Resonance transition periodic orbits in the circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo

2018-04-01

This work studies a special type of cislunar periodic orbits in the circular restricted three-body problem called resonance transition periodic orbits, which switch between different resonances and revolve about the secondary with multiple loops during one period. In the practical computation, families of multiple periodic orbits are identified first, and then the invariant manifolds emanating from the unstable multiple periodic orbits are taken to generate resonant homoclinic connections, which are used to determine the initial guesses for computing the desired periodic orbits by means of multiple-shooting scheme. The obtained periodic orbits have potential applications for the missions requiring long-term continuous observation of the secondary and tour missions in a multi-body environment.

Improvement of time-delayed feedback control by periodic modulation: analytical theory of Floquet mode control scheme.

PubMed

Just, Wolfram; Popovich, Svitlana; Amann, Andreas; Baba, Nilüfer; Schöll, Eckehard

2003-02-01

We investigate time-delayed feedback control schemes which are based on the unstable modes of the target state, to stabilize unstable periodic orbits. The periodic time dependence of these modes introduces an external time scale in the control process. Phase shifts that develop between these modes and the controlled periodic orbit may lead to a huge increase of the control performance. We illustrate such a feature on a nonlinear reaction diffusion system with global coupling and give a detailed investigation for the Rössler model. In addition we provide the analytical explanation for the observed control features.

Harmonic oscillators and resonance series generated by a periodic unstable classical orbit

NASA Technical Reports Server (NTRS)

Kazansky, A. K.; Ostrovsky, Valentin N.

1995-01-01

The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.

New variational principles for locating periodic orbits of differential equations.

PubMed

Boghosian, Bruce M; Fazendeiro, Luis M; Lätt, Jonas; Tang, Hui; Coveney, Peter V

2011-06-13

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

NASA Technical Reports Server (NTRS)

Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.

1989-01-01

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

The family of planar periodic orbits generated by the equal-mass four-body Schubart interplay orbit

NASA Astrophysics Data System (ADS)

Chopovda, Valerie; Sweatman, Winston L.

2018-05-01

We locate members of a one-parameter family of equal-mass four-body periodic orbits in the plane. The family begins and ends with the rectilinear four-body equal-mass Schubart interplay orbit and passes through a double choreography orbit. The first-order stability of these orbits is computed. Some members of this symmetric family are stable to symmetric perturbations; however, they are unstable when all perturbations are allowed.

Low-energy transfers to cislunar periodic orbits visiting triangular libration points

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo

2018-01-01

This paper investigates the cislunar periodic orbits that pass through triangular libration points of the Earth-Moon system and studies the techniques on design low-energy transfer trajectories. In order to compute periodic orbits, families of impulsive transfers between triangular libration points are taken to generate the initial guesses of periodic orbits, and multiple shooting techniques are applied to solving the problem. Then, varieties of periodic orbits in cislunar space are obtained, and stability analysis shows that the majority of them are unstable. Among these periodic orbits, an unstable periodic orbit in near 3:2 resonance with the Moon is taken as the nominal orbit of an assumed mission. As the stable manifolds of the target orbit could approach the Moon, low-energy transfer trajectories can be designed by combining lunar gravity assist with the invariant manifold structure of the target orbit. In practice, both the natural and perturbed invariant manifolds are considered to obtain the low-energy transfers, which are further refined to the Sun-perturbed Earth-Moon system. Results indicate that (a) compared to the case of natural invariant manifolds, the optimal transfers using perturbed invariant manifolds could reduce flight time at least 50 days, (b) compared to the cheapest direct transfer, the optimal low-energy transfer obtained by combining lunar gravity assist and invariant manifolds could save on-board fuel consumption more than 200 m/s, and (c) by taking advantage of the gravitational perturbation of the Sun, the low-energy transfers could save more fuel consumption than the corresponding ones obtained in the Earth-Moon system.

Periodic Trojan-type orbits in the earth-sun system

NASA Technical Reports Server (NTRS)

Weissman, P. R.; Wetherill, G. W.

1974-01-01

Periodic orbits about the triangular equilibrium points are found for the planar restricted three-body problem using the earth-sun system. The maximum semimajor axis for tadpole orbits ranges from the infinitesimal orbit at 1.000 AU to the near-limiting orbit at 1.00285 AU. Horseshoe orbits are found for 1.0029 to 1.0080 AU, larger horseshoes being unstable because of close approaches to the earth. Using stability tests devised by Rabe (1961, 1962), the limit of stability for nonperiodic orbits is found to occur for maximum semimajor axes near 1.0020 AU. In addition, near-periodic tadpole orbits appear to be stable against perturbations by Jupiter and Venus for periods of at least 10,000 yr. The possibility that minor planets actually exist in such orbits is considered.

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

DOE PAGES

Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; ...

2011-02-10

Here, this article examines the localization of time harmonic high-frequency modal fields in two-dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This article examines the enhancements for these unstable orbits when the opposing mirrors are convex, constructing the high-frequency field in the scar region using elliptic cylinder coordinates in combination with a random reflection phase from the outer chaotic region. Finally, the enhancements when the cavity is symmetric as well as asymmetric about the orbit are examined.

Resonance and Capture of Jupiter Comets

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

A number of Jupiter family comets such as Oterma and Gehrels 3 make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L_1 and L_2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L_1 and L_2 is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L_1 and the other around L_2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold `tubes' associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.

Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

NASA Astrophysics Data System (ADS)

Mirus, Kevin Andrew

In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

THE COMPUTATION OF CHARACTERISTIC EXPONENTS IN THE PLANAR RESTRICTED PROBLEM OF THREE BODIES

DTIC Science & Technology

methods are applied to evaluate the characteristic exponents of Rabe’s Trojan Orbits; they are found to be of the stable type for the ovals, and of...the unstable type for the horse -shoe shaped orbit. When the periodic orbit is symmetric with respect to the axis of syzygies, four independent

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp; Yamada, Michio; Chian, Abraham C.-L.

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originatemore » from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.« less

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

PubMed

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

2015-10-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

Building CX peanut-shaped disk galaxy profiles. The relative importance of the 3D families of periodic orbits bifurcating at the vertical 2:1 resonance

NASA Astrophysics Data System (ADS)

Patsis, P. A.; Harsoula, M.

2018-05-01

Context. We present and discuss the orbital content of a rather unusual rotating barred galaxy model, in which the three-dimensional (3D) family, bifurcating from x1 at the 2:1 vertical resonance with the known "frown-smile" side-on morphology, is unstable. Aims: Our goal is to study the differences that occur in the phase space structure at the vertical 2:1 resonance region in this case, with respect to the known, well studied, standard case, in which the families with the frown-smile profiles are stable and support an X-shaped morphology. Methods: The potential used in the study originates in a frozen snapshot of an N-body simulation in which a fast bar has evolved. We follow the evolution of the vertical stability of the central family of periodic orbits as a function of the energy (Jacobi constant) and we investigate the phase space content by means of spaces of section. Results: The two bifurcating families at the vertical 2:1 resonance region of the new model change their stability with respect to that of most studied analytic potentials. The structure in the side-on view that is directly supported by the trapping of quasi-periodic orbits around 3D stable periodic orbits has now an infinity symbol (i.e. ∞-type) profile. However, the available sticky orbits can reinforce other types of side-on morphologies as well. Conclusions: In the new model, the dynamical mechanism of trapping quasi-periodic orbits around the 3D stable periodic orbits that build the peanut, supports the ∞-type profile. The same mechanism in the standard case supports the X shape with the frown-smile orbits. Nevertheless, in both cases (i.e. in the new and in the standard model) a combination of 3D quasi-periodic orbits around the stable x1 family with sticky orbits can support a profile reminiscent of the shape of the orbits of the 3D unstable family existing in each model.

Controlling chaos faster.

PubMed

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.

Continuation of periodic orbits in the Sun-Mercury elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Peng, Hao; Bai, Xiaoli; Xu, Shijie

2017-06-01

Starting from resonant Halo orbits in the Circular Restricted Three-Body Problem (CRTBP), Multi-revolution Elliptic Halo (ME-Halo) orbits around L1 and L2 points in the Sun-Mercury Elliptic Restricted Three-Body Problem (ERTBP) are generated systematically. Three pairs of resonant parameters M5N2, M7N3 and M9N4 are tested. The first pair shows special features and is investigated in detail. Three separated characteristic curves of periodic orbit around each libration point are obtained, showing the eccentricity varies non-monotonically along these curves. The eccentricity of the Sun-Mercury system can be achieved by continuation method in just a few cases. The stability analysis shows that these orbits are all unstable and the complex instability occurs with certain parameters. This paper shows new periodic orbits in both the CRTBP and the ERTBP. Totally four periodic orbits with parameters M5N2 around each libration points are extracted in the Sun-Mercury ERTBP.

The phase space of boxy-peanut and X-shaped bulges in galaxies - I. Properties of non-periodic orbits

NASA Astrophysics Data System (ADS)

Patsis, P. A.; Katsanikas, M.

2014-12-01

The investigation of the phase-space properties of structures encountered in a dynamical system is essential for understanding their formation and enhancement. In this paper, we explore the phase space in energy intervals where we have orbits that act as building blocks for boxy-peanut (b/p) and `X-shaped' structures in rotating potentials of galactic type. We underline the significance of the rotational tori around the 3D families x1v1 and x1v1' that have been bifurcated from the planar x1 family. These tori play a multiple role: (i) they belong to quasi-periodic orbits that reinforce the local density. (ii) They act as obstacles for the diffusion of chaotic orbits and (iii) they attract a large number of chaotic orbits that become sticky to them. There are also bifurcations of unstable families (x1v2, x1v2'). Their unstable asymptotic curves wind around the x1v1 and x1v1' tori generating orbits with hybrid morphologies between that of x1v1 and x1v2. In addition, a new family of multiplicity 2, called x1mul2, is found to be important for the peanut construction. This family produces stickiness phenomena in the critical area of the radial and vertical inner Lindblad resonances (ILRs) and reinforces b/p bulges. Our work shows also that there are peanut-supporting orbits before the vertical ILR. Non-periodic orbits associated with the x1 family secure this contribution as well as the support of b/p structures at several other energy intervals. Non-linear phenomena associated with complex instability of single and double multiplicity families of periodic orbits show that these structures are not interrupted in regions where such orbits prevail. Depending on the main mechanism behind their formation, boxy bulges exhibit different morphological features. Finally, our analysis indicates that `X' features shaped by orbits in the neighbourhood of x1v1 and x1v1' periodic orbits are pronounced only in side-on or nearly end-on views of the bar.

Using periodic orbits to compute chaotic transport rates between resonance zones.

PubMed

Sattari, Sulimon; Mitchell, Kevin A

2017-11-01

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

Parametric nonfeedback resonance in period doubling systems

NASA Astrophysics Data System (ADS)

Pisarchik, A. N.; Corbalán, R.

1999-02-01

Slow periodic modulation of a control parameter in a period doubling system leads to an interaction between stable and unstable periodic orbits. This causes a resonance in the system response at the modulation frequency. The conditions for this resonance are studied through numerical simulations of quadratic map and laser equations. The results are confirmed by experiments in a CO2 laser with modulated losses.

Amplitude-dependent orbital period in alternating gradient accelerators

DOE PAGES

Machida, S.; Kelliher, D. J.; Edmonds, C. S.; ...

2016-03-16

Orbital period in a ring accelerator and time of flight in a linear accelerator depend on the amplitude of betatron oscillations. The variation is negligible in ordinary particle accelerators with relatively small beam emittance. In an accelerator for large emittance beams like muons and unstable nuclei, however, this effect cannot be ignored. In this study, we measured orbital period in a linear non-scaling fixed-field alternating-gradient accelerator, which is a candidate for muon acceleration, and compared it with the theoretical prediction. The good agreement between them gives important ground for the design of particle accelerators for a new generation of particlemore » and nuclear physics experiments.« less

A note on chaotic unimodal maps and applications.

PubMed

Zhou, C T; He, X T; Yu, M Y; Chew, L Y; Wang, X G

2006-09-01

Based on the word-lift technique of symbolic dynamics of one-dimensional unimodal maps, we investigate the relation between chaotic kneading sequences and linear maximum-length shift-register sequences. Theoretical and numerical evidence that the set of the maximum-length shift-register sequences is a subset of the set of the universal sequence of one-dimensional chaotic unimodal maps is given. By stabilizing unstable periodic orbits on superstable periodic orbits, we also develop techniques to control the generation of long binary sequences.

Bifurcation scenarios for bubbling transition.

PubMed

Zimin, Aleksey V; Hunt, Brian R; Ott, Edward

2003-01-01

Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.

Synchronization of Heterogeneous Oscillators by Noninvasive Time-Delayed Cross Coupling.

PubMed

Jüngling, Thomas; Fischer, Ingo; Schöll, Eckehard; Just, Wolfram

2015-11-06

We demonstrate that nonidentical systems, in particular, nonlinear oscillators with different time scales, can be synchronized if a mutual coupling via time-delayed control signals is implemented. Each oscillator settles on an unstable state, say a fixed point or an unstable periodic orbit, with a coupling force which vanishes in the long time limit. We present the underlying theoretical considerations and numerical simulations, and, moreover, demonstrate the concept experimentally in nonlinear electronic oscillators.

Hysteresis in the trade cycle

NASA Astrophysics Data System (ADS)

Mc Namara, Hugh A.; Pokrovskii, Alexei V.

2006-02-01

The Kaldor model-one of the first nonlinear models of macroeconomics-is modified to incorporate a Preisach nonlinearity. The new dynamical system thus created shows highly complicated behaviour. This paper presents a rigorous (computer aided) proof of chaos in this new model, and of the existence of unstable periodic orbits of all minimal periods p>57.

Assessing the physical nature of near-Earth asteroids through their dynamical histories

NASA Astrophysics Data System (ADS)

Fernández, Julio A.; Sosa, Andrea; Gallardo, Tabaré; Gutiérrez, Jorge N.

2014-08-01

We analyze a sample of 139 near-Earth asteroids (NEAs), defined as those that reach perihelion distances q<1.3 au, and that also fulfill the conditions of approaching or crossing Jupiter’s orbit (aphelion distances Q>4.8 au), having Tisserand parameters 24.8 au of cometary origin, but it could be even lower if the NEAs in unstable orbits listed before turn out to be bona fide asteroids from the main belt. This study strengthens the idea that NEAs and comets essentially are two distinct populations, and that periods of dormancy in comets must be rare. Most likely, active comets in near-Earth orbits go through a continuous erosion process in successive perihelion passages until disintegration into meteoritic dust and fragments of different sizes. In this scenario, 289P/Blanpain might be a near-devolatized fragment from a by now disintegrated parent comet.

Unstable Roche-Lobe Overflow of Gaseous Planets

NASA Astrophysics Data System (ADS)

Jackson, Brian

The discoveries of more than 100 roughly Earth-sized bodies with orbital periods less than 1 day, ultra-short-period planets or candidates (USPs), have challenged planet formation theories, and evidence suggests USPs may be the remnants of gaseous planets that shed their atmospheres. Indeed, many hot Jupiters are near Roche-Lobe overflow (RLO), and tidal decay can push them the rest of the way in. Recent work has shown stable RLO (atmospheres lost via a steady outflow and thin accretion disk) probably cannot produce USPs on its own but suggested unstable RLO (atmospheres quickly shed on dynamical timescales) may. In fact, stable RLO may drive overflowing hot Jupiters into unstable RLO, and by analogy with the common-envelope binaries, the core that remains can drive off the gaseous envelope at the cost of its orbital energy. Wellestablished mass-radius relations for gaseous planets, coupled to simple energy and angular momentum considerations, provide a connection between the observed masses and periods for USPs and their putative progenitor gaseous planets, with few free parameters. We propose to investigate the hypothesis that USPs originate through tidal decay and a combination of stable and unstable Roche-lobe overflow of short-period gaseous planets through the following studies: -We will explore the planetary masses, orbital periods, etc. that produce unstable RLO using the Modules for Experiments in Stellar Astrophysics (MESA) suite. -We will relate the observed periods and masses of USPs to their putative progenitor masses and periods to see whether they are consistent with the unstable RLO hypothesis. This proposal is directly relevant to the Exoplanets Research Program since it seeks to "understand the ... physical processes of exoplanets" and "improve understanding of [their] origins" through "theoretical studies ... and modeling'". We also expect that it will have broad impacts on a variety of astrophysical topics: -Ultra-short period planets could provide a glimpse inside gas giants. If our study corroborates the unstable RLO hypothesis, the properties of USPs may represent those of gaseous planet cores, which are almost entirely unconstrained. Even in our own solar system, estimates of the core masses for Jupiter (between 0 and 14 Earth masses) and Saturn (between 8 and 25 Earth masses) have large uncertainties. The upcoming Juno mission will clarify the situation for Jupiter, but it's unclear whether these constraints will directly bear on other planetary systems. -The TESS mission will probably find hundreds of ultra-short-period planets. The Transiting Exoplanet Survey Satellite (TESS) will launch in 2017 and look for shortperiod rocky planets around 500,000 nearby stars. Roughly 0.1% of Sun-like stars host USPs, so TESS should find hundreds of USPs. These planets would be ideal for followup, and a clear framework for their origins would motivate and guide additional TESS observations. -Even if we show they are not remnants of gaseous planets, ultra-short-period planets may serve as probes of the innermost protoplanetary gas disk and betray the presence of additional planets in their host systems. As we discuss below, one other obvious origin scenario involves dynamical interactions in a multi-planet system. Many USPs do not have observed siblings, so this scenario requires that there are additional, unseen planets in those systems. The exact location of USPs may be set, in part, by the inner edge of their maternal gas disk, a sensitive function of the host star's youthful properties.

Towards the computation of time-periodic inertial range dynamics

NASA Astrophysics Data System (ADS)

van Veen, L.; Vela-Martín, A.; Kawahara, G.

2018-04-01

We explore the possibility of computing simple invariant solutions, like travelling waves or periodic orbits, in Large Eddy Simulation (LES) on a periodic domain with constant external forcing. The absence of material boundaries and the simple forcing mechanism make this system a comparatively simple target for the study of turbulent dynamics through invariant solutions. We show, that in spite of the application of eddy viscosity the computations are still rather challenging and must be performed on GPU cards rather than conventional coupled CPUs. We investigate the onset of turbulence in this system by means of bifurcation analysis, and present a long-period, large-amplitude unstable periodic orbit that is filtered from a turbulent time series. Although this orbit is computed on a coarse grid, with only a small separation between the integral scale and the LES filter length, the periodic dynamics seem to capture a regeneration process of the large-scale vortices.

Analysis of Petal Rotation Trajectory Characteristics

NASA Technical Reports Server (NTRS)

Anderson, Rodney L.; Campagnola, Stefano; Buffington, Brent B.

2014-01-01

In this study, the characteristics of petal rotation trajectories are explored in both the two-body and circular restricted three-body problem (CRTBP) models. Petal rotation trajectories alternate long and short resonances of different kinds to rotate the line of apsides. They are typically computed using the patched conic model, and they are used in a number of different missions and mission concepts including Cassini, JUICE, and Europa mission concepts. Petal rotation trajectories are first analyzed here using the patched conic model to quantify their characteristics and search for cases with fast rotation of the line of apsides. When they are computed in the CRTBP, they are unstable periodic orbits with corresponding stable and unstable manifolds. The characteristics of these orbits are explored from a dynamical systems perspective in the second phase of the study.

Orbital stability of the unseen solar companion linked to periodic extinction events

NASA Technical Reports Server (NTRS)

Torbett, M. V.; Smoluchowski, R.

1984-01-01

Evidence from three-dimensional numerical modelling is presented that only cometary orbits with a limited range in inclination with respect to the galactic plane are formally stable for the length of time required to cause periodic extinction events. The calculations were done using Cowell's method employing a fourth-order Runge-Kutta integration scheme in an inertial reference frame in orbit about the Galaxy. Tidal perturbations in the radial direction due to the Galaxy and the Coriolis forces are included. The vertical component of the gravitational field of the galactic disk is superimposed on these forces. The results indicate that orbits for Nemesis that are inclined at more than 30 deg to the galactic plane are not allowed and suggests that the search for Nemesis should be concentrated toward the plane of the Galaxy. Perturbations by passing stars or molecular clouds may make even the low-inclination orbits unstable.

Toward understanding the roaming mechanism in H + MgH → Mg + HH reaction

DOE PAGES

Mauguiere, Frederic A. L.; Collins, Peter; Stamatiadis, Stamatis; ...

2016-02-26

The roaming mechanism in the reaction H + MgH →Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio threedimensional ground electronic state potential energy surface. The reaction dynamics are explored by running trajectories initialized on a four-dimensional dividing surface anchored on three-dimensional normally hyperbolic invariant manifold associated with a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase spacemore » where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. As a result, the complex forming trajectories in the HMgH well can either return to the radical channel or “roam” to the MgHH minimum from where the molecule may react.« less

Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

NASA Technical Reports Server (NTRS)

Belbruno, Edward A.

1990-01-01

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the earth and then ballistically escapes the earth-moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the moon via an unstable periodic orbit using the four-body sun-earth-moon-S/C interaction is described.

Reliability of unstable periodic orbit based control strategies in biological systems.

PubMed

Mishra, Nagender; Hasse, Maria; Biswal, B; Singh, Harinder P

2015-04-01

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

Reliability of unstable periodic orbit based control strategies in biological systems

NASA Astrophysics Data System (ADS)

Mishra, Nagender; Hasse, Maria; Biswal, B.; Singh, Harinder P.

2015-04-01

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

DYNAMICAL INSTABILITIES IN HIGH-OBLIQUITY SYSTEMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tamayo, D.; Nicholson, P. D.; Burns, J. A.

2013-03-01

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations-large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. found that, for planets with obliquities >68. Degree-Sign 875, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we findmore » that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68. Degree-Sign 875. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. For low-eccentricity orbits in the equilibrium Laplace plane, we find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this occurs because radiation pressure modifies the equilibrium Laplace plane.« less

Ballistic capture into lunar and Martian distant retrograde orbits

NASA Astrophysics Data System (ADS)

Bezrouk, Collin J.

Distant retrograde orbits (DROs) are a neutrally stable class of three-body orbits. Because of their stability, DROs cannot be targeted with a low-energy transfer along a stable manifold like unstable three-body orbits in the circular restricted three-body problem (CR3BP). However, in more complicated dynamical models, the effects of small perturbing forces can be exploited to build ballistic capture trajectories (BCTs) into DROs. We develop a method for building sets of BCTs for a particular reference DRO with recommendations for minimizing computational effort. Sets of BCTs are generated in the Earth-Moon system and the Mars-Phobos system due to their applicability to near-term missions and large difference in mass parameters. These BCT sets are stochastically analyzed to determine the range of conditions necessary for using a BCT, such as energy, solar system geometry, and origin. The nature of the DRO after the spacecraft is captured is studied, including minor body flyby altitudes and variations in the size and shape over time. After a spacecraft has used a BCT, it can decrease its sensitivity to perturbations and extend its mission duration with a series of stabilizing maneuvers. Quasi-periodic orbits are constructed in the Earth-Moon CR3BP that lie on the boundary of stability, and closely resemble the DROs that result from using a BCT. Minimum cost transfers are then constructed between these quasi-periodic orbits and a target periodic DRO using a variety of methods for searching and optimizing. It is discovered that BCTs that target planar quasi-periodic DROs can be stabilized for about 15% of the cost of stabilizing a BCT with large out-of-plane motion. Once a spacecraft is in a stable DRO, the long duration evolution of that orbit is of interest. Using a high fidelity dynamical model and numerical precision techniques, the evolution of several DROs in the Earth-Moon system is studied over a period of 30,000 years. The perturbing forces that cause a DRO to transition into an unstable orbit are identified and analyzed. DROs larger than 60,000 km grow in amplitude due to solar gravity until they depart the Moon after several centuries. DROs smaller than 45,000 km remain stable for 25,000 years or more, but decay in size due to the Moon's solid tide bulge, which eventually causes the DRO to depart the Moon. The DROs evolve chaotically and occasionally experience periods of relatively fast amplitude growth when the period of the DRO is in resonance with the frequency of particular perturbing forces.

The rectilinear three-body problem as a basis for studying highly eccentric systems

NASA Astrophysics Data System (ADS)

Voyatzis, G.; Tsiganis, K.; Gaitanas, M.

2018-01-01

The rectilinear elliptic restricted three-body problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity e'=1, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for studying the dynamics of motion around highly eccentric binary systems. Broucke (AIAA J 7:1003-1009, 1969) explored the rectilinear problem and obtained isolated periodic orbits for mass parameter μ =0.5 (equal masses of the primaries). We found that all orbits obtained by Broucke are linearly unstable. We extend Broucke's computations by using a finer search for symmetric periodic orbits and computing their linear stability. We found a large number of periodic orbits, but only eight of them were found to be linearly stable and are associated with particular mean motion resonances. These stable orbits are used as generating orbits for continuation with respect to μ and e'<1. Also, continuation of periodic solutions with respect to the mass of the small body can be applied by using the general TBP. FLI maps of dynamical stability show that stable periodic orbits are surrounded in phase space with regions of regular orbits indicating that systems of very highly eccentric orbits can be found in stable resonant configurations. As an application we present a stability study for the planetary system HD7449.

The Anglo-Australian Planet Search. XXV. A Candidate Massive Saturn Analog Orbiting HD 30177

NASA Astrophysics Data System (ADS)

Wittenmyer, Robert A.; Horner, Jonathan; Mengel, M. W.; Butler, R. P.; Wright, D. J.; Tinney, C. G.; Carter, B. D.; Jones, H. R. A.; Anglada-Escudé, G.; Bailey, J.; O'Toole, Simon J.

2017-04-01

We report the discovery of a second long-period giant planet orbiting HD 30177, a star previously known to host a massive Jupiter analog (HD 30177b: a = 3.8 ± 0.1 au, m sin I = 9.7 ± 0.5 M Jup). HD 30177c can be regarded as a massive Saturn analog in this system, with a = 9.9 ± 1.0 au and m sin I = 7.6 ± 3.1 M Jup. The formal best-fit solution slightly favors a closer-in planet at a ˜ 7 au, but detailed n-body dynamical simulations show that configuration to be unstable. A shallow local minimum of longer period, lower eccentricity solutions was found to be dynamically stable, and hence we adopt the longer period in this work. The proposed ˜32 year orbit remains incomplete; further monitoring of this and other stars is necessary to reveal the population of distant gas giant planets with orbital separations a ˜ 10 au, analogous to that of Saturn.

Alfvén Turbulence Driven by High-Dimensional Interior Crisis in the Solar Wind

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Rempel, E. L.; Macau, E. E. N.; Rosa, R. R.; Christiansen, F.

2003-09-01

Alfvén intermittent turbulence has been observed in the solar wind. It has been previously shown that the interplanetary Alfvén intermittent turbulence can appear due to a low-dimensional temporal chaos [1]. In this paper, we study the nonlinear spatiotemporal dynamics of Alfvén waves governed by the Kuramoto-Sivashinsky equation which describes the phase evolution of a large-amplitude Alfvén wave. We investigate the Alfvén turbulence driven by a high-dimensional interior crisis, which is a global bifurcation caused by the collision of a chaotic attractor with an unstable periodic orbit. This nonlinear phenomenon is analyzed using the numerical solutions of the model equation. The identification of the unstable periodic orbits and their invariant manifolds is fundamental for understanding the instability, chaos and turbulence in complex systems such as the solar wind plasma. The high-dimensional dynamical system approach to space environment turbulence developed in this paper can improve our interpretation of the origin and the nature of Alfvén turbulence observed in the solar wind.

Over a thousand new periodic orbits of a planar three-body system with unequal masses

NASA Astrophysics Data System (ADS)

Li, Xiaoming; Jing, Yipeng; Liao, Shijun

2018-05-01

The three-body problem is common in astronomy, examples of which are the solar system, exoplanets, and stellar systems. Due to its chaotic characteristic, discovered by Poincaré, only three families of periodic three-body orbits were found in 300 years, until 2013 when Šuvakov and Dmitrašinović (2013, Phys. Rev. Lett., 110, 114301) found 13 new periodic orbits of a Newtonian planar three-body problem with equal mass. Recently, more than 600 new families of periodic orbits of triple systems with equal mass were found by Li and Liao (2017, Sci. China-Phys. Mech. Astron., 60, 129511). Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass. None of the families have ever been reported, except the famous "figure-eight" family. In particular, 1223 among these 1349 families are entirely new, i.e., with newly found "free group elements" that have been never reported, even for three-body systems with equal mass. It has been traditionally believed that triple systems are often unstable if they are non-hierarchical. However, all of our new periodic orbits are in non-hierarchical configurations, but many of them are either linearly or marginally stable. This might inspire the long-term astronomical observation of stable non-hierarchical triple systems in practice. In addition, using these new periodic orbits as initial guesses, new periodic orbits of triple systems with three unequal masses can be found by means of the continuation method, which is more general and thus should have practical meaning from an astronomical viewpoint.

Using Solar Radiation Pressure to Control L2 Orbits

NASA Technical Reports Server (NTRS)

Tene, Noam; Richon, Karen; Folta, David

1998-01-01

The main perturbations at the Sun-Earth Lagrange points L1 and L2 are from solar radiation pressure (SRP), the Moon and the planets. Traditional approaches to trajectory design for Lagrange-point orbits use maneuvers every few months to correct for these perturbations. The gravitational effects of the Moon and the planets are small and periodic. However, they cannot be neglected because small perturbations in the direction of the unstable eigenvector are enough to cause exponential growth within a few months. The main effect of a constant SRP is to shift the center of the orbit by a small distance. For spacecraft with large sun-shields like the Microwave Anisotropy Probe (MAP) and the Next Generation Space Telescope (NGST), the SRP effect is larger than all other perturbations and depends mostly on spacecraft attitude. Small variations in the spacecraft attitude are large enough to excite or control the exponential eigenvector. A closed-loop linear controller based on the SRP variations would eliminate one of the largest errors to the orbit and provide a continuous acceleration for use in controlling other disturbances. It is possible to design reference trajectories that account for the periodic lunar and planetary perturbations and still satisfy mission requirements. When such trajectories are used the acceleration required to control the unstable eigenvector is well within the capabilities of a continuous linear controller. Initial estimates show that by using attitude control it should be possible to minimize and even eliminate thruster maneuvers for station keeping.

Reliability of unstable periodic orbit based control strategies in biological systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mishra, Nagender; Singh, Harinder P.; Hasse, Maria

2015-04-15

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry ofmore » the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.« less

A superparticle on the super Riemann surface

NASA Astrophysics Data System (ADS)

Matsumoto, Shuji; Uehara, Shozo; Yasui, Yukinori

1990-02-01

The free motion of a nonrelativistic superparticle on the super Riemann surface (SRS) of genus h≥2 is investigated. Geodesics or classical paths are given explicitly on the super Poincaré upper half-plane SH, a universal covering space of the SRS, and the paths with some suitable initial conditions yield periodic orbits on the SRS. The periodic orbits are unstable and the system is chaotic. Quantum mechanics is solved on the universal covering space SH and the heat kernel is given on the SRS. This leads to a superanalog of the Selberg trace formula. The Selberg super zeta function is introduced whose zero points and poles determine the energy spectrum on the SRS.

Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves.

PubMed

Cuevas-Maraver, J; Kevrekidis, P G; Frantzeskakis, D J; Karachalios, N I; Haragus, M; James, G

2017-07-01

In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a nontrivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of the Peregrine soliton in the evolution variable, namely the Kuznetsov-Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations.

Linking long-term planetary N-body simulations with periodic orbits: application to white dwarf pollution

NASA Astrophysics Data System (ADS)

Antoniadou, Kyriaki I.; Veras, Dimitri

2016-12-01

Mounting discoveries of debris discs orbiting newly formed stars and white dwarfs (WDs) showcase the importance of modelling the long-term evolution of small bodies in exosystems. WD debris discs are, in particular, thought to form from very long-term (0.1-5.0 Gyr) instability between planets and asteroids. However, the time-consuming nature of N-body integrators which accurately simulate motion over Gyrs necessitates a judicious choice of initial conditions. The analytical tools known as periodic orbits can circumvent the guesswork. Here, we begin a comprehensive analysis directly linking periodic orbits with N-body integration outcomes with an extensive exploration of the planar circular restricted three-body problem (CRTBP) with an outer planet and inner asteroid near or inside of the 2:1 mean motion resonance. We run nearly 1000 focused simulations for the entire age of the Universe (14 Gyr) with initial conditions mapped to the phase space locations surrounding the unstable and stable periodic orbits for that commensurability. In none of our simulations did the planar CRTBP architecture yield a long-time-scale (≳0.25 per cent of the age of the Universe) asteroid-star collision. The pericentre distance of asteroids which survived beyond this time-scale (≈35 Myr) varied by at most about 60 per cent. These results help affirm that collisions occur too quickly to explain WD pollution in the planar CRTBP 2:1 regime, and highlight the need for further periodic orbit studies with the eccentric and inclined TBP architectures and other significant orbital period commensurabilities.

Actual Romanian research in post-newtonian dynamics

NASA Astrophysics Data System (ADS)

Mioc, V.; Stavinschi, M.

2007-05-01

We survey the recent Romanian results in the study of the two-body problem in post-Newtonian fields. Such a field is characterized, in general, by a potential of the form U(q)=|q|^{-1}+ something (small, but not compulsorily). We distinguish some classes of post-Newtonian models: relativistic (Schwarzschild, Fock, Einstein PN, Reissner-Nordström, Schwarzschild - de Sitter, etc.) and nonrelativistic (Manev, Mücket-Treder, Seeliger, gravito-elastic, etc.). Generalized models (the zonal-satellite problem, quasihomogeneous fields), as well as special cases (anisotropic Manev-type and Schwarzschild-type models, Popovici or Popovici-Manev photogravitational problem), were also tackled. The methods used in such studies are various: analytical (using mainly the theory of perturbations, but also other theories: functions of complex variable, variational calculus, etc.), geometric (qualitative approach of the theory of dynamical systems), and numerical (especially using the Poincaré-section technique). The areas of interest and the general results obtained focus on: exact or approximate analytical solutions; characteristics of local flows (especially at limit situations: collision and escape); quasiperiodic and periodic orbits; equilibria; symmetries; chaoticity; geometric description of the global flow (and physical interpretation of the phase-space structure). We emphasize some special features, which cannot be met within the Newtonian framework: black-hole effect, oscillatory collisions, radial librations, bounded orbits for nonnegative energy, existence of unstable circular motion (or unstable rest), symmetric periodic orbits within anisotropic models, etc.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, Pablo R.; Rempel, Erico L.; Barroso, Joaquim J.

We study the chaotic dynamics of the Pierce diode, a simple spatially extended system for collisionless bounded plasmas, focusing on the concept of edge of chaos, the boundary that separates transient from asymptotic dynamics. We fully characterize an interior crisis at the end of a periodic window, thereby showing direct evidence of the collision between a chaotic attractor, a chaotic saddle, and the edge of chaos, formed by a period-3 unstable periodic orbit and its stable manifold. The edge of chaos persists after the interior crisis, when the global attractor of the system increases its size in the phase space.

Control of extreme events in the bubbling onset of wave turbulence.

PubMed

Galuzio, P P; Viana, R L; Lopes, S R

2014-04-01

We show the existence of an intermittent transition from temporal chaos to turbulence in a spatially extended dynamical system, namely, the forced and damped one-dimensional nonlinear Schrödinger equation. For some values of the forcing parameter, the system dynamics intermittently switches between ordered states and turbulent states, which may be seen as extreme events in some contexts. In a Fourier phase space, the intermittency takes place due to the loss of transversal stability of unstable periodic orbits embedded in a low-dimensional subspace. We mapped these transversely unstable regions and perturbed the system in order to significantly reduce the occurrence of extreme events of turbulence.

Cardiac arrhythmias and degradation into chaotic behavior prevention using feedback control

NASA Astrophysics Data System (ADS)

Uzelac, Ilija; Sidorov, Veniamin; Wikswo, John; Gray, Richard

2012-02-01

During normal heart rhythm, cardiac cells behave as a set of oscillators with a distribution of phases but with the same frequency. The heart as a dynamical system in a phase space representation can be modeled as a set of oscillators that have closed overlapping orbits with the same period. These orbits are not stable and in the case of disruption of the cardiac rhythm, such as due to premature beats, the system will have a tendency to leave its periodic unstable orbits. If these orbits become attracted to phase singularities, their disruption may lead to chaotic behavior, which appears as a life-threating ventricular fibrillation. By using closed-loop feedback in the form of an adjustable defibrillation shock, any drift from orbits corresponding to the normal rhythm can be corrected by forcing the system to maintain its orbits. The delay through the feedback network coincides with the period of normal heart beats. To implement this approach we developed a 1 kW arbitrary waveform voltage-to-current converter with a 1 kHz bandwidth driven by a photodiode system that records an optical electrocardiogram and provides a feedback signal in real time. Our goal is to determine whether our novel method to defibrillate the heart will require much lower energies than are currently utilized in single shock defibrillators.

Various oscillation patterns in phase models with locally attractive and globally repulsive couplings.

PubMed

Sato, Katsuhiko; Shima, Shin-ichiro

2015-10-01

We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petrovich, Cristobal; Rafikov, Roman; Tremaine, Scott, E-mail: cpetrovi@princeton.edu

Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations (e ≲ 0.1, i ≲ 0.1) generally lead to planet-planet collisions in which the collision product is a planet on a low-eccentricity, low-inclination orbit. This result is inconsistentmore » with the observations. We conclude that eccentricity and inclination excitation from planet-planet scattering must precede migration of planets into short-period orbits. This result constrains theories of planet migration: the semi-major axis must shrink by 1-2 orders of magnitude without damping the eccentricity and inclination.« less

Space augmentation of military high-level waste disposal

NASA Technical Reports Server (NTRS)

English, T.; Lees, L.; Divita, E.

1979-01-01

Space disposal of selected components of military high-level waste (HLW) is considered. This disposal option offers the promise of eliminating the long-lived radionuclides in military HLW from the earth. A space mission which meets the dual requirements of long-term orbital stability and a maximum of one space shuttle launch per week over a period of 20-40 years, is a heliocentric orbit about halfway between the orbits of earth and Venus. Space disposal of high-level radioactive waste is characterized by long-term predictability and short-term uncertainties which must be reduced to acceptably low levels. For example, failure of either the Orbit Transfer Vehicle after leaving low earth orbit, or the storable propellant stage failure at perihelion would leave the nuclear waste package in an unplanned and potentially unstable orbit. Since potential earth reencounter and subsequent burn-up in the earth's atmosphere is unacceptable, a deep space rendezvous, docking, and retrieval capability must be developed.

The role of invariant manifolds in lowthrust trajectory design (part III)

NASA Technical Reports Server (NTRS)

Lo, Martin W.; Anderson, Rodney L.; Lam, Try; Whiffen, Greg

2006-01-01

This paper is the third in a series to explore the role of invariant manifolds in the design of low thrust trajectories. In previous papers, we analyzed an impulsive thrust resonant gravity assist flyby trajectory to capture into Europa orbit using the invariant manifolds of unstable resonant periodic orbits and libration orbits. The energy savings provided by the gravity assist may be interpreted dynamically as the result of a finite number of intersecting invariant manifolds. In this paper we demonstrate that the same dynamics is at work for low thrust trajectories with resonant flybys and low energy capture. However, in this case, the flybys and capture are effected by continuous families of intersecting invariant manifolds.

Invariant polygons in systems with grazing-sliding.

PubMed

Szalai, R; Osinga, H M

2008-06-01

The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system has an attractor that consists of forward sliding orbits. We analyze this attractor in a suitably chosen Poincare section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.

High-frequency electromagnetic scarring in three-dimensional axisymmetric convex cavities

DOE PAGES

Warne, Larry K.; Jorgenson, Roy E.

2016-04-13

Here, this article examines the localization of high-frequency electromagnetic fields in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. When these orbits lead to unstable localized modes, they are known as scars. This article treats the case where the opposing sides, or mirrors, are convex. Particular attention is focused on the normalization through the electromagnetic energy theorem. Both projections of the field along the scarred orbit as well as field point statistics are examined. Statistical comparisons are made with a numerical calculation of the scars run with an axisymmetric simulation.

Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

NASA Technical Reports Server (NTRS)

Coffee, Thomas M.; Anderson, Rodney L.; Lo, Martin W.

2011-01-01

We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

Experimental Control of Thermocapillary Convection in a Liquid Bridge

NASA Technical Reports Server (NTRS)

Petrov, Valery; Schatz, Michael F.; Muehlner, Kurt A.; VanHook, Stephen J.; McCormick, W. D.; Swift, Jack B.; Swinney, Harry L.

1996-01-01

We demonstrate the stabilization of an isolated unstable periodic orbit in a liquid bridge convection experiment. A model independent, nonlinear control algorithm uses temperature measurements near the liquid interface to compute control perturbations which are applied by a thermoelectric element. The algorithm employs a time series reconstruction of a nonlinear control surface in a high dimensional phase space to alter the system dynamics.

Fundamental photon orbits: Black hole shadows and spacetime instabilities

NASA Astrophysics Data System (ADS)

Cunha, Pedro V. P.; Herdeiro, Carlos A. R.; Radu, Eugen

2017-07-01

The standard black holes (BHs) in general relativity, as well as other ultracompact objects (with or without an event horizon) admit planar circular photon orbits. These light rings (LRs) determine several spacetime properties. For instance, stable LRs trigger instabilities and, in spherical symmetry, (unstable) LRs completely determine BH shadows. In generic stationary, axisymmetric spacetimes, nonplanar bound photon orbits may also exist, regardless of the integrability properties of the photon motion. We suggest a classification of these fundamental photon orbits (FPOs) and, using Poincaré maps, determine a criterion for their stability. For the Kerr BH, all FPOs are unstable (similar to its LRs) and completely determine the Kerr shadow. But in non-Kerr spacetimes, stable FPOs may also exist, even when all LRs are unstable, triggering new instabilities. We illustrate this for the case of Kerr BHs with Proca hair, wherein, moreover, qualitatively novel shadows with a cuspy edge exist, a feature that can be understood from the interplay between stable and unstable FPOs. FPOs are the natural generalization of LRs beyond spherical symmetry and should generalize the LRs key role in different spacetime properties.

Test of the Hill Stability Criterion against Chaos Indicators

NASA Astrophysics Data System (ADS)

Satyal, Suman; Quarles, Billy; Hinse, Tobias

2012-10-01

The efficacy of Hill Stability (HS) criterion is tested against other known chaos indicators such as Maximum Lyapunov Exponents (MLE) and Mean Exponential Growth of Nearby Orbits (MEGNO) maps. First, orbits of four observationally verified binary star systems: γ Cephei, Gliese-86, HD41004, and HD196885 are integrated using standard integration packages (MERCURY, SWIFTER, NBI, C/C++). The HS which measures orbital perturbation of a planet around the primary star due to the secondary star is calculated for each system. The LEs spectra are generated to measure the divergence/convergence rate of stable manifolds and the MEGNO maps are generated by using the variational equations of the system during the integration process. These maps allow to accurately differentiate between stable and unstable dynamical systems. Then the results obtained from the analysis of HS, MLE, and MEGNO maps are checked for their dynamical variations and resemblance. The HS of most of the planets seems to be stable, quasi-periodic for at least ten million years. The MLE and the MEGNO maps also indicate the local quasi-periodicity and global stability in relatively short integration period. The HS criterion is found to be a comparably efficient tool to measure the stability of planetary orbits.

Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

NASA Astrophysics Data System (ADS)

Scopa, Stefano; Unterberger, Jéremie; Karevski, Dragi

2018-05-01

We study the unitary dynamics of a 1D gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency . Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

Using heteroclinic orbits to quantify topological entropy in fluid flows

NASA Astrophysics Data System (ADS)

Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.

2016-03-01

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or "ghost," rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Frequency dependence and viral diversity imply chaos in an HIV model

NASA Astrophysics Data System (ADS)

Iwami, Shingo; Nakaoka, Shinji; Takeuchi, Yasuhiro

2006-11-01

In this paper, we consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of CTLs (cytotoxic T-lymphocytes) and rate of elimination of infected cells by CTLs. We show that the interior equilibrium of our model can become unstable without viral diversity and we observe stable periodic orbits. Furthermore, our mathematical models suggest that viral diversity produces strange attractors.

Locally optimal transfer trajectories between libration point orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.

2009-12-01

Techniques from dynamical systems theory and primer vector theory have been applied to the construction of locally optimal transfer trajectories between libration point orbits. When two libration point orbits have different energies, it has been found that the unstable manifold of the first orbit can be connected to the stable manifold of the second orbit with a bridging trajectory. A bounding sphere centered on the secondary, with a radius less than the radius of the sphere of influence of the secondary, was used to study the stable and unstable manifold trajectories. It was numerically demonstrated that within the bounding sphere, the two-body parameters of the unstable and stable manifold trajectories could be analyzed to locate low transfer costs. It was shown that as the two-body parameters of an unstable manifold trajectory more closely matched the two-body parameters of a stable manifold trajectory, the total DeltaV necessary to complete the transfer decreased. Primer vector theory was successfully applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connected the unstable manifold of the first orbit to the stable manifold of the second orbit. Transfer trajectories were constructed between halo orbits in the Sun-Earth and Earth-Moon three-body systems. Multiple solutions were found between the same initial and final orbits, where certain solutions retraced interior portions of the trajectory. All of the trajectories created satisfied the conditions for optimality. The costs of transfers constructed using invariant manifolds were compared to the costs of transfers constructed without the use of invariant manifolds, when data was available. In all cases, the total cost of the transfers were significantly lower when invariant manifolds were used in the transfer construction. In many cases, the transfers that employed invariant manifolds were three to four times more efficient, in terms of fuel expenditure, than the transfer that did not. The decrease in transfer cost was accompanied by an increase in transfer time of flight. Transfers constructed in the Earth-Moon system were shown to be particularly viable for lunar navigation and communication constellations, as excellent coverage of the lunar surface can be achieved during the transfer.

The Updated Multiple Star Catalog

NASA Astrophysics Data System (ADS)

Tokovinin, Andrei

2018-03-01

The catalog of hierarchical stellar systems with three or more components is an update of the original 1997 version. For 2000 hierarchies, the new Multiple Star Catalog (MSC) provides distances, component masses and periods, and supplementary information (astrometry, photometry, identifiers, orbits, notes). The MSC content and format are explained, and its incompleteness and strong observational selection are stressed. Nevertheless, the MSC can be used for statistical studies and is a valuable source for planning observations of multiple stars. Rare classes of stellar hierarchies found in the MSC (with six or seven components, extremely eccentric orbits, planar and possibly resonant orbits, hosting planets) are briefly presented. High-order hierarchies have smaller velocity dispersion compared to triples and are often associated with moving groups. The paper concludes with an analysis of the ratio of periods and separations between inner and outer subsystems. In wide hierarchies, the ratio of semimajor axes, estimated statistically, is distributed between 3 and 300, with no evidence of dynamically unstable systems.

The Fate of Unstable Circumbinary Planets

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2016-03-01

What happens to Tattooine-like planets that are instead in unstable orbits around their binary star system? A new study examines whether such planets will crash into a host star, get ejected from the system, or become captured into orbit around one of their hosts.Orbit Around a DuoAt this point we have unambiguously detected multiple circumbinary planets, raising questions about these planets formation and evolution. Current models suggest that it is unlikely that circumbinary planets would be able to form in the perturbed environment close their host stars. Instead, its thought that the planets formed at a distance and then migrated inwards.One danger such planets face when migrating is encountering ranges of radii where their orbits become unstable. Two scientists at the University of Chicago, Adam Sutherland and Daniel Fabrycky, have studied what happens when circumbinary planets migrate into such a region and develop unstable orbits.Producing Rogue PlanetsTime for planets to either be ejected or collide with one of the two stars, as a function of the planets starting distance (in AU) from the binary barycenter. Colors represent different planetary eccentricities. [Sutherland Fabrycky 2016]Sutherland and Fabrycky used N-body simulations to determine the fates of planets orbiting around a star system consisting of two stars a primary like our Sun and a secondary roughly a tenth of its size that are separated by 1 AU.The authors find that the most common fate for a circumbinary planet with an unstable orbit is ejection from the system; over 80% of unstable planets were ejected. This has interesting implications: if the formation of circumbinary planets is common, this mechanism could be filling the Milky Way with a population of free-floating, rogue planets that no longer are associated with their host star.The next most common outcome for unstable planets is collision with one of their host stars (most often the secondary), resulting inaccretion of the planet onto the star. Only rarely do unstable planets make it through the 10,000-yr integration without being removed from the system via ejection or collision.Tidal EffectsAs a final experiment, the authors also added the effects of tidal stripping, which occurs when the stars of the binary tear away some of the planets mass during close encounters. They found that this alters the orbit of the planets that have close encounters with one of the stars, making it slightly more likely that they can be captured around a star.How can we test these models? When a star tidally strips a planet or accretes a planet in a collision, this process leaves its mark on the star in the form of stellar pollution. By comparing the amount of planetary material in the two stars of a binary, it may be possible to confirm the rates predicted here thereby answering the question of what happens to unstable Tattooines.CitationAdam P. Sutherland and Daniel C. Fabrycky 2016 ApJ 818 6. doi:10.3847/0004-637X/818/1/6

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sattari, Sulimon, E-mail: ssattari2@ucmerced.edu; Chen, Qianting, E-mail: qchen2@ucmerced.edu; Mitchell, Kevin A., E-mail: kmitchell@ucmerced.edu

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding ofmore » ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.« less

Deconstructing an Atmospheric Model: Variability and Response, Unstable Periodic Orbits, and the Fluctuation-Dissipation Theorem

NASA Astrophysics Data System (ADS)

Gritsun, Andrei; Lucarini, Valerio

2016-04-01

Unstable periodic orbits (UPOs) provide the so-called skeletal dynamics of a sufficiently well-behaved chaotic dynamical system and provide a powerful tool for relating the response of the system to its variability. In fact, UPOs constitute natural modes of variability of the system, and resonant behaviour of the response of the system to can be associated to good correspondence between the geometry of one UPO and of the forcing term and between their periodicities. We have here analyzed a simple barotropic model of the atmosphere and constructed and found algorithmically a large number of UPOs. We have then studied the change in the climate resulting from changes in the forcing, in the orography, and in the Eckman friction. The most interesting result is the presence of a strong resonance in the orographic response on time scales of the order of about 3 days, corresponding to forced waves. Interestingly, such a spectral feature is entirely absent from the natural variability of the system and correspond to the excitation of a specific group of UPOs. This clarifies the fact that, as opposed to the case of quasi-equilibrium systems, it is far from obvious to associate forced and free variability in the spirit of the fluctuation-dissipation theorem (FDT). Reassuringly, ysing the complementary point of view of covariant Lyapunov vectors, we discover that the forcing projects substantially in the stable direction of the flow, which is exactly the mathematical setting under which the FDT cannot be applied.

Statespace geometry of puff formation in pipe flow

NASA Astrophysics Data System (ADS)

Budanur, Nazmi Burak; Hof, Bjoern

2017-11-01

Localized patches of chaotically moving fluid known as puffs play a central role in the transition to turbulence in pipe flow. Puffs coexist with the laminar flow and their large-scale dynamics sets the critical Reynolds number: When the rate of puff splitting exceeds that of decaying, turbulence in a long pipe becomes sustained in a statistical sense. Since puffs appear despite the linear stability of the Hagen-Poiseuille flow, one expects them to emerge from the bifurcations of finite-amplitude solutions of Navier-Stokes equations. In numerical simulations of pipe flow, Avila et al., discovered a pair of streamwise localized relative periodic orbits, which are time-periodic solutions with spatial drifts. We combine symmetry reduction and Poincaré section methods to compute the unstable manifolds of these orbits, revealing statespace structures associated with different stages of puff formation.

The information capacity of hypercycles.

PubMed

Silvestre, Daniel A M M; Fontanari, José F

2008-10-21

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates n(m) that can coexist in a hypercycle and show that it is a decreasing function of the length L of the templates. In the case of high replication accuracy we find that the product n(m)L tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits.

Strong quantum scarring by local impurities

PubMed Central

Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa

2016-01-01

We discover and characterise strong quantum scars, or quantum eigenstates resembling classical periodic orbits, in two-dimensional quantum wells perturbed by local impurities. These scars are not explained by ordinary scar theory, which would require the existence of short, moderately unstable periodic orbits in the perturbed system. Instead, they are supported by classical resonances in the unperturbed system and the resulting quantum near-degeneracy. Even in the case of a large number of randomly scattered impurities, the scars prefer distinct orientations that extremise the overlap with the impurities. We demonstrate that these preferred orientations can be used for highly efficient transport of quantum wave packets across the perturbed potential landscape. Assisted by the scars, wave-packet recurrences are significantly stronger than in the unperturbed system. Together with the controllability of the preferred orientations, this property may be very useful for quantum transport applications. PMID:27892510

Strong quantum scarring by local impurities

NASA Astrophysics Data System (ADS)

Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa

2016-11-01

We discover and characterise strong quantum scars, or quantum eigenstates resembling classical periodic orbits, in two-dimensional quantum wells perturbed by local impurities. These scars are not explained by ordinary scar theory, which would require the existence of short, moderately unstable periodic orbits in the perturbed system. Instead, they are supported by classical resonances in the unperturbed system and the resulting quantum near-degeneracy. Even in the case of a large number of randomly scattered impurities, the scars prefer distinct orientations that extremise the overlap with the impurities. We demonstrate that these preferred orientations can be used for highly efficient transport of quantum wave packets across the perturbed potential landscape. Assisted by the scars, wave-packet recurrences are significantly stronger than in the unperturbed system. Together with the controllability of the preferred orientations, this property may be very useful for quantum transport applications.

Strong quantum scarring by local impurities.

PubMed

Luukko, Perttu J J; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J; Räsänen, Esa

2016-11-28

We discover and characterise strong quantum scars, or quantum eigenstates resembling classical periodic orbits, in two-dimensional quantum wells perturbed by local impurities. These scars are not explained by ordinary scar theory, which would require the existence of short, moderately unstable periodic orbits in the perturbed system. Instead, they are supported by classical resonances in the unperturbed system and the resulting quantum near-degeneracy. Even in the case of a large number of randomly scattered impurities, the scars prefer distinct orientations that extremise the overlap with the impurities. We demonstrate that these preferred orientations can be used for highly efficient transport of quantum wave packets across the perturbed potential landscape. Assisted by the scars, wave-packet recurrences are significantly stronger than in the unperturbed system. Together with the controllability of the preferred orientations, this property may be very useful for quantum transport applications.

Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fabrycky, Daniel C.; Lissauer, Jack J.; Ragozzine, Darin

Having discovered 885 planet candidates in 361 multiple-planet systems, Kepler has made transits a powerful method for studying the statistics of planetary systems. The orbits of only two pairs of planets in these candidate systems are apparently unstable. This indicates that a high percentage of the candidate systems are truly planets orbiting the same star, motivating physical investigations of the population. Pairs of planets in this sample are typically not in orbital resonances. However, pairs with orbital period ratios within a few percent of a first-order resonance (e.g. 2:1, 3:2) prefer orbital spacings just wide of the resonance and avoidmore » spacings just narrow of the resonance. Finally, we investigate mutual inclinations based on transit duration ratios. We infer that the inner planets of pairs tend to have a smaller impact parameter than their outer companions, suggesting these planetary systems are typically coplanar to within a few degrees.« less

Chaotic dynamics in the (47171) Lempo triple system

NASA Astrophysics Data System (ADS)

Correia, Alexandre C. M.

2018-05-01

We investigate the dynamics of the (47171) Lempo triple system, also known by 1999 TC36. We derive a full 3D N-body model that takes into account the orbital and spin evolution of all bodies, which are assumed triaxial ellipsoids. We show that, for reasonable values of the shapes and rotational periods, the present best fitted orbital solution for the Lempo system is chaotic and unstable in short time-scales. The formation mechanism of this system is unknown, but the orbits can be stabilised when tidal dissipation is taken into account. The dynamics of the Lempo system is very rich, but depends on many parameters that are presently unknown. A better understanding of this systems thus requires more observations, which also need to be fitted with a complete model like the one presented here.

Bifurcation analysis of a discrete-time ratio-dependent predator-prey model with Allee Effect

NASA Astrophysics Data System (ADS)

Cheng, Lifang; Cao, Hongjun

2016-09-01

A discrete-time predator-prey model with Allee effect is investigated in this paper. We consider the strong and the weak Allee effect (the population growth rate is negative and positive at low population density, respectively). From the stability analysis and the bifurcation diagrams, we get that the model with Allee effect (strong or weak) growth function and the model with logistic growth function have somewhat similar bifurcation structures. If the predator growth rate is smaller than its death rate, two species cannot coexist due to having no interior fixed points. When the predator growth rate is greater than its death rate and other parameters are fixed, the model can have two interior fixed points. One is always unstable, and the stability of the other is determined by the integral step size, which decides the species coexistence or not in some extent. If we increase the value of the integral step size, then the bifurcated period doubled orbits or invariant circle orbits may arise. So the numbers of the prey and the predator deviate from one stable state and then circulate along the period orbits or quasi-period orbits. When the integral step size is increased to a critical value, chaotic orbits may appear with many uncertain period-windows, which means that the numbers of prey and predator will be chaotic. In terms of bifurcation diagrams and phase portraits, we know that the complexity degree of the model with strong Allee effect decreases, which is related to the fact that the persistence of species can be determined by the initial species densities.

Streamwise-Localized Solutions with natural 1-fold symmetry

NASA Astrophysics Data System (ADS)

Altmeyer, Sebastian; Willis, Ashley; Hof, Björn

2014-11-01

It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints.

Effects of structural flexibility of wings in flapping flight of butterfly.

PubMed

Senda, Kei; Obara, Takuya; Kitamura, Masahiko; Yokoyama, Naoto; Hirai, Norio; Iima, Makoto

2012-06-01

The objective of this paper is to clarify the effects of structural flexibility of wings of a butterfly in flapping flight. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. The panel method is employed to simulate the flow field and the aerodynamic forces acting on the wings. The mathematical model is validated by the agreement of the numerical result with the experimentally measured data. Then, periodic orbits of flapping-of-wings flights are parametrically searched in order to fly the butterfly models. Almost periodic orbits are found, but they are unstable. Deformation of the wings is modeled in two ways. One is bending and its effect on the aerodynamic forces is discussed. The other is passive wing torsion caused by structural flexibility. Numerical simulations demonstrate that flexible torsion reduces the flight instability.

(1173) Anchises - thermophysical and dynamical studies of a dynamically unstable Jovian Trojan

NASA Astrophysics Data System (ADS)

Horner, J.; Müller, T. G.; Lykawka, P. S.

2012-07-01

We have performed detailed thermophysical and dynamical modelling of the Jovian Trojan (1173) Anchises. Our results show that this is the most unusual object. By examining observational data of Anchises taken by IRAS, Akari and WISE at wavelengths between 11.5 and 60 μm, together with the variations in its optical light curve, we find that Anchises is most likely an elongated body, with an axis ratio, a/b, of around 1.4. This results in calculated best-fitting dimensions for Anchises of 170 × 121 × 121 km (or an equivalent diameter of 136 +18/-11 km). We find that the observations of Anchises are best fitted by the object having a retrograde sense of rotation, and an unusually high thermal inertia in the range 25-100 J m-2 s-0.5 K-1 (3σ confidence level). The geometric albedo of Anchises is found to be 0.027 (+0.006/-0.007). Anchises therefore has one of the highest published thermal inertias of any object larger than 100 km in diameter, at such large heliocentric distances, as well as being one of the lowest albedo objects ever observed. More observations (visual and thermal) are needed to see whether there is a link between the very shallow phase curve, with almost no opposition effect, and the derived thermal properties for this large Trojan asteroid. Our dynamical investigation of Anchises' orbit has revealed it to be dynamically unstable on time-scales of hundreds of millions of years, similar to the unstable Neptunian Trojans 2001 QR322 and 2008 LC18. Unlike those objects, however, we find that the dynamical stability of Anchises is not a function of its initial orbital elements, the result of the exceptional precision with which its orbit is known. Our results are the first to show that a Jovian Trojan is dynamically unstable, and add further weight to the idea that the planetary Trojans likely represent a significant ongoing contribution to the dynamically unstable Centaur population, the parents of the short-period comets. The observed instability (fully half of all clones of Anchises escape the Solar system within 350 Myr) does not rule out a primordial origin for Anchises, but, when taken in concert with the result of our thermophysical analysis, suggest that it would be a fascinating target for a future study.

Analysis of chaotic saddles in a nonlinear vibro-impact system

NASA Astrophysics Data System (ADS)

Feng, Jinqian

2017-07-01

In this paper, a computational investigation of chaotic saddles in a nonlinear vibro-impact system is presented. For a classical Duffing vibro-impact oscillator, we employ the bisection procedure and an improved stagger-and-step method to present evidence of visual chaotic saddles on the fractal basin boundary and in the internal basin, respectively. The results show that the period saddles play an important role in the evolution of chaotic saddle. The dynamics mechanics of three types of bifurcation such as saddle-node bifurcation, chaotic saddle crisis bifurcation and interior chaotic crisis bifurcation are discussed. The results reveal that the period saddle created at saddle-node bifurcation is responsible for the switch of the internal chaotic saddle to the boundary chaotic saddle. At chaotic saddle crisis bifurcation, a large chaotic saddle can divide into two different chaotic saddle connected by a period saddle. The intersection points between stable and unstable manifolds of this period saddle supply access for chaotic orbits from one chaotic saddle to another and eventually induce the coupling of these two chaotic saddle. Interior chaotic crisis bifurcation is associated with the intersection of stable and unstable manifolds of the period saddle connecting two chaotic invariant sets. In addition, the gaps in chaotic saddle is responsible for the fractal structure.

Migration of Gas Giant Planets in a Gravitationally Unstable Disk

NASA Astrophysics Data System (ADS)

Desai, Karna Mahadev; Steiman-Cameron, Thomas Y.; Michael, Scott; Durisen, Richard H.

2017-01-01

Understanding the migration of giant planets in gravitationally unstable protoplanetary disks is important for understanding planetary system architecture, especially the existence of planets orbiting close to and at large distances from their stars. Migration rates can determine the efficiency of planet formation and survival rates of planets. We present results from simulations of 0.3, 1, and 3 Jupiter-mass planets in a 0.14 M⊙ protoplanetary disk around a 1 M⊙ star, where the disk is marginally unstable to gravitational instabilities (GIs). Each planet is simulated separately. We use CHYMERA, a radiative 3D hydrodynamics code developed by the Indiana University Hydrodynamics Group. The simulations include radiative cooling governed by realistic dust opacities. The planets are inserted into the disk, once the disk has settled into its quasi-steady GI-active phase. We simulate each of the 0.3, 1, and 3 Jupiter-mass planets by inserting it at three different locations in the disk, at the corotation radius and at the inner and outer Lindblad resonances. No matter where placed, the 3 Jupiter-mass planets tend to drift inexorably inward but with a rate that slows after many orbital periods. The 1 Jupiter-mass planets migrate mostly inward, but their motion can be delayed or reversed near the corotation of the two-armed wave. The 0.3 Jupiter-mass planets are much less predictable and frequently migrate outward. We analyze how the density of matter and waves in the disk at different azimuthal locations affect the migration.

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Antoniadou, Kyriaki I.; Libert, Anne-Sophie

2018-06-01

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted three-body problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances, and thus, new families continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consists of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted three-body problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The long-term stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for long-time spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the single-giant planet systems discovered so far.

Bifurcation Gaps in Asymmetric and High-Dimensional Hypercycles

NASA Astrophysics Data System (ADS)

Puig, Júlia; Farré, Gerard; Guillamon, Antoni; Fontich, Ernest; Sardanyés, Josep

Hypercycles are catalytic systems with cyclic architecture. These systems have been suggested to play a key role in the maintenance and increase of information in prebiotic replicators. It is known that for a large enough number of hypercycle species (n > 4) the coexistence of all hypercycle members is governed by a stable periodic orbit. Previous research has characterized saddle-node (s-n) bifurcations involving abrupt transitions from stable hypercycles to extinction of all hypercycle members, or, alternatively, involving the outcompetition of the hypercycle by so-called mutant sequences or parasites. Recently, the presence of a bifurcation gap between a s-n bifurcation of periodic orbits and a s-n of fixed points has been described for symmetric five-member hypercycles. This gap was found between the value of the replication quality factor Q from which the periodic orbit vanishes (QPO) and the value where two unstable (nonzero) equilibrium points collide (QSS). Here, we explore the persistence of this gap considering asymmetries in replication rates in five-member hypercycles as well as considering symmetric, larger hypercycles. Our results indicate that both the asymmetry in Malthusian replication constants and the increase in hypercycle members enlarge the size of this gap. The implications of this phenomenon are discussed in the context of delayed transitions associated to the so-called saddle remnants.

Detecting a Subsurface Ocean From Periodic Orbits at Enceladus

NASA Astrophysics Data System (ADS)

Casotto, S.; Padovan, S.; Russell, R. P.; Lara, M.

2008-12-01

Enceladus is a small icy satellite of Saturn which has been observed by the Cassini orbiter to eject plumes mainly consisting of water vapor from the "tiger stripes" located near its South pole. While tidal heating has been ruled out as an inadequate energy source to drive these eruptions, tidally induced shear stress both along and across the stripes appears to be sufficiently powerful. The internal constitution of Enceladus that fits this model is likely to entail a thin crust and a subcrustal water layer above an undifferentiated interior. Apart from the lack of a core/mantle boundary, the situation is similar to the current hypothetical models of Europa's interior. The determination of the existence of a subsurface fluid layer can therefore be pursued with similar methods, including the study of the gravitational perturbations of tidal origin on an Enceladus orbiter, and the use of altimeter measurements to the tidally deformed surface. The dynamical environment of an Enceladus orbiter is made very unstable by the overwhelming presence of nearby Saturn. The Enceladus sphere of influence is roughly twice its radius. This makes it considerably more difficult to orbit than Europa, whose sphere of influence is ~six times its radius. While low-altitude, near-polar Enceladus orbits suffer extreme instability, recent works have extended the inclination envelope for long-term stable orbits at Enceladus. Several independent methods suggest that ~65 degrees inclination is the maximum attainable for stable, perturbed Keplerian motion. These orbits are non-circular and exist with altitude variations from ~200 to ~300 km. We propose a nominal reference orbit that enjoys long term stability and is favorable for long-term mapping and other scientific experiments. A brief excursion to a lower altitude, slightly higher inclined, yet highly unstable orbit is proposed to improve gravity signatures and enable high resolution, nadir-pointing experiments on the geysers emanating from the tiger- stripes. Near-circular, low altitude highly inclined orbits with arbitrary initial conditions will impact Enceladus if uncontrolled in about 1 to 2 days. To reduce risk and station-keeping requirements we choose periodic orbits in the Hill's plus non-spherical Enceladus model. Despite the instability, the repeat ground track solutions represent equilibria in the dominant terms of the dynamics and therefore extend the uncontrolled lifetimes to ~7 to ~10 days. Round-trip transfers between the two orbital phases is expected to conservatively cost between ~50 and ~100 m/s. We use orbits of different altitudes and inclinations to simulate Earth-based ranging to the orbiter and altimeter measurements to the surface of Enceladus. The simulations are made assuming different tidal responses by adopting different values of the Love numbers. The synthetic measurements are then inverted and the tidal parameters h2 and k2 estimated. Results will be presented in terms of sensitivity of detection of Love numbers to the different orbital geometries. Indications will thus be provided for optimized orbit planning of future exploration missions aimed at investigating the internal structure of the satellite and the detection of its putative subcrustal ocean.

Predator prey oscillations in a simple cascade model of drift wave turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berionni, V.; Guercan, Oe. D.

2011-11-15

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separationmore » for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.« less

Fossil Cores In The Kepler Data

NASA Astrophysics Data System (ADS)

Jackson, Brian

Most gas giant exoplanets with orbital periods < few days are unstable against tidal decay and may be tidally disrupted before their host stars leave the main sequence. These gas giants probably contain rocky/icy cores, and so their cores will be stranded near their progenitor's Roche limit (few hours orbital period). These fossil cores will evade the Kepler mission's transit search because it is focused on periods > 0.5 days, but finding these fossil cores would provide unprecedented insights into planetary interiors and formation ? e.g., they would be a smoking gun favoring formation of gas giants via core accretion. We propose to search for and characterize fossil cores in the Kepler dataset. We will vet candidates using the Kepler photometry and auxiliary data, collect ground-based spectra of the host stars and radial-velocity (RV) and adaptive optics (AO) data to corroborate candidates. We will also constrain stellar tidal dissipation efficiencies (parameterized by Q) by determining our survey's completeness, elucidating dynamical origins and evolution of exoplanets even if we find no fossil cores. Our preliminary search has already found several dozen candidates, so the proposed survey has a high likelihood of success.

Orbital Drivers of Climate Change on Earth and Mars

NASA Astrophysics Data System (ADS)

Zent, A. P.

Oscillations of orbital elements and spin axis orientation affect the climate of both Earth and Mars by redistributing solar power both latitudinally and seasonally, often resulting in secondary changes in reflected and emitted radiation (radiative forcing). Multiple feedback loops between different climatic elements operate on both planets, with the result that climate response is generally nonlinear with simple changes in solar energy. Both insolation history and geochemical climate proxies can be treated as time series data, and analyzed in terms of component frequencies. The correspondence between frequencies measured in climate proxies and orbital oscillations is the key to relating orbital cause and climatic effect. Discussions of both Earth and Mars focus on the last 5-10 m.y., because this is the period in which the orbital history and geologic record are best understood. The terrestrial climate is an extraordinarily complex system, and a vast amount of data is available for analysis. While the geologic record strongly supports the role of Milankovitch cycles as the underlying cause of glacial cycles, orbitally driven insolation changes alone cannot explain the observations in detail. Early Pleistocene glacial cycles responded linearly to the 41-k.y. oscillations in obliquity. However, over the last 1 m.y., glacial/interglacial oscillations have become more extreme as the climate has cooled. Long cooling intervals marked by an oscillating buildup of ice sheets are now followed by brief, intense periods of warming. At the same time, glacial/interglacial cycles have shifted from 41 k.y. to ~100 k.y. No such changes occurred in the solar forcing due to orbital oscillations. While orbital oscillations still appear to pace glacial cycles, their subtle interplay with ice-sheet dynamics and shifts in ocean circulation have come to dominate the late Pleistocene climate system. In contrast to Earth, the martian climate is ostensibly a much simpler system about which we have almost no quantitative data. Lacking climate proxies and chronological data, we are forced to rely on climate modeling and whatever constraints can be extracted from the predominantly remote sensing data available. Obliquity oscillations account for most of the power in historical insolation. Unfortunately, the last 5 m.y. are an anomalous period in Mars' climate history due to a secular decrease in Mars' obliquity. Subsequent to that, however, models and observations are consistent with the hypothesis that during periods of higher obliquity, enhanced polar summer insolation increases atmospheric water vapor and dust content, and ice stability shifted toward the equator. Polar caps become thermodynamically unstable, and much of the surface H2O inventory migrates from high latitudes to the tropics. As obliquity decreases, ice returns to the poles, leaving unstable ice-rich deposits in the mid latitudes that are mantled by dust. Low-obliquity periods entail — at least on occasion — collapse of the atmosphere onto the poles and high-latitude CO2 glaciers. During protracted nodes in obliquity, mid-latitude ice undergoes slow but sustained sublimation and redistribution to the poles. Because of the tremendous breadth of the subject matter, this chapter necessarily presents a high-level overview, and the reader will be compelled to investigate the copious references for a more rigorous explanation of most topics.

Investigating multiphoton phenomena using nonlinear dynamics

NASA Astrophysics Data System (ADS)

Huang, Shu

Many seemingly simple systems can display extraordinarily complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or non-linear) stabilities by adding control functions (which act on the system as external perturbations) to the relevant Hamiltonians. These phase-space structures may be periodic orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of these systems. Recent developments of nonlinear dynamical tools can provide efficient ways of doing so. In the first subtopic of the thesis, we are adding a control function to restore tori at prescribed locations in phase space. In the remainder of the thesis, a control function with parameters is used to change the linear stability of the periodic orbits which govern the processes in question. In this thesis, we report our theoretical analyses on multiphoton ionization of Rydberg atoms exposed to strong microwave fields and the dissociation of diatomic molecules exposed to bichromatic lasers using nonlinear dynamical tools. This thesis is composed of three subtopics. In the first subtopic, we employ local control theory to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding a relatively small control term to the original Hamiltonian. In the second subtopic, we perform periodic orbit analysis to investigate multiphoton ionization driven by a bichromatic microwave field. Our results show quantitative and qualitative agreement with previous studies, and hence identify the mechanism through which short periodic orbits organize the dynamics in multiphoton ionization. In addition, we achieve substantial time savings with this approach. In the third subtopic we extend our periodic orbit analysis to the dissociation of diatomic molecules driven by a bichromatic laser. In this problem, our results based on periodic orbit analysis again show good agreement with previous work, and hence promise more potential applications of this approach in molecular physics.

Recurrence quantification analysis of electrically evoked surface EMG signal.

PubMed

Liu, Chunling; Wang, Xu

2005-01-01

Recurrence Plot is a quite useful tool used in time-series analysis, in particular for measuring unstable periodic orbits embedded in a chaotic dynamical system. This paper introduced the structures of the Recurrence Plot and the ways of the plot coming into being. Then the way of the quantification of the Recurrence Plot is defined. In this paper, one of the possible applications of Recurrence Quantification Analysis (RQA) strategy to the analysis of electrical stimulation evoked surface EMG. The result shows the percent determination is increased along with stimulation intensity.

Control of asteroid retrieval trajectories to libration point orbits

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Sanchez, Joan Pau

2016-09-01

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

Parameter-dependent behaviour of periodic channels in a locus of boundary crisis

NASA Astrophysics Data System (ADS)

Rankin, James; Osinga, Hinke M.

2017-06-01

A boundary crisis occurs when a chaotic attractor outgrows its basin of attraction and suddenly disappears. As previously reported, the locus of a boundary crisis is organised by homo- or heteroclinic tangencies between the stable and unstable manifolds of saddle periodic orbits. In two parameters, such tangencies lead to curves, but the locus of boundary crisis along those curves exhibits gaps or channels, in which other non-chaotic attractors persist. These attractors are stable periodic orbits which themselves can undergo a cascade of period-doubling bifurcations culminating in multi-component chaotic attractors. The canonical diffeomorphic two-dimensional Hénon map exhibits such periodic channels, which are structured in a particular ordered way: each channel is bounded on one side by a saddle-node bifurcation and on the other by a period-doubling cascade to chaos; furthermore, all channels seem to have the same orientation, with the saddle-node bifurcation always on the same side. We investigate the locus of boundary crisis in the Ikeda map, which models the dynamics of energy levels in a laser ring cavity. We find that the Ikeda map features periodic channels with a richer and more general organisation than for the Hénon map. Using numerical continuation, we investigate how the periodic channels depend on a third parameter and characterise how they split into multiple channels with different properties.

Tube dynamics and low energy Earth-Moon transfers in the 4-body system

NASA Astrophysics Data System (ADS)

Onozaki, Kaori; Yoshimura, Hiroaki; Ross, Shane D.

2017-11-01

In this paper, we show a low energy Earth-Moon transfer in the context of the Sun-Earth-Moon-spacecraft 4-body system. We consider the 4-body system as the coupled system of the Sun-Earth-spacecraft 3-body system perturbed by the Moon (which we call the Moon-perturbed system) and the Earth-Moon-spacecraft 3-body system perturbed by the Sun (which we call the Sun-perturbed system). In both perturbed systems, analogs of the stable and unstable manifolds are computed numerically by using the notion of Lagrangian coherent structures, wherein the stable and unstable manifolds play the role of separating orbits into transit and non-transit orbits. We obtain a family of non-transit orbits departing from a low Earth orbit in the Moon-perturbed system, and a family of transit orbits arriving into a low lunar orbit in the Sun-perturbed system. Finally, we show that we can construct a low energy transfer from the Earth to the Moon by choosing appropriate trajectories from both families and patching these trajectories with a maneuver.

Scattering of traveling spots in dissipative systems

NASA Astrophysics Data System (ADS)

Nishiura, Yasumasa; Teramoto, Takashi; Ueda, Kei-Ichi

2005-12-01

One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there occur many collisions among them and its scattering manner is crucial to predict whether periodic structure is realized or not. We focus on the colliding dynamics of traveling spots arising in a three-component system and study how the transition of scattering dynamics is brought about. It has been clarified that hidden unstable patterns called "scattors" and their stable and unstable manifolds direct the traffic flow of orbits before and after collisions. The collision process in general can be decomposed into several steps and each step is controlled by such a scattor, in other words, a network among scattors forms the backbone for scattering dynamics. A variety of input-output relations comes from the complexity of the network as well as high Morse indices of the scattor. The change of transition manners is caused by the switching of the network from one structure to another, and such a change is caused by the singularities of scattors. We illustrate a typical example of the change of transition caused by the destabilization of the scattor. A new instability of the scattor brings a new destination for the orbit resulting in a new input-output relation, for instance, Hopf instability for the scattor of peanut type brings an annihilation.

Gravity Modes Reveal the Internal Rotation of a Post-mass-transfer Gamma Doradus/Delta Scuti Hybrid Pulsator in Kepler Eclipsing Binary KIC 9592855

NASA Astrophysics Data System (ADS)

Guo, Z.; Gies, D. R.; Matson, R. A.

2017-12-01

We report the discovery of a post-mass-transfer Gamma Doradus/Delta Scuti hybrid pulsator in the eclipsing binary KIC 9592855. This binary has a circular orbit, an orbital period of 1.2 days, and contains two stars of almost identical masses ({M}1=1.72 {M}⊙ ,{M}2=1.71 {M}⊙ ). However, the cooler secondary star is more evolved ({R}2=1.96 {R}⊙ ), while the hotter primary is still on the zero-age-main-sequence ({R}1=1.53 {R}⊙ ). Coeval models from single-star evolution cannot explain the observed masses and radii, and binary evolution with mass-transfer needs to be invoked. After subtracting the binary light curve, the Fourier spectrum shows low-order pressure-mode pulsations, and more dominantly, a cluster of low-frequency gravity modes at about 2 day-1. These g-modes are nearly equally spaced in period, and the period spacing pattern has a negative slope. We identify these g-modes as prograde dipole modes and find that they stem from the secondary star. The frequency range of unstable p-modes also agrees with that of the secondary. We derive the internal rotation rate of the convective core and the asymptotic period spacing from the observed g-modes. The resulting values suggest that the core and envelope rotate nearly uniformly, i.e., their rotation rates are both similar to the orbital frequency of this synchronized binary.

Study of an orbiting tethered dumbbell system having positive orbital energy

NASA Technical Reports Server (NTRS)

Arnold, David A.

1988-01-01

For very long tethered systems the sum of the kinetic and potential energy can be positive. The system remains in a circular orbit as long as the masses remain vertically aligned. The system is unstable without constant control of the alignment. If the upper mass rotates forward in the direction of the orbital motion, the system escapes out of orbit. If the upper mass rotates backward, the system falls out of orbit and the lower mass impacts the body around which the system is orbiting.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Antonini, Fabio; Lithwick, Yoram; Hamers, Adrian S.

Gas giants orbiting their host star within the ice line are thought to have migrated to their current locations from farther out. Here we consider the origin and dynamical evolution of observed Jupiters, focusing on hot and warm Jupiters with outer friends. We show that the majority of the observed Jupiter pairs (20 out of 24) are dynamically unstable if the inner planet is placed at ≳1 au distance from the stellar host. This finding is at odds with formation theories that invoke the migration of such planets from semimajor axes ≳1 au due to secular dynamical processes (e.g., secularmore » chaos, Lidov–Kozai [LK] oscillations) coupled with tidal dissipation. In fact, the results of N -body integrations show that the evolution of dynamically unstable systems does not lead to tidal migration but rather to planet ejections and collisions with the host star. This and other arguments lead us to suggest that most of the observed planets with a companion could not have been transported from farther out through secular migration processes. More generally, by using a combination of numerical and analytic techniques, we show that the high- e LK migration scenario can only account for less than 10% of all gas giants observed between 0.1 and 1 au. Simulations of multiplanet systems support this result. Our study indicates that rather than starting on highly eccentric orbits with orbital periods above 1 yr, these “warm” Jupiters are more likely to have reached the region where they are observed today without having experienced significant tidal dissipation.« less

Chaos control by electric current in an enzymatic reaction.

PubMed

Lekebusch, A; Förster, A; Schneider, F W

1996-09-01

We apply the continuous delayed feedback method of Pyragas to control chaos in the enzymatic Peroxidase-Oxidase (PO) reaction, using the electric current as the control parameter. At each data point in the time series, a time delayed feedback function applies a small amplitude perturbation to inert platinum electrodes, which causes redox processes on the surface of the electrodes. These perturbations are calculated as the difference between the previous (time delayed) signal and the actual signal. Unstable periodic P1, 1(1), and 1(2) orbits (UPOs) were stabilized in the CSTR (continuous stirred tank reactor) experiments. The stabilization is demonstrated by at least three conditions: A minimum in the experimental dispersion function, the equality of the delay time with the period of the stabilized attractor and the embedment of the stabilized periodic attractor in the chaotic attractor.

Bifurcation and stability of finite amplitude convection in a rotating layer

NASA Astrophysics Data System (ADS)

Soward, A. M.

1985-01-01

The nature of small amplitude Rayleigh-Bénard convection for a horizontal plane layer of fluid rotating about a vertical axis and heated from below is considered. When the usual approximations are made the evolution of three convective rolls with axes inclined at 60° one to another is described by the coupled non-linear Gause-Lotka-Volterra equations. For sufficiently large rotation rates they have no steady solutions. Instead there is a degenerate time-periodic solution of infinite period in which the phase space trajectory passes successively from one unstable equilibrium point, a single roll, to another (a heteroclinic orbit). In this paper additional terms, which correspond to vertical asymmetries in the physical system, are included and as a result the degeneracy is removed. The steady state and time-periodic solutions are derived and their stability discussed.

Comparison of Low-Energy Lunar Transfer Trajectories to Invariant Manifolds

NASA Technical Reports Server (NTRS)

Anderson, Rodney L.; Parker, Jeffrey S.

2011-01-01

In this study, transfer trajectories from the Earth to the Moon that encounter the Moon at various flight path angles are examined, and lunar approach trajectories are compared to the invariant manifolds of selected unstable orbits in the circular restricted three-body problem. Previous work focused on lunar impact and landing trajectories encountering the Moon normal to the surface, and this research extends the problem with different flight path angles in three dimensions. The lunar landing geometry for a range of Jacobi constants are computed, and approaches to the Moon via invariant manifolds from unstable orbits are analyzed for different energy levels.

Pendulum motions of extended lunar space elevator

NASA Astrophysics Data System (ADS)

Burov, A. A.; Kosenko, I. I.

2014-09-01

In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to "all four sides," to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this property preserved if the pendulum is "very, very long"? It turns out that the answer is negative; namely, if the pendulum length significantly exceeds the Moon radius, then the radial equilibria at which the pendulum is located along the straight line connecting the Earth and Moon centers are Lyapunov stable and the pendulum does not fall in any direction at all. Moreover, if the pendulum goes beyond the collinear libration points, then it can be extended and manufactured from cables. This property was noted by F. A. Tsander and underlies the so-called lunar space elevator (e.g., see [1]). In the plane of the Earth and Moon orbits, there are some other equilibria which turn out to be unstable. The question is, Are there equilibria at which the pendulum is located outside the orbital plane? In this paper, we show that the answer is positive, but such equilibria are unstable in the secular sense. We also study necessary conditions for the stability of lunar pendulum oscillations in the plane of the lunar orbit. It was numerically discovered that stable and unstable equilibria alternate depending on the oscillation amplitude and the angular velocity of rotation. The study of the lunar elevator dynamics originates in [2]. The concept of lunar elevator was developed in detail in [3, 4]. Several classes of equilibria with the finiteness of the Moon size taken into account were studied in [5]. The possibility of location of an orbital station fixed to the Moon surface by a pair of tethers was investigated in [6]. The problem of orientation of the terminal station of the lunar space elevator was studied in [7]. The influence of the tether length variations on the motion of the lunar tether system was considered in [8]. The alternation of stable and unstable flat oscillations is well known in the problem of satellite oscillations in a circular orbit [9, 10].

Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations

NASA Astrophysics Data System (ADS)

Gidea, Marian; de la Llave, Rafael

2018-04-01

We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on the Melnikov potential are generic.

Noise induced stabilization of chaotic free-running laser diode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Virte, Martin, E-mail: mvirte@b-phot.org

In this paper, we investigate theoretically the stabilization of a free-running vertical-cavity surface-emitting laser exhibiting polarization chaos dynamics. We report the existence of a boundary isolating the chaotic attractor on one side and a steady-state on the other side and identify the unstable periodic orbit playing the role of separatrix. In addition, we highlight a small range of parameters where the chaotic attractor passes through this boundary, and therefore where chaos only appears as a transient behaviour. Then, including the effect of spontaneous emission noise in the laser, we demonstrate that, for realistic levels of noise, the system is systematicallymore » pushed over the separating solution. As a result, we show that the chaotic dynamics cannot be sustained unless the steady-state on the other side of the separatrix becomes unstable. Finally, we link the stability of this steady-state to a small value of the birefringence in the laser cavity and discuss the significance of this result on future experimental work.« less

Orbital stability close to asteroid 624 Hektor using the polyhedral model

NASA Astrophysics Data System (ADS)

Jiang, Yu; Baoyin, Hexi; Li, Hengnian

2018-03-01

We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid's mass center when the density increases, and the inner equilibrium point moves close to the asteroid's mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary's equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375 d.

Synchronization in networks with heterogeneous coupling delays

NASA Astrophysics Data System (ADS)

Otto, Andreas; Radons, Günter; Bachrathy, Dániel; Orosz, Gábor

2018-01-01

Synchronization in networks of identical oscillators with heterogeneous coupling delays is studied. A decomposition of the network dynamics is obtained by block diagonalizing a newly introduced adjacency lag operator which contains the topology of the network as well as the corresponding coupling delays. This generalizes the master stability function approach, which was developed for homogenous delays. As a result the network dynamics can be analyzed by delay differential equations with distributed delay, where different delay distributions emerge for different network modes. Frequency domain methods are used for the stability analysis of synchronized equilibria and synchronized periodic orbits. As an example, the synchronization behavior in a system of delay-coupled Hodgkin-Huxley neurons is investigated. It is shown that the parameter regions where synchronized periodic spiking is unstable expand when increasing the delay heterogeneity.

Phase separation and long-wavelength charge instabilities in spin-orbit coupled systems

NASA Astrophysics Data System (ADS)

Seibold, G.; Bucheli, D.; Caprara, S.; Grilli, M.

2015-01-01

We investigate a two-dimensional electron model with Rashba spin-orbit interaction where the coupling constant g=g(n) depends on the electronic density. It is shown that this dependence may drive the system unstable towards a long-wavelength charge density wave (CDW) where the associated second-order instability occurs in close vicinity to global phase separation. For very low electron densities the CDW instability is nesting-induced and the modulation follows the Fermi momentum kF. At higher density the instability criterion becomes independent of kF and the system may become unstable in a broad momentum range. Finally, upon filling the upper spin-orbit split band, finite momentum instabilities disappear in favor of phase separation alone. We discuss our results with regard to the inhomogeneous phases observed at the LaAlO3/SrTiO3 or LaTiO3/SrTiO3 interfaces.

Leaking in history space: A way to analyze systems subjected to arbitrary driving

NASA Astrophysics Data System (ADS)

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2018-03-01

Our aim is to unfold phase space structures underlying systems with a drift in their parameters. Such systems are non-autonomous and belong to the class of non-periodically driven systems where the traditional theory of chaos (based e.g., on periodic orbits) does not hold. We demonstrate that even such systems possess an underlying topological horseshoe-like structure at least for a finite period of time. This result is based on a specifically developed method which allows to compute the corresponding time-dependent stable and unstable foliations. These structures can be made visible by prescribing a certain type of history for an ensemble of trajectories in phase space and by analyzing the trajectories fulfilling this constraint. The process can be considered as a leaking in history space—a generalization of traditional leaking, a method that has become widespread in traditional chaotic systems, to leaks depending on time.

Delivery of Volatiles to Habitable Planets in Extrasolar Planetary Systems

NASA Technical Reports Server (NTRS)

Chambers, John E.; Kress, Monika E.; Bell, K. Robbins; Cash, Michele; DeVincenzi, Donald L. (Technical Monitor)

2000-01-01

The Earth can support life because: (1) its orbit lies in the Sun's habitable zone', and (2) it contains enough volatile material (e.g. water and organics) for life to flourish. However, it seems likely that the Earth was drier when it formed because it accreted in a part of the Sun's protoplanetary nebula that was too hot for volatiles to condense. If this is correct, water and organics must have been delivered to the habitable zone, after dissipation of the solar nebula, from a 'wet zone' in the asteroid belt or the outer solar system, where the nebula was cool enough for volatiles to condense. Material from the wet zone would have been delivered to the Earth by Jupiter and Saturn. Gravitational perturbations from these giant planets made much of the wet zone unstable, scattering volatile-rich planetesimals and protoplanets across the Solar System. Some of these objects ultimately collided with the inner Planets which themselves lie in a stable part of the Solar System. Giant planets are now being discovered orbiting other sunlike stars. To date, these planets have orbits and masses very different from Jupiter and Saturn, such that few if any of these systems is likely to have terrestrial planets in the star's habitable zone. However, new discoveries are anticipated due to improved detector sensitivity and the increase in the timespan of observations. Here we present numerical experiments examining the range of giant-planet characteristics that: (1) allow stable terrestrial Planets to exist in a star's habitable zone, and (2) make a large part of the star's wet zone weakly unstable, thus delivering volatiles to the terrestrial planets over an extended period of time after the dissipation of the solar nebula.

Survival of habitable planets in unstable planetary systems

NASA Astrophysics Data System (ADS)

Carrera, Daniel; Davies, Melvyn B.; Johansen, Anders

2016-12-01

Many observed giant planets lie on eccentric orbits. Such orbits could be the result of strong scatterings with other giant planets. The same dynamical instability that produces these scatterings may also cause habitable planets in interior orbits to become ejected, destroyed, or be transported out of the habitable zone. We say that a habitable planet has resilient habitability if it is able to avoid ejections and collisions and its orbit remains inside the habitable zone. Here we model the orbital evolution of rocky planets in planetary systems where giant planets become dynamically unstable. We measure the resilience of habitable planets as a function of the observed, present-day masses and orbits of the giant planets. We find that the survival rate of habitable planets depends strongly on the giant planet architecture. Equal-mass planetary systems are far more destructive than systems with giant planets of unequal masses. We also establish a link with observation; we find that giant planets with present-day eccentricities higher than 0.4 almost never have a habitable interior planet. For a giant planet with a present-day eccentricity of 0.2 and semimajor axis of 5 au orbiting a Sun-like star, 50 per cent of the orbits in the habitable zone are resilient to the instability. As semimajor axis increases and eccentricity decreases, a higher fraction of habitable planets survive and remain habitable. However, if the habitable planet has rocky siblings, there is a significant risk of rocky planet collisions that would sterilize the planet.

Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems

NASA Astrophysics Data System (ADS)

Spiechowicz, J.; Talkner, P.; Hänggi, P.; Łuczka, J.

2016-12-01

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.

Dynamical instabilities in axisymmetric stellar systems. I - Oblate E6 models

NASA Technical Reports Server (NTRS)

Levison, Harold F.; Duncan, Martin J.; Smith, Bruce F.

1990-01-01

The stability of a set of models based on isothermal oblate E6 elliptical galaxies is studied using N-body techniques. The only stable models are those that are near the isotropic model and have nearly equal number of stars in retrograde and prograde orbits. Fast rotators are unstable to modes that appear to be analogous to the classical streaming instability seen in many disk systems. Systems with a large velocity dispersion in the direction of the cylindrical radius are unstable to modes that appear to be similar to the radial orbit instability observed in some spherical systems. However, evidence is presented that these two instabilities may be related, and an instability criterion that applies to both is constructed.

Bianchi IX dynamics in bouncing cosmologies: homoclinic chaos and the BKL conjecture

NASA Astrophysics Data System (ADS)

Maier, Rodrigo; Damião Soares, Ivano; Valentino Tonini, Eduardo

2015-12-01

We examine the dynamics of a Bianchi IX model with three scale factors on a 4-dim Lorentzian brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. The matter content is a pressureless perfect fluid restricted to the brane, with the embedding consistently satisfying the Gauss-Codazzi equations. The 4-dim Einstein equations on the brane reduce to a 6-dim Hamiltonian dynamical system with additional terms (due to the bulk-brane interaction) that avoid the singularity and implement nonsingular bounces in the model. We examine the complex Bianchi IX dynamics in its approach to the neighborhood of the bounce which replaces the cosmological singularity of general relativity. The phase space of the model presents (i) two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, (ii) two asymptotic de Sitter critical points at infinity, one acting as an attractor to late-time acceleration and (iii) a 2-dim invariant plane, which together organize the dynamics of the phase space. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders R × S 3, where R is a saddle direction and S 3 is the center manifold of unstable periodic orbits, the latter being the nonlinear extension of the center-center sector. By a proper canonical transformation the degrees of freedom of the dynamics are separated into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom associated with the center manifold S 3. The typical dynamical flow is thus an oscillatory mode about the orbits of the invariant plane. The stable and unstable cylinders are spanned by oscillatory orbits about the separatrix towards the bounce, leading to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct simulations. The homoclinic intersection manifold has the topology of R × S 2 consisting of homoclinic orbits biasymptotic to the center manifold S 3. This behavior defines a chaotic saddle associated with S 3, indicating that the intersection points of the cylinders have the nature of a Cantor set with compact support S 2. This is an invariant signature of chaos in the model. We discuss the connection between these properties of the dynamics, namely the oscillatory approach to the bounce together with its chaotic behavior, and analogous features present in the BKL conjecture in general relativity.

Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Múnera, Héctor A., E-mail: hmunera@hotmail.com; Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America

2016-07-07

It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding amore » unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.« less

Stable Orbits in the Didymos Binary Asteroid System - Useful Platforms for Exploration

NASA Astrophysics Data System (ADS)

Damme, Friedrich; Hussmann, Hauke; Wickhusen, Kai; Enrico, Mai; Oberst, Jürgen

2016-04-01

We have analyzed particle motion in binary asteroid systems to search for stable orbits. In particular, we studied the motion of particles near the asteroid 1996 GT (Didymos), proposed as a target for the AIDA mission. The combined gravity fields of the odd-shaped rotating objects moving about each other are complex. In addition, orbiting spacecraft or dust particles are affected by radiation pressure, possibly exceeding the faint gravitational forces. For the numerical integrations, we adopt parameters for size, shape, and rotation from telescopic observations. To simulate the effect of radiation pressure during a spacecraft mission, we apply a spacecraft wing-box shape model. Integrations were carried out beginning in near-circular orbits over 11 days, during which the motion of the particles were examined. Most orbits are unstable with particles escaping quickly or colliding with the asteroid bodies. However, with carefully chosen initial positions, we found stable motion (in the orbiting plane of the secondary) associated with the Lagrangian points (L4 and L5), in addition to horseshoe orbits, where particles move from one of the Lagrangian point to the other. Finally, we examined orbits in 1:2 resonances with the motion of the orbital period of the secondary. Stable conditions depend strongly on season caused by the inclination of the mutual orbit plane with respect to Didymos solar orbit. At larger distance from the asteroid pair, we find the well-known terminator orbits where gravitational attraction is balanced against radiation pressure. Stable orbits and long motion arcs are useful for long tracking runs by radio or Laser instruments and are well-suited for modelling of the ephemerides of the asteroid pair and gravity field mapping. Furthermore, these orbits may be useful as observing posts or as platforms for approach. These orbits may also represent traps for dust particles, an opportunity for dust collection - or possibly a hazard to spacecraft operation.

Homoclinic chaos in axisymmetric Bianchi-IX cosmological models with an ad hoc quantum potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Correa, G. C.; Stuchi, T. J.; Joras, S. E.

2010-04-15

In this work we study the dynamics of the axisymmetric Bianchi-IX cosmological model with a term of quantum potential added. As it is well known, this class of Bianchi-IX models is homogeneous and anisotropic with two scale factors, A(t) and B(t), derived from the solution of Einstein's equation for general relativity. The model we use in this work has a cosmological constant and the matter content is dust. To this model we add a quantum-inspired potential that is intended to represent short-range effects due to the general relativistic behavior of matter in small scales and play the role of amore » repulsive force near the singularity. We find that this potential restricts the dynamics of the model to positive values of A(t) and B(t) and alters some qualitative and quantitative characteristics of the dynamics studied previously by several authors. We make a complete analysis of the phase space of the model finding critical points, periodic orbits, stable/unstable manifolds using numerical techniques such as Poincare section, numerical continuation of orbits, and numerical globalization of invariant manifolds. We compare the classical and the quantum models. Our main result is the existence of homoclinic crossings of the stable and unstable manifolds in the physically meaningful region of the phase space [where both A(t) and B(t) are positive], indicating chaotic escape to inflation and bouncing near the singularity.« less

Discovery of a Detached, Eclipsing 40 Minute Period Double White Dwarf Binary and a Friend: Implications for He+CO White Dwarf Mergers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Warren R.; Kilic, Mukremin; Kosakowski, Alekzander

We report the discovery of two detached double white dwarf (WD) binaries, SDSS J082239.546+304857.19 and SDSS J104336.275+055149.90, with orbital periods of 40 and 46 minutes, respectively. The 40 minute system is eclipsing; it is composed of a 0.30 M {sub ⊙} and a 0.52 M {sub ⊙} WD. The 46 minute system is a likely LISA verification binary. The short 20 ± 2 Myr and ∼34 Myr gravitational-wave merger times of the two binaries imply that many more such systems have formed and merged over the age of the Milky Way. We update the estimated Milky Way He+CO WD binarymore » merger rate and affirm our previously published result: He+CO WD binaries merge at a rate at least 40 times greater than the formation rate of stable mass-transfer AM CVn binaries, and so the majority must have unstable mass-transfer. The implication is that spin–orbit coupling in He+CO WD mergers is weak, or perhaps nova-like outbursts drive He+CO WDs into merger, as proposed by Shen.« less

A note on libration point orbits, temporary capture and low-energy transfers

NASA Astrophysics Data System (ADS)

Fantino, E.; Gómez, G.; Masdemont, J. J.; Ren, Y.

2010-11-01

In the circular restricted three-body problem (CR3BP) the weak stability boundary (WSB) is defined as a boundary set in the phase space between stable and unstable motion relative to the second primary. At a given energy level, the boundaries of such region are provided by the stable manifolds of the central objects of the L1 and L2 libration points, i.e., the two planar Lyapunov orbits. Besides, the unstable manifolds of libration point orbits (LPOs) around L1 and L2 have been identified as responsible for the weak or temporary capture around the second primary of the system. These two issues suggest the existence of natural dynamical channels between the Earth's vicinity and the Sun-Earth libration points L1 and L2. Furthermore, it has been shown that the Sun-Earth L2 central unstable manifolds can be linked, through an heteroclinic connection, to the central stable manifolds of the L2 point in the Earth-Moon three-body problem. This concept has been applied to the design of low energy transfers (LETs) from the Earth to the Moon. In this contribution we consider all the above three issues, i.e., weak stability boundaries, temporary capture and low energy transfers, and we discuss the role played by the invariant manifolds of LPOs in each of them. The study is made in the planar approximation.

LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnes, Rory; Deitrick, Russell; Quinn, Thomas R.

2015-03-10

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs aftermore » several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.« less

Temporary satellite capture of comets by Jupiter

NASA Astrophysics Data System (ADS)

Emel'yanenko, N. Yu.

2012-05-01

This paper studies the dynamical evolution of 97 Jupiter-family comets over an 800-year time period. More than two hundred encounters with Jupiter are investigated, with the observed comets moving during a certain period of time in an elliptic jovicentric orbit. In most cases this is an ordinary temporary satellite capture of a comet in Everhart's sense, not associated with a transition of the small body into Jupiter's family of satellites. The phenomenon occurs outside the Hill sphere with comets with a high Tisserand constant relative to Jupiter; the comets' orbits have a small inclination to the ecliptic plane. An analysis of 236 encounters has allowed the determination within the planar pair two-body problem of a region of orbits in the plane ( a, e) whose semimajor axes and eccentricities contribute to the phenomenon under study. Comets with orbits belonging to this region experience a temporary satellite capture during some of their encounters; the jovicentric distance function has several minima; and the encounters are characterized by reversions of the line of apsides and some others features of their combination that are intrinsic to comets in this region. Therefore, this region is called a region of comets with specific features in their encounters with Jupiter. Twenty encounters (out of 236), whereby the comet enters an elliptic jovicentric orbit in the Hill sphere, are identified and investigated. The size and shape of the elliptic heliocentric orbits enabling this transition are determined. It is found that in 11 encounters the motion of small bodies in the Hill sphere has features the most important of which is multiple minima of the jovicentric distance function. The study of these 20 encounters has allowed the introduction of the concept of temporary gravitational capture of a small body into the Hill sphere. An analysis of variations in the Tisserand constant in these (20) encounters of the observable comets shows that their motion is unstable in Hill's sense.

Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warne, Larry Kevin; Jorgenson, Roy Eberhardt

This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through themore » electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank« less

Stationkeeping of the First Earth-Moon Libration Orbiters: The ARTEMIS Mission

NASA Technical Reports Server (NTRS)

Folta, David; Woodard, Mark; Cosgrove, D.

2011-01-01

Libration point orbits near collinear locations are inherently unstable and must be controlled. For Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) Earth-Moon Lissajous orbit operations, stationkeeping is challenging because of short time scales, large orbital eccentricity of the secondary, and solar gravitational and radiation pressure perturbations. ARTEMIS is the first NASA mission continuously controlled at both Earth-Moon L1 and L2 locations and uses a balance of optimization, spacecraft implementation and constraints, and multi-body dynamics. Stationkeeping results are compared to pre-mission research including mode directions.

Global properties in an experimental realization of time-delayed feedback control with an unstable control loop.

PubMed

Höhne, Klaus; Shirahama, Hiroyuki; Choe, Chol-Ung; Benner, Hartmut; Pyragas, Kestutis; Just, Wolfram

2007-05-25

We demonstrate by electronic circuit experiments the feasibility of an unstable control loop to stabilize torsion-free orbits by time-delayed feedback control. Corresponding analytical normal form calculations and numerical simulations reveal a severe dependence of the basin of attraction on the particular coupling scheme of the control force. Such theoretical predictions are confirmed by the experiments and emphasize the importance of the coupling scheme for the global control performance.

Packed Planetary Systems

NASA Astrophysics Data System (ADS)

Barnes, R.; Greenberg, R.

2005-08-01

Planetary systems display a wide range of appearances, with apparently arbitrary values of semi-major axis, eccentricity, etc. We reduce the complexity of orbital configurations to a single value, δ , which is a measure of how close, over secular timescales ( ˜10,000 orbits), two consecutive planets come to each other. We measure this distance relative to the sum of the radii of their Hill spheres, sometimes referred to as mutual Hill radii (MHR). We determine the closest approach distance by numerically integrating the entire system on coplanar orbits, using minimum masses. For non-resonant systems, close approach occurs during apsidal alignment, either parallel or anti-parallel. For resonant pairs the distance at conjunction determines the closest approach distance. Previous analytic work found that planets on circular orbits were assuredly unstable if they came within 3.5 MHR (i.e. Gladman 1993; Chambers, Wetherill & Boss 1996). We find that most known pairs of jovian planets (including those in our solar system) come within 3.5 -- 7 MHR of each other. We also find that several systems are unstable (their closest approach distance is less than 3.5 MHR). These systems, if they are real, probably exist in an observationally permitted location somewhat different from the current best fit. In these cases, the planets' closest approach distance will most likely also be slightly larger than 3.5 MHR. Most pairs beyond 7 MHR probably experienced post-formation migration (i.e. tidal circularization, inward scattering of small bodies) which moved them further apart. This result is even more remarkable since we have used the minimum masses; most likely the systems are inclined to the line of sight, making the Hill spheres larger, and shrinking δ . This dense packing may reflect a tendency for planets to form as close together as they can without being dynamically unstable. This result further implies there may be a large number of smaller, currently undetectable companions packed in orbits around stars with known planets.

Asymmetric and persistent responses in price volatility of fertilizers through stable and unstable periods

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-01-01

Fertilizers are important to improve agricultural productivity growth. The purpose of this study is to investigate asymmetry, leverage, and persistence of shocks on price volatility of five fertilizers using EGARCH model during stable and unstable time periods, corresponding to before and after 2007 international financial crisis, respectively. Using price data of rock phosphate, triple super phosphate, diammonium phosphate (DAP), urea, and potassium chloride, it is found that fertilizers price volatilities display an apparent asymmetric response to shocks which have much pronounced and permanent effect during unstable period than in during stable period. Such effects should be taken into account whenever volatility modeling of fertilizers is considered, particularly during periods of volatile price.

Development of adaptive control applied to chaotic systems

NASA Astrophysics Data System (ADS)

Rhode, Martin Andreas

1997-12-01

Continuous-time derivative control and adaptive map-based recursive feedback control techniques are used to control chaos in a variety of systems and in situations that are of practical interest. The theoretical part of the research includes the review of fundamental concept of control theory in the context of its applications to deterministic chaotic systems, the development of a new adaptive algorithm to identify the linear system properties necessary for control, and the extension of the recursive proportional feedback control technique, RPF, to high dimensional systems. Chaos control was applied to models of a thermal pulsed combustor, electro-chemical dissolution and the hyperchaotic Rossler system. Important implications for combustion engineering were suggested by successful control of the model of the thermal pulsed combustor. The system was automatically tracked while maintaining control into regions of parameter and state space where no stable attractors exist. In a simulation of the electrochemical dissolution system, application of derivative control to stabilize a steady state, and adaptive RPF to stabilize a period one orbit, was demonstrated. The high dimensional adaptive control algorithm was applied in a simulation using the Rossler hyperchaotic system, where a period-two orbit with two unstable directions was stabilized and tracked over a wide range of a system parameter. In the experimental part, the electrochemical system was studied in parameter space, by scanning the applied potential and the frequency of the rotating copper disk. The automated control algorithm is demonstrated to be effective when applied to stabilize a period-one orbit in the experiment. We show the necessity of small random perturbations applied to the system in order to both learn the dynamics and control the system at the same time. The simultaneous learning and control capability is shown to be an important part of the active feedback control.

Unstable Box Orbits in Cuspy Elliptical Galaxies

NASA Technical Reports Server (NTRS)

Hasan, H.; Pfenniger, D.

1996-01-01

The aim of this work is to gain physical insight into the role played by a concentrated central mass in affecting the shape of elliptical galaxies, by examining its effect on the stability of box orbits which are the backbone of triaxial elliptical galaxies. Ample observational evidence is now available for the existence of a central mass concentration or central cusps in galaxies. The central mass is expected to cause orbital stochasticity and chaotic mixing of orbits, which could have ramifications on galactic evolution. We investigate here the interplay between potential cuspiness and eccentricity on the stability of axial orbits in a scale-free potential in a simple, preliminary attempt to characterize this effect.

Mapping stable direct and retrograde orbits around the triple system of asteroids (45) Eugenia

NASA Astrophysics Data System (ADS)

Araujo, R. A. N.; Moraes, R. V.; Prado, A. F. B. A.; Winter, O. C.

2017-12-01

It is widely accepted that knowing the composition and the orbital evolution of asteroids might help us to understand the process of formation of the Solar system. It is also known that asteroids can represent a threat to our planet. Such an important role has made space missions to asteroids a very popular topic in current astrodynamics and astronomy studies. Taking into account the increasing interest in space missions to asteroids, especially to multiple systems, we present a study that aims to characterize the stable and unstable regions around the triple system of asteroids (45) Eugenia. The goal is to characterize the unstable and stable regions of this system and to make a comparison with the system 2001 SN263, which is the target of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) mission. A new concept was used for mapping orbits, by considering the disturbance received by the spacecraft from all perturbing forces individually. This method has also been applied to (45) Eugenia. We present the stable and unstable regions for particles with relative inclination between 0° and 180°. We found that (45) Eugenia presents larger stable regions for both prograde and retrograde cases. This is mainly because the satellites of this system are small when compared to the primary body, and because they are not close to each other. We also present a comparison between these two triple systems, and we discuss how these results can guide us in the planning of future missions.

Multiparameter bifurcations and mixed-mode oscillations in Q-switched CO2 lasers.

PubMed

Doedel, Eusebius J; Pando L, Carlos L

2014-05-01

We study the origin of mixed-mode oscillations and related bifurcations in a fully molecular laser model that describes CO2 monomode lasers with a slow saturable absorber. Our study indicates that the presence of isolas of periodic mixed-mode oscillations, as the pump parameter and the cavity-frequency detuning change, is inherent to Q-switched CO2 monomode lasers. We compare this model, known as the dual four-level model, to the more conventional 3:2 model and to a CO2 laser model for fast saturable absorbers. In these models, we find similarities as well as qualitative differences, such as the different nature of the homoclinic tangency to a relevant unstable periodic orbit, where the Gavrilov-Shilnikov theory and its extensions may hold. We also show that there are isolas of periodic mixed-mode oscillations in a model for CO2 lasers with modulated losses, as the pump parameter varies. The coarse-grained bifurcation diagrams of the periodic mixed-mode oscillations in these models suggest that these oscillations belong to similar classes.

Periodic equivalence ratio modulation method and apparatus for controlling combustion instability

DOEpatents

Richards, George A.; Janus, Michael C.; Griffith, Richard A.

2000-01-01

The periodic equivalence ratio modulation (PERM) method and apparatus significantly reduces and/or eliminates unstable conditions within a combustion chamber. The method involves modulating the equivalence ratio for the combustion device, such that the combustion device periodically operates outside of an identified unstable oscillation region. The equivalence ratio is modulated between preselected reference points, according to the shape of the oscillation region and operating parameters of the system. Preferably, the equivalence ratio is modulated from a first stable condition to a second stable condition, and, alternatively, the equivalence ratio is modulated from a stable condition to an unstable condition. The method is further applicable to multi-nozzle combustor designs, whereby individual nozzles are alternately modulated from stable to unstable conditions. Periodic equivalence ratio modulation (PERM) is accomplished by active control involving periodic, low frequency fuel modulation, whereby low frequency fuel pulses are injected into the main fuel delivery. Importantly, the fuel pulses are injected at a rate so as not to affect the desired time-average equivalence ratio for the combustion device.

Flare particle acceleration in the interaction of twisted coronal flux ropes

NASA Astrophysics Data System (ADS)

Threlfall, J.; Hood, A. W.; Browning, P. K.

2018-03-01

Aim. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods: We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results: The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.

Numerical investigation of exact coherent structures in turbulent small-aspect-ratio Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Krygier, Michael; Crowley, Christopher J.; Schatz, Michael F.; Grigoriev, Roman O.

2017-11-01

As suggested by recent theoretical and experimental studies, fluid turbulence can be described as a walk between neighborhoods of unstable nonchaotic solutions of the Navier-Stokes equation known as exact coherent structures (ECS). Finding ECS in an experimentally-accessible setting is the first step toward rigorous testing of the dynamical role of ECS in 3D turbulence. We found several ECS (both relative periodic orbits and relative equilibria) in a weakly turbulent regime of small-aspect-ratio Taylor-Couette flow with counter-rotating cylinders. This talk will discuss how the geometry of these solutions guides the evolution of turbulent flow in the simulations. This work is supported by the Army Research Office (Contract # W911NF-15-1-0471).

Chaotic Behaviour of a Driven P-N Junction

NASA Astrophysics Data System (ADS)

Perez, Jose Maria

The chaotic behavior of a driven p-n junction is experimentally examined. Bifurcation diagrams for the system are measured, showing period doubling bifurcations up to f/32, onset of chaos, reverse bifurcations of chaotic bands, and periodic windows. Some of the measured bifurcation diagrams are similar to the bifurcation diagram of the logistic map x(,n+1) = (lamda)x(,n)(1 - x(,n)). A return map is also measured showing approximately a one-dimensional map with a single extremum at low driving voltages. The intermittency route to chaos is experimentally observed to occur near a tangent bifurcation as the system approaches a period 5 window at (lamda) = (lamda)(,5). Data are presented for the dependence of the average laminar length on (epsilon) = (lamda)(,5) - (lamda), and for the probability distribution P(l) vs. l. The effects of additive stochastic noise on period doubling, chaos, windows, and intermittency are examined and are found to agree with the logistic model and universal predictions. Three examples of crisis of the attractor are observed. The crises occur when an unstable orbit intersects the chaotic attractor. A period adding sequence is reported in which wide periodic windows of period 2, 3, 4, ... are observed for increasing driving voltage. The initial period doubling cascade and the period adding sequence are compared to two theoretical models, with reasonable success.

Secular instabilities of Keplerian stellar discs

NASA Astrophysics Data System (ADS)

Kaur, Karamveer; Kazandjian, Mher V.; Sridhar, S.; Touma, Jihad R.

2018-05-01

We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase-space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags that include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the m = 1 mode has positive pattern speed. Waterbags excluding circular orbits (bands) have two linear normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates, and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly, and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.

Radiation Pressure, Poynting-Robertson Drag, and Solar Wind Drag in the Restricted Three-Body Problem

NASA Technical Reports Server (NTRS)

Liou, Jer-Chyi; Zook, Herbert A.; Jackson, A. A.

1995-01-01

In this paper, we examine the effects of radiation pressure, Poynting-Robertson (PR) drag, and solar wind drag on dust grains trapped in mean motion resonances with the Sun and Jupiter in the restricted (negligible dust mass) three-body Problem. We especially examine the evolution of dust grains in the 1:1 resonance. As a first step, the Sun and Jupiter are idealized to both be in circular orbit about a common center of mass (circular restricted three-body problem). From the equation of motion of the dust particle in the rotating reference frame, the drag-induced time rate of change of its Jacobi "constant," C, is then derived and expressed in spherical coordinates. This new mathematical expression in spherical coordinates shows that C, in the 1:1 resonance, both oscillates and secularly increases with increasing time. The new expression gives rise to an easy understanding of how an orbit evolves when the radiation force and solar wind drag are included. All dust grain orbits are unstable in time when PR and solar wind drag are included in the Sun-Jupiter-dust system. Tadpole orbits evolve into horseshoe orbits; and these orbits continuously expand in size to lead to close encounters with Jupiter. Permanent trapping is impossible. Orbital evolutions of a dust grain trapped in the 1:1 resonance in the planar circular, an inclined case, an eccentric case, and the actual Sun-Jupiter case are numerically simulated and compared with each other and show grossly similar time behavior. Resonances other than 1:1 are also explored with the new expression. Stable exterior resonance trapping may be possible under certain conditions. One necessary condition for such a trap is derived. Trapping in interior resonances is shown to be always unstable.

Orbital Injection of the SEDSAT Satellite: Tethered Systems Dynamics and Flight Data Analysis

NASA Technical Reports Server (NTRS)

Lorenzini, Enrico C.; Gullahorn, Gordon E.; Cosmo, Mario L.; Ruiz, Manuel; Pelaez, Jesus

1996-01-01

This report deals with the following topics which are all related to the orbital injection of the SEDSAT satellite: Dynamics and Stability of Tether Oscillations after the First Cut. The dynamics of the tether after the first cut (i.e., without the Shuttle attached to it) is investigated. The tether oscillations with the free end are analyzed in order to assess the stability of the rectilinear configuration in between the two tether cuts; analysis of Unstable Modes. The unstable modes that appear for high libration angles are further investigated in order to determine their occurrences and the possible transition from bound librations to rotations; Orbital Release Strategies for SEDSAT. A parametric analysis of the orbital decay rate of the SEDSAT satellite after the two tether cuts has been carried out as a function of the following free parameters: libration amplitude at the end of deployment, deviation angle from LV at the first cut, and orbital anomaly at the second cut. The values of these parameters that provide a minimum orbital decay rate of the satellite (after the two cuts) have been computed; and Dynamics and Control of SEDSAT. The deployment control law has been modified to cope with the new ejection velocity of the satellite from the Shuttle cargo bay. New reference profiles have been derived as well as new control parameters. Timing errors at the satellite release as a function of the variations of the initial conditions and the tension model parameters have been estimated for the modified control law.

Earth-Moon Libration Point Orbit Stationkeeping: Theory, Modeling and Operations

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.; Woodard, Mark A.

2013-01-01

Collinear Earth-Moon libration points have emerged as locations with immediate applications. These libration point orbits are inherently unstable and must be maintained regularly which constrains operations and maneuver locations. Stationkeeping is challenging due to relatively short time scales for divergence effects of large orbital eccentricity of the secondary body, and third-body perturbations. Using the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission orbit as a platform, the fundamental behavior of the trajectories is explored using Poincare maps in the circular restricted three-body problem. Operational stationkeeping results obtained using the Optimal Continuation Strategy are presented and compared to orbit stability information generated from mode analysis based in dynamical systems theory.

Instability of hooks during bacterial flagellar swimming

NASA Astrophysics Data System (ADS)

Jabbarzadeh, Mehdi; Fu, Henry C.; Henry Fu Team

2016-11-01

In bacteria, a flexible hook transmits torque from the rotary motor at the cell body to the flagellum. Previously, the hook has been modeled as a Kirchhoff rod between the cell body and rotating flagellum. To study effects of the hook's flexibility on the bacteria's swimming speed and trajectory for wide range hook stiffnesses and flagellum configurations, we develop an efficient simplified spring model for the hook by linearizing the Kirchhoff rod. We treat the hydrodynamics of the cell body and helical flagellum using resistance matrices calculated by the method of regularized Stokeslets. We investigate flagellar and swimming dynamics for a range of hook flexibilities and flagellar orientations relative to the cell body and compare the results to models without hook flexibility. We investigate in detail parameters corresponding to E. coli and Vibrio alginolyticus. Generally, the flagellum changes orientation relative to the cell body, undergoing an orbit with the period of the motor rotation. We find that as the hook stiffness decreases, steady-state orbits of the flagellum first become unstable before the hook buckles, which may suggest a new mechanism of flick initiation in run-reverse-flick motility. We also find that for some parameter ranges, there are multiple stable steady state orbits, which may have implications for the tumbling and turning of bacteria.

Saturn's Rings and Associated Ring Plasma Cavity: Evidence for Slow Ring Erosion

NASA Technical Reports Server (NTRS)

Farrell, W. M.; Kurth, W. S.; Gurnett, D. A.; Persoon, A. M.; MacDowall, R. J.

2017-01-01

We re-examine the radio and plasma wave observations obtained during the Cassini Saturn orbit insertion period, as the spacecraft flew over the northern ring surface into a radial distance of 1.3 Rs (over the C-ring). Voyager era studies suggest the rings are a source of micro-meteoroid generated plasma and dust, with theorized peak impact-created plasma outflows over the densest portion of the rings (central B-ring). In sharp contrast, the Cassini Radio and Plasma Wave System (RPWS) observations identify the presence of a ring-plasma cavity located in the central portion of the B-ring, with little evidence of impact-related plasma. While previous Voyager era studies have predicted unstable ion orbits over the C- ring, leading to field-aligned plasma transport to Saturns ionosphere, the Cassini RPWS observations do not reveal evidence for such instability-created plasma fountains. Given the passive ring loss processes observed by Cassini, we find that the ring lifetimes should extend >10(exp 9) years, and that there is limited evidence for prompt destruction (loss in <100 Myrs).

Fragment Production and Survival in Irradiated Disks: A Comprehensive Cooling Criterion

NASA Astrophysics Data System (ADS)

Kratter, Kaitlin M.; Murray-Clay, Ruth A.

2011-10-01

Accretion disks that become gravitationally unstable can fragment into stellar or substellar companions. The formation and survival of these fragments depends on the precarious balance between self-gravity, internal pressure, tidal shearing, and rotation. Disk fragmentation depends on two key factors: (1) whether the disk can get to the fragmentation boundary of Q = 1 and (2) whether fragments can survive for many orbital periods. Previous work suggests that to reach Q = 1, and have fragments survive, a disk must cool on an orbital timescale. Here we show that disks heated primarily by external irradiation always satisfy the standard cooling time criterion. Thus, even though irradiation heats disks and makes them more stable in general, once they reach the fragmentation boundary, they fragment more easily. We derive a new cooling criterion that determines fragment survival and calculate a pressure-modified Hill radius, which sets the maximum size of pressure-supported objects in a Keplerian disk. We conclude that fragmentation in protostellar disks might occur at slightly smaller radii than previously thought and recommend tests for future simulations that will better predict the outcome of fragmentation in real disks.

Saturn's rings and associated ring plasma cavity: Evidence for slow ring erosion

NASA Astrophysics Data System (ADS)

Farrell, W. M.; Kurth, W. S.; Gurnett, D. A.; Persoon, A. M.; MacDowall, R. J.

2017-08-01

We re-examine the radio and plasma wave observations obtained during the Cassini Saturn orbit insertion period, as the spacecraft flew over the northern ring surface into a radial distance of 1.3 Rs (over the C-ring). Voyager era studies suggest the rings are a source of micro-meteoroid generated plasma and dust, with theorized peak impact-created plasma outflows over the densest portion of the rings (central B-ring). In sharp contrast, the Cassini Radio and Plasma Wave System (RPWS) observations identify the presence of a ring-plasma cavity located in the central portion of the B-ring, with little evidence of impact-related plasma. While previous Voyager era studies have predicted unstable ion orbits over the C-ring, leading to field-aligned plasma transport to Saturn's ionosphere, the Cassini RPWS observations do not reveal evidence for such instability-created plasma 'fountains'. Given the passive ring loss processes observed by Cassini, we find that the ring lifetimes should extend >109 years, and that there is limited evidence for prompt destruction (loss in <100 Myrs).

Einstein@Home Discovery of a PALFA Millisecond Pulsar in an Eccentric Binary Orbit

NASA Astrophysics Data System (ADS)

Knispel, B.; Lyne, A. G.; Stappers, B. W.; Freire, P. C. C.; Lazarus, P.; Allen, B.; Aulbert, C.; Bock, O.; Bogdanov, S.; Brazier, A.; Camilo, F.; Cardoso, F.; Chatterjee, S.; Cordes, J. M.; Crawford, F.; Deneva, J. S.; Eggenstein, H.-B.; Fehrmann, H.; Ferdman, R.; Hessels, J. W. T.; Jenet, F. A.; Karako-Argaman, C.; Kaspi, V. M.; van Leeuwen, J.; Lorimer, D. R.; Lynch, R.; Machenschalk, B.; Madsen, E.; McLaughlin, M. A.; Patel, C.; Ransom, S. M.; Scholz, P.; Siemens, X.; Spitler, L. G.; Stairs, I. H.; Stovall, K.; Swiggum, J. K.; Venkataraman, A.; Wharton, R. S.; Zhu, W. W.

2015-06-01

We report the discovery of the millisecond pulsar (MSP) PSR J1950+2414 (P = 4.3 ms) in a binary system with an eccentric (e = 0.08) 22 day orbit in Pulsar Arecibo L-band Feed Array survey observations with the Arecibo telescope. Its companion star has a median mass of 0.3 M⊙ and is most likely a white dwarf (WD). Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star. This process should circularize the orbit, as is observed for the vast majority of binary MSPs, which predominantly have orbital eccentricities e < 0.001. However, four recently discovered binary MSPs have orbits with 0. 027 < e < 0.44; PSR J1950+2414 is the fifth such system to be discovered. The upper limits for its intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population. The large eccentricities are incompatible with the predictions of the standard recycling scenario: something unusual happened during their evolution. Proposed scenarios are (a) initial evolution of the pulsar in a triple system which became dynamically unstable, (b) origin in an exchange encounter in an environment with high stellar density, (c) rotationally delayed accretion-induced collapse of a super-Chandrasekhar WD, and (d) dynamical interaction of the binary with a circumbinary disk. We compare the properties of all five known eccentric MSPs with the predictions of these formation channels. Future measurements of the masses and proper motion might allow us to firmly exclude some of the proposed formation scenarios.

GGA + U studies of the early actinide mononitrides and dinitrides

NASA Astrophysics Data System (ADS)

Obodo, K. O.; Chetty, N.

2013-11-01

We present a detailed comparative study of the electronic and mechanical properties of the early actinide mononitrides and dinitrides within the framework of the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA [PBE]) and GGA + U implementations of density functional theory with the inclusion of spin-orbit coupling. The dependence of selected observables of these materials on the effective U-parameter is investigated in detail. The properties include the lattice constant, bulk modulus, charge density distribution, hybridization of the atomic orbitals, energy of formation and the lattice dynamics. The inclusion of the Hubbard U parameter results in a proper description of the 5f electrons, and is subsequently used in the determination of the structural and electronic properties of these compounds. The mononitrides and dinitrides of the early actinides are metallic except for UN2, which is a semiconductor. These actinide nitrides are non-magnetic with the exception of UN, NpN, PuN, NpN2 and PuN2 that are magnetic systems with orbital-dependent magnetic moments oriented in the z-axis. We observed that ThN2 is elastically unstable to isotropic pressure. We discovered that UN2 is thermodynamically unstable, but may be stabilized by N vacancy formation.

The end-of-life disposal of satellites in libration-point orbits using solar radiation pressure

NASA Astrophysics Data System (ADS)

Soldini, Stefania; Colombo, Camilla; Walker, Scott

2016-04-01

This paper proposes an end-of-life propellant-free disposal strategy for libration-point orbits which uses solar radiation pressure to restrict the evolution of the spacecraft motion. The spacecraft is initially disposed into the unstable manifold leaving the libration-point orbit, before a reflective sun-pointing surface is deployed to enhance the effect of solar radiation pressure. Therefore, the consequent increase in energy prevents the spacecraft's return to Earth. Three European Space Agency missions are selected as test case scenarios: Herschel, SOHO and Gaia. Guidelines for the end-of-life disposal of future libration-point orbit missions are proposed and a preliminary study on the effect of the Earth's orbital eccentricity on the disposal strategy is shown for the Gaia mission.

Dynamical sequestration of the Moon-forming impactor in co-orbital resonance with Earth

NASA Astrophysics Data System (ADS)

Kortenkamp, Stephen J.; Hartmann, William K.

2016-09-01

Recent concerns about the giant impact hypothesis for the origin of the Moon, and an associated "isotope crisis" may be assuaged if the impactor was a local object that formed near Earth. We investigated a scenario that may meet this criterion, with protoplanets assumed to originate in 1:1 co-orbital resonance with Earth. Using N-body numerical simulations we explored the dynamical consequences of placing Mars-mass companions in various co-orbital configurations with a proto-Earth of 0.9 Earth-masses (M⊕). We modeled 162 different configurations, some with just the four terrestrial planets and others that included the four giant planets. In both the 4- and 8-planet models we found that a single Mars-mass companion typically remained a stable co-orbital of Earth for the entire 250 million year (Myr) duration of our simulations (59 of 68 unique simulations). In an effort to destabilize such a system we carried out an additional 94 simulations that included a second Mars-mass co-orbital companion. Even with two Mars-mass companions sharing Earth's orbit about two-thirds of these models (66) also remained stable for the entire 250 Myr duration of the simulations. Of the 28 2-companion models that eventually became unstable 24 impacts were observed between Earth and an escaping co-orbital companion. The average delay we observed for an impact of a Mars-mass companion with Earth was 102 Myr, and the longest delay was 221 Myr. In 40% of the 8-planet models that became unstable (10 out of 25) Earth collided with the nearly equal mass Venus to form a super-Earth (loosely defined here as mass ≥1.7 M⊕). These impacts were typically the final giant impact in the system and often occurred after Earth and/or Venus has accreted one or more of the other large objects. Several of the stable configurations involved unusual 3-planet hierarchical co-orbital systems.

Discovery of a Detached, Eclipsing 40 Minute Period Double White Dwarf Binary and a Friend: Implications for He+CO White Dwarf Mergers

NASA Astrophysics Data System (ADS)

Brown, Warren R.; Kilic, Mukremin; Kosakowski, Alekzander; Gianninas, A.

2017-09-01

We report the discovery of two detached double white dwarf (WD) binaries, SDSS J082239.546+304857.19 and SDSS J104336.275+055149.90, with orbital periods of 40 and 46 minutes, respectively. The 40 minute system is eclipsing; it is composed of a 0.30 M ⊙ and a 0.52 M ⊙ WD. The 46 minute system is a likely LISA verification binary. The short 20 ± 2 Myr and ˜34 Myr gravitational-wave merger times of the two binaries imply that many more such systems have formed and merged over the age of the Milky Way. We update the estimated Milky Way He+CO WD binary merger rate and affirm our previously published result: He+CO WD binaries merge at a rate at least 40 times greater than the formation rate of stable mass-transfer AM CVn binaries, and so the majority must have unstable mass-transfer. The implication is that spin-orbit coupling in He+CO WD mergers is weak, or perhaps nova-like outbursts drive He+CO WDs into merger, as proposed by Shen. Based on observations obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona, and on observations obtained with the Apache Point Observatory 3.5 m telescope, which is owned and operated by the Astrophysical Research Consortium.

EFFECTS OF DYNAMICAL EVOLUTION OF GIANT PLANETS ON SURVIVAL OF TERRESTRIAL PLANETS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsumura, Soko; Ida, Shigeru; Nagasawa, Makiko

2013-04-20

The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these ''stable'' orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that the majority of such test particles are ejected out of the system as a resultmore » of close encounters with giant planets. Here, we show that secular perturbations from giant planets can remove test particles at least down to 10 times smaller than their minimum pericenter distance. Our results indicate that, unless the dynamical instability among giant planets is either absent or quiet like planet-planet collisions, most test particles down to {approx}0.1 AU within the orbits of giant planets at a few AU may be gone. In fact, out of {approx}30% of survived test particles, about three quarters belong to the planet-planet collision cases. We find a good agreement between our numerical results and the secular theory, and present a semi-analytical formula which estimates the dynamically unstable region of the test particles just from the evolution of giant planets. Finally, our numerical results agree well with the observations, and also predict the existence of hot rocky planets in eccentric giant planet systems.« less

The strange case of the missing apocentric librators in the 3:2 resonance. [in asteroidal belt

NASA Technical Reports Server (NTRS)

Ip, W.-H.

1976-01-01

From a comparison of the 2:1 and 3:2 resonances (in the asteroidal belt) two possible explanations to the absence of 3:2 apocentric librators are suggested. The first one is that such 3:2 resonant motion is dynamically unstable. The second interpretation requires the absence of near-circular orbits originally at 4 AU. The latter view, if correct, is inconsistent with cosmogonic models which predict the original orbits of the asteroids to be nearly circular.

Chaos in pseudo-Newtonian black holes with halos

NASA Astrophysics Data System (ADS)

Guéron, E.; Letelier, P. S.

2001-03-01

Newtonian as well as special relativistic dynamics are used to study the stability of orbits of a test particle moving around a black hole with a dipolar halo. The black hole is modeled by either the usual monopole potential or the Paczyńki-Wiita pseudo-Newtonian potential. The full general relativistic similar case is also considered. The Poincaré section method and the Lyapunov characteristic exponents show that the orbits for the pseudo-Newtonian potential models are more unstable than the corresponding general relativistic geodesics.

Is the timing of surgery associated with avascular necrosis after unstable slipped capital femoral epiphysis? A multicenter study.

PubMed

Kohno, Yusuke; Nakashima, Yasuharu; Kitano, Toshio; Irie, Taichi; Kita, Atsushi; Nakamura, Tomoyuki; Endo, Hirosuke; Fujii, Yosuke; Kuroda, Takayuki; Mitani, Shigeru; Kitoh, Hiroshi; Matsushita, Masaki; Hattori, Tadashi; Iwata, Koji; Iwamoto, Yukihide

2017-01-01

An unstable slipped capital femoral epiphysis (SCFE) is associated with a high rate of avascular necrosis (AVN). The etiology of AVN seems to be multifactorial, although it is not thoroughly known. The aims of our study were to determine the rate of AVN after an unstable SCFE and to investigate the risk factors for AVN, specifically evaluating the notion of an "unsafe window", during which medical interventions would increase the risk for AVN. This retrospective multicenter study included 60 patients with an unstable SCFE diagnosed between 1985 and 2014. Timing of surgery was evaluated for three time periods, from acute onset of symptoms to surgery: period I, <24 h; period II, between 24 h and 7 days; and period III, >7 days. Multivariate logistic regression analysis was used to identify risk factors for AVN. Closed reduction and pinning was performed in 43 patients and in situ pinning in 17. Among these cases, 16 patients (27%) developed AVN. The rate of AVN was significantly higher in patients treated by closed reduction and pinning (15/43, 35%) than in those treated by in situ pinning (1/17, 5.9%) (p = 0.022). In patients treated by closed reduction and pinning, the incidence of AVN was 2/11 (18%) in period I, 10/13 (77%) in period II and 3/15 (20%) in period III, showing the significantly higher rate in period II (p = 0.002). The surgery provided in period II was identified as an independent risk factor for the development of AVN. Our rate of AVN was 27% using two classical treatment methods. Time-to-surgery, between 24 h and 7 days, was independently associated with AVN, supporting the possible existence of an "unsafe window" in patients with unstable SCFE treated by closed reduction and pinning. Copyright © 2016 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.

Investigating Long-Range Dependence in American Treasury Bills Variations and Volatilities during Stable and Unstable Periods

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2016-05-01

Detrended fluctuation analysis (DFA) is used to examine long-range dependence in variations and volatilities of American treasury bills (TB) during periods of low and high movements in TB rates. Volatility series are estimated by generalized autoregressive conditional heteroskedasticity (GARCH) model under Gaussian, Student, and the generalized error distribution (GED) assumptions. The DFA-based Hurst exponents from 3-month, 6-month, and 1-year TB data indicates that in general the dynamics of the TB variations process is characterized by persistence during stable time period (before 2008 international financial crisis) and anti-persistence during unstable time period (post-2008 international financial crisis). For volatility series, it is found that; for stable period; 3-month volatility process is more likely random, 6-month volatility process is anti-persistent, and 1-year volatility process is persistent. For unstable period, estimation results show that the generating process is persistent for all maturities and for all distributional assumptions.

Further studies on criteria for the onset of dynamical instability in general three-body systems

NASA Technical Reports Server (NTRS)

Pendleton, Y. J.; Black, D. C.

1983-01-01

Numerical experiments designed for the elucidation of the conditions under which self-gravitating, three-body systems become dynamically unstable are examined of the cases of four orbital configuration types: circular, prograde, and coplanar; circular, retrograde, and coplanar; circular, direct, and inclined; and eccentric, direct, and coplanar. Results indicate that orbital inclination does not significantly affect stability in 'outer planet' configurations, while the stability of 'inner planet' configurations, where the tertiary is in close orbit about one member of the binary, is markedly less affected, once the relative orbital inclination is greater than 50 deg. It is found that the onset of dynamical instability is only weakly dependent on the eccentricity of either the binary or tertiary orbit, as long as the mass of the tertiary is comparable to the reduced mass of the binary.

Small aspect ratio Taylor-Couette flow: onset of a very-low-frequency three-torus state.

PubMed

Lopez, Juan M; Marques, Francisco

2003-09-01

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is SO(2)xZ2. In this paper, we systematically investigate primary and subsequent bifurcations of the basic state, concentrating on a parameter regime where the basic state becomes unstable via Hopf bifurcations. We derive the four distinct cases for the symmetries of the bifurcated orbit, and numerically find two of these. In the parameter regime considered, we also locate the codimension-two double Hopf bifurcation where these two Hopf bifurcations coincide. Secondary Hopf bifurcations (Neimark-Sacker bifurcations), leading to modulated rotating waves, are subsequently found and a saddle-node-infinite-period bifurcation between a stable (node) and an unstable (saddle) modulated rotating wave is located, which gives rise to a very-low-frequency three-torus. This paper provides the computed example of such a state, along with a comprehensive bifurcation sequence leading to its onset.

Disruption of giant comets in the solar system and around other stars

NASA Technical Reports Server (NTRS)

Whitmire, D. P.; Matese, J. J.

1988-01-01

In a standard cometary mass distribution (dN/dM) alpha M(-a), a = 1.5 to 2.0) most of the mass resides in the largest comets. The maximum mass M sub max for which this distribution holds uncertain but there are theoretical and observational indications that M sub max is at least approx. 10(23)g. Chiron, although formally classified as an asteroid, is most likely a giant comet in this mass range. Its present orbit is unstable and it is expected to evolve into a more typical short period comet orbit on a timescale of approx. 10(6) to 10(7)yr. The breakup of a chiron-like comet of mass approx. 10(23)g could in principle produce approx. 10(5) Halley-size comets, or a distribution with an even larger number. If a giant comet was in a typical short period comet orbit, such a breakup could result in a relatively brief comet shower (duration approx. less than 10(6)yr) with some associated terrestrial impacts. However, the most significant climatic effects may not in general be due to the impacts themselves but to the greatly enhanced zodiacal dust cloud in the inner Solar System. (Although this is probably not the case for the unique K-T impact). Researchers used a least Chi square program with error analysis to confirm that the 2 to 5 micrometer excess spectrum of Giclas 29 to 38 can be adequately fitted with either a disk of small inefficient (or efficient) grains or a single temperature black body. Further monitoring of this star may allow discrimination between these two models.

Low-energy ballistic lunar transfers

NASA Astrophysics Data System (ADS)

Parker, Jeffrey S.

A systematic method is developed that uses dynamical systems theory to model, analyze, and construct low-energy ballistic lunar transfers (BLTs). It has been found that low-energy BLTs may be produced by intersecting the stable manifold of an unstable Earth-Moon three-body orbit with the Earth. A spacecraft following such a trajectory is only required to perform a single maneuver, namely, the Trans-Lunar Injection maneuver, in order to complete the transfer. After the Trans-Lunar Injection maneuver, the spacecraft follows an entirely ballistic trajectory that asymptotically approaches and arrives at the target lunar three-body orbit. Because these orbit transfers require no orbit insertion maneuver at the three-body orbit, the transfers may be used to send spacecraft 25--40% more massive than spacecraft sent to the same orbits via conventional, direct transfers. From the targeted three-body orbits, the spacecraft may transfer to nearly any region within the Earth-Moon system, including any location on the surface of the Moon. The systematic methods developed in this research allow low-energy BLTs to be characterized by six parameters. It has been found that BLTs exist in families, where a family of BLTs consists of transfers whose parameters vary in a continuous fashion from one end of the family to the other. The families are easily identified and studied using a BLT State Space Map (BLT Map). The present research studies BLT Maps and has surveyed a wide variety of BLTs that exist in the observed families. It has been found that many types of BLTs may be constructed between 185-km low Earth parking orbits and lunar three-body orbits that require less than 3.27 km/s and fewer than 120 days of transfer time. Under certain conditions, BLTs may be constructed that require less than 3.2 km/s and fewer than 100 days of transfer time. It has been found that BLTs may implement LEO parking orbits with nearly any combination of altitude and inclination; they may depart from their LEO parking orbits nearly any day of each month; and they may target a variety of different classes of unstable Earth-Moon three-body orbits. Finally, studies are provided that address how low-energy transfers impact the design of spacecraft systems and how BLT Maps may be implemented as pragmatic tools in the design of practical lunar missions.

Architecture of Kepler's multi-transiting systems. II. New investigations with twice as many candidates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fabrycky, Daniel C.; Lissauer, Jack J.; Rowe, Jason F.

We report on the orbital architectures of Kepler systems having multiple-planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic mass-radius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ∼96% of the candidate planetary systems are correctly interpreted as true systems. We findmore » that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near first-order resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1.°0-2.°2, for the packed systems of small planets probed by these observations.« less

A new illusion of projected three-dimensional space

NASA Technical Reports Server (NTRS)

Ellis, Stephen R.; Grunwald, Arthur

1987-01-01

When perspective projections of orbital trajectories plotted in local-vertical local-horizontal coordinates are viewed with certain viewing angles, their appearance becomes perceptually unstable. They often lose their trochoidal appearance and reorganize as helices. This reorganization may be due to the viewer's familiarity with coiled springs.

Critical phenomena at the threshold of immediate merger in binary black hole systems: The extreme mass ratio case

NASA Astrophysics Data System (ADS)

Gundlach, Carsten; Akcay, Sarp; Barack, Leor; Nagar, Alessandro

2012-10-01

In numerical simulations of black hole binaries, Pretorius and Khurana [Classical Quantum Gravity 24, S83 (2007)CQGRDG0264-938110.1088/0264-9381/24/12/S07] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n≃-γln⁡|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent γ. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n∞≃0.41/η, where η is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; da Silva, Elton C.; Caldas, Iberê L.

2004-12-01

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincaré recurrence time statistics.

Dynamical analysis of an n‑H‑T cosmological quintessence real gas model with a general equation of state

NASA Astrophysics Data System (ADS)

Ivanov, Rossen I.; Prodanov, Emil M.

2018-01-01

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

Computer Modelling of Functional Aspects of Noise in Endogenously Oscillating Neurons

NASA Astrophysics Data System (ADS)

Huber, M. T.; Dewald, M.; Voigt, K.; Braun, H. A.; Moss, F.

1998-03-01

Membrane potential oscillations are a widespread feature of neuronal activity. When such oscillations operate close to the spike-triggering threshold, noise can become an essential property of spike-generation. According to that, we developed a minimal Hodgkin-Huxley-type computer model which includes a noise term. This model accounts for experimental data from quite different cells ranging from mammalian cortical neurons to fish electroreceptors. With slight modifications of the parameters, the model's behavior can be tuned to bursting activity, which additionally allows it to mimick temperature encoding in peripheral cold receptors including transitions to apparently chaotic dynamics as indicated by methods for the detection of unstable periodic orbits. Under all conditions, cooperative effects between noise and nonlinear dynamics can be shown which, beyond stochastic resonance, might be of functional significance for stimulus encoding and neuromodulation.

Saddle Slow Manifolds and Canard Orbits in [Formula: see text] and Application to the Full Hodgkin-Huxley Model.

PubMed

Hasan, Cris R; Krauskopf, Bernd; Osinga, Hinke M

2018-04-19

Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin-Huxley model is well known for explaining the ionic mechanism that generates the action potential in the squid giant axon. Rubin and Wechselberger (Biol. Cybern. 97:5-32, 2007) nondimensionalized this model and obtained a singularly perturbed system with two fast, two slow variables, and an explicit time-scale ratio ε. The dynamics of this system are complex and feature periodic orbits with a series of action potentials separated by small-amplitude oscillations (SAOs); also referred to as mixed-mode oscillations (MMOs). The slow dynamics of this system are organized by two-dimensional locally invariant manifolds called slow manifolds which can be either attracting or of saddle type.In this paper, we introduce a general approach for computing two-dimensional saddle slow manifolds and their stable and unstable fast manifolds. We also develop a technique for detecting and continuing associated canard orbits, which arise from the interaction between attracting and saddle slow manifolds, and provide a mechanism for the organization of SAOs in [Formula: see text]. We first test our approach with an extended four-dimensional normal form of a folded node. Our results demonstrate that our computations give reliable approximations of slow manifolds and canard orbits of this model. Our computational approach is then utilized to investigate the role of saddle slow manifolds and associated canard orbits of the full Hodgkin-Huxley model in organizing MMOs and determining the firing rates of action potentials. For ε sufficiently large, canard orbits are arranged in pairs of twin canard orbits with the same number of SAOs. We illustrate how twin canard orbits partition the attracting slow manifold into a number of ribbons that play the role of sectors of rotations. The upshot is that we are able to unravel the geometry of slow manifolds and associated canard orbits without the need to reduce the model.

Chaos in navigation satellite orbits caused by the perturbed motion of the Moon

NASA Astrophysics Data System (ADS)

Rosengren, Aaron J.; Alessi, Elisa Maria; Rossi, Alessandro; Valsecchi, Giovanni B.

2015-06-01

Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here, we show that the irregular and haphazard character of these orbits reflects a similar irregularity in the orbits of many celestial bodies in our Solar system. We find that secular resonances, involving linear combinations of the frequencies of nodal and apsidal precession and the rate of regression of lunar nodes, occur in profusion so that the phase space is threaded by a devious stochastic web. As in all cases in the Solar system, chaos ensues where resonances overlap. These results may be significant for the analysis of disposal strategies for the four constellations in this precarious region of space.

Periodic waves in fiber Bragg gratings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.

2008-02-15

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and,more » in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.« less

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Exoplanet recycling in massive white-dwarf debris discs

NASA Astrophysics Data System (ADS)

Van Lieshout, Rik

2017-06-01

When a star evolves into a white dwarf, the planetary system it hosts can become unstable. Planets in such systems may then be scattered onto star-grazing orbits, leading to their tidal disruption as they pass within the white dwarf’s Roche limit. We study the massive, compact debris discs that may arrise from this process using a combination of analytical estimates and numerical modelling. The discs are gravitationally unstable, resulting in an enhanced effective viscosity due to angular momentum transport associated with self-gravity wakes. For disc masses greater than ~1026 g (corresponding to progenitor objects comparable to the Galilean moons), viscous spreading dominates over Poynting-Robertson drag in the outer parts of the disc. In such massive discs, mass is transported both in- and outwards. When the outward-flowing material spreads beyond the Roche limit, it coagulates into new (minor) planets in a process analogous to the ongoing formation of Saturn’s innermost moonlets. This process recycles a substantial fraction of the original disc mass (tens of percents), with the bulk of the mass locked in a single large body orbitting in a 2:1 mean-motion resonance with the Roche limit. As such, the recycling of a tidally disrupted super-Earth could yield an Earth-mass planet on a 10--20 hr orbit. For white dwarfs with a temperature below 6000-7000 K (corresponding to a cooling age of >1--2 Gyr), this orbit is located in the white dwarf’s habitable zone. The recycling process also creates a string of smaller bodies just outside the Roche limit. These may account for the collection of minor planets postulated to orbit white dwarf WD 1145+017.

Outer-planet scattering can gently tilt an inner planetary system

NASA Astrophysics Data System (ADS)

Gratia, Pierre; Fabrycky, Daniel

2017-01-01

Chaotic dynamics are expected during and after planet formation, and a leading mechanism to explain large eccentricities of gas giant exoplanets is planet-planet gravitational scattering. The same scattering has been invoked to explain misalignments of planetary orbital planes with respect to their host star's spin. However, an observational puzzle is presented by Kepler-56, which has two inner planets (b and c) that are nearly coplanar with each other, yet are more than 45° inclined to their star's equator. Thus, the spin-orbit misalignment might be primordial. Instead, we further develop the hypothesis in the discovery paper, that planets on wider orbits generated misalignment through scattering, and as a result gently torqued the inner planets away from the equator plane of the star. We integrated the equations of motion for Kepler-56 b and c along with an unstable outer system initialized with either two or three Jupiter-mass planets. We address here whether the violent scattering that generates large mutual inclinations can leave the inner system intact, tilting it gently. In almost all of the cases initially with two outer planets, either the inner planets remain nearly coplanar with each other in the star's equator plane, or they are scattered violently to high mutual inclination and high spin-orbit misalignment. On the contrary, of the systems with three unstable outer planets, a spin-orbit misalignment large enough to explain the observations is generated 28 per cent of the time for coplanar inner planets, which is consistent with the observed frequency of this phenomenon reported so far. We conclude that multiple-planet scattering in the outer parts of the system may account for this new population of coplanar planets hosted by oblique stars.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Axial interaction free-electron laser

DOEpatents

Carlsten, Bruce E.

1997-01-01

Electron orbits from a helical axial wiggler in an axial guide field are absolutely unstable as power is extracted from the particles. For off-axis beams an axial FEL mechanism exists when the axial electric field in a TM mode is wiggled to interact with the axial velocity of the electrons that form the beam. The interaction strength is comparable to that for helical FELs and is insensitive to beam orbit errors. The orbits for this mechanism are extremely stable in the absence of space charge and lead to high extraction efficiencies without particle phasing incoherence or interception. This interaction mechanism is suitable for use with intense annular electron beams for high power generation at microwave frequencies.

Axial interaction free-electron laser

DOEpatents

Carlsten, B.E.

1997-09-02

Electron orbits from a helical axial wiggler in an axial guide field are absolutely unstable as power is extracted from the particles. For off-axis beams an axial FEL mechanism exists when the axial electric field in a TM mode is wiggled to interact with the axial velocity of the electrons that form the beam. The interaction strength is comparable to that for helical FELs and is insensitive to beam orbit errors. The orbits for this mechanism are extremely stable in the absence of space charge and lead to high extraction efficiencies without particle phasing incoherence or interception. This interaction mechanism is suitable for use with intense annular electron beams for high power generation at microwave frequencies. 5 figs.

Physical properties of the extreme Centaur and super-comet candidate 2013 AZ60

NASA Astrophysics Data System (ADS)

Pál, A.; Kiss, Cs.; Horner, J.; Szakáts, R.; Vilenius, E.; Müller, Th. G.; Acosta-Pulido, J.; Licandro, J.; Cabrera-Lavers, A.; Sárneczky, K.; Szabó, Gy. M.; Thirouin, A.; Sipőcz, B.; Dózsa, Á.; Duffard, R.

2015-11-01

We present estimates of the basic physical properties including size and albedo of the extreme Centaur 2013 AZ60. These properties have been derived from optical and thermal infrared measurements. Our optical measurements revealed a probable full period of ≈9.4 h with a shallow amplitude of 4.5%. By combining optical brightness information and thermal emission data, we are able to derive a diameter of 62.3 ± 5.3 km and a geometric albedo of 2.9%, which corresponds to an extremely dark surface. Additionally, our finding of ≳50 Jm-2 K-1 s- 1/2 for the thermal inertia is also remarkable for objects in such a distance. The results of dynamical simulations yield an unstable orbit, with a 50% probability that the target will be ejected from the solar system within 700 000 yr. The current orbit of this object and its instability could imply a pristine cometary surface. This possibility agrees with the observed low geometric albedo and red photometric colour indices for the object, which match the surface of a dormant comet well, as would be expected for a long-period cometary body approaching perihelion. Although it was approaching ever closer to the Sun, however, the object exhibited star-like profiles in each of our observations, lacking any sign of cometary activity. According to the albedo, 2013 AZ60 is a candidate for the darkest body among the known trans-Neptunian objects.

Urinary testosterone-metabolite levels and dominance rank in male and female bonobos (Pan paniscus).

PubMed

Sannen, Adinda; Van Elsacker, Linda; Heistermann, Michael; Eens, Marcel

2004-04-01

The correlation between testosterone (T) and dominance rank may vary among species, and is expected to become stronger as the importance of aggressive competition for rank increases. However, it may also vary among social situations within a species, showing a stronger correlation during socially unstable periods. Knowledge on this topic in great apes, especially in females, is scant. This study presents the first data on the relationship between T and dominance rank in both sexes of the bonobo ( Pan paniscus). For each period (four socially unstable and two stable ones), linear rank orders were determined and subsequently correlated with the accompanying mean urinary T-metabolite concentrations (measured as immunoreactive 5alpha-androstan-17alpha-ol-3-one). No correlation between these two variables was found for either sex among individuals during socially unstable or stable periods. Also, within an individual over the six periods, no relationship of T with rank could be demonstrated. These results suggest that either the outcomes of aggressions have no influence on T levels, or such clear outcomes appear insufficiently frequent to affect T levels over longer periods. Even during the unstable periods, the rate of aggressions was not higher than during stable periods, suggesting that frequencies of aggression have little effect on rank. Further analyses indeed demonstrated no correlation between frequencies of overall aggressions or any type of aggressive behavior separately, or rank. Perhaps factors other than the frequency of displayed aggressions alone have a marked influence on a bonobo's rank, for example, coalition partners. Overall, in bonobos, T apparently does not form a physiological reflection of social status.

Transfer and capture into distant retrograde orbits

NASA Astrophysics Data System (ADS)

Scott, Christopher J.

This dissertation utilizes theory and techniques derived from the fields of dynamical systems theory, astrodyanamics, celestial mechanics, and fluid mechanics to analyze the phenomenon of satellite capture and interrelated spacecraft transfers in restricted three-body systems. The results extend current knowledge and understanding of capture dynamics in the context of astrodynamics and celestial mechanics. Manifold theory, fast Lyapunov indicator maps, and the classification of space structure facilitate an analysis of the transport of objects from the chaotic reaches of the solar system to the distant retrograde region in the sun-Jupiter system. Apart from past studies this dissertation considers the role of the complex lobe structure encompassing stable regions in the circular restricted three-body problem. These structures are shown to be responsible for the phenomenon of sticky orbits and the transport of objects among stable regions. Since permanent capture can only be achieved through a change in energy, fast Lyapunov indicator maps and other methods which reveal the structure of the conservative system are used to discern capture regions and identify the underpinnings of the dynamics. Fast Lyapunov indicator maps provide an accurate classification of orbits of permanent capture and escape, yet monopolize computational resources. In anticipation of a fully three-dimensional analysis in the dissipative system a new mapping parameter is introduced based on energy degradation and averaged velocity. Although the study specifically addresses the sun-Jupiter system, the qualitative results and devised techniques can be applied throughout the solar system and to capture about extrasolar planets. Extending the analysis beyond the exterior of the stable distant retrograde region fosters the construction of transfer orbits from low-Earth orbit to a stable periodic orbit at the center of the stable distant retrograde region. Key to this analysis is the predictability of collision orbits within the highly chaotic region commonly recognized as a saddle point on the energy manifold. The pragmatic techniques derived from this analysis solve a number of complications apparent in the literature. Notably a reliable methodology for the construction of an arbitrary number of transfer orbits circumvents the requirement of computing specialized periodic orbits or extensive numerical sampling of the phase space. The procedure provides a complete description of the design space accessing a wide range of distant retrograde orbits sizes, insertion points, and parking orbit altitudes in an automated manner. The transfers are studied in a similar fashion to periodic orbits unveiling the intimate relationship among design parameters and phase space structure. An arbitrary number of Earth return periodic orbits can be generated as a by-product. These orbits may be useful for spacecraft that must make a number of passes near the second primary without a reduction in energy. Further analysis of the lobe dynamics and a modification of the transfers to the center of the stable region yields sets of single impulse transfers to sticky distant retrograde orbits. It is shown that the evolution of the phase space structures with energy corresponds to the variation of capture time and target size. Capture phenomenon is related to the stability characteristics of the unstable periodic orbit and the geometry of the corresponding homoclinic tangle at various energies. Future spacecraft with little or no propulsive means may take advantage of these natural trajectories for operations in the region. Temporary capture along a sticky orbit may come before incremental stabilization of the spacecraft by way of a series of small impulsive or a low continuous thrust maneuvers. The requirements of small stabilization maneuver are calculated and compared to a direct transfer to the center of stable region. This mission design may be desirable as any failure in the classic set of maneuvers to the center of the stable region could result in the loss of the spacecraft. A simple low-thrust stabilization method is analyzed in a similar manner to nebular drag. It is shown that stabilization maneuvers initiated within the sticky region can be achieved via a simple control law. Moreover, the sticky region can be used as a staging point for both spiral-in and spiral-out maneuvers. For the spiral in maneuver this negates a large, initial maneuver required to reach the center of the stable region. It is shown that large lengths of orbits exist within the sticky regions which reliably lead to permanent capture. In the case of spiral-out the spacecraft is transported to a highly energetic yet stable orbit about the second primary. From here a small maneuver could allow the spacecraft to access other regions of the solar system.

Bifurcation phenomena in cylindrical convection

NASA Astrophysics Data System (ADS)

Tuckerman, Laurette; Boronska, K.; Bordja, L.; Martin-Witkowski, L.; Navarro, M. C.

2008-11-01

We present two bifurcation scenarios occurring in Rayleigh-Benard convection in a small-aspect-ratio cylinder. In water (Pr=6.7) with R/H=2, Hof et al. (1999) observed five convective patterns at Ra=14200. We have computed 14 stable and unstable steady branches, as well as novel time-dependent branches. The resulting complicated bifurcation diagram, can be partitioned according to azimuthal symmetry. For example, three-roll and dipole states arise from an m=1 bifurcation, four-roll and ``pizza'' branches from m=2, and the ``mercedes'' state from an m=3 bifurcation after successive saddle-node bifurcations via ``marigold'', ``mitsubishi'' and ``cloverleaf'' states. The diagram represents a compromise between the physical tendency towards parallel rolls and the mathematical requirement that primary bifurcations be towards trigonometric states. Our second investigation explores the effect of exact counter-rotation of the upper and lower bounding disks on axisymmetric flows with Pr=1 and R/H=1. The convection threshold increases and, for sufficiently high rotation, the instability becomes oscillatory. Limit cycles originating at the Hopf bifurcation are annihilated when their period becomes infinite at saddle-node-on-periodic-orbit (SNOPER) bifurcations.

Compound Poisson Law for Hitting Times to Periodic Orbits in Two-Dimensional Hyperbolic Systems

NASA Astrophysics Data System (ADS)

Carney, Meagan; Nicol, Matthew; Zhang, Hong-Kun

2017-11-01

We show that a compound Poisson distribution holds for scaled exceedances of observables φ uniquely maximized at a periodic point ζ in a variety of two-dimensional hyperbolic dynamical systems with singularities (M,T,μ ), including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form φ (z)=-ln d(z,ζ ) where d is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a Pólya-Aeppli distibution of index θ . We calculate θ in terms of the derivative of the map T. Furthermore if we define M_n=\\max {φ ,\\ldots ,φ circ T^n} and u_n (τ ) by \\lim _{n→ ∞} nμ (φ >u_n (τ ) )=τ the maximal process satisfies an extreme value law of form μ (M_n ≤ u_n)=e^{-θ τ }. These results generalize to a broader class of functions maximized at ζ , though the formulas regarding the parameters in the distribution need to be modified.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeffries, C.; Perez, J.

For a driven nonlinear oscillator we report direct evidence for three cases of an interior crisis of the attractor, as conjectured by Grebogi, Ott, and Yorke. These crises are sudden and discontinuous changes in the attractor, observed directly from bifurcation diagrams and attractor diagrams (Poincare sections) in real time. The crises arise from intersection of an unstable orbit with the chaotic attractor.

Spin orbit torque based electronic neuron

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sengupta, Abhronil, E-mail: asengup@purdue.edu; Choday, Sri Harsha; Kim, Yusung

2015-04-06

A device based on current-induced spin-orbit torque (SOT) that functions as an electronic neuron is proposed in this work. The SOT device implements an artificial neuron's thresholding (transfer) function. In the first step of a two-step switching scheme, a charge current places the magnetization of a nano-magnet along the hard-axis, i.e., an unstable point for the magnet. In the second step, the SOT device (neuron) receives a current (from the synapses) which moves the magnetization from the unstable point to one of the two stable states. The polarity of the synaptic current encodes the excitatory and inhibitory nature of themore » neuron input and determines the final orientation of the magnetization. A resistive crossbar array, functioning as synapses, generates a bipolar current that is a weighted sum of the inputs. The simulation of a two layer feed-forward artificial neural network based on the SOT electronic neuron shows that it consumes ∼3× lower power than a 45 nm digital CMOS implementation, while reaching ∼80% accuracy in the classification of 100 images of handwritten digits from the MNIST dataset.« less

Migration of Gas Giant Planets in Gravitationally Unstable Disks

NASA Astrophysics Data System (ADS)

Michael, Scott; Durisen, Richard H.; Boley, Aaron C.

2011-08-01

Characterization of migration in gravitationally unstable disks is necessary to understand the fate of protoplanets formed by disk instability. As part of a larger study, we are using a three-dimensional radiative hydrodynamics code to investigate how an embedded gas giant planet interacts with a gas disk that undergoes gravitational instabilities (GIs). This Letter presents results from simulations with a Jupiter-mass planet placed in orbit at 25 AU within a 0.14 M sun disk. The disk spans 5-40 AU around a 1 M sun star and is initially marginally unstable. In one simulation, the planet is inserted prior to the eruption of GIs; in another, it is inserted only after the disk has settled into a quasi-steady GI-active state, where heating by GIs roughly balances radiative cooling. When the planet is present from the beginning, its own wake stimulates growth of a particular global mode with which it strongly interacts, and the planet plunges inward 6 AU in about 103 years. In both cases with embedded planets, there are times when the planet's radial motion is slow and varies in direction. At other times, when the planet appears to be interacting with strong spiral modes, migration both inward and outward can be relatively rapid, covering several AUs over hundreds of years. Migration in both cases appears to stall near the inner Lindblad resonance of a dominant low-order mode. Planet orbit eccentricities fluctuate rapidly between about 0.02 and 0.1 throughout the GI-active phases of the simulations.

Kozai-Lidov disc instability

NASA Astrophysics Data System (ADS)

Lubow, Stephen H.; Ogilvie, Gordon I.

2017-08-01

Recent results by Martin et al. showed in 3D smoothed particle hydrodynamics simulations that tilted discs in binary systems can be unstable to the development of global, damped Kozai-Lidov (KL) oscillations in which the discs exchange tilt for eccentricity. We investigate the linear stability of KL modes for tilted inviscid discs under the approximations that the disc eccentricity is small and the disc remains flat. By using 1D equations, we are able to probe regimes of large ratios of outer to inner disc edge radii that are realistic for binary systems of hundreds of astronomical unit separations and are not easily probed by multidimensional simulations. For order unity binary mass ratios, KL instability is possible for a window of disc aspect ratios H/r in the outer parts of a disc that roughly scale as (nb/n)2 ≲ H/r ≲ nb/n, for binary orbital frequency nb and orbital frequency n at the disc outer edge. We present a framework for understanding the zones of instability based on the determination of branches of marginally unstable modes. In general, multiple growing eccentric KL modes can be present in a disc. Coplanar apsidal-nodal precession resonances delineate instability branches. We determine the range of tilt angles for unstable modes as a function of disc aspect ratio. Unlike the KL instability for free particles that involves a critical (minimum) tilt angle, disc instability is possible for any non-zero tilt angle depending on the disc aspect ratio.

Pseudo-simple heteroclinic cycles in R4

NASA Astrophysics Data System (ADS)

Chossat, Pascal; Lohse, Alexander; Podvigina, Olga

2018-06-01

We study pseudo-simple heteroclinic cycles for a Γ-equivariant system in R4 with finite Γ ⊂ O(4) , and their nearby dynamics. In particular, in a first step towards a full classification - analogous to that which exists already for the class of simple cycles - we identify all finite subgroups of O(4) admitting pseudo-simple cycles. To this end we introduce a constructive method to build equivariant dynamical systems possessing a robust heteroclinic cycle. Extending a previous study we also investigate the existence of periodic orbits close to a pseudo-simple cycle, which depends on the symmetry groups of equilibria in the cycle. Moreover, we identify subgroups Γ ⊂ O(4) , Γ ⊄ SO(4) , admitting fragmentarily asymptotically stable pseudo-simple heteroclinic cycles. (It has been previously shown that for Γ ⊂ SO(4) pseudo-simple cycles generically are completely unstable.) Finally, we study a generalized heteroclinic cycle, which involves a pseudo-simple cycle as a subset.

A Double Dusty Dilemma

NASA Astrophysics Data System (ADS)

Farihi, Jay; Gansicke, Boris; Parsons, Steven

2015-04-01

We have serendipitously discovered the first metal-polluted white dwarf with what appears to be a circumbinary dust disk. Both the atmospheric metals and infrared excess were found by our team a few years ago, but only recently (and much to our surprise) did we measure a spectroscopic periodicity of 2.27 hr which unambiguously identifies this peculiar system as a close binary. Most remarkable for this DDT proposal is that the system must be (highly) dynamically unstable, as a companion and canonical dust disk occupy overlapping orbital regions. We therefore conclude the system must be in a high state of flux and propose a short, single observation with IRAC to compare with our prior flux measurements obtained in late 2009. Any change will prompt an observing campaign for detailed monitoring. We speculate we are witnessing a destructive event in real time, and if correct, this system may yield an unprecedented view into the long-term evolution of circumbinary planetary systems.

A 3D Numerical Study of Gravitational Instabilities in Young Circumbinary Disks

NASA Astrophysics Data System (ADS)

Cai, Kai; Michael, Scott; Durisen, Richard

2013-07-01

Gravitational instabilities (GIs) in protoplanetary disks have been suggested as one of the major formation mechanisms of giant planets. Theoretical and computational studies have indicated that certain family of GIs can be excited in a circumbinary disk, which could lead to enhanced protoplanet formation (e.g., Sellwood & Lin 1989, Boss 2006). We have carried out a 3D simulation of a gravitationally unstable circumbinary disk around a young Sun-like star and a 0.02-Msun companion, both inside the central hole of the disk. Here we present a preliminary comparison between this simulation and a similarly simulated circumstellar disk around a solar-mass star but without the low-mass companion. The GIs stimulated by the binary and those that arise spontaneously are quite different in structure and strength. However, no fragmentation is observed, even after many orbital periods as measured in the outer disk.

Properties of the Tent map for decimal fractions with fixed precision

NASA Astrophysics Data System (ADS)

Chetverikov, V. M.

2018-01-01

The one-dimensional discrete Tent map is a well-known example of a map whose fixed points are all unstable on the segment [0,1]. This map leads to the positivity of the Lyapunov exponent for the corresponding recurrent sequence. Therefore in a situation of general position, this sequence must demonstrate the properties of deterministic chaos. However if the first term of the recurrence sequence is taken as a decimal fraction with a fixed number “k” of digits after the decimal point and all calculations are carried out accurately, then the situation turns out to be completely different. In this case, first, the Tent map does not lead to an increase in significant digits in the terms of the sequence, and secondly, demonstrates the existence of a finite number of eventually periodic orbits, which are attractors for all other decimal numbers with the number of significant digits not exceeding “k”.

Minimally invasive surgery for thyroid eye disease.

PubMed

Naik, Milind Neilkant; Nair, Akshay Gopinathan; Gupta, Adit; Kamal, Saurabh

2015-11-01

Thyroid eye disease (TED) can affect the eye in myriad ways: proptosis, strabismus, eyelid retraction, optic neuropathy, soft tissue changes around the eye and an unstable ocular surface. TED consists of two phases: active, and inactive. The active phase of TED is limited to a period of 12-18 months and is mainly managed medically with immunosuppression. The residual structural changes due to the resultant fibrosis are usually addressed with surgery, the mainstay of which is orbital decompression. These surgeries are performed during the inactive phase. The surgical rehabilitation of TED has evolved over the years: not only the surgical techniques, but also the concepts, and the surgical tools available. The indications for decompression surgery have also expanded in the recent past. This article discusses the technological and conceptual advances of minimally invasive surgery for TED that decrease complications and speed up recovery. Current surgical techniques offer predictable, consistent results with better esthetics.

An instability due to the nonlinear coupling of p-modes to g-modes: Implications for coalescing neutron star binaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinberg, Nevin N.; Arras, Phil; Burkart, Joshua, E-mail: nevin@mit.edu

2013-06-01

A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω {sub a} excites a pair of secondary waves of frequency ω {sub b} + ω {sub c} ≅ ω {sub a}. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ω {sub b} + ω {sub c} >> ω {sub a}. We show that a p-mode can couple so stronglymore » to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f {sub gw} ≳ 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δφ ≳ 1 radian) that accumulate primarily at low frequencies (f {sub gw} ≲ 50 Hz) and (2) heat the neutron star core to a temperature of T ∼ 10{sup 10} K. Since there are at least ∼100 unstable p-g daughter pairs, Δφ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously thought.« less

Open quantum random walks: Bistability on pure states and ballistically induced diffusion

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2013-12-01

Open quantum random walks (OQRWs) deal with quantum random motions on a line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from the usual diffusion to ballistically induced diffusion with a large mean free path and large effective diffusion constant at large times. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.

Unstable low-mass planetary systems as drivers of white dwarf pollution

NASA Astrophysics Data System (ADS)

Mustill, Alexander J.; Villaver, Eva; Veras, Dimitri; Gänsicke, Boris T.; Bonsor, Amy

2018-05-01

At least 25 {per cent} of white dwarfs show atmospheric pollution by metals, sometimes accompanied by detectable circumstellar dust/gas discs or (in the case of WD 1145+017) transiting disintegrating asteroids. Delivery of planetesimals to the white dwarf by orbiting planets is a leading candidate to explain these phenomena. Here, we study systems of planets and planetesimals undergoing planet-planet scattering triggered by the star's post-main-sequence mass loss, and test whether this can maintain high rates of delivery over the several Gyr that they are observed. We find that low-mass planets (Earth to Neptune mass) are efficient deliverers of material and can maintain the delivery for Gyr. Unstable low-mass planetary systems reproduce the observed delayed onset of significant accretion, as well as the slow decay in accretion rates at late times. Higher-mass planets are less efficient, and the delivery only lasts a relatively brief time before the planetesimal populations are cleared. The orbital inclinations of bodies as they cross the white dwarf's Roche limit are roughly isotropic, implying that significant collisional interactions of asteroids, debris streams and discs can be expected. If planet-planet scattering is indeed responsible for the pollution of white dwarfs, many such objects, and their main-sequence progenitors, can be expected to host (currently undetectable) super-Earth planets on orbits of several au and beyond.

Precessional Instability in Binary Black Holes with Aligned Spins.

PubMed

Gerosa, Davide; Kesden, Michael; O'Shaughnessy, Richard; Klein, Antoine; Berti, Emanuele; Sperhake, Ulrich; Trifirò, Daniele

2015-10-02

Binary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been test beds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is antialigned. Spins in these configurations are unstable to precession to large misalignment when the binary separation r is between the values r(ud±)=(√(χ(1))±√(qχ(2)))(4)(1-q)(-2)M, where M is the total mass, q≡m(2)/m(1) is the mass ratio, and χ(1) (χ(2)) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near the merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.

Was Proxima captured by Alpha Centauri A and B?

NASA Astrophysics Data System (ADS)

Feng, F.; Jones, H. R. A.

2018-01-01

The nearest stellar system consists of the stars Proxima, Alpha Centauri A and B and at least one planet Proxima b. The habitability of Proxima b and any other planets are likely to be significantly influenced by the orbital evolution of the system. To study the dynamical evolution of the system, we simulate the motions of Proxima and Alpha Centauri A and B due to the perturbations from the Galactic tide and stellar encounters in a Monte Carlo fashion. From 100 clones, we find that 74 per cent orbits of Proxima Centauri are bound to Alpha Centauri A and B while 17 per cent and 9 per cent orbits become unbound in the simulations over the past and future 5 Gyr. If the system migrated outward in the Milky Way to its current location, more than 50 per cent of clones could become unstable in backward simulations. The ratio of unstable clones increases with the simulation time-scale and encounter rate. This provides some evidence for a capture scenario for the formation of the current triple system. Despite large uncertainties, the metallicity difference between Proxima and Alpha Centauri A and B is also suggestive of their different origin. None the less, further improvements in the available data and models will be necessary for a reliable assessment of the history of the Proxima-Alpha Centauri system and its impact on the habitability of Proxima b.

Stability of general-relativistic accretion disks

NASA Astrophysics Data System (ADS)

Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

2011-02-01

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a Γ-law equation of state with Γ=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.

Nature of the wiggle instability of galactic spiral shocks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Woong-Tae; Kim, Yonghwi; Kim, Jeong-Gyu, E-mail: wkim@astro.snu.ac.kr, E-mail: kimyh@astro.snu.ac.kr, E-mail: jgkim@astro.snu.ac.kr

Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral potential to form galactic spiral shocks. While numerical simulations typically show that spiral shocks are unstable to wiggle instability (WI) even in the absence of magnetic fields and self-gravity, its physical nature has remained uncertain. To clarify the mechanism behind the WI, we conduct a normal-mode linear stability analysis and nonlinear simulations assuming that the disk is isothermal and infinitesimally thin. We find that the WI is physical, originating from the generation of potential vorticity at a deformed shock front, rather than Kelvin-Helmholtz instabilities as previously thought. Since gasmore » in galaxy rotation periodically passes through the shocks multiple times, the potential vorticity can accumulate successively, setting up a normal mode that grows exponentially with time. Eigenfunctions of the WI decay exponentially downstream from the shock front. Both shock compression of acoustic waves and a discontinuity of shear across the shock stabilize the WI. The wavelength and growth time of the WI depend on the arm strength quite sensitively. When the stellar-arm forcing is moderate at 5%, the wavelength of the most unstable mode is about 0.07 times the arm-to-arm spacing, with the growth rate comparable to the orbital angular frequency, which is found to be in good agreement with the results of numerical simulations.« less

Endothelial Dysfunction and Blood Viscosity Inpatients with Unstable Angina in Different Periods of a Solar Activity

NASA Astrophysics Data System (ADS)

Parshina, S. S.; Tokaeva, L. K.; Dolgova, E. M.; Afanas'yeva, T. N.; Strelnikova, O. A.

The origin of hemorheologic and endothelial defects in patients with unstable angina (comparing with healthy persons) is determined by a solar activity period: the blood viscosity increases in a period of high solar activity in the vessels of small, medium and macro diameters, a local decompensate dysfunction of small vessels endothelium had been fixed (microcirculation area). In the period of a low solar activity there is an increase of a blood viscosity in vessels of all diameters, generalized subcompensated endothelial dysfunction is developed (on the background of the III phase blood clotting activating). In the period of a high solar activity a higher blood viscosity had been fixed, comparing with the period of a low solar activity.

Climatic impact of glacial cycle polar motion: Coupled oscillations of ice sheet mass and rotation pole position

USGS Publications Warehouse

Bills, Bruce G.; James, Thomas S.; Mengel, John G.

1999-01-01

Precessional motion of Earth's rotation axis relative to its orbit is a well-known source of long-period climatic variation. It is less well appreciated that growth and decay of polar ice sheets perturb the symmetry of the global mass distribution enough that the geographic location of the rotation axis will change by at least 15 km and possibly as much as 100 km during a single glacial cycle. This motion of the pole will change the seasonal and latitudinal pattern of temperatures. We present calculations, based on a diurnal average energy balance, which compare the summer and winter temperature anomalies due to a 1° decrease in obliquity with those due to a 1° motion of the rotation pole toward Hudson Bay. Both effects result in peak temperature perturbations of about 1° Celsius. The obliquity change primarily influences the amplitude of the seasonal cycle, while the polar motion primarily changes the annual mean temperatures. The polar motion induced temperature anomaly is such that it will act as a powerful negative feedback on ice sheet growth. We also explore the evolution of the coupled system composed of ice sheet mass and pole position. Oscillatory solutions result from the conflicting constraints of rotational and thermal stability. A positive mass anomaly on an otherwise featureless Earth is in rotational equilibrium only at the poles or the equator. The two polar equilibria are rotationally unstable, and the equatorial equilibrium, though rotationally stable, is thermally unstable. We find that with a plausible choice for the strength of coupling between the thermal and rotational systems, relatively modest external forcing can produce significant response at periods of 104–106 years, but it strongly attenuates polar motion at longer periods. We suggest that these coupled oscillations may contribute to the observed dominance of 100 kyr glacial cycles since the mid-Pleistocene and will tend to stabilize geographic patterns that are suitable to glaciations.

Observations of Tidal Straining Within Two Different Ocean Environments in the East China Sea: Stratification and Near-Bottom Turbulence

NASA Astrophysics Data System (ADS)

Yang, Wei; Wei, Hao; Zhao, Liang

2017-11-01

Tidal straining describes the straining effect induced by the vertical shear of oscillatory tidal currents that act on horizontal density gradients. It tends to create tidal periodic stratification and modulate the turbulence in the bottom boundary layer (BBL). Here, we present observations of current, hydrology and turbulence obtained at two mooring stations that are characterized by two typical hydrological environments in the East China Sea (ECS). One is located adjacent to the Changjiang River's mouth, and the other is located over a sloping shelf which is far from the freshwater sources. Tidal straining induces a semidiurnal switching between stable and unstable stratification at both stations. Near-bottom high-frequency velocity measurements further reveal that the dissipation rate of turbulent kinetic energy (TKE) is highly elevated during periods when unstable stratification occurs. A comparison between the TKE dissipation rate (ɛ) and the shear production (P) further reveals that the near-bottom mixing is locally shear-induced most of the time except during the unstable stratification period. Within this period, the magnitude of dissipation exceeds the expected value based on the law of the wall by an order of magnitude. The buoyancy flux that calculated by the balance method is too small to compensate for the existing discrepancy between the dissipation and shear production. Another plausible candidate is the advection of TKE, which may play an important role in the TKE budget during the unstable stratification period.

A delay differential model of ENSO variability: parametric instability and the distribution of extremes

NASA Astrophysics Data System (ADS)

Zaliapin, I.; Ghil, M.; Thompson, S.

2007-12-01

We consider a Delay Differential Equation (DDE) model for El-Nino Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in the ENSO dynamics: delayed negative feedback and seasonal forcing. Descriptive and metric stability analyses of the model are performed in a complete 3D space of its physically relevant parameters. Existence of two regimes --- stable and unstable --- is reported. The domains of the regimes are separated by a sharp neutral curve in the parameter space. The detailed structure of the neutral curve become very complicated (possibly fractal), and individual trajectories within the unstable region become highly complex (possibly chaotic) as the atmosphere-ocean coupling increases. In the unstable regime, spontaneous transitions in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values occur, for purely periodic, seasonal forcing. This indicates (via the continuous dependence theorem) the existence of numerous unstable solutions responsible for the complex dynamics of the system. In the stable regime, only periodic solutions are found. Our results illustrate the role of the distinct parameters of ENSO variability, such as strength of seasonal forcing vs. atmosphere ocean coupling and propagation period of oceanic waves across the Tropical Pacific. The model reproduces, among other phenomena, the Devil's bleachers (caused by period locking) documented in other ENSO models, such as nonlinear PDEs and GCMs, as well as in certain observations. We expect such behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.

Einstein@Home DISCOVERY OF A PALFA MILLISECOND PULSAR IN AN ECCENTRIC BINARY ORBIT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knispel, B.; Allen, B.; Lyne, A. G.

2015-06-10

We report the discovery of the millisecond pulsar (MSP) PSR J1950+2414 (P = 4.3 ms) in a binary system with an eccentric (e = 0.08) 22 day orbit in Pulsar Arecibo L-band Feed Array survey observations with the Arecibo telescope. Its companion star has a median mass of 0.3 M{sub ⊙} and is most likely a white dwarf (WD). Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star. This process should circularize the orbit, as is observed for the vast majority of binary MSPs, which predominantly have orbitalmore » eccentricities e < 0.001. However, four recently discovered binary MSPs have orbits with 0. 027 < e < 0.44; PSR J1950+2414 is the fifth such system to be discovered. The upper limits for its intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population. The large eccentricities are incompatible with the predictions of the standard recycling scenario: something unusual happened during their evolution. Proposed scenarios are (a) initial evolution of the pulsar in a triple system which became dynamically unstable, (b) origin in an exchange encounter in an environment with high stellar density, (c) rotationally delayed accretion-induced collapse of a super-Chandrasekhar WD, and (d) dynamical interaction of the binary with a circumbinary disk. We compare the properties of all five known eccentric MSPs with the predictions of these formation channels. Future measurements of the masses and proper motion might allow us to firmly exclude some of the proposed formation scenarios.« less

Stationkeeping Approach for the Microwave Anisotropy Probe (MAP)

NASA Technical Reports Server (NTRS)

Rohrbaugh, Dave; Schiff, Conrad

2002-01-01

The Microwave Anisotropy Probe was successfully launched on June 30, 2001 and placed into a Lissajous orbit about the L2 Sun-Earth-Moon libration point. However, the L2 libration point is unstable which necessitates occasional stationkeeping maneuvers in order to maintain the spacecraft s Lissajous orbit. Analyses were performed in order to develop a feasible L2 stationkeeping strategy for the MAP mission. The resulting strategy meets the allotted fuel budget, allowing for enough fuel to handle additional he1 taxes, while meeting the attitude requirements for the maneuvers. Results from the first two stationkeeping maneuvers are included.

NEXT GENERATION OF TELESCOPES OR DYNAMICS REQUIRED TO DETERMINE IF EXO-MOONS HAVE PROGRADE OR RETROGRADE ORBITS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Karen M.; Fujii, Yuka

2014-08-20

We survey the methods proposed in the literature for detecting moons of extrasolar planets in terms of their ability to distinguish between prograde and retrograde moon orbits, an important tracer of the moon formation channel. We find that most moon detection methods, in particular, sensitive methods for detecting moons of transiting planets, cannot observationally distinguishing prograde and retrograde moon orbits. The prograde and retrograde cases can only be distinguished where the dynamical evolution of the orbit due to, e.g., three body effects is detectable, where one of the two cases is dynamically unstable, or where new observational facilities, which canmore » implement a technique capable of differentiating the two cases, come online. In particular, directly imaged planets are promising targets because repeated spectral and photometric measurements, which are required to determine moon orbit direction, could also be conducted with the primary interest of characterizing the planet itself.« less

Dynamical behavior of lean swirling premixed flame generated by change in gravitational orientation

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Miyano, Takaya; Shepherd, Ian

2010-11-01

The dynamic behavior of flame front instability in lean swirling premixed flame generated by the effect of gravitational orientation has been experimentally investigated in this work. When the gravitational direction is changed relative to the flame front, i.e., in inverted gravity, an unstably fluctuating flame (unstable flame) is formed in a limited domain of equivalence ratio and swirl number (Gotoda. H et al., Physical Review E, vol. 81, 026211, 2010). The time history of flame front fluctuations show that in the buoyancy-dominated region, chaotic irregular fluctuation with low frequencies is superimposed on the dominant periodic oscillation of the unstable flame. This periodic oscillation is produced by unstable large-scale vortex motion in combustion products generated by a change in the buoyancy/swirl interaction due to the inversion of gravitational orientation. As a result, the dynamic behavior of the unstable flame becomes low-dimensional deterministic chaos. Its dynamics maintains low-dimensional deterministic chaos even in the momentum-dominated region, in which vortex breakdown in the combustion products clearly occurs. These results were clearly demonstrated by the use of nonlinear time series analysis based on chaos theory, which has not been widely applied to the investigation of combustion phenomena.

Modal Control of a Satellite in Orbit about L3.

DTIC Science & Technology

1980-12-01

the right- half of the complex plane , are removed via the controller moving the unstable roots from the right- half to the left- half of the ...complex plane . Simultaneously, the other system roots remain in their original locations in the complex plane . Since the Poincare exponents of Hamiltonian... half - plane , the conjugate root in the left- half -

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

NASA Technical Reports Server (NTRS)

Vaughan, William W.; Friedman, Mark J.; Monteiro, Anand C.

1993-01-01

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.

2018-04-01

The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.

Origin of orbital periods in the sedimentary relative paleointensity records

NASA Astrophysics Data System (ADS)

Xuan, Chuang; Channell, James E. T.

2008-08-01

Orbital cycles with 100 kyr and/or 41 kyr periods, detected in some sedimentary normalized remanence (relative paleointensity) records by power spectral analysis or wavelet analysis, have been attributed either to orbital forcing of the geodynamo, or to lithologic contamination. In this study, local wavelet power spectra (LWPS) with significance tests have been calculated for seven relative paleointensity (RPI) records from different regions of the world. The results indicate that orbital periods (100 kyr and/or 41 kyr) are significant in some RPI records during certain time intervals, and are not significant in others. Time intervals where orbital periods are significant are not consistent among the RPI records, implying that orbital periods in these RPI records may not have a common origin such as orbital forcing on the geodynamo. Cross-wavelet power spectra (|XWT|) and squared wavelet coherence (WTC) between RPI records and orbital parameters further indicate that common power exists at orbital periods but is not significantly coherent, and exhibits variable phase relationships, implying that orbital periods in RPI records are not caused directly by orbital forcing. Similar analyses for RPI records and benthic oxygen isotope records from the same sites show significant coherence and constant in-phase relationships during time intervals where orbital periods were significant in the RPI records, indicating that orbital periods in the RPI records are most likely due to climatic 'contamination'. Although common power exists at orbital periods for RPI records and their normalizers with significant coherence during certain time intervals, phase relationships imply that 'contamination' (at orbital periods) is not directly due to the normalizers. Orbital periods are also significant in the NRM intensity records, and 'contamination' in RPI records can be attributed to incomplete normalization of the NRM records. Further tests indicate that 'contamination' is apparently not directly related to physical properties such as density or carbonate content, or to the grain size proxy κARM/ κ. However, WTC between RPI records and the grain size proxy ARM/IRM implies that ARM/IRM does reflect the 'contamination' in some RPI records. It appears that orbital periods were introduced into the NRM records (and have not been normalized when calculating RPI records) through magnetite grain size variations reflected in the ARM/IRM grain size proxy. The orbital power in ARM/IRM for some North Atlantic sites is probably derived from bottom-current velocity variations that are orbitally modulated and are related to the vigor of thermohaline circulation and the production of North Atlantic Deep Water (NADW). In the case of ODP Site 983, the orbital power in RPI appears to exhibit a shift from 41-kyr to 100-kyr period at the mid-Pleistocene climate transition (˜750 ka), reinforcing the climatic origin of these orbital periods. RPI records from the Atlantic and Pacific oceans, and RPI records with orbital periods eliminated by band-pass filters, are highly comparable with each other in the time domain, and are coherent and in-phase in time-frequency space, especially at non-orbital periods, indicating that 'contamination', although present (at orbital periods) is not debilitating to these RPI records as a global signal that is primarily of geomagnetic origin.

GJ 581 update: Additional evidence for a Super-Earth in the habitable zone

NASA Astrophysics Data System (ADS)

Vogt, S. S.; Butler, R. P.; Haghighipour, N.

2012-08-01

We present an analysis of the significantly expanded HARPS 2011 radial velocity data set for GJ 581 that was presented by Forveille et al. (2011). Our analysis reaches substantially different conclusions regarding the evidence for a Super-Earth-mass planet in the star's Habitable Zone. We were able to reproduce their reported χν2 and RMS values only after removing some outliers from their models and refitting the trimmed down RV set. A suite of 4000 N-body simulations of their Keplerian model all resulted in unstable systems and revealed that their reported 3.6σ detection of e=0.32 for the eccentricity of GJ 581e is manifestly incompatible with the system's dynamical stability. Furthermore, their Keplerian model, when integrated only over the time baseline of the observations, significantly increases the χν2 and demonstrates the need for including non-Keplerian orbital precession when modeling this system. We find that a four-planet model with all of the planets on circular or nearly circular orbits provides both an excellent self-consistent fit to their RV data and also results in a very stable configuration. The periodogram of the residuals to a 4-planet all-circular-orbit model reveals significant peaks that suggest one or more additional planets in this system. We conclude that the present 240-point HARPS data set, when analyzed in its entirety, and modeled with fully self-consistent stable orbits, by and of itself does offer significant support for a fifth signal in the data with a period near 32 days. This signal has a false alarm probability of <4 % and is consistent with a planet of minimum mass 2.2 M_⊙, orbiting squarely in the star's habitable zone at 0.13 AU, where liquid water on planetary surfaces is a distinct possibility.

Analytical model for orbital debris environmental management

NASA Technical Reports Server (NTRS)

Talent, David L.

1990-01-01

A differential equation, also referred to as the PIB (particle-in-a-box) model, expressing the time rate of change of the number of objects in orbit, is developed, and its applicability is illustrated. The model can be used as a tool for the assessment of LEO environment stability, and as a starting point for the development of numerical evolutionary models. Within the context of the model, evolutionary scenarios are examined, and found to be sensitive to the growth rate. It is determined that the present environment is slightly unstable to catastrophic growth, and that the number of particles on orbit will continue to increase until approximately 2250-2350 AD, with a maximum of 2,000,000. The model is expandable to the more realistic (complex) case of multiple species in a multiple-tier system.

Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

NASA Astrophysics Data System (ADS)

Li, Feng-Guo; Ai, Bao-Quan

2011-06-01

Noise can induce inverse period-doubling transition and chaos. The effects of the colored noise on periodic orbits, of the different periodic sequences in the logistic map, are investigated. It is found that the dynamical behaviors of the orbits, induced by an exponentially correlated colored noise, are different in the mergence of transition, and the effects of the noise intensity on their dynamical behaviors are different from the effects of the correlation time of noise. Remarkably, the noise can induce new periodic orbits, namely, two new orbits emerge in the period-four sequence at the bifurcation parameter value μ = 3.5, four new orbits in the period-eight sequence at μ = 3.55, and three new orbits in the period-six sequence at μ = 3.846, respectively. Moreover, the dynamical behaviors of the new orbits clearly show the resonancelike response to the colored noise.

Feedback control for stabilizing chaotic spiral waves during cardiac ventricular fibrillation

NASA Astrophysics Data System (ADS)

Uzelac, Ilija; Wikswo, John; Gray, Richard

2011-03-01

The cardiac arrhythmias that lead to ventricular fibrillation (VF) arise from electrical spiral waves (SW) rotating within the heart with a characteristic period τ . A single drifting SW can degenerate into a chaotic system of multiple SWs and VF. Hence early SW detection and termination is crucial to prevent VF. Time-delayed feedback control (TDFC) is well known approach for stabilizing unstable periodic orbits embedded in chaotic attractors. We hypothesize that cardiac SWs can be stabilized by TDFC with a time-delay of τ . Implementing this approach will require precise, closed-loop control of the charge delivered to the heart during the defibrillation process. To do this, we have developed a 2 kW arbitrary-waveform voltage-to-current converter (V2CC) with a 1 kHz bandwidth that can deliver up to 5 A at 400 V for 500 ms, and a photodiode system for recording in real time an optical electrocardiogram, OECG(t). The feedback signal driving the V2CC will be the time-difference (OECG(t) - OECG(t-T), where we hypothesize that T is τ , the period of the SW. This may dramatically decrease defibrillation voltages by using a defibrillation waveform customized to the VF event, unlike commercial capacitor defibrillators. Supported in part by NIH R01 HL58241-11 through ARRA 2009.

Connecting orbits and invariant manifolds in the spatial restricted three-body problem

NASA Astrophysics Data System (ADS)

Gómez, G.; Koon, W. S.; Lo, M. W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2004-09-01

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. These tubes can be used to construct new spacecraft trajectories, such as a 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. This work extends the results to the three-dimensional case. Besides providing a full description of different kinds of libration motions in a large vicinity of these points, this paper numerically demonstrates the existence of heteroclinic connections between pairs of libration orbits, one around the libration point L1 and the other around L2. Since these connections are asymptotic orbits, no manoeuvre is needed to perform the transfer from one libration point orbit to the other. A knowledge of these orbits can be very useful in the design of missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.

Nonlinear time-periodic models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria

PubMed Central

Taylor, Graham K; Żbikowski, Rafał

2005-01-01

Previous studies of insect flight control have been statistical in approach, simply correlating wing kinematics with body kinematics or force production. Kinematics and forces are linked by Newtonian mechanics, so adopting a dynamics-based approach is necessary if we are to place the study of insect flight on its proper physical footing. Here we develop semi-empirical models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria. We use instantaneous force–moment measurements from individual locusts to parametrize the nonlinear rigid body equations of motion. Since the instantaneous forces are approximately periodic, we represent them using Fourier series, which are embedded in the equations of motion to give a nonlinear time-periodic (NLTP) model. This is a proper mathematical generalization of an earlier linear-time invariant (LTI) model of locust flight dynamics, developed using previously published time-averaged versions of the instantaneous force recordings. We perform various numerical simulations, within the fitted range of the model, and across the range of body angles used by free-flying locusts, to explore the likely behaviour of the locusts upon release from the tether. Solutions of the NLTP models are compared with solutions of the nonlinear time-invariant (NLTI) models to which they reduce when the periodic terms are dropped. Both sets of models are unstable and therefore fail to explain locust flight stability fully. Nevertheless, whereas the measured forces include statistically significant harmonic content up to about the eighth harmonic, the simulated flight trajectories display no harmonic content above the fundamental forcing frequency. Hence, manoeuvre control in locusts will not directly reflect subtle changes in the higher harmonics of the wing beat, but must operate on a coarser time-scale. A state-space analysis of the NLTP models reveals orbital trajectories that are impossible to capture in the LTI and NLTI models, and inspires the hypothesis that asymptotic orbital stability is the proper definition of stability in flapping flight. Manoeuvre control on the scale of more than one wing beat would then consist in exciting transients from one asymptotically stable orbit to another. We summarize these hypotheses by proposing a limit-cycle analogy for flapping flight control and suggest experiments for verification of the limit-cycle control analogy hypothesis. PMID:16849180

Periodic Orbit Families in the Gravitational Field of Irregular-shaped Bodies

NASA Astrophysics Data System (ADS)

Jiang, Yu; Baoyin, Hexi

2016-11-01

The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies. In the present work, we adopt a polyhedron shape model for providing an accurate representation of irregular-shaped bodies and employ the model to calculate their corresponding gravitational and effective potentials. We also investigate the characteristics of periodic orbit families and the continuation of periodic orbits. We prove a fact, which provides a conserved quantity that permits restricting the number of periodic orbits in a fixed energy curved surface about an irregular-shaped body. The collisions of Floquet multipliers are maintained during the continuation of periodic orbits around the comet 1P/Halley. Multiple bifurcations in the periodic orbit families about irregular-shaped bodies are also discussed. Three bifurcations in the periodic orbit family have been found around the asteroid 216 Kleopatra, which include two real saddle bifurcations and one period-doubling bifurcation.

A Survey of Ballistic Transfers to the Lunar Surface

NASA Technical Reports Server (NTRS)

Anderson, Rodney L.; Parker, Jeffrey S.

2011-01-01

In this study techniques are developed which allow an analysis of a range of different types of transfer trajectories from the Earth to the lunar surface. Trajectories ranging from those obtained using the invariant manifolds of unstable orbits to those derived from collision orbits are analyzed. These techniques allow the computation of trajectories encompassing low-energy trajectories as well as more direct transfers. The range of possible trajectory options is summarized, and a broad range of trajectories that exist as a result of the Sun's influence are computed and analyzed. The results are then classified by type, and trades between different measures of cost are discussed.

End of Life Disposal for Three Libration Point Missions through Manipulation of the Jacobi Constant and Zero Velocity Curves

NASA Technical Reports Server (NTRS)

Peterson, Jeremy D.; Brown, Jonathan M.

2015-01-01

The aim of this investigation is to determine the feasibility of mission disposal by inserting the spacecraft into a heliocentric orbit along the unstable manifold and then manipulating the Jacobi constant to prevent the spacecraft from returning to the Earth-Moon system. This investigation focuses around L1 orbits representative of ACE, WIND, and SOHO. It will model the impulsive delta-V necessary to close the zero velocity curves after escape through the L1 gateway in the circular restricted three body model and also include full ephemeris force models and higher fidelity finite maneuver models for the three spacecraft.

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

NASA Technical Reports Server (NTRS)

Gomez, G.; Koon, W. S.; Lo, Martin W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2001-01-01

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

INTRODUCING CAFein, A NEW COMPUTATIONAL TOOL FOR STELLAR PULSATIONS AND DYNAMIC TIDES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valsecchi, F.; Farr, W. M.; Willems, B.

2013-08-10

Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which does not suffer from the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extension of the Riccati method to investigate dynamic tides in close binaries.more » We demonstrate CAFein's capabilities as a stellar pulsation code both in the adiabatic and non-adiabatic regimes, by reproducing previously published eigenfrequencies of a polytrope, and by successfully identifying the unstable modes of a stellar model in the {beta} Cephei/SPB region of the Hertzsprung-Russell diagram. Finally, we verify CAFein's behavior in the dynamic tides regime by investigating the effects of dynamic tides on the eigenfunctions and orbital and spin evolution of massive main sequence stars in eccentric binaries, and of hot Jupiter host stars. The plethora of asteroseismic data provided by NASA's Kepler satellite, some of which include the direct detection of tidally excited stellar oscillations, make CAFein quite timely. Furthermore, the increasing number of observed short-period detached double white dwarfs (WDs) and the observed orbital decay in the tightest of such binaries open up a new possibility of investigating WD interiors through the effects of tides on their orbital evolution.« less

Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability

NASA Astrophysics Data System (ADS)

Barker, Adrian J.; Braviner, Harry J.; Ogilvie, Gordon I.

2016-06-01

We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders ℓ ≤ 5, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when n/Ω ≲ -1, where n and Ω are the orbital and spin angular frequencies, respectively) if the tidal amplitude is sufficiently large. We also explore the instability in a rigid ellipsoidal container, which is found to be quantitatively similar to that with a realistic free surface. Finally, we study the effect of rotation and tidal deformation on mode frequencies. We find that larger rotation rates and larger tidal deformations both decrease the frequencies of the prograde sectoral surface gravity modes. This increases the prospect of their tidal excitation, potentially enhancing the tidal response over expectations from linear theory. In a companion paper, we use our results to interpret global simulations of the elliptical instability.

Topological classification of periodic orbits in the Kuramoto-Sivashinsky equation

NASA Astrophysics Data System (ADS)

Dong, Chengwei

2018-05-01

In this paper, we systematically research periodic orbits of the Kuramoto-Sivashinsky equation (KSe). In order to overcome the difficulties in the establishment of one-dimensional symbolic dynamics in the nonlinear system, two basic periodic orbits can be used as basic building blocks to initialize cycle searching, and we use the variational method to numerically determine all the periodic orbits under parameter ν = 0.02991. The symbolic dynamics based on trajectory topology are very successful for classifying all short periodic orbits in the KSe. The current research can be conveniently adapted to the identification and classification of periodic orbits in other chaotic systems.

Apparent Disk-mass Reduction and Planetisimal Formation in Gravitationally Unstable Disks in Class 0/I Young Stellar Objects

NASA Astrophysics Data System (ADS)

Tsukamoto, Y.; Okuzumi, S.; Kataoka, A.

2017-04-01

We investigate the dust structure of gravitationally unstable disks undergoing mass accretion from the envelope, envisioning its application to Class 0/I young stellar objects (YSOs). We find that the dust disk quickly settles into a steady state and that, compared to a disk with interstellar medium (ISM) dust-to-gas mass ratio and micron-sized dust, the dust mass in the steady state decreases by a factor of 1/2 to 1/3, and the dust thermal emission decreases by a factor of 1/3 to 1/5. The latter decrease is caused by dust depletion and opacity decrease owing to dust growth. Our results suggest that the masses of gravitationally unstable disks in Class 0/I YSOs are underestimated by a factor of 1/3 to 1/5 when calculated from the dust thermal emission assuming an ISM dust-to-gas mass ratio and micron-sized dust opacity, and that a larger fraction of disks in Class 0/I YSOs is gravitationally unstable than was previously believed. We also investigate the orbital radius {r}{{P}} within which planetesimals form via coagulation of porous dust aggregates and show that {r}{{P}} becomes ˜20 au for a gravitationally unstable disk around a solar mass star. Because {r}{{P}} increases as the gas surface density increases and a gravitationally unstable disk has maximum gas surface density, {r}{{P}}˜ 20 {au} is the theoretical maximum radius for planetesimal formation. We suggest that planetesimal formation in the Class 0/I phase is preferable to that in the Class II phase because a large amount of dust is supplied by envelope-to-disk accretion.

Patient or visitor, mentally disturbed individuals may pose a safety threat.

PubMed

2004-09-01

As the hospital point of entry, EDs often are the first place unstable individuals can threaten others. Have specific procedures outlined for visitors and for mentally unstable patients. Cooperate closely with your security department, but always retain clinical control. Periodically review and update your procedures, and have staff re-educated annually.

From stable to unstable anomaly-induced inflation

NASA Astrophysics Data System (ADS)

Netto, Tibério de Paula; Pelinson, Ana M.; Shapiro, Ilya L.; Starobinsky, Alexei A.

2016-10-01

Quantum effects derived through conformal anomaly lead to an inflationary model that can be either stable or unstable. The unstable version requires a large dimensionless coefficient of about 5× {10}^8 in front of the {R}^2 term that results in the inflationary regime in the R+{R}^2 ("Starobinsky") model being a generic intermediate attractor. In this case the non-local terms in the effective action are practically irrelevant, and there is a `graceful exit' to a low curvature matter-like dominated stage driven by high-frequency oscillations of R - scalarons, which later decay to pairs of all particles and antiparticles, with the amount of primordial scalar (density) perturbations required by observations. The stable version is a genuine generic attractor, so there is no exit from it. We discuss a possible transition from stable to unstable phases of inflation. It is shown that this transition is automatic if the sharp cut-off approximation is assumed for quantum corrections in the period of transition. Furthermore, we describe two different quantum mechanisms that may provide a required large {R}^2-term in the transition period.

Quasi-periodic accretion and gravitational waves from oscillating `toroidal neutron stars' around a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Rezzolla, Luciano; Font, José A.

2003-05-01

We present general relativistic hydrodynamics simulations of constant specific angular momentum tori orbiting a Schwarzschild black hole. These tori are expected to form as a result of stellar gravitational collapse, binary neutron star merger or disruption, can reach very high rest-mass densities and behave effectively as neutron stars but with a toroidal topology (i.e. `toroidal neutron stars'). Here our attention is focused on the dynamical response of these objects to axisymmetric perturbations. We show that upon the introduction of perturbations, these systems either become unstable to the runaway instability or exhibit a regular oscillatory behaviour, resulting in a quasi-periodic variation of the accretion rate as well as of the mass quadrupole. The latter, in particular, is responsible for the emission of intense gravitational radiation for which the signal-to-noise ratio at the detector is comparable to or larger than the typical one expected in stellar-core collapse, making these new sources of gravitational waves potentially detectable. We discuss a systematic investigation of the parameter space in both the linear and non-linear regimes, providing estimates of how the gravitational radiation emitted depends on the mass of the torus and on the strength of the perturbation.

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

PERIODIC ORBIT FAMILIES IN THE GRAVITATIONAL FIELD OF IRREGULAR-SHAPED BODIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Yu; Baoyin, Hexi, E-mail: jiangyu_xian_china@163.com

The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies. In the present work, we adopt a polyhedron shape model for providing an accurate representation of irregular-shaped bodies and employ the model to calculate their corresponding gravitational and effective potentials. We also investigate the characteristics of periodic orbit families and the continuation of periodic orbits. We prove a fact, which provides a conserved quantity that permits restricting the number of periodic orbits in a fixedmore » energy curved surface about an irregular-shaped body. The collisions of Floquet multipliers are maintained during the continuation of periodic orbits around the comet 1P/Halley. Multiple bifurcations in the periodic orbit families about irregular-shaped bodies are also discussed. Three bifurcations in the periodic orbit family have been found around the asteroid 216 Kleopatra, which include two real saddle bifurcations and one period-doubling bifurcation.« less

The Case for a Geocentric rather than Heliocentric Origin of the Late Stage Heavy Bombardment (LHB) of the Moon and Tidal Evolution of its Orbit

NASA Astrophysics Data System (ADS)

Davis, P. M.; Stacey, F. D.

2009-12-01

Melt breccia samples returned from the Apollo mission have dates that suggest that the impacts that formed major basins on the Moon occurred between 3.8 and 4.0 Ga i.e., about 0.6 G years after Lunar formation. Three models have been proposed to explain the LHB. Heliocentric models including (1) The period marked the end of large-scale impacts associated with planetary formation and (2) It corresponded to a spike in impacts associated with major reorientation of the solar system (the ‘Nice model’), when the orbits Jupiter and Saturn became resonant, causing the orbits of Uranus and Neptune to become unstable and grow, scattering cometary and asteroidal fragments into Earth-Moon crossing orbits, and a geocentric model (3) It was due to collision with the last of a series of moonlets formed during Earth accretion which were swept up by tidal regression of a large Moon that had been formed near the Earth by a giant impact. While there is no smoking gun for any of these scenarios we will discuss a possible scenario for (3). Numerical calculations show that tidal regression of a large inner Moon sequentially traps exterior smaller moonlets into 2:1 resonance. Resonant trapping rapidly increases the eccentricity of their orbits causing them to become Moon-crossing. If the orbital radii of the moonlets had a resonance or Bode's law-type distribution, for the last collision to take place at 0.6 Gy, the Moon would have been at ~40 RE when it took place. One of the implications is that the associated LHB impacts would have significantly less relative velocity than those derived from asteroidal or cometary distances associated with (1) or (2). This may explain the low content of vapor condensate in the Lunar breccias. The tidal evolution from ~40 RE at 0.6 Gy requires a lower tidal friction than at present, but this has been evident for many years from tidal rhythmite data.

Soleus and lateral gastrocnemius H-reflexes during standing with unstable footwear.

PubMed

Friesenbichler, Bernd; Lepers, Romuald; Maffiuletti, Nicola A

2015-05-01

Unstable footwear has been shown to increase lower extremity muscle activity, but the reflex response to perturbations induced by this intervention is unknown. Twenty healthy subjects stood in stable and unstable footwear conditions (presented randomly) while H-reflex amplitude and background muscle activity were measured in the soleus and lateral gastrocnemius (LG) muscles. Wearing unstable footwear resulted in larger H-reflexes (normalized to the maximal M-wave) for the LG (+12%; P = 0.025), but not for the soleus (+4%; P > 0.05). Background activity of both muscles was significantly higher in the unstable condition. The H-reflex facilitation observed with unstable footwear was unexpected, as challenging postural conditions usually result in reflex depression. Increased muscle activity, decreased presynaptic inhibition, and/or more forward postural position may have (over-)compensated the expected reflex depression. Differences between LG and soleus H-reflex modulation may be due to diverging motor unit recruitment thresholds. © 2015 Wiley Periodicals, Inc.

Toroidal Geometry Stabilizing a Latitudinal Ring of Point Vortices on a Torus

NASA Astrophysics Data System (ADS)

Sakajo, Takashi; Shimizu, Yuuki

2018-06-01

We carry out the linear stability analysis of a polygonal ring configuration of N point vortices, called an N-ring, along the line of latitude θ _0 on a torus with the aspect ratio α . Deriving a criterion for the stability depending on the parameters N, θ _0 and α , we reveal how the aspect ratio α contributes to the stability of the N-ring. While the N-ring necessarily becomes unstable when N is sufficiently large for fixed α , the stability is closely associated with the geometric property of the torus for variable α ; for low aspect ratio α ˜ 1, N=7 is a critical number determining the stability of the N-ring when it is located along a certain range of latitudes, which is an analogous result to those in a plane and on a sphere. On the other hand, the stability is determined by the sign of curvature for high aspect ratio α ≫ 1. That is to say, the N-ring is neutrally stable if it is located on the inner side of the toroidal surface with a negative curvature, while the N-ring on its outer side with a positive curvature is unstable. Furthermore, based on the linear stability analysis, we describe nonlinear evolution of the N-ring when it becomes unstable. It is difficult to deal with this problem, since the evolution equation of the N point vortices is formulated as a Hamiltonian system with N degrees of freedom, which is in general non-integrable. Thus, we reduce the Hamiltonian system to a simple integrable system by introducing a cyclic symmetry. Owing to this reduction, we successfully find some periodic orbits in the reduced system, whose local bifurcations and global transitions for variable α are characterized in terms of the fundamental group of the torus.

GPS Space Service Volume: Ensuring Consistent Utility Across GPS Design Builds for Space Users

NASA Technical Reports Server (NTRS)

Bauer, Frank H.; Parker, Joel Jefferson Konkl; Valdez, Jennifer Ellen

2015-01-01

GPS availability and signal strength originally specified for users on or near surface of Earth with transmitted power levels specified at edge-of-Earth, 14.3 degrees. Prior to the SSV specification, on-orbit performance of GPS varied from block build to block build (IIA, IIRM, IIF) due to antenna gain and beam width variances. Unstable on-orbit performance results in significant risk to space users. Side-lobe signals, although not specified, were expected to significantly boost GPS signal availability for users above the constellation. During GPS III Phase A, NASA noted significant discrepancies in power levels specified in GPS III specification documents, and measured on-orbit performance. To stabilize the signal for high altitude space users, NASA DoD team in 2003-2005 led the creation of new Space Service Volume (SSV) definition and specifications.

Why is the rapid burster different from all other galactic-bulge X-ray sources?

NASA Astrophysics Data System (ADS)

Milgrom, M.

1987-01-01

It is suggested that the rapid X-ray burster exhibits unique behavior because it contains a neutron star whose stellar radius is smaller than the minimum radius of a circular orbit that is stable according to general relativity. The star accretes from a disk that extends down to the last stable orbit. In this state, the disk is unstable against a rapid fall and accretion of its innermost part onto the star. The sudden dumping of mass gives rise to a burst of X-rays. The disk then heals, refilling the inner region at a pace that is dictated mainly by the global accretion rate, in order to ready itself for the next burst. In all other galactic-bulge-type sources, the neutron star is larger than the last stable orbit.

Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2015-07-01

The dynamic stability of dynamical systems with time-periodic stiffness is addressed here. Cracked rotor systems with time-periodic stiffness are well-known examples of such systems. Time-varying area moments of inertia at the cracked element cross-section of a cracked rotor have been used to formulate the time-periodic finite element stiffness matrix. The semi-infinite coefficient matrix obtained by applying the harmonic balance (HB) solution to the finite element (FE) equations of motion is employed here to study the dynamic stability of the system. Consequently, the sign of the determinant of a scaled version of a sub-matrix of this semi-infinite coefficient matrix at a finite number of harmonics in the HB solution is found to be sufficient for identifying the major unstable zones of the system in the parameter plane. Specifically, it is found that the negative determinant always corresponds to unstable zones in all of the systems considered. This approach is applied to a parametrically excited Mathieu's equation, a two degree-of-freedom linear time-periodic dynamical system, a cracked Jeffcott rotor and a finite element model of the cracked rotor system. Compared to the corresponding results obtained by Floquet's theory, the sign of the determinant of the scaled sub-matrix is found to be an efficient tool for identifying the major unstable zones of the linear time-periodic parametrically excited systems, especially large-scale FE systems. Moreover, it is found that the unstable zones for a FE cracked rotor with an open transverse crack model only appear at the backward whirl. The theoretical and experimental results have been found to agree well for verifying that the open crack model excites the backward whirl amplitudes at the critical backward whirling rotational speeds.

Vertical Structure of Heat and Momentum Transport in the Urban Surface Layer

NASA Astrophysics Data System (ADS)

Hrisko, J.; Ramamurthy, P.

2017-12-01

Vertical transport of heat and momentum during convective periods is investigated in the urban surface layer using eddy covariance measurements at 5 levels. The Obukhov length is used to divide the dataset into distinct stability regimes: weakly unstable, unstable and very unstable. Our preliminary analysis indicates critical differences in the transport of heat and momentum as the instability increases. Particularly, during periods of increased instability the vertical heat flux deviates from surface layer similarity theory. Further analysis of primary quadrant sweeps and ejections also indicate deviations from the theory, alluding that ejections dominate during convective periods for heat transport, but equally contribute with sweeps for momentum transport. The transport efficiencies of momentum at all 5 levels uniformly decreases as the instability increases, in stark contrast the heat transport efficiencies increase non-linearly as the instability increases. Collectively, these results demonstrate the breakdown of similarity theory during convective periods, and reaffirm that revised and improved methods for characterizing heat and momentum transport in urban areas is needed. These implications could ultimately advance weather prediction and estimation of scalar transport for urban areas susceptible to weather hazards and large amounts of pollution.

Twist number and order properties of periodic orbits

NASA Astrophysics Data System (ADS)

Petrisor, Emilia

2013-11-01

A less studied numerical characteristic of periodic orbits of area preserving twist maps of the annulus is the twist or torsion number, called initially the amount of rotation Mather (1984) [2]. It measures the average rotation of tangent vectors under the action of the derivative of the map along that orbit, and characterizes the degree of complexity of the dynamics. The aim of this paper is to give new insights into the definition and properties of the twist number and to relate its range to the order properties of periodic orbits. We derive an algorithm to deduce the exact value or a demi-unit interval containing the exact value of the twist number. We prove that at a period-doubling bifurcation threshold of a mini-maximizing periodic orbit, the new born doubly periodic orbit has the absolute twist number larger than the absolute twist of the original orbit after bifurcation. We give examples of periodic orbits having large absolute twist number, that are badly ordered, and illustrate how characterization of these orbits only by their residue can lead to incorrect results. In connection to the study of the twist number of periodic orbits of standard-like maps we introduce a new tool, called 1-cone function. We prove that the location of minima of this function with respect to the vertical symmetry lines of a standard-like map encodes a valuable information on the symmetric periodic orbits and their twist number.

Servicing and Deployment of National Resources in Sun-Earth Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Beckman, Mark; Mar, Greg C.; Mesarch, Michael; Cooley, Steven; Leete, Steven J.

2002-01-01

Spacecraft travel between the Sun-Earth system, the Earth-Moon system, and beyond has received extensive attention recently. The existence of a connection between unstable regions enables mission designers to envision scenarios of multiple spacecraft traveling cheaply from system to system, rendezvousing, servicing, and refueling along the way. This paper presents examples of transfers between the Sun-Earth and Earth-Moon systems using a true ephemeris and perturbation model. It shows the (Delta)V costs associated with these transfers, including the costs to reach the staging region from the Earth. It explores both impulsive and low thrust transfer trajectories. Additionally, analysis that looks specifically at the use of nuclear power in libration point orbits and the issues associated with them such as inadvertent Earth return is addressed. Statistical analysis of Earth returns and the design of biased orbits to prevent any possible return are discussed. Lastly, the idea of rendezvous between spacecraft in libration point orbits using impulsive maneuvers is addressed.

Roto-orbital dynamics of a triaxial rigid body around a sphere. Relative equilibria and stability

NASA Astrophysics Data System (ADS)

Crespo, F.; Ferrer, S.

2018-06-01

We study the roto-orbital motion of a triaxial rigid body around a sphere, which is assumed to be much more massive than the triaxial body. The associated dynamics of this system, which consists of a normalized Hamiltonian with respect to the fast angles (partial averaging), is investigated making use of variables referred to the total angular momentum. The first order approximation of this model is integrable. We carry out the analysis of the relative equilibria, which hinges principally in the dihedral angle between the orbital and rotational planes and the ratio among the moments of inertia ρ = (B - A) / (2 C - B - A) . In particular, the dynamics of the body frame, though formally given by the classical Euler equations, experiences changes of stability in the principal directions related to the roto-orbital coupling. When ρ = 1 / 3 , we find a family of relative equilibria connected to the unstable equilibria of the free rigid body.

Design and optimal control of on-orbit servicing trajectory for target vehicle in non-coplanar elliptical orbit

NASA Astrophysics Data System (ADS)

Zhou, Wenyong; Yuan, Jianping; Luo, Jianjun

2005-11-01

Autonomous on-orbit servicing provides flexibility to space systems and has great value both in civil and in military. When a satellite performs on-orbit servicing tasks, flying around is the basic type of motion. This paper is concerned with the design and control problems of a chaser satellite flying around a target spacecraft in non-coplanar elliptical orbit for a long time. At first, a mathematical model used to design a long-term flying around trajectory is presented, which is applicable to the situation that the target spacecraft flies in an elliptical orbit. The conditions of the target at the centre of the flying around path are deduced. Considering the safety and task requirements, a long-term flying around trajectory is designed. Taking into account perturbations and navigation errors which can cause the trajectory unstable and mission impossible, a two-impulse control method is put forward. Genetic algorithm is used to minimize the cost function which considers fuel consumption and bias simultaneously. Some simulation works are carried out and the results indicate the flying around mathematical model and the trajectory control method can be used in the design and control of a long-term flying around trajectory.

Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin S.; Moses, Gregory; Young, Todd

2016-05-01

We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, O k , k=1,\\ldots,p , have two-dimensional unstable manifolds that contain orbits connecting each O k to the next two equilibrium points O k+1 and O k+2 in the chain ({{O}p+1}={{O}1} ). We show that the union of these equilibria and their unstable manifolds form a two-dimensional surface with a boundary that is homeomorphic to a cylinder if p is even and a Möbius strip if p is odd. If, further, each equilibrium in the chain satisfies a condition called ‘dissipativity’, then this surface is asymptotically stable.

Typical motions in multiple systems

NASA Technical Reports Server (NTRS)

Anosova, Joanna P.

1990-01-01

In very old times, people counted - one, two, many. The author wants to show that they were right. Consider the motions of isolated bodies: (1) N = 1 - simple motion; (2) N = 2 - Keplerian orbits; and (3) N = 3 - this is the difficult problem. In general, this problem can be studied only by computer simulations. The author studied this problem over many years (see, e.g., Agekian and Anosova, 1967; Anosova, 1986, 1989 a,b). The principal result is that two basic types of dynamics take place in triple systems. The first special type is the stable hierarchical systems with two almost Keplerian orbits. The second general type is the unstable triple systems with complicated motions of the bodies. By random choice of the initial conditions, by the Monte-Carlo method, the stable systems comprised about approx. 10% of the examined cases; the unstable systems comprised the other approx. 90% of cases under consideration. In N greater than 3, the studies of dynamics of such systems by computer simulations show that we have in general also the motions roughly as at the cases 1 - 3 with the relative negative or positive energies of the bodies. In the author's picture, the typical trajectories of the bodies in unstable triple systems of the general type of dynamics are seen. Such systems are disrupted always after close triple approaches of the bodies. These approaches play a role like the gravitational slingshot. Often, the velocities of escapers are very large. On the other hand, the movie also shows the dynamical processes of a formation, dynamical evolution and disruption of the temporary wide binaries in triples and a formation of final hard massive binaries in the final evolution of triples.

Influence of prolonged wearing of unstable shoes on upright standing postural control.

PubMed

Sousa, Andreia S P; Macedo, Rui; Santos, Rubim; Sousa, Filipa; Silva, Andreia; Tavares, João Manuel R S

2016-02-01

To study the influence of prolonged wearing of unstable shoes on standing postural control in prolonged standing workers. The participants were divided into two groups: one wore unstable shoes while the other wore conventional shoes for 8weeks. Stabilometry parameters related to centre of pressure (CoP), rambling (RM) and trembling (TR) as well as the total agonist/antagonist muscle activity, antagonist co-activation and reciprocal activation were evaluated during upright standing, before and after the 8weeks period. In both moments, the subjects were evaluated wearing the unstable shoes and in barefoot. The unstable shoe condition presented increased CoP displacement related variables and decreased co-activation command compared to barefoot before and after the intervention. The prolonged wearing of unstable shoes led to: (1) reduction of medial-lateral CoP root mean square and area; (2) decreased anteroposterior RM displacement; (3) increased anteroposterior RM mean velocity and mediolateral RM displacement; (4) decreased anteroposterior TR RMS; and (5) increased thigh antagonist co-activation in the unstable shoe condition. The unstable shoe condition is associated to a higher destabilising effect that leads to a selection of more efficient and accurate postural commands compared to barefoot. Prolonged wearing of unstable shoes provides increased effectiveness and performance of the postural control system, while wearing of unstable shoes in upright standing, that are reflected by changes in CoP related variables and by a reorganisation of postural control commands. Copyright © 2015 Elsevier B.V. All rights reserved.

On the role of disks in the formation of stellar systems: A numerical parameter study of rapid accretion

DOE PAGES

Kratter, Kaitlin M.; Matzner, Christopher D.; Krumholz, Mark R.; ...

2009-12-23

We study rapidly accreting, gravitationally unstable disks with a series of idealized global, numerical experiments using the code ORION. Our numerical parameter study focuses on protostellar disks, showing that one can predict disk behavior and the multiplicity of the accreting star system as a function of two dimensionless parameters which compare the infall rate to the disk sound speed and orbital period. Although gravitational instabilities become strong, we find that fragmentation into binary or multiple systems occurs only when material falls in several times more rapidly than the canonical isothermal limit. The disk-to-star accretion rate is proportional to the infallmore » rate and governed by gravitational torques generated by low-m spiral modes. Furthermore, we also confirm the existence of a maximum stable disk mass: disks that exceed ~50% of the total system mass are subject to fragmentation and the subsequent formation of binary companions.« less

Tidal interactions of inspiraling compact binaries

NASA Technical Reports Server (NTRS)

Bildsten, Lars; Cutler, Curt

1992-01-01

We discuss the tidal interaction in neutron star-neutron star and neutron star-black hole binaries and argue that they will not be tidally locked during the gravitational inspiral. More specifically, we show that, for inspiraling neutron stars of mass greater than about 1.2 solar mass, the shortest possible tidal synchronization time exceeds the gravitational decay time, so that the neutron star cannot be tidally locked prior to tidal disruption, regardless of its internal viscosity. For smaller mass neutron stars, an implausibly large kinematic viscosity - nearly the speed of light times the stellar radius - is required for tidal locking. We also argue that the mass transfer which occurs when the neutron star reaches the tidal radius will be unstable in neutron star-black hole binaries, and the instability will destroy the neutron star in a few orbital periods. The implications of our work for the detection of these sources by LIGO and other gravitational wave observatories and for the gamma-ray burst scenarios of Paczynski (1986, 1991) are discussed.

Stickiness in Hamiltonian systems: From sharply divided to hierarchical phase space

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; Motter, Adilson E.; Kantz, Holger

2006-02-01

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent γ=2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.

Studies of planetary scale waves and instabilities in support of the geophysical fluid flow cell experiment on USML-2

NASA Technical Reports Server (NTRS)

Hart, J. E.

1995-01-01

High resolution numerical simulations of thermal convection in a rapidly rotating channel with gravity perpendicular to the rotation vector are described. The convecting columns are subject to a beta-effect resulting from cross-channel topographic vortex stretching. The symmetries of the problem allow many invariant wavenumber sets, and this property is associated with the existence of stable multiple-equilibria at modest supercriticality. The transition to chaotic behavior involves the production of intermittent unstable orbits off a two-torus in energy space. At very high Rayleigh number (of order 10(exp 6) to 10(exp 7)) the motion can be turbulent, depending on the size of beta. However, the turbulence is usually characterized by an almost-periodic formation of patches of small scale convection that cause regular pulsations in the accompanying strong zonal jets. The processes maintaining these flows may be related to those responsible for the zonal currents on Jupiter and for cyclic variability on the Sun.

Prebifurcation periodic ghost orbits in semiclassical quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kus, M.; Haake, F.; Delande, D.

1993-10-04

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions of the stationary-phase equation, not corresponding to real classical periodic orbits, give additional contributions to the propagator which can be important, especially near bifurcations. We reveal the existence and relevance of such periodic ghost orbits for a kicked top.

From Order to Chaos in Earth Satellite Orbits

NASA Astrophysics Data System (ADS)

Gkolias, Ioannis; Daquin, Jérôme; Gachet, Fabien; Rosengren, Aaron J.

2016-11-01

We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.

Reanalysis of the orbital period variations of two DLMR overcontact binaries: FG Hya and GR Vir

NASA Astrophysics Data System (ADS)

Zhang, Xu-Dong; Yu, Yun-Xia; Xiang, Fu-Yuan; Hu, Ke

2017-12-01

We investigate orbital period changes of two deep, low mass ratio (DLMR) overcontact W UMa-type binaries, FG Hya and GR Vir. It is found that the orbital period of FG Hya shows a cyclic change with a period of {P}{mod}=54.44 {yr}. The cyclic oscillation may be due to a third body in an eccentric orbit, while the orbital period of GR Vir shows a periodic variation with a period of {P}{mod}=28.56 {yr} and an amplitude of A = 0.0352 d. The periodic variation of GR Vir can be interpreted as a result of either the light-time effect of an unseen third body or the magnetic activity cycle.

GEO Population Estimates using Optical Survey Data

NASA Technical Reports Server (NTRS)

Barker, Edwin S.; Matney, Mark J.

2007-01-01

Optical survey data taken using the NASA Michigan Orbital Debris Survey Telescope (MODEST) gives us an opportunity to statistically sample faint object population in the Geosynchronous (GEO) and near-GEO environment. This paper will summarize the MODEST survey work that has been conducted by NASA since 2002, and will outline the techniques employed to arrive at the current population estimates in the GEO environment for dim objects difficult to detect and track using current systems in the Space Surveillance Network (SSN). Some types of orbits have a higher detection rate based on what parts of the GEO belt is being observed, a straightforward statistical technique is used to debias these observations to arrive at an estimate of the total population potentially visible to the telescope. The size and magnitude distributions of these fainter debris objects are markedly different from the catalogued population. GEO debris consists of at least two different populations, one which follows the standard breakup power law and one which has anomalously high Area-to-Mass Ratios (1 to approx. 30 square meters per kilogram; a sheet of paper = approx. 13 square meters per kilogram). The Inter-Agency Space Debris Coordination Committee (IADC) is investigating objects in GEO orbits with anomalously high Area-to-Mass Ratios (AMRs). The ESA Space Debris Telescope discovered this population and has and its properties of inclinations (0 to 30 degrees), changing eccentricities (0 and 0.6), and mean motions (approx. 1 rev), will be presented. The accepted interpretation of this orbital behavior is that solar radiation pressure drives the perturbations causing time varying inclinations and eccentricities. The orbital parameters are unstable for this population and thus difficult to predict. Their dim visual magnitudes and photometric variability make observations a challenge. The IADC has enlisted a series of observatories (participating institutions: University of Michigan/CTIO, Astronomical Institute University of Bern, Boeing LTS / AMOS, Keldysh Institute of Applied Mathematics) at different longitudes. Complete observational coverage over periods of days to months will provide a better understanding of the properties, such as solar radiation pressure effects on orbital elements, size, shape, attitude, color variations, and spectral characteristics. Results from recent observational programs will be summarized, and includes a description of the orbit elements prediction processes, a summary of the metric tracking performance, and some photometric characteristics of this class of debris.

An Instability in Narrow Planetary Rings

NASA Astrophysics Data System (ADS)

Weiss, J. W.; Stewart, G. R.

2003-08-01

We will present our work investigating the behavior of narrow planetary rings with low dispersion velocities. Such narrow a ring will be initially unstable to self-gravitational collapse. After the collapse, the ring is collisionally very dense. At this stage, it is subject to a new instability. Waves appear on the inner and outer edges of the ring within half of an orbital period. The ring then breaks apart radially, taking approximately a quarter of an orbital period of do so. As clumps of ring particles expand radially away from the dense ring, Kepler shear causes these clumps to stretch out azimuthally, and eventually collapse into a new set of dense rings. Small-scale repetitions of the original instability in these new rings eventually leads to a stabilized broad ring with higher dispersion velocities than the initial ring. Preliminary results indicate that this instability may be operating on small scales in broad rings in the wake-like features seen by Salo and others. Some intriguing properties have been observed during this instability. The most significant is a coherence in the epicyclic phases of the particles. Both self-gravity and collisions in the ring operated to create and enforce this coherence. The coherence might also be responsible for the instability to radial expansion. We also observe that guiding centers of the particles do not migrate to the center of the ring during the collapse phase of the ring. In fact, guiding centers move radially away from the core of the ring during this phase, consistent with global conservation of angular momentum. We will show the results of our simulations to date, including movies of the evolution of various parameters. (Audiences members wanting popcorn are advised to bring their own.) This work is supported by a NASA Graduate Student Research Program grant and by the Cassini mission.

Performance and technical feasibility comparison of reusable launch systems: A synthesis of the ESA winged launcher studies

NASA Astrophysics Data System (ADS)

Berry, W.; Grallert, H.

1996-02-01

The paper presents a synthesis of the performance and technical feasibility assessment of 7 reusable launcher types, comprising 13 different vehicles, studied by European Industry for ESA in the ESA Winged Launcher Study in the period January 1988 to May 1994. The vehicles comprised single-stage-to-orbit (SSTO) and two-stage-to-orbit (TSTO) vehicles, propelled by either air-breathing/rocket propulsion or entirely by rocket propulsion. The results showed that an SSTO vehicle of the HOTOL-type, propelled by subsonic combustion air-breathing/rocket engines could barely deliver the specified payload mass and was aerodynamically unstable; that a TSTO vehicle of the Saenger type, employing subsonic combustion airbreathing propulsion in its first stage and rocket propulsion in its second stage, could readily deliver the specified payload mass and was found to be technically feasible and versatile; that an SSTO vehicle of the NASP type, propelled by supersonic combustion airbreathing/rocket propulsion was able to deliver a reduced payload mass, was very complex and required very advanced technologies; that an air-launched rocket propelled vehicle of the Interim HOTOL type, although technically feasible, could deliver only a reduced payload mass, being constrained by the lifting capability of the carrier airplane; that three different, entirely rocket-propelled vehicles could deliver the specified payload mass, were technically feasible but required relatively advanced technologies.

Spin axis of (2953) Vysheslavia and its implications

NASA Astrophysics Data System (ADS)

Vokrouhlický, D.; Brož, M.; Michałowski, T.; Slivan, S. M.; Colas, F.; Šarounová, L.; Velichko, F. P.

2006-01-01

Photometric observations made during the years 2000-2005 are used to determine the pole orientation of (2953) Vysheslavia, a ≃15-km size member of the Koronis family. We find admissible solutions for ecliptic latitude and longitude of the rotation pole P: β=-64°±10° and λ=11°±8° or P: β=-68°±8° and λ=192°±8°. These imply obliquity values γ=154°±14° and γ=157°±11°, respectively. The sidereal rotation period is P=0.2622722±0.0000018 day. This result is interesting for two reasons: (i) the obliquity value between 90° and 180° is consistent with a prediction done by Vokrouhlický et al. [Vokrouhlický, D., Brož, M., Farinella, P., Knežević, Z., 2001. Icarus 150, 78-93] that Vysheslavia might have been transported to its unstable orbit by the Yarkovsky effect, and (ii) with the obliquity close to 180°, Vysheslavia seems to belong to one of the two distinct groups in the Koronis family found recently by Slivan [Slivan, S.M., 2002. Nature 419, 49-51], further supporting the case of dichotomy in the spin axis distribution in this family. We also argue against the possibility that Vysheslavia reached its current orbit by a recent collisional breakup.

Error behavior of multistep methods applied to unstable differential systems

NASA Technical Reports Server (NTRS)

Brown, R. L.

1977-01-01

The problem of modeling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulas. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulas and two different stepsizes to illustrate the appropriateness of the criteria.

Optimal trajectories for aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Venkataraman, P.

1983-01-01

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Melnikov processes and chaos in randomly perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Yagasaki, Kazuyuki

2018-07-01

We consider a wide class of randomly perturbed systems subjected to stationary Gaussian processes and show that chaotic orbits exist almost surely under some nondegenerate condition, no matter how small the random forcing terms are. This result is very contrasting to the deterministic forcing case, in which chaotic orbits exist only if the influence of the forcing terms overcomes that of the other terms in the perturbations. To obtain the result, we extend Melnikov’s method and prove that the corresponding Melnikov functions, which we call the Melnikov processes, have infinitely many zeros, so that infinitely many transverse homoclinic orbits exist. In addition, a theorem on the existence and smoothness of stable and unstable manifolds is given and the Smale–Birkhoff homoclinic theorem is extended in an appropriate form for randomly perturbed systems. We illustrate our theory for the Duffing oscillator subjected to the Ornstein–Uhlenbeck process parametrically.

Dynamical and observational constraints on satellites in the inner Pluto-Charon system

NASA Technical Reports Server (NTRS)

Stern, S. Alan; Parker, Joel William; Duncan, Martin J.; Snowdall, J. Clark, Jr.; Levison, Harold F.

1994-01-01

It is not known if Pluto has other satellites besides its massive partner Charon. In the past, searches for additional satellites in the Pluto-Charon system have extended from the solar-tidal stability boundary (approximately 90 arcsec from Pluto) inward to about 1 arcsec from Pluto. Here we further explore the inner (i.e., less than 10 arcsec) region of the Pluto-Charon system to determine where additional satellites might lie. In particular, we report on (1) dynamical simulations to delineate the region where unstable orbits lie around Charon, (2) dynamical simulations which use the low orbital eccentricity of Charon to constrain the mass of any third body near Pluto, and (3) analysis of Hubble Space Telescope (HST) archival images to search for satellites in the inner Pluto-Charon system. Although no objects were found, significant new constraints on bodies orbiting in the inner Pluto-Charon system were obtained.

The Spacelab Instrument Pointing System (IPS) and its first flight

NASA Astrophysics Data System (ADS)

Heusmann, H.; Wolf, P.

1985-11-01

The development of the Instrument Pointing System (IPS) as part of Spacelab's experimental apparatus for open Pallet direct space exposure, and its test flight aboard the Shuttle Orbiter are discussed. The IPS is a three-axis-controlled platform with stellar, sun and earth pointing modes, and a better than 1 arcsec pointing ability. The development of an 'inside-out gimbal' configuration with the platform acting like a joint between the unstable Shuttle and the inertially stabilized payload facilitated close to hemispherical pointing and the adaptability for payloads of almost any size. Gimbal axes torquers counteract Orbiter acceleration due to crew movement and thruster firings, and facilitate target acquisition and precision pointing, by command from a crew-engaged computer preprogrammed for all possible control steps. Carrying an experimental solar-physics payload, the IPS correctly performed all intended functions and withstood launch and orbital loads. Several anomalies were detected and successfully corrected in-flight.

Infrared Spectroscopy of Symbiotic Stars. II. Orbits for Five S-Type Systems with Two-Year Periods

NASA Astrophysics Data System (ADS)

Fekel, Francis C.; Hinkle, Kenneth H.; Joyce, Richard R.; Skrutskie, Michael F.

2000-12-01

Infrared radial velocities have been used to determine orbital elements for the cool giants of five well-known symbiotic systems, Z And, AG Dra, V443 Her, AX Per, and FG Ser, all of which have orbital periods near the two-year mean period for S-type symbiotics. The new orbits are in general agreement with previous orbits derived from optical velocities. From the combined optical and infrared velocities, improved orbital elements for the five systems have been determined. Each of the orbital periods has been determined solely from the radial-velocity data. The orbits are circular and have quite small mass functions of 0.001-0.03 Msolar. The infrared velocities of AG Dra do not show the large orbital velocity residuals found for its optical radial velocities.

Proton elastic scattering from stable and unstable nuclei - Extraction of nuclear densities

NASA Astrophysics Data System (ADS)

Sakaguchi, H.; Zenihiro, J.

2017-11-01

Progress in proton elastic scattering at intermediate energies to determine nuclear density distributions is reviewed. After challenges of about 15 years to explain proton elastic scattering and associated polarization phenomena at intermediate energies, we have reached to some conclusions regarding proton elastic scattering as a means of obtaining nuclear densities. During this same period, physics of unstable nuclei has become of interest, and the density distributions of protons and neutrons play more important roles in unstable nuclei, since the differences in proton and neutron numbers and densities are expected to be significant. As such, proton elastic scattering experiments at intermediate energies using the inverse kinematic method have started to determine density distributions of unstable nuclei. In the region of unstable nuclei, we are confronted with a new problem when attempting to find proton and neutron densities separately from elastic proton scattering data, since electron scattering data for unstable nuclei are not presently available. We introduce a new means of determining proton and neutron densities separately by double-energy proton elastic scattering at intermediate energies.

Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J4 of both primaries

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Tyokyaa, Richard K.

2016-10-01

In this paper, we study the locations and stability of triangular points in the elliptic restricted three-body problem when both primaries are taken as oblate spheroids with oblateness up to J4. The positions of the triangular points are seen to be affected by oblateness of the primaries and the eccentricity of their orbits. The triangular points are conditionally stable for 0<μ<μc0<μ<μc and unstable for μc≤μ≤12μc≤μ≤12, where μcμc is the critical mass parameter depending on the oblateness coefficients J2iJ2i (i =1,2) and the eccentricity of the orbits. We further observe that both coefficients J2 and J4, semi-major axis and the eccentricity have destabilizing tendencies resulting in a decrease in the size of the region of stability with an increase in the parameters involved. Knowing that, in general, the triangular equilibrium points are stable for 0<μ<μc0<μ<μc, in particular systems (Alpha Centauri, X1X1 Bootis, Sirius and Kruger 60) this does not hold and such points are unstable.

Passive magnetic bearing systems stabilizer/bearing utilizing time-averaging of a periodic magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Post, Richard F.

A high-stiffness stabilizer/bearings for passive magnetic bearing systems is provide where the key to its operation resides in the fact that when the frequency of variation of the repelling forces of the periodic magnet array is large compared to the reciprocal of the growth time of the unstable motion, the rotating system will feel only the time-averaged value of the force. When the time-averaged value of the force is radially repelling by the choice of the geometry of the periodic magnet array, the Earnshaw-related unstable hit motion that would occur at zero rotational speed is suppressed when the system ismore » rotating at operating speeds.« less

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, L. D., E-mail: lachlan.smith@monash.edu; CSIRO Mineral Resources, Clayton, Victoria 3800; Rudman, M.

2016-05-15

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversalmore » in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.« less

The Effect of Protoplanetary Disk Cooling Times on the Formation of Gas Giant Planets by Gravitational Instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boss, Alan P., E-mail: aboss@carnegiescience.edu

2017-02-10

Observational evidence exists for the formation of gas giant planets on wide orbits around young stars by disk gravitational instability, but the roles of disk instability and core accretion for forming gas giants on shorter period orbits are less clear. The controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process. The latter refers largely to the handling of radiative transfer in three-dimensional (3D) hydrodynamical models, which controls heating and cooling processes in gravitationally unstable disks, and hence dense clump formation. A suite of models using the β cooling approximation is presented here.more » The initial disks have masses of 0.091 M {sub ⊙} and extend from 4 to 20 au around a 1 M {sub ⊙} protostar. The initial minimum Toomre Qi values range from 1.3 to 2.7, while β ranges from 1 to 100. We show that the choice of Q {sub i} is equal in importance to the β value assumed: high Q{sub i} disks can be stable for small β , when the initial disk temperature is taken as a lower bound, while low Q{sub i} disks can fragment for high β . These results imply that the evolution of disks toward low Q{sub i} must be taken into account in assessing disk fragmentation possibilities, at least in the inner disk, i.e., inside about 20 au. The models suggest that if low Q{sub i} disks can form, there should be an as yet largely undetected population of gas giants orbiting G dwarfs between about 6 au and 16 au.« less

Closed almost-periodic orbits in semiclassical quantization of generic polygons

PubMed

Biswas

2000-05-01

Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally nonclassical in origin. We show here that, for the class of generic polygonal billiards, the corrections are predominantly classical in origin owing to the contributions from closed almost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumber periodic families but have comparable weights. They are hence indispensable for semiclassical quantization.

Linear and nonlinear stability of periodic orbits in annular billiards.

PubMed

Dettmann, Carl P; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear and nonlinear stability of periodic orbits in annular billiards

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Long-term orbital period behaviour of low mass ratio contact binaries GR Vir and FP Boo

NASA Astrophysics Data System (ADS)

Ćetinkaya, Halil; Soydugan, Faruk

2017-02-01

In this study, we investigated orbital period variations of two low mass ratio contact binaries GR Vir and FP Boo based on published minima times. From the O-C analysis, it was found that FP Boo indicates orbital period decrease while the period of GR Vir is increasing. Mass transfer process was used to explain increase and decrease in the orbital periods. In the O-C diagrams of both systems periodic variations also exist. Cyclic changes can be explained as being the result of a light-travel time effect via a third component around the eclipsing binaries. In order to interpret of cyclic orbital period changes for GR Vir, which has late-type components, possible magnetic activity cycles of the components have been also considered.

The influence of unstable modified wall squat exercises on the posture of female university students

PubMed Central

Lee, Yoonmi

2015-01-01

[Purpose] The purpose of this study was to examine the effect of unstable modified wall squat exercises on the posture of female university students. [Subjects] The subjects of this study were 30 female university students who were equally and randomly allocated to an unstable modified wall squat exercises group the experimental group and a stable modified wall squat exercises group the control group. [Methods] Both groups performed their respective exercises for 30 minutes three times per week over a six-week period. Using BackMapper, trunk inclination, trunk imbalance, pelvic position, pelvic torsion, pelvic rotation, and position of the scapulae were evaluated. [Results] The unstable modified wall squat exercises group obtained significant results for trunk inclination, trunk imbalance, pelvic position, pelvic torsion, position of the scapulae, while the stable modified wall squat exercises group obtained significant results for trunk imbalance and pelvic position. [Conclusion] Unstable modified wall squat exercises may be applied as a method to correct the posture of average adults. PMID:26356770

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Lebois, Ryan; Carrico, John P., Jr.

2013-01-01

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Longshore Sediment Transport Rate Calculated Incorporating Wave Orbital Velocity Fluctuations

DTIC Science & Technology

2006-09-01

distribution of longshore sediment transport in the surf zone is necessary in the design and planning of groins, jetties, weirs and pipeline landfalls...transported by any current. Breaker height is defined as the vertical distance between the wave crest and the preceding wave trough at incipient...terminology; spilling breakers occur if the wave crest becomes unstable and flows down the front face of the wave producing a foamy water surface; plunging

FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gkolias, Ioannis; Gachet, Fabien; Daquin, Jérôme

We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically,more » we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.« less

Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS

NASA Technical Reports Server (NTRS)

Folta, D. C.; Pavlak, T. A.; Howell, K. C.; Woodard, M. A.; Woodfork, D. W.

2010-01-01

In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

NASA Technical Reports Server (NTRS)

Ross, Shane D.; Grover, Piyush

2007-01-01

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.

Magnetorotational Instability in Eccentric Disks

NASA Astrophysics Data System (ADS)

Chan, Chi-Ho; Krolik, Julian H.; Piran, Tsvi

2018-03-01

Eccentric disks arise in such astrophysical contexts as tidal disruption events, but it is unknown whether the magnetorotational instability (MRI), which powers accretion in circular disks, operates in eccentric disks as well. We examine the linear evolution of unstratified, incompressible MRI in an eccentric disk orbiting a point mass. We consider vertical modes of wavenumber k on a background flow with uniform eccentricity e and vertical Alfvén speed {v}{{A}} along an orbit with mean motion n. We find two mode families, one with dominant magnetic components, the other with dominant velocity components. The former is unstable at {(1-e)}3 {f}2≲ 3, where f\\equiv {{kv}}{{A}}/n, and the latter at e ≳ 0.8. For f 2 ≲ 3, MRI behaves much like in circular disks, but the growth per orbit declines slowly with increasing e; for f 2 ≳ 3, modes grow by parametric amplification, which is resonant for 0 < e ≪ 1. MRI growth and the attendant angular momentum and energy transport happen chiefly near pericenter, where orbital shear dominates magnetic tension.

Analysis of turbulence characteristics over the northern Tibetan Plateau area

NASA Astrophysics Data System (ADS)

Li, M. S.; Ma, Y. M.; Ma, W. Q.; Hu, Z. Y.; Ishikawa, H.; Su, Z. B.; Sun, G. L.

2006-07-01

Based on CATOP/Tibet [Coordinated Enhanced Observing Period (CEOP) Asia-Australia Monsoon Project (CA-IMP) on the Tibetan Plateau) turbulent data collected at the Bujiao (BJ) site of the Nagqu area, the turbulent structure and transportation characteristics in the near surface layer during summer are analyzed. The main results show that the relationship between the normalized standard deviation of 3D wind speed and stability satisfies the similarity law tinder both unstable and stable stratifications. The relations of normalized standard deviation of temperature and specific humidity to stability only obey the "-1/3 power law." tinder unstable conditions. In the case of stable stratifications, their relations to stability are dispersing. The sensible heat dominates in the dry period, while in the wet period, the latent heat is larger than the sensible heat.

AN EXTENDED AND MORE SENSITIVE SEARCH FOR PERIODICITIES IN ROSSI X-RAY TIMING EXPLORER/ALL-SKY MONITOR X-RAY LIGHT CURVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levine, Alan M.; Bradt, Hale V.; Chakrabarty, Deepto

2011-09-01

We present the results of a systematic search in {approx}14 years of Rossi X-ray Timing Explorer All-Sky Monitor (ASM) data for evidence of periodicities. Two variations of the commonly used Fourier analysis search method have been employed to significantly improve upon the sensitivity achieved by Wen et al. in 2006, who also searched for periodicities in ASM data. In addition, the present search is comprehensive in terms of sources studied and frequency range covered, and has yielded the detection of the signatures of the orbital periods of eight low-mass X-ray binary systems and of ten high-mass X-ray binaries not listedmore » in the tables of Wen et al. Orbital periods, epochs, signal amplitudes, modulation fractions, and folded light curves are given for each of these systems. Seven of the orbital periods are the most precise reported to date. In the course of this work, the 18.545 day orbital period of IGR J18483-0311 was co-discovered, and the first detections in X-rays were made of the {approx}3.9 day orbital period of LMC X-1 and the {approx}3.79 hr orbital period of 4U 1636-536. The results inform future searches for orbital and other periodicities in X-ray binaries.« less

Orbital period variability in the eclipsing pulsar binary PSR B1957+20: Evidence for a tidally powered star

NASA Technical Reports Server (NTRS)

Applegate, James H.; Shaham, Jacob

1994-01-01

Recent observations indicate that the eclipsing pulsar binary PSR B1957+20 undergoes alternating epochs of orbital period increase and decrease. We apply a model developed to explain orbital period changes of alternating sign in other binaries to the PSR B1957+20 system and find that it fits the pulsars observations well. The novel feature of the PSR B1957+20 system is that the energy flow in the companion needed to power the orbital period change mechanism can be supplied by tidal dissipation, making the companion the first identified tidally powered star. The flow of energy in the companion drives magnetic activity, which underlies the observed orbital period variations. The magnetic activity and the wind driven by the pulsar irradiation results in a torque on the spin of the companion. This torque holds the companion out of synchronous rotation, causing tidal dissipation of energy. We propose that the progenitor had a approximately 2 hr orbital period and a companion mass of 0.1-0.2 solar mass, and the system is evolving to longer orbital periods by mass and angular momentum loss on a timescale of 10(exp 8) yr.

Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.

2005-09-01

We analyze nearly periodic solutions in the plane problem of three equal-mass bodies by numerically simulating the dynamics of triple systems. We identify families of orbits in which all three points are on one straight line (syzygy) at the initial time. In this case, at fixed total energy of a triple system, the set of initial conditions is a bounded region in four-dimensional parameter space. We scan this region and identify sets of trajectories in which the coordinates and velocities of all bodies are close to their initial values at certain times (which are approximately multiples of the period). We classify the nearly periodic orbits by the structure of trajectory loops over one period. We have found the families of orbits generated by von Schubart’s stable periodic orbit revealed in the rectilinear three-body problem. We have also found families of hierarchical, nearly periodic trajectories with prograde and retrograde motions. In the orbits with prograde motions, the trajectory loops of two close bodies form looplike structures. The trajectories with retrograde motions are characterized by leafed structures. Orbits with central and axial symmetries are identified among the families found.

Periodic orbits of the integrable swinging Atwood's machine

NASA Astrophysics Data System (ADS)

Nunes, Ana; Casasayas, Josefina; Tufillaro, Nicholas

1995-02-01

We identify all the periodic orbits of the integrable swinging Atwood's machine by calculating the rotation number of each orbit on its invariant tori in phase space, and also providing explicit formulas for the initial conditions needed to generate each orbit.

Constraining the Physics of AM Canum Venaticorum Systems with the Accretion Disk Instability Model

NASA Technical Reports Server (NTRS)

Cannizzo, John K.; Nelemans, Gijs

2015-01-01

Recent work by Levitan et al. has expanded the long-term photometric database for AM CVn stars. In particular, their outburst properties are well correlated with orbital period and allow constraints to be placed on the secular mass transfer rate between secondary and primary if one adopts the disk instability model for the outbursts. We use the observed range of outbursting behavior for AM CVn systems as a function of orbital period to place a constraint on mass transfer rate versus orbital period. We infer a rate approximately 5 x 10(exp -9) solar mass yr(exp -1) ((P(sub orb)/1000 s)(exp -5.2)). We show that the functional form so obtained is consistent with the recurrence time-orbital period relation found by Levitan et al. using a simple theory for the recurrence time. Also, we predict that their steep dependence of outburst duration on orbital period will flatten considerably once the longer orbital period systems have more complete observations.

[Treatment aspects of unstable angina. Costs and payments for DRG].

PubMed

Brunelli, C; Spallarossa, P; Pasdera, A; Bezante, G P; Zorzet, F; Rossettin, P

1998-01-01

Patients with unstable angina fall into a wide prognostic and therapeutic spectrum but, in general, have great access to specialty care and invasive procedures. In the modern era, in which admissions for unstable angina outnumber those for myocardial infarction, and growing economic pressures are placed on health care systems, cardiologists must re-examine clinical strategies for treating unstable angina in the light of health-cost accounting. The aims of the present study were to examine the current management of patients admitted to our cardiology department and to calculate the medical costs. A patient schedule was drawn up to prospectively register the number and type of cardiac processes carried out during hospitalization for all unstable angina patients in the period between March 1st and May 30th, 1995. Time (minutes) actually spent by both physicians and nurses for each cardiac process were carefully recorded in order to calculate the activity budget. The effective economic budget was built for each cardiac process taking into account salaries, consumable supplies, equipment service contracts, depreciation and indirect medical and non medical costs for CCU and ward. Based to the Diagnosis Related Groups (DRG) system, 53 out of 318 patients (16%) were admitted with documented or suspected unstable angina and allocated to discharge into four DRGs: DRG 140-medically treated unstable angina: 18 patients; DRG 124-unstable angina with angiography: 16 patients; DRG 122-unstable angina evolving in myocardial infarction: 6 patients; DRG 112-unstable angina with angioplasty: 13 patients. The mean cost for hospitalized patient with unstable angina was 5,574,958 Italian Liras (DRG 140 = 2,687,719; DRG 124 = 2,800,347; DRG 122 = 6,086,563; DRG 112 = 12,751,454). The difference in costs was essentially related to the procedures involved in medical care, DRGs with expensive cardiac processes having higher costs. Furthermore, these data show a deep discrepancy between "real" costs and current DRG reimbursement. In conclusion, data show the standard management of unstable angina at our center; calculating the true costs of unstable angina is the first step towards maximizing resources and optimizing benefits.

Rational orbits around charged black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Misra, Vedant; Levin, Janna; Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027

2010-10-15

We show that all eccentric timelike orbits in Reissner-Nordstroem spacetime can be classified using a taxonomy that draws upon an isomorphism between periodic orbits and the set of rational numbers. By virtue of the fact that the rationals are dense, the taxonomy can be used to approximate aperiodic orbits with periodic orbits. This may help reduce computational overhead for calculations in gravitational wave astronomy. Our dynamical systems approach enables us to study orbits for both charged and uncharged particles in spite of the fact that charged particle orbits around a charged black hole do not admit a simple one-dimensional effectivemore » potential description. Finally, we show that comparing periodic orbits in the Reissner-Nordstroem and Schwarzschild geometries enables us to distinguish charged and uncharged spacetimes by looking only at the orbital dynamics.« less

Effects of constant immigration on the dynamics and persistence of stable and unstable Drosophila populations

PubMed Central

Dey, Snigdhadip; Joshi, Amitabh

2013-01-01

Constant immigration can stabilize population size fluctuations but its effects on extinction remain unexplored. We show that constant immigration significantly reduced extinction in fruitfly populations with relatively stable or unstable dynamics. In unstable populations with oscillations of amplitude around 1.5 times the mean population size, persistence and constancy were unrelated. Low immigration enhanced persistence without affecting constancy whereas high immigration increased constancy without enhancing persistence. In relatively stable populations with erratic fluctuations of amplitude close to the mean population size, both low and high immigration enhanced persistence. In these populations, the amplitude of fluctuations relative to mean population size went down due to immigration, and their dynamics were altered to low-period cycles. The effects of immigration on the population size distribution and intrinsic dynamics of stable versus unstable populations differed considerably, suggesting that the mechanisms by which immigration reduced extinction risk depended on underlying dynamics in complex ways. PMID:23470546

Periodic orbits of solar sail equipped with reflectance control device in Earth-Moon system

NASA Astrophysics Data System (ADS)

Yuan, Jianping; Gao, Chen; Zhang, Junhua

2018-02-01

In this paper, families of Lyapunov and halo orbits are presented with a solar sail equipped with a reflectance control device in the Earth-Moon system. System dynamical model is established considering solar sail acceleration, and four solar sail steering laws and two initial Sun-sail configurations are introduced. The initial natural periodic orbits with suitable periods are firstly identified. Subsequently, families of solar sail Lyapunov and halo orbits around the L1 and L2 points are designed with fixed solar sail characteristic acceleration and varying reflectivity rate and pitching angle by the combination of the modified differential correction method and continuation approach. The linear stabilities of solar sail periodic orbits are investigated, and a nonlinear sliding model controller is designed for station keeping. In addition, orbit transfer between the same family of solar sail orbits is investigated preliminarily to showcase reflectance control device solar sail maneuver capability.

NASA Educational Briefs for the Classroom. Orbits of Bodies in Space

NASA Technical Reports Server (NTRS)

1982-01-01

The difference between an orbit and a revolution is explained and it is shown why space shuttle Columbia's period of revolution was longer than its orbital period. Parameters of orbits examined include apoapsis, periapsis, apogee, perigee, aphelion, perihelion, orbital plane, and inclination. Orbit velocity and duration, Newton's law of gravitation, and Kepler's three laws of motion are considered. The principles involved in geostationary satellites are also explored.

On the orbital stability of pendulum-like vibrations of a rigid body carrying a rotor

NASA Astrophysics Data System (ADS)

Yehia, Hamad M.; El-Hadidy, E. G.

2013-09-01

One of the most notable effects in mechanics is the stabilization of the unstable upper equilibrium position of a symmetric body fixed from one point on its axis of symmetry, either by giving the body a suitable angular velocity or by adding a suitably spinned rotor along its axis. This effect is widely used in technology and in space dynamics. The aim of the present article is to explore the effect of the presence of a rotor on a simple periodic motion of the rigid body and its motion as a physical pendulum. The equation in the variation for pendulum vibrations takes the form in which α depends on the moments of inertia, ρ on the gyrostatic momentum of the rotor and ν (the modulus of the elliptic function) depends on the total energy of the motion. This equation, which reduces to Lame's equation when ρ = 0, has not been studied to any extent in the literature. The determination of the zones of stability and instability of plane motion reduces to finding conditions for the existence of primitive periodic solutions (with periods 4 K( ν), 8 K( ν)) with those parameters. Complete analysis of primitive periodic solutions of this equation is performed analogously to that of Ince for Lame's equation. Zones of stability and instability are determined analytically and illustrated in a graphical form by plotting surfaces separating them in the three-dimensional space of parameters. The problem is also solved numerically in certain regions of the parameter space, and results are compared to analytical ones.

Spectroscopic orbits of symbiotic stars - Preliminary results

NASA Technical Reports Server (NTRS)

Garcia, M. R.

1986-01-01

The present search for radial velocity variations due to orbital motions in symbiotic stars involved observations of 17 such stars at approximately 1-month intervals, as well as of radial velocity variations in the M-giant primary in nine stars. The observed radial velocity curves are commensurate with those expected from a group of binaries having random sin i and about 20 km/sec orbital velocities. Four of the orbital periods thus suggested for seven stars confirm previously known photometric periods, while one confirms a previously known orbital period and two are completely new. Knowledge of the orbits allows identification of those symbiotics that are close to filling their Roche lobes.

The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems. Complex instability

NASA Astrophysics Data System (ADS)

Ollé, Mercè; Pacha, Joan R.

1999-11-01

In the present work we use certain isolated symmetric periodic orbits found in some limiting Restricted Three-Body Problems to obtain, by numerical continuation, families of symmetric periodic orbits of the more general Spatial Elliptic Restricted Three Body Problem. In particular, the Planar Isosceles Restricted Three Body Problem, the Sitnikov Problem and the MacMillan problem are considered. A stability study for the periodic orbits of the families obtained - specially focused to detect transitions to complex instability - is also made.

Semiclassical relation between open trajectories and periodic orbits for the Wigner time delay.

PubMed

Kuipers, Jack; Sieber, Martin

2008-04-01

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive from it all terms in the periodic orbit formula for the time delay. The main ingredient in this calculation are correlations between scattering trajectories which are due to trajectories that approach the trapped periodic orbits closely. The equivalence between the two pictures is also demonstrated by considering correlation functions of the time delay. A corresponding calculation for the conductance gives no periodic orbit contributions in leading order.

Orbital and Collisional Evolution of the Irregular Satellites

NASA Astrophysics Data System (ADS)

Nesvorný, David; Alvarellos, Jose L. A.; Dones, Luke; Levison, Harold F.

2003-07-01

The irregular moons of the Jovian planets are a puzzling part of the solar system inventory. Unlike regular satellites, the irregular moons revolve around planets at large distances in tilted and eccentric orbits. Their origin, which is intimately linked with the origin of the planets themselves, is yet to be explained. Here we report a study of the orbital and collisional evolution of the irregular satellites from times after their formation to the present epoch. The purpose of this study is to find out the features of the observed irregular moons that can be attributed to this evolution and separate them from signatures of the formation process. We numerically integrated ~60,000 test satellite orbits to map orbital locations that are stable on long time intervals. We found that the orbits highly inclined to the ecliptic are unstable due to the effect of the Kozai resonance, which radially stretches them so that satellites either escape from the Hill sphere, collide with massive inner moons, or impact the parent planet. We also found that prograde satellite orbits with large semimajor axes are unstable due to the effect of the evection resonance, which locks the orbit's apocenter to the apparent motion of the Sun around the parent planet. In such a resonance, the effect of solar tides on a resonant moon accumulates at each apocenter passage of the moon, which causes a radially outward drift of its orbital apocenter; once close to the Hill sphere, the moon escapes. By contrast, retrograde moons with large orbital semimajor axes are long-lived. We have developed an analytic model of the distant satellite orbits and used it to explain the results of our numerical experiments. In particular, we analytically studied the effect of the Kozai resonance. We numerically integrated the orbits of the 50 irregular moons (known by 2002 August 16) for 108 yr. All orbits were stable on this time interval and did not show any macroscopic variations that would indicate instabilities operating on longer time spans. The average orbits calculated from this experiment were then used to probe the collisional evolution of the irregular satellite systems. We found that (1) the large irregular moons must have collisionally eliminated many small irregular moons, thus shaping their population to the currently observed structures; (2) some dynamical families of satellites could have been formed by catastrophic collisions among the irregular moons; and (3) Phoebe's surface must have been heavily cratered by impacts from an extinct population of Saturnian irregular moons, much larger than the present one. We therefore suggest that the Cassini imaging of Phoebe in 2004 can be used to determine the primordial population of small irregular moons of Saturn. In such a case, we will also better understand the overall efficiency of the formation process of the irregular satellites and the physical conditions that existed during planetary formation. We discovered two dynamical families of tightly clustered orbits within the Jovian retrograde group. We believe that these two clusters may be the remnants of two collisionally disrupted bodies. We found that the entire Jovian retrograde group and the Saturnian inclination groups were not produced by single breakups, because the ejection velocities derived from the orbital structures of these groups greatly exceed values calculated by modern numerical models of collisional breakups. Taken together, the evidence presented here suggests that many properties of the irregular moons previously assigned to their formation process may have resulted from their later dynamical and collisional evolution. Finally, we have found that several irregular moons, namely, Pasiphae, Sinope, S/2001 J10, S/2000 S5, S/2000 S6, and S/2000 S3, have orbits characterized by secular resonances. The orbits of some of these moons apparently evolved by some slow dissipative process in the past and became captured in tiny resonant volumes.

Two bodies with high eccentricity around the cataclysmic variable QS Vir

NASA Astrophysics Data System (ADS)

Almeida, Leonardo A.; Jablonski, Francisco

2011-11-01

QS Vir is an eclipsing cataclysmic variable with 3.618 hrs orbital period. This system has the interesting characteristics that it does not show mass transfer between the components through the L1 Lagrangian point and shows a complex orbital period variation history. Qian et al. (2010) associated the orbital period variations to the presence of a giant planet in the system plus angular momentum loss via magnetic braking. Parsons et al. (2010) obtained new eclipse timings and observed that the orbital period variations associated to a hypothetical giant planet disagree with their measurements and concluded that the decrease in orbital period is part of a cyclic variation with period ~16 yrs. In this work, we present 28 new eclipse timings of QS Vir and suggest that the orbital period variations can be explained by a model with two circumbinary bodies. The best fitting gives the lower limit to the masses M1 sin(i) ~ 0.0086 M⊙ and M2 sin(i) ~ 0.054 M⊙ orbital periods P1 ~ 14.4 yrs and P2 ~ 16.99 yrs, and eccentricities e1 ~ 0.62 and e2~0.92 for the two external bodies. Under the assumption of coplanarity among the two external bodies and the inner binary, we obtain a giant planet with ~0.009 M⊙ and a brown dwarf with ~ 0.056 M⊙ around the eclipsing binary QS Vir.

Long-term orbital evolution of short-period comets found in Project Cosmo-DICE

NASA Technical Reports Server (NTRS)

Nakamura, Tsuko; Yoshikawa, Makoto

1992-01-01

Orbital evolutions of about 160 short-period (SP) comets are numerically integrated for 4400 years in the framework of a realistic dynamical model. By the round-trip error in closure test, a reliable time space of the integrated orbits is estimated for each comet. Majority of the SP comets with their Tisserand's constant(J) between 2.8 and 3.1 are found to evolve within the past 1000-2000 years from the orbits whose perihelia are near the Jovian orbit to the orbits with perihelia of 1-2 AU. This evolution is much more rapid than that expected from Monte Carlo simulations based on symmetric distribution of planetary perturbations, thus suggesting that asymmetry of perturbation distribution play an important role in cometary evolution. Several comets are shown to evolve from the near-Saturn orbits and then to be handed over under the control of Jupiter. We also find that a few comets were captured from long-period orbits (a = 75-125 AU) via only a few close encounters with Jupiter. It is confirmed that the captured SP comets of low-inclination with 2.7 less than J less than 3.1 show more or less strong chaotic behavior. On the other hand, comets with longer orbital period and/or of high inclination reveal slow or quasi-periodic orbital evolution.

Further studies of the pulsation period and orbital elements of Centaurus X-3

NASA Technical Reports Server (NTRS)

Fabbiano, G.; Schreier, E. J.

1977-01-01

The long- and short-term variability of the 4.8-s pulsation and the 2.1-day orbital periods of Centaurus X-3 are studied. The pulsation period decreases over 4 yr with a fractional change of -0.00028 per yr, but with rms fluctuations of 0.0002 s. In August-September 1972, a continuous transition from speedup to slowdown was observed. The orbital period also decreases over 4 yr with decrease of approximately 8 millionths per yr, and with significant fluctuations of the order of 0.00001 day over months. The orbital eccentricity is found to be about 0.0008. The pulsation-period variability is found to be consistent with a near balance between the Alfven and corotation radii in an accretion-disk model. The orbital-period variability is interpreted in terms of tidal circularization and possible mass transfer and loss.

The long-period librations of large synchronous icy moons

NASA Astrophysics Data System (ADS)

Yseboodt, Marie; Van Hoolst, Tim

2014-11-01

A moon in synchronous rotation has longitudinal librations because of its non-spherical mass distribution and its elliptical orbit around the planet. We study the long-period librations of the Galilean satellites and Titan and include deformation effects and the existence of a subsurface ocean. We take into account the fact that the orbit is not keplerian and has other periodicities than the main period of orbital motion around Jupiter or Saturn due to perturbations by the Sun, other planets and moons. An orbital theory is used to compute the orbital perturbations due to these other bodies. For Titan we also take into account the large atmospheric torque at the semi-annual period of Saturn around the Sun.We numerically evaluate the amplitude and phase of the long-period librations for many interior structure models of the icy moons constrained by the mass, radius and gravity field.

A model of energetic ion effects on pressure driven tearing modes in tokamaks

DOE PAGES

Halfmoon, M. R.; Brennan, D. P.

2017-06-05

Here, the effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping in the particle distribution, in an otherwise cylindrical model. The focus is onmore » a configuration that is driven unstable to the m/n = 2/1 mode by increasing pressure, where m is the poloidal mode number and n is the toroidal. The particles and pressure can affect the mode both in the core region where there can be low and reversed shear and outside the resonant surface in significant positive shear. The results show that the energetic ions damp and stabilize the mode when orbiting in significant positive shear, increasing the marginal stability boundary. However, the inner core region contribution with low and reversed shear can drive the mode unstable. This effect of shear on the energetic ion pressure contribution is found to be consistent with the literature. These results explain the observation that the 2/1 mode was found to be damped and stabilized by energetic ions in delta δf-MHD simulations of tokamak experiments with positive shear throughout, while the 2/1 mode was found to be driven unstable in simulations of experiments with weakly reversed shear in the core. This is also found to be consistent with related experimental observations of the stability of the 2/1 mode changing significantly with core shear.« less

A model of energetic ion effects on pressure driven tearing modes in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Halfmoon, M. R.; Brennan, D. P.

Here, the effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping in the particle distribution, in an otherwise cylindrical model. The focus is onmore » a configuration that is driven unstable to the m/n = 2/1 mode by increasing pressure, where m is the poloidal mode number and n is the toroidal. The particles and pressure can affect the mode both in the core region where there can be low and reversed shear and outside the resonant surface in significant positive shear. The results show that the energetic ions damp and stabilize the mode when orbiting in significant positive shear, increasing the marginal stability boundary. However, the inner core region contribution with low and reversed shear can drive the mode unstable. This effect of shear on the energetic ion pressure contribution is found to be consistent with the literature. These results explain the observation that the 2/1 mode was found to be damped and stabilized by energetic ions in delta δf-MHD simulations of tokamak experiments with positive shear throughout, while the 2/1 mode was found to be driven unstable in simulations of experiments with weakly reversed shear in the core. This is also found to be consistent with related experimental observations of the stability of the 2/1 mode changing significantly with core shear.« less

Stability and evolution of orbits around the binary asteroid 175706 (1996 FG3): Implications for the MarcoPolo-R mission

NASA Astrophysics Data System (ADS)

Hussmann, Hauke; Oberst, Jürgen; Wickhusen, Kai; Shi, Xian; Damme, Friedrich; Lüdicke, Fabian; Lupovka, Valery; Bauer, Sven

2012-09-01

In support of the MarcoPolo-R mission, we have carried out numerical simulations of spacecraft trajectories about the binary asteroid 175706 (1996 FG3) under the influence of solar radiation pressure. We study the effects of (1) the asteroid's mass, shape, and rotational parameters, (2) the secondary's mass, shape, and orbit parameters, (3) the spacecraft's mass, surface area, and reflectivity, and (4) the time of arrival, and therefore the relative position to the sun and planets. We have considered distance regimes between 5 and 20 km, the typical range for a detailed characterization of the asteroids - primary and secondary - with imaging systems, spectrometers and by laser altimetry. With solar radiation pressure and gravity forces of the small asteroid competing, orbits are found to be unstable, in general. However, limited orbital stability can be found in the so-called Self-Stabilized Terminator Orbits (SSTO), where initial orbits are circular, orbital planes are oriented approximately perpendicular to the solar radiation pressure, and where the orbital plane of the spacecraft is shifted slightly (between 0.2 and 1 km) from the asteroid in the direction away from the sun. Under the effect of radiation pressure, the vector perpendicular to the orbit plane is observed to follow the sun direction. Shape and rotation parameters of the asteroid as well as gravitational perturbations by the secondary (not to mention sun and planets) were found not to affect the results. Such stable orbits may be suited for long radio tracking runs, which will allow for studying the gravity field. As the effect of the solar radiation pressure depends on the spacecraft mass, shape, and albedo, good knowledge of the spacecraft model and persistent monitoring of the spacecraft orientation are required.

The contact condition influence on stability and energy efficiency of quadruped robot

NASA Astrophysics Data System (ADS)

Lei, Jingtao; Wang, Tianmiao; Gao, Feng

2008-10-01

Quadruped robot has attribute of serial and parallel manipulator with multi-loop mechanism, with more DOF of each leg and intermittent contact with ground during walking, the trot gait of quadruped robot belongs to dynamic waking, compared to the crawl gait, the walking speed is higher, but the robot becomes unstable, it is difficult to keep dynamically stable walking. In this paper, we mainly analyze the condition for the quadruped robot to realize dynamically stable walking, establish centroid orbit equation based on ZMP (Zero Moment Point) stability theory, on the other hand , we study contact impact and friction influence on stability and energy efficiency. Because of the periodic contact between foots and ground, the contact impact and friction are considered to establish spring-damp nonlinear dynamics model. Robot need to be controlled to meet ZMP stability condition and contact constraint condition. Based on the virtual prototyping model, we study control algorithm considering contact condition, the contact compensator and friction compensator are adopted. The contact force and the influence of different contact conditions on the energy efficiency during whole gait cycle are obtained.

Numerical simulations in stochastic mechanics

NASA Astrophysics Data System (ADS)

McClendon, Marvin; Rabitz, Herschel

1988-05-01

The stochastic differential equation of Nelson's stochastic mechanics is integrated numerically for several simple quantum systems. The calculations are performed with use of Helfand and Greenside's method and pseudorandom numbers. The resulting trajectories are analyzed both individually and collectively to yield insight into momentum, uncertainty principles, interference, tunneling, quantum chaos, and common models of diatomic molecules from the stochastic quantization point of view. In addition to confirming Shucker's momentum theorem, these simulations illustrate, within the context of stochastic mechanics, the position-momentum and time-energy uncertainty relations, the two-slit diffraction pattern, exponential decay of an unstable system, and the greater degree of anticorrelation in a valence-bond model as compared with a molecular-orbital model of H2. The attempt to find exponential divergence of initially nearby trajectories, potentially useful as a criterion for quantum chaos, in a periodically forced oscillator is inconclusive. A way of computing excited energies from the ground-state motion is presented. In all of these studies the use of particle trajectories allows a more insightful interpretation of physical phenomena than is possible within traditional wave mechanics.

Manual Thrombus Aspiration and the Improved Survival of Patients With Unstable Angina Pectoris Treated With Percutaneous Coronary Intervention (30 Months Follow-Up).

PubMed

Yildiz, Bekir S; Bilgin, Murat; Zungur, Mustafa; Alihanoglu, Yusuf I; Kilic, Ismail D; Buber, Ipek; Ergin, Ahmet; Kaftan, Havane A; Evrengul, Harun

2016-02-01

The clinical effect of intracoronary thrombus aspiration during percutaneous coronary intervention in patients with unstable angina pectoris is unknown. In this study, we aimed to assess how thrombus aspiration during percutaneous coronary intervention affects in-hospital and 30-month mortality and complications in patients with unstable angina pectoris.We undertook an observational cohort study of 645 consecutive unstable angina pectoris patients who had performed percutaneous coronary intervention from February 2011 to March 2013. Before intervention, 159 patients who had culprit lesion with thrombus were randomly assigned to group 1 (thrombus aspiration group) and group 2 (stand-alone percutaneous coronary intervention group). All patients were followed-up 30 months until August 2015.Thrombus aspiration was performed in 64 patients (46%) whose cardiac markers (ie, creatinine kinase [CK-MB] mass and troponin T) were significantly lower after percutaneous coronary intervention than in those of group 2 (CK-MB mass: 3.80 ± 1.11 vs 4.23 ± 0.89, P = 0.012; troponin T: 0.012 ± 0.014 vs 0.018 ± 0.008, P = 0.002). Left ventricular ejection fraction at 6, 12, and 24 months postintervention was significantly higher in the group 1. During a mean follow-up period of 28.87 ± 6.28 months, mortality rates were 6.3% in the group 1 versus 12.9% in the group 2. Thrombus aspiration was also associated with significantly less long-term mortality in unstable angina pectoris patients (adjusted HR: 4.61, 95% CI: 1.16-18.21, P = 0.029).Thrombus aspiration in the context of unstable angina pectoris is associated with a limited elevation in cardiac enzymes during intervention that minimises microembolization and significantly improves both of epicardial flow and myocardial perfusion, as shown by angiographic TIMI flow grade and frame count. Thrombus aspiration during percutaneous coronary intervention in unstable angina pectoris patients has better survival over a 30-month follow-up period.

The structure and stability of orbits in Hoag-like ring systems

NASA Astrophysics Data System (ADS)

Bannikova, Elena Yu

2018-05-01

Ring galaxies are amazing objects exemplified by the famous case of Hoag's Object. Here the mass of the central galaxy may be comparable to the mass of the ring, making it a difficult case to model mechanically. In a previous paper, it was shown that the outer potential of a torus (ring) can be represented with good accuracy by the potential of a massive circle with the same mass. This approach allows us to simplify the problem of the particle motion in the gravitational field of a torus associated with a central mass by replacing the torus with a massive circle. In such a system, there is a circle of unstable equilibrium that we call `Lagrangian circle' (LC). Stable circular orbits exist only in some region limited by the last possible circular orbit related to the disappearance of the extrema of the effective potential. We call this orbit `the outermost stable circular orbit' (OSCO) by analogy with the innermost stable circular orbit (ISCO) in the relativistic case of a black hole. Under these conditions, there is a region between OSCO and LC where the circular motion is not possible due to the competition between the gravitational forces by the central mass and the ring. As a result, a gap in the matter distribution can form in Hoag-like system with massive rings.

NEWLY DISCOVERED PLANETS ORBITING HD 5319, HD 11506, HD 75784 AND HD 10442 FROM THE N2K CONSORTIUM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giguere, Matthew J.; Fischer, Debra A.; Brewer, John M.

2015-01-20

Initially designed to discover short-period planets, the N2K campaign has since evolved to discover new worlds at large separations from their host stars. Detecting such worlds will help determine the giant planet occurrence at semi-major axes beyond the ice line, where gas giants are thought to mostly form. Here we report four newly discovered gas giant planets (with minimum masses ranging from 0.4 to 2.1 M {sub Jup}) orbiting stars monitored as part of the Next 2000 target stars (N2K) Doppler Survey program. Two of these planets orbit stars already known to host planets: HD 5319 and HD 11506. Themore » remaining discoveries reside in previously unknown planetary systems: HD 10442 and HD 75784. The refined orbital period of the inner planet orbiting HD 5319 is 641 days. The newly discovered outer planet orbits in 886 days. The large masses combined with the proximity to a 4:3 mean motion resonance make this system a challenge to explain with current formation and migration theories. HD 11506 has one confirmed planet, and here we confirm a second. The outer planet has an orbital period of 1627.5 days, and the newly discovered inner planet orbits in 223.6 days. A planet has also been discovered orbiting HD 75784 with an orbital period of 341.7 days. There is evidence for a longer period signal; however, several more years of observations are needed to put tight constraints on the Keplerian parameters for the outer planet. Lastly, an additional planet has been detected orbiting HD 10442 with a period of 1043 days.« less

Chondrule-forming Shock Fronts in the Solar Nebula: A Possible Unified Scenario for Planet and Chondrite Formation

NASA Astrophysics Data System (ADS)

Boss, A. P.; Durisen, R. H.

2005-03-01

Chondrules are millimeter-sized spherules found throughout primitive chondritic meteorites. Flash heating by a shock front is the leading explanation of their formation. However, identifying a mechanism for creating shock fronts inside the solar nebula has been difficult. In a gaseous disk capable of forming Jupiter, the disk must have been marginally gravitationally unstable at and beyond Jupiter's orbit. We show that this instability can drive inward spiral shock fronts with shock speeds of up to ~10 km s-1 at asteroidal orbits, sufficient to account for chondrule formation. The mixing and transport of solids in such a disk, combined with the planet-forming tendencies of gravitational instabilities, results in a unified scenario linking chondrite production with gas giant planet formation.

Energetic and dynamical instability of spin-orbit coupled Bose-Einstein condensate in a deep optical lattice

NASA Astrophysics Data System (ADS)

Yu, Zi-Fa; Chai, Xu-Dan; Xue, Ju-Kui

2018-05-01

We investigate the energetic and dynamical instability of spin-orbit coupled Bose-Einstein condensate in a deep optical lattice via a tight-binding model. The stability phase diagram is completely revealed in full parameter space, while the dependence of superfluidity on the dispersion relation is illustrated explicitly. In the absence of spin-orbit coupling, the superfluidity only exists in the center of the Brillouin zone. However, the combination of spin-orbit coupling, Zeeman field, nonlinearity and optical lattice potential can modify the dispersion relation of the system, and change the position of Brillouin zone for generating the superfluidity. Thus, the superfluidity can appear in either the center or the other position of the Brillouin zone. Namely, in the center of the Brillouin zone, the system is either superfluid or Landau unstable, which depends on the momentum of the lowest energy. Therefore, the superfluidity can occur at optional position of the Brillouin zone by elaborating spin-orbit coupling, Zeeman splitting, nonlinearity and optical lattice potential. For the linear case, the system is always dynamically stable, however, the nonlinearity can induce the dynamical instability, and also expand the superfluid region. These predicted results can provide a theoretical evidence for exploring the superfluidity of the system experimentally.

Orbital variability in the eclipsing pulsar binary PSR B1957+20

NASA Technical Reports Server (NTRS)

Arzoumanian, Z.; Fruchter, A. S.; Taylor, J. H.

1994-01-01

We have conducted timing observations of the eclipsing millisecond binary pulsar PSR B1957+20, extending the span of data on this pulsar to more than five years. During this time the orbital period of the system has varied by roughly Delta P(sub b)/P(sub b) = 1.6 x 10(exp -7), changing quardratically with time and displaying with time and displaying an orbital period second derivative of P(sub b) = (1.43 +/- 0.08) x 10(exp -18)/sec. The previous measurement of a large negative orbital period derivative reflected only the short-term behavior of the system during the early observations; the orbital period derivative is now positive. If, as we suspect, the PSR B1957+20 system is undergoing quasi-cyclic orbital period variations similar to those found in other close binaries such as Algol and RS CVn, then the 0.025 solar mass companion to PSR B1957+20 is most likely non-degenerate, convective, and magnetically active.

Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps

NASA Astrophysics Data System (ADS)

Qin, Wen-Xin; Wang, Ya-Nan

2018-06-01

A non-exact monotone twist map φbarF is a composition of an exact monotone twist map φ bar with a generating function H and a vertical translation VF with VF ((x , y)) = (x , y - F). We show in this paper that for each ω ∈ R, there exists a critical value Fd (ω) ≥ 0 depending on H and ω such that for 0 ≤ F ≤Fd (ω), the non-exact twist map φbarF has an invariant Denjoy minimal set with irrational rotation number ω lying on a Lipschitz graph, or Birkhoff (p , q)-periodic orbits for rational ω = p / q. Like the Aubry-Mather theory, we also construct heteroclinic orbits connecting Birkhoff periodic orbits, and show that quasi-periodic orbits in these Denjoy minimal sets can be approximated by periodic orbits. In particular, we demonstrate that at the critical value F =Fd (ω), the Denjoy minimal set is not uniformly hyperbolic and can be approximated by smooth curves.

Chromospherically Active Stars. XXV. HD 144110=EV Draconis, a Double-lined Dwarf Binary

NASA Astrophysics Data System (ADS)

Fekel, Francis C.; Henry, Gregory W.; Lewis, Ceteka

2005-08-01

New spectroscopic and photometric observations of HD 144110 have been used to obtain an improved orbital element solution and determine some basic properties of the system. This chromospherically active, double-lined spectroscopic binary has an orbital period of 1.6714012 days and a circular orbit. We classify the components as G5 V and K0 V and suggest that they are slightly metal-rich. The photometric observations indicate that the rotation of HD 144110 is synchronous with the orbital period. Despite the short orbital period, no evidence of eclipses is seen in our photometry.

Fluorination utilizing thermodynamically unstable fluorides and fluoride salts thereof

DOEpatents

Bartlett, Neil; Whalen, J. Marc; Chacon, Lisa

2000-12-12

A method for fluorinating a carbon compound or cationic carbon compound utilizes a fluorination agent selected from thermodynamically unstable nickel fluorides and salts thereof in liquid anhydrous hydrogen fluoride. The desired carbon compound or cationic organic compound to undergo fluorination is selected and reacted with the fluorination agent by contacting the selected organic or cationic organic compound and the chosen fluorination agent in a reaction vessel for a desired reaction time period at room temperature or less.

QPO Constraints on Neutron Stars

NASA Technical Reports Server (NTRS)

Miller, M. Coleman

2005-01-01

The kilohertz frequencies of QPOs from accreting neutron star systems imply that they are generated in regions of strong gravity, close to the star. This suggests that observations of the QPOs can be used to constrain the properties of neutron stars themselves, and in particular to inform us about the properties of cold matter beyond nuclear densities. Here we discuss some relatively model-insensitive constraints that emerge from the kilohertz QPOs, as well as recent developments that may hint at phenomena related to unstable circular orbits outside neutron stars.

Stability of standing wave for the fractional nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Peng, Congming; Shi, Qihong

2018-01-01

In this paper, we study the stability and instability of standing waves for the fractional nonlinear Schrödinger equation i∂tu = (-Δ)su - |u|2σu, where (t ,x ) ∈R × RN, 1/2