We present direct, real-time observations of emergent magnetic monopole dynamics in highly frustrated artificial spin ice.

Real growing networks such as the World Wide Web or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabási-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean-field rate equation for clustering. This is solved for a specific case with the result $C\left(k\right)\mathrm{}\sim 1/k$ for the clustering of a node of degree k. This mean-field exponent agrees with simulations, and reproduces the clustering of many real networks.

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the $m=1\mathrm{}$ case of the Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.

Cellular phones are now offering an ubiquitous means for scientists to observe life: how people act, move and respond to external influences. They can be utilized as measurement devices of individual persons and for groups of people of the social context and the related interactions. The picture of human life that emerges shows complexity, which is manifested in such data in properties of the spatiotemporal tracks of individuals. We extract from smartphone-based data for a set of persons important locations such as “home”, “work” and so forth over fixed length time-slots covering the days in the data-set (see also [1], [2]). This set of typical places is heavy-tailed, a power-law distribution with an exponent close to −1.7. To analyze the regularities and stochastic features present, the days are classified for each person into regular, personal patterns. To this are superimposed fluctuations for each day. This randomness is measured by “life” entropy, computed both before and after finding the clustering so as to subtract the contribution of a number of patterns. The main issue that we then address is how predictable individuals are in their mobility. The patterns and entropy are reflected in the predictability of the mobility of the life both individually and on average. We explore the simple approaches to guess the location from the typical behavior, and of exploiting the transition probabilities with time from location or activity A to B. The patterns allow an enhanced predictability, at least up to a few hours into the future from the current location. Such fixed habits are most clearly visible in the working-day length.

The spatial fluctuations of deformation are studied in the creep in Andrade's power law and the logarithmic phases, using paper samples. Measurements by the digital image correlation technique show that the relative strength of the strain rate fluctuations increases with time, in both creep regimes. In the Andrade creep phase characterized by a power-law decay of the strain rate ϵt$\sim${}t-$\theta${}, with $\theta${}$\approx${}0.7, the fluctuations obey $\Delta${}ϵt$\sim${}t-$\gamma${}, with $\gamma${}$\approx${}0.5. The local deformation follows a data collapse appropriate for a phase transition. Similar behavior is found in a crystal plasticity model, with a jamming or yielding transition.

Portevin–Le Chatelier deformation bands obey predictions of a simple mean-field model of critical avalanche dynamics.