Narrow Results

In nature many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex behavior of these systems, many models have been proposed and tested so far. This paper deals with an extension of the Vicsek model, by including a second zone of repulsion, where each agent attempts to maintain a minimum distance from the others. The consideration of this zone in our study seems to play an important role during the travel of agents in the two-dimensional (2D) flocking models. Our numerical investigations show that depending on the basic ingredients such as repulsion radius (R₁), effect of density of agents (ρ) and noise (η), our nonequilibrium system can undergo a kinetic phase transition from no transport to finite net transport. For different values of ρ, kinetic phase diagrams in the plane (η ,R₁) are found. Implications of these findings are discussed.

In the Vicsek Model (VM), self-driven individuals try to adopt the direction of movement of their neighbors under the influence of noise, thus leading to a noise-driven order–disorder phase transition. By implementing the so-called Vectorial Noise (VN) variant of the VM (i.e. the VM-VN model), this phase transition has been shown to be discontinuous (first-order). In this paper, we perform an extensive complex network study of VM-VN flocks and show that their topology can be described as highly clustered, assortative, and nonhierarchical. We also study the behavior of the VM-VN model in the case of "frozen flocks" in which, after the flocks are formed using the full dynamics, particle displacements are suppressed (i.e. only rotations are allowed). Under this kind of restricted dynamics, we show that VM-VN flocks are unable to support the ordered phase. Therefore, we conclude that the particle displacements at every time-step in the VM-VN dynamics are a key element needed to sustain long-range ordering throughout.

In this paper, Davydov–Chaban approach to study collective motion of atomic nuclei has been mentioned in detail. First by considering a shifted Killingbeck potential, we obtain the wave function of such system by taking an ansatz method. Then we consider a special case of shifted Killingbeck potential to recover known results.

In this work, we consider the phase transition from ordered to disordered states that occur in the Vicsek model of self-propelled particles. This model was proposed to describe the emergence of collective order in swarming systems. When noise is added to the motion of the particles, the onset of collective order occurs through a dynamical phase transition. Based on their numerical results, Vicsek and his colleagues originally concluded that this phase transition was of second order (continuous). However, recent numerical evidence seems to indicate that the phase transition might be of first order (discontinuous), thus challenging Vicsek's original results. In this work, we review the evidence supporting both aspects of this debate. We also show new numerical results indicating that the apparent discontinuity of the phase transition may in fact be a numerical artifact produced by the artificial periodicity of the boundary conditions.

Collective behavior in animal groups such as schools of fish, swarms of insects or flocks of birds, although a phenomenon widely studied in biological systems, is subject of great interdisciplinary interest. An important tool to describe the dynamics of collective motion and ordered live organisms is the concept of self-propelled particles. Proposed by Vicsek and collaborators, it was considered in this model only as an (single) interaction rule, set as alignment, where particles align to motion the nearest neighbors. In this paper, we have considered a variant of this model by adding a second rule called repulsion zone, where particles repel each other at short distances, in order to investigate the influence of this zone on directional order of the particles.

In nature, many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex motion of these systems, we study the Vicsek model of self-propelled particles (SPP) which is an important tool to investigate the behavior of collective motion of live organisms. This model reproduces the biological behavior patterns in the two-dimensional (2D) space. Within the framework of this model, the particles move with the same absolute velocity and interact locally in the zone of orientation by trying to align their direction with that of the neighbors. In this paper, we model the collective movement of SPP using an agent-based model which follows biologically motivated behavioral rules, by adding a second region called the attraction zone, where each particles move towards each other avoiding being isolated. Our main goal is to present a detailed numerical study on the effect of the zone of attraction on the kinetic phase transition of our system. In our study, the consideration of this zone seems to play an important role in the cohesion. Consequently, in the directional orientation, the zone that we added forms the compact particle group. In our simulation, we show clearly that the model proposed here can produce two collective behavior patterns: torus and dynamic parallel group. Implications of these findings are discussed.

In this paper, we used a self-propelled particle model to study the transition between phases of collective behavior observed in animal aggregates. In these systems, transitions occur when individuals shift from one collective state to another. We investigated transitions induced by both the speed and the noise. Statistical quantities that characterize the phase transition driven by noise, such as order parameter, the Binder cumulant and the susceptibility were analyzed, and we used the finite-size scaling theory to estimate the critical exponent ratios $\beta /\nu$ and $\gamma /\nu$.

The aim of this paper is to study and discuss the effect of three zones (repulsion zone, orientation zone and attraction zone) on the phase transition in 2D-collective moving particles. Our main motivation is to better understand the complex behavior of non-equilibrium multi-agent system by extending the earlier and original model proposed by Viscek et al. [T. Viscek et al., Phys. Rev. Lett.75 (1995) 1226] for one zone. The analysis is performed over different situations by using a numerical simulation method. It is found that the radius R₂ of orientation zone plays an important role in the system. In effect, by varying the parameter R₂ a phase transition can be achieved from disordered moving of individuals to a group to highly aligned collective motion. The results also show that, the critical value of R₂ at which the transition emerges depends strongly on the size of the repulsion zone but not on the size of attraction one.

In this paper, we discuss the universality of the critical exponents β and δ found in the Viscek model for one zone of interaction in the 2D flocking model. Within the framework of this model, the particles move with the same absolute velocity v₀ and interact locally by trying to align their direction with that of neighbors. In this paper, we include a second zone of interaction named zone of repulsion R₁, where each agent attempts to maintain a minimum distance from the others. Our model results show that in order to maintain an order in a flock with higher density, it is necessary to decrease the region of repulsion around each individual. Depending on the noise and on the density, the order parameter v_a is found to scale as and , respectively. Our findings show that the exponents β and δ depend strongly on the size of the repulsion zone and on the density ρ, indicating the non-universality of these critical exponents. The analysis is performed over different situations by using a numerical simulation technique.

While the slow dynamics in glassy liquids are known to be accompanied by collective motions undetectable with static structure factor and requiring four-point space-time correlations for their detection, it is usually difficult to calculate such correlations analytically. In the present study, a system of Brownian particles in a (quasi-)one-dimensional passageway is taken as an example to demonstrate the usefulness of displacement correlation. In the purely one-dimensional case (known as the single-file diffusion) with overtaking forbidden, the diffusion slows down and collective motion is captured by displacement correlation both calculated here numerically and analytically. On the other hand, displacement correlation vanishes if overtaking is allowed, which leads to normal diffusion.

In this work, we study some states of collective behavior observed in groups of animals. For this end we consider an agent-based model with biologically motivated behavioral rules where the speed is treated as an independent stochastic variable, and the motion direction is adjusted in accord with alignment and attractive interactions. Four types of collective behavior have been observed: disordered motion, collective rotation, coherent collective motion, and formation flight. We investigate the case when transitions between collective states depend on both the speed and the attraction between individuals. Our results show that, to any size of the attraction, small speeds are associated to the coherent collective motion, while collective rotation is more and more pronounced for high speed since the attraction radius is large enough.

In self-propelled particle models, the interactions are generally subject to some type of noise, which is introduced either during or after the interactions between the particles. Here, self-propelled particles are subject to two different types of noise. If the orientation between them is less than a certain rate $\beta$, a vectorial noise is introduced in each particle–particle interaction, otherwise, an angular noise is introduced in the average direction of motion, already calculated, of neighboring particles. We vary the rate $\beta$ over a wide range ($\beta <\pi$) and study the change in the nature of the phase transition. The product-moment correlation coefficient between the order parameter and the hybrid noise, is calculated. We found that in the combination of the two types of noise, the critical noise decreases with increasing the parameter $\beta$, and by analysis of the Binder cumulant we estimate the value of $\beta$ as from which begins to appear the effects of the vectorial noise on the phase transition.

In nature, living organisms move in a collective state of aggregation, this collective motion is influenced by the nature of the environment, the obstacles refocused during the movement and the local interaction between individuals, this interaction is responsible for avoiding collision between each individual. In this paper, we study numerically the collective motion of self-organized organisms by expanding the Langevin dynamics, in which we have modeled the interaction between individuals by an elastic force. Modeling the interaction between individuals using an elastic force gives remarkable results. This interaction has an important effect if the individuals are dispersed a lot in space, but if a certain number of particles N is exceeded, this force is of no importance and the saturation velocity becomes constant. The results of the numerical simulation show that the average velocity of the individuals goes through a transient regime before reaching the permanent regime. Moreover, the results show that the system represents a transition from a nonequilibrium state to an equilibrium state, which is similar to a second-phase transition (paramagnetic/ferromagnetic) in the absence of the magnetic field; this phase transition is observable if the distance between two individuals is greater than a critical radius noted $R_c$.

The emergence of order from initial disordered movement in self-propelled collective motion is an instance of nonequilibrium phase transition, which is known to be first order in the thermodynamic limit. Here, we introduce a multiplicative scalar noise model of collective motion as a modification of the original Vicsek model, which more closely mimics the particles’ behavior. We allow for more individual movement in sparsely populated neighborhoods, the mechanism of which is not incorporated in the original Vicsek model. This is especially important in the low velocity and density regime where the probability of a clear neighborhood is relatively high. The modification, thus, removes the shortcoming of the Vicsek model in predicting continuous phase transition in this regime. The onset of collective motion in the proposed model is numerically studied in detail, indicating a first-order phase transition in both high and low velocity/density regimes for systems with comparatively smaller size which is computationally desirable.

We present a new model for multi-agent dynamics where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate around it adopting different configurations. In this manner, the body attitude is described by three orthonormal axes giving an element in $\mathrm{\text{SO}}(3)$ (rotation matrix). Agents try to coordinate their body attitudes with the ones of their neighbours. In this paper, we give the individual-based model (particle model) for this dynamics and derive its corresponding kinetic and macroscopic equations.

Motivated by the success of kinetic theory in the description of observables in intermediate and high energy heavy-ion collisions, we apply kinetic theory to the physics of supernova explosions. The algorithmic implementation for the high-density phase of the iron core collapse is discussed.

In this paper, the ratio of the mass coefficients for the γ-vibrational and rotational motion for the well deformed axially symmetric nuclei is calculated. Calculations are performed based on the Cranking model approach. The results obtained show that the microscopic model based on the Woods–Saxon nuclear mean field potential and the pairing forces with a constant strength coefficient qualitatively explain the existing experimental data on the ratio of the mass coefficients. The important role of the blocking effect in the calculation of the mass coefficients is demonstrated.

In the last 10 years, we have observed an important increase of interest in the application of time-dependent energy density functional (TD-EDF) theory. This approach allows to treat nuclear structure and nuclear reaction from small to large amplitude dynamics in a unified framework. The possibility to perform unrestricted three-dimensional simulations using state-of-the-art effective interactions has opened new perspectives. In the present paper, an overview of applications where the predictive power of TD-EDF has been benchmarked is given. A special emphasize is made on processes that are of astrophysical interest. Illustrations discussed here include giant resonances, fission, binary and ternary collisions leading to fusion, transfer and deep inelastic processes.

The scissors mode structure is studied in the actinides within the Wigner Function Moments method. The theory predicts a splitting of the scissors mode into three branches due to spin degrees of freedom. The excitation energies and $B(M1)$ transition probabilities for the scissors states are calculated for even–even axial nuclei of the actinide mass region. The origin of the double-humped structure of the scissors spectrum observed in the lightest actinides is discussed. The energy centroids and integrated $M1$ strengths for the transuranium nuclides up to ${}^{256}$No are predicted. The results of calculations for ${}^{232}$Th, ${}^{238}$U and ${}^{254}$No are compared with available experimental data.

The antiferromagnetic properties of nuclei are studied within the Wigner function moments method. The solution of the time dependent Hartree–Fock–Bogoliubov equations predicts four low-lying $1^{+}$ states. Three of them are known as various scissors modes. Fourth state is disposed below all scissors modes and represents one of three branches of $2^{+}$ multiplet which can exist in spherical nuclei and which is split in deformed nuclei. It is discovered, that the antiferromagnetic properties of nuclei lead to the splitting of $2^{+}$ states already at the zero deformation. It is shown that the splitting caused by nuclear antiferromagnetism is comparable to the Zeeman splitting in an external uniform magnetic field.