Collective Motion Of Particles Research Articles

From kinetic flocking model of Cucker–Smale type to self-organized hydrodynamic model

We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker–Smale model with a confining potential in a mesoscopic scale to the macroscopic limit system for self-propelled individuals, which is derived formally by Aceves-Sánchez et al. in 2019. In the traditional kinetic equation with collisions, for example, Boltzmann-type equations, the key properties that connect the kinetic and fluid regimes are: the linearized collision operator (linearized collision operator around the equilibrium), denoted by [Formula: see text], is symmetric, and has a nontrivial null space (its elements are called collision invariants) which include all the fluid information, i.e. the dimension of Ker([Formula: see text]) is equal to the number of fluid variables. Furthermore, the moments of the collision invariants with the kinetic equations give the macroscopic equations. The new feature and difficulty of the corresponding problem considered in this paper is: the linearized operator [Formula: see text] is not symmetric, i.e. [Formula: see text], where [Formula: see text] is the dual of [Formula: see text]. Moreover, the collision invariants lies in Ker([Formula: see text]), which is called generalized collision invariants (GCI). This is fundamentally different with classical Boltzmann-type equations. This is a common feature of many collective motions of self-propelled particles with alignment in living systems, or many active particle system. Another difficulty (also common for active system) is involved by the normalization of the direction vector, which is highly nonlinear. In this paper, using Cucker–Smale model as an example, we develop systematically a GCI-based expansion method, and micro–macro decomposition on the dual space, to justify the limits to the macroscopic system, a non-Euler-type hyperbolic system. We believe our method has wide applications in the collective motions and active particle systems.

Dynamics of magnetization growth and relaxation in ferrofluids.

The dynamics of the growth and relaxation of the magnetization in ferrofluids are determined using theory based on the Fokker-Planck-Brown equation, and Brownian-dynamics simulations. Magnetization growth starting from an equilibrium nonmagnetized state in zero field, and following an instantaneous application of a uniform field of arbitrary strength, is studied with and without interparticle interactions. Similarly, magnetization relaxation is studied starting from an equilibrium magnetized state in a field of arbitrary strength, and following instantaneous removal of the field. In all cases, the dynamics are studied in terms of the time-dependent magnetization m(t). The field strength is described by the Langevin parameter α, the strength of the interparticle interactions is described by the Langevin susceptibility χ_{L}, and the individual particles undergo Brownian rotation with time τ_{B}. For noninteracting particles, the average growth time decreases with increasing α due to the torque exerted by the field, while the average relaxation time stays constant at τ_{B}; with vanishingly weak fields, the timescales coincide. The same basic picture emerges for interacting particles, but the weak-field timescales are larger due to collective particle motions, and the average relaxation time exhibits a weak, nonmonotonic field dependence. A comparison between theoretical and simulation results is excellent for noninteracting particles. For interacting particles with χ_{L}=1 and 2, theory and simulations are in qualitative agreement, but there are quantitative deviations, particularly in the weak-field regime, for reasons that are connected with the description of interactions using effective fields.

Extraction of Mechanical Work from Collective Motion of Pt Catalytic Particles Induced by Chemical Reactions

Extraction of Mechanical Work from Collective Motion of Pt Catalytic Particles Induced by Chemical Reactions

Discovering dynamic laws from observations: The case of self-propelled, interacting colloids.

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equationof motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Collective motion of catalytic particles driven by abiotic aerobic metabolism

The phenomenon of collective motion of Pt particles (primary particles and aggregates) immersed in water containing organic fuels has been observed. Over time, these Pt particles tend to aggregate into numerous schools at the bottom of the container. Subsequently, unique spatiotemporal patterns emerge, including repetitive fission/fusion dynamics and dispersing/clustering synchronization among schools. Notably, the species of organic fuels influence the observed patterns. Pt particles exhibit self-propulsion through catalytic oxidation of organic fuels by dissolved oxygen, mirroring the chemical mechanism seen in living organisms. This contrast with previous studies on chemically propelled objects underscores the biomimetic nature of the system, highlighting its resemblance to living processes. This self-propelled system, operating with an aerobic metabolic mechanism, presents a valuable real-world model for elucidating the fundamental principles underlying collective motion in living organisms.

Emergent dynamics: Collective motions of polar active particles on surfaces

In this study, we focus on the collective dynamics of polar active particles navigating across three distinct surfaces, each characterized by its own unique blend of topological and geometrical properties. The behavior of these active particles is influenced by a multitude of factors, including self-propulsion, inter-particle interactions, surface constraints, and under-damped stochastic forces simulated via Ornstein–Uhlenbeck processes. Our exploration unveils the prevailing collective patterns observed within these systems across three surface types: a sphere, a torus, and a landscape featuring hills and valleys, each distinguished by its specific topological and geometrical attributes. We underscore the profound impact of surface curvature and symmetry on the sustainable spatial-temporal dynamics witnessed. Our findings illuminate how the interplay between substantial surface curvature and particular symmetrical characteristics gives rise to a diverse spectrum of spatial-temporal patterns. Notably, we discern that high curvature tends to drive collective motion toward cyclic rotation on spheres and tori, or spatial-temporal periodic traveling ring patterns on landscapes with hills and valleys. Additionally, we observe that rough surfaces and the incorporation of excluded volume effects can disrupt the complexity of these collective spatial-temporal patterns. Through this investigation, we provide invaluable insight into the intricate interplay of curvature and symmetry, profoundly shaping collective behaviors among active particles across varied surfaces.

Collective queuing motion of self-propelled particles with leadership and experience

The coordinated and ordered collective behavior arising from dispersed and local self-organizing interactions among individuals is widely observed in many biological communities. For populations engaging in group foraging or migration, complex societies with multiple hierarchical levels are common. A prevalent scenario involves two dominant levels, one corresponding to leaders and the other composed of followers. In this paper, we explore how a group can be influenced by a set of leaders to organize and move in a coordinated manner towards a preferred direction. Specifically, we balance social interactions among group members through two weighted factors, corresponding to the leadership and experience of leaders. Through computer simulations, we observe a linear relationship between the proportion of leaders guiding group movement and the group size, with larger groups requiring a higher proportion of leaders while maintaining initial density. Additionally, we identify an optimal leadership interval where group movement performance enhances with increasing leadership up to a certain point, beyond which it starts to decline. Similar patterns are observed concerning individual visual field, indicating the existence of an optimal interval for visual angle. Our findings not only contribute to understanding collective motion in natural biological systems but also provide new insights into effective leadership mechanisms in artificial swarm systems.

New pathways to control the evolution of the atomic motion in metallic glasses

Metallic glass formers are a relatively new entry in glass physics, which has attracted large interest in both physics and materials science communities due to the unique mechanical and structural properties of these materials. Physical aging is however one of the main obstacle to their widespread use as it affects their properties at all length scales. The knowledge of the microscopic mechanisms inducing aging and relaxation is therefore extremely important for both fundamental and applied sciences. In this article we present a review of the recent advances made with the X-ray photon correlation spectroscopy technique on the study of the collective particle motion and physical aging in metallic glasses at the atomic level. We show that a careful tuning of the sample preparation or the application of specific thermal protocols have the potential to drive the glass into more aged or rejuvenated microscopic configurations with different stabilities.

Observation of the Electromagnetic Field Effect via Charge-Dependent Directed Flow in Heavy-Ion Collisions at the Relativistic Heavy Ion Collider

The deconfined quark-gluon plasma (QGP) created in relativistic heavy-ion collisions enables the exploration of the fundamental properties of matter under extreme conditions. Noncentral collisions can produce strong magnetic fields on the order of 1018 G, which offers a probe into the electrical conductivity of the QGP. In particular, quarks and antiquarks carry opposite charges and receive contrary electromagnetic forces that alter their momenta. This phenomenon can be manifested in the collective motion of final-state particles, specifically in the rapidity-odd directed flow, denoted as v1(y). Here, we present the charge-dependent measurements of dv1/dy near midrapidities for π±, K±, and p(p¯) in Au+Au and isobar (Ru4496+Ru4496 and Zr4096+Zr4096) collisions at sNN=200 GeV, and in Au+Au collisions at 27 GeV, recorded by the STAR detector at the Relativistic Heavy Ion Collider. The combined dependence of the v1 signal on collision system, particle species, and collision centrality can be qualitatively and semiquantitatively understood as several effects on constituent quarks. While the results in central events can be explained by the u and d quarks transported from initial-state nuclei, those in peripheral events reveal the impacts of the electromagnetic field on the QGP. Our data put valuable constraints on the electrical conductivity of the QGP in theoretical calculations. Published by the American Physical Society 2024

Collective motion of chiral particles in complex noise environments.

Collective motion of chiral particles in complex noise environments is investigated based on the Vicsek model. In the model, we added chirality, along with complex noise, affecting particles clustering motion. Particles can only avoid noise interference in a specific channel, and this consideration is more realistic due to the complexity of the environment. Via simulations, we find that the channel proportion, p, critically influences chiral particle synchronization. Specifically, we observe a disorder-order transition at critical [Formula: see text], only when [Formula: see text], the system can achieve global synchronization. Combined with our definition of spatial distribution parameter and observation of the model, the reason is that particles begin to escape from the noise region under the influence of complex noise. In addition, the value of [Formula: see text] increases linearly with velocity, while it decreases monotonically with the increase in chirality and interaction radius. Interestingly, an appropriate noise amplitude minimizes [Formula: see text]. Our findings may inspire novel strategies to manipulate self-propelled particles of distinct chirality to achieve desired spatial migration and global synchronization.

Confinement effect of inter-arm interactions on glass formation in star polymer melts.

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Complex motion of steerable vesicular robots filled with active colloidal rods

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system’s geometrical and material properties, such as the aspect ratio and Péclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments.

The theory of kinetic effects on resistive wall mode stability in tokamaks

Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. The theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.

A Compact Particle Detector for Space-Based Applications: Development of a Low-Energy Module (LEM) for the NUSES Space Mission

NUSES is a planned space mission aiming to test new observational and technological approaches related to the study of relatively low-energy cosmic rays, gamma rays, and high-energy astrophysical neutrinos. Two scientific payloads will be hosted onboard the NUSES space mission: Terzina and Zirè. Terzina will be an optical telescope readout by SiPM arrays, for the detection and study of Cerenkov light emitted by Extensive Air Showers generated by high-energy cosmic rays and neutrinos in the atmosphere. Zirè will focus on the detection of protons and electrons up to a few hundred MeV and to 0.1–10 MeV photons and will include the Low Energy Module (LEM). The LEM will be a particle spectrometer devoted to the observation of fluxes of relatively low-energy electrons in the 0.1–7-MeV range and protons in the 3–50 MeV range along the Low Earth Orbit (LEO) followed by the hosting platform. The detection of Particle Bursts (PBs) in this Physics channel of interest could give new insight into the understanding of complex phenomena such as eventual correlations between seismic events or volcanic activity with the collective motion of particles in the plasma populating van Allen belts. With its compact sizes and limited acceptance, the LEM will allow the exploration of hostile environments such as the South Atlantic Anomaly (SAA) and the inner Van Allen Belt, in which the anticipated electron fluxes are on the order of 106 to 107 electrons per square centimeter per steradian per second. Concerning the vast literature of space-based particle spectrometers, the innovative aspect of the LEM resides in its compactness, within 10 × 10 × 10 cm3, and in its “active collimation” approach dealing with the problem of multiple scattering at these very relatively low energies. In this work, the geometry of the detector, its detection concept, its operation modes, and the hardware adopted will be presented. Some preliminary results from the Monte Carlo simulation (Geant4) will be shown.

Active Ising Models of flocking: a field-theoretic approach

Using an approach based on Doi-Peliti field theory, we study several different Active Ising Models (AIMs), in each of which collective motion (flocking) of self-propelled particles arises from the spontaneous breaking of a discrete symmetry. We test the predictive power of our field theories by deriving the hydrodynamic equations for the different microscopic choices of aligning processes that define our various models. At deterministic level, the resulting equations largely confirm known results, but our approach has the advantage of allowing systematic generalization to include noise terms. Study of the resulting hydrodynamics allows us to confirm that the various AIMs share the same phenomenology of a first-order transition from isotropic to flocked states whenever the self-propulsion speed is nonzero, with an important exception for the case where particles align only pairwise locally. Remarkably, this variant fails entirely to give flocking—an outcome that was foreseen in previous work, but is confirmed here and explained in terms of the scalings of various terms in the hydrodynamic limit. Finally, we discuss our AIMs in the limit of zero self-propulsion where the ordering transition is continuous. In this limit, each model is still out of equilibrium because the dynamical rules continue to break detailed balance, yet it has been argued that an equilibrium universality class (Model C) prevails. We study field-theoretically the connection between our AIMs and Model C, arguing that these particular models (though not AIMs in general) lie outside the Model C class. We link this to the fact that in our AIMs without self-propulsion, detailed balance is not merely still broken, but replaced by a different dynamical symmetry in which the dynamics of the particle density is independent of the spin state.Graphical .

The collective motion of self-propelled particles affected by the spatial-dependent noise based on Vicsek rules

The collective motion of self-propelled particles affected by the spatial-dependent noise based on Vicsek rules

Slow and fast particles in shear-driven jamming: Critical behavior.

We do extensive simulations of a simple model of shear-driven jamming in two dimensions to determine and analyze the velocity distribution at different densities ϕ around the jamming density ϕ_{J} and at different low shear strain rates, γ[over ̇]. We then find that the velocity distribution is made up of two parts which are related to two different physical processes which we call the slow process and the fast process as they are dominated by the slower and the faster particles, respectively. Earlier scaling analyses have shown that the shear viscosity η, which diverges as the jamming density is approached from below, consists of two different terms, and we present strong evidence that these terms are related to the two different processes: the leading divergence is due to the fast process, whereas the correction-to-scaling term is due to the slow process. The analysis of the slow process is possible thanks to the observation that the velocity distribution for different γ[over ̇] and ϕ at and around the shear-driven jamming transition has a peak at low velocities and that the distribution has a constant shape up to and slightly above this peak. We then find that it is possible to express the contribution to the shear viscosity due to the slow process in terms of height and position of the peak in the velocity distribution and find that this contribution matches the correction-to-scaling term, determined through a standard critical scaling analysis. A further observation is that the collective particle motion is dominated by the slow process. In contrast to the usual picture in critical phenomena with a direct link between the diverging correlation length and a diverging order parameter, we find that correlations and shear viscosity decouple since they are controlled by different sets of particles and that shear-driven jamming is thus an unusual kind of critical phenomenon.

Long time gyrokinetic equations

The aim of this text is to elucidate the oscillating patterns (see C. Cheverry [Res. Rep. Math. (2018)]) which are generated in a toroidal plasma by a strong external magnetic field and a nonzero electric field. It is also to justify and then study new modulation equations which are valid for longer times than before. Oscillating coherent structures are induced by the collective motions of charged particles which satisfy a system of ODEs implying a large parameter, the gyrofrequency ε − 1 ≫ 1 \varepsilon ^{-1} \gg 1 . By exploiting the properties of underlying integrable systems, we can complement the KAM picture (see G. Benettin and P. Sempio [Nonlinearity 7 (1994), pp. 281–303]; M. Braun [SIAM Rev. 23 (1981), pp. 61–93]) and go beyond the classical results about gyrokinetics (see M. Bostan [Multiscale Model. Simul. 8 (2010), pp. 1923–1957]; A. J. Brizard and T. S. Hahm [Rev. Modern Phys. 79 (2007), pp. 421–468]). The purely magnetic situation was addressed by C. Cheverry [Comm. Math. Phys. 338 (2015), pp. 641–703; J. Differential Equations 262 (2017), pp. 2987–3033]. We are concerned here with the numerous additional difficulties due to the influence of a nonzero electric field.

Magnetic density separation of particles in honeycomb-generated wake turbulence

Magnetic density separation (MDS) is a technique for separating granular materials based on mass density. MDS uses magnetically responsive fluids and engineered magnetic fields to create a vertical gradient of apparent mass density inside the fluid. We present a numerical study to investigate the effect of honeycomb wake turbulence on the motion of almost neutrally buoyant spherical particles in a magnetized fluid. A four-way coupled Euler-Lagrange approach is used where particles are effectively treated as finite-size point particles. It is shown that the honeycomb-generated wake turbulence increases the levitation time of the particles. The presence of particles results in an earlier break-up of the individual velocity profiles stemming from the honeycomb cells. The effects of honeycomb geometry and cell Reynolds number on the collective motion of particles and turbulence properties are investigated, where the choice for the best honeycomb is a trade-off between the separation error and the particle flux.

Weak ergodicity breaking and anomalous diffusion in collective motion of active particles under spatiotemporal disorder.

The effects of spatiotemporal disorder, i.e., both the noise and quenched disorder, on the dynamics of active particles in two dimensions are investigated. We demonstrate that within the tailored parameter regime, nonergodic superdiffusion and nonergodic subdiffusion occur in the system, identified by the observable quantities (the mean squared displacement and ergodicity-breaking parameter) averaged over both the noise and realizations of quenched disorder. Their origins are attributed to the competition effects between the neighbor alignment and spatiotemporal disorder on the collective motion of active particles. These results may be helpful for further understanding the nonequilibrium transport process of active particles, as well as for detection of the transport of self-propelled particles in complex and crowded environments.