We derive and analyze second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations (RSDO-ADE) in one-dimensional (1D) and two-dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed-order advection-dispersion equations into multiterm Riesz space fractional advection-dispersion equations (MT-RSDO-ADE) by using the midpoint quadrature rule. Secondly, we propose a second-order accurate implicit numerical method for the MT-RSDO-ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO-ADE in 1D case. Then we discuss the RSDO-ADE in 2D case. For 2D case, we propose a new second-order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis.

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With the increased focus on Internet privacy, especially after the exposure of PRISM(an Internet surveillance program), anonymous communication have been getting more and more attentions. One of the most widely used anonymous communication systems is I2P(Invisible Internet Project). And as opposed to Tor's(another popular anonymous communication system) directory-based approach, which provides a centralized directory server to manage the overall 'view' of the network, I2P is fully distributed and self organizing, which aims to avoid attackers' enumeration of all I2P's routers. In this paper, based on I2P's operating mechanism, we presented two passive and two active methods to discover I2P routers. In a more than two week's collecting experiment, about 25640 routers were discovered everyday, which turned out to be an almost full coverage(94.9%) of the I2P network compared with the data announced on the official website [1]. And based on the routers collected, this paper further made a preliminary analysis of both the I2P network's overall status and its security. The result showed that I2P is a well structured P2P network, while some powerful attackers operating several routers are still possible to perform compromise attack to break I2P users' anonymity given the current I2P's security mechanism. Finally, this paper discussed some countermeasures to improve the security of the I2P network.

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