A Novel Approach to Discontinuous Bond Percolation Transition

We introduce a bond percolation procedure on a $D$-dimensional lattice where two neighbouring sites are connected by $N$ channels, each operated by valves at both ends. Out of a total of $N$, randomly chosen $n$ valves are open at every site. A bond is said to connect two sites if there is at least one channel between them, which has open valves at both ends. We show analytically that in all spatial dimensions, this system undergoes a discontinuous percolation transition in the $N\to \infty$ limit when $\gamma =\frac{\ln n}{\ln N}$ crosses a threshold. It must be emphasized that, in contrast to the ordinary percolation models, here the transition occurs even in one dimensional systems, albeit discontinuously. We also show that a special kind of discontinuous percolation occurs only in one dimension when $N$ depends on the system size.Comment: 6 pages, 6 eps figure

Sampling properties of directed networks

For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.Comment: 21 pages, 11 figure

Random elastic networks : strong disorder renormalization approach

For arbitrary networks of random masses connected by random springs, we define a general strong disorder real-space renormalization (RG) approach that generalizes the procedures introduced previously by Hastings [Phys. Rev. Lett. 90, 148702 (2003)] and by Amir, Oreg and Imry [Phys. Rev. Lett. 105, 070601 (2010)] respectively. The principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or a spring constant. To explain the accuracy of the strong disorder RG rules, we compare with the Aoki RG rules that are exact at fixed frequency.Comment: 8 pages, v2=final versio

Two-dimensional SIR epidemics with long range infection

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart. As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For $\sigma=2$ we find generic power laws with $\sigma-$dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on $\sigma$ in the regime $0<\sigma <2$, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for $\sigma$ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder {\it et al.}. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.Comment: 14 pages, including 29 figure

How to share underground reservoirs

Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fractal dimension ${1.55\pm0.03}$, the set of all lines has dimension ${1.69\pm0.02}$. The size distribution of the loops follows a power law and the evolution of the set of lines exhibits a tricritical point described by a crossover with a negative dimension at criticality

Exact solutions for mass-dependent irreversible aggregations

We consider the mass-dependent aggregation process (k + 1) X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with k neighbors in one dimension, or-in the well-mixed case-with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite-size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed

Dual Mechanical Port Machine Based Hybrid Electric Vehicle Using Reduced Switch Converters

Due to the increased environmental pollution, hybrid vehicles have attracted enormous attention in today's society. The two most important factors in designing these vehicles are size and weight. For this purpose, some researchers have presented the use of the dual-mechanical-port machine (DMPM) in hybrid electric vehicles (HEVs). This paper presents two modified converter topologies with a reduced number of switching devices for use on DMPM-based HEVs, with the goal of reducing the overall size and weight of the system. Beside the design of the DMPM in the series-parallel HEV structure along with the energy management unit, the conventional back-to-back (BB) converter is replaced with nine-switch (NS) and five-leg (FL) converters. These converters have never been examined for the DMPM-based HEV, and therefore, the objective of this paper is to reveal the operational characteristics and power flow mechanism of this machine using the NS and FL converters. The simulation analysis is carried out using MATLAB/Simulink considering all HEV operational modes. In addition, two proposed and the conventional converters are compared in terms of losses, maximum achievable voltages, required dc-link voltages, the rating of the components, and torque ripple, and finally, a recommendation is made based on the obtained results