arXiv subjects

Petter Holme

Publications and source records attributed to Petter Holme.

156 records · Page 9Linked to original sources

arXiv2003

Phase Transitions in the Two-Dimensional Random Gauge XY Model

The two-dimensional random gauge \xy model, where the quenched random variables are magnetic bond angles uniformly distributed within $[-rπ, rπ]$ ($0 \leq r \leq 1$), is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature $T$ and the disorder strength $r$, and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength $r$ for sufficiently low $T$. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.

cond-mat.supr-con↗

arXiv2003

Congestion and centrality in traffic flow on complex networks

The central points of communication network flow has often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the underlying network structure. In this work we investigate the relationship between centrality measures and the density of traffic for some simple particle hopping models on networks with emerging scale-free degree distributions. We also study how the speed of the dynamics are affected by the underlying network structure. Among other conclusions, we find that, even at low traffic densities, the dynamical measure of traffic density (the occupation ratio) has a non-trivial dependence on the static centrality (quantified by "betweenness centrality"), which non-central vertices getting a comparatively large portion of the traffic.

cond-mat.dis-nn↗

arXiv2002

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.

cond-mat.dis-nn↗

arXiv2002

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.

cond-mat.dis-nn↗

arXiv2002

Subnetwork hierarchies of biochemical pathways

We present a method to decompose biochemical networks into subnetworks based on the global geometry of the network. This method enables us to analyse the full hierarchical organisation of biochemical networks and is applied to 43 organisms from the WIT database. Two types of biochemical networks are considered: metabolic networks and whole-cellular networks (also including e.g. information processes). Conceptual and quantitative ways of describing the hierarchical ordering are discussed. The general picture of the metabolic networks arising from our study is that of a few core-clusters centred around the most highly connected substances enclosed by other substances in outer shells, and a few other well-defined subnetworks.

cond-mat.dis-nn↗

arXiv2002

Vertex overload breakdown in evolving networks

We study evolving networks based on the Barabasi-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanche-like breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case is also studied). Implications on the growth of the Internet is discussed.

cond-mat.dis-nn↗

arXiv2002

Attack vulnerability of complex networks

We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending order of the degree and the betweenness centrality, calculated for either the initial network or the current network during the removal procedure. It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Furthermore, the correlation between the betweenness centrality and the degree in complex networks is studied.

cond-mat.dis-nn↗

arXiv2001

A Zero-Temperature Study of Vortex Mobility in Two-Dimensional Vortex Glass Models

Three different vortex glass models are studied by examining the energy barrier against vortex motion across the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which is interpreted as evidence for a low-temperature phase with zero resistivity. Associated with the large energy barriers is a breaking of ergodicity which explains why the well established results from equilibrium studies could fail. The behavior of the more realistic random pinning model is however different with decreasing energy barriers a no finite critical temperature.

cond-mat.supr-con↗

arXiv2001

Growing Scale-Free Networks with Tunable Clustering

We extend the standard scale-free network model to include a ``triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks like the power-law degree distribution and the small average geodesic length, but with the high-clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter - the average number of triad formation trials per time step.

cond-mat.dis-nn↗

arXiv2001

XY model in small-world networks

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte-Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally-coupled XY model.

cond-mat.stat-mech↗

arXiv2000

The Transition in the Two-Dimensional Step Model: A Kosterlitz-Thouless Transition in Disguise

Evidence for a Kosterlitz-Thouless transition in the 2D step model is obtained from Monte Carlo determinations of the helicity modulus. It is argued that the free energy of a single vortex at the center of the system depends logarithmically on the system size in spite of the fact that the spin interaction is not harmonic for small differences in the spin angles. We conclude that this is the reason for the Kosterlitz-Thouless transition in the 2D step model and that the harmonic spin interaction not is a necessary requirement.

cond-mat.stat-mech↗

arXiv1999

High-Tc Superconductors in Applied Magnetic Fields Parallel to the CuO Planes: First Order Transition with Slow Onset of Resistivity

The three dimensional uniformly frustrated XY model is used as a model of a high temperature superconductor in an applied magnetic field parallel to the CuO-planes. Through Monte Carlo simulations with anisotropy $η^2 = 10$ on large lattices we find evidence for a first order transition. Earlier simulations and theoretical treatments are discussed and the experimentally found smooth onset of resistivity is suggested to be due to a large potential barrier against vortex line motion above $T_c$ present for perfect alignment of the applied field.

cond-mat↗