanpei, Akio; Soga, Yukihiro; Ito, Kiyokazu; Himura, Haruhiko
2015-06-29
A trilinear phase space analysis is applied for dynamics of three electron clumps confined with a Penning-Malmberg trap. We show that the Aref’s concept of phase space describe the observed features of the dynamics of three point vortices qualitatively. In vacuum, phase point P moves to physical region boundary in phase space, i.e. triangular configuration cannot be kept. With the addition of a low level background vorticity distribution (BGVD), the excursion of the clumps is reduced and the distance between P and stable point does not extend in the phase space.
An Analytical Singularity-Free Solution to the J2 Perturbation Problem
NASA Technical Reports Server (NTRS)
Bond, V. R.
1979-01-01
The development of a singularity-free solution of the J2 problem in satellite theory is presented. The procedure resembles that of Lyndane who rederives Brouwer's satellite theory using Poincare elements. A comparable procedure is used in this report in which the satellite theory of Scheifele, who used elements similar to the Delaunay elements but in the extended phase space, is rederived using Poincare elements also in the extended phase space. Only the short-period effects due to J2 are included.
Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence
Tatsuno, T.; Dorland, W.; Plunk, G. G.; Schekochihin, A. A.; Barnes, M.
2009-07-03
Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.
Singular Lorentz-violating Lagrangians and associated Finsler structures
NASA Astrophysics Data System (ADS)
Colladay, Don; McDonald, Patrick
2015-10-01
Several Lagrangians associated with classical limits of Lorentz-violating fermions in the standard model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin couplings are present, the Lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive-definite quadratic form defined on a desingularized variety.
Dimensional Mutation and Spacelike Singularities
Silverstein, Eva; /SLAC /Stanford U., Phys. Dept.
2005-10-28
I argue that critical string theory on a Riemann surface of genus h >> 1 crosses over, when the surface approaches the string scale in size, to a background of supercritical string theory with effective central charge as large as 2h. Concrete evidence for this proposal is provided by the high energy density of states (realized on the Riemann surface side by strings wrapping nontrivial elements of the fundamental group) and by a linear sigma model which at large h approximates the time evolution through the initial transition. This suggests that cosmological singularities arising in negatively curved FRW backgrounds may be replaced by a phase of supercritical string theory.
Timelike BKL singularities and chaos in AdS/CFT
NASA Astrophysics Data System (ADS)
Shaghoulian, Edgar; Wang, Huajia
2016-06-01
We study the nature of a family of curvature singularities which are precisely the timelike cousins of the spacelike singularities studied by Belinski, Khalatnikov, and Lifshitz (BKL). We show that the approach to the singularity can be modeled by a billiard ball problem on hyperbolic space, just as in the case of BKL. For pure gravity, generic chaotic behavior is retained in (3 + 1) dimensions, and we provide evidence that it disappears in higher dimensions. We speculate that such singularities, if occurring in AdS/CFT and of the chaotic variety, may be interpreted as (transient) chaotic renormalization group flows which exhibit features reminiscent of chaotic duality cascades.
Phase space optics: an engineering tool for illumination design
NASA Astrophysics Data System (ADS)
Herkommer, Alois M.; Rausch, Denise
2012-06-01
For imaging design aberration theory provides solid ground for the layout and development of optical systems. Together with general design rules it will guide the optical engineer towards a valid starting point for his system. Illumination design is quite different: Often first system layouts are based on experience, rather than on a systematic approach. In addition radiometric nomenclature and definitions can be quite confusing, due to the variety of radiant performance definitions. Also at a later stage in the design, the performance evaluation usually requires extensive statistical raytracing, in order to confirm the specified energetic quantities. In general it would therefore be helpful for illumination designers, especially beginners, to have an engineering tool, which allows a fast, systematic and illustrative access to illumination design problems. We show that phase space methods can provide such a tool and moreover allow a consistent approach to radiometry. Simple illustrative methods can be used to layout and understand even complex illumination components like integrator rods and optical arrays.
Phase Space Dissimilarity Measures for Structural Health Monitoring
Bubacz, Jacob A; Chmielewski, Hana T; Pape, Alexander E; Depersio, Andrew J; Hively, Lee M; Abercrombie, Robert K; Boone, Shane
2011-11-01
A novel method for structural health monitoring (SHM), known as the Phase Space Dissimilarity Measures (PSDM) approach, is proposed and developed. The patented PSDM approach has already been developed and demonstrated for a variety of equipment and biomedical applications. Here, we investigate SHM of bridges via analysis of time serial accelerometer measurements. This work has four aspects. The first is algorithm scalability, which was found to scale linearly from one processing core to four cores. Second, the same data are analyzed to determine how the use of the PSDM approach affects sensor placement. We found that a relatively low-density placement sufficiently captures the dynamics of the structure. Third, the same data are analyzed by unique combinations of accelerometer axes (vertical, longitudinal, and lateral with respect to the bridge) to determine how the choice of axes affects the analysis. The vertical axis is found to provide satisfactory SHM data. Fourth, statistical methods were investigated to validate the PSDM approach for this application, yielding statistically significant results.
Phase-space estimate of satellite coverage time
Canavan, G.H.
1992-05-01
This note derives a phase-space estimate of the overlap in satellite coverage and evaluates its impact on the time for a constellation to cover some specified area. The satellites` motion is treated as random in the calculation of the overlaps. Enough passes are prescribed to assure that an adequate probability of observing each area is accumulated. For 0.9--0.99 probabilities of coverage, overlaps increase the time for coverage by factors of 2--4 over no-overlap estimates. This model also gives the probability of different vintages of data. If a given constellation covers the whole Earth in the no-overlap time T{sub 0}, the average vintage of the data over the earth will then be the average
Phase-space estimate of satellite coverage time
Canavan, G.H.
1992-05-01
This note derives a phase-space estimate of the overlap in satellite coverage and evaluates its impact on the time for a constellation to cover some specified area. The satellites' motion is treated as random in the calculation of the overlaps. Enough passes are prescribed to assure that an adequate probability of observing each area is accumulated. For 0.9--0.99 probabilities of coverage, overlaps increase the time for coverage by factors of 2--4 over no-overlap estimates. This model also gives the probability of different vintages of data. If a given constellation covers the whole Earth in the no-overlap time T{sub 0}, the average vintage of the data over the earth will then be the average
Phase-space dissimilarity measures for industrial and biomedical applications
NASA Astrophysics Data System (ADS)
Protopopescu, V. A.; Hively, L. M.
2005-12-01
One of the most important problems in time-series analysis is the suitable characterization of the dynamics for timely, accurate, and robust condition assessment of the underlying system. Machine and physiological processes display complex, non-stationary behaviors that are affected by noise and may range from (quasi-)periodic to completely irregular (chaotic) regimes. Nevertheless, extensive experimental evidence indicates that even when the systems behave very irregularly (e.g., severe tool chatter or cardiac fibrillation), one may assume that - for all practical purposes - the dynamics are confined to low dimensional manifolds. As a result, the behavior of these systems can be described via traditional nonlinear measures (TNM), such as Lyapunov exponents, Kolmogorov entropy, and correlation dimension. While these measures are adequate for discriminating between clear-cut regular and chaotic dynamics, they are not sufficiently sensitive to distinguish between slightly different irregular (chaotic) regimes, especially when data are noisy and/or limited. Both machine and physiological dynamics usually fall into this latter category, creating a massive stumbling block to prognostication of abnormal regimes. We present here a recently developed approach that captures more efficiently changes in the underlying dynamics. We start with process-indicative, time-serial data that are checked for quality and discarded if inadequate. Acceptable data are filtered to remove confounding artifacts (e.g., sinusoidal variation in three-phase electrical signals or eye-blinks and muscular activity in EEG). The artifact-filtered data are then used to recover the essential features of the underlying dynamics via standard time-delay, phase-space reconstruction. One of the main results of this reconstruction is a discrete approximation of the distribution function (DF) on the attractor. Unaltered dynamics yield an unchanging geometry of the attractor and the visitation frequencies of
Computational methods for microfluidic microscopy and phase-space imaging
NASA Astrophysics Data System (ADS)
Pegard, Nicolas Christian Richard
Modern optical devices are made by assembling separate components such as lenses, objectives, and cameras. Traditionally, each part is optimized separately, even though the trade-offs typically limit the performance of the system overall. This component-based approach is particularly unfit to solve the new challenges brought by modern biology: 3D imaging, in vivo environments, and high sample throughput. In the first part of this thesis, we introduce a general method to design integrated optical systems. The laws of wave propagation, the performance of available technology, as well as other design parameters are combined as constraints into a single optimization problem. The solution provides qualitative design rules to improve optical systems as well as quantitative task-specific methods to minimize loss of information. Our results have applications in optical data storage, holography, and microscopy. The second part of this dissertation presents a direct application. We propose a more efficient design for wide-field microscopy with coherent light, based on double transmission through the sample. Historically, speckle noise and aberrations caused by undesired interferences have made coherent illumination unpopular for imaging. We were able to dramatically reduce speckle noise and unwanted interferences using optimized holographic wavefront reconstruction. The resulting microscope not only yields clear coherent images with low aberration---even in thick samples---but also increases contrast and enables optical filtering and in-depth sectioning. In the third part, we develop new imaging techniques that better respond to the needs of modern biology research through implementing optical design optimization. Using a 4D phase-space distribution, we first represent the state and propagation of incoherent light. We then introduce an additional degree of freedom by putting samples in motion in a microfluidic channel, increasing image diversity. From there, we develop a
An Effective Method to Accurately Calculate the Phase Space Factors for β - β - Decay
Neacsu, Andrei; Horoi, Mihai
2016-01-01
Accurate calculations of the electron phase space factors are necessary for reliable predictions of double-beta decay rates and for the analysis of the associated electron angular and energy distributions. We present an effective method to calculate these phase space factors that takes into account the distorted Coulomb field of the daughter nucleus, yet it allows one to easily calculate the phase space factors with good accuracy relative to the most exact methods available in the recent literature.
On the Group of Translations and Inversions of Phase Space and the Wigner Functions
NASA Astrophysics Data System (ADS)
Dahl, Jens Peder
1982-04-01
Grossmann and Royer have recently shown that the Wigner functions are closely related to the set of all translations and inversions of phase space. This allows the phase space representation of quantum mechanics to be constructed directly on the group of phase space translations and inversions. Starting from this observation, we have derived analytical expressions for the matrix elements of the translation and inversion operators, in the harmonic oscillator representation, without introducing coordinate or momentum wavefunctions.
Phase-locked laser array having a non-uniform spacing between lasing regions
NASA Technical Reports Server (NTRS)
Ackley, Donald E. (Inventor)
1986-01-01
A phase-locked semiconductor array wherein the lasing regions of the array are spaced an effective distance apart such that the modes of oscillation of the different lasing regions are phase-locked to one another. The center-to-center spacing between the lasing regions is non-uniform. This variation in spacing perturbs the preferred 180.degree. phase difference between adjacent lasing regions thereby providing an increased yield of arrays exhibiting a single-lobed, far-field radiation pattern.
On coherent-state representations of quantum mechanics: Wave mechanics in phase space
NASA Astrophysics Data System (ADS)
Møller, Klaus B.; Jørgensen, Thomas G.; Torres-Vega, Gabino
1997-05-01
In this article we argue that the state-vector phase-space representation recently proposed by Torres-Vega and co-workers [introduced in J. Chem. Phys. 98, 3103 (1993)] coincides with the totality of coherent-state representations for the Heisenberg-Weyl group. This fact leads to ambiguities when one wants to solve the stationary Schrödinger equation in phase space and we devise two schemes for the removal of these ambiguities. The physical interpretation of the phase-space wave functions is discussed and a procedure for computing expectation values as integrals over phase space is presented. Our formal points are illustrated by two examples.
Singular Continuations of Attractors
NASA Astrophysics Data System (ADS)
Giraldo, A.; Sanjurjo, J. M. R.
2009-01-01
We study dynamical and topological properties of the singularities of continuations of attractors of flows on manifolds. Despite the fact that these singularities are not isolated invariant sets, they share many of the properties of attractors; in particular, they have finitely generated Čech homology and cohomology, and they have the Čech homotopy type of attractors. This means that, from a global point of view, the singularities of continuations are topological objects closely related to finite polyhedra. The global structure is preserved even for weaker forms of continuation. An interesting case occurs with the Lorenz system for parameter values close to the situation of preturbulence. A general result, motivated by this particular case, is presented.
NASA Astrophysics Data System (ADS)
Gil, José J.; Ossikovski, Razvigor; José, Ignacio San
2016-04-01
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical depolarizer has the property of fully randomizing, the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, of potential usefulness to experimentalists dealing with such media.
Gil, José J; Ossikovski, Razvigor; José, Ignacio San
2016-04-01
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance or because its associated canonical depolarizer has the property of fully randomizing the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed, and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, which are of potential usefulness to experimentalists dealing with such media. PMID:27140769
Mirror Symmetry for Quasi-Homogeneous Singularities
NASA Astrophysics Data System (ADS)
Rathnakumara, Himal; Jarvis, Tyler
2008-10-01
I will present an introduction to mirror symmetry in the context of string theory. Then I will describe an instance of mirror symmetry for singularties defined by quasi-homogeneous polynomials in weighted projective spaces. Milnor rings and the FJRW (Fan-Jarvis-Ruan-Witten) rings associated with these singularities and their relation to the Landua-Ginzburg A model and the Landua-Ginzburg B model will be explained. Results of the calculations for certain singularities for which the mirror symmetry conjecture has been verified will be presented.
Singular Dimensions of theN= 2 Superconformal Algebras. I
NASA Astrophysics Data System (ADS)
Dörrzapf, Matthias; Gato-Rivera, Beatriz
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3).
NASA Technical Reports Server (NTRS)
1984-01-01
The large space structures technology development missions to be performed on an early manned space station was studied and defined and the resources needed and the design implications to an early space station to carry out these large space structures technology development missions were determined. Emphasis is being placed on more detail in mission designs and space station resource requirements.
Slow Dynamics Due to Singularities of Hierarchical Learning Machines
NASA Astrophysics Data System (ADS)
Inoue, H. P. M.; Okada, M.
Recently, slow dynamics in learning ofneural networks has been known to be closely related to singularities, which exist in parameter spaces of hierarchical learning models. To show the influence of singular structure on learning dynamics, we take statistical mechanical approaches and investigate online-learning dynamics under various learning scenario with different relationship between optimum and singularities. From the investigation, we found a quasi-plateau phenomenon which differs from the well known plateau. The quasi-plateau and plateau become extremely serious when an optimal point is in a neighborhood of a singularity. The quasi-plateau and plateau disappear in the natural gradient learning, which takes singular structures into account and uses Riemannian measure for the parameter space.
Generalised partition functions: inferences on phase space distributions
NASA Astrophysics Data System (ADS)
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.
Kalay, Berfin; Demiralp, Metin
2015-03-10
This work is a new extension to our a very recent work whose paper will appear in the proceedings of a very recent international conference. What we have done in the previous work is the use of a weight operator to suppress the singularities causing nonexistence of some of temporal Maclaurin expansion coefficients. The weight operator has been constructed in such a way that certain number of expectation values of position operator’s first positive integer powers with and without the chosen weight operator match. Therein this match has not been considered for the momentum operator’s corresponding power expectation values and a finite linear combination of the spatial variable’s first reciprocal powers has been used in the construction of the weight operator. Here, that approach is extended to the case where matches for both position and momentum operators are considered and the weight operator involves finite linear combinations of the spatial variable’s both positive integer powers and their reciprocals.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Selected tether applications in space: Phase 2. Executive summary
NASA Technical Reports Server (NTRS)
Thorson, M. H.; Lippy, L. J.
1985-01-01
The application of tether technology has the potential to increase the overall performance efficiency and capability of the integrated space operations and transportation systems through the decade of the 90s. The primary concepts for which significant economic benefits were identified are dependent on the space station as a storage device for angular momentum and as an operating base for the tether system. Concepts examined include: (1) tether deorbit of shuttle from space station; (2) tethered orbit insertion of a spacecraft from shuttle; (3) tethered platform deployed from space station; (4) tether-effected rendezvous of an OMV with a returning OTV; (5) electrodynamic tether as an auxiliary power source for space station; and (6) tether assisted launch of an OTV mission from space station.
Singular Vectors' Subtle Secrets
ERIC Educational Resources Information Center
James, David; Lachance, Michael; Remski, Joan
2011-01-01
Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.
Weyl Calculus in Phase Space and the Torres-Vega and Frederick Equation
Gosson, Maurice de
2006-01-04
We show that the Schroedinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of Weyl calculus provided that one lets Heisenberg-Weyl operators act on functions (or half-densities) defined on phase space. We interpret our results in terms of deformation quantization.
Deformed phase space Kaluza-Klein cosmology and late time acceleration
NASA Astrophysics Data System (ADS)
Sabido, M.; Yee-Romero, C.
2016-06-01
The effects of phase space deformations on Kaluza-Klein cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables. In the deformed model, we find an accelerating scale factor and therefore infer the existence of an effective cosmological constant from the phase space deformation parameter β.
Analysis of local ionospheric time varying characteristics with singular value decomposition
NASA Astrophysics Data System (ADS)
Jakobsen, Jakob; Knudsen, Per; Jensen, Anna B. O.
2010-07-01
In this paper, a time series from 1999 to 2007 of absolute total electron content (TEC) values has been computed and analyzed using singular value decomposition (SVD). The data set has been computed using a Kalman Filter and is based on dual frequency GPS data from three reference stations in Denmark located in the midlatitude region. The station separation between the three stations is 132-208 km (the time series of the TEC can be freely downloaded at
NASA Astrophysics Data System (ADS)
Heiblum, Reuven H.; Altaratz, Orit; Koren, Ilan; Feingold, Graham; Kostinski, Alexander B.; Khain, Alexander P.; Ovchinnikov, Mikhail; Fredj, Erick; Dagan, Guy; Pinto, Lital; Yaish, Ricki; Chen, Qian
2016-06-01
We study the evolution of warm convective cloud fields using large eddy simulations of continental and trade cumulus. Individual clouds are tracked a posteriori from formation to dissipation using a 3-D cloud-tracking algorithm, and results are presented in the phase space of center of gravity altitude versus cloud liquid water mass (CvM space). The CvM space is shown to contain rich information on cloud field characteristics, cloud morphology, and common cloud development pathways, together facilitating a comprehensive understanding of the cloud field. In this part we show how the meteorological (thermodynamic) conditions that determine the cloud properties are projected on the CvM phase space and how changes in the initial conditions affect the clouds' trajectories in this space. This part sets the stage for a detailed microphysical analysis that will be shown in part II.
Unfolding the singularities in superspace
NASA Astrophysics Data System (ADS)
Fischer, Arthur E.
1983-12-01
A method is described for unfolding the singularities in superspace,mathcal{G} = mathfrak{M}/mathfrak{D}, the space of Riemannian geometries of a manifoldM. This unfolded superspace is described by the projection mathcal{G}_{Fleft( M right)} = {mathfrak{M} × Fleft( M right)}/mathfrak{D} to mathfrak{M}/mathfrak{D} = mathcal{G} whereF(M) is the frame bundle ofM. The unfolded spacemathcal{G}_{Fleft( M right)} is infinite-dimensional manifold without singularities. Moreover, as expected, the unfolding ofmathcal{G}_{Fleft( M right)} at each geometry [g o] ∈mathcal{G} is parameterized by the isometry groupIg o (M) of g0. Our construction is natural, is generally covariant with respect to all coordinate transformations, and gives the necessary information at each geometry to makemathcal{G} a manifold. This construction is a canonical and geometric model of a nonrelativistic construction that unfolds superspace by restricting to those coordinate transformations that fix a frame at a point. These particular unfoldings are tied together by an infinite-dimensional fiber bundleE overM, associated with the frame bundleF(M), with standard fibermathcal{G}_{Fleft( M right)}, and with fiber at a point inM being the particular noncanonical unfolding ofmathcal{G} based at that point. ThusE is the totality of all the particular unfoldings, and so is a grand unfolding ofmathcal{G}.
Common features in phase-space networks of frustrated spin models and lattice-gas models
NASA Astrophysics Data System (ADS)
Wang, Feng; Peng, Yi; Han, Yilong
2012-02-01
We mapped the phase spaces of the following four models into networks: (1a) the Ising antiferromagnet on triangular lattice at the ground state and (1b) above the ground state, (2) the six-vertex model (i.e. square ice or spin ice), (3) 1D lattice gas and (4) 2D lattice gas. Their phase-space networks share some common features including the Gaussian degree distribution, the Gaussian spectral density, and the small-world properties. Models 1a, 2 and 3 with long-range correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range correlations in real space exhibit non-fractal phase spaces. This result supports one of the untested assumptions in Tsallis's non-extensive statistics.
Cosmic evolution from phase transition of three-dimensional flat space.
Bagchi, Arjun; Detournay, Stephane; Grumiller, Daniel; Simón, Joan
2013-11-01
Flat space cosmology spacetimes are exact time-dependent solutions of three-dimensional gravity theories, such as Einstein gravity or topologically massive gravity. We exhibit a novel kind of phase transition between these cosmological spacetimes and the Minkowski vacuum. At sufficiently high temperature, (rotating) hot flat space tunnels into a universe described by flat space cosmology. PMID:24237503
Trajectories and causal phase-space approach to relativistic quantum mechanics
Holland, P.R.; Kyprianidis, A.; Vigier, J.P.
1987-05-01
The authors analyze phase-space approaches to relativistic quantum mechanics from the viewpoint of the causal interpretation. In particular, they discuss the canonical phase space associated with stochastic quantization, its relation to Hilbert space, and the Wigner-Moyal formalism. They then consider the nature of Feynman paths, and the problem of nonlocality, and conclude that a perfectly consistent relativistically covariant interpretation of quantum mechanics which retains the notion of particle trajectory is possible.
Integrated study plan for space bioprocessing (phase 1)
NASA Technical Reports Server (NTRS)
1977-01-01
Current economic evaluation and analytical techniques are applied to decision problems faced by the space bioprocessing program. NASA decision makers are enabled to choose candidate substances, after ranking them according to their potential economic benefit. The determination of appropriate evaluation techniques necessary to obtain measures of potential economic benefits which result from the pursuit of various space bioprocessing endeavors are focused upon. The treatment of each disease is impacted by a successful outcome of space bioprocessing and specify data and other input needs for each candidate substance.
Space Station Freedom - Approaching the critical design phase
NASA Technical Reports Server (NTRS)
Kohrs, Richard H.; Huckins, Earle, III
1992-01-01
The status and future developments of the Space Station Freedom are discussed. To date detailed design drawings are being produced to manufacture SSF hardware. A critical design review (CDR) for the man-tended capability configuration is planned to be performed in 1993 under the SSF program. The main objective of the CDR is to enable the program to make a full commitment to proceed to manufacture parts and assemblies. NASA recently signed a contract with the Russian space company, NPO Energia, to evaluate potential applications of various Russian space hardware for on-going NASA programs.
Geometric phase in a flat space for electromagnetic scalar waves.
Luis, Alfredo
2006-08-15
We show the existence of a fundamental geometric phase for classical electromagnetic fields arising after cyclic paths in a plane instead of a sphere. This phase is dispersive, is not related to polarization, distinguishes geometrical from wave optics, and can be easily measured in an interferometric arrangement. PMID:16880859
On the limit cycles of a class of planar singular perturbed differential equations.
Wu, Yuhai; Zhou, Jingjing
2014-01-01
Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. PMID:25143973
On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
Zhou, Jingjing
2014-01-01
Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. PMID:25143973
Research opportunities in space motion sickness, phase 2
NASA Technical Reports Server (NTRS)
Talbot, J. M.
1983-01-01
Space and motion sickness, the current and projected NASA research program, and the conclusions and suggestions of the ad hoc Working Group are summarized. The frame of reference for the report is ground-based research.
Space station gas compressor technology study program, phase 1
NASA Technical Reports Server (NTRS)
Hafele, B. W.; Rapozo, R. R.
1989-01-01
The objectives were to identify the space station waste gases and their characteristics, and to investigate compressor and dryer types, as well as transport and storage requirements with tradeoffs leading to a preliminary system definition.
Space shuttle auxiliary power unit study, phase 2
NASA Technical Reports Server (NTRS)
Binsley, R. L.; Krause, A. A.; Maddox, R. D.; Marcy, R. D.; Siegler, R. S.
1972-01-01
A study was performed to establish the preliminary design of the space shuttle auxiliary power unit. Details of the analysis, optimizations, and design of the components, subsystems and systems are presented.
NASA Astrophysics Data System (ADS)
Mitra, Abhas
2009-04-01
We point out that the space-time void inferred by Castro [J. Math. Phys. 49, 042501 (2008)] results from his choice of a discontinuous radial gauge. Further since the integration constant α0=2M0 (G =c=1) occurring in the vacuum Hilbert/Schwarzschild solution of a neutral "point mass" is zero [Arnowitt et al., in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), Chap. 7, p. 227; also Phys. Rev. Lett. 4, 375 (1960). A. Mitra, Adv. Space Res. 38, 2917 (2006); Proceedings of the XIth Marcel-Grossmann Conference on General Relativity (World Scientific, Singapore, 2008), Vol. 3, p. 1968], Castro's gauge reduces to the well behaved and physical Hilbert gauge. Physically this means that true Hilbert/Schwarzschild black holes have unique gravitational mass M =0. Accordingly, the unphysical space-time void inferred by Castro is actually nonexistent.
New singularities in unexpected places
NASA Astrophysics Data System (ADS)
Barrow, John D.; Graham, Alexander A. H.
2015-09-01
Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe.
Multimegawatt space nuclear power supply: Phase 1, Final report
Not Available
1989-02-17
The preliminary safety assessment report analyzes the potential radiological risk of the integrated MSNPS with the launch vehicle including interface with the weapon system. Most emphasis will be placed the prime power concept design. Safety problems can occur any time during the entire life cycle of the system including contingency phases. The preliminary safety assessment report is to be delivered at the end of phase 2. This assessment will be the basis of the safety requirements which will be applied to the design of the MSNPS as it develops in subsequent phases. The assessment also focuses design activities on specific high-risk scenarios and missions that may impact safety.
NASA Astrophysics Data System (ADS)
Duplij, Steven
2015-09-01
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number of velocities) is proposed. The equations of motion become first-order differential equations, and they coincide with those of multi-time dynamics, if a certain condition is imposed. In a singular theory, this condition is fulfilled in the case of the coincidence of the number of generalized momenta with the rank of the Hessian matrix. The noncanonical generalized velocities satisfy a system of linear algebraic equations, which allows an appropriate classification of singular theories (gauge and nongauge). A new antisymmetric bracket (similar to the Poisson bracket) is introduced, which describes the time evolution of physical quantities in a singular theory. The origin of constraints is shown to be a consequence of the (unneeded in our formulation) extension of the phase space, when the new bracket transforms into the Dirac bracket. Quantization is briefly discussed.
Multimegawatt space nuclear power supply: Phase 1, Final report
Not Available
1989-02-17
The Phase 2 program objectives are to (1) demonstrate concept feasibility, (2) develop a preliminary design, and (3) complete Phase 3 engineering development and ground test plans. The approach to accomplish these objectives is to prove technical feasibility of our baseline design early in the program while maintaining flexibility to easily respond to changing requirements and advances in technology. This approach recognizes that technology is advancing rapidly while the operational phase MSNPS is 15 to 20 years in the future. This plan further recognizes that the weapons platform and Advanced Launch System (ALS) are in very early program definition stages; consequently, their requirements, interfaces, and technological basis will evolve. This document outlines the Phase 2 plan along with task scheduling of the various program aspects.
NASA Astrophysics Data System (ADS)
Pavelko, A. A.; Shilkina, L. A.; Reznichenko, L. A.; Dudkina, S. I.; Andryushina, I. N.; Yurasov, Yu. I.; Andryushin, K. P.; Razumovskaya, O. N.
2015-12-01
The boundaries of the phase states of solid solutions in the rhombohedral region of the Pb(Zr1‒ x Ti x )O3 (0 ≤ x ≤ 1.00) system and the curve of the R3 c → R3 m phase transition have been refined on the basis of detailed (with a small concentration step) high-temperature (25°C ≤ T ≤ 700°C) studies of the structural characteristics and frequencies of the piezoelectric resonance of the radial oscillation mode of polarized ceramic samples. It has been shown that, in the range 0.07 ≤ x ≤ 0.20, the transition curve practically coincides with the generally accepted one and, in the interval 0.20 ≤ x ≤ 0.36, it differs from the latter by a nonmonotonic behavior and agrees in the boundaries and regions of the phase states. The curve of the transition from the region of coexistence of the R- and Rh 1-phases in the clusterized state to a region with single Rh 1-phase in the interval of concentrations 0.08 ≤ x ≤ 0.12 and temperatures 200-250°C has been constructed. The full x- T phase diagram of the Pb(Zr1- x Ti x )O3 system has been presented. Dispersion spectra of solid solutions on variation in the frequency of the measuring electric field in the interval of 25-106 Hz have been studied, and their correlation with singularities of the phase portrait has been established.
Space station contamination control study: Internal combustion, phase 1
NASA Technical Reports Server (NTRS)
Ruggeri, Robert T.
1987-01-01
Contamination inside Space Station modules was studied to determine the best methods of controlling contamination. The work was conducted in five tasks that identified existing contamination control requirements, analyzed contamination levels, developed outgassing specification for materials, wrote a contamination control plan, and evaluated current materials of offgassing tests used by NASA. It is concluded that current contamination control methods can be made to function on the Space Station for up to 1000 days, but that current methods are deficient for periods longer than about 1000 days.
Discrete phase-space structure of n-qubit mutually unbiased bases
Klimov, A.B.; Romero, J.L.; Bjoerk, G.; Sanchez-Soto, L.L.
2009-01-15
We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2{sup n}) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.
Large space telescope, phase A. Volume 3: Optical telescope assembly
NASA Technical Reports Server (NTRS)
1972-01-01
The development and characteristics of the optical telescope assembly for the Large Space Telescope are discussed. The systems considerations are based on mission-related parameters and optical equipment requirements. Information is included on: (1) structural design and analysis, (2) thermal design, (3) stabilization and control, (4) alignment, focus, and figure control, (5) electronic subsystem, and (6) scientific instrument design.
Space radiation hazards to Project Skylab photographic film, phase 2
NASA Technical Reports Server (NTRS)
Hill, C. W.; Neville, C. F.
1971-01-01
The results of a study of space radiation hazards to Project Skylab photographic film are presented. Radiation components include trapped protons, trapped electrons, bremsstrahlung, and galactic cosmic radiation. The shielding afforded by the Skylab cluster is taken into account with a 5000 volume element mathematical model. A preliminary survey of expected proton spectrometer data is reported.
Large space telescope, phase A. Volume 4: Scientific instrument package
NASA Technical Reports Server (NTRS)
1972-01-01
The design and characteristics of the scientific instrument package for the Large Space Telescope are discussed. The subjects include: (1) general scientific objectives, (2) package system analysis, (3) scientific instrumentation, (4) imaging photoelectric sensors, (5) environmental considerations, and (6) reliability and maintainability.
Large space telescope, phase A. Volume 5: Support systems module
NASA Technical Reports Server (NTRS)
1972-01-01
The development and characteristics of the support systems module for the Large Space Telescope are discussed. The following systems and described: (1) thermal control, (2) electrical, (3) communication and data landing, (4) attitude control system, and (5) structural features. Analyses of maintainability and reliability considerations are included.
Phase-space representation of a non-Hermitian system with PT symmetry
NASA Astrophysics Data System (ADS)
Praxmeyer, Ludmila; Yang, Popo; Lee, Ray-Kuang
2016-04-01
We present a phase-space study of a non-Hermitian Hamiltonian with PT symmetry based on the Wigner distribution function. For an arbitrary complex potential, we derive a generalized continuity equation for the Wigner function flow and calculate the related circulation values. Studying the vicinity of an exceptional point, we show that a PT -symmetric phase transition from an unbroken PT -symmetry phase to a broken one is a second-order phase transition.
Deep Space Habitat Concept of Operations for Transit Mission Phases
NASA Technical Reports Server (NTRS)
Hoffman, Stephen J.
2011-01-01
The National Aeronautics and Space Administration (NASA) has begun evaluating various mission and system components of possible implementations of what the U.S. Human Spaceflight Plans Committee (also known as the Augustine Committee) has named the flexible path (Anon., 2009). As human spaceflight missions expand further into deep space, the duration of these missions increases to the point where a dedicated crew habitat element appears necessary. There are several destinations included in this flexible path a near Earth asteroid (NEA) mission, a Phobos/Deimos (Ph/D) mission, and a Mars surface exploration mission that all include at least a portion of the total mission in which the crew spends significant periods of time (measured in months) in the deep space environment and are thus candidates for a dedicated habitat element. As one facet of a number of studies being conducted by the Human Spaceflight Architecture Team (HAT) a workshop was conducted to consider how best to define and quantify habitable volume for these future deep space missions. One conclusion reached during this workshop was the need for a description of the scope and scale of these missions and the intended uses of a habitat element. A group was set up to prepare a concept of operations document to address this need. This document describes a concept of operations for a habitat element used for these deep space missions. Although it may eventually be determined that there is significant overlap with this concept of operations and that of a habitat destined for use on planetary surfaces, such as the Moon and Mars, no such presumption is made in this document.
Equilibrium Phase Behavior of a Continuous-Space Microphase Former
NASA Astrophysics Data System (ADS)
Zhuang, Yuan; Zhang, Kai; Charbonneau, Patrick
2016-03-01
Periodic microphases universally emerge in systems for which short-range interparticle attraction is frustrated by long-range repulsion. The morphological richness of these phases makes them desirable material targets, but our relatively coarse understanding of even simple models hinders controlling their assembly. We report here the solution of the equilibrium phase behavior of a microscopic microphase former through specialized Monte Carlo simulations. The results for cluster crystal, cylindrical, double gyroid, and lamellar ordering qualitatively agree with a Landau-type free energy description and reveal the nontrivial interplay between cluster, gel, and microphase formation.
Transverse emittance and phase space program developed for use at the Fermilab A0 Photoinjector
Thurman-Keup, R.; Johnson, A.S.; Lumpkin, A.H.; Ruan, J.; /Fermilab
2011-03-01
The Fermilab A0 Photoinjector is a 16 MeV high intensity, high brightness electron linac developed for advanced accelerator R&D. One of the key parameters for the electron beam is the transverse beam emittance. Here we report on a newly developed MATLAB based GUI program used for transverse emittance measurements using the multi-slit technique. This program combines the image acquisition and post-processing tools for determining the transverse phase space parameters with uncertainties. An integral part of accelerator research is a measurement of the beam phase space. Measurements of the transverse phase space can be accomplished by a variety of methods including multiple screens separated by drift spaces, or by sampling phase space via pepper pots or slits. In any case, the measurement of the phase space parameters, in particular the emittance, can be drastically simplified and sped up by automating the measurement in an intuitive fashion utilizing a graphical interface. At the A0 Photoinjector (A0PI), the control system is DOOCS, which originated at DESY. In addition, there is a library for interfacing to MATLAB, a graphically capable numerical analysis package sold by The Mathworks. It is this graphical package which was chosen as the basis for a graphical phase space measurement system due to its combination of analysis and display capabilities.
NASA Astrophysics Data System (ADS)
Hajian, K.; Sheikh-Jabbari, M. M.
2016-02-01
We provide a general formulation for calculating conserved charges for solutions to generally covariant gravitational theories with possibly other internal gauge symmetries, in any dimensions and with generic asymptotic behaviors. These solutions are generically specified by a number of exact (continuous, global) symmetries and some parameters. We define "parametric variations" as field perturbations generated by variations of the solution parameters. Employing the covariant phase space method, we establish that the set of these solutions (up to pure gauge transformations) form a phase space, the solution phase space, and that the tangent space of this phase space includes the parametric variations. We then compute conserved charge variations associated with the exact symmetries of the family of solutions, caused by parametric variations. Integrating the charge variations over a path in the solution phase space, we define the conserved charges. In particular, we revisit "black hole entropy as a conserved charge" and the derivation of the first law of black hole thermodynamics. We show that the solution phase space setting enables us to define black hole entropy by an integration over any compact, codminesion-2, smooth spacelike surface encircling the hole, as well as to a natural generalization of Wald and Iyer-Wald analysis to cases involving gauge fields.
Singularities in Optimal Structural Design
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Guptill, J. D.; Berke, L.
1992-01-01
Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.
Singularities in optimal structural design
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Guptill, J. D.; Berke, L.
1992-01-01
Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.
EDITORIAL: The plurality of optical singularities
NASA Astrophysics Data System (ADS)
Berry, Michael; Dennis, Mark; Soskin, Marat
2004-05-01
This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the
Inflationary perturbation theory is geometrical optics in phase space
NASA Astrophysics Data System (ADS)
Seery, David; Mulryne, David J.; Frazer, Jonathan; Ribeiro, Raquel H.
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "δN" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Scaling and the start-up phase of space industrialization
NASA Technical Reports Server (NTRS)
Criswell, D. R.
1979-01-01
By terrestrial standards very little mass is needed to construct the space portion of a 10,000 megawatt (10 GW) power system. Use of lunar materials makes it reasonable to consider alternatives to silicon solar cells for conversion of sunlight to electricity and thereby avoid present major problems associated with solar cell production. Machinery needed on the moon to excavate lunar materials and deliver them to a transport system, to beneficiate lunar materials, to produce glasses and ceramics from lunar materials and to chemically process lunar materials into their major oxides and elements are minor mass fractions of the total mass of equipment needed in space to produce an SPS. In addition the processing equipment can throughput several hundred times their own mass each year with very little requirement for makeup mass from earth.
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Frazer, Jonathan; Mulryne, David J.; Ribeiro, Raquel H. E-mail: D.Mulryne@qmul.ac.uk E-mail: R.Ribeiro@damtp.cam.ac.uk
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ({sup t}ransport equations{sup )}, analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar 'δN' Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of f{sub NL} in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Painleve singularity analysis applied to charged particle dynamics during reconnection
Larson, J.W.
1992-01-01
For a plasma in the collisionless regime, test-particle modelling can lend some insight into the macroscopic behavior of the plasma, e.g. conductivity and heating. A common example for which this technique is used is a system with electric and magnetic fields given by B = [delta]yx + zy + yz and E = [epsilon]z, where [delta], [gamma], and [epsilon] are constant parameters. This model can be used to model plasma behavior near neutral lines, ([gamma] = 0), as well as current sheets ([gamma] = 0, [delta] = 0). The integrability properties of the particle motion in such fields might affect the plasma's macroscopic behavior, and the author has asked the question [open quotes]For what values of [delta], [gamma], and [epsilon] is the system integrable [close quotes] To answer this question, the author has employed Painleve singularity analysis, which is an examination of the singularity properties of a test particle's equations of motion in the complex time plane. This analysis has identified two field geometries for which the system's particle dynamics are integrable in terms of the second Painleve transcendent: the circular O-line case and the case of the neutral sheet configuration. These geometries yield particle dynamics that are integrable in the Liouville sense (i.e., there exist the proper number of integrals in involution) in an extended phase space which includes the time as a canonical coordinate, and this property is also true for nonzero [gamma]. The singularity property tests also identified a large, dense set of X-line and O-line field geometries that yield dynamics that may possess the weak Painleve property. In the case of the X-line geometries, this result shows little relevance to the physical nature of the system, but the existence of a dense set of elliptical O-line geometries with this property may be related to the fact that for [epsilon] positive, one can construct asymptotic solutions in the limit t [yields] [infinity].
Singular parabolic equations of second order on manifolds with singularities
NASA Astrophysics Data System (ADS)
Shao, Yuanzhen
2016-01-01
The main aim of this article is to establish an Lp-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the singular ends of the manifolds. Such a theory is of importance for the study of elliptic and parabolic equations on non-compact, or even incomplete manifolds, with or without boundary.
Modular space station phase B extension: Mass properties
NASA Technical Reports Server (NTRS)
Duffey, L. A.
1971-01-01
The MSS system, capable of supporting a six-man crew, is described as consisting of four common station modules, two special modules (core and power), and a cargo module arranged in a cruciform. The station buildup, and space station subsystems including environmental control life support, electrical power, guidance and control are also described. The MSS system weights are presented for design-to-weight, closeout weights, and shuttle payload weights.
Phase-space description of plasma waves. Part 1. Linear theory
NASA Astrophysics Data System (ADS)
Biro, T.; Rönnmark, K.
1992-06-01
We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.
Emittance and Phase Space Exchange for Advanced Beam Manipulation and Diagnostics
Xiang, Dao; Chao, Alex; /SLAC
2012-04-27
Alternative chicane-type beam lines are proposed for exact emittance exchange between transverse phase space (x,x') and longitudinal phase space (z,{delta}), where x is the transverse position, x' is the transverse divergence, and z and {delta} are relative longitudinal position and energy deviation with respect to the reference particle. Methods to achieve exact phase space exchanges, i.e., mapping x to z, x' to {delta}, z to x, and {delta} to x', are suggested. Schemes to mitigate and completely compensate for the thick-lens effect of the transverse cavity on emittance exchange are studied. Some applications of the phase space exchange for advanced beam manipulation and diagnostics are discussed.
Phase III Simplified Integrated Test (SIT) results - Space Station ECLSS testing
NASA Technical Reports Server (NTRS)
Roberts, Barry C.; Carrasquillo, Robyn L.; Dubiel, Melissa Y.; Ogle, Kathryn Y.; Perry, Jay L.; Whitley, Ken M.
1990-01-01
During 1989, phase III testing of Space Station Freedom Environmental Control and Life Support Systems (ECLSS) began at Marshall Space Flight Center (MSFC) with the Simplified Integrated Test. This test, conducted at the MSFC Core Module Integration Facility (CMIF), was the first time the four baseline air revitalization subsystems were integrated together. This paper details the results and lessons learned from the phase III SIT. Future plans for testing at the MSFC CMIF are also discussed.
Experimental method of optical coherence characterization in phase-space measurement
NASA Astrophysics Data System (ADS)
Li, Jie-En; Fu, Jhih-Syuan; Hsiao, Ming-Shu; Tien, Chung-Hao
2015-09-01
A novel approach of phase-space measurement made its debut with the experimental result. We first designed an experiment based on the Young's interferometer to characterization the optical coherence property of light source. A well-known algorithm called Hough transformation was applied to deal with the misalignment of micro-lens array by post-processing. The phase-space image of plane wave was then reconstructed from the realigned raw image. Finally, the properties of this system were discussed.
Multiple transition states and roaming in ion-molecule reactions: A phase space perspective
NASA Astrophysics Data System (ADS)
Mauguière, Frédéric A. L.; Collins, Peter; Ezra, Gregory S.; Farantos, Stavros C.; Wiggins, Stephen
2014-01-01
We provide a dynamical interpretation of the recently identified ‘roaming' mechanism for molecular dissociation reactions in terms of geometrical structures in phase space. These are NHIMs (Normally Hyperbolic Invariant Manifolds) and their stable/unstable manifolds that define transition states for ion-molecule association or dissociation reactions. The associated dividing surfaces rigorously define a roaming region of phase space, in which both reactive and non reactive trajectories can be trapped for arbitrarily long times.
Subpicosecond electron bunch train production using a phase-space exchange technique
Sun, Y.-E.; Piot, P.; Johnson, A.S.; Lumpkin, A.H.; Maxwell, T.J.; Ruan, J.; Thurman-Keup, R.M.; /Fermilab
2011-03-01
Our recent experimental demonstration of a photoinjector electron bunch train with sub-picosecond structures is reported in this paper. The experiment is accomplished by converting an initially horizontal beam intensity modulation into a longitudinal phase space modulation, via a beamline capable of exchanging phase-space coordinates between the horizontal and longitudinal degrees of freedom. The initial transverse modulation is produced by intercepting the beam with a multislit mask prior to the exchange. We also compare our experimental results with numerical simulations.
Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform.
Alieva, T; Bastiaans, M J
2000-12-01
The ambiguity function and Cohen's class of bilinear phase-space distributions are represented in a quasipolar coordinate system instead of in a Cartesian system. Relationships between these distributions and the fractional Fourier transform are derived; in particular, derivatives of the ambiguity function are related to moments of the fractional power spectra. A simplification is achieved for the description of underspread signals, for optical beam characterization, and for the generation of signal-adaptive phase-space distributions. PMID:11140493
Linear processes in high dimensions: Phase space and critical properties.
Mastromatteo, Iacopo; Bacry, Emmanuel; Muzy, Jean-François
2015-04-01
In this work we investigate the generic properties of a stochastic linear model in the regime of high dimensionality. We consider in particular the vector autoregressive (VAR) model and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable phase and an unstable phase. We find that along the transition region separating the two regimes the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become power laws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of self-interaction are naturally characterized by this type of slow relaxation of the correlations. PMID:25974473
Linear processes in high dimensions: Phase space and critical properties
NASA Astrophysics Data System (ADS)
Mastromatteo, Iacopo; Bacry, Emmanuel; Muzy, Jean-François
2015-04-01
In this work we investigate the generic properties of a stochastic linear model in the regime of high dimensionality. We consider in particular the vector autoregressive (VAR) model and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable phase and an unstable phase. We find that along the transition region separating the two regimes the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become power laws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of self-interaction are naturally characterized by this type of slow relaxation of the correlations.
Phase 1 Space Fission Propulsion System Design Considerations
NASA Technical Reports Server (NTRS)
Houts, Mike; VanDyke, Melissa; Godfroy, Tom; Pedersen, Kevin; Martin, James; Carter, Robert; Dickens, Ricky; Salvail, Pat; Hrbud, Ivana; Rodgers, Stephen L. (Technical Monitor)
2001-01-01
Fission technology can enable rapid, affordable access to any point in the solar system. If fission propulsion systems are to be developed to their full potential; however, near-term customers must be identified and initial fission systems successfully developed, launched, and operated. Studies conducted in fiscal year 2001 (IISTP, 2001) show that fission electric propulsion (FEP) systems operating at 80 kWe or above could enhance or enable numerous robotic outer solar system missions of interest. At these power levels it is possible to develop safe, affordable systems that meet mission performance requirements. In selecting the system design to pursue, seven evaluation criteria were identified: safety, reliability, testability, specific mass, cost, schedule, and programmatic risk. A top-level comparison of three potential concepts was performed: an SP-100 based pumped liquid lithium system, a direct gas cooled system, and a heatpipe cooled system. For power levels up to at least 500 kWt (enabling electric power levels of 125-175 kWe, given 25-35% power conversion efficiency) the heatpipe system has advantages related to several criteria and is competitive with respect to all. Hardware-based research and development has further increased confidence in the heatpipe approach. Successful development and utilization of a "Phase 1" fission electric propulsion system will enable advanced Phase 2 and Phase 3 systems capable of providing rapid, affordable access to any point in the solar system.
Singular eigenfunctions for shearing fluids I
Balmforth, N.J.; Morrison, P.J.
1995-02-01
The authors construct singular eigenfunctions corresponding to the continuous spectrum of eigenvalues for shear flow in a channel. These modes are irregular as a result of a singularity in the eigenvalue problem at the critical layer of each mode. They consider flows with monotonic shear, so there is only a single critical layer for each mode. They then solve the initial-value problem to establish that these continuum modes, together with any discrete, growing/decaying pairs of modes, comprise a complete basis. They also view the problem within the framework of Hamiltonian theory. In that context, the singular solutions can be viewed as the kernel of an integral, canonical transformation that allows us to write the fluid system, an infinite-dimensional Hamiltonian system, in action-angle form. This yields an expression for the energy in terms of the continuum modes and provides a means for attaching a characteristic signature (sign) to the energy associate with each eigenfunction. They follow on to consider shear-flow stability within the Hamiltonian framework. Next, the authors show the equivalence of integral superpositions of the singular eigenfunctions with the solution derived with Laplace transform techniques. In the long-time limit, such superpositions have decaying integral averages across the channel, revealing phase mixing or continuum damping. Under some conditions, this decay is exponential and is then the fluid analogue of Landau damping. Finally, the authors discuss the energetics of continuum damping.
Self-similarity of phase-space networks of frustrated spin models and lattice gas models
NASA Astrophysics Data System (ADS)
Peng, Yi; Wang, Feng; Han, Yilong
2013-03-01
We studied the self-similar properties of the phase-spaces of two frustrated spin models and two lattice gas models. The frustrated spin models included (1) the anti-ferromagnetic Ising model on a two-dimensional triangular lattice (1a) at the ground states and (1b) above the ground states and (2) the six-vertex model. The two lattice gas models were (3) the one-dimensional lattice gas model and (4) the two-dimensional lattice gas model. The phase spaces were mapped to networks so that the fractal analysis of complex networks could be applied, i.e. the box-covering method and the cluster-growth method. These phase spaces, in turn, establish new classes of networks with unique self-similar properties. Models 1a, 2, and 3 with long-range power-law correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range exponential correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of untested assumptions in Tsallis nonextensive statistics. Hong Kong GRC grants 601208 and 601911
Space shuttle phase B. Volume 1: Executive summary
NASA Technical Reports Server (NTRS)
1972-01-01
A study was conducted to identify the differences among total system concepts of space shuttle configurations. Emphasis was placed on concepts that lead to selection of a system that performs the missions within budget and schedule constraints. The spectrum of launch vehicle configurations is illustrated. An inboard profile of the spacecraft is presented to show the interior arrangement of the major subsystems. The performance prediction of the spacecraft during specified portions of the mission is analyzed. A cost comparison of the various concepts is included.
Space qualified Nd:YAG laser (phase 1 - design)
NASA Technical Reports Server (NTRS)
Foster, J. D.; Kirk, R. F.
1971-01-01
Results of a design study and preliminary design of a space qualified Nd:YAG laser are presented. A theoretical model of the laser was developed to allow the evaluation of the effects of various parameters on its performance. Various pump lamps were evaluated and sum pumping was considered. Cooling requirements were examined and cooling methods such as radiation, cryogenic and conductive were analysed. Power outputs and efficiences of various configurations and the pump and laser lifetime are discussed. Also considered were modulation and modulating methods.
Development of CCD imaging sensors for space applications, phase 1
NASA Technical Reports Server (NTRS)
Antcliffe, G. A.
1975-01-01
The results of an experimental investigation to develop a large area charge coupled device (CCD) imager for space photography applications are described. Details of the design and processing required to achieve 400 X 400 imagers are presented together with a discussion of the optical characterization techniques developed for this program. A discussion of several aspects of large CCD performance is given with detailed test reports. The areas covered include dark current, uniformity of optical response, square wave amplitude response, spectral responsivity and dynamic range.
Alternate space shuttle concepts study: Design requirements and phased programs evaluation
NASA Technical Reports Server (NTRS)
1971-01-01
A study to determine program and technical alternatives to the design of the space shuttle orbiter is described. The alternatives include a phased approach, involving orbiter development and operation with an expendable booster for an interim period, as well as design variations to the basic vehicle. The space shuttle orbiter configurations and predicted performance parameters are presented.
Classical resolution of black hole singularities via wormholes
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.
2016-03-01
In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature.
Singular and nonlinear processes in applied mathematics. Final technical report
Tabor, M.
1998-08-05
A wide range of research topics were supported under this grant. These included: (1) complex space time singularities in nonlinear differential equations; (2) singularities in magneto-hydrodynamics; (3) the dynamics of knots and curves; and (4) the structure and dynamics of foams and grain boundaries. A brief summary of results achieved in each of these four areas is given below along with the associated publications acknowledging DOE support.
Space Fission Propulsion Testing and Development Progress. Phase 1
NASA Technical Reports Server (NTRS)
VanDyke, Melissa; Houts, Mike; Pedersen, Kevin; Godfroy, Tom; Dickens, Ricky; Poston, David; Reid, Bob; Salvail, Pat; Ring, Peter; Rodgers, Stephen L. (Technical Monitor)
2001-01-01
Successful development of space fission systems will require an extensive program of affordable and realistic testing. In addition to tests related to design/development of the fission system, realistic testing of the actual flight unit must also be performed. Testing can be divided into two categories, non-nuclear tests and nuclear tests. Full power nuclear tests of space fission systems we expensive, time consuming, and of limited use, even in the best of programmatic environments. If the system is designed to operate within established radiation damage and fuel burn up limits while simultaneously being designed to allow close simulation of heat from fission using resistance heaters, high confidence in fission system performance and lifetime can be attained through a series of non-nuclear tests. Non-nuclear tests are affordable and timely, and the cause of component and system failures can be quickly and accurately identified. MSFC is leading a Safe Affordable Fission Engine (SAFE) test series whose ultimate goal is the demonstration of a 300 kW flight configuration system using non-nuclear testing. This test series is carried out in collaboration with other NASA centers, other government agencies, industry, and universities. If SAFE-related nuclear tests are desired they will have a high probability of success and can be performed at existing nuclear facilities. The paper describes the SAFE non-nuclear test series, which includes test article descriptions, test results and conclusions, and future test plans.
Phase 1 space fission propulsion system testing and development progress
NASA Astrophysics Data System (ADS)
van Dyke, Melissa; Houts, Mike; Pedersen, Kevin; Godfroy, Tom; Dickens, Ricky; Poston, David; Reid, Bob; Salvail, Pat; Ring, Peter
2001-02-01
Successful development of space fission systems will require an extensive program of affordable and realistic testing. In addition to tests related to design/development of the fission system, realistic testing of the actual flight unit must also be performed. Testing can be divided into two categories, non-nuclear tests and nuclear tests. Full power nuclear tests of space fission systems are expensive, time consuming, and of limited use, even in the best of programmatic environments. If the system is designed to operate within established radiation damage and fuel burn up limits while simultaneously being designed to allow close simulation of heat from fission using resistance heaters, high confidence in fission system performance and lifetime can be attained through a series of non-nuclear tests. Non-nuclear tests are affordable and timely, and the cause of component and system failures can be quickly and accurately identified, MSFC is leading a Safe Affordable Fission Engine (SAFE) test series whose ultimate goal is the demonstration of a 300 kW flight configuration system using non-nuclear testing. This test series is carried out in collaboration with other NASA centers, other government agencies, industry, and universities. If SAFE-related nuclear tests are desired, they will have a high probability of success and can be performed at existing nuclear facilities. The paper describes the SAFE non-nuclear test series, which includes test article descriptions, test results and conclusions, and future test plans. .
Phase 1 Space Fission Propulsion Energy Source Design
NASA Technical Reports Server (NTRS)
Houts, Mike; VanDyke, Melissa; Godfroy, Tom; Pedersen, Kevin; Martin, James; Dickens, Ricky; Salvail, Pat; Hrbud, Ivana; Carter, Robert; Rodgers, Stephen L. (Technical Monitor)
2002-01-01
Fission technology can enable rapid, affordable access to any point in the solar system. If fission propulsion systems are to be developed to their full potential; however, near-term customers must be identified and initial fission systems successfully developed, launched, and operated. Studies conducted in fiscal year 2001 (IISTP, 2001) show that fission electric propulsion (FEP) systems with a specific mass at or below 50 kg/kWjet could enhance or enable numerous robotic outer solar system missions of interest. At the required specific mass, it is possible to develop safe, affordable systems that meet mission requirements. To help select the system design to pursue, eight evaluation criteria were identified: system integration, safety, reliability, testability, specific mass, cost, schedule, and programmatic risk. A top-level comparison of four potential concepts was performed: a Testable, Passive, Redundant Reactor (TPRR), a Testable Multi-Cell In-Core Thermionic Reactor (TMCT), a Direct Gas Cooled Reactor (DGCR), and a Pumped Liquid Metal Reactor.(PLMR). Development of any of the four systems appears feasible. However, for power levels up to at least 500 kWt (enabling electric power levels of 125-175 kWe, given 25-35% power conversion efficiency) the TPRR has advantages related to several criteria and is competitive with respect to all. Hardware-based research and development has further increased confidence in the TPRR approach. Successful development and utilization of a "Phase I" fission electric propulsion system will enable advanced Phase 2 and Phase 3 systems capable of providing rapid, affordable access to any point in the solar system.
Modeling of recombinant yeast cells: reduction of phase space.
Birol, G; Birol, I; Kirdar, B; Onsan, Z I
1997-01-01
The mechanism of starch fermentation by recombinant Saccharomyces cerevisiae in batch reactor is studied. Experiments were carried in the presence and absence of oxygen, with different initial starch concentrations. A variety of data concerning biotic and abiotic phases are collected. Nonlinear data analysis techniques are used to determine the block diagram of the system under study. Data analysis and processing reported here, are believed to form a basis in further work in structured modeling of biological systems, recombinant yeast cultures in particular. PMID:9603032
Naked singularities in initial surfaces
Wojtkiewicz, J. )
1990-03-15
We consider a singular hypersurface {Sigma}, carrying time-symmetric initial data for the Einstein equations. We assume that the area of the arbitrary two-sphere, enclosing the singularity, is bounded from below by some positive constant. A conformally flat ring,'' or pancake'' singularities having sufficiently large Euclidean radius, can serve as examples. We prove that if the Arnowitt-Deser-Misner mass associated with such a hypersurface is small enough, then this singularity is naked (i.e., it is not entirely surrounded by an apparent horizon). We suggest that a similar effect appears also for general (i.e., non-time-symmetric) hypersurfaces.
Updating the singular value decomposition
NASA Astrophysics Data System (ADS)
Davies, Philip I.; Smith, M. I. Matthew I.
2004-09-01
The spectral decomposition of a symmetric matrix A with small off-diagonal and distinct diagonal elements can be approximated using a direct scheme of R. Davies and Modi (Linear Algebra Appl. 77 (1986) 61). In this paper a generalization of this method for computing the singular value decomposition of close-to-diagonal is presented. When A has repeated or "close" singular values it is possible to apply the direct method to split the problem in two with one part containing the well-separated singular values and one requiring the computation of the "close" singular values.
Natural environment design criteria for the space station program definition phase
NASA Technical Reports Server (NTRS)
Vaughan, W. W.
1984-01-01
The natural environment design criteria requirements for use in the Space Station and its Elements (SSPE) definition phase studies are presented. The atmospheric dynamic and thermodynamic environments, meteoroids, radiation, physical constants are addressed. It is intended to enable all groups involved in the definition phase studies to proceed with a common and consistent set of natural environment criteria requirements.
PARAS program: Phased array radio astronomy from space
NASA Technical Reports Server (NTRS)
Jakubowski, Antoni K.; Haynes, David A.; Nuss, Ken; Hoffmann, Chris; Madden, Michael; Dungan, Michael
1992-01-01
An orbiting radio telescope is proposed which, when operated in a Very Long Baseline Interferometry (VLBLI) scheme, would allow higher (than currently available) angular resolution and dynamic range in the maps, and the ability of observing rapidly changing astronomical sources. Using a passive phases array technology, the proposed design consists of 656 hexagonal modules forming a 150 meter diameter dish. Each observatory module is largely autonomous, having its own photovoltaic power supply and low-noise receiver and processor for phase shifting. The signals received by the modules are channeled via fiber optics to the central control computer in the central bus module. After processing and multiplexing, the data is transmitted to telemetry stations on the ground. The truss frame supporting each observatory pane is a hybrid structure consisting of a bottom graphite/epoxy tubular triangle and rigidized inflatable Kevlar tubes connecting the top observatory panel and bottom triangle. Attitude control and stationkeeping functions are performed by a system of momentum wheels in the bus and four propulsion modules located at the compass points on the periphery of the observatory dish. Each propulsion module has four monopropellant thrusters and six hydrazine arcjets, the latter supported by a nuclear reactor. The total mass of the spacecraft is 22,060 kg.
Project PARAS: Phased array radio astronomy from space
NASA Technical Reports Server (NTRS)
Nuss, Kenneth; Hoffmann, Christopher; Dungan, Michael; Madden, Michael; Bendakhlia, Monia
1992-01-01
An orbiting radio telescope is proposed which, when operated in a very long baseline interferometry (VLBI) scheme, would allow higher than currently available angular resolution and dynamic range in the maps and the ability to observe rapidly changing astronomical sources. Using passive phased array technology, the proposed design consists of 656 hexagonal modules forming a 150-m diameter antenna dish. Each observatory module is largely autonomous, having its own photovoltaic power supply and low-noise receiver and processor for phase shifting. The signals received by the modules are channeled via fiber optics to the central control computer in the central bus module. After processing and multiplexing, the data are transmitted to telemetry stations on the ground. The truss frame supporting each observatory panel is a novel hybrid structure consisting of a bottom graphite/epoxy tubular triangle and rigidized inflatable Kevlar tubes connecting the top observatory panel and the bottom triangle. Attitude control and station keeping functions will be performed by a system of momentum wheels in the bus and four propulsion modules located at the compass points on the periphery of the observatory dish. Each propulsion module has four monopropellant thrusters and four hydrazine arcjets, the latter supported by either a photovoltaic array or a radioisotope thermoelectric generator. The total mass of the spacecraft is about 20,500 kg.
Schubert calculus and singularity theory
NASA Astrophysics Data System (ADS)
Gorbounov, Vassily; Petrov, Victor
2012-02-01
Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces, it has to be redesigned when applied to other generalized cohomology theories such as the equivariant, the quantum cohomology, K-theory, and cobordism. All this cohomology theories are different deformations of the ordinary cohomology. In this note, we show that there is, in some sense, the universal deformation of Schubert calculus which produces the above mentioned by specialization of the appropriate parameters. We build on the work of Lerche Vafa and Warner. The main conjecture these authors made was that the classical cohomology of a Hermitian symmetric homogeneous manifold is a Jacobi ring of an appropriate potential. We extend this conjecture and provide a simple proof. Namely, we show that the cohomology of the Hermitian symmetric space is a Jacobi ring of a certain potential and the equivariant and the quantum cohomology and the K-theory is a Jacobi ring of a particular deformation of this potential. This suggests to study the most general deformations of the Frobenius algebra of cohomology of these manifolds by considering the versal deformation of the appropriate potential. The structure of the Jacobi ring of such potential is a subject of well developed singularity theory. This gives a potentially new way to look at the classical, the equivariant, the quantum and other flavors of Schubert calculus.
Space shuttle electromagnetic environment experiment. Phase A: Definition study
NASA Technical Reports Server (NTRS)
Haber, F.; Showers, R. M.; Kocher, C.; Forrest, L. A., Jr.
1976-01-01
Methods for carrying out measurements of earth electromagnetic environment using the space shuttle as a measurement system platform are herein reported. The goal is to provide means for mapping intentional and nonintentional emitters on earth in the frequency range 0.4 to 40 GHz. A survey was made of known emitters using available data from national and international regulatory agencies, and from industry sources. The spatial distribution of sources, power levels, frequencies, degree of frequency re-use, etc., found in the survey, are here presented. A concept is developed for scanning the earth using a directive antenna whose beam is made to rotate at a fixed angle relative to the nadir; the illuminated area swept by the beam is of the form of cycloidal annulus over a sphere. During the beam's sojourn over a point, the receiver sweeps in frequency over ranges in the order of octave width using sweeping filter bandwidths sufficient to give stable readings.
Free-space microwave power transmission study, phase 3
NASA Technical Reports Server (NTRS)
Brown, W. C.
1975-01-01
The results of an investigation of the technology of free-space power transmission by microwave beam are presented. A description of the steps that were taken to increase the overall dc to dc efficiency of microwave power transmission from 15 percent to over 50 percent is given. Included in this overall efficiency were the efficiencies of the dc to microwave conversion, the microwave transmission itself, and the microwave to dc conversion. Improvements in launching the microwave beam with high efficiency by means of a dual mode horn resulted in 95 percent of the output of the microwave generator reaching the receiving area. Emphasis was placed upon successive improvements in reception and rectification of the microwave power, resulting in the design of a rectenna device for this purpose whose efficiency was 75 percent. The procedures and the hardware developed were the basis for tests certified by the Jet Propulsion Laboratory in which an overall dc to dc efficiency of 54 percent was achieved.
Phase-space representation and polarization domains of random electromagnetic fields.
Castaneda, Roman; Betancur, Rafael; Herrera, Jorge; Carrasquilla, Juan
2008-08-01
The phase-space representation of stationary random electromagnetic fields is developed by using electromagnetic spatial coherence wavelets. The propagation of the field's power and states of spatial coherence and polarization results from correlations between the components of the field vectors at pairs of points in space. Polarization domains are theoretically predicted as the structure of the field polarization at the observation plane. In addition, the phase-space representation provides a generalization of the Poynting theorem. Theoretical predictions are examined by numerically simulating the Young experiment with electromagnetic waves. The experimental implementation of these results is a current subject of research. PMID:18670539
3D imaging of translucent media with a plenoptic sensor based on phase space optics
NASA Astrophysics Data System (ADS)
Zhang, Xuanzhe; Shu, Bohong; Du, Shaojun
2015-05-01
Traditional stereo imaging technology is not working for dynamical translucent media, because there are no obvious characteristic patterns on it and it's not allowed using multi-cameras in most cases, while phase space optics can solve the problem, extracting depth information directly from "space-spatial frequency" distribution of the target obtained by plenoptic sensor with single lens. This paper discussed the presentation of depth information in phase space data, and calculating algorithms with different transparency. A 3D imaging example of waterfall was given at last.
Jesmanowicz, Andrzej; Nencka, Andrew S; Li, Shi-Jiang; Hyde, James S
2011-01-01
Whole brain functional connectivity magnetic resonance imaging requires acquisition of a time course of gradient-recalled (GR) volumetric images. A method is developed to accelerate this acquisition using GR echo-planar imaging and radio frequency (RF) slice phase tagging. For N-fold acceleration, a tailored RF pulse excites N slices using a uniform-field transmit coil. This pulse is the Fourier transform of the profile for the N slices with a predetermined RF phase tag on each slice. A multichannel RF receive coil is used for detection. For n slices, there are n/N groups of slices. Signal-averaged reference images are created for each slice within each slice group for each member of the coil array and used to separate overlapping images that are simultaneously received. The time-overhead for collection of reference images is small relative to the acquisition time of a complete volumetric time course. A least-squares singular value decomposition method allows image separation on a pixel-by-pixel basis. Twofold slice acceleration is demonstrated using an eight-channel RF receive coil, with application to resting-state functional magnetic resonance imaging in the human brain. Data from six subjects at 3 T are reported. The method has been extended to half k-space acquisition, which not only provides additional acceleration, but also facilitates slice separation because of increased signal intensity of the central lines of k-space coupled with reduced susceptibility effects. PMID:22432957
Space observations of cold-cloud phase change
Choi, Yong-Sang; Lindzen, Richard S.; Ho, Chang-Hoi; Kim, Jinwon
2010-01-01
This study examines the vertically resolved cloud measurements from the cloud-aerosol lidar with orthogonal polarization instrument on Aqua satellite from June 2006 through May 2007 to estimate the extent to which the mixed cloud-phase composition can vary according to the ambient temperature, an important concern for the uncertainty in calculating cloud radiative effects. At -20 °C, the global average fraction of supercooled clouds in the total cloud population is found to be about 50% in the data period. Between -10 and -40 °C, the fraction is smaller at lower temperatures. However, there are appreciable regional and temporal deviations from the global mean (> ± 20%) at the isotherm. In the analysis with coincident dust aerosol data from the same instrument, it appears that the variation in the supercooled cloud fraction is negatively correlated with the frequencies of dust aerosols at the -20 °C isotherm. This result suggests a possibility that dust particles lifted to the cold cloud layer effectively glaciate supercooled clouds. Observations of radiative flux from the clouds and earth’s radiant energy system instrument aboard Terra satellite, as well as radiative transfer model simulations, show that the 20% variation in the supercooled cloud fraction is quantitatively important in cloud radiative effects, especially in shortwave, which are 10 - 20 W m-2 for regions of mixed-phase clouds affected by dust. In particular, our results demonstrate that dust, by glaciating supercooled water, can decrease albedo, thus compensating for the increase in albedo due to the dust aerosols themselves. This has important implications for the determination of climate sensitivity. PMID:20534562
The space time variety of the hyperradiance from phase-locked soliton oscillators
NASA Astrophysics Data System (ADS)
Lin, Chang; Lin, Mai-mai
2008-12-01
The hyperradiance from phase-locked soliton oscillators is investigated by using the numerical simulation method for the perturbed sine-Gordon equation. Space-time variety for the emitted power from phase-locked soliton oscillators have been diffusely exhibited for the two magnetically coupled long Josephson junctions, operated in singlefluxon modes and involving the family of solutions. We derive some simulation results of space-time character, having the extensive physics meaning, for the theory for superradiance from phase-locked oscillators.
LONGITUDINAL PHASE SPACE CHARACTERIZATION OF ELECTRON BUNCHES AT THE JLAB FEL FACILITY
Shukui Zhang; Stephen Benson; David Douglas; David Hardy; George Neil; Michelle D. Shinn
2006-08-27
We report longitudinal phase space measurements of short electron bunches at the 10kW Free-Electron Laser Facility at Jefferson Lab using broadband synchrotron radiation and a remotely controlled fast streak camera. Accurate measurements are possible because the optical transport system uses only reflective components that do not introduce dispersion. The evolution of longitudinal phase space of the electron beam can be observed in real time while phases of accelerator RF components are being adjusted. This fast and efficient diagnostic enhances the suite of machine setup tools available to JLab FEL operators and applies to other accelerators. The results for certain beam setups will be presented.
Energy content of stormtime ring current from phase space mapping simulations
Chen, M.W.; Schulz, M.; Lyons, L.R.
1993-08-20
The authors perform a model study to account for the increase in energy content of the trapped-particle population which occurs during the main phase of major geomagnetic storms. They consider stormtime particle transport in the equatorial region of the magnetosphere. They start with a phase space distribution of the ring current before the storm, created by a steady state transport model. They then use a previously developed guiding center particle simulation to map the stormtime ring current phase space, following Liouville's theorem. This model is able to account for the ten to twenty fold increase in energy content of magnetospheric ions during the storm.
The effective two-dimensional phase space of cosmological scalar fields
NASA Astrophysics Data System (ADS)
Edwards, David C.
2016-08-01
It has been shown by Remmen and Carroll [1] that, for a model universe which contains only a kinetically canonical scalar field minimally coupled to gravity it is possible to choose `special coordinates' to describe a two-dimensional effective phase space. The special, non-canonical, coordinates are phi,dot phi and the ability to describe an effective phase space with these coordinates empowers the common usage of phi‑dot phi as the space to define inflationary initial conditions. This paper extends the result to the full Horndeski action. The existence of a two-dimensional effective phase space is shown for the general case. Subsets of the Horndeski action, relevant to cosmology are considered as particular examples to highlight important aspects of the procedure.
Phase 1 Space Fission Propulsion System Testing and Development Progress
NASA Technical Reports Server (NTRS)
VanDyke, Melissa; Houts, Mike; Godfroy, Tom; Dickens, Ricky; Poston, David; Kapernick, Rick; Reid, Bob; Salvail, Pat; Ring, Peter; Schafer, Charles (Technical Monitor)
2001-01-01
Successful development of space fission systems requires an extensive program of affordable and realistic testing. In addition to tests related to design/development of the fission system, realistic testing of the actual flight unit must also be performed. If the system is designed to operate within established radiation damage and fuel burn up limits while simultaneously being designed to allow close simulation of heat from fission using resistance heaters, high confidence in fission system performance and lifetime can be attained through a series of non-nuclear tests. The Safe Affordable Fission Engine (SAFE) test series, whose ultimate goal is the demonstration of a 300 kW flight configuration system, has demonstrated that realistic testing can be performed using non-nuclear methods. This test series, carried out in collaboration with other NASA centers, other government agencies, industry, and universities, successfully completed a testing program with a 30 kWt core, Stirling engine, and ion engine configuration. Additionally, a 100 kWt core is in fabrication and appropriate test facilities are being reconfigured. This paper describes the current SAFE non-nuclear tests, which includes test article descriptions, test results and conclusions, and future test plans.
Phase 1 space fission propulsion system testing and development progress
NASA Astrophysics Data System (ADS)
van Dyke, Melissa; Houts, Mike; Godfroy, Tom; Dickens, Ricky; Poston, David; Kapernick, Rick; Reid, Bob; Salvail, Pat; Ring, Peter
2002-01-01
Successful development of space fission systems requires an extensive program of affordable and realistic testing. In addition to tests related to design/development of the fission system, realistic testing of the actual flight unit must also be performed. If the system is designed to operate within established radiation damage and fuel burn up limits while simultaneously being designed to allow close simulation of heat from fission using resistance heaters, high confidence in fission system performance and lifetime can be attained through a series of non-nuclear tests. The Safe Affordable Fission Engine (SAFE) test series, whose ultimate goal is the demonstration of a 300 kW flight configuration system, has demonstrated that realistic testing can be performed using non-nuclear methods. This test series, carried out in collaboration with other NASA centers, other government agencies, industry, and universities, successfully completed a testing program with a 30 kWt core. Stirling engine, and ion engine configuration. Additionally, a 100 kWt core is in fabrication and appropriate test facilities are being reconfigured. This paper describes the current SAFE non-nuclear tests, which includes test article descriptions, test results and conclusions, and future test plans. .
Phase 1 space fission propulsion system testing and development progress
NASA Astrophysics Data System (ADS)
Dyke, Melissa Van; Houts, Mike; Godfroy, Tom; Dickens, Ricky; Poston, David; Kapernick, Rick; Reid, Bob; Salvail, Pat; Ring, Peter
2002-01-01
Successful development of space fission systems requires an extensive program of affordable and realistic testing. In addition to tests related to design/development of the fission system, realistic testing of the actual flight unit must also be performed. If the system is designed to operate within established radiation damage and fuel burn up limits while simultaneously being designed to allow close simulation of heat from fission using resistance heaters, high confidence in fission system performance and lifetime can be attained through a series of non-nuclear tests. The Safe Affordable Fission Engine (SAFE) test series, whose ultimate goal is the demonstration of a 300 kW flight configuration system, has demonstrated that realistic testing can be performed using non-nuclear methods. This test series, carried out in collaboration with other NASA centers, other government agencies, industry, and universities, successfully completed a testing program with a 30 kWt core. Stirling engine, and ion engine configuration. Additionally, a 100 kWt core is in fabrication and appropriate test facilities are being reconfigured. This paper describes the current SAFE non-nuclear tests, which includes test article descriptions, test results and conclusions, and future test plans.
NASA Astrophysics Data System (ADS)
Meierhenrich, Uwe J.; Cason, Julie R. L.; Szopa, Cyril; Sternberg, Robert; Raulin, François; Thiemann, Wolfram H.-P.; Goesmann, Fred
2013-12-01
The European Space Agency's Rosetta mission was launched in March 2004 in order to reach comet 67P/Churyumov-Gerasimenko by August 2014. The Cometary Sampling and Composition experiment (COSAC) onboard the Rosetta mission's lander "Philae" has been designed for the cometary in situ detection and quantification of organic molecules using gas chromatography coupled to mass spectrometry (GC-MS). The GC unit of COSAC is equipped with eight capillary columns that will each provide a specific stationary phase for molecular separation. Three of these stationary phases will be used to chromatographically resolve enantiomers, as they are composed of liquid polymers of polydimethylsiloxane (PDMS) to which chiral valine or cyclodextrin units are attached. Throughout the ten years of Rosetta's journey through space to reach comet 67P, these liquid stationary phases have been exposed to space vacuum, as the capillary columns within the COSAC unit were not sealed or filled with carrier gas. Long term exposures to space vacuum can cause damage to such liquid stationary phases as key monomers, volatiles, and chiral selectors can be vaporized and lost in transit. We have therefore exposed identical spare units of COSAC's chiral stationary phases over eight years to vacuum conditions mimicking those experienced in space and we have now investigated their resolution capabilities towards different enantiomers both before and after exposure to space vacuum environments. We have observed that enantiomeric resolution capabilities of these chiral liquid enantioselective stationary phases has not been affected by exposure to space vacuum conditions. Thus we conclude that the three chiral stationary phases of the COSAC experiment onboard the Rosetta mission lander "Philae" can be considered to have maintained their resolution capacities throughout their journey prior to cometary landing in November 2014.
Painting phase spaces to put frozen orbits in context
NASA Astrophysics Data System (ADS)
Coffey, S.; Deprit, A.; Deprit, E.
1991-08-01
Frozen orbits are orbits whose average eccentricities and inclinations are constant. It is shown how bifurcations create frozen orbits near the critical inclination at a given energy; in particular how, due to a symmetry breaking when the odd zonal harmonics are admitted in the model, the evolution along the sequences of frozen orbits differs drastically from the one obtained when only the even zonal harmonics are taken in. A model problem involving the first nine zonal harmonics fits very well, according to the findings, the very long term orbital behavior of satellites in the Molnya class; in that model, quite clearly almost circular frozen orbits are detected at low inclinations, and an inclination slightly above the critical one is identified where there exists a circular frozen orbit. The techniques used in this paper are a mix of symbolic manipulations by computers, global representation of phase flow in color by means of massively parallel processors, and interaction between graphics and numerical analysis at the screen of a workstation.
Cosmological singularities encoded in IR boundary correlations
NASA Astrophysics Data System (ADS)
Bzowski, Adam; Hertog, Thomas; Schillo, Marjorie
2016-05-01
We study the dynamics near big crunch singularities produced in asymptotic AdS cosmologies using gauge/gravity duality. The dual description consists of a constant mass deformation of ABJM theory on de Sitter space and is well-defined and stable for small deformations. We identify the critical deformation where the theory becomes unstable at weak and at strong coupling. Using spacelike geodesics anchored on the boundary we compute two-point correlators of ABJM operators of large dimensions. Near the critical deformation a second saddle point contribution enters, in which the spacelike geodesics probe the high curvature region near the singularity. Its contribution strongly enhances the long-distance correlations. This has a natural interpretation in the weakly coupled boundary theory where the critical point corresponds to a massless limit.
ERIC Educational Resources Information Center
Avital, Doron
2007-01-01
This paper will examine an unresolved tension inherent in the question of art and argue for the idea of a singular rule as a natural resolution. In so doing, the structure of a singular rule will be fully outlined and its paradoxical constitution will be resolved. The tension I mention above unfolds both as a matter of history and as a product of…
NASA Technical Reports Server (NTRS)
Peters, Bruce; Wingo, Dennis; Bower, Mark; Amborski, Robert; Blount, Laura; Daniel, Alan; Hagood, Bob; Handley, James; Hediger, Donald; Jimmerson, Lisa
1990-01-01
The separation of fluid phases in microgravity environments is of importance to environmental control and life support systems (ECLSS) and materials processing in space. A successful fluid phase separation experiment will demonstrate a proof of concept for the separation technique and add to the knowledge base of material behavior. The phase separation experiment will contain a premixed fluid which will be exposed to a microgravity environment. After the phase separation of the compound has occurred, small samples of each of the species will be taken for analysis on the Earth. By correlating the time of separation and the temperature history of the fluid, it will be possible to characterize the process. The experiment has been integrated into space available on a manifested Get Away Special (GAS) experiment, CONCAP 2, part of the Consortium for Materials Complex Autonomous Payload (CAP) Program, scheduled for STS-42. The design and the production of a fluid phase separation experiment for rapid implementation at low cost is presented.
Performance evaluation of digital phase-locked loops for advanced deep space transponders
NASA Technical Reports Server (NTRS)
Nguyen, T. M.; Hinedi, S. M.; Yeh, H.-G.; Kyriacou, C.
1994-01-01
The performances of the digital phase-locked loops (DPLL's) for the advanced deep-space transponders (ADT's) are investigated. DPLL's considered in this article are derived from the analog phase-locked loop, which is currently employed by the NASA standard deep space transponder, using S-domain to Z-domain mapping techniques. Three mappings are used to develop digital approximations of the standard deep space analog phase-locked loop, namely the bilinear transformation (BT), impulse invariant transformation (IIT), and step invariant transformation (SIT) techniques. The performance in terms of the closed loop phase and magnitude responses, carrier tracking jitter, and response of the loop to the phase offset (the difference between in incoming phase and reference phase) is evaluated for each digital approximation. Theoretical results of the carrier tracking jitter for command-on and command-off cases are then validated by computer simulation. Both theoretical and computer simulation results show that at high sampling frequency, the DPLL's approximated by all three transformations have the same tracking jitter. However, at low sampling frequency, the digital approximation using BT outperforms the others. The minimum sampling frequency for adequate tracking performance is determined for each digital approximation of the analog loop. In addition, computer simulation shows that the DPLL developed by BT provides faster response to the phase offset than IIT and SIT.
Computing singularities of perturbation series
Kvaal, Simen; Jarlebring, Elias; Michiels, Wim
2011-03-15
Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schroedinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be useful for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with {delta}-function interactions for which Moeller-Plesset perturbation theory is considered and the radius of convergence found.
Singularities in soft-impacting systems
NASA Astrophysics Data System (ADS)
Kundu, Soumya; Banerjee, Soumitro; Ing, James; Pavlovskaia, Ekaterina; Wiercigroch, Marian
2012-03-01
In this paper, the character of the normal form map in the neighbourhood of a grazing orbit is investigated for four possible configurations of soft impacting systems. It is shown that, if the spring in the impacting surface is relaxed, the impacting side of the map has a power of 3/2, but if the spring is pre-stressed the map has a square root singularity. The singularity appears only in the trace of the Jacobian matrix and not in the determinant. Under all conditions, the determinant of the Jacobian matrix varies continuously across the grazing condition. However, if the impacting surface has a damper, the determinant decreases exponentially with increasing penetration. It is found that the system behaviour is greatly dependent upon a parameter m, given by 2ω0/ω, and that the singularity disappears for integer values of m. Thus, if the parameters are chosen to obtain an integer value of m, one can expect no abrupt change in behaviour as the system passes through the grazing condition from a non-impacting mode to an impacting mode with increasing excitation amplitude. The above result has been tested on an experimental rig, which showed a persistence of a period-1 orbit across the grazing condition for integer values of m, but an abrupt transition to a chaotic orbit or a high-period orbit for non-integer values of m. Finally, through simulation, it is shown that the condition for vanishing singularity is not a discrete point in the parameter space. This property is valid over a neighbourhood in the parameter space, which shrinks for larger values of the stiffness ratio k2/k1.
Vojta, Thomas; Igo, John; Hoyos, José A
2014-07-01
We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions. PMID:25122283
Looking for phase-space structures in star-forming regions: an MST-based methodology
NASA Astrophysics Data System (ADS)
Alfaro, Emilio J.; González, Marta
2016-03-01
We present a method for analysing the phase space of star-forming regions. In particular we are searching for clumpy structures in the 3D sub-space formed by two position coordinates and radial velocity. The aim of the method is the detection of kinematic segregated radial velocity groups, that is, radial velocity intervals whose associated stars are spatially concentrated. To this end we define a kinematic segregation index, tilde{Λ }(RV), based on the Minimum Spanning Tree graph algorithm, which is estimated for a set of radial velocity intervals in the region. When tilde{Λ }(RV) is significantly greater than 1 we consider that this bin represents a grouping in the phase space. We split a star-forming region into radial velocity bins and calculate the kinematic segregation index for each bin, and then we obtain the spectrum of kinematic groupings, which enables a quick visualization of the kinematic behaviour of the region under study. We carried out numerical models of different configurations in the sub-space of the phase space formed by the coordinates and the that various case studies illustrate. The analysis of the test cases demonstrates the potential of the new methodology for detecting different kind of groupings in phase space.
Temperature and phase-space density of a cold atom cloud in a quadrupole magnetic trap
NASA Astrophysics Data System (ADS)
Ram, S. P.; Mishra, S. R.; Tiwari, S. K.; Rawat, H. S.
2014-08-01
We present studies on modifications in the temperature, number density and phase-space density when a laser-cooled atom cloud from optical molasses is trapped in a quadrupole magnetic trap. Theoretically, for a given temperature and size of the cloud from the molasses, the phase-space density in the magnetic trap is shown first to increase with increasing magnetic field gradient and then to decrease with it after attaining a maximum value at an optimum value of the magnetic-field gradient. The experimentally-measured variation in the phase-space density in the magnetic trap with changing magnetic field gradient is shown to exhibit a similar trend. However, the experimentally-measured values of the number density and the phase-space density are much lower than the theoretically-predicted values. This is attributed to the experimentally-observed temperature in the magnetic trap being higher than the theoretically-predicted temperature. Nevertheless, these studies can be useful for setting a higher phase-space density in the trap by establishing an optimal value of the field gradient for a quadrupole magnetic trap.
NASA Astrophysics Data System (ADS)
Zhang, M.; Zou, W.; Chen, T.; Kim, L.; Khan, A.; Haffty, B.; Yue, N. J.
2014-01-01
A common approach to implementing the Monte Carlo method for the calculation of brachytherapy radiation dose deposition is to use a phase space file containing information on particles emitted from a brachytherapy source. However, the loading of the phase space file during the dose calculation consumes a large amount of computer random access memory, imposing a higher requirement for computer hardware. In this study, we propose a method to parameterize the information (e.g., particle location, direction and energy) stored in the phase space file by using several probability distributions. This method was implemented for dose calculations of a commercial Ir-192 high dose rate source. Dose calculation accuracy of the parameterized source was compared to the results observed using the full phase space file in a simple water phantom and in a clinical breast cancer case. The results showed the parameterized source at a size of 200 kB was as accurate as the phase space file represented source of 1.1 GB. By using the parameterized source representation, a compact Monte Carlo job can be designed, which allows an easy setup for parallel computing in brachytherapy planning.
Spaced-antenna wind estimation using an X-band active phased-array weather radar
NASA Astrophysics Data System (ADS)
Venkatesh, Vijay
Over the past few decades, several single radar methods have been developed to probe the kinematic structure of storms. All these methods trade angular-resolution to retrieve the wind-field. To date, the spaced-antenna method has been employed for profiling the ionosphere and the precipitation free lower atmosphere. This work focuses on applying the spaced-antenna method on an X-band active phased-array radar for high resolution horizontal wind-field retrieval from precipitation echoes. The ability to segment the array face into multiple displaced apertures allows for flexible spaced-antenna implementations. The methodology employed herein comprises of Monte-Carlo simulations to optimize the spaced-antenna system design and analysis of real data collected with the designed phased-array system. The contribution that underpins this dissertation is the demonstration of qualitative agreement between spaced-antenna and Doppler beam swinging retrievals based on real data. First, simulations of backscattered electric fields at the antenna array elements are validated using theoretical expressions. Based on the simulations, the degrees of freedom in the spaced-antenna system design are optimized for retrieval of mean baseline wind. We show that the designed X-band spaced-antenna system has lower retrieval uncertainty than the existing S-band spaced-antenna implementation on the NWRT. This is because of the flexibility to synthesize small overlapping apertures and the ability to obtain statistically independent samples at a faster rate at X-band. We then demonstrate a technique to make relative phase-center displacement measurements based on simulations and real data from the phased-array spaced-antenna system. This simple method uses statistics of precipitation echoes and apriori beamwidth measurements to make field repeatable phase-center displacement measurements. Finally, we test the hypothesis that wind-field curvature effects are common to both the spaced-antenna and
Quantum phase-space picture of Bose-Einstein condensates in a double well
Mahmud, Khan W.; Perry, Heidi; Reinhardt, William P.
2005-02-01
We present a quantum phase-space model of the Bose-Einstein condensate (BEC) in a double-well potential. In a quantum two-mode approximation we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase-space information is extracted from the stationary quantum states using the Husimi distribution function. We show that the mean-field phase-space characteristics of a nonrigid physical pendulum arises from the exact quantum states, and that only 4-8 particles per well are needed to reach the semiclassical limit. For a driven double-well BEC, we show that the classical chaotic dynamics is manifest in the dynamics of the quantum states. Phase-space analogy also suggests that a {pi} phase-displaced wave packet put on the unstable fixed point on a separatrix bifurcates to create a superposition of two pendulum rotor states--a macroscopic superposition state of BEC. We show that the choice of initial barrier height and ramping, following a {pi} phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.
Phase and Pupil Amplitude Recovery for JWST Space-Optics Control
NASA Technical Reports Server (NTRS)
Dean, B. H.; Zielinski, T. P.; Smith, J. S.; Bolcar, M. R.; Aronstein, D. L.; Fienup, J. R.
2010-01-01
This slide presentation reviews the phase and pupil amplitude recovery for the James Webb Space Telescope (JWST) Near Infrared Camera (NIRCam). It includes views of the Integrated Science Instrument Module (ISIM), the NIRCam, examples of Phase Retrieval Data, Ghost Irradiance, Pupil Amplitude Estimation, Amplitude Retrieval, Initial Plate Scale Estimation using the Modulation Transfer Function (MTF), Pupil Amplitude Estimation vs lambda, Pupil Amplitude Estimation vs. number of Images, Pupil Amplitude Estimation vs Rotation (clocking), and Typical Phase Retrieval Results Also included is information about the phase retrieval approach, Non-Linear Optimization (NLO) Optimized Diversity Functions, and Least Square Error vs. Starting Pupil Amplitude.
Cosmological singularities in Born-Infeld determinantal gravity
NASA Astrophysics Data System (ADS)
Bouhmadi-López, Mariam; Chen, Che-Yu; Chen, Pisin
2014-12-01
The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the big bang singularity. This theory is formulated on the Weitzenböck space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity free for a certain region of the parameter space in which the divergence of the Hubble rate in the high-energy regime is substituted by a de Sitter stage or a bounce in a Friedmann-Lemaître-Robertson-Walker universe, cosmological singularities—such as a big rip, big bang, big freeze, and sudden singularities—can emerge in other regions of the configuration space of the theory. We also show that all these singular events exist even though the universe is filled with a perfect fluid with a constant equation of state.
3D imaging in volumetric scattering media using phase-space measurements.
Liu, Hsiou-Yuan; Jonas, Eric; Tian, Lei; Zhong, Jingshan; Recht, Benjamin; Waller, Laura
2015-06-01
We demonstrate the use of phase-space imaging for 3D localization of multiple point sources inside scattering material. The effect of scattering is to spread angular (spatial frequency) information, which can be measured by phase space imaging. We derive a multi-slice forward model for homogenous volumetric scattering, then develop a reconstruction algorithm that exploits sparsity in order to further constrain the problem. By using 4D measurements for 3D reconstruction, the dimensionality mismatch provides significant robustness to multiple scattering, with either static or dynamic diffusers. Experimentally, our high-resolution 4D phase-space data is collected by a spectrogram setup, with results successfully recovering the 3D positions of multiple LEDs embedded in turbid scattering media. PMID:26072807
High-order continuum kinetic method for modeling plasma dynamics in phase space
Vogman, G. V.; Colella, P.; Shumlak, U.
2014-12-15
Continuum methods offer a high-fidelity means of simulating plasma kinetics. While computationally intensive, these methods are advantageous because they can be cast in conservation-law form, are not susceptible to noise, and can be implemented using high-order numerical methods. Advances in continuum method capabilities for modeling kinetic phenomena in plasmas require the development of validation tools in higher dimensional phase space and an ability to handle non-cartesian geometries. To that end, a new benchmark for validating Vlasov-Poisson simulations in 3D (x,vx,vy) is presented. The benchmark is based on the Dory-Guest-Harris instability and is successfully used to validate a continuum finite volumemore » algorithm. To address challenges associated with non-cartesian geometries, unique features of cylindrical phase space coordinates are described. Preliminary results of continuum kinetic simulations in 4D (r,z,vr,vz) phase space are presented.« less
Unified matrix approach to the description of phase-space rotators.
Gitin, Andrey V
2016-03-01
In optics, the rotation of a phase-space can be realized via light propagation through both an inhomogeneous medium with a radial gradient of refractive index and two special kinds of mirror-symmetrical optical systems suggested by Lohmann. Although light propagation through Lohmann's systems is described in terms of matrix optics, light propagation through the gradient-index medium is traditionally described as a solution of the wave equation. The difference in these descriptions hinders the understanding of the phase-space rotators. Fortunately, there is a matrix description of light propagation through a gradient-index medium too. A general description of the phase-space rotators is presented, which can be used to treat light propagation through both Lohmann's systems and the gradient-index medium in a unified matrix manner. PMID:26974609
Space shuttle main engine definition (phase B). Volume 2: Avionics. [for space shuttle
NASA Technical Reports Server (NTRS)
1971-01-01
The advent of the space shuttle engine with its requirements for high specific impulse, long life, and low cost have dictated a combustion cycle and a closed loop control system to allow the engine components to run close to operating limits. These performance requirements, combined with the necessity for low operational costs, have placed new demands on rocket engine control, system checkout, and diagnosis technology. Based on considerations of precision environment, and compatibility with vehicle interface commands, an electronic control, makes available many functions that logically provide the information required for engine system checkout and diagnosis.
Amateur Radio on the International Space Station - Phase 2 Hardware System
NASA Technical Reports Server (NTRS)
Bauer, F.; McFadin, L.; Bruninga, B.; Watarikawa, H.
2003-01-01
The International Space Station (ISS) ham radio system has been on-orbit for over 3 years. Since its first use in November 2000, the first seven expedition crews and three Soyuz taxi crews have utilized the amateur radio station in the Functional Cargo Block (also referred to as the FGB or Zarya module) to talk to thousands of students in schools, to their families on Earth, and to amateur radio operators around the world. Early on, the Amateur Radio on the International Space Station (ARISS) international team devised a multi-phased hardware development approach for the ISS ham radio station. Three internal development Phases. Initial Phase 1, Mobile Radio Phase 2 and Permanently Mounted Phase 3 plus an externally mounted system, were proposed and agreed to by the ARISS team. The Phase 1 system hardware development which was started in 1996 has since been delivered to ISS. It is currently operational on 2 meters. The 70 cm system is expected to be installed and operated later this year. Since 2001, the ARISS international team have worked to bring the second generation ham system, called Phase 2, to flight qualification status. At this time, major portions of the Phase 2 hardware system have been delivered to ISS and will soon be installed and checked out. This paper intends to provide an overview of the Phase 1 system for background and then describe the capabilities of the Phase 2 radio system. It will also describe the current plans to finalize the Phase 1 and Phase 2 testing in Russia and outlines the plans to bring the Phase 2 hardware system to full operation.
Singularity spectrum of fractal signals from wavelet analysis: Exact results
Bacry, E.; Muzy, J.F.; Arneodo, A. )
1993-02-01
The multifractal formalism for singular measures is revisited using the wave transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimension D(h) of the set of singularities of Hoelder exponent h can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of order n, provided one uses an analyzing wavelet that possesses at least N > n vanishing moments. However, it is shown that a C[infinity] behavior generally induces a phase transition in the D(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the number N of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.
The fault monitoring and diagnosis knowledge-based system for space power systems: AMPERES, phase 1
NASA Technical Reports Server (NTRS)
Lee, S. C.
1989-01-01
The objective is to develop a real time fault monitoring and diagnosis knowledge-based system (KBS) for space power systems which can save costly operational manpower and can achieve more reliable space power system operation. The proposed KBS was developed using the Autonomously Managed Power System (AMPS) test facility currently installed at NASA Marshall Space Flight Center (MSFC), but the basic approach taken for this project could be applicable for other space power systems. The proposed KBS is entitled Autonomously Managed Power-System Extendible Real-time Expert System (AMPERES). In Phase 1 the emphasis was put on the design of the overall KBS, the identification of the basic research required, the initial performance of the research, and the development of a prototype KBS. In Phase 2, emphasis is put on the completion of the research initiated in Phase 1, and the enhancement of the prototype KBS developed in Phase 1. This enhancement is intended to achieve a working real time KBS incorporated with the NASA space power system test facilities. Three major research areas were identified and progress was made in each area. These areas are real time data acquisition and its supporting data structure; sensor value validations; development of inference scheme for effective fault monitoring and diagnosis, and its supporting knowledge representation scheme.
Evolution of electron beam phase space distribution in a high-gain FEL
Webb,S.D.; Litvinenko, V. N.
2009-08-23
FEL-based coherent electron cooling (CEC) offers a new avenue to achieve high luminosities in high energy colliders such as RHIC, LHC, and eRHIC. Traditional treatments consider the FEL as an amplifier of optical waves with specific initial conditions, focusing on the resulting field. CEC requires knowledge of the phase space distribution of the electron beam in the FEL. We present 1D analytical results for the phase space distribution of an electron beam with an arbitrary initial current profile, and discuss approaches of expanding to 3D results.
Nonlinear satellite wakes in planetary rings. I - Phase-space kinematics
NASA Technical Reports Server (NTRS)
Stewart, Glen R.
1991-01-01
The explicit expression presently derived for the phase-space density of a planetary ring subjected to perturbations by a proximate satellite recovers the usual perturbed-streamline equations by drawing first-order moments of the phase-space density. The surface density obtained is positive-definite in virtue of taking the ring particles' finite-velocity dispersion into account. The satellite-wake local mean velocity components deviate from the streamline equations' sinusoidal form; this deviation grows as the wake moves downstream from the shepherding satellite.
Phase-space dynamics of ionization injection in plasma-based accelerators.
Xu, X L; Hua, J F; Li, F; Zhang, C J; Yan, L X; Du, Y C; Huang, W H; Chen, H B; Tang, C X; Lu, W; Yu, P; An, W; Joshi, C; Mori, W B
2014-01-24
The evolution of beam phase space in ionization injection into plasma wakefields is studied using theory and particle-in-cell simulations. The injection process involves both longitudinal and transverse phase mixing, leading initially to a rapid emittance growth followed by oscillation, decay, and a slow growth to saturation. An analytic theory for this evolution is presented and verified through particle-in-cell simulations. This theory includes the effects of injection distance (time), acceleration distance, wakefield structure, and nonlinear space charge forces, and it also shows how ultralow emittance beams can be produced using ionization injection methods. PMID:24484147
GPU-based Monte Carlo radiotherapy dose calculation using phase-space sources
NASA Astrophysics Data System (ADS)
Townson, Reid W.; Jia, Xun; Tian, Zhen; Jiang Graves, Yan; Zavgorodni, Sergei; Jiang, Steve B.
2013-06-01
A novel phase-space source implementation has been designed for graphics processing unit (GPU)-based Monte Carlo dose calculation engines. Short of full simulation of the linac head, using a phase-space source is the most accurate method to model a clinical radiation beam in dose calculations. However, in GPU-based Monte Carlo dose calculations where the computation efficiency is very high, the time required to read and process a large phase-space file becomes comparable to the particle transport time. Moreover, due to the parallelized nature of GPU hardware, it is essential to simultaneously transport particles of the same type and similar energies but separated spatially to yield a high efficiency. We present three methods for phase-space implementation that have been integrated into the most recent version of the GPU-based Monte Carlo radiotherapy dose calculation package gDPM v3.0. The first method is to sequentially read particles from a patient-dependent phase-space and sort them on-the-fly based on particle type and energy. The second method supplements this with a simple secondary collimator model and fluence map implementation so that patient-independent phase-space sources can be used. Finally, as the third method (called the phase-space-let, or PSL, method) we introduce a novel source implementation utilizing pre-processed patient-independent phase-spaces that are sorted by particle type, energy and position. Position bins located outside a rectangular region of interest enclosing the treatment field are ignored, substantially decreasing simulation time with little effect on the final dose distribution. The three methods were validated in absolute dose against BEAMnrc/DOSXYZnrc and compared using gamma-index tests (2%/2 mm above the 10% isodose). It was found that the PSL method has the optimal balance between accuracy and efficiency and thus is used as the default method in gDPM v3.0. Using the PSL method, open fields of 4 × 4, 10 × 10 and 30 × 30 cm
NASA Technical Reports Server (NTRS)
Roberts, B. C.; Carrasquillo, R. L.; Dubiel, M. Y.; Ogle, K. Y.; Perry, J. L.; Whitley, K. M.
1990-01-01
A description of the phase 3 simplified integrated test (SIT) conducted at the Marshall Space Flight Center (MSFC) Core Module Integration Facility (CMIF) in 1989 is presented. This was the first test in the phase 3 series integrated environmental control and life support systems (ECLSS) tests. The basic goal of the SIT was to achieve full integration of the baseline air revitalization (AR) subsystems for Space Station Freedom. Included is a description of the SIT configuration, a performance analysis of each subsystem, results from air and water sampling, and a discussion of lessons learned from the test. Also included is a full description of the preprototype ECLSS hardware used in the test.
A Gaussian wave packet phase-space representation of quantum canonical statistics
Coughtrie, David J.; Tew, David P.
2015-07-28
We present a mapping of quantum canonical statistical averages onto a phase-space average over thawed Gaussian wave-packet (GWP) parameters, which is exact for harmonic systems at all temperatures. The mapping invokes an effective potential surface, experienced by the wave packets, and a temperature-dependent phase-space integrand, to correctly transition from the GWP average at low temperature to classical statistics at high temperature. Numerical tests on weakly and strongly anharmonic model systems demonstrate that thermal averages of the system energy and geometric properties are accurate to within 1% of the exact quantum values at all temperatures.
The application of the phase space time evolution method to electron shielding
NASA Technical Reports Server (NTRS)
Cordaro, M. C.; Zucker, M. S.
1972-01-01
A computer technique for treating the motion of charged and neutral particles and called the phase space time evolution method was developed. This technique employs the computer's bookkeeping capacity to keep track of the time development of a phase space distribution of particles. This method was applied to a study of the penetration of electrons. A 1 MeV beam of electrons normally incident on a semi-infinite slab of aluminum was used. Results of the calculation were compared with Monte Carlo calculations and experimental results. Time-dependent PSTE electron penetration results for the same problem are presented.
GPU-based Monte Carlo radiotherapy dose calculation using phase-space sources.
Townson, Reid W; Jia, Xun; Tian, Zhen; Graves, Yan Jiang; Zavgorodni, Sergei; Jiang, Steve B
2013-06-21
A novel phase-space source implementation has been designed for graphics processing unit (GPU)-based Monte Carlo dose calculation engines. Short of full simulation of the linac head, using a phase-space source is the most accurate method to model a clinical radiation beam in dose calculations. However, in GPU-based Monte Carlo dose calculations where the computation efficiency is very high, the time required to read and process a large phase-space file becomes comparable to the particle transport time. Moreover, due to the parallelized nature of GPU hardware, it is essential to simultaneously transport particles of the same type and similar energies but separated spatially to yield a high efficiency. We present three methods for phase-space implementation that have been integrated into the most recent version of the GPU-based Monte Carlo radiotherapy dose calculation package gDPM v3.0. The first method is to sequentially read particles from a patient-dependent phase-space and sort them on-the-fly based on particle type and energy. The second method supplements this with a simple secondary collimator model and fluence map implementation so that patient-independent phase-space sources can be used. Finally, as the third method (called the phase-space-let, or PSL, method) we introduce a novel source implementation utilizing pre-processed patient-independent phase-spaces that are sorted by particle type, energy and position. Position bins located outside a rectangular region of interest enclosing the treatment field are ignored, substantially decreasing simulation time with little effect on the final dose distribution. The three methods were validated in absolute dose against BEAMnrc/DOSXYZnrc and compared using gamma-index tests (2%/2 mm above the 10% isodose). It was found that the PSL method has the optimal balance between accuracy and efficiency and thus is used as the default method in gDPM v3.0. Using the PSL method, open fields of 4 × 4, 10 × 10 and 30 × 30 cm
Free space optical communication link using a silicon photonic optical phased array
NASA Astrophysics Data System (ADS)
Rabinovich, William S.; Goetz, Peter G.; Pruessner, Marcel; Mahon, Rita; Ferraro, Mike S.; Park, Doe; Fleet, Erin; DePrenger, Michael J.
2015-03-01
Many components for free space optical communication systems have shrunken in size over the last decade. However, the steering systems have remained large and power hungry. Non-mechanical beam steering offers a path to reducing the size of these systems. Optical phased arrays can allow integrated beam steering elements. One of the most important aspects of an optical phased array technology is its scalability to a large number of elements. Silicon photonics can potentially offer this scalability using CMOS foundry techniques. In this paper a small-scale silicon photonic optical phased array is demonstrated for both the transmitter and receiver functions in a free space optical link. The device using an array of thermo-optically controlled waveguide phase shifters and demonstrates one-dimensional steering with a single control electrode. Transmission of a digitized video data stream over the link is shown.
Phase-space description of plasma waves: Linear and nonlinear theory
NASA Astrophysics Data System (ADS)
Biro, Thomas
1992-11-01
A (r,k) phase description of waves in plasmas is developed by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, the proper form of the current response function, is discussed. On the analogy of the particle distribution function f(v,r,t), a wave density N(k,r,t) is introduced on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows the damping or growth of wave density along rays to be described. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, a very general formula for the second order nonlinear current is obtained in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. Kinetic equations for weakly inhomogeneous and turbulent plasmas are derived, including the effects of inhomogeneous turbulence, wave convection and refraction.
Phased Array Ultrasonic Examination of Space Shuttle Main Engine Nozzle Weld
NASA Technical Reports Server (NTRS)
James, S.; Engel, J.; Kimbrough, D.; Suits, M.; McCool, Alex (Technical Monitor)
2001-01-01
This paper describes a Phased Array Ultrasonic Examination that was developed for the examination of a limited access circumferential Inconel 718 fusion weld of a Space Shuttle Main Engine Nozzle - Cone. The paper discusses the selection and formation criteria used for the phased array focal laws, the reference standard that simulated hardware conditions, the examination concept, and results. Several unique constraints present during this examination included limited probe movement to a single axis and one-sided access to the weld.
Phase space gradient of dissipated work and information: A role of relative Fisher information
Yamano, Takuya
2013-11-15
We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated work in phase space. We present a universal constraint on it via the logarithmic Sobolev inequality. Furthermore, we point out that a possible expression of the lower bound indicates a deep connection in terms of the relative entropy and the Fisher information of the canonical distributions.
Chemical potential driven phase transition of black holes in anti-de Sitter space
NASA Astrophysics Data System (ADS)
Galante, Mario; Giribet, Gaston; Goya, Andrés; Oliva, Julio
2015-11-01
Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit a phase transition at low temperature whose end point is an asymptotically anti-de Sitter black hole with a scalar field profile that is regular everywhere outside and on the horizon. This provides a tractable model to study the phase transition of hairy black holes in anti-de Sitter space in which the backreaction on the geometry can be solved analytically.
Space cryogenics components based on the thermomechanical effect - Vapor-liquid phase separation
NASA Technical Reports Server (NTRS)
Yuan, S. W. K.; Frederking, T. H. K.
1989-01-01
Applications of the thermomechanical effect has been qualified including incorporation in large-scale space systems in the area of vapor-liquid phase separation (VLPS). The theory of the porous-plug phase separator is developed for the limit of a high thermal impedance of the solid-state grains. Extensions of the theory of nonlinear turbulent flow are presented based on experimental results.
Singular field response and singular screening of vacancies in antiferromagnets.
Wollny, Alexander; Andrade, Eric C; Vojta, Matthias
2012-10-26
For isolated vacancies in ordered local-moment antiferromagnets we show that the magnetic-field linear-response limit is generically singular: The magnetic moment associated with a vacancy in zero field is different from that in a finite field h in the limit h→0(+). The origin is a universal and singular screening cloud, which moreover leads to perfect screening as h→0(+) for magnets which display spin-flop bulk states in the weak-field limit. PMID:23215218
Extending the scanning angle of a phased array antenna by using a null-space medium.
Sun, Fei; He, Sailing
2014-01-01
By introducing a columnar null-space region as the reference space, we design a radome that can extend the scanning angle of a phased array antenna (PAA) by a predetermined relationship (e.g. a linear relationship between the incident angle and steered output angle can be achieved). After some approximation, we only need two homogeneous materials to construct the proposed radome layer by layer. This kind of medium is called a null-space medium, which has been studied and fabricated for realizing hyper-lenses and some other devices. Numerical simulations verify the performance of our radome. PMID:25355198
Extending the scanning angle of a phased array antenna by using a null-space medium
NASA Astrophysics Data System (ADS)
Sun, Fei; He, Sailing
2014-10-01
By introducing a columnar null-space region as the reference space, we design a radome that can extend the scanning angle of a phased array antenna (PAA) by a predetermined relationship (e.g. a linear relationship between the incident angle and steered output angle can be achieved). After some approximation, we only need two homogeneous materials to construct the proposed radome layer by layer. This kind of medium is called a null-space medium, which has been studied and fabricated for realizing hyper-lenses and some other devices. Numerical simulations verify the performance of our radome.
Extending the scanning angle of a phased array antenna by using a null-space medium
Sun, Fei; He, Sailing
2014-01-01
By introducing a columnar null-space region as the reference space, we design a radome that can extend the scanning angle of a phased array antenna (PAA) by a predetermined relationship (e.g. a linear relationship between the incident angle and steered output angle can be achieved). After some approximation, we only need two homogeneous materials to construct the proposed radome layer by layer. This kind of medium is called a null-space medium, which has been studied and fabricated for realizing hyper-lenses and some other devices. Numerical simulations verify the performance of our radome. PMID:25355198
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
NASA Technical Reports Server (NTRS)
Elgradechi, Amine M.
1993-01-01
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
NASA Technical Reports Server (NTRS)
1974-01-01
The 12 month Phase A Conceptual Design Study of the Atmospheric, Magnetospheric and Plasmas in Space (AMPS) payload performed within the Program Development Directorate of the Marshall Space Flight Center is presented. The AMPS payload makes use of the Spacelab pressurized module and pallet, is launched by the space shuttle, and will have initial flight durations of 7 days. Scientific instruments including particle accelerators, high power transmitters, optical instruments, and chemical release devices are mounted externally on the Spacelab pallet and are controlled by the experimenters from within the pressurized module. The capability of real-time scientist interaction on-orbit with the experiment is a major characteristic of AMPS.
Holographic phase space: c-functions and black holes as renormalization group flows
NASA Astrophysics Data System (ADS)
Paulos, Miguel F.
2011-05-01
We construct a mathcal{N} -function for Lovelock theories of gravity, which yields a holographic c-function in domain-wall backgrounds, and seemingly generalizes the concept for black hole geometries. A flow equation equates the monotonicity properties of mathcal{N} with the gravitational field, which has opposite signs in the domain-wall and black hole backgrounds, due to the presence of negative/positive energy in the former/latter, and accordingly mathcal{N} monotonically decreases/increases from the UV to the IR. On AdS spaces the mathcal{N} -function is related to the Euler anomaly, and at a black hole horizon it is generically proportional to the entropy. For planar black holes, mathcal{N} diverges at the horizon, which we interpret as an order N 2 increase in the number of effective degrees of freedom. We show how mathcal{N} can be written as the ratio of the Wald entropy to an effective phase space volume, and using the flow equation relate this to Verlinde's notion of gravity as an entropic force. From the effective phase space we can obtain an expression for the dual field theory momentum cut-off, matching a previous proposal in the literature by Polchinski and Heemskerk. Finally, we propose that the area in Planck units counts states, not degrees of freedom, and identify it also as a phase space volume. Written in terms of the proper radial distance β, it takes the suggestive form of a canonical partition function at inverse temperature β, leading to a "mean energy" which is simply the extrinsic curvature of the surface. Using this we relate this definition of holographic phase space with the effective phase space appearing in the mathcal{N} -function.
Pickup Ion Phase Space Distributions at Titan in a Three Dimensional Exosphere
NASA Technical Reports Server (NTRS)
Hartle, Richard; Sittler, Edward
2006-01-01
The composition and structure of neutral exospheres imbedded in moving plasmas can be determined by measurements of the velocity distributions of their pickup ion progeny. In turn, the velocity distributions are dependent on the spatial structure of the neutral source gases. Since Titan's neutral exosphere extends into the Saturn's magnetosphere (or solar wind) and well above its ionopause, it serves as a good place to analyze such characteristics. They are analyzed using pickup ion measurements made by the Cassini Plasma Spectrometer (CAPS) at Titan [e.g., Hartle et al., 2006] and an ion kinetic model. An early version of the model [Hartle and Sittler, 2007] is an expression describing the phase space density of pickup ions, which is derived from the Vlasov equation with an ion source that explicitly accounts for the velocity and spatial variation of the exosphere source gases. The current version used here includes exosphere source gases in three dimensions. A fundamental parameter of the phase space densities is the ratio of the gyroradius to the neutral scale height alpha, = r(sub g)/H. Titan's exosphere structure yields pickup ions whose phase space distributions are beam-like when alpha >> 1 and fluid-like when alpha << 1. Downstream from the source peak, the light pickup ions, with alpha << 1, are easily observed because their phase space densities are almost uniform over the orbit phases. On the other hand, the phase space distributions of the heavier ions, with alpha >> 1, peak over narrow velocity and spatial ranges. This beam-like nature makes it considerably more difficult to observe heavy ions because their downstream positions and viewing directions are narrowly constrained. Examples of these extremes will be discussed.
Visibility of a spacetime singularity
Joshi, Pankaj S.
2007-02-15
We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultradense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of nonspacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed nonspacelike curves which also necessarily escape from the same. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.
Singularity Resolution in Quantum Gravity
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2014-03-01
In recent years, progress in understanding of the quantization of cosmological spacetimes using techniques of loop quantum gravity, has led to important insights on the resolution of singularities. With a rigorous loop quantization of isotropic and anisotropic spacetimes and development of sophisticated numerical techniques, it is now possible to explore in detail the structure of spacetime in the Planck regime and extract new physics of the very early universe. Investigations of quantization of various spacetimes indicates that classical singularities such as the big bang are avoided, and quantum evolution results in a bounce of the scale factor. The resolution of singularities seems to occur without any assumption on the initial state for quantum evolution or the equation of state of matter. In this talk, we will review some of the main developments in this direction and provide an up to date summary of the novel results obtained on the resolution of singularities in various models in loop quantum gravity.
Phase-space structure of the Buckingham's two-body problem
NASA Astrophysics Data System (ADS)
Pricopi, D.; Popescu, E.
2016-06-01
In this paper, we study the global flow for the two-body problem associated to the Buckingham potential. For this, using McGehee-type transformations, we write the regularized equations of motion. Then, reducing the 4-dimensional phase space to a 2-dimension one, the global flow in the phase plane is described for all possible values of the parameters of the potential and those of the energy and angular momentum constants. Every phase trajectory is interpreted in terms of physical motion, our problem being depicted both geometrically and physically.
NASA Technical Reports Server (NTRS)
Deuser, Mark S.; Vanalstine, James M.; Vellinger, John C.; Wessling, Francis C.; Lundquist, Charles A.
1992-01-01
Traditional separation techniques are inadequate for many new bioprocessing challenges. Innovative separation methods such as aqueous two phase partitioning are needed to perpetuate bioprocess commercialization. Aqueous two phase polymer partitioning systems provide a process for separating biological materials when combined with microgravity. An innovative space qualified apparatus developed for carrying out separations by partitioning in immiscible polymer systems under mirogravity conditions is described. The apparatus offers an innovative approach to low gravity bioseparations in general and phase partitioning in particular. These capabilities support NASA's interest in serving the biotechnology research community and providing quantitative data in the gravity dependent components of separation processes.
Inflation, singular instantons, and eleven dimensional cosmology
NASA Astrophysics Data System (ADS)
Hawking, S. W.; Reall, Harvey S.
1999-01-01
We investigate cosmological solutions of eleven dimensional supergravity compactified on a squashed seven manifold. The effective action for the four dimensional theory contains scalar fields describing the size and squashing of the compactifying space. The potential for these fields consists of a sum of exponential terms. At early times only one such term is expected to dominate. The condition for an exponential potential to admit inflationary solutions is derived and it is shown that inflation is not possible in our model. The criterion for an exponential potential to admit a Hawking-Turok instanton is also derived. It is shown that the instanton remains singular in eleven dimensions.
Parametric studies of phase change thermal energy storage canisters for Space Station Freedom
NASA Technical Reports Server (NTRS)
Kerslake, Thomas W.
1991-01-01
Phase Change Materials (PCM) canister parametric studies are discussed wherein the thermal-structural effects of changing various canister dimensions and contained PCM mass values are examined. With the aim of improving performance, 11 modified canister designs are analyzed and judged relative to a baseline design using five quantitative performance indicators. Consideration is also given to qualitative factors such as fabrication/inspection, canister mass production, and PCM containment redundancy. Canister thermal analyses are performed using the finite-difference based computer program NUCAM-2DV. Thermal-stresses are calculated using closed-form solutions and simplifying assumptions. Canister wall thickness, outer radius, length, and contained PCM mass are the parameters considered for this study. Results show that singular canister design modifications can offer improvements on one or two performance indicators. Yet, improvement in one indicator is often realized at the expense of another. This confirms that the baseline canister is well designed. However, two alternative canister designs, which incorporate multiple modifications, are presented that offer modest improvements in mass or thermal performance, respectively.
On the Construction of Property Based Diabatizations: Diabolical Singular Points.
Zhu, Xiaolei; Yarkony, David R
2015-12-17
Diabatizations achieved by diagonalization of a property operator or as the extremum of a molecular property are numerous and widely used, although for a particular system a given property method may have limited accuracy or even fail catastrophically. These failures are usually analyzed in terms of limitations of the chosen property or method. Here we introduce an alternative perspective, failure attributable to singularities in the defining equations. The singular subspace is analogous to the conical intersection seam in potential energy surfaces. Using the archetypical NH3 nonadiabatic photodissociation, it is shown that for two states the diabatization condition has singularities on a subspace of dimension N - 2, where N = 3N(atom) - 6, is the number of internal coordinates. This singular subspace is distinct from the N - 2-dimensional seam of conical intersections of the electronic Hamiltonian and results incorrectly, in singular derivative couplings between diabatic states in unexpected regions of nuclear coordinate space. Simple indicators are developed that provide ways to anticipate and avoid these singularities. PMID:26444643
Molecular phase space transport in water: Non-stationary random walk model
NASA Astrophysics Data System (ADS)
Nerukh, Dmitry; Ryabov, Vladimir; Taiji, Makoto
2009-11-01
Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).
Plimak, L.I.; Fleischhauer, M.; Olsen, M.K.; Collett, M.J.
2003-01-01
We present an introduction to phase-space techniques (PST) based on a quantum-field-theoretical (QFT) approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation (even after phase-space doubling) and hence fail to produce a stochastic differential equation (SDE), we show how the system in question may be approximated via stochastic difference equations (S{delta}E). Second, we show that introducing sources into the SDE's (or S{delta}E's) generalizes them to a full quantum nonlinear stochastic response problem (thus generalizing Kubo's linear reaction theory to a quantum nonlinear stochastic response theory). Third, we establish general relations linking quantum response properties of the system in question to averages of operator products ordered in a way different from time normal. This extends PST to a much wider assemblage of operator products than are usually considered in phase-space approaches. In all cases, our approach yields a very simple and straightforward way of deriving stochastic equations in phase space.
Hénon-Heiles interaction for hydrogen atom in phase space
NASA Astrophysics Data System (ADS)
da Cruz Filho, J. S.; Amorim, R. G. G.; Ulhoa, S. C.; Khanna, F. C.; Santana, A. E.; Vianna, J. D. M.
2016-03-01
Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase space are introduced and analyzed under physical basis. The hydrogen atom is explored in the same context. Then we add a Hénon-Heiles potential to the hydrogen atom in order to explore chaotic features.
Phase Space Approach for S2 arrow S0 internal conversion in the benzene molecule.
NASA Astrophysics Data System (ADS)
Kallush, Shimshon; Segev, Bilha; Sergeev, Alexei; Heller, Eric J.
2000-06-01
The theoretical problem of finding propensity rules for the partition of energy between competing vibrations in a radiationless vibronic relaxation transition, is converted by the phase-space method of [1,2] to the simple mathematical problem of finding a maximum for a simple function under a constraint. The function is the Wigner function of the initial state and the constraint is energy conservation, defining an accepting energy surface in phase space. We apply this phase space method for finding propensity rules for vibronic transitions when the Frack-Condon factors are exponentially small to the classical example of the benzene molecule. We extend the method to forbidden transitions and include in the analysis non-harmonic force-field effects. Using the phase space analysis, we explain the non-classical behavior of the S_2arrow S0 relaxation of the benzene. Given the energy gap, reasonable displacements and recently calculated force fields [3] we show that almost all the energy must go to C-H stretching. Non-harmonic effects increase in this case the transition rate but do not change the partition of energy between the accepting vibrational modes. [1] E.J. Heller and D. Beck, Chem. Phys. Lett. 202, 350 (1993). [2] B. Segev and E.J. Heller, Journal of Chemical Physics, 112, 4004-4013 (2000). [3] A. Miani, E. Cane, P. Palmieri, A. Trombetti,N.C. Handy, J. Chem. Phys., 112, 248-259 (2000).
Phase space and jet definitions in soft-collinear effective theory
Cheung, William Man-Yin; Luke, Michael; Zuberi, Saba
2009-12-01
We discuss consistent power counting for integrating soft and collinear degrees of freedom over arbitrary regions of phase space in the soft-collinear effective theory, and illustrate our results at one-loop with several jet algorithms: JADE, Sterman-Weinberg and k{sub perpendicular}. Consistently applying soft-collinear effective theory power counting in phase space, along with nontrivial zero-bin subtractions, prevents double counting of final states. The resulting phase space integrals over soft and collinear regions are individually ultraviolet divergent, but the phase space ultraviolet divergences cancel in the sum. Whether the soft and collinear contributions are individually infrared safe depends on the jet definition. We show that while this is true at one-loop for JADE and Sterman-Weinberg, the k{sub perpendicular} algorithm does not factorize into individually infrared safe soft and collinear pieces in dimensional regularization. We point out that this statement depends on the ultraviolet regulator, and that in a cutoff scheme the soft functions are infrared safe.
ERIC Educational Resources Information Center
de Silva, Chamelle R.; Chigona, A.; Adendorff, S. A.
2016-01-01
Among its many affordances, the interactive whiteboard (IWB) as a digital space for children's dialogic engagement in the Foundation Phase classroom remains largely under-exploited. This paper emanates from a study which was undertaken in an attempt to understand how teachers acquire knowledge of emerging technologies and how this shapes their…
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
NASA Astrophysics Data System (ADS)
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
On the nonclassical character of the phase-space representations of quantum mechanics
NASA Astrophysics Data System (ADS)
Guz, W.
1985-02-01
The quasiclassical representations of quantum theory, generalizing the concept of a phase-space representation of quantum mechanics, are studied with particular emphasis on some questions connected with the Jordan structure of the classical and quantum algebras of observables. A generalized version of the theorem of Gleason, Kahane, and Zelazko is used to establish some nonclassical features of these representations.
Phase-space spinor amplitudes for spin-1/2 systems
NASA Astrophysics Data System (ADS)
Watson, P.; Bracken, A. J.
2011-04-01
The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-(1)/(2) is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-(1)/(2) magnetic dipole in a time-dependent magnetic field.
Phase-space analysis of convection in a /sup 3/He - superfluid /sup 4/He solution
Haucke, H.; Maeno, Y.
1982-01-01
Observations have been made on thermal convection below 1K in a dilute solution of /sup 3/He in superfluid /sup 4/He contained in a cylindrical cell of aspect ratio GAMMA = 1.20. Complicated oscillatory phenomena were observed with a high degree of reproducibility using two temperature sensors. Phase-space analysis suggests a description in terms of strange-attractor dynamics.
Numerical method for estimating the size of chaotic regions of phase space
Henyey, F.S.; Pomphrey, N.
1987-10-01
A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs. (LSP)
New singularities for Stokes waves
NASA Astrophysics Data System (ADS)
Crew, Samuel C.; Trinh, Philippe H.
2016-07-01
In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of $120^\\circ$. Here, the complex velocity scales like $f^{1/3}$ where $f$ is the complex potential. Later in 1973, Grant showed that for any wave away from the steepest configuration, the singularity $f = f^*$ moves into the complex plane, and is of order $(f-f^*)^{1/2}$ (J. Fluid Mech., vol. 59, 1973, pp. 257-262). Grant conjectured that as the highest wave is approached, other singularities must coalesce at the crest so as to cancel the square-root behaviour. Despite recent advances, the complete singularity structure of the Stokes wave is still not well understood. In this work, we develop numerical methods for constructing the Riemann surface that represents the extension of the water wave into the complex plane. We show that a countably infinite number of distinct singularities exists on other branches of the solution, and that these singularities coalesce as Stokes' highest wave is approached.
Not Available
1991-06-07
A new class of X-band phase shifters using the distributed Josephson inductance (DJI) effect were delivered to NRL for the HTS Space Experiment project. Phase shifts were observed above 77 K, and large phase shifts were observed at 65 K and below. This narrow-band device was developed as a first step to a broadband device. A total of 40 HTS SQUIDs were successfully integrated into a monolithic circuit. Measurement of the temperature dependance of the Q of a resonator in June 1990 and in February 1991 showed no significant change due to aging. A total of seven X-band phase shifters were fabricated, and five were delivered to Naval Research Laboratory. The HTS phase shifter consists of a low loss YBa2Cu3O7 microstrip resonator with 40 SQUID devices monolithically imbedded into the transmission line. This narrow-band device was developed as a first step to a broadband device.
Phased array components for the High Temperature Superconducting Space Experiment (HTSSE)
NASA Astrophysics Data System (ADS)
1991-06-01
A new class of X-band phase shifters using the distributed Josephson inductance (DJI) effect were delivered to NRL for the HTS Space Experiment project. Phase shifts were observed above 77 K, and large phase shifts were observed at 65 K and below. This narrow-band device was developed as a first step to a broadband device. A total of 40 HTS SQUIDs were successfully integrated into a monolithic circuit. Measurement of the temperature dependence of the Q of a resonator in June 1990 and in February 1991 showed no significant change due to aging. A total of seven X-band phase shifters were fabricated, and five were delivered to Naval Research Laboratory. The HTS phase shifter consists of a low loss YBa2Cu3O7 microstrip resonator with 40 SQUID devices monolithically imbedded into the transmission line. This narrow-band device was developed as a first step to a broadband device.
Decryption with incomplete cyphertext and multiple-information encryption in phase space.
Xu, Xiaobin; Wu, Quanying; Liu, Jun; Situ, Guohai
2016-01-25
Recently, we have demonstrated that information encryption in phase space offers security enhancement over the traditional encryption schemes operating in real space. However, there is also an important issue with this technique: increasing the cost for data transmitting and storage. To address this issue, here we investigate the problem of decryption using incomplete cyphertext. We show that the analytic solution under the traditional framework set the lower limit of decryption performance. More importantly, we demonstrate that one just needs a small amount of cyphertext to recover the plaintext signal faithfully using compressive sensing, meaning that the amount of data that needs to transmit and store can be significantly reduced. This leads to multiple information encryption so that we can use the system bandwidth more effectively. We also provide an optical experimental result to demonstrate the plaintext recovered in phase space. PMID:26832552
Simulated response of top-hat electrostatic analysers - importance of phase-space resolution
NASA Astrophysics Data System (ADS)
De Marco, Rossana; Bruno, Roberto; D'Amicis, Raffaella; Federica Marcucci, Maria; Servidio, Sergio; Valentini, Francesco
2016-04-01
We use a numerical code able to reproduce the angular/energy response of a typical electrostatic analyzer of top-hat type starting from velocity distribution functions (VDFs) generated by numerical imulations.The simulations are based on the Hybrid Vlasov-Maxwell (HVM) numerical algorithm which integrates the Vlasov equation for the ion distribution function in multi-dimensional geometry in phase space, while the electrons are treated as a fluid. Virtual satellites launched through the simulation box measure the particle VDFs. Such VDFs are interpolated into a spacecraft reference frame and moved from the simulation Cartesian grid to energy-angular coordinates to mimic the response of a real electrostatic sensor in the solar wind and in the magnetosheath for different conditions. We discuss the results of this study with respect to the importance of phase-space resolution for a space plasma experiment meant to investigate kinetic plasma regime.
Real-time transverse-emittance and phase-space monitor
NASA Astrophysics Data System (ADS)
Song, J.; Piot, P.; Legg, R.; Kehne, D.; Li, R.; Feldl, E.; Jordan, K.; Denard, J.-C.; Krafft, G. A.; Neil, G. R.; Bohn, C. L.
1998-02-01
A real-time multislit [1]transverse-emittance monitor has been developed for diagnosing the space-charge-dominated beam in the 10 MeV injection line of the FEL at Thomas Jefferson National Accelerator Facility (formerly CEBAF). It gives emittance, Twiss parameters, and phase-space contours (without any symmetry assumptions) at the update rate of 1 Hz. It reduces measurement noise in real-time, and incorporates a special algorithm for constructing the phase-space matrix, which yields more accurate results by sweeping the beam across the slits. In this paper we will discuss issues relevant to the software design and implementation. Experimental results obtained from a 250 keV photocathode gun will also be presented and compared with other methods and with PARMELA simulations.
Curved singular beams for three-dimensional particle manipulation
Zhao, Juanying; Chremmos, Ioannis D.; Song, Daohong; Christodoulides, Demetrios N.; Efremidis, Nikolaos K.; Chen, Zhigang
2015-01-01
For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark “hole” in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications. PMID:26166011
Curved singular beams for three-dimensional particle manipulation.
Zhao, Juanying; Chremmos, Ioannis D; Song, Daohong; Christodoulides, Demetrios N; Efremidis, Nikolaos K; Chen, Zhigang
2015-01-01
For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark "hole" in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications. PMID:26166011
The effect of phase angle and wing spacing on tandem flapping wings
NASA Astrophysics Data System (ADS)
Broering, Timothy M.; Lian, Yong-Sheng
2012-12-01
In a tandem wing configuration, the hindwing often operates in the wake of the forewing and, hence, its performance is affected by the vortices shed by the forewing. Changes in the phase angle between the flapping motions of the fore and the hind wings, as well as the spacing between them, can affect the resulting vortex/wing and vortex/vortex interactions. This study uses 2D numerical simulations to investigate how these changes affect the leading dege vortexes (LEV) generated by the hindwing and the resulting effect on the lift and thrust coefficients as well as the efficiencies. The tandem wing configuration was simulated using an incompressible Navier-Stokes solver at a chord-based Reynolds number of 5 000. A harmonic single frequency sinusoidal oscillation consisting of a combined pitch and plunge motion was used for the flapping wing kinematics at a Strouhal number of 0.3. Four different spacings ranging from 0.1 chords to 1 chord were tested at three different phase angles, 0°, 90° and 180°. It was found that changes in the spacing and phase angle affected the timing of the interaction between the vortex shed from the forewing and the hindwing. Such an interaction affects the LEV formation on the hindwing and results in changes in aerodynamic force production and efficiencies of the hindwing. It is also observed that changing the phase angle has a similar effect as changing the spacing. The results further show that at different spacings the peak force generation occurs at different phase angles, as do the peak efficiencies.
Optical authentication based on moiré effect of nonlinear gratings in phase space
NASA Astrophysics Data System (ADS)
Liao, Meihua; He, Wenqi; Wu, Jiachen; Lu, Dajiang; Liu, Xiaoli; Peng, Xiang
2015-12-01
An optical authentication scheme based on the moiré effect of nonlinear gratings in phase space is proposed. According to the phase function relationship of the moiré effect in phase space, an arbitrary authentication image can be encoded into two nonlinear gratings which serve as the authentication lock (AL) and the authentication key (AK). The AL is stored in the authentication system while the AK is assigned to the authorized user. The authentication procedure can be performed using an optoelectronic approach, while the design process is accomplished by a digital approach. Furthermore, this optical authentication scheme can be extended for multiple users with different security levels. The proposed scheme can not only verify the legality of a user identity, but can also discriminate and control the security levels of legal users. Theoretical analysis and simulation experiments are provided to verify the feasibility and effectiveness of the proposed scheme.
NASA Technical Reports Server (NTRS)
Romanofsky, Robert R.
2007-01-01
Though there are a few examples of scanning phased array antennas that have flown successfully in space, the quest for low-cost, high-efficiency, large aperture microwave phased arrays continues. Fixed and mobile applications that may be part of a heterogeneous exploration communication architecture will benefit from the agile (rapid) beam steering and graceful degradation afforded by phased array antennas. The reflectarray promises greater efficiency and economy compared to directly-radiating varieties. Implementing a practical scanning version has proven elusive. The ferroelectric reflectarray, under development and described herein, involves phase shifters based on coupled microstrip patterned on Ba(x)Sr(1-x)TiO3 films, that were laser ablated onto LaAlO3 substrates. These devices outperform their semiconductor counterparts from X- through and K-band frequencies. There are special issues associated with the implementation of a scanning reflectarray antenna, especially one realized with thin film ferroelectric phase shifters. This paper will discuss these issues which include: relevance of phase shifter loss; modulo 2(pi) effects and phase shifter transient effects on bit error rate; scattering from the ground plane; presentation of a novel hybrid ferroelectric-semiconductor phase shifter; and the effect of mild radiation exposure on phase shifter performance.
Naked singularity resolution in cylindrical collapse
Kurita, Yasunari; Nakao, Ken-ichi
2006-03-15
In this paper, we study the gravitational collapse of null dust in cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the backreaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the naked singularity. In this case, although this naked singularity satisfies the strong curvature condition by Krolak (limiting focusing condition), geodesics which hit the singularity can be extended uniquely across the singularity. Therefore, we may say that the collapsing null dust passes through the singularity formed by itself and then leaves for infinity. Finally, the singularity completely disappears and the flat spacetime remains.
Mixed semiclassical-classical propagators for the Wigner phase space representation.
Koda, Shin-Ichi
2016-04-21
We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency. PMID:27389210
Mixed semiclassical-classical propagators for the Wigner phase space representation
NASA Astrophysics Data System (ADS)
Koda, Shin-ichi
2016-04-01
We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.
MMIC linear-phase and digital modulators for deep space spacecraft X-band transponder applications
NASA Technical Reports Server (NTRS)
Mysoor, Narayan R.; Ali, Fazal
1991-01-01
The design concepts, analyses, and development of GaAs monolithic microwave integrated circuit (MMIC) linear-phase and digital modulators for the next generation of space-borne communications systems are summarized. The design approach uses a compact lumped element quadrature hybrid and Metal Semiconductor Field Effect Transistors (MESFET)-varactors to provide low loss and well-controlled phase performance for deep space transponder (DST) applications. The measured results of the MESFET-diode show a capacitance range of 2:1 under reverse bias, and a Q of 38 at 10 GHz. Three cascaded sections of hybrid-coupled reflection phase shifters were modeled and simulations performed to provide an X-band (8415 +/- 50 MHz) DST phase modulator with +/- 2.5 radians of peak phase deviation. The modulator will accommodate downlink signal modulation with composite telemetry and ranging data, with a deviation linearity tolerance of +/- 8 percent and insertion loss of less than 8 +/- 0.5 dB. The MMIC digital modulator is designed to provide greater than 10 Mb/s of bi-phase modulation at X-band.
Dynamics of learning in multilayer perceptrons near singularities.
Cousseau, Florent; Ozeki, Tomoko; Amari, Shun-Ichi
2008-08-01
The dynamical behavior of learning is known to be very slow for the multilayer perceptron, being often trapped in the "plateau." It has been recently understood that this is due to the singularity in the parameter space of perceptrons, in which trajectories of learning are drawn. The space is Riemannian from the point of view of information geometry and contains singular regions where the Riemannian metric or the Fisher information matrix degenerates. This paper analyzes the dynamics of learning in a neighborhood of the singular regions when the true teacher machine lies at the singularity. We give explicit asymptotic analytical solutions (trajectories) both for the standard gradient (SGD) and natural gradient (NGD) methods. It is clearly shown, in the case of the SGD method, that the plateau phenomenon appears in a neighborhood of the critical regions, where the dynamical behavior is extremely slow. The analysis of the NGD method is much more difficult, because the inverse of the Fisher information matrix diverges. We conquer the difficulty by introducing the "blow-down" technique used in algebraic geometry. The NGD method works efficiently, and the state converges directly to the true parameters very quickly while it staggers in the case of the SGD method. The analytical results are compared with computer simulations, showing good agreement. The effects of singularities on learning are thus qualitatively clarified for both standard and NGD methods. PMID:18701364
Gao, Zhong-Ke; Jin, Ning-De; Wang, Wen-Xu; Lai, Ying-Cheng
2010-07-01
The dynamics of two-phase flows have been a challenging problem in nonlinear dynamics and fluid mechanics. We propose a method to characterize and distinguish patterns from inclined water-oil flow experiments based on the concept of network motifs that have found great usage in network science and systems biology. In particular, we construct from measured time series phase-space complex networks and then calculate the distribution of a set of distinct network motifs. To gain insight, we first test the approach using time series from classical chaotic systems and find a universal feature: motif distributions from different chaotic systems are generally highly heterogeneous. Our main finding is that the distributions from experimental two-phase flows tend to be heterogeneous as well, suggesting the underlying chaotic nature of the flow patterns. Calculation of the maximal Lyapunov exponent provides further support for this. Motif distributions can thus be a feasible tool to understand the dynamics of realistic two-phase flow patterns. PMID:20866710
GPS-Like Phasing Control of the Space Solar Power System Transmission Array
NASA Technical Reports Server (NTRS)
Psiaki, Mark L.
2003-01-01
The problem of phasing of the Space Solar Power System's transmission array has been addressed by developing a GPS-like radio navigation system. The goal of this system is to provide power transmission phasing control for each node of the array that causes the power signals to add constructively at the ground reception station. The phasing control system operates in a distributed manner, which makes it practical to implement. A leader node and two radio navigation beacons are used to control the power transmission phasing of multiple follower nodes. The necessary one-way communications to the follower nodes are implemented using the RF beacon signals. The phasing control system uses differential carrier phase relative navigation/timing techniques. A special feature of the system is an integer ambiguity resolution procedure that periodically resolves carrier phase cycle count ambiguities via encoding of pseudo-random number codes on the power transmission signals. The system is capable of achieving phasing accuracies on the order of 3 mm down to 0.4 mm depending on whether the radio navigation beacons operate in the L or C bands.
NASA Astrophysics Data System (ADS)
Beckwith, Andrew
When initial radius of the universe in four dimensions and there is only ONE repeating universe then the initial radius goes to zero or gets very close to zero if Stoica actually derived Einstein equations are used in a formalism which remove in four dimensions the big bang singularity pathology. So then the reason for Planck length no longer holds. This assumes a repeating single universe. We present a given entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto , and show that there are consequences due to initial entanged entropy for a time dependent horizon radius in cosmology, with (flat space conditions) horizon radius as equal to conformal time Even if the 3 dimensional spatial length goes to zero. This construction preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if in four dimensions we have the initial radii going to zero We also find that in the case of a multiverse, that such considerations will not hold and that cosmic singularities have a different characteristic in the multiverse setting than in the single universe repeated over and over again. i.e. using an argument borrowed and modified from Kauffman, the multiverse will not mandate ‘perfect’ singularities. The existence of a multiverse may allow for non zero singularities in lieu with the Kauffman argument cited at the end of the document, plus the lower pre big bang temperatures which may allow for the survivial of gravitons just before the onset of the cosmological expansion phase, if a multiverse exists embedding our present universe
Singular values, nematic disclinations, and emergent biaxiality.
Čopar, Simon; Dennis, Mark R; Kamien, Randall D; Žumer, Slobodan
2013-05-01
Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame that can be extracted from the tensorial description of the nematic order vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. The degrees of freedom are unveiled in the form of quasidefects and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase. PMID:23767474
Phase space analysis and classification of sonar echoes in shallow-water channels
NASA Astrophysics Data System (ADS)
Okopal, Greg
A primary objective of active sonar systems is to detect, locate, and classify objects, such as mines, ships, and biologics, based on their sonar backscatter. A shallow-water ocean channel is a challenging environment in which to classify sonar echoes because interactions of the sonar signal with the ocean surface and bottom induce frequency-dependent changes (especially dispersion and damping) in the signal as it propagates, the effects of which typically grow with range. Accordingly, the observed signal depends not only on the initial target backscatter, but also the propagation channel and how far the signal has propagated. These propagation effects can increase the variability of observed target echoes and degrade classification performance. Furthermore, uncertainty of the exact propagation channel and random variations within a channel cause classification features extracted from the received sonar echo to behave as random variables. With the goal of improving sonar signal classification in shallow-water environments, this work develops a phase space framework for studying sound propagation in channels with dispersion and damping. This approach leads to new moment features for classification that are invariant to dispersion and damping, the utility of which is demonstrated via simulation. In addition, the accuracy of a previously developed phase space approximation method for range-independent pulse propagation is analyzed and shown to be greater than the accuracy of the standard stationary phase approximation for both large and small times/distances. The phase space approximation is also extended to range dependent propagation. Finally, the phase space approximation is used to investigate the random nature of moment features for classification by calculating the moments of the moment features under uncertain and random channel assumptions. These moments of the moment features are used to estimate probability distribution functions for the moment features, and
Vacuum spacetimes with controlled singularities and without symmetries
NASA Astrophysics Data System (ADS)
Chruściel, Piotr T.; Klinger, Paul
2015-08-01
We show the existence of a family of four-dimensional vacuum spacetimes with asymptotically velocity-dominated singularities and without symmetries. The solutions are obtained using Fuchsian methods and are parametrized by several free functions of all space coordinates which control their asymptotic expansion.
Zero-g experiments with a He II active phase separator for space application
NASA Technical Reports Server (NTRS)
Denner, H. D.; Klipping, G.; Lueders, K.; Ruppert, U.; Stahnke, F.; Szuecs, Z.; Elleman, D.; Petrac, D.
1984-01-01
An active phase separator (APS) for temperature control of He II space cooling systems was tested in a zero-g environment during a series of parabolic flights on a NASA KC 135 aircraft. The APS provides for liquid-gas separation and features an annular gap, a downstream heat exchanger and an upstream ball closure. The apparatus was operated during acceleration and floating and in two different heat load situations. The tests confirmed that adequate mass flow rates could be maintained using a vacuum pump to simulate space vacuum and that residual liquid could be evaporated from the heat exchanger after closing a ball valve to seal off flows.
Homoclinic orbits around spinning black holes. II. The phase space portrait
Perez-Giz, Gabe; Levin, Janna
2009-06-15
In paper I in this series, we found exact expressions for the equatorial homoclinic orbits: the separatrix between bound and plunging, whirling and not whirling motion. As a companion to that physical space study, in this paper we paint a phase space portrait of the homoclinic orbits that includes exact expressions for the actions and fundamental frequencies. Additionally, we develop a reduced Hamiltonian description of Kerr motion that allows us to track groups of trajectories with a single global clock. This facilitates a variational analysis, whose stability exponents and eigenvectors could potentially be useful for future studies of families of black hole orbits and their associated gravitational waveforms.
Advanced ceramic fabric body mounted radiator for Space Station Freedom Phase O design
Webb, B.J.; Antoniak, Z.I.; Pauley, K.A.
1990-06-01
A body mounted radiator concept constructed of advanced ceramic fabric materials for use with the Phase 0 design of Space Station Freedom is described. The radiator is expected to weigh between 1.4 and 3.5 kg/m{sup 2} of single sided radiating surface, use ammonia working fluid, be highly deployable, and exhibit good reliability characteristics. This compares well with the 11.8 kg/m{sup 2} for two sided radiators proposed for the current space station design.
The Phase-Space Structure of Cold Dark Matter in the Universe
NASA Astrophysics Data System (ADS)
Shandarin, Sergei
2015-01-01
A novel method allowing to compute density, velocity and other fields in cosmological N-body simulations with unprecedentedly high spatial resolution is described. It is based on the tessellation of the three-dimensional manifold representing cold dark matter in six-dimensional phase space. The density, velocity and other fields are computed by projecting the tessellation on configuration space. The application of this technique to cosmological N-body simulations in ΛCDM cosmology reveals a far more elaborate cosmic web then dot plots or self-adaptive SPH. In addition, this method allows to uniquely define physical voids and identify and study the caustic surfaces directly.
NASA Technical Reports Server (NTRS)
Cadogan, Dave; Lingo, Bob
1996-01-01
In July of 1996, ILC Dover was awarded Phase 1 of a contract for NASA to develop a prototype Power Assisted Space Suit glove to enhance the performance of astronauts during Extra-Vehicular Activity (EVA). This report summarizes the work performed to date on Phase 1, and details the work to be conducted on Phase 2 of the program. Phase 1 of the program consisted of research and review of related technical sources, concept brainstorming, baseline design development, modeling and analysis, component mock-up testing, and test data analysis. ILC worked in conjunction with the University of Maryland's Space Systems Laboratory (SSL) to develop the power assisted glove. Phase 2 activities will focus on the design maturation and the manufacture of a working prototype system. The prototype will be tested and evaluated in conjunction with existing space suit glove technology to determine the performance enhancement anticipated with the implementation of the power assisted joint technology in space suit gloves.