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Correlated effects of energetic electrons at 6.6 earth radius equator and auroral zone during magnetospheric substorms
The laminar flow between a rotating and a stationary disk with inflow was analyzed. Solutions to the dimensionless governing equations are sought by expanding each of the velocity components in powers of inverse radius. The equations to leading order are those for the configuration with no inflow. The subsequent orders yield sets of linear ordinary differential equations. Solutions are obtained for the first two of these subsequent orders. The solutions indicate that inflow tends to increase the magnitude of the azimuthal velocity in the flow between the two disks and to decrease the torque on the rotating disk. For Prandtl number one, an energy integral is obtained which relates the temperature distribution to the velocity distribution for all Reynolds numbers and therefore eliminates the needs for separate solution of the energy equation.
We describe the X-ray pulse profile models we use and how we use them to analyze Neutron Star Interior Composition Explorer(NICER)observations of rotation-powered millisecond pulsars to obtain information about the mass–radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. and Riley et al. and describe a cross-verification of computations of the pulse profiles of a star with R/M 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. and Riley et al. by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass–radius plane that are statistically consistent with one another, and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar’s spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in the estimates made using this technique, some of which may warrant further investigation.
We present the set of deep Neutron Star Interior Composition Explorer (NICER) X-ray timing observations of the nearby rotation-powered millisecond pulsars PSRs J0437−4715, J0030+0451, J1231−1411, and J2124−3358, selected as targets for constraining the mass–radius relation of neutron stars and the dense matter equation of state (EoS) via modeling of their pulsed thermal X-ray emission. We describe the instrument, observations, and data processing/reduction procedures, as well as the series of investigations conducted to ensure that the properties of the data sets are suitable for parameter estimation analyses to produce reliable constraints on the neutron star mass–radius relation and the dense matter EoS. We find that the long-term timing and flux behavior and the Fourier domain properties of the event data do not exhibit any anomalies that could adversely affect the intended measurements. From phase-selected spectroscopy, we find that emission from the individual pulse peaks is well described by a single-temperature hydrogen atmosphere spectrum, with the exception of PSR J0437−4715, for which multiple temperatures are required.
A bubble of air, trapped at the center of a spherical container of water on the surface of which spherical sound waves are maintained by transducers, may emit light, a phenomenon known as sonoluminescence. The surface of the bubble expands and contracts in obedience to the Rayleigh-Lamb equation, which requires knowledge of the gas pressure on the surface of the bubble. In many investigations of bubble pulsations, it is assumed that the air in the bubble moves adiabatically. To understand sonoluminescence, however, it is necessary to allow for the possibility that shocks are generated within the bubble. We couple the Rayleigh-Lamb equation governing the bubble radius to Euler's equations governing the motion of air in the bubble, and solve the two equations simultaneously. The air is modelled by a van der Waals gas. Results are presented for a number of slightly different conditions of excitation, but in which the response of the system is widely different.
We have developed a global fully three-dimensional magnetohydrodynamic solar wind model for the region that extends from the coronal base to 100 AU. The simulation domain consists of tree spherical shell subdomains with computational boundaries between them placed at 20 solar radii and 0.3 AU. The location of the first boundary ensures that the flow at the boundary is both supersonic and super-Alfvenic. A steady-state solution in the innermost (coronal) region is obtained by the time-relaxation method. The solution uses a tilted dipole model or solar magnetograms as the boundary condition at the coronal base and includes a flux of Alfven waves in the WKB approximation which provide additional acceleration for the coronal outflow in the open field regions. The intermediate region solution is constructed by the integration of steady-state equations along radius using a marching scheme. The outer region solution (0.3-100 AU) is obtained again by the time relaxation and takes into account turbulence transport and heating as well as heating, flow deceleration, and other effects due to the interstellar pickup protons treated as a separate fluid. We use the model to simulate the global steady-state structure of the solar wind from the coronal base to the heliospheric boundary and compare the results with Ulysses and Voyager observations.
Bridgman crystal growth can be conducted in the so-called "detached" solidification regime, where the growing crystal is detached from the crucible wall. A small gap between the growing crystal and the crucible wall, of the order of 100 micrometers or less, can be maintained during the process. A meniscus is formed at the bottom of the melt between the crystal and crucible wall. Under proper conditions, growth can proceed without collapsing the meniscus. The meniscus shape plays a key role in stabilizing the process. Thermal and other process parameters can also affect the geometrical steady-state stability conditions of solidification. The dynamic stability theory of the shaped crystal growth process has been developed by Tatarchenko. It consists of finding a simplified autonomous set of differential equations for the radius, height, and possibly other process parameters. The problem then reduces to analyzing a system of first order linear differential equations for stability. Here we apply a modified version of this theory for a particular case of detached solidification. Approximate analytical formulas as well as accurate numerical values for the capillary stability coefficients are presented. They display an unexpected singularity as a function of pressure differential. A novel approach to study the thermal field effects on the crystal shape stability has been proposed. In essence, it rectifies the unphysical assumption of the model that utilizes a perturbation of the crystal radius along the axis as being instantaneous. It consists of introducing time delay effects into the mathematical description and leads, in general, to stability over a broader parameter range. We believe that this novel treatment can be advantageously implemented in stability analyses of other crystal growth techniques such as Czochralski and float zone methods.
Radial intensity scans of a Voyager 2 high phase angle image of Titan have been inverted to yield vertical extinction profiles at 1 deg intervals around the limb. A detached haze layer with peak particle number densities of about 0.2 cu/cm exists at all latitudes south of about 45 N, and at an altitude of 300-350 km. The optical depth 0.01 level lies at a radius of 2932 + or - 5 km at the equator and at a radius of 2915 + or - 10 km over the poles (altitudes of 357 + or - 5 and 340 + or - 10 km, respectively). In addition to the haze layer at 300-350 km, there is a small enhancement in the extinction at about 450 km which exists at all latitudes between 75 deg S and about 60 deg N.
Visual photometry, which measures reflected solar radiation, can be combined with infrared radiometry, which measures absorbed and reradiated solar energy, to determine the albedo and hence the radius of small solar system objects. Equations and graphical solutions for radius and albedo are presented for cases where the object is at opposition, in equilibrium with the insolation, and has unit values for phase integral and infrared emissivities. Each of these assumptions is then discussed, and expressions are given for the dependence of the derived parameters on the assumptions. The Galilean satellites, whose radii are well known, provide a calibration of this technique. Applications are then discussed to Saturn's satellites Iapetus and Rhea and to asteroids (1) Ceres, (4) Vesta, and (324) Bamberga. It is shown that the technique is not subject to major systematic errors and that it is possible to derive radii, particularly for dark objects, with uncertainties of less than 10%.
An aerothermodynamic analysis of the forebody aeroshell of the Stardust Sample Return Capsule is carried out by using the axisymmetric viscous shock-layer equations with and without fully coupled radiation and ablation. Formulation of the viscous shock-layer equations with shoulder radius as the length scale and implementation of the Vigneron pressure condition allow resolution of the flowfield over the shoulder. With a predominantly supersonic outflow over the shoulder, a globally iterated solution or viscous shock-layer equations can be obtained. The stagnation-point results are obtained along a specified trajectory, whereas detailed calculations along the body are provided at the peak-heating point. The equilibrium calculations with ablation injection are the focus of the present study because of the lack of a general chemical nonequilibrium analysis that accounts for both surface and flowfield effect. The equilibrium calculations also provide a simple way to conserve surface (and flowfield) elemental composition for the current small ablation injection rates, where the surface elemental composition is a mixture of freestream and ablator elements. Therefore, the coupled laminar and turbulent flow solutions with radiation and ablation are obtained by using the equilibrium flow chemistry, whereas a nonequilibrium chemistry model is used for solutions without ablation and turbulence. Various computed results are compared with those obtained by the other researchers.
Finite beta effects on interchange mode in weakly unstable plasma calculated in finite Larmor radius limit - differential equation to obtain stability properties of arbitrary systems
Laminar collisionless fast and slow shock wave theory by finite-Larmor-radius hydromagnetic fluid equations
Orbit determination from two position vectors and periapsis radius, introducing polar equation for conic to obtain solution
After the corotation resonance with an exterior satellite proved inapplicable to the Neptune ring arc confinement, a search for other mechanisms settled on the possible influence of Neptune's magnetic field. The areas of greater optical depth around the ring are much dustier than the low optical depth regions. These particles reside in a plasma; therefore, they must carry some charge. The components of Neptune's magnetic field on the equator at the radius of the ring arcs as a function of Neptunian longitude are shown. The components are those of an offset tilted dipole model. Although the dipole model is probably not a good approximation so close to the planet, the magnitude of the field that is given is probably close to the actual value. The possible importance of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic force to the central gravitation attraction with the field strength of B = 0.01 gauss at the ring distance. A preferred position in the orbit for magnetically perturbed particles seems to require a commensurability between the rotation of the planet and the motion of the particle in the orbit. The period of rotation is assumed to be that of the radio bursts at 16.11 hours. However, without a model for the radio emission, one cannot be absolutely sure. Jupiter's decametric radiation depends on Io's orbital position as well as the rotation, so a synodic periodicity might be appropriate. But the latter radiation is highly directed, whereas Neptune's was seen all along the spacecraft trajectory on the 16.11 hour schedule, i.e., with no shifts in phase relative to a fixed longitude on the planet. The ring orbital period is 10.536 hours which is not commensurate with the rotation period. If the 16.11 hours is interpreted as a synodic period between the rotation and a satellite motion, the closest rotation periods to 16 hours are 15.9 hours if the satellite is 1989N4 and 18.2 hours if the satellite is Triton. The former is near a 3:2 resonance with the ring particle motion. The problem deserves some more thought before a possible herding of small particles by the magnetic field is abandoned.
This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.
The motion of the bubble radius and of the air trapped inside the bubble during sonoluminescence are determined self-consistently by coupling the solution of the Rayleigh-Plesset equation governing the bubble radius to the solution of Euler's equations for the motion of air in the bubble. Results are presented for three slightly different conditions of excitation, in two of which shocks are formed during the collapse of the bubble, and in which such high temperatures are attained that the air is ionized. Estimates are made of the duration and intensity of the light then radiated by the plasma.
Series inverse in powers of time and radius of convergence for universal form of Kepler equation, discussing recursion formulas for coefficients
Coplanar waveguide (CPW) and grounded coplanar waveguide (GCPW) radial line double stub resonators are experimentally characterized with respect to stub radius and sector angle. A simple closed-form design equation, which predicts the resonance radius of the stub, is presented. Use of a double stub resonator as a lowpass filter or as a harmonic suppression filter is demonstrated, and design rules are given.