The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N -body simulations.
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.     

On cross-correlating weak lensing surveys

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal-to-noise ratio, such as the Supernova/Acceleration Probe ( SNAP ). However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys that probe the same part of the sky. In this paper we study various measures that are useful in cross-correlating weak lensing surveys with diverse survey strategies. Using two different statistics – the shear components and the aperture mass – we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross-correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey.     

概率赋范空间的S-凸和K-凸

文献[1][2]认为M－PN空间是局部凸的。通过定理说明这个结论对t-模T（a,b)≥min(a,b)时成立。又通过反例表明，当t-模型T（a,b)=max(a b-1,0）时无论邻域Nθ（ε，λ）概率有界还是概率半有界结论均不成立。还讨论了Takahashi凸性并对S－凸和K－凸作了比较。     

THE CHARACTERISTIC OF MARINE ENVIRONMENT IN LINGDINGYANG ESTUARY

1 HYDROLOGIC FEATURES Lingdingyang Estuary, located at the middle south of Guangdong Province, is a bell-shaped estuary with a north-south direction. Its area is about 2100km2. The north of Qi′ao Island and Inner-Lingding Island, and the south of Humen are grouped as Neilingdingyang Estuary, having an area of 1041km2. Affected by topography, runoff and tide, its dynamic condition is very complicated. Different water areas have different hydrologic features. The topography under …     

The pairwise velocity dispersion of galaxies: effects of non-radial motions

I discuss the effect of non-radial motions on the small-scale peculiar pairwise velocity dispersions (PVD) of galaxies in a cold dark matter (CDM) model and calculate the PVD for the SCDM model by means of the refined cosmic virial theorem (CVT), taking account of non-radial motions by means of the Del Popolo & Gambera model. I compare the results of the present model with the data from Davis & Peebles, the IRAS value at 1  h ⁻¹ Mpc of Fisher et al. and Marzke et al. I show that while the SCDM model disagrees with the observed values, as pointed out by several authors, taking account of non-radial motions produces smaller values for the PVD. At r ≤1  h ⁻¹ Mpc the result is in agreement with Bartlett & Blanchard. In the light of this last paper, the result may be also read as a strong dependence of the CVT prediction on the model chosen to describe the mass distribution around galaxies, suggesting that the CVT cannot be taken as a direct evidence for a low-density Universe. Similarly to what is shown by Del Popolo & Gambera and Del Popolo et al., the agreement of our model to the observational data is because of a scale-dependent bias induced by the presence of non-radial motions. As the assumptions on which CVT is based have been questioned by several authors, I also calculated the PVD using the redshift distortion in the redshift-space correlation function, ξ _z( r _p, π), and compared it with the PVD measured from the Las Campanas Redshift Survey by Jing et al. The result confirms that non-radial motions influence the PVD making them agree better with the observed data.     

Parameter information from non-linear cosmological fields

We develop a general formalism for analysing parameter information from non-Gaussian cosmic fields. The method can be adapted to include the non-linear effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity field surveys as part of parameter estimation. It can also be used as a test of non-Gaussianity of the cosmic microwave background. Generalizing maximum-likelihood analysis to second order, we calculate the non-linear Fisher information matrix and likelihood surfaces in parameter space. To this order we find that the information content is always increased by including non-linearity. Our methods are applied to a realistic model of a galaxy redshift survey, including non-linear evolution, galaxy bias, shot-noise and redshift-space distortions to second order. We find that including non-linearities allows all of the degeneracies between parameters to be lifted. Marginalized parameter uncertainties of a few per cent will then be obtainable using forthcoming galaxy redshift surveys.     

模糊划分矩阵在岩土参数概率分布中的应用

讨论如何在小样本条件下用已有的过程经验与试验资料确定岩土参数概率分布,用模糊划分矩阵与BAYES方法相结合,给出由小样本试验数据确定岩土参数的概率分布。