Toroidal Region Research Articles

Estimation of the nozzle with the stepped divergent section in critical flow regime

A sonic nozzle with a toroidal inlet region, cylindrical throat and a stepped diffuser with cylindrical sections were considered. An analytical method was proposed for estimating the required pressure drop for the nozzle operating in a critical flow regime. The results of analytical estimation of the pressure buildup in the nozzle steps were compared with the ones of numerical simulation. It is shown that replacing the conical divergent section of ISO 9300 standard nozzle with easy-to-manufacture stepped divergent section leads to a twofold increase in the required pressure drop for the nozzle operating in the critical flow regime, which in many cases is acceptable.

Crust–magnetosphere coupling during magnetar evolution and implications for the surface temperature

We study the coupling of the force-free magnetosphere to the long-term internal evolution of a magnetar. We allow the relation between the poloidal and toroidal stream functions - that characterizes the magnetosphere - to evolve freely without constraining its particular form. We find that, on time-scales of the order of kyr, the energy stored in the magnetosphere gradually increases, as the toroidal region grows and the field lines expand outwards. This continues until a critical point is reached beyond which force-free solutions for the magnetosphere can no longer be constructed, likely leading to some large-scale magnetospheric reorganization. The energy budget available for such events can be as high as several $10^{45}\,$erg for fields of $10^{14}\,$G. Subsequently, starting from the new initial conditions, the evolution proceeds in a similar manner. The time-scale to reach the critical point scales inversely with the magnetic field amplitude. Allowing currents to pass through the last few meters below the surface, where the magnetic diffusivity is orders of magnitude larger than in the crust, should give rise to a considerable amount of energy deposition through Joule heating. We estimate that the effective surface temperature could increase locally from $\sim 0.1\,$keV to $\sim 0.3 - 0.6\,$keV, in good agreement with observations. Similarly, the power input from the interior into the magnetosphere could be as high as $10^{35} - 10^{36}\,$erg/s, which is consistent with peak luminosities observed during magnetar outbursts. Therefore, a detailed treatment of currents flowing through the envelope may be needed to explain the thermal properties of magnetars.

Basic Displacements in the Problem of Core Perturbations of a Thin Isochronous Vortex Ring

Periodic perturbations in the core of a thin isochronous vortex ring in an inviscid incompressible fluid are investigated in the linear approximation. The aim of the study is to construct the system of basic displacements, namely, the complete system of solutions of the Helmholtz equation for vorticity perturbations inside the core of a vortex ring with a given frequency in the form of expansion in the ring thinness parameter μ. The structure of basic displacements depends substantially on the fact to what extent the frequency of the forcing action is close to the resonance frequencies of the system. If the difference between these frequencies is small, then, in addition to the ring thinness μ, the second small parameters arises in the problem. This leads to significant complication of the procedure of obtaining the solution and appearance of considerable corrections in the subsequent approximations of the expansion procedure. The case of isochronous vortex ring in which the periods of revolution of liquid particles are identical is considered. Obtaining the threedimensional oscillations in such flows turns out to be the simplest since there are no perturbations of the continuous spectrum for the isochronous ring. The system of basic displacements is the necessary element in deriving the dispersion relation for the eigen-oscillations of the vortex ring. The solutions obtained can also serve as an instrument to analyze the reaction of flows with curvilinear vortex lines or flows localized in toroidal regions to the external excitation.

Dynamics and Formation of Obscuring Tori in AGNs

We considered the evolution of a self-gravitating clumpy torus in the gravitational field of the central mass of an active galactic nucleus (AGN) in the framework of the N-body problem. The initial conditions take into account winds with different opening angles. Results of our N-body simulations show that the clouds moving on orbits with a spread in inclinations and eccentricities form a toroidal region. The velocity of the clouds at the inner boundary of the torus is lower than in a disk model that can explain the observed rotation curves. We discuss the scenario of torus formation related with the beginning of the AGN stage.

The Størmer problem for an aligned rotator

The effective potential energy of the particles in the field of rotating uniformly magnetized celestial body is investigated. The axis of rotation coincides with the axis of the magnetic field. Electromagnetic field of the body is composed of a dipole magnetic and quadrupole electric fields. The geometry of the trapping regions is studied as a function of the magnetic field magnitude and the rotation speed of the body. Examples of the potential energy topology for different values of these parameters are given. The main difference from the classical St{\o}rmer problem is that the single toroidal trapping region predicted by St{\o}rmer is divided into equatorial and off-equatorial trapping regions. Applicability of the idealized model of a rotating uniformly magnetized sphere with a vacuum magnetosphere to real celestial bodies is discussed.

Global Current Circuit Structure in a Resistive Pulsar Magnetosphere Model

Abstract Pulsar magnetospheres have strong magnetic fields and large amounts of plasma. The structures of these magnetospheres are studied using force-free electrodynamics. To understand pulsar magnetospheres, discussions must include their outer region. However, force-free electrodynamics is limited in it does not handle dissipation. Therefore, a resistive pulsar magnetic field model is needed. To break the ideal magnetohydrodynamic (MHD) condition , Ohm’s law is used. This work introduces resistivity depending upon the distance from the star and obtain a self-consistent steady state by time integration. Poloidal current circuits form in the magnetosphere while the toroidal magnetic field region expands beyond the light cylinder and the Poynting flux radiation appears. High electric resistivity causes a large space scale poloidal current circuit and the magnetosphere radiates a larger Poynting flux than the linear increase outside of the light cylinder radius. The formed poloidal-current circuit has width, which grows with the electric conductivity. This result contributes to a more concrete dissipative pulsar magnetosphere model.

Ideal relaxation of the Hopf fibration

Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.

A comparison of outer electron radiation belt dropouts during solar wind stream interface and magnetic cloud driven storms

Energetic electrons are trapped in the Earth’s radiation belts which occupy a toroidal region between 3 and 7 \(\hbox {R}_{\mathrm{E}}\) above the Earth’s surface. Rapid loss of electrons from the radiation belts is known as dropouts. The source and loss mechanisms regulating the radiation belts population are not yet understood entirely, particularly during geomagnetic storm times. Nevertheless, the dominant loss mechanism may require an event based study to be better observed. Utilizing multiple data sources from the year 1997–2007, this study identifies radiation belt electron dropouts which are ultimately triggered when solar wind stream interfaces (SI) arrived at Earth, or when magnetic clouds (MC) arrived. Using superposed epoch analysis (SEA) technique, a synthesis of multiple observations is performed to reveal loss mechanism which might, perhaps, be a major contributor to radiation belt losses under SI and MC driven storms. Results show an abrupt slower decaying precipitation of electron peak (about 3000 counts/sec) on SI arrival within 5.05 \(< L\) < 6.05, which persist till 0.5 day before gradual recovery. This pattern is interpreted as an indication of depleted electrons from bounce lost cone via precipitating mechanism known as relativistic electron microburst. On the other hand, MC shows a pancake precipitating peak extending to lower L (Plasmapause); indicating a combination of electron cyclotron harmonic (ECH) and whistler mode waves as the contributing mechanisms.

Disjoining pressure and structure of a fluid confined between nanoscale surfaces

The grand canonical Monte Carlo (GCMC) simulation method has been used to estimate the disjoining pressure and to obtain the distribution of the density of the adsorbed Lennard-Jones fluid in finite narrow slits between nanosized surfaces of graphite. The influence of the radius of the cross section of the slit and the chemical potential on the properties has been considered. Different contributions from fluid-fluid, fluid-solid and solid–solid interactions to the solvation force have been analyzed. Significant effects of the chemical potential are observed for the finite slits. The oscillatory behaviour of the mean density and the disjoining pressure depends on the width of a finite slit is similarly to this of an infinite slit. A decrease of the chemical potential leads to some reduction of absolute values of the disjoining pressure and the mean density. Edge effects are exhibited in larger values of the local pressure on the central area of the finite slit than on its periphery. The toroidal region with a high concentration of the adsorbed fluid appears out of the slit near its edge. Predictions of the asymptotic theory for finite slits in equilibrium with liquid fluid phase have been confirmed.

Acoustic levitation of soap bubbles in air: Beyond the half-wavelength limit of sound

We report on the behavior of levitated soap bubbles in a single-axis acoustic field. For a single bubble, its surface in the polar regions is under compression, but in the equatorial region, it is under suction. Levitation becomes unstable when the height of the bubble approaches half the wavelength of the sound wave because horizontal fluctuations lead to a negative recovery force and a negative levitation force. Vertically stacked double bubbles notably can be stable under levitation if their total vertical length is ∼5λ/6, significantly beyond λ/2 in consequence of the formation of a toroidal high-pressure region around the waist of the two bubbles. Our results provide a deeper insight into the stability of acoustic levitation and the coupling between bubbles and sound field.

Non-stationary local thermoacoustic phase relationships in a gas turbine combustor

A framework is presented for analyzing the local instantaneous phase difference between non-stationary heat release rate and pressure oscillations that is appropriate for use in high-pressure liquid-fueled combustors. High-speed OH* chemiluminescence images were used as a qualitative marker of the heat release rate, from which the local phase shift relative to the pressure was calculated using the Hilbert transform technique. Two types of behavior were observed during time sequences with constant amplitude pressure oscillations. For the first behavior, a region with out-of-phase pressure and heat release rate oscillations moved upstream along the nozzle shear layer towards the nozzle. For the second behavior, transitions occurred between out-of-phase oscillations in a region along the centerline and a toroidal region close to the nozzle. For time periods with increasing amplitude pressure fluctuations, in-phase heat release rate and pressure oscillations developed throughout the upstream portion of the combustor. These in-phase oscillations could extend along the burner centerline and towards the downstream portion of the combustor. This behavior is reversed during time periods with decreasing amplitude pressure oscillations; the upstream portion of the combustor transitions to featuring regions with out-of-phase oscillations.

Stable photon orbits in stationary axisymmetric electrovacuum spacetimes

We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordstr\"om di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a di-hole, via a selection of Poincar\'e sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electrovacuum; but not in pure vacuum.

Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring

We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro-)vacuum exact solutions of Einstein's equations, we first considered the Majumdar--Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach--Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do {\em not} involve rotation and the negative value is achieved due to the {\em electric}-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather non-trivial landscapes {\em outside} the horizon.

Effects and Location of Coplanar and Noncoplanar PCB in a Lipid Bilayer: A Solid-State NMR Study.

Coplanar and noncoplanar polychlorinated biphenyls (PCBs) are known to have different routes and degree of toxicity. Here, the effects of noncoplanar PCB 52 and coplanar PCB 77 present at 2 mol % in a model system consisting of POPC liposomes (50% hydrated) are investigated by solid-state (13)C and (31)P NMR at 298 K. Both PCBs intercalate horizontally in the outer part of the bilayer, near the segments of the acyl chain close to the glycerol group. Despite similar membrane locations, the coplanar PCB 77 shows little effect on the bilayer properties overall, except for the four nearest neighboring lipids, while the effect of PCB 52 is more dramatic. The first ∼2 layers of lipids around each PCB 52 in the bilayer form a high fluidity lamellar phase, whereas lipids beyond these layers form a lamellar phase with a slight increase in fluidity compared to a bilayer without PCB 52. Further, a third high mobility domain is observed. The explanation for this is the interference of several high fluidity lamellar phases caused by interactions of PCB 52 molecules in different leaflets of the model bilayer. This causes formation of high curvature toroidal region in the bilayer and might induce formation of channels.

Gaussian beams for a linearized cold plasma confined in a torus

We consider a system of linear pde describing a cold plasma in a toroidal region in three-dimensional space. This system simulates the passage of a laser beam through the TOKAMAK, it consists of 9 equations for the electric field and the velocities of electrons and ions in a given magnetic field. Asymptotic solutions describing high-frequency Gaussian beams are constructed using the theory of Maslov complex germ in a fairly effective form. The solutions of the system are localized in the neighborhood of the beam passing through the toroidal domain (the camera). The equations for a ray take into account the density of particles in the camera and don't ``feel'' the presence of the magnetic field because of the high frequency of the Gaussian beam; the dependence on the magnetic field is contained in the amplitude of the electric field. Before the TOKAMAK camera the amplitude of the Gaussian beam is the same as in free space, but after the camera the amplitude vector rotates under the influence of the magnetic field. The formula for the angle of rotation is given explicitly. An analytical-numerical algorithm based on the asymptotic solutions is used to analyze the parameters of the magnetic field in the TOKAMAK.

INFRARED TIME LAGS FOR THE PERIODIC QUASAR PG 1302-102

The optical light curve of the quasar PG 1302-102 at z = 0.278 shows a strong, smooth 5.2 year periodic signal, detectable over a period of ~20 years. Although the interpretation of this phenomenon is still uncertain, the most plausible mechanisms involve a binary system of two supermassive black holes with a subparsec separation. At this close separation, the nuclear black holes in PG 1302-102 will likely merge within ~ 10^5 years due to gravitational wave emission alone. Here, we report the rest-frame near-infrared time lags for PG 1302-102. Compiling data from WISE and Akari, we confirm that the periodic behavior reported in the optical light curve from Graham et al. is reproduced at infrared wavelengths, with best-fit observed-frame 3.4 and 4.6 µm time lags of (2219 ± 153, 2408 ± 148) days for a near face-on orientation of the torus, or (4103 ± 153, 4292 ± 148) days for an inclined system with relativistic Doppler boosting in effect. The periodicity in the infrared light curves and the light-travel time of the accretion disk photons to reach the dust glowing regions support that a source within the accretion disk is responsible for the optical variability of PG 1302-102, echoed at the farther out dusty regions. The implied distance of this dusty, assumed toroidal region is ~1.5 pc for a near face-on geometry or ~1.1 pc for the relativistic Doppler-boosted case.

An Algorithm for Segmenting CAD Meshes Based on the Gaussian Map

Segmenting and recognizing the feature of CAD meshes enhance the efficiency of model reusing and editing in the design of complex mechanical products. An algorithm for segmenting CAD meshes based on the Gaussian map is presented. The Gaussian map of the triangular faces is constructed and the adjacent connectivity of the point in the Gaussian sphere is also created. The points are classified into several patches by k-means method, and each patch is separated into sub-patches by the region growing method. The small patch is merged into adjacent patch, and then the planar region, the cylindrical region, the conical region, the spherical region, and the toroidal region are recognized and merged into the similar regions based on the adjacent matrix of each patch. The empirical results show that the proposed algorithm is efficient and robust in clustering and recognizing CAD models of complex mechanical product.

Many-faced cells and many-edged faces in 3D Poisson–Voronoi tessellations

Motivated by recent new Monte Carlo data we investigate a heuristic asymptotic theory that applies to n-faced 3D Poisson–Voronoi cells in the limit of large n. We show how this theory may be extended to n-edged cell faces. It predicts the leading order large-n behavior of the average volume and surface area of the n-faced cell, and of the average area and perimeter of the n-edged face. Such a face is shown to be surrounded by a toroidal region of volume n/λ (with λ the seed density) that is void of seeds. Two neighboring cells sharing an n-edged face are found to have their seeds at a typical distance that scales as n−1/6 and whose probability law we determine. We present a new data set of 4 × 109 Monte Carlo generated 3D Poisson–Voronoi cells, larger than any before. Full compatibility is found between the Monte Carlo data and the theory. Deviations from the asymptotic predictions are explained in terms of subleading corrections whose powers in n we estimate from the data.

VORTEX CREEP AGAINST TOROIDAL FLUX LINES, CRUSTAL ENTRAINMENT, AND PULSAR GLITCHES

A region of toroidally oriented quantized flux lines must exist in the proton superconductor in the core of the neutron star. This region will be a site of vortex pinning and creep. Entrainment of the neutron superfluid with the crustal lattice leads to a requirement of superfluid moment of inertia associated with vortex creep in excess of the available crustal moment of inertia. This will effect constraints on the equation of state. The toroidal flux region provides the moment of inertia necessary to complement the crust superfluid with postglitch relaxation behavior fitting the observations.

Axisymmetric and stationary magnetic field structures in neutron star crusts under various boundary conditions

AbstractWe have calculated many Hall equilibrium states within the neutron star crust under various boundary conditions in order to investigate the influences of the boundary conditions clearly. We have found two important features of these solutions. First, the magnitude of the core magnetic fields affects the toroidal to total magnetic field energy ratio within the crust (Et/E). If the core magnetic fields are vanished, the crustal toroidal magnetic fields become weak and the typical energy ratio is only Et / E ~ 0.1%. If the core magnetic fields are strong, however, the crustal toroidal magnetic fields become strong and the typical ratio reaches Et / E ~ 15%. Second, the core toroidal magnetic fields and the twisted magnetosphere around the star make the size of the crustal toroidal magnetic field regions large. Therefore if the strong core magnetic fields have strong toroidal component, both strength and size of the crustal toroidal magnetic fields become large. These results show that the Hall MHD evolutions would be deeply affected by both inner and outer boundary conditions.