Developing scaling relations for the yield strength of nanoporous gold

In this work, the applicability of Gibson and Ashby’s porous scaling relations to nanoporous metals is discussed, and an updated equation is proposed for relating the yield strength of nanoporous gold to the yield strength of individual gold ligaments that form the porous structure. This new relation is derived from experimental measurements obtained by small-scale tensile testing and by nanoindentation, and incorporates the average ligament diameter. Nanoindentation data, obtained experimentally by the authors as well as reported by others in the literature, are reconciled with tensile test measurements previously reported by the present authors. The values of ligament yield strength calculated with the new scaling relation are found to agree with data reported from mechanical testing of nanowires, and the scaling relation thus represents a bridge between nanowire and nanoporous metal behaviour. In addition, calculations of yield strength for nanoporous gold samples with various ligament size and relative density are consistent with the experimentally determined values.     

Connectivity degrees in the threshold preferential attachment model

In this paper we present a study of the connectivity degrees of the threshold preferential attachment model, a generalization of the Barabási-Albert model to heterogeneous complex networks. The threshold model incorporates the states of the nodes in its preferential linking rule and assumes that the affinity between network nodes follows an inverse relationship with the distance between their states. We numerically analyze the connectivity degrees of the model, studying the influence of the main parameters on the distribution of connectivity degrees and its statistics, the average degree and highest degree of the network. We show that such statistics exhibit markedly different behaviors in the dependence on the model parameters, particularly as regards the interaction threshold. Nevertheless, we show that the two statistics converge in the limit of null threshold and often exhibit scaling that can be described by power laws of the model parameters.     

Nonexistence of Self-Similar Singularities for the 3D Incompressible Euler Equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations if the vorticity decays sufficiently fast near infinity in . By a similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in . This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions. The work was supported partially by the KOSEF Grant no. R01-2005-000-10077-0, and KRF Grant (MOEHRD, Basic Research Promotion Fund).     

Molecular dynamics study of the shear strength and fracture behavior of nanoporous graphene membranes

We perform molecular dynamics (MD) simulations to study the structural response and fracture characteristics of nanoporous graphene (NPG) membranes subjected to shear loading. The effects of porosity, temperature, and shear velocity on the mechanical responses of NPG membranes are examined. The results show that the wrinkling of the membrane becomes more obvious with increasing strain. Fractures occur around holes on the long diagonal of the NPG parallelogram, and fracture stress in the NPG membrane decreases with increasing porosity. In addition, the effect of shear velocity on the shear modulus decreases with increasing porosity. The fracture strain of NPG membranes with different porosities obviously decreases with increasing temperature. The results enhance our understanding of the shear mechanical properties of NPG membranes and are helpful for the design and application of high-performance NPG membranes.     

Inevitable self-similar topology of binary trees and their diverse hierarchical density

Self-similar topology, which can be characterized as power law size distribution, has been found in diverse tree networks ranging from river networks to taxonomic trees. In this study, we find that the statistical self-similar topology is an inevitable consequence of any full binary tree organization. We show this by coding a binary tree as a unique bifurcation string. This coding scheme allows us to investigate trees over the realm from deterministic to entirely random trees. To obtain partial random trees, partial random perturbation is added to the deterministic trees by an operator similar to that used in genetic algorithms. Our analysis shows that the hierarchical density of binary trees is more diverse than has been described in earlier studies. We find that the connectivity structure of river networks is far from strict self-similar trees. On the other hand, organization of some social networks is close to deterministic supercritical trees.     

Synchronization on overlapping community network

In this paper, we propose a simple random network model with overlapping communities controlled by several parameters, and investigate the influence of the overlapping community structure on the synchronization behavior under different parameters. It is found that the synchronizability of the network is mainly influenced by the overlapping size of the communities and the connectivity density of the overlapped group to the other interrelated communities, and has nothing to do with the intra-connectivity of the overlapped group. In addition, it is found that the highly interconnected communities can be almost synchronized in a given time scale, whereas the overlapped group is far from synchronization. Furthermore, the instantaneous frequencies of the nodes in the communities and their overlapped group are also investigated, which show that the nodes in the overlapped group will exhibit a remarkable oscillation with a weighted mean frequency of the other correlative communities.     

A method for vibrational assessment of cortical bone

Large bones from many anatomical locations of the human skeleton consist of an outer shaft (cortex) surrounding a highly porous internal region (trabecular bone) whose structure is reminiscent of a disordered cubic network. Age related degradation of cortical and trabecular bone takes different forms. Trabecular bone weakens primarily by loss of connectivity of the porous network, and recent studies have shown that vibrational response can be used to obtain reliable estimates for loss of its strength. In contrast, cortical bone degrades via the accumulation of long fractures and changes in the level of mineralization of the bone tissue. In this paper, we model cortical bone by an initially solid specimen with uniform density to which long fractures are introduced; we find that, as in the case of trabecular bone, vibrational assessment provides more reliable estimates of residual strength in cortical bone than is possible using measurements of density or porosity.     

Deterministic self-similar models of complex networks based on very symmetric graphs

Using very symmetric graphs we generalize several deterministic self-similar models of complex networks and we calculate the main network parameters of our generalization. More specifically, we calculate the order, size and the degree distribution, and we give an upper bound for the diameter and a lower bound for the clustering coefficient. These results yield conditions under which the network is a self-similar and scale-free small world network. We remark that all these conditions are posed on a small base graph which is used in the construction. As a consequence, we can construct complex networks having prescribed properties. We demonstrate this fact on the clustering coefficient. We propose eight new infinite classes of complex networks. One of these new classes is so rich that it is parametrized by three independent parameters.     

Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds

We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquely isoperimetric in manifolds that are Schwarzschild–anti-deSitter at infinity. These results have important repercussions for our understanding of spacelike hypersurfaces in Lorentzian space-times which are asymptotic to null infinity. In fact, as an application of our results, we verify the asymptotically hyperbolic Penrose inequality in the special case of the existence of connected isoperimetric regions of all volumes.     

Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α⁽¹⁾ and α⁽²⁾ for SS and SR interactions, respectively. The effect of variation of α⁽¹⁾ and α⁽²⁾ on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.     

Isolation and Connectivity in Random Geometric Graphs with Self-similar Intensity Measures

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson distributed, and the probability of no isolated nodes is equal to the probability the whole graph is connected. Here we examine these properties for several self-similar node distributions, including smooth and fractal, uniform and nonuniform, and finitely ramified or otherwise. We show that nonuniformity can break the Poisson distribution property, but it strengthens the link between isolation and connectivity. It also stretches out the connectivity transition. Finite ramification is another mechanism for lack of connectivity. The same considerations apply to fractal distributions as smooth, with some technical differences in evaluation of the integrals and analytical arguments.     

A Resiliency-Connectivity metric in wireless sensor networks with key predistribution schemes and node compromise attacks

Applications for wireless sensor networks require widespread, highly reliable communications even in the face of adversarial influences. Maintaining connectivity and secure communications between entities are vital networking properties towards ensuring the successful and accurate completion of desired sensing tasks. We examine the required communication range for nodes in a wireless sensor network with respect to several parameters. Network properties such as key predistribution schemes and node compromise attacks are modelled with several network parameters and studied in terms of how they influence global network connectivity. These networks are physically vulnerable to malicious behavior by way of node compromise attacks that may affect global connectivity. We introduce a metric that determines the resilience of a network employing a key predistribution scheme with respect to node compromise attacks. In this work,we provide the first study of global network connectivity and its relationship to node compromise attacks. Existing work considers the relationship between the probability of node compromise and the probability of link compromise and the relationship of the probability of secure link establishment and overall network connectivity for the Erdős network model. Here, we present novel work which combines these two relationships to study the relationship between node compromise attacks and global network connectivity. Our analysis is performed with regard to large-scale networks; however, we provide simulation results for both large-scale and small-scale networks. First, we derive a single expression to determine the required communication radius for wireless sensor networks to include the effects of key predistribution schemes. From this, we derive an expression for determining required communication range after an adversary has compromised a fraction of the nodes in the network. The required communication range represents the resource usage of nodes in a network to cope with key distribution schemes and node compromise attacks. We introduce the Resiliency-Connectivity metric, which measures the resilience of a network in expending its resources to provide global connectivity in adverse situations.     

Modelling of the influence of dihedral angle,volume fractions,particle size and coordination on the driving forces for sintering of dual phase systems

The equilibrium shape of solid particles in an aggregate immersed in a liquid or in a gas results from the minimization of interface energy. A model is developed for expressing the dependence of the solid–solid and solid–second phase interface areas on the system parameters: phase volume fractions, dihedral angle, particle size and coordination. The model aims at allowing quantitative assessment of the role of these parameters on the driving force for sintering. The representative volume element is a cone of which the apex angle accounts for the average particle coordination. In order to comply with the uniformity of interface curvature, the solid–second phase interfaces are described using the mathematics of the Delaunay surfaces. The results are compared with the solutions obtained by approximating the interface shape by the revolution of an arc of circle around the cone axis. This approximation does not involve a significant loss of precision.     

Injection Molding of Wood–Fiber/Plastic Composite Foams

This paper investigates the feasibility of injection-molded wood–fiber/high-density polyethylene (HDPE) composite foams that can replace injection-molded HDPE solids in industrial applications. The study applies injection foam molding technology using a physical blowing agent to a wood–fiber/HDPE composite, and examines the effects of the processing parameters on the dimensional and mechanical properties and cell density of the composite foams. In addition, the physical properties and cost of wood–fiber/HDPE composite foams are compared with those of solid HDPE. The experimental results show that wood–fiber/HDPE composite foams that have a 20% weight reduction have superior physical properties, such as density, dimensional properties (68% decrease of shrinkage and 91% decrease of warpage) and mechanical properties (28% increase of Young's modulus). Furthermore, the cost analysis confirms that wood–fiber/HDPE composite foams are much less expensive (by 40%) than HDPE. Therefore, it is concluded that wood–fiber/HDPE composite foams are strong candidates for replacing current injection-molded HDPE products.     

"WHIMPERS" IN SELF-SIMILAR COSMOLOGIES

We examine how self-similarity influences the occurrence & nature of singularities in self-similar cosmologies. There exists a density divergence due to a conformal factor in any Self-similar model. If we discuss the singularity problem in an "unphysical" homogeneous model which is conformally related to the self-similar model, it is easy to show-that in a Class D model with -36/2, singularity bebaviour is similar to that in homogeneous comrologies; The Boyer-Ehlers analysis of Killing geodesicsic has been generalized to the self-similar case. Some new Penrosediagrams are given.     

Excitable elements controlled by noise and network structure

We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we apply a mean-field theory for the network and then use a Gaussian approximation to obtain a closed set of deterministic differential equations. These equations govern the order parameters of the network. We find that a uniform decrease in the number of connections per element in a homogeneous network merely shifts the bifurcation thresholds without producing qualitative changes in the network dynamics. In contrast, heterogeneity in the number of connections leads to bifurcations in the excitable regime. In particular we show that a critical value of noise intensity for the saddle-node bifurcation decreases with growing connectivity variance. The corresponding critical values for the onset of global oscillations (Hopf bifurcation) show a non-monotone dependency on the structural heterogeneity, displaying a minimum at moderate connectivity variances.     

Synchronizability of chaotic logistic maps in delayed complex networks

We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two regimes of synchronization, depending on the distribution of delays: when the delays are sufficiently heterogeneous the network synchronizes on a steady-state (that is unstable for the uncoupled maps); when the delays are homogeneous, it synchronizes in a time-dependent state (that is either periodic or chaotic). Using two global indicators we quantify the synchronizability on the two regimes, focusing on the roles of the network connectivity and the topology. The connectivity is measured in terms of the average number of links per node, and we consider various topologies (scale-free, small-world, star, and nearest-neighbor with and without a central hub). With weak connectivity and weak coupling strength, the network displays an irregular oscillatory dynamics that is largely independent of the topology and of the delay distribution. With heterogeneous delays, we find a threshold connectivity level below which the network does not synchronize, regardless of the network size. This minimum average number of neighbors seems to be independent of the delay distribution. We also analyze the effect of self-feedback loops and find that they have an impact on the synchronizability of small networks with large coupling strengths. The influence of feedback, enhancing or degrading synchronization, depends on the topology and on the distribution of delays.     

1/ƒ noise spectrum on self-similar cascade of bifurcation processes

Using the analogy of an electric network we show that a self-similar process of the decay of macroscopic current fluctuation can give a 1/? like noise spectrum.     

Forward Discretely Self-Similar Solutions of the Navier–Stokes Equations

Extending the work of Jia and ?verák on self-similar solutions of the Navier–Stokes equations, we show the existence of large, forward, discretely self-similar solutions.     

Disease spreading in structured scale-free networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. Received 16 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: yamir@ictp.trieste.it