Astrophysical Implications of the Recent Shocked Deuterium Experiments

In the last few years, deuterium has been the focus of a high level of laboratory activity that was sparked by a disagreement on the experimental value of the maximum compression along the Hugoniot. Astrophysically, the uncertainty in the EOS of hydrogen is most consequential in models of the interiors of Jupiter and Saturn since a significant fraction of their mass falls in the region where the EOS uncertainty is largest. We present a study of the range of interior structures allowed by the shock-compression experiments on deuterium and constrained by astrophysical observations of the two planets. We find that the EOS uncertainty must be reduced to less than 3% along the planet’s isentrope to get good interior models of Jupiter. These models provide values for the mass of a core of heavy elements (other than H and He) and the total mass of heavy elements in these planets. The amount and distribution of heavy elements are quite sensitive to the EOS of hydrogen and constitute important clues to their formation process.     

Advances in radiative transfer

This review describes advances in radiative transfer theory since about 1985. We stress fundamental aspects and emphasize modern methods for the numerical solution of the transfer equation for spatially multidimensional problems, for both unpolarized and polarized radiation. We restrict the discussion to two-level atoms with noninverted populations for given temperature, density and velocity fields. Unfortunately this article was originally published with typesetter's errors: The correct publication date was 25 February 2006, not 3 January 2006. The content was not in the final form. The publishers wish to apologize for this mistake. The online version of the original version can be found at /10.1007/s00159-005-0025-8.     

A method solving kepler's equation without transcendental function evaluations

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fast as Halley's method, Nijenhuis's method, and others.     

The inverse problem for pulsating neutron stars: a 'fingerprint analysis' for the supranuclear equation of state

We study the problem of detecting, and inferring astrophysical information from, gravitational waves from a pulsating neutron star. We show that the fluid f and p modes, as well as the gravitational-wave w modes, may be detectable from sources in our own Galaxy, and investigate how accurately the frequencies and damping rates of these modes can be inferred from a noisy gravitational-wave data stream. Based on the conclusions of this discussion we propose a strategy for revealing the supranuclear equation of state using the neutron star fingerprints: the observed frequencies of an f and a p mode. We also discuss how well the source can be located in the sky using observations with several detectors.     

Properties of iron at the Earth's core conditions

Summary. The phase diagram of iron up to 330 GPa is solved using the experimental data of static high pressure (up to 11 GPa) and the experimental data of shock wave data (up to 250 GPa). A solution for the highest triple point is found ( P = 280 GPa and T = 5760 K) by imposing the thermodynamic constraints of triple points. This pressure of the triple point is less than the pressure of the inner core–outer core boundary of the Earth. These results indicate that the density of iron at the inner core–outer core boundary pressure is close to 13 g cm⁻³, which lies close to the seismic solutions of the Earth at that pressure. It is thus concluded that the Earth's inner core is very likely to be virtually pure iron in its hexagonal close packed (hcp) phase.
It is shown that four properties of the Earth's inner core determined from seismology are close in value to the corresponding properties of hcp iron at inner core conditions: density, bulk modulus, longitudinal velocity, and Poisson's ratio. The density–pressure profile of hcp iron at inner core conditions matches the density–pressure profile of the inner core as determined by seismic methods, within the spread of values given by recent seismic models.
This indicates that the Earth is slowly cooling, the Earth's inner core is growing by crystallization, and the impurities of the core are concentrated in the outer core. The calculated temperature at the Earth's centre is 6450 K.     

Adjoint method for the optimum planning of industrial pollutant sources

The deterioration of air quality is threatening the life and health of people. Scientists in China and other countries have done a great deal of research work on the details of air pollution and the methods of preven-tion and control during the past decades. Up to now, most of the achievements are concentrated on the techniques of controlling pollutant sources and the programs of reduction, which focus on the improve-ment of air quality and the restoration of environment. The techniques of con…     

一种地物直角平差纠正的新方法

由于测量存在观测误差,故根据测得的矩形地物特征点坐标数据,绘制的地物图形都不能严格是矩形,即地物直角条件不能严格成立。虽然目前的数字测图软件(如南方CASS 7.0)已提供了直角纠正功能,但它是一种简单机械的直角化方法,而不是进行平差纠正。为此,研究了一种以实际测量的地物特征点坐标为观测值进行地物直角平差纠正的算法,并以C#语言实现了该系统。实验证明,该系统能够更方便、更合理地实现对地物的直角纠正处理。     

基于GIS的小流域土壤侵蚀与产沙的简化模拟

将泥沙输移能力公式与USLE公式相结合,建立了一个简化的分布式小流域产沙模型,并将其应用于川中丘陵区小流域的土壤侵蚀与泥沙输移的空间分布模拟。得到的主要结论:1.该模型适用于川中丘陵区小流域产沙的模拟;2.魏城河流域1980—1987年8 a平均土壤侵蚀量为16.8×104t,侵蚀模数为675.8 t/(km2.a),模拟得到的输沙模数为238.6 t/(km2.a),泥沙输移比为0.35;3.魏城河流域主要以微度侵蚀为主,占到全流域总面积的68%,强度侵蚀占流域面积的1%,主要分布在坡度较陡的流域边缘地带;4.相对其他因子,降雨与坡度对该流域侵蚀产沙的影响更为突出。     

非线性Schrödinger方程的一个线性化紧致差分格式

对非线性Schrödinger方程给出了一个线性化紧致差分格式,运用不动点定理和能量方法证明了格式的唯一可解性,还运用能量方法和数学归纳法,避开困难的先验估计,证明格式在空间方向和时间方向分别具有四阶和二阶精度,数值算例验证了格式的精度和数值稳定性.