Symplectic adaptive algorithm for solving nonlinear two-point boundary value problems in Astrodynamics

In this paper, from a Hamiltonian point of view, the nonlinear optimal control problems are transformed into nonlinear two-point boundary value problems, and a symplectic adaptive algorithm based on the dual variational principle is proposed for solving the nonlinear two-point boundary value problem. The state and the costate variables within a time interval are approximated by using the Lagrange polynomial and the costate variables at two ends of the time interval are taken as independent variables. Then, based on the dual variational principle, the nonlinear two-point boundary value problems are replaced by a system of nonlinear equations which can preserve the symplectic structure of the nonlinear optimal control problem. Furthermore, the computational efficiency of the proposed symplectic algorithm is improved by using the adaptive multi-level iteration idea. The performance of the proposed algorithm is tested by the problems of Astrodynamics, such as the optimal orbital rendezvous problem and the optimal orbit transfer between halo orbits.     

Anomalous magnetic viscosity in accretion disks with q-distributed plasmas

Based on the equations of the self-generated magnetic field in the q-distributed plasmas, the studies show that the magnetic field is modulationally unstable by the perturbation method and the equations have self-similar collapse solution. The anomalous magnetic viscosity of accretion disks generates from highly spatially intermittent flux of the self-generated magnetic field. In addition, the anomalous viscosity coefficient is 8 orders more than the molecular viscosity and is modified by the adjustable index q, which may preferably explain the observations.     

The Plasma and Magnetic Field Characteristics of a Double Discontinuity in Interplanetary Space

A double discontinuity is a rarely observed compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer in the downstream region. In this paper, we report the observations of a double discontinuity detected by Wind on May 15, 1997. This double discontinuity is found to be the front boundary of a magnetic cloud boundary layer. We strictly identify the shock layer and the rotational discontinuity layer by using the high-resolution plasma and magnetic field data from Wind. The observed jump conditions of the upstream and downstream region of the slow shock layer are in good agreement with the Rankine – Hugoniot relations. The flow speeds in the shock frame U _n <V _Acos θ _Bn on both sides of the slow shock layer. In the upstream region, the slow Mach number M _s1=U _n1/V _s1 is 1.95 (above unity), and in the downstream region, the slow Mach number M _s2=U _n2/V _s2 is 0.31 (below unity). Here V _A and V _s represent the Alfvén speed and the local slow magnetosonic speed, respectively, and θ _Bn is the angle between the direction of the magnetic field and the shock normal. The magnetic cloud boundary layer observed by Wind was also detected by Geotail 48 min later when the spacecraft was located outside the bow shock of the magnetosphere. However, Geotail observations showed that its front boundary was no longer a double discontinuity and the rotational discontinuity layer disappeared, indicating that this double discontinuity was unstable when propagating from Wind to Geotail.     

J1128+592: a highly variable IDV source

Short time‐scale radio variations of compact extragalactic radio quasars and blazars known as IntraDay Variability (IDV) can be explained in at least some sources as a propagation effect; the variations are interpreted as scintillation of radio waves in the turbulent interstellar medium of the Milky Way. One of the most convincing observational arguments in favor of a propagation‐induced variability scenario is the observed annual modulation in the characteristic time scale of the variation due to the Earth's orbital motion. So far there are only two sources known with a well‐constrained seasonal cycle. Annual modulation has been proposed for a few other less well‐documented objects. However, for some other IDV sources source‐intrinsic structural variations which cause drastic changes in the variability time scale were also suggested. J1128+592 is a recently discovered, highly variable IDV source. Previous, densely time‐sampled flux‐density measurements with the Effelsberg 100‐m radio telescope (Germany) and the Urumqi 25‐m radio telescope (China), strongly indicate an annual modulation of the time scale. The most recent 4 observations in 2006/7, however, do not fit well to the annual modulation model proposed before. In this paper, we investigate a possible explanation of this discrepancy. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

Radio Observations at 232 MHz and Multifrequency Spectral Studies of SNR HB21

Radio observational results at 232 MHz and multifrequency studies of supernova remnant (SNR) HB21 are presented. Its integrated flux density at 232 MHz is about 390 ± 30 Jy. Both the integrated spectral index and the spatial variations of spectral index of the remnant were calculated by combining the new map at 232 MHz with previously published maps made at 408, 1420, 2695, and 4750 MHz. The SNR has an integrated spectral index of about α = -0.43(S _ν ∝ ν^α) between 232 and 4750 MHz. In general the spectral index varies from –0.5 in southeast and west regions of the remnant to –0.3 in the central region and near the northwest edge. The new data of 232 MHz reveals that there is interaction between the remnant and the surrounding gas along the east edge of the remnant which causes the spectrum flattening at low frequency, while the very good agreement between the structure of X-ray emission and the central flat spectrum area suggests that the existence of thermal emission is the reason of spectrum flattening in the area. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytical Study of Supernova Remnant Non-Stationary Expansions

We study analytically the Rayleigh–Taylor instability in expanding supernova gas shell. The instability appears at the inner shell surface accelerated by blowing pulsar wind. The most dangerous perturbations correspond to wavelengths comparable to the shell thickness. We analyze the fragility of the supernova remnant shell in function of the initial perturbation amplitude and the shell thickness.     

Short-Term Periodicity in Solar Mean Magnetic Field during Activity Maximum and Minimum Periods

The short-term periodicity in the solar mean magnetic field (SMMF) observed at the Wilcox Solar Observatory during the last four activity cycles is investigated by using Lomb?CScargle periodograms. Our results show that the SMMF has main periods of about 27, 13.5, and 9 days in both the maximum and minimum years of each activity cycle. The SMMF has the most dominant period of about 27 days during the activity maxima. However, during the activity minimum years the 13.5-day periodicity is the most significant, except for the minimum of 1984??C?1986. These results indicate that the distribution of active regions in the activity maximum years is quite different from that in the minimum years.     

Comparison of Line-of-Sight Magnetograms Taken by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager and Solar and Heliospheric Observatory/Michelson Doppler Imager

We compare line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) and the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). The line-of-sight magnetic signal inferred from the calibrated MDI data is greater than that derived from the HMI data by a factor of 1.40. This factor varies somewhat with center-to-limb distance. An upper bound to the random noise for the 1′′ resolution HMI 720-second magnetograms is 6.3 Mx?cm^?2, and 10.2 Mx?cm^?2 for the 45-second magnetograms. Virtually no p-mode leakage is seen in the HMI magnetograms, but it is significant in the MDI magnetograms. 12-hour and 24-hour periodicities are detected in strong fields in the HMI magnetograms. The newly calibrated MDI full-disk magnetograms have been corrected for the zero-point offset and underestimation of the flux density. The noise is 26.4 Mx?cm^?2 for the MDI one-minute full-disk magnetograms and 16.2 Mx?cm^?2 for the five-minute full-disk magnetograms observed with four-arcsecond resolution. The variation of the noise over the Sun’s disk found in MDI magnetograms is likely due to the different optical distortions in the left- and right-circular analyzers, which allows the granulation and p-mode to leak in as noise. Saturation sometimes seen in sunspot umbrae in MDI magnetograms is caused by the low intensity and the limitation of the onboard computation. The noise in the HMI and MDI line-of-sight magnetic-field synoptic charts appears to be fairly uniform over the entire map. The noise is 2.3 Mx?cm^?2 for HMI charts and 5.0 Mx?cm^?2 for MDI charts. No evident periodicity is found in the HMI synoptic charts.