Granular self-organization by autotuning of friction

Abstract

A monolayer of granular spheres in a cylindrical vial, driven continuously by an orbital shaker and subjected to a symmetric confining centrifugal potential, self-organizes to form a distinctively asymmetric structure which occupies only the rear half-space. It is marked by a sharp leading edge at the potential minimum and a curved rear. The area of the structure obeys a power-law scaling with the number of spheres. Imaging shows that the regulation of motion of individual spheres occurs via toggling between two types of motion, namely, rolling and sliding. A low density of weakly frictional rollers congregates near the sharp leading edge whereas a denser rear comprises highly frictional sliders. Experiments further suggest that because the rolling and sliding friction coefficients differ substantially, the spheres acquire a local time-averaged coefficient of friction within a large range of intermediate values in the system. The various sets of spatial and temporal configurations of the rollers and sliders constitute the internal states of the system. Experiments demonstrate and simulations confirm that the global features of the structure are maintained robustly by autotuning of friction through these internal states, providing a previously unidentified route to self-organization of a many-body system.riven, dissipative, and nonlinear many-body systems are capable of self-organizing (1). Examples include avalanches in sand piles (2), earthquakes (3), pinned or depinned disordered systems (4), and animals in collective locomotion patterns (5). The selforganized state in these systems is usually characterized by a macroscopically observable or measurable quantity, for example, the slope of a sand pile or the appearance of large-scale coherent motion of motile objects. The robustness of these selforganized states against external perturbation is achieved through feedback processes which suitably change the internal states of the system. It is thus important to identify the relevant internal states of the system and the feedback mechanism at play to understand the self-organization process itself. Such knowledge is useful, for example, in deciphering the connection between spatial structures and a frequently encountered complex rheology of flowing particulate systems (6), designing adaptive locomotion strategies and decentralized-decision modular robots (7) and swarm robotics (8), and understanding behavioral patterns of active matter (9). For a wide variety of such systems, the basic ingredient of the feedback processes should be, but seldom is, achievable by a set of simple rules via which the individual component responds to a changing environment.Over the last decade, flow properties of moving granular systems, as archetypes of driven dissipative systems, have been extensively studied (10, 11). The emphasis in these studies has been on understanding their flow behavior (10), occasional loss of translational mobility caused by jamming, which leads to self-organization of stress patterns (12, 13), and differenti...

A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

“…The interesting question of understanding the behaviour of the large clusters of dumbbells that form in the bottom of the cylinder is more in line with other studies on granular objects in a rotating cylinder apparatus (e.g. [15,20,21]) or the formation of large-scale patterns in granular matter (e.g. [22]), and is outside the scope of this paper.…”

Tuning of friction noise by accessing the rolling-sliding option

“…Lempel-Ziv-Welch (LZW) algorithm is a commonly used lossless data compression algorithm [5][6][7][8]. It starts out with a dictionary of 256 characters (in the case of 8 bits) and uses those as the standard character set.…”

“…The balls can access two motional states -(i) rolling and(ii) sliding [8][9][10]. They will be referred to as 'rollers' and 'sliders' respectively.…”

Kinetics of orbitally shaken particles constrained to two dimensions

“…The simulated results of these works show qualitative correspondence with experimental data obtained from systems of macroscopic particles. Among available options [20][21][22], orbital shaking is a useful agitation method for macroscopic setups to study the dynamics and interactions of granular matter [23][24][25][26][27][28]. In particular, Scherer et al studied the swirling motion of rolling spherical particles [29].…”