Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Effects of Three Gorges Reservoir (TGR) water storage in June 2003 on Yangtze River sediment entering the estuary

International audienceThe world-greatest water conservancy project, Three Gorges Reservoir (TGR), stored water for the first time in June 2003, which provides an excellent opportunity to examine its effects on the sediment entering the Yangtze River estuary. A daily record dataset of water discharge and suspended sediment concentration (SSC) of the Yangtze River measured at Datong (the controlling hydrological gauging station into the estuary) from May 15 to July of 2003 spanning the water storage, together with a monthly record dataset of runoff, sediment load and SSC measured at Datong from 1953 to 2003, were used to examine the effects of the TGR water storage in June 2003 on the Yangtze River sediment entering the estuary. The results show that the unnaturally clearer water due to the TGR sedimentation resulted by the water storage in June 2003 brought the Yangtze River markedly decreased SSC and sediment load entering the estuary both during the TGR water storage and in the second half year of 2003. The Yangtze River water and sediment discharges into the estuary from 15 May to 15 July in 2003 spanning the TGR water storage clearly indicated three phases: (1) pre-water storage of the TGR from 15 May to 25 May, during this phase, SSC and sediment load increased with water discharge increasing; (2) water storage of the TGR from 25 May to 10 June (including the preparation phase from 25 May to 31 May), during this phase, SSC and sediment load decreased dramatically with water discharge decreasing; and (3) post-water storage of the TGR, at the beginning, SSC, sediment load and water discharge basically remained at a relatively low value until the end of June, and since then, SSC and sediment load increased gradually with water discharge increasing. In addition, the real total sediment load was reduced by 2456.07×104 t than the estimated total sediment load during the period from 27 May to 2 July in 2003

Chaotic Properties of Subshifts Generated by a Non-Periodic Recurrent Orbit

The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a non-periodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts

Core-Selecting Auctions for Dynamically Allocating Heterogeneous VMs in Cloud Computing

In a cloud market, the cloud provider provisions heterogeneous virtual machine (VM) instances from its resource pool, for allocation to cloud users. Auction-based allocations are efficient in assigning VMs to users who value them the most. Existing auction design often overlooks the heterogeneity of VMs, and does not consider dynamic, demand-driven VM provisioning. Moreover, the classic VCG auction leads to unsatisfactory seller revenues and vulnerability to a strategic bidding behavior known as shill bidding. This work presents a new type of core-selecting VM auctions, which are combinatorial auctions that always select bidder charges from the core of the price vector space, with guaranteed economic efficiency under truthful bidding. These auctions represent a comprehensive three-phase mechanism that instructs the cloud provider to judiciously assemble, allocate, and price VM bundles. They are proof against shills, can improve seller revenue over existing auction mechanisms, and can be tailored to maximize truthfulness.published_or_final_versio

Resource allocation and power control to maximize the overall system survival time for mobile cells with a D2D underlay

The limited battery life of user equipment (UE) is always one of the key concerns of mobile users and a critical factor that could limit device-to-device (D2D) communications. In this letter, considering that UEs may have different residual battery energy levels, we define the overall system survival time as the minimal expected battery lifetime of all transmitting UEs in a cell. We then propose to maximize the overall system survival time by jointly optimizing the resource allocation and power control (RAPC) D2D links and conventional cellular links. Subject to the transmission rate requirement of each link, the joint optimization problem is formulated as a mixed integer non-linear programming problem, which is solved by a game theory-based distributed approach. Simulation results demonstrate that our game theory-based RAPC approach can enormously prolong the overall system survival time as compared with existing RAPC approaches

An accuracy measurement method for star trackers based on direct astronomic observation.

Star tracker is one of the most promising optical attitude measurement devices and it is widely used in spacecraft for its high accuracy. However, how to realize and verify such an accuracy remains a crucial but unsolved issue until now. The authenticity of the accuracy measurement method of a star tracker will eventually determine the satellite performance. A new and robust accuracy measurement method for a star tracker based on the direct astronomical observation is proposed here. In comparison with the conventional method with simulated stars, this method utilizes real navigation stars as observation targets which makes the measurement results more authoritative and authentic. Transformations between different coordinate systems are conducted on the account of the precision movements of the Earth, and the error curves of directional vectors are obtained along the three axes. Based on error analysis and accuracy definitions, a three-axis accuracy evaluation criterion has been proposed in this paper, which could determine pointing and rolling accuracy of a star tracker directly. Experimental measurements confirm that this method is effective and convenient to implement. Such a measurement environment is close to the in-orbit conditions and it can satisfy the stringent requirement for high-accuracy star trackers.This work was financially supported by the National High Technology Research and Development Program of China (863 Program) (No. 2012AA121503), National Natural Science Foundation of China (No. 61377012 and No. 51522505) and the China Postdoctoral Science Foundation (No. 2015M570091).This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/srep2259

Bulk Fermi surface coexistence with Dirac surface state in Bi2_2Se3_3: a comparison of photoemission and Shubnikov-de Haas measurements

Shubnikov de Haas (SdH) oscillations and Angle Resolved PhotoEmission Spectroscopy (ARPES) are used to probe the Fermi surface of single crystals of Bi2Se3. We find that SdH and ARPES probes quantitatively agree on measurements of the effective mass and bulk band dispersion. In high carrier density samples, the two probes also agree in the exact position of the Fermi level EF, but for lower carrier density samples discrepancies emerge in the position of EF. In particular, SdH reveals a bulk three-dimensional Fermi surface for samples with carrier densities as low as 10^17cm-3. We suggest a simple mechanism to explain these differences and discuss consequences for existing and future transport studies of topological insulators.Comment: 5 mages, 5 figure