Nature of segregation of reactants in diffusion controlled A+B reactions: Role of mobility in forming compact clusters

We investigate the A+B=0 bimolecular chemical reaction taking place in low-dimensional spaces when the mobilities of the two reacting species are not equal. While the case of different reactant mobilities has been previously reported as not affecting the scaling of the reactant densities with time, but only the pre-exponential factor, the mechanism for this had not been explained before. By using Monte-Carlo simulations we show that the nature of segregation is very different when compared to the normal case of equal reactant mobilities. The clusters of the mobile species are statistically homogeneous and randomly distributed in space, but the clusters of the less mobile species are much more compact and restricted in space. Due to the asymmetric mobilities, the initial symmetric random density fluctuations in time turn into asymmetric density fluctuations. We explain this trend by calculating the correlation functions for the positions of particles for the several different cases

Scale-free networks resistant to intentional attacks

We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure such networks surprisingly remain very robust even under removal of a large fraction of their nodes, which in some cases can be up to 70%. The degree distribution $P(k)$ of these structures is such that for small values of the degree $k$ the distribution is constant with $k$, up to a critical value $k_c$, and thereafter it decays with $k$ with the usual power law. We describe in detail a model for such a scale-free network with this modified degree distribution, and we show both analytically and via simulations, that this model can adequately describe all the features and breakdown characteristics of these attacks. We have found several experimental networks with such features, such as for example the IMDB actors collaboration network or the citations network, whose resilience to attacks can be accurately described by our model.Comment: 5 pages, 4 figure

Models for designing pipe-grade polyethylenes to resist rapid crack propagation

Plastic pipeline systems have now become dominant for fuel-gas and water distribution networks. Although they have an impressive service record failures do occur, with Rapid Crack Propagation being characterised as the least probable but most potentially catastrophic one. This study investigates the effect of structural morphology and bulk residual strains on the RCP performance of polyethylene pipes, and proposes a new methodology for predicting a safe service envelope. During crack propagation in PE pipes, the fracture surface has two distinct regions; plane strain and plane stress. In addition to the Instrumented Charpy, Reversed Charpy, High Speed Double Torsion, Dynamic Mechanical Analysis and uniaxial tensile testing, S4 tests of extruded pipe specimens were employed in order to evaluate the structural and fracture parameters of pipe grade resins in these two fracture modes on pipe. A new experimental technique, which modified the pipe bore crystallinity without altering the residual strain field (as evaluated from slit ring tests) showed that the bore surface layer properties had much less influence on RCP than previously thought. Parallel with the experimental work, modeling of the fracture mechanisms was also undertaken. Using previous models in the field, such as the adiabatic decohesion model, the plane strain fracture toughness was evaluated while the plane stress fracture toughness was evaluated either from the Reversed Charpy or from the stability of adiabatic drawing in a tensile test. A mixed mode, temperature sensitive toughness was finally evaluated, leading to an overall fracture properties assessment for polyethylene pipes which could be compared directly to the crack driving force during RCP in pipe. By employing a new mathematical approach, which incorporated both the effects of residual strains and pipe stiffness behind the pressure decay length, a previous basic analytical RCP model was further developed and compared to more elaborate finite element and finite volume solutions. The new results were also compared to S4 experiments using high-speed photography and showed that the new methodology could be employed by the end user even when testing facilities are not directly availabl

Reaction-diffusion processes on correlated and uncorrelated scale-free networks

We compare reaction-diffusion processes of the $A+A\to 0$ type on scale-free networks created with either the configuration model or the uncorrelated configuration model. We show via simulations that except for the difference in the behavior of the two models, different results are observed within the same model when the minimum number of connections for a node varies from $k_{\rm min}=1$ to $k_{\rm min}=2$. This difference is attributed to the varying local properties of the two systems. In all cases we are able to identify a power law behavior of the density decay with time with an exponent $f>1$, considerably larger than its lattice counterpart

Fracture mechanics analysis of arc shaped specimens for pipe grade polymers

Accepted versio

Percolation of randomly distributed growing clusters

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low initial values of $p$ we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a site to belong to the finally formed spanning cluster, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.Comment: 5 pages, 7 figure

Static and dynamic behavior of multiplex networks under interlink strength variation

It has recently been suggested \cite{Radicchi2013} that in a two-level multiplex network, a gradual change in the value of the "interlayer" strength $p$ can provoke an abrupt structural transition. The critical point $p^*$ at which this happens is system-dependent. In this article, we show in a similar way as in \cite{Garrahan2014} that this is a consequence of the graph Laplacian formalism used in \cite{Radicchi2013}. We calculate the evolution of $p^{*}$ as a function of system size for ER and RR networks. We investigate the behavior of structural measures and dynamical processes of a two-level system as a function of $p$, by Monte-Carlo simulations, for simple particle diffusion and for reaction-diffusion systems. We find that as $p$ increases there is a smooth transition from two separate networks to a single one. We cannot find any abrupt change in static or dynamic behavior of the underlying system.Comment: 8 pages, 5 figure

Anomalous biased diffusion in networks

We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the packet/particle to travel at every hop towards a site which is along the shortest path to the target node. We investigate the scaling of the mean first passage time (MFPT) with the size of the network. We find by using theoretical analysis and computer simulations that for Random Regular (RR) and Erd\H{o}s-R\'{e}nyi (ER) networks, there exists a threshold probability, $p_{th}$, such that for $p<p_{th}$ the MFPT scales anomalously as $N^\alpha$, where $N$ is the number of nodes, and $\alpha$ depends on $p$. For $p>p_{th}$ the MFPT scales logarithmically with $N$. The threshold value $p_{th}$ of the bias parameter for which the regime transition occurs is found to depend only on the mean degree of the nodes. An exact solution for every value of $p$ is given for the scaling of the MFPT in RR networks. The regime transition is also observed for the second moment of the probability distribution function, the standard deviation.Comment: 13 Pages, To appear in PR