Chaos and elliptical galaxies

Recent results on chaos in triaxial galaxy models are reviewed. Central mass concentrations like those observed in early-type galaxies - either stellar cusps, or massive black holes — render most of the box orbits in a triaxial potential stochastic. Typical Liapunov times are 3–5 crossing times, and ensembles of stochastic orbits undergo mixing on timescales that are roughly an order of magnitude longer. The replacement of the regular orbits by stochastic orbits reduces the freedom to construct self-consistent equilibria, and strong triaxiality can be ruled out for galaxies with sufficiently high central mass concentrations.     

Using bright ellipticals as dark energy cosmic clocks

The age of the Universe has been increasingly constrained by different techniques, such as the observations of type Ia supernovae (SNIa) at high redshift or dating the stellar populations of globular clusters. In this paper, we present a complementary approach using the colours of the brightest elliptical galaxies in clusters over a wide redshift range  ( z ≲ 1)  . We put new and independent bounds on the dark energy equation of state parametrized by a constant pressure-to-density ratio   w _Q  and by a parameter (ξ) which determines the scaling between the matter and dark energy densities. We find that accurate estimates of the metallicities of the stellar populations in moderate and high-redshift cluster galaxies can pose stringent constraints on the parameters that describe dark energy. Our results are in good agreement with the analysis of dark energy models using SNIa data as a constraint. Accurate estimates of the metallicities of stellar populations in cluster galaxies at   z ≲ 2  will make this approach a powerful complement to studies of cosmological parameters using high-redshift SNIa.     

Hammerstein型非线性积分方程解的存在性

该文采用化为积分方程组的方法 ,利用锥上不动点指数计算 ,在不要求非线性项 f (x,u)非负的情况下 ,证明 Hammerstein型非线性积分方程 φ(x) =∫Gκ(x,y) f (y,φ(y) ) dy非平凡解和多解存在性的一些新的结果。此结果可用来证明非线性常微分方程两点边值问题解的存在性。     

随机Dirichlet问题解的调和展开

针对重力学随机Dirichlet问题,通过适当地对边界检验函数的分解,并在随机边界样本空间中提取确定性部分的对偶基,本文将随机Dirichlet问题的一般解展开为一随机系数的调和级数形式。     

Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.