Self-Propelled Particles with Velocity Reversals and Ferromagnetic Alignment: Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order.

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.

Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits.

We provide numerical evidence that a finite-dimensional inertial manifold on which the dynamics of a chaotic dissipative dynamical system lives can be constructed solely from the knowledge of a set of unstable periodic orbits. In particular, we determine the dimension of the inertial manifold for the Kuramoto-Sivashinsky system and find it to be equal to the "physical dimension" computed previously via the hyperbolicity properties of covariant Lyapunov vectors.

Long-range ordering of vibrated polar disks.

Vibrated polar disks have been used experimentally to investigate collective motion of driven particles, where fully ordered asymptotic regimes could not be reached. Here we present a model reproducing quantitatively the single, binary, and collective properties of this granular system. Using system sizes not accessible in the laboratory, we show in silico that true long-range order is possible in the experimental system. Exploring the model's parameter space, we find a phase diagram qualitatively different from that of dilute or pointlike particle systems.

Nonperturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation.

We present the implementation of the Blaizot-Méndez-Wschebor approximation scheme of the nonperturbative renormalization group we present in detail, which allows for the computation of the full-momentum dependence of correlation functions. We discuss its significance and its relation with other schemes, in particular, the derivative expansion. Quantitative results are presented for the test ground of scalar O(N) theories. Besides critical exponents, which are zero-momentum quantities, we compute the two-point function at criticality in the whole momentum range in three dimensions and, in the high-temperature phase, the universal structure factor. In all cases, we find very good agreement with the best existing results.

Solutions of renormalization-group flow equations with full momentum dependence.

We demonstrate the power of a recently proposed approximation scheme for the nonperturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow equations obtained within this scheme and compute the two-point functions of the O(N) theories at criticality, in two and three dimensions. Excellent results are obtained for both universal and nonuniversal quantities at modest numerical cost.

Characterizing dynamics with covariant Lyapunov vectors.

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the Lyapunov exponents.

Active and passive particles: modeling beads in a bacterial bath.

A simple model for the motion of passive particles in a bath of active, self-propelled ones is introduced. It is argued that this approach provides the correct framework within which to cast the recent experimental results obtained by Wu and Libchaber [Phys Rev. Lett. 84, 3017 (2000)] for the diffusive properties of polystyrene beads displaced by bacteria suspended in a two-dimensional fluid film. Our results suggest that superdiffusive behavior should indeed be generically observed in the transition region marking the onset of collective motion.

Critical coarsening without surface tension: the universality class of the voter model.

We show that the two-dimensional voter model, usually considered to be only a marginal coarsening system, represents a broad class of models for which phase ordering takes place without surface tension. We argue that voter-like growth is generically observed at order-disorder nonequilibrium transitions solely driven by interfacial noise between dynamically symmetric absorbing states.

Rare-event induced binding transition of heteropolymers.

Sequence heterogeneity broadens the binding transition of a polymer onto a linear or planar substrate. This effect is analyzed in a real-space renormalization group scheme designed to capture the statistics of rare events. In the strongly disordered regime, binding initiates at an exponentially rare set of "good contacts." Renormalization of the contact potential yields a Kosterlitz--Thouless-type transition in any dimension. This and other predictions are confirmed by extensive numerical simulations of a directed polymer interacting with a columnar defect.

Comment on "Phase ordering in chaotic map lattices with conserved dynamics"

Angelini, Pellicoro, and Stramaglia [Phys. Rev. E 60, R5021 (1999)] claim that the phase ordering of two-dimensional systems of sequentially updated chaotic maps with conserved "order parameter" does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e., synchronously updated coupled map lattices, which are exempt from these crossover effects, and allow for precise estimates of persistence exponents in this case.