Scale-Free Networks are Ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small world networks which is known to be d ~ lnN, we show, using analytical arguments, that scale free networks with 2<a<3 have a much smaller diameter, behaving as d ~ lnlnN. For a=3, our analysis yields d ~ lnN/lnlnN, as obtained by Bollobas and Riordan, while for a>3, d ~ lnN. We also show that, for any a>2, one can construct a deterministic scale free network with d ~ lnlnN, and this construction yields the lowest possible diameter.Comment: Latex, 4 pages, 2 eps figures, small corrections, added explanation

Conceptual design of the enhanced coolant purification systems for the European HCLL and HCPB test blanket modules

The Coolant Purification Systems (CPSs) is one of the most relevant ancillary systems of European Helium Cooled Lead Lithium (HCLL) and Helium Cooled Pebble Bed (HCPB) Test Blanket Modules (TBMs) which are currently in the preliminary design phase in view of their installation and operation in ITER. The CPS implements mainly two functions: the extraction and concentration of the tritium permeated from the TBM modules into the primary cooling circuit and the chemistry control of helium primary coolant. During the HCLL and HCPB-TBSs (Test Blanket Systems) Conceptual Design Review (CDR) in 2015 it was recognized the need of reducing the tritium permeation into the Port Cell #16 of ITER. To achieve this and, then, to lower the tritium partial pressure in the Helium Cooling Systems in normal operation, the helium flow-rate treated by each CPS has been increased of almost one order of magnitude. In 2017, to satisfy the CDR outcomes and the new design requirements requested by Fusion for Energy (F4E, the European Domestic Agency for ITER), ENEA performed a preliminary design of the “enhanced” CPSs. This paper presents the current design of the “enhanced” CPSs, focusing on design requirements, assumptions, selection of technologies and preliminary components sizing

High-performance lead-acid batteries enabled by Pb and PbO2 nanostructured electrodes: Effect of operating temperature

Lead-acid batteries are now widely used for energy storage, as result of an established and reliable technology. In the last decade, several studies have been carried out to improve the performance of this type of batteries, with the main objective to replace the conventional plates with innovative electrodes with improved stability, increased capacity and a larger active surface. Such studies ultimately aim to improve the kinetics of electrochemical conversion reactions at the electrode-solution interface and to guarantee a good electrical continuity during the repeated charge/discharge cycles. To achieve these objectives, our contribution focuses on the employment of nanostructured electrodes. In particular, we have obtained nanostructured electrodes in Pb and PbO2 through electrosynthesis in a template consisting of a nanoporous polycarbonate membrane. These electrodes are characterized by a wider active surface area, which allows for a better use of the active material, and for a consequent increased specific energy compared to traditional batteries. In this research, the performance of lead-acid batteries with nanostructured electrodes was studied at 10 C at temperatures of 25, −20 and 40 °C in order to evaluate the efficiency and the effect of temperature on electrode morphology. The batteries were assembled using both nanostructured electrodes and an AGM-type separator used in commercial batteries

Nanostructured Lead Electrodes with Reduced Graphene Oxide for High-Performance Lead–Acid Batteries

Nanostructured Pb electrodes consisting of nanowire arrays were obtained by electrodeposition, to be used as negative electrodes for lead–acid batteries. Reduced graphene oxide was added to improve their performances. This was achieved via the electrochemical reduction of graphene oxide directly on the surface of nanowire arrays. The electrodes with and without reduced graphene oxide were tested in a 5 M sulfuric acid solution using a commercial pasted positive plate and an absorbed glass mat separator in a zero-gap configuration. The electrodes were tested in deep cycling conditions with a very low cut-off potential. Charge–discharge tests were performed at 5C. The electrode with reduced graphene oxide outperformed the electrode without reduced graphene oxide, as it was able to work with a very high utilization of active mass and efficiency. A specific capacity of 258 mAhg−1–very close to the theoretical one–was achieved, and the electrode lasted for more than 1000 cycles. On the other hand, the electrode without reduced graphene oxide achieved a capacity close to 230 mAhg−1, which corresponds to a 90% of utilization of active mass

Fabrication of CZTSe/CIGS Nanowire Arrays by One-Step Electrodeposition for Solar-Cell Application

The paper reports some preliminary results concerning the manufacturing process of CuZnSnSe (CZTSe) and CuInGaSe (CIGS) nanowire arrays obtained by one-step electrodeposition for p-n junction fabrication. CZTSe nanowires were obtained through electrodeposition in a polycarbonate membrane by applying a rectangular pulsed current, while their morphology was optimized by appropriately setting the potential and the electrolyte composition. The electrochemical parameters, including pH and composition of the solution, were optimized to obtain a mechanically stable array of nanowires. The samples were characterized by scanning electron microscopy, Raman spectroscopy, and energy-dispersion spectroscopy. The nanostructures obtained showed a cylindrical shape with an average diameter of about 230 nm and a length of about 3 m, and were interconnected due to the morphology of the polycarbonate membrane. To create the p-n junctions, first a thin film of CZTSe was electrodeposited to avoid direct contact between the ZnS and Mo. Subsequently, an annealing process was carried out at 500 °C in a S atmosphere for 40 min. The ZnS was obtained by chemical bath deposition at 95 °C for 90 min. Finally, to complete the cell, ZnO and ZnO:Al layers were deposited by magnetron-sputtering

On the Correlation Between CO Absorption and Far-Ultraviolet Non-Linear Extinction Toward Galactic OB Stars

A sample of 59 sight lines to reddened Galactic OB stars was examined for correlations of the strength of the CO Fourth Positive (A - X) absorption band system with the ultraviolet interstellar extinction curve parameters. We used archival high-dispersion NEWSIPS IUE spectra to measure the CO absorption for comparison to parametric fits of the extinction curves from the literature. A strong correlation with the non-linear far-UV curvature term was found with greater absorption, normalized to E(B-V), being associated with more curvature. A weaker trend with the linear extinction term was also found. Mechanisms for enhancing CO in dust environments exhibiting high non-linear curvature are discussed.Comment: 10 pages, including 6 figures. LaTeX2e (emulateapj5.sty). To appear in ApJ, Sep 20, 200

Diameters in preferential attachment models

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PA-models. There is a substantial amount of literature proving that, quite generally, PA-graphs possess power-law degree sequences with a power-law exponent \tau>2. We prove that the diameter of the PA-model is bounded above by a constant times \log{t}, where t is the size of the graph. When the power-law exponent \tau exceeds 3, then we prove that \log{t} is the right order, by proving a lower bound of this order, both for the diameter as well as for the typical distance. This shows that, for \tau>3, distances are of the order \log{t}. For \tau\in (2,3), we improve the upper bound to a constant times \log\log{t}, and prove a lower bound of the same order for the diameter. Unfortunately, this proof does not extend to typical distances. These results do show that the diameter is of order \log\log{t}. These bounds partially prove predictions by physicists that the typical distance in PA-graphs are similar to the ones in other scale-free random graphs, such as the configuration model and various inhomogeneous random graph models, where typical distances have been shown to be of order \log\log{t} when \tau\in (2,3), and of order \log{t} when \tau>3

Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo

Shannon dimensionality of quantum channels and its application to photon entanglement

We introduce the concept of Shannon dimensionality D as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens-coupled to a single-mode fiber. We can deduce the value of D directly from the observed two-photon coincidence fringe. In our experiment, D varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that D = 50 is experimentally within reach.Comment: 4 pages, 3 figures, accepted for Physical Review Letter