Collective Motion Of Particles Research Articles

Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Microscopic dynamics of stress relaxation in a nanocolloidal soft glass

We report x-ray photon correlation spectroscopy (XPCS) experiments with in situ rheometry performed on a soft glass composed of a concentrated suspension of charged silica nanoparticles subjected to step strains that induce yielding and flow. The XPCS measurements characterize the particle-scale and mesoscale motions within the glass that underlie the highly protracted decay of the macroscopic stress following the step strains. These dynamics are anisotropic, with slow, convective particle motion along the direction of the preceding shear that persists for surprisingly large times and that is accompanied by intermittent motion in the perpendicular (vorticity) direction. A close correspondence between the convective dynamics and stress relaxation is demonstrated by power-law scaling between the characteristic velocity of the collective particle motion and the rate of stress decay.

Shear stress response of active liquid crystal suspensions

ABSTRACTWe consider the shear stress response of suspensions of active liquid crystals in dilute regime based on a kinetic model. Perturbation analysis reveals the low shear active viscous plateau and the monotonic dependence of the apparent viscosity on the volume fraction of active liquid crystals. Activity induced thinning or thickening can also be inferred from the analysis. And the remarkable superfluidlike transition can be predicted where the viscous loss can be totally overcome by the collective motion of active particles. Our numerical simulation results of the kinetic model equations further confirm the theoretic predictions and provide the shear stress response of active suspensions at both low and large shear rates.

Collective motion of chiral Brownian particles controlled by a circularly-polarized laser beam.

We demonstrate the emergence of circular collective motion in a system of spherical light-propelled Brownian particles. Light-propulsion occurs as consequence of the coupling between the chirality of polymeric particles - left (L)- or right (R)-type - and the circularly-polarized light that irradiates them. Irradiation with light that has the same helicity as the particle material leads to a circular cooperative vortical motion between the chiral Brownian particles. In contrast, opposite circular-polarization does not induce such coupling among the particles but only affects their Brownian motion. The mean angular momentum of each particle has a value and sign that distinguishes between chiral activity dynamics and typical Brownian motion. These outcomes have relevant implications for chiral separation technologies and provide new strategies for optical torque tunability in mesoscopic optical array systems, micro- and nanofabrication of light-activated engines with selective control and collective motion.

МОДЕЛИРОВАНИЕ ДВИЖЕНИЯ ЧАСТИЦЫ В НАКЛОННОЙ ПЛОСКОСТИ ПОД ДЕЙСТВИЕМ ПОТОКА ВОДЫ

Работа посвящена моделированию процессов гравитационного обогащения полезных ископаемых. В ней представлены результаты исследования движения частиц в наклонной плоскости под действием потока воды. При разработке математических моделей коллективного движения частиц в устройствах необходимо знание вероятности положения одной частицы в устройстве. Целью настоящей работы является определение вероятности положения частицы на наклонной плоскости при заданных условиях. При определении вероятности положения частицы используется метод ансамблей Гиббса. Возможные положения частицы на рабочей поверхности устройства определяются законом движения, который получается интегрированием уравнения движения. При стационарных процессах концентрация точек этого множества согласно методу Гиббса представляет собой распределение вероятности местонахождения частицы в рассматриваемом пространстве. С целью проверки данной математической модели разработана экспериментальная установка, которая представляет собой емкость в виде плоского полого прямоугольного параллелепипеда, расположенного под некоторым углом к горизонту, с изотропным потоком воды. Свинцовые маркеры, двигаясь под действием потока воды и силы тяжести по наклонной плоскости, падают в ячейки, расположенные в нижней части емкости. Количество дробинок в ячейках позволяет оценить распределение частиц в нижней части устройства в зависимости от скорости потока воды и угла наклона рабочей поверхности. На основе разработанной математической модели рассчитано вероятное распределение частиц вдоль нижней грани рабочей поверхности устройства. Сравнение и анализ полученных теоретических и экспериментальных результатов показали хорошую корреляцию полученных данных. The work is devoted to modeling the processes of gravitational enrichment of minerals. It presents the results of a study of the motion of particles in an inclined plane under the influence of a stream of water. When developing mathematical models of the collective motion of particles in devices, it is necessary to know the probability for the position of one particle in the device. The aim of this work is to determine the probability for the particle position on an inclined plane under given conditions, for which the Gibbs ensemble method is used. The possible positions of the particles on the working surface of the device are determined by the law of motion, which is obtained by integrating the equation of motion. In stationary processes, the concentration of points of this set, according to the Gibbs method, is the probability distribution for the location of a particle in the space under consideration. In order to verify this mathematical model, an experimental setup has been developed which is represented by a container in the form of a flat hollow rectangular parallelepiped located at an angle to the horizon with an isotropic water flow. Lead markers, moving under the influence of the stream of water and gravity along the inclined plane, fall in the cells located in the lower part of the tank. The number of pellets in the cells allows us to estimate the distribution of the particles in the lower part of the device depending on the speed of the water flow and the angle of inclination of the working surface. Based on the developed mathematical model, the probable distribution of particles along the lower face of the working surface of the device is calculated. Comparison and analysis of the theoretical and experimental results showed a good correlation of the data.

Glass-transition asymptotics in two theories of glassy dynamics: Self-consistent generalized Langevin equation and mode-coupling theory.

We contrast the generic features of structural relaxation close to the idealized glass transition that are predicted by the self-consistent generalized Langevin equation theory (SCGLE) against those that are predicted by the mode-coupling theory of the glass transition (MCT). We present an asymptotic solution close to conditions of kinetic arrest that is valid for both theories, despite the different starting points that are adopted in deriving them. This in particular provides the same level of understanding of the asymptotic dynamics in the SCGLE as was previously done only for MCT. We discuss similarities and different predictions of the two theories for kinetic arrest in standard glass-forming models, as exemplified through the hard-sphere system. Qualitative differences are found for models where a decoupling of relaxation modes is predicted, such as the generalized Gaussian core model, or binary hard-sphere mixtures of particles with very disparate sizes. These differences, which arise in the distinct treatment of the memory kernels associated to self- and collective motion of particles, lead to distinct scenarios that are predicted by each theory for partially arrested states and in the vicinity of higher-order glass-transition singularities.

A hybrid model of collective motion of discrete particles under alignment and continuum chemotaxis

In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles. In particular we rely on a hybrid description in which the agents are discrete entities, while the chemoattractant is considered as a continuous signal. The proposed model is then studied both from an analytical and a numerical point of view. From the analytic point of view we prove, globally in time, existence and uniqueness of the solution. Then, the asymptotic behaviour of a linearised version of the system is investigated. Through a suitable Lyapunov functional we show that for $t\rightarrow +\infty$, the migrating aggregate exponentially converges to a state in which all the particles have a same position with zero velocity. Finally, we present a comparison between the analytical findings and some numerical results, concerning the behaviour of the full nonlinear system.

Numerical study of condensation in a Fermi-like model of counterflowing particles via Gini coefficient

The collective motion of self-driven particles shows interesting novel phenomena such as swarming and the emergence of patterns. We have recently proposed a model for counterflowing particles that captures this idea and exhibits clogging transitions. This model is based on a generalization of the Fermi–Dirac statistics wherein the maximal occupation of a cell is used. Here we present a detailed study comparing synchronous and asynchronous stochastic dynamics within this model. We show that an asynchronous updating scheme supports the mobile-clogging transition and eliminates some mobility anomalies that are present in synchronous Monte Carlo simulations. Moreover, we show that this transition is dependent upon its initial conditions. Although the Gini coefficient was originally used to model wealth inequalities, we show that it is also efficient for studying the mobile-clogging transition. Finally, we compare our stochastic simulation with direct numerical integration of partial differential equations used to describe this model.

On the Disordered, Collective and Patterned Movements of Media. Qualitative Analysis of Movements

The motion of elements is classified from a topological aspect. We separate three different, disordered, collective and patterned motion forms of media. We will reveal what concrete shapes the different type media take. In case of a limited number of particles, a discrete description is suitable for tracking the mechanic behavior of the medium. In case of the large of a number of particles we apply in some sense continuous mathematical model according to the motion occurring in the medium instead of a discrete description. We postulate a statistical distribution to the disordered motion; we "distribute" the particles for the collective motion in the physical space and apply a differential geometric description. We assign continuous flow lines to the regular patterned motion of the medium with free particles while we assign energy dissipation to the flow image an irregular patterned motion. In the case of deformable solid body built by periodically arranged rigid bodies the state functions with discrete domain of definition are represented by functions with continuous domain of definition. Granular conglomerations seem to be the only such medium, which allow tracking of the state of all granules.Disordered motion leads to thermodynamic - statistical description. The collective motion of free particles leads to the description of the laminar flow of particles, the collective motion of fixed particles leads to the classical continuum. The patterned motion of free particles leads to the description of vortex or turbulent flow, the patterned motion of fixed particles leads to grid continua.

Diffusion in Porous Media: Phenomena and Mechanisms

Two distinct but interconnected approaches can be used to model diffusion in fluids; the first focuses on dynamics of an individual particle, while the second deals with collective (effective) motion of (infinitely many) particles. We review both modeling strategies, starting with Langevin’s approach to a mechanistic description of the Brownian motion in free fluid of a point-size inert particle and establishing its relation to Fick’s diffusion equation. Next, we discuss its generalizations which account for a finite number of finite-size particles, particle’s electric charge, and chemical interactions between diffusing particles. That is followed by introduction of models of molecular diffusion in the presence of geometric constraints (e.g., the Knudsen and Fick–Jacobs diffusion); when these constraints are imposed by the solid matrix of a porous medium, the resulting equations provide a pore-scale representation of diffusion. Next, we discuss phenomenological Darcy-scale descriptors of pore-scale diffusion and provide a few examples of other processes whose Darcy-scale models take the form of linear or nonlinear diffusion equations. Our review is concluded with a discussion of field-scale models of non-Fickian diffusion.

Coupling and decoupling between translational and rotational dynamics in supercooled monodisperse soft Janus particles.

We perform dynamics simulations to investigate the translational and rotational glassy dynamics in a glass-forming liquid of monodisperse soft Janus particles. We find that, with decreasing temperature, the mean-square angular displacement shows no clear plateau in the caging region, in contrast with the apparent caging behavior of translational motion. By defining a reorientational mean-square angular displacement, the caging behavior of rotational motion can be recognized. On approaching the glass transition (decreasing temperature), the coupling between translational and rotational relaxation increases, while the coupling between translational and rotational diffusion decreases, whereas the coupling between translational and reorientational diffusion increases. The strong decoupling between translational and rotational diffusion is due to the suppressed translational mobility but promoted rotational mobility of soft Janus particles. We think that the low-T SE and SED decoupling is mainly attributed to hopping motion of soft Janus particles, whereas the high-T SE and SED decoupling is mainly attributed to collective cage motion of soft Janus particles. Our results demonstrate that interaction anisotropy has a critical effect on the translational and rotational dynamics of soft Janus particles.

Swarming in the Dirt: Ordered Flocks with Quenched Disorder.

The effect of quenched (frozen) disorder on the collective motion of active particles is analyzed. We find that active polar systems are far more robust against quenched disorder than equilibrium ferromagnets. Long-ranged order (a nonzero average velocity ⟨v⟩) persists in the presence of quenched disorder even in spatial dimensions d=3; in d=2, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs. In equilibrium systems, only quasi-long-ranged order in d=3 and short-ranged order in d=2 are possible. Our theoretical predictions for two dimensions are borne out by simulations.

Hydrodynamic theory of flocking in the presence of quenched disorder

The effect of quenched (frozen) orientational disorder on the collective motion of active particles is analyzed. We find that, as with annealed disorder (Langevin noise), active polar systems are far more robust against quenched disorder than their equilibrium counterparts. In particular, long ranged order (i.e., the existence of a non-zero average velocity $\langle {\bf v} \rangle$) persists in the presence of quenched disorder even in spatial dimensions $d=3$, while it is destroyed even by arbitrarily weak disorder in $d \le 4$ in equilibrium systems. Furthermore, in $d=2$, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs when quenched disorder is present, in contrast to the short-ranged order that is all that can survive in equilibrium. These predictions are borne out by simulations in both two and three dimensions.

Magnetically-Programmable Cylindrical Microparticles by Facile Reaping Method

Various shapes of magnetically-programmed polyethylene glycol (PEG)-based particles with Fe3O4 blocks were harvested by a facile reaping method. Specifically, elastic PEG-based particles can be obtained by applying uniform shear stress onto the array of densely-populated PEG/Fe3O4 microstructures. A simple theory based on geometric and material properties was developed based on experimental observations to produce highly uniform cylindrical microparticles in a cost-effective manner. We analyzed the force balance of hairy architectures to explain the uniform cutting process, which is based on operating zones with various geometries and material elasticity. Here, the alignments of mono-/multi-dispersed iron oxide (Fe3O4) in microparticles can be tunable by changing the external magnetic field during replications. Furthermore, the collective reversible motions of different magneto-responsive PEG particles were observed when the external magnetic field was controlled, wherein such behaviors can be applied in potential medial applications such as controllable drug-delivery or microrobotics.

Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking.

Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes.

Reynolds-number-dependent dynamical transitions on hydrodynamic synchronization modes of externally driven colloids.

The collective dynamics of externally driven N_{p}-colloidal systems (1≤N_{p}≤4) in a confined viscous fluid have been investigated using three-dimensional direct numerical simulations with fully resolved hydrodynamics. The dynamical modes of collective particle motion are studied by changing the particle Reynolds number as determined by the strength of the external driving force and the confining wall distance. For a system with N_{p}=3, we found that at a critical Reynolds number a dynamical mode transition occurs from the doublet-singlet mode to the triplet mode, which has not been reported experimentally. The dynamical mode transition was analyzed in detail from the following two viewpoints: (1) spectrum analysis of the time evolution of a tagged particle velocity and (2) the relative acceleration of the doublet cluster with respect to the singlet particle. For a system with N_{p}=4, we found similar dynamical mode transitions from the doublet-singlet-singlet mode to the triplet-singlet mode and further to the quartet mode.

Quantum Effect on Elementary Process of Diffusion and Collective Motion of Brown Particles

The correlation between the Schrodinger equation and the diffusion equation revealed that the relation of material wave is not a hypothesis but an actual one valid in a material regardless of the photon energy. Using the relations of material wave and uncertain principle, the quantum effect on elementary process of diffusion is discussed. As a result, the diffusivity is obtained as a universal expression applicable to any problem of diffusion phenomena. The Gauss theorem in theory and the Kirkendall effect in experimentation reveal the necessity of the coordinate transformation for a diffusion equation. The mathematical method for solving an interdiffusion problem of many elements system is established. The phase shift of the obtained analytical solution indicates the correlation between the solutions of each diffusion equation expressed by a fixed coordinate system and by a moving coordinate system. Based on the coordinate transformation theory, some unsolved problems of diffusion theory are reasonably solved and also some new important findings are discussed in relation to matters in the existing diffusion theory.

Change in collective motion of colloidal particles driven by an optical vortex with driving force and spatial confinement.

We studied the change in collective behavior of optically driven colloidal particles on a circular path. The particles are simultaneously driven by the orbital angular momentum of an optical vortex beam generated by holographic optical tweezers. The driving force is controlled by the topological charge l of the vortex. By varying the driving force and spatial confinement, four characteristic collective motions were observed. The collective behavior results from the interplay between the optical interaction, hydrodynamic interaction and spatial confinement. Varying the topological charge of an optical vortex not only induces changes in driving force but also alters the stability of three-dimensional optical trapping. The switch between dynamic clustering and stable clustering was observed in this manner. Decreasing the cell thickness diminishes the velocity of the respective particles and increases the spatial confinement. A jamming-like characteristic collective motion appears when the thickness is small and the topological charge is large. In this regime, a ring of equally-spaced doublets was spontaneously formed in systems composed of an even number of particles.

Collective motion of active Brownian particles with polar alignment.

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

Collective motion of rod-shaped self-propelled particles through collision.

Self-propelled rods, which propel by themselves in the direction from the tail to the head and align nematically through collision, have been well-investigated theoretically. Various phenomena including true long-range ordered phase with the Giant number fluctuations, and the collective motion composed of many vorices were predicted using the minimal mathematical models of self-propelled rods. Using filamentous bacteria and running microtubules, we found that the predicted phenomena by the minimal models occur in the real world. This strongly indicates that there exists the unified description of self-propelled rods independent of the details of the systems. The theoretically predicted phenomena and the experimental results concerning the phenomena are reviewed.