The 2-D lattice theory of Flower Constellations

The 2-D lattice theory of Flower Constellations, generalizing Harmonic Flower Constellations (the symmetric subset of Flower Constellations) as well as the Walker/ Mozhaev constellations, is presented here. This theory is a new general framework to design symmetric constellations using a $2\times 2$ 2 × 2 lattice matrix of integers or by its minimal representation, the Hermite normal form. From a geometrical point of view, the phasing of satellites is represented by a regular pattern (lattice) on a two-Dimensional torus. The 2-D lattice theory of Flower Constellations does not require any compatibility condition and uses a minimum set of integer parameters whose meaning are explored throughout the paper. This general minimum-parametrization framework allows us to obtain all symmetric distribution of satellites. Due to the $J_2$ J 2 effect this design framework is meant for circular orbits and for elliptical orbits at critical inclination, or to design elliptical constellations for the unperturbed Keplerian case.     

3-Dimensional Necklace Flower Constellations

A new approach in satellite constellation design is presented in this paper, taking as a base the 3D Lattice Flower Constellation Theory and introducing the necklace problem in its formulation. This creates a further generalization of the Flower Constellation Theory, increasing the possibilities of constellation distribution while maintaining the characteristic symmetries of the original theory in the design.     

Secular frequencies of 3-D exoplanetary systems

Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes. Anne-Sophie Libert is FNRS Research Fellow.     

3-D Helioseismology: Rings and Horizontal Flows

We investigate the conditions under which general scalar-tensor gravity theories relax towards General Relativity. We extend the work of Damour and Nordtvedt [2] by studying the effects of the inclusion of a cosmological potential term. When the universe is either radiation dominated or vacuum, we find that Einstein's gravity is indeed a cosmological attractor and, also, that the universe exhibits inflationary expansion. This latter feature provides another striking argument in favour of the inflationary paradigm, which in the present setting arises without the intervention of the usual inflaton field. This revised version was published online in July 2006 with corrections to the Cover Date.     

3-D period doubling and magnetic moments of particles

Several invariant properties of matter seem to fit remarkably well to quantized values obtained from Planck domain units by period doubling in three dimensions. The units are defined using natural constants only. Such properties include the elementary electric charge, electron and proton rest energies and others. It has been shown by W. G. Tifft that the quantized redshifts of galaxies fit the pattern, too. Magnetic moments of the electron, proton, neutron, muon and lambda particles also seem to obey the doubling rule. The same number of doublings seems to yield the electron and proton rest masses and magnetic moments correspondingly. The proton rest mass is E₀×2^–64 and the magnetic moment µ _o × 2⁶⁴, where E₀ and µ _o are the Planck domain units. The corresponding exponent of 2 for the electron is 75.66. The units for the proton and the electron differ by a factor of . The magnetic moment of the muon suggests a close relationship between the magnetic structures of the muon and the proton, whereas the lambda particle seems to be related to the neutron. Reasons for the supposed existence of quantized 3-d time are represented.     

基于iHCO通信卫星的CAPS星座优化研究

中国区域定位系统(Chinese Area Positioning System,CAPS)把寿命末期的地球静止轨道(Geostationary Earth Orbit,GEO)通信卫星推到比GEO轨道高约200 km的倾斜高圆轨道(inclined Highly Circular Orbit,iHCO),卫星相对地球向西漂移。利用该类卫星组建CAPS导航星座,可以实现全球范围内的导航通信覆盖。重点开展基于iHCO通信卫星的CAPS星座优化研究,结果表明:利用GEO通信卫星和iHCO通信卫星组成的星座可以实现较好的空间星座布局,可以满足一般导航用户的需要。     

The MSDOL Project: Assimilation of Gomos Ozone Data in a 3-D chemistry-transport model

In the frame of the preparation of the use of ENVISAT data, the EEC is supporting the MSDOL project: Monitoring of the Stratospheric Depletion of the Ozone Layer. The purpose is to assimilate the 400 vertical profiles of Ozone recorded each day by the experiment GOMOS (on the future ESA ENVISAT spacecraft ) in a 3-D chemistry-transport model, where the winds are the ECMWF analysis. The sequentially assimilated model will better represent the reality since all single measurements are extrapolated in space and time through chemistry and transport. The assimilated model will serve at least two purposes : the comparison with other data sets, and the estimate of the evolution of ozone as a function of time and space.The 3-D model is derived from the stratospheric chemistry-transport Rose model, in which the internally generated dynamics is replaced by the actual wind field.     

3-D radiative line transfer for be star envelopes

Based on numerical three-dimensional radiative line transfer calculations H emission line profiles of circumstellar Be star envelopes have been derived. The results show that the socalled winebottle-type emission line profiles can be explained by the combination of rotational broadening and non-coherent scattering in optically thick Keplerian disks. In a further calculation the stellar wind model of Be star envelopes has been re-investigated assuming an additional expansion component in the velocity field. The resulting asymmetric winebottle-type profiles and asymmetric shell-type emission lines with blue-shifted central depressions are in contradiction with the observed line shapes. It is concluded that isotropic stationary outflows are not suitable to explain observed asymmetric emission line profiles of Be stars.     

传统星座的五帝座考证

中国传统星座中的紫微垣五帝内座和太微垣五帝座,都是古人为天上最高统治者天帝,在一年不同的五时处于不同方位处理政务而设的坐位。将五帝座作黄帝和四方之帝的坐位是"纬书"类的附会,与星座命名的本义相悖,由此造成不必要的混乱,一直延续至今,因此就有必要进行考证,给予澄清。     

A multi-spiral set of solutions of a 3-D Hamiltonian system

Various sets of periodic solutions of a 3-D Hamiltonian system crossing perpendicularly thez=0 plane are presented. These sets form a main multi-spiral pattern and two secondary ones which have three focal points. The main pattern is inside a stochastic region that surrounds a simple complex unstable periodic orbit, while the two secondary patterns are parts of a stochastic sea. Through these regions the stochastic region communicates with the stochastic sea.     

A global numerical 3-D MHD model of the solar wind

A fully three-dimensional, steady-state global model of the solar corona and the solar wind is developed. A numerical, self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and the Earth's orbit. Boundary conditions are provided by the solar magnetic field observations. A steady-state solution is sought as a temporal relaxation to the dynamic equilibrium in the region of transonic flow near the Sun and then traced to the orbit of the Earth in supersonic flow region. The unique features of the proposed model are: (a) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (b) inferring the global structure of the interplanetary medium between the solar photosphere and 1 AU based on large-scale solar magnetic field data. As an experimental test for the proposed technique, photospheric magnetic field data for CR 1682 are used to prescribe boundary condition near the Sun and results of a simulation are compared with spacecraft measurements at 1 AU. The comparison demonstrates a qualitative agreement between computed and observed parameters. While the difference in densities is still significant, the 3-D model better reproduces variations of the solar wind velocity than does the 2-D model presented earlier (Usmanov, 1993).     

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A global 3-D simulation of interplanetary dynamics in June 1991

The global dynamics of the solar wind and interplanetary magnetic field in June 1991 is simulated based on a fully three-dimensional, time-dependent numerical MHD model. The numerical simulation includes eight transient disturbances associated with the major solar flares of June 1991. The unique features of the present simulation are: (i) the disturbances are originated at the coronal base (1R _s) and their propagation through inhomogeneous ambient solar wind is simulated out to 1.5 AU; (ii) as a background for the transients, the global steady-state solar wind structure inferred from the 3-D steady-state model (Usmanov, 1993c) is used. The parameters of the initial pulses are prescribed in terms of the near-Sun shock velocities (as inferred from the metric Type II radio burst observations) relative to the preshock steady-state flow parameters at the flare sites. The computed parameters at the Earth's location for the period 1–18 June, 1991 are compared with the available observations of the interplanetary magnetic field, solar wind velocity, density, and with variation of the geomagnetic activityK _pindex.     

3-D MHD SIMULATION OF X-TYPE COALESCENCE OF TWO CURRENT-LOOPS

We present simulation results of X-type coalescence of two current-loops, by using a 3-D resistive MHD code. The results are compared with the limb flare observed by Yohkoh on 2 August, 1993 at 08:30 UT, which is a good example of partial X-type coalescence. It is shown that the maximum temperature enhancement near the cross-point of the two loops, obtained from the simulation, agrees well with the observations when the plasma is 0.08.     

Iron meteorite bulk densities determined via 3-D laser imaging

This study tested the feasibility of using 3-D laser imaging to measure the bulk density of iron meteorites. 3-D laser imaging is a technique in which a 3-D model of an object is built after aligning and merging individual detailed images of its surface. Assuming that the mass of the object is known, the volume of the model is calculated by software and an estimate of bulk density can be obtained by dividing mass by volume. The 3-D laser imaging technique was used to determine the density of 46 fragments from 11 different iron meteorites. The technique proved to be robust and was applied successfully to study samples ranging close to four orders of magnitude in mass (8 g to 156 kg) and exhibiting a variety of surface textures (e.g., cracks, regmaglypts), reflectivities (e.g., polished surfaces, fusion crust, rust), and morphologies (e.g., sharp angular edges, shrapnel tendrils). Three metrics were considered to estimate the error associated with density measurements: the range accuracy of the laser camera, image alignment error, and inter-operator variability during model building. Inter-operator variability was the largest source of error and was highest when assembling models of samples which either lacked distinctive features or were very complex in shape. Excluding two anomalous Zagora samples where silicate inclusions might have lowered density, the densities measured using 3-D laser imaging ranged from 6.98 to 7.93 g cm⁻³, consistent with previous studies. There is overlap between bulk density and iron meteorite class, and therefore bulk density cannot be used in isolation as a classification criterion. It is a good indicator, however, of weathering effects and of the potential presence of low-density inclusions.     

Periodic orbits and their bifurcations in a 3-D system

We study some simple periodic orbits and their bifurcations in the Hamiltonian . We give the forms of the orbits, the characteristics of the main families, and some existence diagrams and stability diagrams. The existence diagram of the family 1a contains regions that are stable (S), simply unstable (U), doubly unstable (DU) and complex unstable (). In the regionsS andU there are lines of equal rotation numberm/n. Along these lines we have bifurcations of families of periodic orbits of multiplicityn. When these lines reach the boundary of the complex unstable region, they are tangent to it. Inside the region there are linesm/n, along which the orbits 1a, describedn-times, are doubly unstable; however, along these lines there are no bifurcations ofn-ple periodic orbits. The families bifurcating from 1a exist only in certain regions of the parameter space (, ). The limiting lines of these regions join at particular points representing collisions of bifurcations. These collisions of bifurcations produce a nonuniqueness of the various families of periodic orbits. The complicated structure of the various bifurcations can be understood by constructing appropriate stability diagrams.     

二维CCD图象数据压缩

本文着重指出了在今后处理大面积CCD图象数据过程中,所将面临的数据存贮困难问题.本文提出了一种有效的不丢失天文信息的压缩CCD图象数据的方法,对银纬b=-60°的一个天区的试验表明,压缩后的图象数据仅为原图象数据的1/30左右,并且可以十分方便地进行图象再现及再处理。在压缩数据过程中,我们在剑桥APM底片扫描机参数化施密特照相底片的基础上,重新安排了CCD图象上天体的对应参数,并视天体的大小及形状,有效地提取保存了天体周围矩阵信息.