149 research outputs found
Large-scale collective properties of self-propelled rods
We study, in two space dimensions, the large-scale properties of collections
of constant-speed polar point particles interacting locally by nematic
alignment in the presence of noise. This minimal approach to self-propelled
rods allows one to deal with large numbers of particles, revealing a
phenomenology previously unseen in more complicated models, and moreover
distinctively different from both that of the purely polar case (e.g. the
Vicsek model) and of active nematics.Comment: Submitted to Phys. Rev. Let
Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions
The synchronization transition between two coupled replicas of
spatio-temporal chaotic systems in 2+1 dimensions is studied as a phase
transition into an absorbing state - the synchronized state. Confirming the
scenario drawn in 1+1 dimensional systems, the transition is found to belong to
two different universality classes - Multiplicative Noise (MN) and Directed
Percolation (DP) - depending on the linear or nonlinear character of damage
spreading occurring in the coupled systems. By comparing coupled map lattice
with two different stochastic models, accurate numerical estimates for MN in
2+1 dimensions are obtained. Finally, aiming to pave the way for future
experimental studies, slightly non-identical replicas have been considered. It
is shown that the presence of small differences between the dynamics of the two
replicas acts as an external field in the context of absorbing phase
transitions, and can be characterized in terms of a suitable critical exponent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen
Fast moving of a population of robots through a complex scenario
Swarm robotics consists in using a large number of coordinated autonomous robots, or agents, to accomplish one or more tasks, using local and/or global rules. Individual and collective objectives can be designed for each robot of the swarm. Generally, the agents' interactions exhibit a high degree of complexity that makes it impossible to skip nonlinearities in the model. In this paper, is implemented both a collective interaction using a modified Vicsek model where each agent follows a local group velocity and the individual interaction concerning internal and external obstacle avoidance. The proposed strategies are tested for the migration of a unicycle robot swarm in an unknown environment, where the effectiveness and the migration time are analyzed. To this aim, a new optimal control method for nonlinear dynamical systems and cost functions, named Feedback Local Optimality Principle - FLOP, is applied
Emergence of chaotic behaviour in linearly stable systems
Strong nonlinear effects combined with diffusive coupling may give rise to
unpredictable evolution in spatially extended deterministic dynamical systems
even in the presence of a fully negative spectrum of Lyapunov exponents. This
regime, denoted as ``stable chaos'', has been so far mainly characterized by
numerical studies. In this manuscript we investigate the mechanisms that are at
the basis of this form of unpredictable evolution generated by a nonlinear
information flow through the boundaries. In order to clarify how linear
stability can coexist with nonlinear instability, we construct a suitable
stochastic model. In the absence of spatial coupling, the model does not reveal
the existence of any self-sustained chaotic phase. Nevertheless, already this
simple regime reveals peculiar differences between the behaviour of finite-size
and that of infinitesimal perturbations. A mean-field analysis of the truly
spatially extended case clarifies that the onset of chaotic behaviour can be
traced back to the diffusion process that tends to shift the growth rate of
finite perturbations from the quenched to the annealed average. The possible
characterization of the transition as the onset of directed percolation is also
briefly discussed as well as the connections with a synchronization transition.Comment: 30 pages, 8 figures, Submitted to Journal of Physics
Continuous theory of active matter systems with metric-free interactions
We derive a hydrodynamic description of metric-free active matter: starting
from self-propelled particles aligning with neighbors defined by "topological"
rules, not metric zones, -a situation advocated recently to be relevant for
bird flocks, fish schools, and crowds- we use a kinetic approach to obtain
well-controlled nonlinear field equations. We show that the density-independent
collision rate per particle characteristic of topological interactions
suppresses the linear instability of the homogeneous ordered phase and the
nonlinear density segregation generically present near threshold in metric
models, in agreement with microscopic simulations.Comment: Submitted to Physical Review Letter
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 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.Comment: 4 pages, 3 figures, submitted to Physical Review letter
Nonequilibrium wetting of finite samples
As a canonical model for wetting far from thermal equilibrium we study a
Kardar-Parisi-Zhang interface growing on top of a hard-core substrate.
Depending on the average growth velocity the model exhibits a non-equilibrium
wetting transition which is characterized by an additional surface critical
exponent theta. Simulating the single-step model in one spatial dimension we
provide accurate numerical estimates for theta and investigate the distribution
of contact points between the substrate and the interface as a function of
time. Moreover, we study the influence of finite-size effects, in particular
the time needed until a finite substrate is completely covered by the wetting
layer for the first time.Comment: 17 pages, 8 figures, revisio
Universal mean-field upper bound for the generalization gap of deep neural networks
Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalization gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimized given a specific realization of the remaining weights. We show how these results-combined with ideas from statistical learning theory-provide a stringent asymptotic upper bound on the generalization gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and N-out (where N-out is the size of the last layer) and N-out << P, the generalization gap approaches zero faster than 2N(out)/P, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks
Collective Lyapunov modes
We show, using covariant Lyapunov vectors in addition to standard Lyapunov
analysis, that there exists a set of collective Lyapunov modes in large chaotic
systems exhibiting collective dynamics. Associated with delocalized Lyapunov
vectors, they act collectively on the trajectory and hence characterize the
instability of its collective dynamics. We further develop, for
globally-coupled systems, a connection between these collective modes and the
Lyapunov modes in the corresponding Perron-Frobenius equation. We thereby
address the fundamental question of the effective dimension of collective
dynamics and discuss the extensivity of chaos in presence of collective
dynamics.Comment: 24 pages, 15 figures; display error correction of Fig.11 and other
minor changes (v2
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