Angular Degrees Research Articles

Realization of quantum permutation algorithm in high dimensional Hilbert space**Project supported by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China (Grant Nos. 11374008, 11374238, 11374239, and 11534008).

Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light’s orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light’s orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.

Crossing the dividing surface of transition state theory. IV. Dynamical regularity and dimensionality reduction as key features of reactive trajectories.

The atom-diatom interaction is studied by classical mechanics using Jacobi coordinates (R, r, θ). Reactivity criteria that go beyond the simple requirement of transition state theory (i.e., PR* > 0) are derived in terms of specific initial conditions. Trajectories that exactly fulfill these conditions cross the conventional dividing surface used in transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) only once. Furthermore, they are observed to be strikingly similar and to form a tightly packed bundle of perfectly collimated trajectories in the two-dimensional (R, r) configuration space, although their angular motion is highly specific for each one. Particular attention is paid to symmetrical transition states (i.e., either collinear or T-shaped with C2v symmetry) for which decoupling between angular and radial coordinates is observed, as a result of selection rules that reduce to zero Coriolis couplings between modes that belong to different irreducible representations. Liapunov exponents are equal to zero and Hamilton's characteristic function is planar in that part of configuration space that is visited by reactive trajectories. Detailed consideration is given to the concept of average reactive trajectory, which starts right from the saddle point and which is shown to be free of curvature-induced Coriolis coupling. The reaction path Hamiltonian model, together with a symmetry-based separation of the angular degree of freedom, provides an appropriate framework that leads to the formulation of an effective two-dimensional Hamiltonian. The success of the adiabatic approximation in this model is due to the symmetry of the transition state, not to a separation of time scales. Adjacent trajectories, i.e., those that do not exactly fulfill the reactivity conditions have similar characteristics, but the quality of the approximation is lower. At higher energies, these characteristics persist, but to a lesser degree. Recrossings of the dividing surface then become much more frequent and the phase space volumes of initial conditions that generate recrossing-free trajectories decrease. Altogether, one ends up with an additional illustration of the concept of reactive cylinder (or conduit) in phase space that reactive trajectories must follow. Reactivity is associated with dynamical regularity and dimensionality reduction, whatever the shape of the potential energy surface, no matter how strong its anharmonicity, and whatever the curvature of its reaction path. Both simplifying features persist during the entire reactive process, up to complete separation of fragments. The ergodicity assumption commonly assumed in statistical theories is inappropriate for reactive trajectories.

Subperiodic trigonometric subsampling: A numerical approach

We show that Gauss-Legendre quadrature applied to trigonometric polynomials on subintervals of the period can be competitive with subperiodic trigonometric Gaussian quadrature. For example with intervals corresponding to few angular degrees, relevant for regional scale models on the earth surface, we see a subsampling ratio of one order of magnitude already at moderate trigonometric degrees.

Abstract 11871: Morphologic Features Predict Late Adverse Events in Uncomplicated Stanford Type-B Aortic Dissection

Introduction: Medical treatment of uncomplicated Stanford type-B aortic dissection (AD) is associated with a high rate of late adverse events (AE). Endografting may prevent late complications, however, initial trials failed to demonstrate a survival benefit in the first two years. We hypothesize that morphologic features at the initial hospitalization are associated with AE and could aid in the risk stratification of patients with AD. Methods: Eighty-three patients with acute uncomplicated type-B AD were retrospectively identified at two aortic centers in the US and EU. Multiple clinical and morphologic features - including true vs. false lumen blood supply - were identified on high-quality CT scans and followed. Multivariable Cox proportional hazards regression was used to evaluate the associations between candidate predictors and AE - defined as rapid growth, aneurysm formation (≥6cm), organ ischemia, and fatal or non-fatal aortic rupture, and develop an internally validated risk score. Results: AE were observed in 33 patients over a median 850 (IQR 247-1824) days follow up. Five significant predictors were identified in the multivariable model: Connective tissue disease (HR 2.94, 95% CI: 1.29 - 6.72, p= 0.01), circumferential extent of false lumen in angular degrees (HR 1.03, 95% CI: 1.01 - 1.04, p= 0.003), maximum aortic diameter in mm (HR 1.10, 95% CI: 1.02 - 1.18, p= 0.015), false lumen outflow in mL/min (HR 0.999, 95% CI: 0.998 - 1.000, p= 0.055), and number of intercostal arteries (HR 0.89, 95% CI: 0.80 - 0.98), p= 0.024). A model combining these five factors was constructed to calculate patient specific risk scores allowing stratification into high, intermediate, and low risk terciles. The model showed good discriminatory ability with an optimism-corrected c-statistic of 70.1%. Conclusion: Morphologic features predict late AE in uncomplicated type-B AD. If externally validated this may identify high-risk patients who benefit from early endografting.

DETECTION OF SOLAR-LIKE OSCILLATIONS, OBSERVATIONAL CONSTRAINTS, AND STELLAR MODELS FOR θ CYG, THE BRIGHTEST STAR OBSERVED BY THE KEPLER MISSION

ABSTRACT θ Cygni is an F3 spectral type magnitude V = 4.48 main-sequence star that was the brightest star observed by the original Kepler spacecraft mission. Short-cadence (58.8 s) photometric data using a custom aperture were first obtained during Quarter 6 (2010 June–September) and subsequently in Quarters 8 and 12–17. We present analyses of solar-like oscillations based on Q6 and Q8 data, identifying angular degree l = 0, 1, and 2 modes with frequencies of 1000–2700 μHz, a large frequency separation of 83.9 ± 0.4 μHz, and maximum oscillation amplitude at frequency ν max = 1829 ± 54 μHz. We also present analyses of new ground-based spectroscopic observations, which, combined with interferometric angular diameter measurements, give T eff = 6697 ± 78 K, radius 1.49 ± 0.03 R ⊙, [Fe/H] = −0.02 ± 0.06 dex, and log g = 4.23 ± 0.03. We calculate stellar models matching these constraints using the Yale Rotating Evolution Code and the Asteroseismic Modeling Portal. The best-fit models have masses of 1.35–1.39 M ⊙ and ages of 1.0–1.6 Gyr. θ Cyg’s T eff and log g place it cooler than the red edge of the γ Doradus instability region established from pre-Kepler ground-based observations, but just at the red edge derived from pulsation modeling. The pulsation models show γ Dor gravity modes driven by the convective blocking mechanism, with frequencies of 1–3 cycles per day (11 to 33 μHz). However, gravity modes were not seen in Kepler data; one signal at 1.776 cycles per day (20.56 μHz) may be attributable to a faint, possibly background, binary.

The search of radio transients in the RATAN-600 radio telescope surveys

AbstractWe present the results of the search of variable sources and transient events in the archive data of the sky surveys conducted on 3.9 GHz on the RATAN-600 radio telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) in 1980-1994. 17% of the total studied sources can be attributed to the variables in radio range. About half of them has significant variations in optical brightness according to the data of the catalogs. At the level of 3-5 r.m.s. we found three transient events. Two weak events probably associated with AGN activities or with cataclysmic events such as GRB and a supernova flash. The nature of the third event has not been established. According to our estimation the surface density of radio transients is 0.03 on one square angular degree with the detection level 8–11 mJy on 3.94 GHz.

Large-aperture telescopes in the problems of near-Earth astronomy

Telescopes with aperture higher than 3 m and with travel rate of optical axis of more than 4 angular degrees per second are examined. These telescopes are used for estimating the situation in near-Earth space. Up to now, there are three telescopes with such parameters: SOR, AMOS, SST (all in the United States). A telescope of the same class with aperture of 3.12 m (information telescope TI-3.12) is under completion at Altai Optical Laser Center. The main technical performances of the TI-3.12 telescope are described in the paper. Current problems are defined and ways for their solution are presented.

Orbital Angular Momentum-Entanglement Frequency Transducer.

Entanglement is a vital resource for realizing many tasks such as teleportation, secure key distribution, metrology, and quantum computations. To effectively build entanglement between different quantum systems and share information between them, a frequency transducer to convert between quantum states of different wavelengths while retaining its quantum features is indispensable. Information encoded in the photon's orbital angular momentum (OAM) degrees of freedom is preferred in harnessing the information-carrying capacity of a single photon because of its unlimited dimensions. A quantum transducer, which operates at wavelengths from 1558.3 to 525nm for OAM qubits, OAM-polarization hybrid-entangled states, and OAM-entangled states, is reported for the first time. Nonclassical properties and entanglements are demonstrated following the conversion process by performing quantum tomography, interference, and Bell inequality measurements. Our results demonstrate the capability to create an entanglement link between different quantum systems operating in a photon's OAM degrees of freedom, which will be of great importance in building a high-capacity OAM quantum network.

Vision-based sensing of UAV attitude and altitude from downward in-flight images

Autonomous unmanned aerial vehicles (UAVs) often carry video cameras as part of their payload. Outdoor video captured by such cameras can be used to estimate the attitude and altitude of the UAV by detecting the location of the horizon in the video frames. This paper presents a video frame processing algorithm for estimating the pitch and roll of a UAV, as well as its altitude. The frames are obtained from a downward pointing video camera equipped with a fisheye lens. These open-loop estimates can serve as redundant data used to implement graceful-degradation in the event that the main closed-loop control sensors fail, or for fault-tolerance purposes to augment inertial sensors for increased accuracy. The estimated values had a mean error of ±0.7 angular degrees for roll and ±0.9 angular degrees for pitch, while the altitude estimation from the video had a mean error of ±0.9 meters. The results are presented and compared to actual attitude and altitude values obtained from a traditional inertial measurement unit and, in the case of altitude comparison, an absolute air pressure sensor. The algorithm was developed on a personal computer to work at 10 frames per second and uses only simple image processing functions that can be deployed using open source libraries on lightweight computing boards capable of image processing.

Effects of grading and particle characteristics on small strain properties of granular materials

A series of drained triaxial compression tests was conducted in order to evaluate the effects of grading and particle characteristics on the small strain stiffness of a wide variety of granular materials. To evaluate the quasi-elastic deformation property at small strain levels around 0.001% by static measurement, many small vertical cycles were applied at two isotropic stress states. The effects of maximum and mean particle diameters, fines content, coefficient of uniformity, and degree of particle angularity on the quasi-elastic vertical Young׳s moduli, Evs, by the static measurement were investigated. Within the limited range of grading and particle characteristics tested in the present study, the results showed that: (1) the Evs values were generally independent of maximum and mean particle diameters; (2) the Evs values seemed to decrease with increasing coefficient of uniformity; (3) the effects of fines content and particle angularity on the Evs values were not clear; and (4) the effects of the effective confining pressure on the above-mentioned three trends were insignificant.

Finite-key security analysis for multilevel quantum key distribution

We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite-key-length scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d-level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d-level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.

J-factors of short DNA molecules.

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain end boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length (N) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates.

Geometrical product specifications: A structure of linear dimensions tolerances

The paper reveals the relationship of linear dimensions tolerances with other geometrical specifications: coordinates, deviations of position and deviations of surface configuration of component geometric features. The dependence of the precision structure of the linear dimensions on the functional purpose of features. The basic concept of the paper is informativeness of the feature, which represents the total number of linear and angular degrees of freedom, constrained by the feature in the component at operation. The very informativeness of the feature determines the two-dimensional linear-angular composition of the structure of the linear size, its tolerance and standard grade. This paper discusses only the linear dimensions of the features involved in couplings and forming fits.

Excitation of high orbital angular momentum Rydberg states with Laguerre–Gauss beams

We consider the excitation of Rydberg states through photons carrying an intrinsic orbital angular momentum degree of freedom. Laguerre–Gauss modes, with a helical wave-front structure, correspond to such a set of laser beams, which carry units of orbital angular momentum in their propagation direction, with ℓ0 the winding number. We demonstrate that, in a proper geometry setting, this orbital angular momentum can be transferred to the internal degrees of freedom of the atoms, thus violating the standard dipole selection rules. Higher orbital angular momentum states become accessible through a single photon excitation process. We investigate how the spacial structure of the Laguerre–Gauss beam affects the radial coupling strength, assuming the simplest case of hydrogen-like wavefunctions. Finally we discuss a generalization of the angular momentum coupling, in order to include the effects of the fine and hyperfine splitting, in the context of the Wigner–Eckart theorem.

Non-radial pulsation in first overtone Cepheids of the Small Magellanic Cloud

We analyse photometry for 138 first overtone Cepheids from the Small Magellanic Cloud, in which Optical Gravitational Lensing Experiment (OGLE) team discovered additional variability with period shorter than first overtone period, and period ratios in the (0.60, 0.65) range. In the Petersen diagram these stars form three well separated sequences. The additional variability cannot correspond to other radial mode. This form of pulsation is still puzzling. We find that amplitude of the additional variability is small, typically 2-4 per cent of the first overtone amplitude, which corresponds to 2-5 mmag. In some stars we find simultaneously two close periodicities corresponding to two sequences in the Petersen diagram. The most important finding is the detection of power excess at half the frequency of the additional variability (at subharmonic) in 35 per cent of the analysed stars. Interestingly, power excess at subharmonic frequency is detected mostly for stars of the middle sequence in the Petersen diagram (74 per cent), incidence rate is much lower for stars of the top sequence (31 per cent), and phenomenon is not detected for stars of the bottom sequence. The amplitude and/or phase of the additional periodicities strongly vary in time. Similar form of pulsation is observed in first overtone RR Lyrae stars. Our results indicate that the nature and cause of this form of pulsation is the same in the two groups of classical pulsators; consequently, a common model explaining this form of pulsation should be searched for. Our results favour the theory of the excitation of non-radial modes of angular degrees 7, 8 and 9, proposed recently by Dziembowski.

New X-Ray Tomography Method Based on the 3D Radon Transform Compatible with Anisotropic Sources.

In this work, we propose a novel computed tomography (CT) approach for three-dimensional (3D) object reconstruction, based on a generalized tomographic geometry with two-dimensional angular sampling (two angular degrees of freedom). The reconstruction is based on the 3D Radon transform and is compatible with anisotropic beam conditions. This allows isotropic 3D imaging with a source, which can be extended along one direction for increased flux, while high resolution is achieved by a small source size only in the orthogonal direction. This novel scheme for analytical CT is demonstrated by numerical simulations and proof-of-concept experiments. In this way high resolution and coherence along a single direction determines the reconstruction quality of the entire 3D data set, opening up, for example, new opportunities to achieve nanoscale resolution and/or phase contrast with low brilliance sources such as laboratory x-ray or neutron sources.

Observation of Four-Photon Orbital Angular Momentum Entanglement.

We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing.

Self powered solar tracker for Low Concentration PV (LCPV) systems

A design and performance of a new self powered LCPV solar trackers using bifacial solar cells and a concentrating mirror is described in the report. This design does not need additional power supply nor cables and so it is cheaper than classical PV power plants with many cables. The power supply bifacial PV panels are simultaneously used as sun sensors. The new tracker design with bifacial solar cells was successfully used at big MW range PV power plants. The very simple self powered tracker with concentrating mirror was successfully tested at Low Concentration PV (LCPV) systems. The tracking accuracy is less than ±1 angular degree.

Nanoscale rotary apparatus formed from tight-fitting 3D DNA components.

We report a nanoscale rotary mechanism that reproduces some of the dynamic properties of biological rotary motors in the absence of an energy source, such as random walks on a circle with dwells at docking sites. Our mechanism is built modularly from tight-fitting components that were self-assembled using multilayer DNA origami. The apparatus has greater structural complexity than previous mechanically interlocked objects and features a well-defined angular degree of freedom without restricting the range of rotation. We studied the dynamics of our mechanism using single-particle experiments analogous to those performed previously with actin-labeled adenosine triphosphate synthases. In our mechanism, rotor mobility, the number of docking sites, and the dwell times at these sites may be controlled through rational design. Our prototype thus realizes a working platform toward creating synthetic nanoscale rotary motors. Our methods will support creating other complex nanoscale mechanisms based on tightly fitting, sterically constrained, but mobile, DNA components.