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This editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications focus on classical problems of swarms theory, on crowd dynamics related to virus contagion problems, and to multiscale problems related to the derivation of models at a large scale from the mathematical description at the microscopic scale. A critical analysis of the overall contents of the issue is proposed, with the aim to provide a forward look to research perspectives.

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

In a numerical experiment, it is found that at least three localized stationary breather type modes can exist in a chain of Rayleigh oscillators with a nonlinear coupling between them: immobile, “slow,” and “fast” dissipative breathers. The dynamics of synchronous motions of chain elements depends on the relation of characteristic time scales of the system related to the frequency of the oscillators and rigidity of the coupling between them; it is multistable.

Symmetry breaking and the emergence of self-organized patterns is the hallmark of complexity. Here, we demonstrate that a sessile drop, containing titania powder particles with negligible self-propulsion, exhibits a transition to collective motion leading to self-organized flow patterns. This phenomenology emerges through a novel mechanism involving the interplay between the chemical activity of the photocatalytic particles, which induces Marangoni stresses at the liquid–liquid interface, and the geometrical confinement provided by the drop. The response of the interface to the chemical activity of the particles is the source of a significantly amplified hydrodynamic flow within the drop, which moves the particles. Furthermore, in ensembles of such active drops long-ranged ordering of the flow patterns within the drops is observed. We show that the ordering is dictated by a chemical communication between drops, i.e., an alignment of the flow patterns is induced by the gradients of the chemicals emanating from the active particles, rather than by hydrodynamic interactions., Complex systems exhibit unique properties like spontaneous symmetry breaking and self-organization. Singh et al. show that catalytically active, non-propelling particles can induce steady vortical flows within a drop, as well as flow alignment between neighboring drops.

The joint chemiluminescence of luminol and lophine, initiated by active particles that are generated by the decomposition of hydrogen peroxide by hemin, is studied by spectral-kinetic recording.

We examine the interplay of motility and information exchange in a model of run-and-tumble active particles where the particle's motility is encoded as a bit of information that can be exchanged upon contact according to the rules of AND and OR logic gates in a circuit. Motile AND particles become non-motile upon contact with a non-motile particle. Conversely, motile OR particles remain motile upon collision with their non-motile counterparts. AND particles that have become non-motile additionally "reawaken", i.e., recover their motility, at a fixed rate $\mu$, as in the SIS (Susceptible, Infected, Susceptible) model of epidemic spreading, where an infected agent can become healthy again, but keeps no memory of the recent infection, hence it is susceptible to a renewed infection. For $\mu=0$, both AND and OR particles relax irreversibly to absorbing states of all non-motile or all motile particles, respectively. The relaxation kinetics is, however, faster for OR particles that remain active throughout the process. At finite $\mu$, the AND dynamics is controlled by the interplay between reawakening and collision rates. The system evolves to a state of all motile particles (an absorbing state in the language of absorbing phase transitions) for $\mu>\mu_c$ and to a mixed state with coexisting motile and non-motile particles (an active state in the language of absorbing phase transitions) for $\mu

Dipolar active particles describe a class of self-propelled, biological or artificial particles equipped with an internal (typically magnetic) dipole moment. Because of the interplay between self-propulsion and dipole-dipole interactions, complex collective behavior is expected to emerge in systems of such particles. Here, we use Brownian dynamics simulations to explore this collective behavior. We focus on the structures that form in small systems in spatial confinement. We quantify the type of structures that emerge and how they depend on the self-propulsion speed and the dipolar (magnetic) strength of the particles. We observe that the dipolar active particles self-assemble into chains and rings. The dominant configuration is quantified with an order parameter for chain and ring formation and shown to depend on the self-propulsion speed and the dipolar magnetic strength of the particles. In addition, we show that the structural configurations are also affected by the confining walls. To that end, we compare different confining geometries and study the impact of a reorienting 'wall torque' upon collisions of a particle with a wall. Our results indicate that dipolar interactions can further enhance the already rich variety of collective behaviors of active particles.

We present a modified conserved lattice gas (CLG) model in two dimensions with a thermal noise parameter, P = exp(−1/T), where T is the effective temperature. In particular, we focus on the interplay of thermal noise P and the total density of particles ρ in the CLG model. The universality class of the case of 0

International audience; The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives.

We study the nonequilibrium interaction of two isotropic chemically-active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed-point---a phenomenon that cannot be captured under the far-field approximation. We find that due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size, or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects are originated from a self-generated neighbor-reflected chemical gradient, similar to interactions of a self-propelling phoretic particle and a flat substrate.

Cell migration through extracellular matrices is critical to many physiological processes, such as tissue development, immunological response and cancer metastasis. Previous models including persistent random walk (PRW) and Lévy walk only explain the migratory dynamics of some cell types in a homogeneous environment. Recently, it was discovered that the intracellular actin flow can robustly ensure a universal coupling between cell migratory speed and persistence for a variety of cell types migrating in the in vitro assays and live tissues. However, effects of the correlation between speed and persistence on the macroscopic cell migration dynamics and patterns in complex environments are largely unknown. In this study, we developed a Monte Carlo random walk simulation to investigate the motility, the search ability and the search efficiency of a cell moving in both homogeneous and porous environments. The cell is simplified as a dimensionless particle, moving according to PRW, Lévy walk, random walk with linear speed-persistence correlation (linear RWSP) and random walk with nonlinear speed-persistence correlation (nonlinear RWSP). The coarse-grained analysis showed that the nonlinear RWSP achieved the largest motility in both homogeneous and porous environments. When a particle searches for targets, the nonlinear coupling of speed and persistence improves the search ability (i.e. find more targets in a fixed time period), but sacrifices the search efficiency (i.e. find less targets per unit distance). Moreover, both the convex and concave pores restrict particle motion, especially for the nonlinear RWSP and Lévy walk. Overall, our results demonstrate that the nonlinear correlation of speed and persistence has the potential to enhance the motility and searching properties in complex environments, and could serve as a starting point for more detailed studies of active particles in biological, engineering and social science fields.

Complex interactions between cellular systems and their surrounding extracellular matrices are emerging as important mechanical regulators of cell functions such as proliferation, motility, and cell death, and such cellular systems are often characterized by pulsating acto-myosin activities. Here, using an active gel model, we numerically explore the spontaneous flow generation by activity pulses in the presence of a viscoelastic medium. The results show that cross-talk between the activity-induced deformations of the viscoelastic surroundings with the time-dependent response of the active medium to these deformations can lead to the reversal of spontaneously generated active flows. We explain the mechanism behind this phenomenon based on the interaction between the active flow and the viscoelastic medium. We show the importance of relaxation timescales of both the polymers and the active particles and provide a phase-space over which such spontaneous flow reversals can be observed. Our results suggest new experiments investigating the role of controlled pulses of activity in living systems ensnared in complex mircoenvironments., 10 pages, 3 figures

Using a minimal model of active Brownian discs, we study the effect of a crucial parameter, namely the softness of the inter-particle repulsion, on motility-induced phase separation. We show that an increase in particle softness reduces the ability of the system to phase-separate and the system exhibit a delayed transition. After phase separation, the system state properties can be explained by a single relevant lengthscale, the effective inter-particle distance. We estimate this lengthscale analytically and use it to rescale the state properties at dense phase for systems with different interaction softness. Using this lengthscale, we provide a scaling relation for the time taken to phase separate which shows a high sensitivity to the interaction softness., 8 pages, 12 figures. Significant changes: The form of the critical radius rc is new, with a better physical understanding of the system. Which neither changes the scaling nor the exponenets of the system. Fig.11 is a new addition in the appendix

We present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble \emph{Bacillus subtilis} bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into $xy$-space, the edges of the SwIMs act as one-way barriers, consistent with the experiments., Comment: 11 pages, 8 figures

Suspensions of motile active particles with space-dependent activity form characteristic polarization and density patterns. Recent single-particle studies for planar activity landscapes identified several quantities associated with emergent density-polarization patterns that are solely determined by bulk variables. Naive thermodynamic intuition suggests that these results might hold for arbitrary activity landscapes mediating bulk regions, and thus could be used as benchmarks for simulations and theories. However, the considered system operates in a nonequilibrium steady state and we prove by construction that the quantities in question lose their simple form for curved activity landscapes. Specifically, we provide a detailed analytical study of polarization and density profiles induced by radially symmetric activity steps, and of the total polarization for the case of a general radially symmetric activity landscape. While the qualitative picture is similar to the planar case, all the investigated variables depend not only on bulk variables but also comprise geometry-induced contributions. We verified that all our analytical results agree with exact numerical calculations.

Hydrodynamic interactions (HIs) are important in biophysics research because they influence both the collective and the individual behaviour of microorganisms and self-propelled particles. For instance, HIs at the micro-swimmer level determine the attraction or repulsion between individuals, and hence their collective behaviour. Meanwhile, HIs between swimming appendages (e.g. cilia and flagella) influence the emergence of swimming gaits, synchronised bundles and metachronal waves. In this study, we address the issue of HIs between slender filaments separated by a distance larger than their contour length (d>L) by means of asymptotic calculations and numerical simulations. We first derive analytical expressions for the extended resistance matrix of two arbitrarily-shaped rigid filaments as a series expansion in inverse powers of d/L>1. The coefficients in our asymptotic series expansion are then evaluated using two well-established methods for slender filaments, resistive-force theory (RFT) and slender-body theory (SBT), and our asymptotic theory is verified using numerical simulations based on SBT for the case of two parallel helices. The theory captures the qualitative features of the interactions in the regime d/L>1, which opens the path to a deeper physical understanding of hydrodynamically governed phenomena such as inter-filament synchronisation and multiflagellar propulsion. To demonstrate the usefulness of our results, we next apply our theory to the case of two helices rotating side-by-side, where we quantify the dependence of all forces and torques on the distance and phase difference between them. Using our understanding of pairwise HIs, we then provide physical intuition for the case of a circular array of rotating helices. Our theoretical results will be useful for the study of HIs between bacterial flagella, nodal cilia, and slender microswimmers.

One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a one-dimensional harmonic chain of $N$ active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the moment-generating function for the heat flow in the steady state. We employ our general framework to explicitly compute the moment-generating function for two example single-particle systems. Further, we analytically obtain the scaled cumulants for the heat flow for the chain. Numerical Langevin simulations confirm the long-time analytical expressions for first and second cumulants for the heat flow for a two-particle chain., Comment: 23 pages, 7 figures, Major revision

Experimental data on the active Brownian motion of single particles in the RF (radio-frequency) discharge plasma under the influence of thermophoretic force, induced by laser radiation, depending on the material and type of surface of the particle, are presented. Unlike passive Brownian particles, active Brownian particles, also known as micro-swimmers, move directionally. It was shown that different dust particles in gas discharge plasma can convert the energy of a surrounding medium (laser radiation) into the kinetic energy of motion. The movement of the active particle is a superposition of chaotic motion and self-propulsion.

We study the escape problem for interacting, self-propelled particles confined to a disk, where particles can exit through one open slot on the circumference. Within a minimal two-dimensional Vicsek model, we numerically study the statistics of escape events when the self-propelled particles can be in a flocking state. We show that while an exponential survival probability is characteristic for noninteracting self-propelled particles at all times, the interacting particles have an initial exponential phase crossing over to a subexponential late-time behavior. We use a phenomenological model based on nonstationary Poisson processes which includes the Allee effect to explain this subexponential trend and perform numerical simulations for various noise intensities.

Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.

One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers., 7 pages, 5 figures, and 5 pages supplemental material

Researchers make systems of self-propelled particles produce the same large-scale dynamics as passive-particle systems.

The co-localization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. It can therefore play the role of a smoking gun for the mesoscale detection of intrinsic microscopic activity. We employ the active-Brownian-particle (ABP) model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step, including situations with an orientation-dependent propulsion speed. Our results agree well with measurement data for a hot microswimmer presented in the companion paper [1] and can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species ``run-and-tumble'' model., 21 pages, 11 figures

We report a novel state of active matter—a swirlonic state. It is comprised of swirlons, formed by groups of active particles orbiting their common center of mass. These quasi-particles demonstrate a surprising behavior: In response to an external load they move with a constant velocity proportional to the applied force, just as objects in viscous media. The swirlons attract each other and coalesce forming a larger, joint swirlon. The coalescence is extremely slow, decelerating process, resulting in a rarified state of immobile quasi-particles. In addition to the swirlonic state, we observe gaseous, liquid and solid states, depending on the inter-particle and self-driving forces. Interestingly, in contrast to molecular systems, liquid and gaseous states of active matter do not coexist. We explain this unusual phenomenon by the lack of fast particles in active matter. We perform extensive numerical simulations and theoretical analysis. The predictions of the theory agree qualitatively and quantitatively with the simulation results.

Biological cells generate intricate structures by sculpting their membrane from within to actively sense and respond to external stimuli or to explore their environment1–4. Several pathogenic bacteria also provide examples of how localized forces strongly deform cell membranes from inside, leading to the invasion of neighbouring healthy mammalian cells5. Giant unilamellar vesicles have been successfully used as a minimal model system with which to mimic biological cells6–11, but the realization of a minimal system with localized active internal forces that can strongly deform lipid membranes from within and lead to dramatic shape changes remains challenging. Here we present a combined experimental and simulation study that demonstrates how self-propelled particles enclosed in giant unilamellar vesicles can induce a plethora of non-equilibrium shapes and active membrane fluctuations. Using confocal microscopy, in the experiments we explore the membrane response to local forces exerted by self-phoretic Janus microswimmers. To quantify dynamic membrane changes, we perform Langevin dynamics simulations of active Brownian particles enclosed in thin membrane shells modelled by dynamically triangulated surfaces. The most pronounced shape changes are observed at low and moderate particle loadings, with the formation of tether-like protrusions and highly branched, dendritic structures, whereas at high volume fractions globally deformed vesicle shapes are observed. The resulting state diagram predicts the conditions under which local internal forces generate various membrane shapes. A controlled realization of such distorted vesicle morphologies could improve the design of artificial systems such as small-scale soft robots and synthetic cells. Experiments and simulations show that local non-equilibrium forces exerted by self-propelled particles trapped inside a giant unilamellar lipid vesicle induce dramatic shape changes in the vesicle.

We report on the emergence of stable self-propelled bound defects in monolayers of active nematics, which form virtual full-integer topological defects in the form of vortices and asters. Through numerical simulations and analytical arguments, we identify the phase space of the bound defect formation in active nematic monolayers. It is shown that an intricate synergy between the nature of active stresses and the flow-aligning behavior of active particles can stabilize the motion of self-propelled positive half-integer defects into specific bound structures. Our findings therefore, uncover conditions for the formation of full integer topological defects in active nematics with the potential for triggering further experiments and theories.

Effective interaction between two asymmetric wedges immersed in a two-dimensional active bath is investigated by computer simulations. The attraction–repulsion transition of effective force between two asymmetric wedges is subjected to the relative position of two wedges, the wedge-to-wedge distance, the active particle density, as well as the apex angle of two wedges. By exchanging the position of the two asymmetric wedges in an active bath, firstly a simple attraction–repulsion transition of effective force occurs, completely different from passive Brownian particles. Secondly the transition of effective force is symmetric for the long-range distance between two asymmetric wedges, while it is asymmetric for the short-range case. Our investigations may provide new possibilities to govern the motion and assembly of microscopic objects by taking advantage of the self-driven behaviour of active particles.

It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different motility. In this paper, using numerical simulations in the dilute limit, we investigate how motility parameters (time of persistence and velocity) impact the narrow-escape time of active particles from circular domains. We show that the escape time undergoes a crossover between two asymptotic regimes. The control parameters of the crossover is the ratio between the persistence length of the active motion and the typical length scale of the circular domain. We explore the possibility of taking advantage of this finding for sorting active particles by motility parameters.

International audience; We revisit motility-induced phase separation in two models of active particles interacting by pair-wise repulsion. We show that the resulting dense phase contains gas bubbles distributed algebraically up to a typically large cutoff scale. At large enough system size and/or global density, all the gas may be contained inside the bubbles, at which point the system is microphase-separated with a finite cutoff bubble scale. We observe that the ordering is anomalous, with different dynamics for the coarsening of the dense phase and of the gas bubbles. This phenomenology is reproduced by a "reduced bubble model" that implements the basic idea of reverse Ostwald ripening put forward in Tjhung et al. [Phys. Rev. X 8, 031080 (2018)]. Self-propelled particles interacting solely with steric repulsion are well known to be able to spontaneously separate into a macroscopic dense cluster and a residual gas, in spite of the absence of explicit attraction forces. This motility-induced phase separation (MIPS) [1] of active particles has become a cornerstone of the physics of dry active matter (in which the fluid surrounding particles is neglected). As such, it has driven many theoretical works [2-7] as well as countless numerical studies (see, e.g. [8-15] to name a few prominent ones). The motil-ity reduction resulting from persistent collisions, which leads to MIPS, is a generic ingredient encountered both in living and synthetic active matter [16-19]. Despite its purely non-equilibrium origin, MIPS was initially described as a conventional phase separation between two homogeneous macroscopic phases. It was first predicted in models of quorum-sensing particles [2] where particle speed decreases with the local density, without two-body interactions. In this case, equilibrium-like thermodynamics can be constructed to account quantitatively for phase coexistence [20]. For systems of repulsive disks, attempts were made to model the speed reduction due to collisions by a quorum-sensing interaction [3, 8, 10], but the results are not satisfactory, due to fundamental differences between the two cases [5, 21]. There is indeed mounting evidence that more complex physics is at play in systems of repulsive disks. In particular , the surface tension between the dense phase and the gas, defined via the Laplace law, has been measured to be negative [20, 22, 23], triggering a spate of controversy[24]. This was rationalized at field theoretical level by including terms that break detailed balance in the classical theory for equilibrium liquid-gas phase separation. In this active Model B+ (AMB+), surface tension can become negative for some parameter values, in which case Ost-wald ripening is reversed for vapor bubbles while still remaining normal for liquid droplets. This means that small vapor bubbles, contrary to the standard scenario, grow at the expense of larger ones due to a diffusion flux. When this happens, simulations of AMB+ lead to either a bubbly fluid interpreted as microphase separation, or to the coexistence of a dense phase populated of bubbles with an outer gas [7]. There is in fact incidental evidence for such a bubbly liquid at particle level [9, 11, 12, 20, 22], but it has not yet been studied per se. Very recently, Ca-porusso et al [25] have shown more clearly that in systems with hard-core interactions, the dense phase is made of hexatic subdomains and interstitial gas regions. In this Letter we show, within two standard particle models displaying MIPS, that not only the dense phase is endowed with bubbles, but also that these are distributed algebraically up to some cutoff scale that we observe to grow with system size. Finite-size scaling based on this observation suggests that, as system size increases, more and more of the gas is contained in bubbles. At large densities, we are able to observe the vanishing of the macroscopic gas reservoir, and the system is then microphase-separated with bubbles of all sizes up to a maximal bubble size that depends on the average density. Moreover, the coarsening of bubbles is anomalous with the typical length scale growing as t 0.22. We elucidate the basic mechanisms at play, and show, within a reduced model implementing reversed Ostwald ripening for gas bubbles, that they indeed lead to a self-organized critical dynamics. Self-organized critical phase coexistence. We first consider the paradigmatic active brownian particles (ABPs) introduced in [8]. Self-propelled by a force of constant magnitude F 0 along its internal polarity u i = (cos θ i , sin θ i), particle i evolves according to the over-damped Langevin equations governing its position r i and polar angle θ i : r i = µ i (F 0 u i + F i) + η i ;θ i = η i (1) where F i = − j =i ∇V (r i − r j) is the force exerted on particle i by the other particles. We choose the pair potential to be a short-range harmonic repulsion V (r) = k 2 (σ − r) 2 if r < σ and 0 otherwise with k the arXiv:2007.03587v1 [cond-mat.stat-mech] 7 Jul 2020

Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling.By modelling the droplet lattice as a memory-endowed system with spatially nonlocal coupling, we herein rationalise the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or sub-critical Hopf bifurcation \emph{via} a systematic weakly nonlinear analysis, rationalising experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system., Comment: 27 pages, 8 figures

Asymmetric obstacles can be exploited to direct the motion and induce sorting of run-and-tumble particles. In this work, we show that flocking particles which follow the Vicsek model aligning rules experience collective trapping in the presence of a wall of funnels made of chevrons, concentrating at the opposite side of the wall of funnels to run-and-tumble particles. Flocking particles can be completely trapped or exhibit a dynamical trapping behaviour; these two regimes open the door to the design of a system with two perpendicular flows of active particles. This systematic study broadens our understanding of the emergence of collective motion of microorganisms in confined environments and directs the design of new microfluidic devices able to control these collective behaviours, The authors acknowledge funding from Grant FIS2016-78847-P of the MICINN UCM/Santander PR26/16-10B-2 and the Consejo Nacional de Ciencia y Tecnología (CONACYT, Mexico) through Grant No. 242589. F. A. acknowledges support from the Juan de la Cierva program (FJCI-2017-33580). The project that gave rise to these results received the support of a fellowship from ‘‘la Caixa’’ Foundation (ID 100010434). The fellowship code is LCF/BQ/LI18/11630021. R. M. thanks MICINN for the award of a FPI pre-doctoral grant (BES-2017-081108) and J. L. A. acknowledges the support of the IFIMAC (MDM-2014-0377) and NVIDIA corporation with the donation of the Titan Xp GPU used for this research

We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 (2015)] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length $Ll{L}^{*}$ and for high tumbling rates $\ensuremath{\lambda}g{\ensuremath{\lambda}}^{*}$, with threshold values ${L}^{*}$ and ${\ensuremath{\lambda}}^{*}$ which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs.

Transport and separation of binary mixtures of active and passive particles are investigated in the presence of temperature differences. It is found that temperature differences can strongly affect the rectification and separation of the mixtures. For active particles, there exists an optimal temperature difference at which the rectified efficiency is maximal. Passive particles are not propelled and move by collisions with active particles, so the response to temperature differences is more complicated. By changing the system parameters, active particles can change their directions, while passive particles always move in the same direction. The simulation results show that the separation of mixtures is sensitive to the system parameters, such as the angular velocity, the temperature difference, and the polar alignment. The mixed particles can be completely separated under certain conditions.

This paper deals with the modeling of wealth distribution considering a society with non-constant population and non-conservative wealth trades. The modeling approach is based on the kinetic theory of active particles, where individuals are distinguished by a scalar variable (the activity) which expresses their social state. A qualitative analysis of the model focusing on asymptotic behaviors and measurement of inequality through the Gini coefficient is presented. Finally, some specific case-studies are proposed in order to carry out numerical experiments to validate our model, characterize societies and investigate emerging behaviors. Fil: Buffa, Bruno Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Torres, German Ariel. Instituto de Modelado e Innovación Tecnológica (Consejo Nacional de Investigaciones Científicas y Técnicas - Universidad Nacional del Nordeste); Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina

Active particles are widely recognized to potentially revolutionize technologies in numerous biomedical applications. However, the physical origin behind cellular uptake of these particles in the nonequilibrium state remains scarcely understood. Here we combine Brownian dynamics simulation as well as theoretical analysis to provide the criterion for cellular uptake of active particles, related to various physical attributes. Upon enhancing the activity, the uptake efficiency for the active particles with tilted orientation is examined to be nonmonotonic, in stark contrast to the monotonic dependence for active particles orientated normally to the membrane. This can be attributed to the interplay between membrane adhesion energy and kinetic energy of active particles, resulting in unique kinetic pathways. Furthermore, a theoretical model that captures the essential physics of the cellular endocytosis process is developed to reproduce this nonmonotonic feature. The results are of immediate interest to understand and tune activity-mediated cellular interaction and internalization of such emerging colloids.

We study the cooperation and segregation dynamics of binary mixtures of active and passive particles on a sphere. According to the competition between rotational diffusion and polar alignment, we find three distinct phases: a mixed phase and two different demixed phases. When rotational diffusion dominates the dynamics, the demixing is due to the aggregation of passive particles, where active and passive particles respectively occupy two hemispheres. When polar alignment is dominated, the demixing is caused by the aggregation of active particles, where active particles occupy the equator of the sphere and passive particles occupy the two poles of the sphere. In this case, there exist a circulating band cluster and two cambered surface clusters, which is a purely curvature-driven effect with no equivalent in the planar model. When rotational diffusion and polar alignment are comparable, particles are completely mixed. Our findings are relevant to the experimental pursuit of segregation dynamics of binary mixtures on curved surfaces.

The presence of active forces in various biological and artificial systems may change how those systems behave when forced. We present a minimal model of a suspension of passive or active swimmers driven on the boundaries by time-dependent forcing. In particular, we consider a time-periodic drive from which we determine the linear response functions of the suspension. The meaning of these response functions are interpreted in terms of the storage and dissipation of energy through the particles within the system. We find that while a slowly driven active system responds in a way similar to a passive system with a re-defined diffusion constant, a rapidly driven active system exhibits a novel behavior related to a change in the motoring activity of the particles due to the external drive.

Using simulations and experiments, we demonstrate that the effective interaction between passive particles in an active bath substantially depends on an external constraint suffered by the passive particles. Particularly, the effective interaction between two free passive particles, which is directly measured in simulation, is qualitatively different from the one between two fixed particles. Moreover, we find that the friction experienced by the passive particles---a kinematic constraint---similarly influences the effective interaction. These remarkable features are in significant contrast to the equilibrium cases, and mainly arise from the accumulation of the active particles near the concave gap formed by the passive spheres. This constraint dependence not only deepens our understanding of the ``active depletion force,'' but also provides an additional tool to tune the effective interactions in an active bath.

Light provides a powerful means of controlling physical behavior of materials but is rarely used to power and guide active matter systems. We demonstrate optical control of liquid crystalline topological solitons dubbed “skyrmions”, which recently emerged as highly reconfigurable inanimate active particles capable of exhibiting emergent collective behaviors like schooling. Because of a chiral nematic liquid crystal’s natural tendency to twist and its facile response to electric fields and light, it serves as a testbed for dynamic control of skyrmions and other active particles. Using ambient-intensity unstructured light, we demonstrate large-scale multifaceted reconfigurations and unjamming of collective skyrmion motions powered by oscillating electric fields and guided by optically-induced obstacles and patterned illumination.

Many microorganisms regulate their behaviour according to the density of neighbours. Such quorum sensing is important for the communication and organisation within bacterial populations. In contrast to living systems, where quorum sensing is determined by biochemical processes, the behaviour of synthetic active particles can be controlled by external fields. Accordingly they allow to investigate how variations of a density-dependent particle response affect their self-organisation. Here we experimentally and numerically demonstrate this concept using a suspension of light-activated active particles whose motility is individually controlled by an external feedback-loop, realised by a particle detection algorithm and a scanning laser system. Depending on how the particles’ motility varies with the density of neighbours, the system self-organises into aggregates with different size, density and shape. Since the individual particles’ response to their environment is almost freely programmable, this allows for detailed insights on how communication between motile particles affects their collective properties., Bacteria communicate and organize via quorum sensing which is determined by biochemical processes. Here the authors aim to reproduce this behaviour in a system of synthetic active particles whose motion is induced by an external beam which is in turn controlled by a feedback-loop which mimics quorum sensing.

Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization. At equilibrium, the structure is encoded through specific interactions, at an unfavorable entropic cost for the system. An alternative approach, widely used by Nature, uses energy input to bypass the entropy bottleneck and develop features otherwise impossible at equilibrium. Dissipative building blocks that inject energy locally were made available by recent advance in colloidal science but have not been used to control self-assembly. Here we show the robust formation of self-powered rotors and dynamical superstructures from active particles and harness non-equilibrium phoretic phenomena to tailor interactions and direct self-assembly. We use a photoactive component that consumes fuel, hematite, to devise phototactic microswimmers that form self-spinning microgears following spatiotemporal light patterns. The gears are coupled via their chemical clouds and constitute the elementary bricks of synchronized superstructures, which autonomously regulate their dynamics. The results are quantitatively rationalized on the basis of a stochastic description of diffusio-phoretic oscillators dynamically coupled by chemical gradients to form directional interactions. Our findings demonstrate that non-equilibrium phenomena can be harnessed to shape interactions and program hierarchical constructions. It lays the groundwork for the self-assembly of dynamical architectures and synchronized micro-machinery.

The transport of active and passive particles plays central roles in diverse biological phenomena and engineering applications. In this paper, we present a theoretical investigation of a system consisting of an active particle and a passive particle in a confined micro-fluidic flow. The introduction of an external flow is found to induce the capture of the passive particle by the active particle via long-range hydrodynamic interactions among the particles. This hydrodynamic capture mechanism relies on an attracting stable equilibrium configuration formed by the particles, which occurs when the external flow intensity exceeds a certain threshold. We evaluate this threshold by studying the stability of the equilibrium configurations analytically and numerically. Furthermore, we study the dynamics of typical capture and non-capture events and characterize the basins of attraction of the equilibrium configurations. Our findings reveal a critical dependence of the hydrodynamic capture mechanism on the external flow intensity. Through adjusting the external flow intensity across the stability threshold, we demonstrate that the active particle can capture and release the passive particle in a controllable manner. Such a capture-and-release mechanism is desirable for biomedical applications such as the capture and release of therapeutic payloads by synthetic micro-swimmers in targeted drug delivery.

Rectified transport of chiral self-propelled particles is numerically investigated in a two-dimensional channel with varied upper wall. Due to the chirality of active particles, the transversal asymmetry can break the symmetry of the system and induce a longitudinal net transport. It is found that the variation of the channel walls can strongly affect the rectified transport. There exist optimal values of the parameters (the variation parameter, the self-propelled velocity, the angular velocity, and the translational diffusion) at which the scaled average velocity takes its maximal value.

Many active particles, both of biological and synthetic origin, can have a light controllable propulsion speed, a property that in biology is commonly referred to as photokinesis. Here we investigate directed transport of photokinetic particles by traveling light patterns. We find general expressions for the current in the cases where the motility wave, induced by light, shifts very slowly or very quickly. These asymptotic formulas are independent of the shape of the wave and are valid for a wide class of active particle models. Moreover we derive an exact solution for the one-dimensional "run and tumble" model. Our results could be used to design time-varying illumination patterns for fast and efficient spatial reconfiguration of photokinetic colloids or bacteria.

Rectification of interacting active particles is numerically investigated in a two-dimensional time-oscillating potential. It is found that the oscillation of the potential and the self-propulsion of active particles are two different types of nonequilibrium driving, which can induce net currents with opposite directions. For a given asymmetry of the potential, the direction of the transport is determined by the competition of the self-propulsion and the oscillation of the potential. There exists an optimal oscillating angular frequency (or self-propulsion speed) at which the average velocity takes its maximal positive or negative value. Remarkably, when the oscillation of the potential competes with the self-propulsion, the average velocity can change direction several times due to the change in the oscillating frequency. Especially, particles with different self-propulsion velocities will move in opposite directions and can be separated. Our results provide a novel and convenient method for controlling and manipulating the transport (or separation) of active particles.

We consider Activated Random Walk (ARW), a model which generalizes the Stochastic Sandpile, one of the canonical examples of self organized criticality. Informally ARW is a particle system on $\mathbb{Z}$ with mass conservation. One starts with a mass density $\mu>0$ of initially active particles, each of which performs a symmetric random walk at rate one and falls asleep at rate $\lambda>0$. Sleepy particles become active on coming in contact with other active particles. We investigate the question of fixation/non-fixation of the process, and show for small enough $\lambda$, the critical mass density for fixation is strictly less than one. Moreover, the critical density goes to zero as $\lambda$ tends to zero. This settles a long standing open question., Comment: 29 pages, 4 figures. Final version. To appear in Comm. Math. Phys

Rectified transport of the active–passive mixture chain is numerically investigated in periodic confined structures. Due to the out-of-equilibrium property of active particles in the chain, the whole chain can be rectified. It is found that the interaction between particles can significantly affect the rectified transport. When all particles in the chain are active, the directed velocity decreases monotonously with increasing the interaction strength. When the particles are mixture, on increasing the interaction strength, the directed velocity firstly decreases to its minimal value, then increases to its maximal value, and finally decreases to zero. In addition, there exist optimal parameters (self-propelled velocity, the natural length of the spring) at which the average velocity is maximal.

Large-scale collective behavior in suspensions of many particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter., the revised version will appear in Soft Matter

Active matter exhibits remarkable collective behavior in which flows, continuously generated by active particles, are intertwined with the orientational order of these particles. The relationship remains poorly understood as the activity and order are difficult to control independently. Here we demonstrate important facets of this interplay by exploring dynamics of swimming bacteria in a liquid crystalline environment with pre-designed periodic splay and bend in molecular orientation. The bacteria are expelled from the bend regions and condense into polar jets that propagate and transport cargo unidirectionally along the splay regions. The bacterial jets remain stable even when the local concentration exceeds the threshold of bending instability in a non-patterned system. Collective polar propulsion and different role of bend and splay are explained by an advection-diffusion model and by numerical simulations that treat the system as a two-phase active nematic. The ability of prepatterned liquid crystalline medium to streamline the chaotic movements of swimming bacteria into polar jets that can carry cargo along a predesigned trajectory opens the door for potential applications in cell sorting, microscale delivery and soft microrobotics., Comment: Main text (17 pages and 5 figures) and supplementary materials (10 pages and 4 figures)

Terrestrial experiments on active particles, such as Volvox, involve gravitational forces, torques and accompanying monopolar fluid flows. Taking these into account, we analyse the dynamics of a pair of self-propelling, self-spinning active particles between widely separated parallel planes. Neglecting flow reflected by the planes, the dynamics of orientation and horizontal separation is symplectic, with a Hamiltonian exactly determining limit cycle oscillations. Near the bottom plane, gravitational torque damps and reflected flow excites this oscillator, sustaining a second limit cycle that can be perturbatively related to the first. Our work provides a theory for dancing Volvox and highlights the importance of monopolar flow in active matter., 6 figures, 2 tables, 5 pages main + 6 S.I