Dynamics of Rumor Spreading in Complex Networks

We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allow us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer to peer communication networks and social spreading phenomena.Comment: Final version to appear in PR

Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part II: Application to the Many-Body Problem

We analyze the ground state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [11]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean field plus spin wave approach. First, we determine shifts in the mean field phase border, which are most pronounced in the low density regime. Second, the investigation of the strong coupling limit reveals the existence of a new collective mode, which emerges as a consequence of enhanced symmetries in this regime. Third, we show that the Ising type phase transition, driven first order via the competition of long wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.Comment: 22 pages, 5 figure

Observability of Quantum Criticality and a Continuous Supersolid in Atomic Gases

We analyze the Bose-Hubbard model with a three-body hardcore constraint by mapping the system to a theory of two coupled bosonic degrees of freedom. We find striking features that could be observable in experiments, including a quantum Ising critical point on the transition from atomic to dimer superfluidity at unit filling, and a continuous supersolid phase for strongly bound dimers.Comment: 4 pages, 2 figures, published version (Editor's suggestion

Large Area Crop Inventory Experiment (LACIE). Intensive test site assessment report

There are no author-identified significant results in this report

Spreading of Persistent Infections in Heterogeneous Populations

Up to now, the effects of having heterogeneous networks of contacts have been studied mostly for diseases which are not persistent in time, i.e., for diseases where the infectious period can be considered very small compared to the lifetime of an individual. Moreover, all these previous results have been obtained for closed populations, where the number of individuals does not change during the whole duration of the epidemics. Here, we go one step further and analyze, both analytically and numerically, a radically different kind of diseases: those that are persistent and can last for an individual's lifetime. To be more specific, we particularize to the case of Tuberculosis' (TB) infection dynamics, where the infection remains latent for a period of time before showing up and spreading to other individuals. We introduce an epidemiological model for TB-like persistent infections taking into account the heterogeneity inherent to the population structure. This sort of dynamics introduces new analytical and numerical challenges that we are able to sort out. Our results show that also for persistent diseases the epidemic threshold depends on the ratio of the first two moments of the degree distribution so that it goes to zero in a class of scale-free networks when the system approaches the thermodynamic limit.Comment: 12 pages and 2 figures. Revtex format. Submitted for publication

Focus on out-of-equilibrium dynamics in strongly interacting one-dimensional systems

In the past few years, there have been significant advances in understanding out-of-equilibrium dynamics in strongly interacting many-particle quantum systems. This is the case for 1D dynamics, where experimental advances - both with ultracold atomic gases and with solid state systems - have been accompanied by advances in theoretical methods, both analytical and numerical. This 'focus on' collection brings together 17 new papers, which together give a representative overview of the recent advances

Don't break a leg: Running birds from quail to ostrich prioritise leg safety and economy in uneven terrain

Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics

Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments

We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to a theory with two coupled bosonic degrees of freedom with polynomial interactions, which have a natural interpretation as single particles and two-particle states. The procedure can be seen as a proper quantization of the Gutzwiller mean field theory. The theory is conveniently evaluated in the framework of the quantum effective action, for which the usual symmetry principles are now supplemented with a ``constraint principle'' operative on short distances. We test the theory via investigation of scattering properties of few particles in the limit of vanishing density, and we address the complementary problem in the limit of maximum filling, where the low lying excitations are holes and di-holes on top of the constraint induced insulator. This is the first of a sequence of two papers. The application of the formalism to the many-body problem, which can be realized with atoms in optical lattices with strong three-body loss, is performed in a related work [14].Comment: 21 pages, 5 figure

Heating and cooling in stellar coronae: coronal rain on a young Sun

Recent observations of rapidly-rotating cool dwarfs have revealed H$\alpha$ line asymmetries indicative of clumps of cool, dense plasma in the stars' coronae. These clumps may be either long-lived (persisting for more than one stellar rotation) or dynamic. The fastest dynamic features show velocities greater than the escape speed, suggesting that they may be centrifugally ejected from the star, contributing to the stellar angular momentum loss. Many however show lower velocities, similar to coronal rain observed on the Sun. We present 2.5D magnetohydrodynamic simulations of the formation and dynamics of these condensations in a rapidly rotating ($P_{\rm rot}~=~ 1 \ \mathrm{day}$) young Sun. Formation is triggered by excess surface heating. This pushes the system out of thermal equilibrium and triggers a thermal instability. The resulting condensations fall back towards the surface. They exhibit quasi-periodic behaviour, with periods longer than typical periods for solar coronal rain. We find line-of-sight velocities for these clumps in the range $50 \ \mathrm{km} \ \mathrm{s}^{-1}$ (blue shifted) to $250 \ \mathrm{km} \ \mathrm{s}^{-1}$(red shifted). These are typical of those inferred from stellar H$\alpha$line asymmetries, but the inferred clump masses of$3.6\times 10^{14}\ \mathrm{g}$are significantly smaller. We find that a maximum of$\simeq~3\%$ of the coronal mass is cool clumps. We conclude that coronal rain may be common in solar like stars, but may appear on much larger scales in rapid rotators.Comment: 11 pages, 5 figure