Spontaneous collective motion, as in some flocks of bird and schools of fish, is an example of an emergent phenomenon. Such phenomena are at present of great interest and physicists have put forward a number of theoretical results that so far lack experimental verification. In animal behaviour studies, large-scale data collection is now technologically possible, but data are still scarce and arise from observations rather than controlled experiments. Multicellular biological systems, such as bacterial colonies or tissues, allow more control, but may have many hidden variables and interactions, hindering proper tests of theoretical ideas. However, in systems on the subcellular scale such tests may be possible, particularly in in vitro experiments with only few purified components. Motility assays, in which protein filaments are driven by molecular motors grafted to a substrate in the presence of ATP, can show collective motion for high densities of motors and attached filaments. This was demonstrated recently for the actomyosin system, but a complete understanding of the mechanisms at work is still lacking. Here we report experiments in which microtubules are propelled by surface-bound dyneins. In this system it is possible to study the local interaction: we find that colliding microtubules align with each other with high probability. At high densities, this alignment results in self-organization of the microtubules, which are on average 15 µm long, into vortices with diameters of around 400 µm. Inside the vortices, the microtubules circulate both clockwise and anticlockwise. On longer timescales, the vortices form a lattice structure. The emergence of these structures, as verified by a mathematical model, is the result of the smooth, reptation-like motion of single microtubules in combination with local interactions (the nematic alignment due to collisions)--there is no need for long-range interactions. Apart from its potential relevance to cortical arrays in plant cells and other biological situations, our study provides evidence for the existence of previously unsuspected universality classes of collective motion phenomena.

Spontaneous motion of an oil droplet driven by nonequilibrium chemical conditions is reported. It is shown that the droplet undergoes regular rhythmic motion under appropriately designed boundary conditions, whereas it exhibits random motion in an isotropic environment. This study is a novel manifestation on the direct energy transformation of chemical energy into regular spatial motion under isothermal conditions. A simple mathematical equation including noise reproduces the essential feature of the transition from irregularity into periodic regular motion. Our results will inspire the theoretical study on the mechanism of molecular motors in living matter, working under significant influence of thermal fluctuation.

An alcohol (pentanol) droplet exhibits spontaneous motion on an aqueous solution, driven by a solutal Marangoni effect. We found that the droplets mode of motion is controlled by its volume. A droplet with a volume of less than 0.1 microl shows irregular translational motion, whereas intermediate-sized droplets of 0.1-200 microl show vectorial motion. When the volume is above 300 microl, the droplet splits into smaller drops. These experimental results regarding mode selection are interpreted in terms of the wave-number selection depending on the droplet volume.

We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.

We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an OrnsteinUhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a telegraphic noise process is at play, explaining thus the emergence and structure of the vortex lattices observed here and in motility assay experiments.PACS numbers: 05.65.+b, 45.70.Vn, 87.18.Gh Self-propelled particles are nowadays commonly used to study collective motion and more generally "dry" active matter, where the surrounding fluid is neglected. Real world relevant situations include shaken granular particles [1][2][3][4][5], active colloids [6][7][8], bio-filaments displaced by motor proteins [9][10][11]. The trajectories of moving living organisms (from bacteria to large animals such as fish, birds and even human crowds) are also routinely modeled by such particles, see e.g. [12][13][14][15][16][17].Many of these 'active particles' travel at near-constant speed with their dynamics modeled as a persistent random walk with some stochastic component acting directly on their orientation [18]. This noise, which represents external and/or internal perturbations, produces jagged irregular trajectories. Most of the recent results on active matter have been obtained in this context of overdamped dynamics.In many situations, however, the overdamped approximation is not justified. In particular, trajectories can be essentially smooth, as for chemically propelled rods [19,20], birds, some large fish that swim steadily [16], or even biofilaments in motility assays with a high density of molecular motors [10]. Whether underdamped dynamics can make a difference at the level of collective asymptotic properties is largely unknown. Interesting related progress was recently reported for starling flocks [21]. Underdamped "spin" variables are instrumental there for efficient, fast transfer of information through the flock, allowing swift turns in response to threats during which speed is modulated in a well coordinated manner. In the other examples cited above, speed remains nearlyconstant and the persistently turning tracks of fish or microtubules reveal some finite, possibly large, memory of the curvature. In this context an Ornstein-Uhlenbeck (OU) process acting on the angular velocity was shown to be a quantitatively-valid representation [10,16]. The collective motion of self-propelled particles with such underdamped angular dynamics remains largely unknown.In this Letter, we explore minimal models of aligning self-propelled particles with memory similar to that used in [10] to study the emergence of large-scale vortices in mot...

We propose a novel framework for the spontaneous motion of a droplet coupled with internal dynamic patterns generated in a reaction-diffusion system. The spatio-temporal order of the chemical reaction gives rise to inhomogeneous surface tension and results in self-propulsion driven by the surrounding flow due to the Marangoni effect. Numerical calculations of internal patterns together with theoretical results of the flow fields at low Reynolds number well reproduces the experimental results obtained using a droplet of Belousov-Zhabotinsky (BZ) reaction medium.PACS numbers: 82.40. Ck, 47.54.Fj, 47.63.mf, 68.03.Cd Spatio-temporal patterns are widely seen in living systems; target, spiral, stripe, and dot patterns have been observed at various scales from the interior of a cell to a swarm of cells. Most of studies have been focused on patterns at larger scales, which can be successfully reproduced using reaction-diffusion dynamics [1]. In contrast, it is only recently that internal patterns in a single cell have been visualized. These patterns are expected to relate to cellular functions; examples include calcium ions for signal transduction [2], Min proteins for cell division [3], and actin cytoskelton for mechanical properties [4]. Although pattern formation in a cell is expected to be analyzed in the framework of a reaction-diffusion system, as demonstrated in in vitro experiments [3], sufficient understanding on the connection between pattern formation and cellular function is awaited. In this paper, we focus motility, as a typical aspect of cellular functions, arising from internal patterns.Several artificial systems imitating cell motility have been proposed as self-propelled particles [5]. Although no external force is exerted on the particles (force-free condition), the motion is induced by the asymmetric distribution of an electric field, concentration of chemicals, temperature, and so on. These asymmetric distributions are either a priori embedded in the asymmetry of the surface properties of the self-propelled objects [6], or a posteriori created by nonlinear effects; motion itself destabilizes symmetric distribution, for instance, through advective flow [7]. In both cases, however, most studies have focused on motion under steady distributions.In order to understand the dynamic features of cell motility, a system connecting dynamic pattern with mo- * Corresponding author. E-mail: kitahata@physics.s.chiba-u.ac.jp. tion is desirable. In fact, experimental and numerical evidence of chemo-mechanical coupling in such systems has been demonstrated [8,9]. In this letter, we propose a theoretical framework for a chemical system exhibiting self-organized patterns, leading to spontaneous motion. We consider that the Marangoni effect is suitable for this purpose as it has been shown to drive an object under force-free conditions by an inhomogeneous interfacial tension arising from a gradient in chemical concentration [10,11]. In our system, the energy supply and consumption can generate a pattern in a droplet ...

We investigate a simple experimental system using candles; stable combustion is seen when a single candle burns, while oscillatory combustion is seen when three candles burn together. If we consider a set of three candles as a component oscillator, two oscillators, that is, two sets of three candles, can couple with each other, resulting in both in-phase and antiphase synchronization depending on the distance between the two sets. The mathematical model indicates that the oscillatory combustion in a set of three candles is induced by a lack of oxygen around the burning point. Furthermore, we suggest that thermal radiation may be an essential factor of the synchronization.

Chemical control of the spontaneous motion of a reactive oil droplet moving on a glass substrate under an aqueous phase is reported. Experimental results show that the self-motion of an oil droplet is confined on an acid-treated glass surface. The transient behavior of oil-droplet motion is also observed with a high-speed video camera. A mathematical model that incorporates the effect of the glass surface charge is built based on the experimental observation of oil-droplet motion. A numerical simulation of this mathematical model reproduced the essential features concerning confinement of oil droplet motion within a certain chemical territory and also its transient behavior. Our results may shed light on physical aspects of reactive spreading and a chemotaxis in living things.