Case Of Orbits Research Articles

The stress–pressure lag in MRI turbulence and its implications for thermal instability in accretion discs

ABSTRACT The classical alpha-disc model assumes that the turbulent stress scales linearly with – and responds instantaneously to – the pressure. It is likely, however, that the stress possesses a non-negligible relaxation time and will lag behind the pressure on some time-scale. To measure the size of this lag we carry out unstratified 3D magnetohydrodynamic shearing box simulations with zero-net-magnetic-flux using the finite-volume code pluto. We impose thermal oscillations of varying periods via a cooling term, which in turn drives oscillations in the turbulent stress. Our simulations reveal that the stress oscillations lag behind the pressure by ∼5 orbits in cases where the oscillation period is several tens of orbits or more. We discuss the implication of our results for thermal and viscous overstability in discs around compact objects.

Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials

We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral galaxies. These potentials are known for providing building blocks to support observed features such as the peanut, or X-shaped bulge, in the former case and the spiral arms in the latter. We investigate the possibility that these structures are reinforced, apart by regular orbits, also by orbits in the vicinity of complex unstable periodic orbits. We examine the evolution of the phase space structure in the immediate neighbourhood of the periodic orbits in cases where the stability of a family presents a successive transition from stability to complex instability and then to stability again, as energy increases. We find that we have a gradual reshaping of invariant structures close to the transition points and we trace this evolution in both models. We conclude that for time scales significant for the dynamics of galaxies, there are weakly chaotic orbits associated with complex unstable periodic orbits, which should be considered as structure-supporting, since they reinforce the morphological features we study.

Stable habitable zones of single Jovian planet systems

With continued improvement in telescope sensitivity and observational techniques, the search for rocky planets in stellar habitable zones is entering an exciting era. With so many exoplanetary systems available for follow-up observations to find potentially habitable planets, one needs to prioritise the ever-growing list of candidates. We aim to determine which of the known planetary systems are dynamically capable of hosting rocky planets in their habitable zones, with the goal of helping to focus future planet search programs. We perform an extensive suite of numerical simulations to identify regions in the habitable zones of single Jovian planet systems where Earth mass planets could maintain stable orbits, specifically focusing on the systems in the Catalog of Earth-like Exoplanet Survey Targets (CELESTA). We find that small, Earth-mass planets can maintain stable orbits in cases where the habitable zone is largely, or partially, unperturbed by a nearby Jovian, and that mutual gravitational interactions and resonant mechanisms are capable of producing stable orbits even in habitable zones that are significantly or completely disrupted by a Jovian. Our results yield a list of 13 single Jovian planet systems in CELESTA that are not only capable of supporting an Earth-mass planet on stable orbits in their habitable zone, but for which we are also able to constrain the orbits of the Earth-mass planet such that the induced radial velocity signals would be detectable with next generation instruments.

Partial integrability of 3d Bohmian trajectories

In this paper we study the integrability of 3d Bohmian trajectories of a system of quantum harmonic oscillators. We show that the initial choice of quantum numbers is responsible for the existence (or not) of an integral of motion which confines the trajectories on certain invariant surfaces. We give a few examples of orbits in cases where there is or there is not an integral and make some comments on the impact of partial integrability in Bohmian Mechanics. Finally, we make a connection between our present results for the integrability in the 3d case and analogous results found in the 2d and 4d cases.

Skull Metastasis From Intrahepatic Cholangiocarcinoma: Report of 3 Cases and Review of the Literature

Skull metastases occur in patients with various malignancies; however, those resulting from intrahepatic cholangiocarcinoma (ICC) have been rarely reported. In our hospital, 324 patients were diagnosed with metastatic brain or skull tumors from June 1969 to June 2011, but only 3 of them (0.9%) developed skull metastases from ICC. We report the case of 3 patients with skull metastases from ICC. A combination of computed tomography (CT), contrast-enhanced magnetic resonance imaging (MRI), 18F-fluorodeoxyglucose positron emission tomography (FDG-PET), and methionine-PET were used for imaging. Sites of tumors were the lateral left orbit and right parietal bone in case 1, the left parietal bone, left temporal bone, and lateral left orbit in case 2, the right petrous bone, right occipital bone, and upper cervical vertebra in case 3. The metastases were confirmed to have originated from ICC by biopsy in two of the cases and diagnosed by MRI and FDG-PET in case 2. Radiosurgery and radiotherapy had positive effects on symptom improvement and cosmetic problems.

Optimal reorientation of a spacecraft's orbit using a jet thrust orthogonal to the orbital plane

The problem of the optimal control of the orientation of a spacecraft's orbit using magnitude-constrained control, i.e., the jet thrust vector perpendicular to the orbital plane, is considered. Under such control the spacecraft's orbit rotates in space as an unalterable (non-deformable) figure. A combined functional, equal to the weighted sum of the reorientation time and an integral quadratic (with respect to the control) quality functional, or equal to the weighted sum of the reorientation time and the control momentum (the characteristic velocity) during reorientation of the orbit serves as an optimality criterion. A quaternion differential equation of the orientation of the orbital system of coordinates and the maximum principle are used to solve the problem. A differential boundary-value problem with a dimension of ten is formulated to construct the optimal control and the optimal trajectory for reorientating the orbit. Control laws that satisfy the necessary optimality conditions are obtained (in the form of functions of conjugate variables). Quaternion and scalar first integrals of the equations of the problem are found, and transversality conditions that do not contain Lagrange undetermined multipliers are devised. It is shown that the original boundary-value problem reduces (with simultaneous simplification of the equations of the problem) to a new boundary-value problem of a smaller dimension equal the three, whose equations for a circular orbit in the case of maximum speed are integrated in trigonometric functions. Such a reduction is possible owing to the self-conjugation of the quaternion differential equation of the orientation of the orbital system of coordinates of the spacecraft and the use of a new quaternion variable that is related to the quaternion first integral by a rotational transformation. It is found that the switching function of the control is described by a system of three first-order differential equations, which reduce to a linear inhomogeneous second-order equation with constant coefficients for a circular orbit in the time-optimal case and to the Duffing equation in the case of an integral quadratic quality functional. It is also shown that for a circular orbit in the time-optimal case the problem reduces to solving a third-order non-linear algebraic system. An example of a numerical solution of the problem is presented. ©2012.

Plain X-ray and computed tomography of the orbit in cases and suspected cases of intraocular foreign body

To evaluate the roles of plain X-ray and computed tomography (CT) orbital imaging in cases and suspected cases of intraocular foreign body (IOFB). Retrospective review of clinical and radiological data relating to 204 consecutive cases and suspected cases of IOFB.SettingRoyal Victoria Eye and Ear Hospital, Dublin, Ireland. Plain X-rays were performed in the absence of clinically evident ocular penetration in 177 (87%) cases, and no IOFB was demonstrated in any of these radiographs. Twenty-seven (13%) plain X-ray radiographs were obtained in the presence of clinically evident ocular penetration, and an IOFB was clinically visible in 19 (70%) of these cases. CT scans were undertaken in 21 (10%) of the 204 patients. Of these CT images, 9 (43%) and 12 (57%) were undertaken in the absence and presence of clinically evident ocular penetration, respectively. None (0%) and all (100%) of the CT scans obtained in the absence and presence of clinically evident ocular penetration demonstrated an IOFB, respectively. Plain X-ray and CT orbital imaging are non-contributory in the absence of clinically evident ocular penetration. In the presence of clinically evident ocular penetration, and where an IOFB is clinically visible, plain X-ray orbital radiography may have a role in excluding multiple IOFBs. In the presence of clinically evident ocular penetration, but where an IOFB is not clinically visible, CT orbital imaging remains the investigation of choice, and the role of pre-CT plain X-ray orbital radiography, as recommended by the guidelines of the Royal College of Radiologists, merits re-evaluation.

Particle swarm optimization: an efficient method for tracing periodic orbits in three-dimensional galactic potentials

We propose particle swarm optimization (PSO) as an alternative method for locating periodic orbits in a three-dimensional (3D) model of barred galaxies. We develop an appropriate scheme that transforms the problem of finding periodic orbits into the problem of detecting global minimizers of a function, which is defined on the Poincare surface section of the Hamiltonian system. By combining the PSO method with deflection techniques, we succeeded in tracing systematically several periodic orbits of the system. The method succeeded in tracing the initial conditions of periodic orbits in cases where Newton iterative techniques had difficulties. In particular, we found families of two- and three-dimensional periodic orbits associated with the inner 8:1 to 12:1 resonances, between the radial 4:1 and corotation resonances of our 3D Ferrers bar model. The main advantages of the proposed algorithm are its simplicity, its ability to work using function values solely, and its ability to locate many periodic orbits per run at a given Jacobian constant. Ke yw ords: methods: numerical - galaxies: kinematics and dynamics - galaxies: structure.

Three-vortex motion with zero total circulation: Addendum

Beginning with general remarks on vortex systems with zero net circulation, the three-vortex problem is considered and solved explicitly in the following special cases: 1. The distance between two vortices is small compared to the distance to the third, with two subcases: the neighboring vortices (i) have the same sign, (ii) have opposite signs. 2. The impulse of the system is small compared to the product of a typical vortex strength and the biggest distance found (at any time) between vortices. Formulas and rules for the construction of the orbits in case 2 are given; they include the circular paths that are found for zero impulse. These special cases are typical for the orbits in the different regions found between the separatrices of the Hamiltonian. Transitional paths are discussed in the case where the vortex circulations have the ratio 1∶1∶−2. In this case, it is shown (by inspection) that the Hamiltonian is a harmonic function. Actually, the Hamiltonian is a harmonic function whenever the sum of the three circulations is zero, as shown in an “Addendum” by Prof. Hassan Aref. This is an essential result for the full understanding of the problem under consideration.