Effects of interedge scattering on the Wigner crystallization in graphene nanoribbons

We investigate the effects of coupling between the two zigzag edges of graphene nanoribbons on the Wigner crystallization of electrons and holes using a combination of tight-binding, mean field Hubbard and many-body configuration interaction methods. We show that the thickness of the nanoribbon plays a crucial role in the formation of Wigner crystal. For ribbon widths smaller than 16 \mbox{\AA}, increased kinetic energy overcomes the long-range Coulomb repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38 \mbox{\AA} wide, strong Wigner localization is observed for even number of electrons, revealing an even-odd effect also found in Coulomb blockade addition spectrum. Interedge correlations are found to be strong enough to allow simultaneous crystallization on both edges, although an applied electric field can decouple the two edges. Finally, we show that Wigner crystallization can also occurs for holes, albeit weaker than for electrons.Comment: Accepted for publication in PR

Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $\lambda$ and the Hurst index of such processes is one of the fundamental problem in the literature. We present some iterative method for estimation of the scale and Hurst parameters which is addressed for semi-selfsimilar processes with stationary increments. This method is based on some flexible sampling scheme and evaluating sample variance of increments in each scale intervals $[\lambda^{n-1}, \lambda^n)$, $n\in \mathbb{N}$. For such iterative method we find the initial estimation for the scale parameter by evaluating cumulative sum of moving sample variances and also by evaluating sample variance of preceding and succeeding moving sample variance of increments. We also present a new efficient method for estimation of Hurst parameter of selfsimilar processes. As an example we introduce simple fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary increments. We present some simulations and numerical evaluation to illustrate the results and to estimate the scale for sfBm as a semi-selfsimilar process. We also present another simulation and show the efficiency of our method in estimation of Hurst parameter by comparing its performance with some previous methods.Comment: 15 page

A Social Network-Based Peer-To-Peer Model For Resource Discovery

Peer-to-Peer (P2P) systems are distributed systems consisting of interconnected nodes which provide scalability, fault tolerance, decentralized coordination, self-organization, anonymity, distributed resources and services sharing, lower cost of ownership and better support for creating ad hoc networks. Data sharing, a subset of resource sharing, is one of the attractive topic in P2P systems. Because of autonomy of the nodes, decentralized coordination and volatility of network caused by the autonomy, data sharing is not an easy task in P2P system. Furthermore, there is no guarantee that a node stays in the network for a specific period of time. Hence, the answers to a particular query may be retrieved from different nodes every time. Moreover, the lack of centralized coordinators makes this process harder. These problems in P2P systems lead to a well known problem which is called resource discovery