Brownian motion of ellipsoidal particles on a granular magnetic bath

Two-step crystallisation in a 2D active magnetic granular system confined by a parabolic potential

We studied the two-step crystallisation process of a magnetic active 2D-granular system placed on different lens concaveness and under the action of an alternating magnetic field which controls its effective temperature. We have observed that the two-step features of the crystallisation process are more evident as the depth of the parabolic potential increases. At the initial formation of the nucleus, as a first step, in the central region of the lens an amorphous aggregate is formed. In an ulterior second step, this disordered aggregate, due to the effective temperature and the perturbations caused by the impacts of free particles moving in the surrounding region, evolves to an ordered crystalline structure. The nucleus size is larger for deeper concaveness of the parabolic potential. However, if the depth of the parabolic potential exceeds a certain value, the reordering process of the second step does not occur. The crystal growth occurs similarly; small disordered groups of particles join the nucleus, forming an amorphous shell of particles which experiments a rearranging while the aggregate grows. In the explored range of the depths of the parabolic potential, crystallisation generally occurs quicker as the deeper parabolic potential is. Also, aggregates are more clearly round-shaped as parabolic potential depth increases. On the contrary, the structures are more branched for a smaller depth of the parabolic potential. We studied the structural changes and features in the system by using the sixth orientational order parameter and the packing fraction.

Magnetized granular particles running and tumbling on the circle S^{1}

It has been shown that a nonvibrating magnetic granular system, when fed by an alternating magnetic field, behaves with most of the distinctive physical features of active matter systems. In this work, we focus on the simplest granular system composed of a single magnetized spherical particle allocated in a quasi-one-dimensional circular channel that receives energy from a magnetic field reservoir and transduces it into a running and tumbling motion. The theoretical analysis, based on the run-and-tumble model for a circle of radius R, forecasts the existence of a dynamical phase transition between an erratic motion (disordered phase) when the characteristic persistence length of the run-and-tumble motion, ℓ_{c}<R/2, to a persistent motion (ordered phase) when ℓ_{c}>R/2. It is found that the limiting behaviors of these phases correspond to Brownian motion on the circle and a simple uniform circular motion, respectively. Furthermore, it is qualitatively shown that the smaller the magnetization of a particle, the larger the persistence length. It is so at least within the experimental limit of validity of our experiments. Our results show a very good agreement between theory and experiment.

Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system

We study a quasi-two-dimensional macroscopic system of magnetic spherical particles settled on a shallow concave dish under a temporally oscillating magnetic field. The system reaches a stationary state where the energy losses from collisions and friction with the concave dish surface are compensated by the continuous energy input coming from the oscillating magnetic field. Random particle motions show some similarities with the motions of atoms and molecules in a glass or a crystal-forming fluid. Because of the curvature of the surface, particles experience an additional force toward the center of the concave dish. When decreasing the magnetic field, the effective temperature is decreased and diffusive particle motion slows. For slow cooling rates we observe crystallization, where the particles organize into a hexagonal lattice. We study the birth of the crystalline nucleus and the subsequent growth of the crystal. Our observations support nonclassical theories of crystal formation. Initially a dense amorphous aggregate of particles forms, and then in a second stage this aggregate rearranges internally to form the crystalline nucleus. As the aggregate grows, the crystal grows in its interior. After a certain size, all the aggregated particles are part of the crystal and after that crystal growth follows the classical theory for crystal growth.

Crystallisation in a two-dimensional granular system at constant temperature

We study the crystallisation processes occurring in a nonvibrating two-dimensional magnetic granular system at various fixed values of the effective temperature. In this system, the energy loss due to dissipative effects is compensated by the continuous energy input coming into the system from a sinusoidal magnetic field. When this balance leads to high values of the effective temperature, no aggregates are formed, because particles’ kinetic energy prevents them from aggregating. For lower effective temperatures, formation of small aggregates is observed. The smaller the values of the applied field’s amplitude, the larger the number of these disordered aggregates. One also observes that when clusters form at a given effective temperature, the average effective diffusion coefficient decreases as time increases. For medium values of the effective temperature, formation of small crystals is observed. We find that the sixth bond-orientational order parameter and the number of bonds, when considering more than two, are very sensitive for exhibiting the order in the system, even when crystals are still very small.