Transitions in a self-propelled-particles model with coupling of accelerations

Abstract

We consider a three dimensional, generalized version of the original SPP model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the self-propelled particles (SPP-s) depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter s determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of s the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We argue that in nature evolutionary processes can drive the strategy variable s towards the critical point, where information exchange between the units of a system is maximal. InroductionCollective motion of organisms (e.g. fish schools, bird flocks, bacterial colonies) exhibits a large variety of emergent phenomena [1,2,3,4,5,6,7,8]. Synchronized motion, symmetrical group formations (e.g., V shaped) or swirling patterns emerge in spite of the apparently simple behavioral rules of the individual flock members [9,10]. The self propelled particles (SPP) model was proposed by Vicsek et al.[11] to describe the onset of ordered motion within a group of self-propelled particles in the presence of perturbations. Taking into the effects of fluctuations inevitably present in biological systems was an essential generalization of the prior deterministic flocking models such as that of Reynolds [12]. The original model considers point-like particles moving at constant velocity on a two dimensional surface with periodic boundary conditions. The only rule is that, at each time step, every particle approximates, with some uncertainty, the average direction of motion of the particles within its neighborhood of radius R. This model exhibits spontaneous self-organization; by decreasing the noise parameter, the system undergoes a kinetic phase transition from a disordered state to an ordered one where all the particles move approximately in the same direction. Due its simplicity and analogy with biological systems comprised of many, locally interacting particles, the SPP model soon became a reference model for the flocking behavior of organisms [13,14,15,16,17,18,19,20,21,22,23].The individual based behavioral rules, determining collective motion, are of particular interest. Important elements of behavioral rules are the nature of the perceived information and the affected behavioral traits. [24,25,26]. A frequent assumption in models is that the information, perceived by the particles, is restricted to the velocity of their neighbors. The interaction range is usually defined by metric distances, but Ballerini et al. [24] recently showed that topological distance is the one determining the flocking of starlings. The assumption of reflecting on the momentary velocity only may not be enough for adequately describing a number o...

Swarming, schooling, milling: phase diagram of a data-driven fish school model

“…A well studied case is the transition to orientational order observed in the popular Vicsek model [12][13][14]. Similar transitions have been described in self-propelled particle models by varying the value of parameters such as the blind angle [15], individual speed [16] or a 'strategy parameter' [17], which ponders a behavioural compromise between aligning with neighbours and reacting to their direction changes.…”

Keeping speed and distance for aligned motion

“…[51] and the various forms of ex plicit velocity alignment, further particle-based model com ponents contributing to flocking include attraction and ad hesion [12,51,[53][54][55][56][57], anisotropy [32,58,59], inelastic col lisions [41], and coupled accelerations [60]. In particular, in models with explicit velocity alignment it was foundby a mapping to the majority voter model-that extrinsic noise (also called: vectorial noise) leads to a discontinuous transition [57], It may appear that the derivation in Ref.…”

Differential optical spectropolarimetric imaging system assisted by liquid crystal devices for skin imaging

“…In this process the cell proliferation passes transient stages. One can identify patterns which are similar to those in the work of Vicsek et al 32 where positional and spatial trajectories of particles were shown to be very similar to the trajectories the cancer cells plough within the healthy tissue.…”

“…The conjecture is that the HOUSX * parameter represents the cell movement or formation for four tissue conditions, benign, atypic, dysplasm, and neoplasm. The patterns resemble a characteristic of cell proliferation or cell movements as numerically explained by Vicsek et al 32 (see Fig. 7) for general particle movement.…”