We show that the space in which scientific, technological and economic activities interplay with each other can be mathematically shaped using techniques from statistical physics of networks. We build a holistic view of the innovation system as the tri-layered network of interactions among these many activities (scientific publication, patenting, and industrial production in different sectors), also taking into account the possible time delays. Within this construction we can identify which capabilities and prerequisites are needed to be competitive in a given activity, and even measure how much time is needed to transform, for instance, the technological know-how into economic wealth and scientific innovation, being able to make predictions with a very long time horizon. We find empirical evidence that, at the aggregate scale, technology is the best predictor for industrial and scientific production over the upcoming decades.

Long-range interacting systems, while relaxing to equilibrium, often get trapped in long-lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system in a quasistationary state (QSS) responds to an external perturbation. We consider a long-range system that evolves under deterministic Hamilton dynamics. The perturbation is taken to couple to the canonical coordinates of the individual constituents. Our study is based on analyzing the Vlasov equation for the single-particle phase-space distribution. The QSS represents a stable stationary solution of the Vlasov equation in the absence of the external perturbation. In the presence of small perturbation, we linearize the perturbed Vlasov equation about the QSS to obtain a formal expression for the response observed in a single-particle dynamical quantity. For a QSS that is homogeneous in the coordinate, we obtain an explicit formula for the response. We apply our analysis to a paradigmatic model, the Hamiltonian mean-field model, which involves particles moving on a circle under Hamiltonian dynamics. Our prediction for the response of three representative QSSs in this model (the water-bag QSS, the Fermi-Dirac QSS, and the Gaussian QSS) is found to be in good agreement with N-particle simulations for large N. We also show the long-time relaxation of the water-bag QSS to the Boltzmann-Gibbs equilibrium state.

We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to "arch" solutions forming a globally polar, smectic arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics. arXiv:1904.12708v1 [cond-mat.soft]

Mean-field theory tells us that the classical critical exponent of susceptibility is twice that of magnetization. However, linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances, in the low-energy phase. We clarify that this strange exponent is due to the existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by N-body simulations for the equilibrium states and a family of quasistationary states.

We show that fore-aft asymmetry, a generic feature of living organisms and some active matter systems, can have a strong influence on the collective properties of even the simplest flocking models. Specifically, an arbitrarily weak asymmetry favoring front neighbors changes qualitatively the phase diagram of the Vicsek model. A region where many sharp traveling band solutions coexist is present at low noise strength, below the Toner-Tu liquid, at odds with the phase-separation scenario well describing the usual isotropic model. Inside this region, a 'banded liquid' phase with algebraic density distribution coexists with band solutions. Linear stability analysis at the hydrodynamic level suggests that these results are generic and not specific to the Vicsek model.Non-reciprocal (effective) interactions are interesting but rather rare in physical systems [1]. They are, however, likely to be more common in active matter. A nice example of action-reaction symmetry breaking was given recently by Soto and Golestanian for catalytically active colloids [2]. A strong case is that of self-propelled objects interacting solely via volume exclusion: their shape governs their effective interaction (e.g. aligning or not) and thus their collective behavior [3]. In the context of animal and human collective motion, asymmetric interactions are quite generic, and this asymmetry lies mostly in the relative position and weight of neighbors: the importance and quality of the information perceived by living organisms usually varies with its origin: In animal groups one often -but not always, cf. the cannibalistic behavior of locusts in [4,5]-expects that frontal stimuli such as neighbor positions matter more to an individual than events taking place in its back. Somewhat surprisingly, this generic fore-aft asymmetry has not been much investigated per se. It is explicitly mentioned in some works [6], and implicitly present in a number of models, see, e.g. [7], and the rather complicated escape-pursuit mechanisms introduced in [8,9] to describe marching locusts, or the 'motion guided attention' of [10]. It can even be found in variants of simple flocking models such as the Vicsek model, where local alignment of constantspeed particles competes with noise [22][23][24]. In [15][16][17][18][19], the introduction of a limited angle of vision was shown to have an influence on the shape of cohesive moving groups, on the degree of ordering, etc. Asymmetric interactions are also present in 'metric-free' models introduced in the context of bird flocks [11][12][13][14].In all cases mentioned above, it was not shown that fore-aft asymmetry alone can lead to qualitatively new collective phenomena. Recently, though, the influence of fore-aft asymmetric neighbors was investigated in the context of flocking models incorporating fast 'inertial spin' variables [20,21]. Both these works argue that the combination of asymmetric neighbors and fast variables induces new collective behavior.In this Letter, we show that fore-aft asymmetry alone has a strong i...

We investigate the dynamics of a small long-range interacting system, in contact with a large long-range thermal bath. Our analysis reveals the existence of striking anomalies in the energy flux between the bath and the system. In particular, we find that the evolution of the system is not influenced by the kinetic temperature of the bath, as opposed to what happens for short-range collisional systems. As a consequence, the system may get hotter also when its initial temperature is larger than the bath temperature. This observation is explained quantitatively in the framework of the collisionless Vlasov description of toy models with long-range interactions and shown to be valid whenever the Vlasov picture applies, from cosmology to plasma physics.

We introduce and study in two dimensions a new class of dry, aligning active matter that exhibits a direct transition to orientational order, without the phase-separation phenomenology usually observed in this context. Characterized by self-propelled particles with velocity reversals and a ferromagnetic alignment of polarities, systems in this class display quasi-long-range polar order with continuously varying scaling exponents, yet a numerical study of the transition leads to conclude that it does not belong to the Berezinskii-Kosterlitz-Thouless universality class but is best described as a standard critical point with an algebraic divergence of correlations. We rationalize these findings by showing that the interplay between order and density changes the role of defects.

We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann-Ginzburg-Landau approach. The hydrodynamic equations are obtained from a Boltzmann equation expressed in terms of an expansion in spherical harmonics. All their transport coefficients are given with explicit dependences on particle-level parameters. The linear stability analysis of their spatiallyhomogeneous solutions is presented. While the equations derived for the polar case (original Vicsek model with ferromagnetic alignment) and their solutions do not differ much from their 2D counterparts, the active nematics case exhibits remarkable differences: we find a true discontinuous transition to order with a bistability region, and cholesteric solutions whose stability we discuss.