We propose a simple microscopic model for active nematic particles similar in spirit to the Vicsek model for self-propelled polar particles. In two dimensions, we show that this model exhibits a Kosterlitz-Thouless-like transition to quasi-long-range orientational order and that in this nonequilibrium context, the ordered phase is characterized by giant density fluctuations, in agreement with the predictions of Ramaswamy et al.

We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an OrnsteinUhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a telegraphic noise process is at play, explaining thus the emergence and structure of the vortex lattices observed here and in motility assay experiments.PACS numbers: 05.65.+b, 45.70.Vn, 87.18.Gh Self-propelled particles are nowadays commonly used to study collective motion and more generally "dry" active matter, where the surrounding fluid is neglected. Real world relevant situations include shaken granular particles [1][2][3][4][5], active colloids [6][7][8], bio-filaments displaced by motor proteins [9][10][11]. The trajectories of moving living organisms (from bacteria to large animals such as fish, birds and even human crowds) are also routinely modeled by such particles, see e.g. [12][13][14][15][16][17].Many of these 'active particles' travel at near-constant speed with their dynamics modeled as a persistent random walk with some stochastic component acting directly on their orientation [18]. This noise, which represents external and/or internal perturbations, produces jagged irregular trajectories. Most of the recent results on active matter have been obtained in this context of overdamped dynamics.In many situations, however, the overdamped approximation is not justified. In particular, trajectories can be essentially smooth, as for chemically propelled rods [19,20], birds, some large fish that swim steadily [16], or even biofilaments in motility assays with a high density of molecular motors [10]. Whether underdamped dynamics can make a difference at the level of collective asymptotic properties is largely unknown. Interesting related progress was recently reported for starling flocks [21]. Underdamped "spin" variables are instrumental there for efficient, fast transfer of information through the flock, allowing swift turns in response to threats during which speed is modulated in a well coordinated manner. In the other examples cited above, speed remains nearlyconstant and the persistently turning tracks of fish or microtubules reveal some finite, possibly large, memory of the curvature. In this context an Ornstein-Uhlenbeck (OU) process acting on the angular velocity was shown to be a quantitatively-valid representation [10,16]. The collective motion of self-propelled particles with such underdamped angular dynamics remains largely unknown.In this Letter, we explore minimal models of aligning self-propelled particles with memory similar to that used in [10] to study the emergence of large-scale vortices in mot...

The cross-wavelet transform (XWT) is a powerful tool for testing the proposed connections between two time series. Because of XWT’s skeletal structure, which is based on the wavelet transform, it is suitable for the analysis of nonstationary periodic signals. Recent work has shown that the power spectrum based on the wavelet transform can produce a deviation, which can be corrected by choosing a proper rectification scale. In this study, it is shown that the standard application of the XWT can also lead to a biased result. A corrected version of the standard XWT was constructed using the scale of each series as normalizing factors. This correction was first tested with an artificial example involving two series built from combinations of two harmonic series with different amplitudes and frequencies. The standard XWT applied to this example produces a biased result, whereas the correct result is obtained with the use of the proposed normalization. This analysis was then applied to a real geophysical situation with important implications to climate modulation on the northwestern Brazilian coast. The linkage between the relative humidity and the shortwave radiation measurements, obtained from the 8°S, 30°W Autonomous Temperature Line Acquisition System (ATLAS) buoy of the Southwestern Extension of the Prediction and Research Moored Array in the Tropical Atlantic (PIRATA-SWE), was explored. The analysis revealed the importance of including the correction in order to not overlook any possible connections. The requirements of incorporating this correction in the XWT calculations are emphasized.

We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number. PACS: 05.45.+b,82.40.Bj,05.70.Ln Spatio-temporal complex dynamics [1,2] is one of the present focus of research in nonlinear phenomena. Much effort has been devoted to the characterization of different dynamical phases and transitions between them for model equations such as the Complex Ginzburg-Landau Equation (CGLE) [1,[3][4][5][6][7][8][9][10][11]. One of the main questions driving these studies is whether concepts brought from statistical mechanics can be useful for describing complex nonequilibrium systems [3,12]. In this paper we give a characterization of the spatio-temporal configurations that occur in the Phase Turbulence (PT) regime of the CGLE (described below), for a finite system, in terms of a global wavenumber. This quantity plays the role of an order parameter classifying different phases. We show that in the PT regime there is an instability such that a conservation law for the global wavenumber occurs only for wavenumbers within a finite range that depends on the point in parameter space. Our study is statistical in the sense that averages over ensembles of initial conditions are used. Our results allow a characterization of the transition from PT to Defect or Amplitude Turbulence (DT) (another known dynamical regime of the CGLE) as the line in parameter space in which the range of conserved global wavenumbers shrinks to zero.The CGLE is an amplitude equation for a complex field A(x, t) describing universal features of the dynamics of extended systems near a Hopf bifurcation [1,7]. Figure 1). FIG. 1.Regions of the parameter [c1, c2]-space for the CGLE displaying different kinds of regular and chaotic behavior. Lines L1, L3 were determined in [3][4][5].