An important characteristic of flocks of birds, school of fish, and many similar assemblies of selfpropelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system. PACS numbers: 05.70. Fh, 87.17.Jj, The collective motion of a group of autonomous particles is a subject of intense research that has potential applications in biology, physics and engineering [1,2,3]. One of the most remarkable characteristics of systems such as a flock of birds, a school of fish or a swarm of locusts, is the emergence of ordered states in which the particles move in the same direction, in spite of the fact that the interactions between the particles are (presumably) of short range. Given that these systems are generally out of equilibrium, the emergence of ordered states cannot be accounted for by the standard theorems in statistical mechanics that explain the existence of ordered states in equilibrium systems typified by ferromagnets.A particularly simple model to describe the collective motion of a group of self-propelled particles was proposed by Vicsek et al. [4]. In this model each particle tends to move in the average direction of motion of its neighbors while being simultaneously subjected to noise. As the amplitude of the noise increases the system undergoes a phase transition from an ordered state in which the particles move collectively in the same direction, to a disordered state in which the particles move independently in random directions. This phase transition was originally thought to be of second order. However, due to a lack of a general formalism to analyze the collective dynamics of the Vicsek model, the nature of the phase transition (i.e. whether it is second or first order) has been brought into question [5].In this letter we show that the nature of the phase transition can depend strongly on the way in which the noise is introduced into these systems. We illustrate this by presenting analytical results on two different network systems that are closely related to the self-propelled particle models. We show that in these two network models the phase transition switches from second to first order when the way in which the noise is introduced changes from the one presented in [4] to the one described in [5].The first network model, which we will refer to as the vectorial network model, consists of a network of N 2D-vectors (represented as complex numbers), {σ 1 = e iθ...

In the context of an extension of Axelrod's model for social influence, we study the interplay and competition between the cultural drift, represented as random perturbations, and mass media, introduced by means of an external homogeneous field. Unlike previous studies [J. C. González-Avella et al, Phys.Rev. E 72, 065102(R) (2005)], the mass media coupling proposed here is capable of affecting the cultural traits of any individual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (culturally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external field is found to induce cultural ordering, a behavior opposite to 1

In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters’ fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified Lagrangian treatment. Noise enters into our model in an especially realistic way: it incorporates correlations, is highly nonlinear, and it leads to a unique collective behavior. Our results show distinct stability regions and an apparent change in the nature of one class of noise-induced phase transitions, with respect to the mean velocity of the group, as the range of the velocity-alignment interaction increases. This phase-transition change comes accompanied with drastic modifications of the microscopic dynamics, from nonintermittent to intermittent. Our results facilitate the understanding of the origin of the phase transitions present in other treatments.

Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.

In this work, we report the thermal characterization of platelike composite samples made of polyester resin and magnetite inclusions. By means of photoacoustic spectroscopy and thermal relaxation, the thermal diffusivity, conductivity and volumetric heat capacity of the samples were experimentally measured. The volume fraction of inclusions was systematically varied in order to study the changes in the effective thermal conductivity of the composites. In some samples, a static magnetic field was applied during the polymerization process resulting in anisotropic inclusion distributions. Our results show a decrease in the thermal conductivity of some of the anisotropic samples compared to the isotropic randomly distributed ones. Our analysis indicates that the development of elongated inclusion structures leads to the formation of magnetite and resin domains causing this effect. We correlate the complexity of the inclusion structure with the observed thermal response by a multifractal and lacunarity analysis. All the experimental data are contrasted with the well known Maxwell-Garnett's effective media approximation for composite materials.

By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to farfrom-equilibrium ones exhibiting collective motion, long-range order and giant number fluctuations, features typically associated to ordered phases of models where self-propulsion is considered.PACS numbers: 05.70.Fh, 05.70.Ln Collective motion is an ubiquitous phenomenon in biological groups such as flocks of birds, schools of fishes, swarms of insects, etc. The study of these far-fromequilibrium systems has attracted great interest over the last few decades, as the spontaneous emergence of such ordered phases and coordinated behavior, arising from local interactions, cannot be accounted for by the standard theorems of statistical mechanics [1].Introduced almost twenty years ago, the seminal model by Vicsek et al.[2] provided a simple tool to study the transition to collective motion, in a non-equilibrium situation, taking into account two basic ingredients: the selfpropulsive character of the particles and a local velocityalignment interaction among them. Due to the discrete nature of the model, a given particle instantaneously orients its direction of motion along the average direction of motion of its neighbors within a radius R, while stochastic perturbations are considered by adding a random angle ("noise") to this direction. In two dimensions, the system displays an ordered phase characterized by collective motion with long-range order and giant number fluctuations [3], just below a critical value of the noise intensity that depends on the particle density. It is in this respect that this model can be considered as a paradigm of non-equilibrium phase transitions, since such ordered phases are forbidden in equilibrium (for Heisenberg-like models) by the Mermin-Wagner-Hohenberg theorem [4]. Above this value, the ordered phase breaks down into a stationary, disordered and out-of-equilibrium one.Over the years, many generalizations of the model have been developed, keeping self-propulsion as an essential ingredient for the phase transition to take place, in combination with interactions of the "social" type among the particles such as velocity-alignment [5,6]. This has led to the development of sophisticated nonlinear friction terms [7,8], a bias that may be justified arguing, on the one hand, that the concept of self-propelled (or active Brownian) particles captures the natural ability (seen in many biological systems) for the agents to develop motion by themselves [9,10] and, on the other, that it is an important ingredient for pattern formation in models of collective motion [11].In this Letter, we study the emergence of collective motion in a two-dimensional system of N passive Brownian (not-self-propelled) partic...

In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that leads to the instability of the equilibrium phase relies on the competition between two time scales, namely, the mean collision time of the Brownian particles in a thermal bath and the time it takes for a particle to orient its direction of motion along the direction of motion of the group.