Self-similar solutions of semilinear wave equations with a focusing nonlinearity

We prove that in three space dimensions a nonlinear wave equation $u_{tt}-\Delta u = u^p$ with $p\geq 7$ being an odd integer has a countable family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio

Zigzag transitions and nonequilibrium pattern formation in colloidal chains

Paramagnetic colloidal particles that are optically trapped in a linear array can form a zigzag pattern when an external magnetic field induces repulsive interparticle interactions. When the traps are abruptly turned off, the particles form a nonequilibrium expanding pattern with a zigzag symmetry, even when the strength of the magnetic interaction is weaker than that required to break the linear symmetry of the equilibrium state. We show that the transition to the equilibrium zigzag state is always potentially possible for purely harmonic traps. For anharmonic traps that have a finite height, the equilibrium zigzag state becomes unstable above a critical anharmonicity. A normal mode analysis of the equilibrium line configuration demonstrates that increasing the magnetic field leads to a hardening and softening of the spring constants in the longitudinal and transverse directions, respectively. The mode that first becomes unstable is the mode with the zigzag symmetry, which explains the symmetry of nonequilibrium patterns. Our analytically tractable models help to give further insight into the way that the interplay of such factors as the length of the chain, hydrodynamic interactions, thermal fluctuations affect the formation and evolution of the experimentally observed nonequilibrium patterns.Comment: 16 pages, 8 figures; to appear in the Journal of Chemical Physic

Social Sensing of Floods in the UK

"Social sensing" is a form of crowd-sourcing that involves systematic analysis of digital communications to detect real-world events. Here we consider the use of social sensing for observing natural hazards. In particular, we present a case study that uses data from a popular social media platform (Twitter) to detect and locate flood events in the UK. In order to improve data quality we apply a number of filters (timezone, simple text filters and a naive Bayes `relevance' filter) to the data. We then use place names in the user profile and message text to infer the location of the tweets. These two steps remove most of the irrelevant tweets and yield orders of magnitude more located tweets than we have by relying on geo-tagged data. We demonstrate that high resolution social sensing of floods is feasible and we can produce high-quality historical and real-time maps of floods using Twitter.Comment: 24 pages, 6 figure

Pattern formation in colloidal explosions

We study the non-equilibrium pattern formation that emerges when magnetically repelling colloids, trapped by optical tweezers, are abruptly released, forming colloidal explosions. For multiple colloids in a single trap we observe a pattern of expanding concentric rings. For colloids individually trapped in a line, we observe explosions with a zigzag pattern that persists even when magnetic interactions are much weaker than those that break the linear symmetry in equilibrium. Theory and computer simulations quantitatively describe these phenomena both in and out of equilibrium. An analysis of the mode spectrum allows us to accurately quantify the non-harmonic nature of the optical traps. Colloidal explosions provide a new way to generate well-characterized non-equilibrium behaviour in colloidal systems.Comment: New restructured version (supplementary material goes into main text, no change of content), added journal reference and DOI information; 6 pages, 6 figures, published in Europhysics Letters (EPL

Transport of a colloidal particle driven across a temporally oscillating optical potential energy landscape

A colloidal particle is driven across a temporally oscillating one-dimensional optical potential energy landscape and its particle motion is analysed. Different modes of dynamic mode locking are observed and are confirmed with the use of phase portraits. The effect of the oscillation frequency on the mode locked step width is addressed and the results are discussed in light of a high-frequency theory and compared to simulations. Furthermore, the influence of the coupling between the particle and the optical landscape on mode locking is probed by increasing the maximum depth of the optical landscape. Stronger coupling is seen to increase the width of mode locked steps. Finally, transport across the temporally oscillating landscape is studied by measuring the effective diffusion coefficient of a mobile particle, which is seen to be highly sensitive to the driving velocity and mode locking

Perturbation theory in a pure exchange non-equilibrium economy

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that if the economic agents have static preferences, which are also homogeneous in any of the steady states, the final wealth distribution is independent of the dynamics of the non-equilibrium theory. In particular, it is completely determined in terms of the initial conditions, and it is independent of the probability, and the network of interaction between agents. We show that the main effect of the network is to determine the relaxation time via the usual eigenvalue gap as in random walks on graphs.Comment: 7 pages, 2 figure