Stability of the classical type of relative equilibria of a rigid body in the J2 problem
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system.

title: Pair-distribution function and its coupling-constant average for the spin-polarized electron gas.
abstract: The pair-distribution function g describes physical correlations between electrons, while its average g\ifmmode\bar\else\textasciimacron\fi{} over coupling constant generates the exchange-correlation energy. The former is found from the latter by g=(1-${\mathit{a}}_{0}$\ensuremath{\partial}/\ensuremath{\partial}${\mathit{a}}_{0}$)g\ifmmode\bar\else\textasciimacron\fi{}, where ${\mathit{a}}_{0}$ is the Bohr radius. We present an analytic representation of g\ifmmode\bar\else\textasciimacron\fi{} (and hence g) in real space for a uniform electron gas with density parameter ${\mathit{r}}_{\mathit{s}}$ and spin polarization \ensuremath{\zeta}. This expression has the following attractive features: (1) The exchange-only contribution is treated exactly, apart from oscillations we prefer to ignore. (2) The correlation contribution is correct in the high-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0) and nonoscillatory long-range (R\ensuremath{\rightarrow}\ensuremath{\infty}) limits. (3) The value and cusp are properly described in the short-range (R\ensuremath{\rightarrow}0) limit. (4) The normalization and energy integrals are respected. The result is found to agree with the pair-distribution function g from Ceperley's quantum Monte Carlo calculation. Estimates are also given for the separate contributions from parallel and antiparallel spin correlations, and for the long-range oscillations at a high finite density.

title: Observation of the 2005 January 20 GLE event using Yangbajing. solar neutron telescope & neutron monitor
abstract: A solar cosmic rays Ground Level Enhancement (GLE) event associated with a X7.1/2b solar flare in 2005 January 20 was observed by the Yangbajing solar neutron telescope(SNT) and neutron monitor(NM), located at Yangbajing Tibet(90.53 degrees E, 30.11 degrees N, 4310m a.s.l) with the highest vertical geomagnetic cut-off rigidity of 14.1GV in NM network. The statistical significance of the counting rate enhancement recorded by solar neutron telescope in > 40MeV channel was 3.7 sigma in the time window of 07:00-07:05UT and 6.0 sigma in the time window of 07:00-07:20UT, respectively. The onset time of 06:51-06:52UT for this GLE event was clearly observed by the Yangbajing NM. Our observation indicates that solar protons have been accelerated up to energies of > 10GeV during this solar event.

title: Accurate and simple analytic representation of the electron-gas correlation energy.
abstract: We propose a simple analytic representation of the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$ for a uniform electron gas, as a function of density parameter ${\mathit{r}}_{\mathit{s}}$ and relative spin polarization \ensuremath{\zeta}. Within the random-phase approximation (RPA), this representation allows for the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$ behavior as ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Close agreement with numerical RPA values for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,0), ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,1), and the spin stiffness ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$)=${\mathrm{\ensuremath{\partial}}}^{2}$${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$, \ensuremath{\zeta}=0)/\ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}^{2}$, and recovery of the correct ${\mathit{r}}_{\mathit{s}}$ln${\mathit{r}}_{\mathit{s}}$ term for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [ (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can.  (1980)] or by Perdew and Zunger (PZ) . While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the \ensuremath{\zeta}-dependent coefficients in the high- and low-density expansions, and the ${\mathit{r}}_{\mathit{s}}$-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}^{\mathrm{\ensuremath{\sigma}}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) is evaluated for use in self-consistent density-functional calculations.

title: The Influence of Radial Stellar Migration on the Chemical Evolution of the Milky Way
abstract: Stellar migration is an important dynamical process in the Galactic disk. Here we model radial stellar migration in the Galactic disk with an analytical method, then add it to a detailed Galactic chemical evolution model to study the influence of radial stellar migration on the chemical evolution of the Milky Way, especially for the abundance gradients. We found that the radial stellar migration in the Galactic disk can make the profile of the G-dwarf metallicity distribution of the solar neighborhood taller and narrower, and thus it becomes another solution to the "G-dwarf problem." It can also scatter the age-metallicity relation. However, after migration, the abundance distributions along the Galactic radius do not change much; namely, the abundance gradients would not be flattened by the radial stellar migration, which is different from the predictions of many theoretical works. However, it can flatten the radial gradients of the mean chemical abundance of stars, and older stars possess flatter abundance gradients than younger stars. The most significant effect of radial stellar migration on the chemical abundance is that at a certain position it scatters the abundance of stars from a relatively concentrated value to a range.

title: DIMENSION EMERGENCE, HOLOGRAPHY AND QUANTUM GRAVITY
abstract: In this paper, we try to give an alternative interpretation of the holography principle. We argue that the space or time may be regarded as emerging from quantum mechanics as an evolutive parameter. The lower D-dimensional theory is related to a corresponding (D+1)-theory by a mysterious quantum system. Then from the higher-dimensional theory, under a new dimension reduction mechanism we obtain the corresponding results. We also try to incorporate the gauge field into the reduction, roughly identifying Aμ with Nμ which is the shift vector in the ADM-like decomposition of space–time metric. In the end, we extend to the gravitational field, and obtain a relation $\tilde{M}^3 = \kappa M_{\rm Pl}^2$ with a cutoff factor κ, from a different view.

title: Recent results from E802 and E859
abstract: Recent single-particle inclusive measurements and two-particle correlation data from E802 and its succesor, E859, are presented. The K + / π + ratio observed for collisions of 14.6 A·GeV 28 Si ions on various targets is presented as a function of both forward and transverse energy. Source sizes are determined via interferometry using π + , π − , K + and proton pairs.

title: The Young Exoplanet Transit Initiative (YETI)
abstract: We present the Young Exoplanet Transit Initiative (YETI), in which we use several 0.2 to 2.6-m telescopes around the world to monitor continuously young (≤100 Myr), nearby (≤1 kpc) stellar clusters mainly to detect young transiting planets (and to study other variability phenomena on time-scales from minutes to years). The telescope network enables us to observe the targets continuously for several days in order not to miss any transit. The runs are typically one to two weeks long, about three runs per year per cluster in two or three subsequent years for about ten clusters. There are thousands of stars detectable in each field with several hundred known cluster members, e.g. in the first cluster observed, Tr-37, a typical cluster for the YETI survey, there are at least 469 known young stars detected in YETI data down to R = 16.5 mag with sufficient precision of 50 millimag rms (5 mmag rms down to R = 14.5 mag) to detect transits, so that we can expect at least about one young transiting object in this cluster. If we observe ∼10 similar clusters, we can expect to detect ∼10 young transiting planets with radius determinations. The precision given above is for a typical telescope of the YETI network, namely the 60/90-cm Jena telescope (similar brightness limit, namely within ±1 mag, for the others) so that planetary transits can be detected. For targets with a periodic transit-like light curve, we obtain spectroscopy to ensure that the star is young and that the transiting object can be sub-stellar; then, we obtain Adaptive Optics infrared images and spectra, to exclude other bright eclipsing stars in the (larger) optical PSF; we carry out other observations as needed to rule out other false positive scenarios; finally, we also perform spectroscopy to determine the mass of the transiting companion. For planets with mass and radius determinations, we can calculate the mean density and probe the internal structure. We aim to constrain planet formation models and their time-scales by discovering planets younger than ∼100 Myr and determining not only their orbital parameters, but also measuring their true masses and radii, which is possible so far only by the transit method. Here, we present an overview and first results (

title: TRACKING PARTICLES THROUGH A GENERAL MAGNETIC FIELD
abstract: A method that tracks particles directly through a general magneticfielddescribedina 3Dfield tablewasaddedto the code elegantrecently. It was realized by convertingan arbitrary particle’s motion to a combination of free-drift motion and centripetal motion through the coordinate system rotation and using a general linear interpolation tool developed at the Advanced Photon Source (APS). This method has been tested by tracking particles through conventional magnetic elements (dipole, sextupole, etc.) to verify reference coordinate system conversions, tracking accuracy, and long-term tracking stability. Results show a very good agreement between this new method and the traditional method. This method is not designed to replace mature traditional methods that have been used in most tracking codes. Rather, it is useful for magnets with complicated field profiles or for studying edge effects.

title: ALICE technical design report of the time-of-flight system (TOF)