Types Of Collective Motion Research Articles

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting.

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

Collective motion in a sheet of microswimmers

Self-propelled particles such as bacteria or algae swimming through a fluid are non-equilibrium systems where particle motility breaks microscopic detailed balance, often resulting in large-scale collective motion. Previous theoretical work has identified long-ranged hydrodynamic interactions as the driver of collective motion in unbounded suspensions of rear-actuated (“pusher”) microswimmers. In contrast, most experimental studies of collective motion in microswimmer suspensions have been carried out in restricted geometries where both the swimmers’ motion and their long-range flow fields become altered due to the proximity of a boundary. Here, we study numerically a minimal model of microswimmers in such a restricted geometry, where the particles move in the midplane between two no-slip walls. For pushers, we demonstrate collective motion with short-ranged order, in contrast with the long-ranged flows observed in unbounded systems. For front-actuated (“puller”) microswimmers, we discover a long-wavelength density instability resulting in the formation of dense microswimmer clusters. Both types of collective motion are fundamentally different from their previously studied counterparts in unbounded domains. Our results show that this difference is dictated by the geometrical restriction of the swimmers’ motion, while hydrodynamic screening due to the presence of a wall is subdominant in determining the suspension’s collective state.

Bacteria send signals from beyond the grave

Swarming is a type of collective motion in bacteria. But it turns out that moving isn’t the only thing swarming bacteria do together. They also send signals that turn on antibiotic resistance mecha...

Self-organisation and convection of confined magnetotactic bacteria

Collective motion is found at all scales in biological and artificial systems, and extensive research is devoted to describing the interplay between interactions and external cues in collective dynamics. Magnetotactic bacteria constitute a remarkable example of living organisms for which motion can be easily controlled remotely. Here, we report a new type of collective motion where a uniform distribution of magnetotactic bacteria is rendered unstable by a magnetic field. A new state of “bacterial magneto-convection” results, wherein bacterial plumes emerge spontaneously perpendicular to an interface and develop into self-sustained flow convection cells. While there are similarities to gravity driven bioconvection and the Rayleigh–Bénard instability, these rely on a density mismatch between layers of the fluids. Remarkably, here no external forces are applied on the fluid and the magnetic field only exerts an external torque aligning magnetotactic bacteria with the field. Using a theoretical model based on hydrodynamic singularities, we capture quantitatively the instability and the observed long-time growth. Bacterial magneto-convection represents a new class of collective behaviour resulting only from the balance between hydrodynamic interactions and external alignment.

Analysis of push-forward model for swarm-like collective motions

A system that operates as a whole through interactions between its constituent individuals, each of which operates autonomously, is called an autonomous decentralized system. This type of system is increasingly attracting attention in the fields of biology and engineering as a system that flexibly adapts to changes in external environments. In this paper, a push-forward model is proposed as a simple model to generate various collective motions in groups. The push-forward model can be used to generate four types of collective motions, including one where “if an individual flies out of the group, the direction in which the entire group is heading changes accordingly.” This motion could not be generated using conventional group models. In this study, the group collective motions obtained from the push-forward model are classified using evaluation indices, and the mechanisms of their development are discussed. Moreover, an evaluation is conducted using scale-free correlation, an index that expresses “group likeness,” which is derived from actual observations of bird flocks.

Effects of agent's orientation in 2D flocking models

Various different types of collective motions have attracted attention from physicists; this is a fascinating phenomenon, resulting from the very simple interactions between individuals (particles/cells). Our aim is to contribute to elucidating the motion of collective behavior of a non-equilibrium multi-agent system. In this context, the topic of this manuscript is to study the effect of the zone of orientation on the collective motion in two-dimensional space. In this investigation, we extend the model suggested by Viscek et al. for only a single interaction radius. In our proposed model, the particles corresponding to agents locally interacting with their neighbors according to simple rules depending on the particular condition. At each time step the velocity of an agent depends on their direction and is perturbed by an external noise η. Particularly, we show that with a specific fixed parameter a phase transition can be achieved, from disordered motion of particles to ordered motion, by varying the radius of orientation R2 and the value of the density. Furthermore, the value of R2 at which the transition emerges depends strongly on the size of repulsion zone R1. The study is performed over different situations via a numerical simulation technique. Implications of these findings are discussed in the section of simulation results.

Exotic rotations and triaxiality in Nd nuclei

We have recently studied the Nd nuclei up to very high spins and identified a multitude of bands which are interpreted as the manifestation of a nucleus with stable triaxial shape, presenting various types of collective motion: tilted axis and principal axis rotation, wobbling motion, chiral bands. Seniority isomers built on nearly spherical shapes up to very high spins, surrounded by coexisting triaxial bands, have also been observed. The new results obtained from the systematics of the high-spin bands of Nd nuclei are discussed.

Competing γ-rigid and γ-stable vibrations in neutron-rich Gd and Dy isotopes

An exactly separable version of the Bohr Hamiltonian which combines the γ-stable and γ-rigid axial vibration-rotation is used to describe the collective properties of few neutron-rich transitional nuclei. The coupling between the two types of collective motion is managed through a rigidity parameter which also influences the geometry of the shape phase space. While the γ-angular part of the problem associated to axially symmetric shapes is treated within the small angles approximation and the stiff γ oscillation hypothesis, the β vibration is described by means of a Davidson potential. The resulting model have three free parameters not counting the scale and was successfully applied for the description of the collective spectra for few heavier isotopes of Gd and Dy. In both cases a critical nucleus was identified through a discontinuous behavior in respect to the rigidity parameter and relevant experimental observables.

Collective coordinate theory for light pulses in fibers: The reduced projection operators

Abstract We consider optical waveguides in which light pulses may execute complex dynamical behaviors including translational motions accompanied with strong internal vibrations. Such systems necessarily generate various types of collective motion, in which each collective mode is describable by a collective coordinate. We present a novel projection operator formalism for deriving the equations of motion of the collective coordinates and coupled fields. This formalism is built up by treating separately the dynamics of the pulse phase and that of its amplitude, that is, by using two distinct projection operators (one for the amplitude, and the other one for the phase). This new pair of operators, which we call reduced projection operators , has as main virtue of having dimension reduced by half as compared to that of the conventional operators that includes both pulse amplitude and phase together. The main interest of the reduced projection operators lies in the ease with which the equations of motion are derived when compared with the amount of algebra needed to obtain the same equations from the conventional projection operators. We provide examples of concrete situations that illustrate the effectiveness of the collective-coordinate approach based on the reduced projection operators.

Exotic rotations and seniority isomers in Nd nuclei

We have recently studied the Nd nuclei up to very high spins and identified several bands, which were interpreted as the manifestation of various types of collective motion: tilted axis rotation, principal axis rotation along the short and long axes, wobbling motion, chiral bands. All these types of excitation have been observed in 138Nd and are discussed in the framework of the tilted axis cranking (TAC) and cranked Nilsson-Strutinsky (CNS) models.

Fine structure of the nuclear scissors mode (new type of collective motion)

The coupled dynamics of low-lying modes (including scissors) and various giant quadrupole resonances are studied with the help of Wigner Function Moments method generalized to take into account spin degrees of freedom. Equations of motion for collective variables are derived on the basis of Time Dependent Hartree-Fock equations in the model of harmonic oscillator with spin orbital interaction plus quadrupole-quadrupole residual interaction. Enlisting the spin allows one to introduce into consideration new types of nuclear collective motion.

Self-organization in two-dimensional swarms

We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered swarms, rings, and droplets. We construct a "phase diagram," which summarizes our results as it delineates phase transitions (all discontinuous) between disordered swarms and vortical flocks on one hand and bound vortical flocks and expanding formations on the other. One of the transition lines is found to have a close analogy with the temperature-driven gas-liquid transition, in finite clusters with the same interparticle potential. Furthermore, we report on a type of flocking which takes place in the presence of a uniform external driver. Altogether, our results set a rather firm stage for experimental refinement and/or falsification of this class of models.

Global Motions of the Nuclear Pore Complex: Insights from Elastic Network Models

The nuclear pore complex (NPC) is the gate to the nucleus. Recent determination of the configuration of proteins in the yeast NPC at ∼5 nm resolution permits us to study the NPC global dynamics using coarse-grained structural models. We investigate these large-scale motions by using an extended elastic network model (ENM) formalism applied to several coarse-grained representations of the NPC. Two types of collective motions (global modes) are predicted by the ENMs to be intrinsically favored by the NPC architecture: global bending and extension/contraction from circular to elliptical shapes. These motions are shown to be robust against tested variations in the representation of the NPC, and are largely captured by a simple model of a toroid with axially varying mass density. We demonstrate that spoke multiplicity significantly affects the accessible number of symmetric low-energy modes of motion; the NPC-like toroidal structures composed of 8 spokes have access to highly cooperative symmetric motions that are inaccessible to toroids composed of 7 or 9 spokes. The analysis reveals modes of motion that may facilitate macromolecular transport through the NPC, consistent with previous experimental observations.

MACH CONES AND HYDRODYNAMIC FLOW: PROBING BIG BANG MATTER IN THE LABORATORY

A critical discussion of the present signals for the phase transition to quark-gluon plasma (QGP) is given. Since hadronic rescattering models predict much larger flow than observed from 1 to 50 A GeV laboratory bombarding energies, this observation is interpreted as potential evidence for a first-order phase transition at high baryon density. A detailed discussion of the collective flow as a barometer for the equation of state (EoS) of hot dense matter at RHIC follows. Here, hadronic rescattering models can explain < 30% of the observed elliptic flow v2for pT> 2 GeV / c . This is interpreted as an evidence for the production of superdense matter at RHIC. The connection of v2to jet suppression is examined. A study of Mach shocks generated by fast partonic jets propagating through the QGP is given. The main goal is to take into account different types of collective motion during the formation and evolution of this matter. A significant deformation of Mach shocks in central Au + Au collisions at RHIC and LHC energies as compared to the case of jet propagation in a static medium is predicted. A new hydrodynamical study of jet energy loss is presented.

Dynamical properties of cluster in the Hamiltonian Mean Field model

We investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster in the Hamiltonian Mean Field model. Particle are clustered in the ordered low-energy phase in this model. However, when the number of particles is finite, some particles can acquire a high energy and leave the cluster. Hence, below the critical energy, the fully-clustered and excited states appear by turns. First, we show that the numerically computed time-averaged trapping ratio agrees with that obtained by a statistical average performed for the Boltzmann–Gibbs stationary solution of the Vlasov equation. Second, we found numerically that the probability distribution of the lifetime of the fully-clustered state is not exponential but follows instead a power law. This means that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Therefore, although an average trapping ratio exists, there appear to be no typical trapping ratio in the probabilistic sense. Finally, we discuss the dynamical mechanism using a modified model.

Coarse-grained analysis of stochasticity-induced switching between collective motion states.

A single animal group can display different types of collective motion at different times. For a one-dimensional individual-based model of self-organizing group formation, we show that repeated switching between distinct ordered collective states can occur entirely because of stochastic effects. We introduce a framework for the coarse-grained, computer-assisted analysis of such stochasticity-induced switching in animal groups. This involves the characterization of the behavior of the system with a single dynamically meaningful "coarse observable" whose dynamics are described by an effective Fokker-Planck equation. A "lifting" procedure is presented, which enables efficient estimation of the necessary macroscopic quantities for this description through short bursts of appropriately initialized computations. This leads to the construction of an effective potential, which is used to locate metastable collective states, and their parametric dependence, as well as estimate mean switching times.

Clusters die hard: Time-correlated excitation in the Hamiltonian mean field model

The Hamiltonian mean field (HMF) model has a low-energy phase where N particles are trapped inside a cluster. Here, we investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster. Since the single particle dynamics of the HMF model resembles the one of a simple pendulum, each particle can be identified as a high-energy particle (HEP) or a low-energy particle (LEP), depending on whether its energy is above or below the separatrix energy. We then define the trapping ratio as the ratio of the number of LEP to the total number of particles and the “fully-clustered” and “excited” dynamical states as having either no HEP or at least one HEP. We analytically compute the phase-space average of the trapping ratio by using the Boltzmann–Gibbs stable stationary solution of the Vlasov equation associated with the N → ∞ limit of the HMF model. The same quantity, obtained numerically as a time average, is shown to be in very good agreement with the analytical calculation. Another important feature of the dynamical behavior of the system is that the dynamical state changes transitionally: the “fully-clustered” and “excited” states appear in turn. We find that the distribution of the lifetime of the “fully-clustered” state obeys a power law. This means that clusters die hard, and that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Such behavior should not be specific of the HMF model and appear also in systems where itinerancy among different “quasi-stationary” states has been observed. It is also possible that it could mimick the behavior of transient motion in molecular clusters or some observed deterministic features of chemical reactions.

Mach shocks induced by partonic jets in expanding quark–gluon plasma

We study Mach shocks generated by fast partonic jets propagating through a deconfined strongly-interacting matter. Our main goal is to take into account different types of collective motion during the formation and evolution of this matter. We predict a significant deformation of Mach shocks in central Au + Au collisions at RHIC and LHC energies as compared to the case of jet propagation in a static medium. The observed broadening of the near-side two-particle correlations in pseudorapidity space is explained by the Bjorken-like longitudinal expansion. Three-particle correlation measurements are proposed for a more detailed study of the Mach shock waves.

Coordinated collective motion in a motile particle group with a leader

We study the collective dynamics of a group of motile particles with a leader. The leader is unaffected by the particle members whereas each member is influenced by the leader and the other members. By using coupled oscillators theory and Lyapunov function method, we show how the group dynamics depends on the motion of the leader and the coupling weights among all particles. Generally speaking, two types of collective motions will occur, depending on different ranges of the coupling weights among the member particles. One is that all the member particles will move in the same direction and the other is that all the member particles move in such a way that the weighted centroid of the group approaches a fixed position. In each case, all the member particles eventually move in the same manner except for the directions of the motion in certain cases. Numerical simulations are worked out to demonstrate the theoretical results. The study suggests potential approaches to control a group motion by steering the motion of the leader and adjusting coupling patterns. This is of practical interest in applications of multiagent systems.

Euroball results on nuclei at high spin and far from stability

Large gamma detector arrays are an essential tool for modern spectroscopy of nuclei both in their high spin regime and far from the stability line. The Euroball spectrometer has been operating for almost six years at the heavy-ion accelerators of Legnaro and Strasbourg covering a broad physics program which led to advances in nuclear structure studies at high angular momentum and of very exotic nuclei. In this talk I will give an overview of the most recent results of Euroball including new types of collective motion at high spin and studies of exotic neutron-deficient nuclei along the N=Z line. I will also briefly mention the new scientific opportunities offered by the Euroball detectors coupled to the FRS, PRISMA and RITU spectrometers at GSI, Legnaro and Jyva¨skyla¨, respectively.