The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.     

Effects of cluster galaxies on arc statistics

We present the results of a set of numerical simulations evaluating the effect of cluster galaxies on arc statistics.
We perform a first set of gravitational lensing simulations using three independent projections for each of nine different galaxy clusters obtained from N -body simulations. The simulated clusters consist of dark matter only. We add a population of galaxies to each cluster, mimicking the observed luminosity function and the spatial galaxy distribution, and repeat the lensing simulations including the effects of cluster galaxies, which themselves act as individual lenses. Each galaxy is represented by a spherical Navarro, Frenk & White density profile.
We consider the statistical distributions of the properties of the gravitational arcs produced by our clusters with and without galaxies. We find that the cluster galaxies do not introduce perturbations strong enough to significantly change the number of arcs and the distributions of lengths, widths, curvature radii and length-to-width ratios of long arcs. We find some changes to the distribution of short-arc properties in the presence of cluster galaxies. The differences appear in the distribution of curvature radii for arc lengths smaller than 12 arcsec, while the distributions of lengths, widths and length-to-width ratios are significantly changed only for arcs shorter than 4 arcsec.     

Gravitational field routing strategy considering the distribution of traffic flow

Traffic flow transmission is a constantly important aspect of complex networks, geographical information science, and other science and engineering fields. Previous studies have shown that vehicle flow is more strongly correlated with morphological properties of streets than those of axial lines. In addition, street-based topological representations are more suitable for vehicle flow prediction, as well as more memory-oriented and global in nature. In this study, we construct a dual graph to represent the street–street relationship and propose a routing strategy for networks on the basis of gravitational field theory. We aim to diminish traffic congestion and enhance the transmission performance of networks. We borrow from gravitational field theory in establishing a gravitational field stimulated by a node in packet transmission and in defining the corresponding gravitational field equation. On the basis of this study, we present a mathematical model and a routing strategy. Experimental results indicate that compared with the shortest path routing strategy, the proposed method considerably enhances network capacity and effectively balances network traffic flow, especially for congested networks. We achieve critical gravitation that can always maximize network capacity, regardless of the values of other parameters.     

自容式压力验潮仪水位观测值影响因素与改正

自容式压力验潮仪是目前海道测量水位观测的常用设备。在实际应用中,由于忽略了环境因素及其变化对水位观测精度的影响,可能获取不到高质量的水位观测数据,进而影响到海道测量成果的数据质量。在简要分析自容式压力验潮仪水位测量原理的基础上,利用数值计算方法,探讨了气压、密度和重力加速度变化对自容式压力验潮仪观测水位的影响规律,并提出了提高自容式压力验潮仪水位观测精度的一般改正方法。     

引力场梯度张量的非奇异公式推导

传统的引力场梯度计算公式在两极附近存在奇异性,需要换用其他的非奇异计算公式。从奇异性产生的原因入手,并结合勒让德函数的有关性质,推导了一组新的计算公式。实际计算验证了该公式的正确性和有效性。     

Pulsar timing residuals due to individual non-evolving gravitational wave sources

The pulsar timing residuals induced by gravitational waves from non- evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The or- bits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities.     

Probing the dark side of the Universe with weak gravitational lensing effects

Arising from gravitational deflections of light rays by large-scale structures in the Universe, weak-lensing effects have been recognized as one of the most important probes in cosmological studies. In this paper, we review the main progress in weak-lensing analyses, and discuss the challenges in future investigations aiming to understand the dark side of the Universe with unprecedented precisions.