Small Orbit Research Articles

Regularity–Partial Chaos–Regularity Transition and Overlapped KAM Scenarios in a Conservative System of Two Linearly Coupled Double-Well Oscillators

For linearly coupled double-well oscillators the regularity–partial chaos–regularity transition is found. First, an incomplete KAM scenario develops with increasing energy, from integrable pattern comprising in-phase and out-of-phase small elliptic orbits towards a partial chaos, with a deformed regular island immersed in a chaotic sea. At a critical energy a new deformed island appears as a mirror image. Above the critical energy the inverse KAM scenario leads to gradual destruction of partial chaos and to the appearance of large elliptic orbits which correspond to the large-amplitude limit governed by uncoupled oscillators with cubic anharmonicities.

Enhanced inverse bremsstrahlung heating rates in a strong laser field

Test particle studies of electron scattering on ions in an oscillatory electromagnetic field have shown that standard theoretical assumptions of small angle collisions and phase independent orbits are incorrect for electron trajectories with drift velocities smaller than quiver velocity amplitude. This leads to significant enhancement of the electron energy gain and the inverse bremsstrahlung heating rate in strong laser fields. Nonlinear processes such as Coulomb focusing and correlated collisions of electrons being brought back to the same ion by the oscillatory field are responsible for large angle, head-on scattering processes. The statistical importance of these trajectories has been examined for mono-energetic beam-like, Maxwellian and highly anisotropic electron distribution functions. A new scaling of the inverse bremsstrahlung heating rate with drift velocity and laser intensity is discussed.

Parotocinclus planicauda, a new species of the subfamily Hypoptopomatinae from southeastern Brazil (Ostariophysi: Loricariidae).

Parotocinclus planicauda, a new species from a tributary of the Doce River drainage in Minas Gerais State, Brazil, is distinguished from all other species of the genus by the presence of a caudal peduncle almost quadrangular in cross section; the anterior position of the adipose fin, close to the dorsal fin insertion; and very small orbits. A key to the Parotocinclus species of eastern Brazilian coastal rivers south of the São Francisco River is provided.

Halting Planet Migration by Photoevaporation from the Central Source

The recent discovery of Jupiter mass planets orbiting at a few AU from their stars complements earlier detections of massive planets on very small orbits. The short-period orbits strongly suggest that planet migration has occurred, with the likely mechanism being tidal interactions between the planets and the gas disks out of which they formed. The newly discovered long-period planets, together with the gas giant planets in our solar system, show that migration is either absent or rapidly halted in at least some systems. We propose a mechanism for halting type II migration at several AU in a gas disk. Photoevaporation of the disk by irradiation from the central star can produce a gap in the disk at a few AU, preventing planets outside the gap from migrating down to the star. This would result in an excess of systems with planets at or just outside the photoevaporation radius.

Existence of traveling wave solutions in a diffusive predator-prey model.

We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R(4). The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.

Effect of a large-gradient radial electric field on plasma current in a spherical torus

A description of the guiding field line (GFL) model is presented for spherical torus geometry. The model is extended to cover small banana orbits that are trapped either above or below the midplane. Comparison of the model with the fluid and neoclassical theories demonstrates correctness of the model, though it shows that the model is not exactly equivalent to them. The GFL model provides a more general description for the orbit-squeezing effect resulting from the large gradient of the radial electric field. It shows that not only does the deformation of banana orbits, but also the change of the passing particles' orbits, affect the current in plasma. Besides, it appears that the change of the orbits' shape, as projected on the magnetic surface, contributes to modification of the current along with the radial squeezing/expanding. Distortion of the current by the gradient of the electric field is found to be predominantly in the direction parallel to the magnetic field, while almost no effect is seen for the perpendicular component.

Delayed–feedback control of chaotic roll motion of a flooded ship in waves

In this paper, we investigate the use of delayed feedback to control the chaotic roll motion of a flooded ship in waves. The dynamics of the roll motion is described by four–dimensional non–autonomous equations reflecting the interaction between the ship body and flooded water. A small periodic orbit was stabilized from a large chaotic attractor by applying delayed feedback to the model equations. The chaotic attractor and the periodic orbit correspond to heavy complicated roll motion and light simple roll motion close to the static balance between the ship and water, respectively. The achieved motion is very desirable from the viewpoint of the naval architecture engineer. We also analysed the dependence of the periodic–orbit stabilization on parameters controlling the chaotic roll motion.

Outcomes of surgical (pars plicata and limbal lensectomy, vitrectomy) and non-surgical management of persistent fetal vasculature (PFV): an analysis of 54 eyes.

To identify clinical characteristics associated with outcomes of treatment for persistent fetal vasculature (PFV based on a modified classification. In this noncomparative case series, 54 eyes of 47 consecutive patients with PFV managed from 1981 until 1998 at a tertiary eye hospital were reviewed. Pars plicata lensectomy and vitrectomy was performed in 34 eyes and translimbal lensectomy and vitrectomy in five. Fifteen eyes were managed non-surgically. The following outcomes were measured: 1) "Visual improvement", defined as at least one Zipf's category improvement of best corrected final vision as compared with initial visual acuity, provided that final vision of CSUM (central, steady, unmaintained) equal to 20/100-20/30 was obtained. 2) "Cosmetic acceptability", defined as the absence of the following: small orbit, externally small appearing eye with microcornea and hypotony, eye deviation more than 35 prism diopters without strabismus surgery and corneal opacity. Six eyes were inoperable. In 10 out of 33 operated eyes (30.3%) improvement of vision was obtained including four eyes with an anterior form and six eyes with a combined form of PFV. In univariate analysis, factors such as anterior form of PFV surgery in the combined form and having a normal retina, had a weak association with a higher chance of visual improvement. In multivariate regression analysis the likelihood of unacceptable cosmetic appearance was higher in females than males (OR = 10.5), and in bilateral cases (OR = 7.9). Offspring of consanguineous marriages had more severe forms of PFV. Although visual potential is limited in PFV some eyes with an anterior or combined form and normal retina achieved improvement of visual acuity after surgery. However, statistically no single factor except sex and bilateral PFV (for cosmetic unacceptability) reliably predicted the results of treatment. Therapy should be individualized based on clinical findings. Genetic studies in offspring of consanguineous marriages with PFV may prove informative.

Slow oscillations of magnetoresistance in quasi-two-dimensional metals.

Slow oscillations of the interlayer magnetoresistance observed in the layered organic metal beta-(BEDT-TTF)(2)IBr(2) are shown to originate from the slight warping of its Fermi surface rather than from independent small cyclotron orbits. Unlike the usual Shubnikov-de Haas effect, these oscillations are not affected by the temperature smearing of the Fermi distribution and can therefore become dominant at high enough temperatures. We suggest that the slow oscillations are a general feature of clean quasi-two-dimensional metals and discuss possible applications of the phenomenon.

Magnetization in the Ultraquantum Limit

The magnetization below and far above the quantum limit for small Fermi surface orbits has been measured in the metallic compound LaRhIn(5). The magnetization due to a pocket of Fermi surface that comprises less than 1 part in 10(4) of the total Brillouin zone volume, and for which the quantum limit is approximately 7 T, leads to the appearance of an overall sample magnetic moment at fields between 7 and 32 T. This moment arises from diamagnetic currents produced by electrons in the ultraquantum limit. A model calculation of the origin and magnitude of the effect is in excellent agreement with the measured field dependence of the induced magnetization.

Eccentric Extrasolar Planets: The Jumping Jupiter Model

Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding 10 8 y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of “hot Jupiters” in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit.

SPECT breast imaging combining horizontal and vertical axes of rotation

Vertical-axis-of-rotation (VAOR) geometries, in which a gamma camera orbits a pendulous breast of a prone patient, have been proposed for SPECT breast imaging. Dedicated VAOR systems would be advantageous since they allow for minimal radius of rotation around the breast, which improves resolution-sensitivity tradeoffs, and there is less attenuation and scatter between the breast and the camera. However, the torso may not be viewed at enough angles to estimate contamination from torso activity. Also, VAOR geometries may involve camera tilt to scan for tumors near the chest wall. These tilted VAOR projections may be insufficient to establish even breast activity alone. Thus, we investigated the utility of designing VAOR systems to function inside some general-purpose horizontal-axis-of-rotation (HAOR) scanners, with the HAOR scanner orbiting a 192/spl deg/ angular range posteriorly, alleviating the insufficient-data problems. We simulated the expected projection data from six various-sized lesions with different activity concentrations in the breast and axilla, additionally considering the contribution from background activity from the torso. The data were then statistically reconstructed considering 360/spl deg/ HAOR, VAOR plus small additional arcs and combined HAOR-VAOR orbits, and the results were compared with the known activity concentration distribution. Substantial improvement in the noise versus bias was observed in the breast and axilla, an important and otherwise difficult region to image.

Dynamics in the Center Manifold Around L2 in the Quasi-Bicircular Problem

The quasi-bicircular problem (QBCP) is a restricted four body problem where three masses, Earth-Moon-Sun, are revolving in a quasi-bicircular motion (i.e. a coherent motion close to bicircular), the fourth mass being small and not influencing the motion of the three primaries. The QBCP is a Hamiltonian system with three degrees of freedom and depending periodically on time. The L2 point of the QBCP is defined geometrically. It is not an equilibrium point, but there is a small periodic orbit around L2, which has the same stability character center × center × saddle as the L2 libration point of the restricted three body problem (RTBP). The study of orbits around L2 can be useful for the design of future space missions. To give a full description of the different types of orbits in a neighbourhood of L2, it is necessary to skip the hyperbolic part of the Hamiltonian. This is accomplished by the computation of the Hamiltonian reduced to the center manifold around L2 up to high order. The methodology followed for our computations is explained in a general way so it can be applied to any other Hamiltonian system with an equilibrium point having some elliptic and some hyperbolic directions.

Risk Factors Associated With Complications of Orbital Surgery in Children

To assess the overall complication rate of orbitotomies performed in children and to determine the nature of complication to identify possible risk factors. Thirty children <13 years underwent 33 orbitotomies for space-occupying lesions of the orbit or orbital decompression. A detailed evaluation of the surgical procedures and outcomes was conducted. Follow up averaged 2.5 years (range: 6 months to 5 years). The complication rate was 20% (2 of 10 cases) for anterior orbitotomies, 40% (8 of 20 cases) for primary lateral orbitotomies, and 100% (3 of 3 cases) for secondary orbitotomies. Dense amblyopia was noted in 6 of 9 patients. Major complications were frozen eyeball, diplopia, and ptosis. Less serious complications were enophthalmos, internal ophthalmoplegia, dry eye, and eyelid retraction. Six patients underwent extraocular surgery, levator muscle surgery, or both at a later date. Although the scope of complications is the same in children as in adults, the frequency of cystic benign lesions and small orbits in children can cause more frequent serious complications. Additionally, dense amblyopia of a complicated nature makes visual outcome unpredictable. The most significant risk factors identified were the need for a secondary procedure for recurring pathology and the presence of an intraconal lesion.

On periodic homeomorphisms of spheres

The purpose of this paper is to study how small orbits of periodic homemorphisms of spheres can be.

A reevaluation of Proneotherium repenningi from the Miocene Astoria Formation of Oregon and its position as a basal odobenid (Pinnipedia: Mammalia)

ABSTRACT New crania, dentitions, and postcrania of the fossil pinniped, Proneotherium repenningi are described from the early to middle Miocene-age Astoria Formation of Lincoln County, Oregon. This sample includes specimens of four adult individuals; all probably males. The skull of Proneotherium repenningi shares many generalized features with basal pinnipeds (e.g., species of Enaliarctos) including its overall elongation, low profile, low sagittal crest, well developed lambdoidal crests, slender zygomatic arches, small orbits, slightly arched palate, dental formulae, and distinct embrasure pit. Proneotherium, however, differs from species of Enaliarctos in possession of a continuous and horizontal crest connecting the mastoid and paroccipital processes and in having a less secodont dentition. The molariform premolar dentition of Proneotherium is noteworthy and can be interpreted as representing the initial stage in a morphologic series that extends through Neotherium to Imagotaria. This morphologic series reflects a functional change from a shearing dentition to more of a piercing dentition and from a dentition capable of processing food (i.e., chewing) to a dentition that serves primarily to seize and hold prey. The hindlimb anatomy of Proneotherium provides important information concerning the evolution of aquatic adaptations and clearly shows that many pinniped innovations (short and broad femur, long and slender tibia, and elongated metatarsals I and V [relative to metatarsal III]) evolved very early. Evaluation of available specimens of Proneotherium supports recognition of a single species, Proneotherium repenningi. A cladistic analysis utilizing 24 cranial, dental and postcranial characters supports monophyly of the genus Proneotherium and suggests a close sister group relationship with another basal walrus, Prototaria. The parsimony analysis also confirms the monophyly of the Odobenidae, which is here defined as the clade containing the most recent common ancestor of Proneotherium and Odobenus and all of its descendants including Prototaria, Neotherium, Imagotaria, the dusignathines, and the odobenines.

The cranium of Parapithecus grangeri, an Egyptian Oligocene anthropoidean primate.

A nearly complete skull of Parapithecus grangeri from the early Oligocene of Egypt is described. The specimen is relatively undistorted and is undoubtedly the most complete higher primate skull yet found in the African Oligocene, which also makes it the most complete Oligocene primate cranium worldwide. Belonging in superfamily Parapithecoidea, a group regarded by some as the sister group to all other Anthropoidea, this skull reveals important information about the radiation of stem anthropoideans. This cranium is about 15% larger than size estimates based on a fragmentary cranium of its contemporary and close relative Apidium phiomense. It is about the same size as that of the gray gentle lemur, Hapalemur griseus, or of platyrrhines such as the owl monkey, Aotus trivirgatus, or the titi monkey, Callicebus torquatus. Comparatively small orbits and size differences in jaws and teeth show it was both diurnal and dimorphic. This is the only specimen of the species that shows (from sockets) that there were four small upper incisors. Several mandibular specimens of the species establish that there were no permanent lower incisors and that the symphysis was fused. Like other early anthropoideans this species possessed a lower encephalization quotient and less-developed orbital frontality than later anthropoideans. There is full postorbital closure and fusion of the metopic suture, and the ectotympanic forms a rim to the auditory aperture. A probable frontal/alisphenoid contact is a potentially derived resemblance to Catarrhini. A proposed separate genus for the species P. grangeri is not sustained.

Scientific objectives of the DYNAMO mission

DYNAMO is a small Mars orbiter planned to be launched in 2005 or 2007, in the frame of the NASA/ CNES Mars exploration program. It is aimed at improving gravity and magnetic field resolution, in order to better understand the magnetic, geologic and thermal history of Mars, and at characterizing current atmospheric escape, which is still poorly constrained. These objectives are achieved by using a low periapsis orbit, similar to the one used by the Mars Global Surveyor spacecraft during its aerobraking phases. The proposed periapsis altitude for DYNAMO of 120–130 km, coupled with the global distribution of periapses to be obtained during one Martian year of operation, through about 5000 low passes, will produce a magnetic/gravity field data set with approximately five times the spatial resolution of MGS. Additional data on the internal structure will be obtained by mapping the electric conductivity. Low periapsis provides a unique opportunity to investigate the chemical and dynamical properties of the deep ionosphere, thermosphere, and the interaction between the atmosphere and the solar wind, therefore atmospheric escape, which may have played a crucial role in removing atmosphere and water from the planet.

On the Origin of the Trojan Asteroids: Effects of Jupiter's Mass Accretion and Radial Migration

We present analytic and numerical results which illustrate the effects of Jupiter's accretion of nebular gas and the planet's radial migration on its Trojan companions. Initially, we approximate the system by the planar circular restricted three-body problem and assume small Trojan libration amplitudes. Employing an adiabatic invariant calculation, we show that Jupiter's 30-fold growth from a 10 M ⊕ core to its present mass causes the libration amplitudes of Trojan asteroids to shrink by a factor of about 2.5 to ∼40% of their original size. The calculation also shows that Jupiter's radial migration has comparatively little effect on the Trojans; inward migration from 6.2 to 5.2 AU causes an increase in Trojan libration amplitudes of ∼4%. In each case, the area enclosed by small tadpole orbits, if made dimensionless by using Jupiter's semimajor axis, is approximately conserved. Similar adiabatic invariant calculations for inclined and eccentric Trojans show that Jupiter's mass growth leaves the asteroids' eccentricities and inclinations essentially unchanged, while 1 AU of inward migration causes an increase in both of these quantities by ∼4%. Numerical integrations confirm and extend these analytic results. We demonstrate that our predictions remain valid for Trojans with small libration amplitudes even when the asteroids have low, but nonzero, eccentricities and inclinations and/or Jupiter has an eccentricity similar to its present value. The integrations also show that Trojans with large libration amplitudes, including horseshoe orbits, are even more strongly affected by Jupiter's mass growth and radial migration than simple scaling from our analytic results would suggest. Further, the numerical runs demonstrate that Jupiter's predicted mass growth is sufficient to cause the capture of asteroids initially on horseshoe orbits into stable tadpole orbits. Thus, if Jupiter captured most of its Trojan companions before or while it accreted gas, as seems probable, then Jupiter's growth played a significant role in stabilizing Trojan objects by systematically driving them to lower libration amplitudes.

A NEW TEMNOSPONDYL AMPHIBIAN FROM THE LATE TRIASSIC OF TEXAS

Abstract A skull representing a new genus and species of Late Triassic temnospondyl, Rileymillerus cosgriffi, is described from the Cooper Canyon Formation, upper Dockum Group of Garza County, Texas. Rileymillerus resembles Latiscopus disjunctus in size and proportions, but the very poorly preserved unique type specimen of L. disjunctus indicates that the taxon should be considered a nomen dubium. Characters of R. cosgriffi include its small size combined with relatively small laterally-facing orbits, relatively high skull, lack of lateral line canals, lateral exposure of the palatine on the skull surface, and lack of otic notch/quadrate angle. No postcranial material can be definitely associated, although we describe a partial vertebral column that might pertain to R. cosgriffi. Relationships of R. cosgriffi are uncertain. The possibilities of a close relationship to Almsauridae, Tupilakosauridae or (especially) Brachyopoidea are explicitly examined, but for the present we consider R. cosgriffi as Temnos...