Vibrot, a simple device for the conversion of vibration into rotation mediated by friction: preliminary evaluation

Surface-energy ratchet motor with geometrical symmetry driven by biased random walk

A geometrically symmetric gear with asymmetric surface wettability exhibits one-way spin on a vibrating water bed. On the side face of the gear, a parafilm was coated to create asymmetry in the surface energy. The gear shows fluctuations in both directions within a shorter timescale; however, for a longer timescale, the gear exhibits a one-way spin. This unique motion is generated by a stochastic process with a biased driving force produced by the interaction between the vibrating water surface and the side face of the gear. This new model resembles an active Brownian ratchet. Until now, most ratchet motors, which obtain regular motion from nonthermal fluctuations, utilize a geometrical ratchet structure. However, in this study, the surface energy forms a ratchet that rectifies the noisy motion.

Collective dynamics of dipolar self-propelled particles

We present a numerical study of the collective behavior of self-propelled particles for which dipolar interactions are considered. These are obtained by introducing pointlike magnetic dipoles in the particles. Various dynamical regimes are found depending on three major parameters: the density of particles, the ratio Γ defined as the competition between kinetic energy and potential magnetic energy, as well as the orientation of the magnetic dipoles inherent to the particles. Patterns such as chains, vortices, flocks, and strips have been obtained.

Density-mediated spin correlations drive edge-to-bulk flow transition in active chiral matter

We demonstrate that edge currents develop in active chiral matter due to boundary shielding over a wide range of densities corresponding to a gas, fluid, and crystal. The system is composed of spinning disk-shaped grains with chirally arranged tilted legs confined in a circular vibrating chamber. The edge currents are shown to increasingly drive circulating bulk flows with area fraction as percolating clusters develop due to increasing spin-coupling between neighbors mediated by frictional contacts. Edge currents are observed even in the dilute limit. While, at low area fraction, the average flux vanishes except within a distance that is of the order of a particle diameter of the boundary, the penetration depth grows with increasing area fraction until a solid-body rotation is achieved corresponding to the highest packing, where the particles are fully caged with hexagonal order and spin in phase with the entire packing. A coarse-grained model, based on the increased collisional interlocking of the particles with area fraction and the emergence of order, captures the observed flow fields.

High-energy velocity tails in uniformly heated granular materials

We experimentally investigate the velocity distributions of quasi-two-dimensional granular materials uniformly heated by an electromagnetic vibrator, where the translational velocity and the rotation of a single particle are Gaussian and independent. We observe the non-Gaussian distributions of particle velocity, with the density-independent high-energy tails characterized by an exponent of β=1.50±0.03 for volume fractions of 0.111≤ϕ≤0.832, covering a wide range of structures and dynamics. Surprisingly, our results are not only in excellent agreement with the prediction of the kinetic theories of granular gas but also hold for an extremely high-volume fraction of ϕ=0.832 where the granular material forms a crystalline solid and the kinetic theory of granular gas fails fantastically. Our experiment suggests that the density-independent high-energy velocity tails of β=1.50 are a characteristic of uniformly heated granular matter.

Dynamics of a vibration-driven single disk

Granular particles exhibit rich collective behaviors on vibration beds, but the motion of an isolated particle is not well understood even for uniform particles with a simple shape such as disks or spheres. Here we measured the motion of a single disk confined to a quasi-two-dimensional horizontal box on a vertically vibrating stage. The translational displacements obey compressed exponential distributions whose exponent [Formula: see text] increases with the frequency, while the rotational displacements exhibit unimodal distributions at low frequencies and bimodal distributions at high frequencies. During short time intervals, the translational displacements are subdiffusive and negatively correlated, while the rotational displacements are superdiffusive and positively correlated. After prolonged periods, the rotational displacements become diffusive and their correlations decay to zero. Both the rotational and the translational displacements exhibit white noise at low frequencies, and blue noise for translational motions and Brownian noise for rotational motions at high frequencies. The translational kinetic energy obeys Boltzmann distribution while the rotational kinetic energy deviates from it. Most energy is distributed in translational motions at low frequencies and in rotational motions at high frequencies, which violates the equipartition theorem. Translational and rotational motions are not correlated. These experimental results show that the random diffusion of such driven particles is distinct from thermal motion in both the translational and rotational degrees of freedom, which poses new challenges to theory. The results cast new light on the motion of individual particles and the collective motion of driven granular particles.

Surfactants and rotelles in active chiral fluids

Surfactant molecules migrate to interfaces, reduce interfacial tension, and form micelles. All of these behaviors occur at or near equilibrium. Here, we describe active analogs of surfactants that operate far from equilibrium in active chiral fluids. Unlike molecular surfactants, the amphiphilic character of surfactants in active chiral fluids is a consequence of their activity. Our fluid of choice is a mixture of spinners that demixes into left-handed and right-handed chiral fluid domains. We realize spinners in experiment with three-dimensionally printed vibrots. Vibrot surfactants are chains of vibrots containing both types of handedness. Experiments demonstrate the affinity of double-stranded chains to interfaces, where they glide along and act as mixing agents. Simulations access larger systems in which single-stranded chains form spinning vesicles, termed rotelles. Rotelles are the chiral analogs of micelles. Rotelle formation is a ratchet mechanism catalyzed by the vorticity of the chiral fluid and only exist far from equilibrium.

Swirlonic state of active matter

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.

Rotational Transport via Spontaneous Symmetry Breaking in Vibrated Disk Packings

It is shown that vibrated packings of frictional disks self-organize cooperatively onto a rotational-transport state where the long-time angular velocity ω[over ¯]_{i} of each disk i is nonzero. Steady rotation is mediated by the spontaneous breaking of local reflection symmetry, arising when the cages in which disks are constrained by their neighbors acquire quenched disorder at large packing densities. Experiments and numerical simulation of this unexpected phenomenon show excellent agreement with each other, revealing two rotational phases as a function of excitation intensity, respectively, the low-drive (LDR) and the moderate-drive (MDR) regimes. In the LDR, interdisk contacts are persistent and rotation happens due to frictional sliding. In the MDR, disks bounce against each other, still forming a solid phase. In the LDR, simple energy-dissipation arguments are provided, that support the observed dependence of the typical rotational velocity on excitation strength.

Oscillating collective motion of active rotors in confinement

Due to its inherent out-of-equilibrium nature, active matter in confinement may exhibit collective behavior absent in unconfined systems. Extensive studies have indicated that hydrodynamic or steric interactions between active particles and boundary play an important role in the emergence of collective behavior. However, besides introducing external couplings at the single-particle level, the confinement also induces an inhomogeneous density distribution due to particle-position correlations, whose effect on collective behavior remains unclear. Here, we investigate this effect in a minimal chiral active matter composed of self-spinning rotors through simulation, experiment, and theory. We find that the density inhomogeneity leads to a position-dependent frictional stress that results from interrotor friction and couples the spin to the translation of the particles, which can then drive a striking spatially oscillating collective motion of the chiral active matter along the confinement boundary. Moreover, depending on the oscillation properties, the collective behavior has three different modes as the packing fraction varies. The structural origins of the transitions between the different modes are well identified by the percolation of solid-like regions or the occurrence of defect-induced particle rearrangement. Our results thus show that the confinement-induced inhomogeneity, dynamic structure, and compressibility have significant influences on collective behavior of active matter and should be properly taken into account.

The Notched Stick, an ancient vibrot example

An intriguing simple toy, commonly known as the Notched Stick, is discussed as an example of a “vibrot”, a device designed and built to yield conversion of mechanical vibrations into a rotational motion. The toy, that can be briefly described as a propeller fixed on a stick by means of a nail and free to rotate around it, is investigated from both an experimental and a numerical point of view, under various conditions and settings, to investigate the basic working principles of the device.

The conversion efficiency from vibration to rotational motion turns out to be very small, or even not detectable at all, whenever the propeller is tightly connected to the stick nail and perfectly axisymmetrical with respect to the nail axis; the small effects possibly observed can be ascribed to friction forces. In contrast, the device succeeds in converting vibrations into rotations when the propeller center of mass is not aligned with the nail axis, a condition occurring when either the nail-propeller coupling is not tight or the propeller is not completely axisymmetrical relative to the nail axis. The propeller rotation may be induced by a process of parametric resonance for purely vertical oscillations of the nail, by ordinary resonance if the nail only oscillates horizontally or, finally, by a combination of both processes when nail oscillations take place in an intermediate direction. Parametric resonance explains the onset of rotations also when the weight of the propeller is negligible. In contrast with what is commonly claimed in the literature, the possible elliptical motion of the nail, due to a composition of two harmonic motions of the same frequency imposed along orthogonal directions, seems unnecessary to determine the propeller rotation.

Inertial delay of self-propelled particles

The motion of self-propelled massive particles through a gaseous medium is dominated by inertial effects. Examples include vibrated granulates, activated complex plasmas and flying insects. However, inertia is usually neglected in standard models. Here, we experimentally demonstrate the significance of inertia on macroscopic self-propelled particles. We observe a distinct inertial delay between orientation and velocity of particles, originating from the finite relaxation times in the system. This effect is fully explained by an underdamped generalisation of the Langevin model of active Brownian motion. In stark contrast to passive systems, the inertial delay profoundly influences the long-time dynamics and enables new fundamental strategies for controlling self-propulsion in active matter.

Symmetry-reversals in chiral active matter

We perform experiments on an active granular material composed of individually-driven, spinning disks confined within a circular arena. Small bumps at the outer edges of the disks provide a variable amount of interparticle coupling in the form of geometric friction. The disks each spin counter-clockwise, but undergo a transition in their collective circulation around the center of the arena, from a clockwise orbit to a counter-clockwise orbit, as a function of packing fraction φ. We identify that, unlike for vibrated granular gases, the particles' velocity distributions are Gaussian over a large range of φ. By fitting the speed distribution to a Maxwell-Boltzmann distribution, we identify a temperature-like parameter which is a universal function of φ; this parameter is also equal to the mean translational energy of the particles. We quantify the collective circulation via its solid-body-like rotation rate, and find that this is a universal function centered around a critical packing fraction. In addition, the ratio of orbital kinetic energy to spin kinetic energy is also a universal function for non-zero geometric friction. These findings highlight the important role of both the type of driving and the interparticle interactions (here, geometric friction) in controlling the collective behavior of active granular systems.

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component i to be approximately proportional to 2σ_{i}+〈σ〉, where σ_{i} is the diameter of the disk and 〈σ〉 is the mean diameter.

Boundaries Control Collective Dynamics of Inertial Self-Propelled Robots

Simple ingredients, such as well-defined interactions and couplings for the velocity and orientation of self-propelled objects, are sufficient to produce complex collective behavior in assemblies of such entities. Here, we use assemblies of rodlike robots made motile through self-vibration. When confined in circular arenas, dilute assemblies of these rods act as a gas. Increasing the surface fraction leads to a collective behavior near the boundaries: polar clusters emerge while, in the bulk, gaslike behavior is retained. The coexistence between a gas and surface clusters is a direct consequence of inertial effects as shown by our simulations. A theoretical model, based on surface mediated transport accounts for this coexistence and illustrates the exact role of the boundaries. Our study paves the way towards the control of collective behavior: By using deformable but free to move arenas, we demonstrate that the surface induced clusters can lead to directed motion, while the topology of the surface states can be controlled by biasing the motility of the particles.

Rotating robots move collectively and self-organize

Biological organisms and artificial active particles self-organize into swarms and patterns. Open questions concern the design of emergent phenomena by choosing appropriate forms of activity and particle interactions. A particularly simple and versatile system are 3D-printed robots on a vibrating table that can perform self-propelled and self-spinning motion. Here we study a mixture of minimalistic clockwise and counter-clockwise rotating robots, called rotors. Our experiments show that rotors move collectively and exhibit super-diffusive interfacial motion and phase separate via spinodal decomposition. On long time scales, confinement favors symmetric demixing patterns. By mapping rotor motion on a Langevin equation with a constant driving torque and by comparison with computer simulations, we demonstrate that our macroscopic system is a form of active soft matter.

Velocity Distribution of a Homogeneously Driven Two-Dimensional Granular Gas

The theory of homogeneously driven granular gases of hard particles predicts that the stationary state is characterized by a velocity distribution function with overpopulated high-energy tails as compared to the exponential decay valid for molecular gases. While this fundamental theoretical result was confirmed by numerous numerical simulations, an experimental confirmation is still missing. Using self-rotating active granular particles, we find a power-law decay of the velocity distribution whose exponent agrees well with the theoretic prediction.

Dynamics of wet granular hexagons

The collective behavior of vibrated hexagonal disks confined in a monolayer is investigated experimentally. Due to the broken circular symmetry, hexagons prefer to rotate upon sufficiently strong driving. Due to the formation of liquid bridges, short-ranged cohesive interactions are introduced upon wetting. Consequently, a nonequilibrium stationary state with the rotating disks self-organized in a hexagonal structure arises. The bond length of the hexagonal structure is slightly smaller than the circumdiameter of a hexagon, indicating geometric frustration. This investigation provides an example where the collective behavior of granular matter is tuned by the shape of individual particles.