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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.
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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, â_{c}
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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.
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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.
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We study the Brownian motion of ellipsoidal particles lying on an agitated granular bath composed of magnetic particles. We quantify the mobility of different floating ellipsoidal particles using the mean-square displacement and the mean-square angular displacement, and relate the diffusion coefficients to the bath particle motion. In terms of the particle major radius R, we find the translational diffusion coefficient scales roughly as 1/R^{2} and the rotational diffusion coefficient scales as roughly 1/R^{4}; this is consistent with the assumption that diffusion arises from random kicks of the bath particles underneath the floating particle. By varying the magnetic forcing, the bath particles' diffusivity changes by a factor of ten; over this range, the translational and rotational diffusion of the floating particles change by a factor of 50. However, the ratio of the two diffusion constants for the floating particles is forcing-independent. Unusual aspects of the floating particle motion include non-Gaussian statistics for their displacements.
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A nonvibrating magnetic granular system is studied by using a time series approach. The system consists of steel balls confined inside a circular wall that surrounds a glass plate. Kinetic energy is provided to the particles by the application of an external vertical time-dependent magnetic field of different amplitudes. We carried out a characterization of the system dynamics through the measurement of the correlations present in the time series of positions, in the x-direction, of each particle. In particular, by performing Fourier spectral analysis, we find that the time series are fractal and scale invariant, in such a way that the corresponding Fourier power spectra follow a power law [Formula: see text], with [Formula: see text]. More specifically, we find that the values of [Formula: see text], and therefore the strength of the correlations, increase as the magnetic field also increases. In this way, the present system constitutes an experimental model to generate correlated random walks. Additionally, we show how the introduction of a constant magnetic field breaks down this scale invariance property in the positions of each particle. Finally, we confirm the above results by applying detrended fluctuation analysis.
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We study a two-dimensional system of magnetic particles under an alternating magnetic field. The particles are settled on the surface of a negative lens where they tend to sediment toward the center due to gravity. The effective temperature is controlled by the intensity of the applied magnetic field. The system is cooled down from a gaslike state to a solidlike state at different rates. We observe that for some slow cooling rates the final configuration of system is a hexagonal compact arrange, while for the faster cooling rates the final configurations are glasslike states. We followed the time evolution of the system, which allows us to determine in detail changes in quantities such as the interparticle distance. We determine the glass transition temperature for different cooling rates, finding that such temperature increases as the cooling rate decreases, in contrast with some other glass-forming liquids.
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Applying an unsteady magnetic field to a 2D nonvibrating magnetic granular system induces a random motion in the steel beads with characteristics analogous to that of molecules in a fluid. We investigate the structural characteristics of the solid-like structures generated by different quenching conditions. The applied field is generated by the superposition of a constant field and a collinear sinusoidal field. The system reaches a quasi steady state in which the effective temperature is proportional to the amplitude of the applied field. By reducing the effective temperature at different rates, different cooling rates are produced. A slight inclination of the surface allows us to investigate the effects of small particle concentration gradients. The formation of a wide and rich variety of condensed solid structures, from gel-like and glass-like structures up to crystalline structures, is observed and depends on the cooling rate. We focus our attention on the crystallization process and found this process to be a collective phenomenon. We discuss our results in terms of the measured time evolution of the mean squared displacement, the effective diffusion coefficient, and the radial distribution function.
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The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.
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We study a two-dimensional nonvibrating granular system as a model of a magnetorheological fluid. The system is composed of magnetic steel particles on a horizontal plane under a vertical sinusoidal magnetic field and a horizontal static magnetic field. When the amplitude of the horizontal field is zero, we find that the motion of the particles has characteristics similar to those of Brownian particles. A slowing down of the dynamics is observed as the particle concentration increases or the magnitude of the vertical magnetic field decreases. When the amplitude of the horizontal field is nonzero, the particles interact through effective dipolar interactions. Above a threshold in the amplitude of the horizontal field, particles form chains that become longer and more stable as time increases. For some conditions, at short time intervals, the average chain length as a function of time exhibits scaling behavior. The chain length distribution at a given time is a decreasing exponential function. The behavior of this granular system is consistent with theoretical and experimental results for magnetorheological fluids.
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We studied experimentally a model of a glass-forming liquid on the basis of a nonvibrating magnetic granular system under an unsteady magnetic field. A sudden quenching was produced that drove the system from a liquid state to a different final state with lower temperature; the latter could be a liquid state or a solid state. We determined the mean-squared displacement in temporal windows to obtain the dynamic evolution of the system, and we determined the radial distribution function to obtain its structural characteristics. The results were analyzed using the intermediate scattering function and the effective potential between two particles. We observed that when quenching drives the system to a final state in the liquid phase far from the glass-transition temperature, equilibration occurs very quickly. When the final state has a temperature far below the glass-transition temperature, the system reaches its equilibrium state very quickly. In contrast, when the final state has an intermediate temperature but is below that corresponding to the glass transition, the system falls into a state that evolves slowly, presenting aging. The system evolves by an aging process toward more ordered states. However, after a waiting time, the dynamic behavior changes. It was observed that some particles get close enough to overpass the repulsive interactions and form small stable aggregates. In the effective potential curves, it was observed that the emergence of a second effective well due to the attraction quickly evolves and results in a deeper well than the initial effective well due to the repulsion. With the increase in time, more particles fall in the attractive well forming inhomogeneities, which produce a frustration in the aging process.
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A study of the multifractal characteristics of the structure formed by magnetic particles in a dilute magnetorheological fluid is presented. A quasi-two-dimensional magnetorheological fluid sample is simultaneously subjected to a static magnetic field and a sinusoidal magnetic field transverse to each other. We analyzed the singularity spectrum f(α) and the generalized dimension D(q) of the whole structure to characterize the distribution of the aggregates under several conditions of particle concentration, magnetic field intensities, and liquid viscosity. We also obtained the fractal dimension D(g), calculated from the radius of gyration of the chains, to describe the internal distribution of the particles. We present a thermodynamic interpretation of the multifractal analysis, and based on this, we discussed the characteristics of the structure formed by the particles and its relation with previous studies of the average chain length. We have found that this method is useful to quantitatively describe the structure of magnetorheological fluids, especially in systems with high particle concentration where the aggregates are more complex than simple chains or columns.
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A study of lateral aggregation, induced by an oscillatory field, in a magnetorheological fluid based on non-Brownian magnetic particles is presented. We investigate the behavior of chains formed by the particles, due to the simultaneous application of a static magnetic field and a sinusoidal magnetic field transverse to each other. We show that the effective oscillating field enhances the aggregation process. We discuss this result in terms of an effective particle concentration induced by the oscillating field when chains oscillate angularly and sweep the area around them. The oscillating field produces a lateral aggregation similar to that observed in systems composed of Brownian particles which is induced by thermal fluctuations. We study the effect of the oscillating field on the angular amplitude described by single chains. It is observed that the angular amplitude decreases as the frequency of the oscillating field increases; we discuss this behavior numerically in terms of a simple model for this system. Lateral aggregation is studied in detail in isolated pairs of chains of equal length at several conditions of separation and displacement. From the results, a phase diagram is obtained showing the conditions under which aggregation is possible.
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An experimental and theoretical study on the kinetics of the aggregation process of magnetic particles dispersed in mineral oils is presented. A static magnetic field and an oscillating magnetic perturbation are applied on the dispersion. In the low-particle concentrations, the effects on the aggregation of the frequency, the concentration of particles and the viscosity of the liquid are analyzed. It was found that the behavior of the cluster length as a function of the main control parameters can be accurately characterized by scaling relations. The physical characteristics of the aggregates are discussed in relation to measurements of viscosity as a function of time.
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We study pattern formation and the aggregation processes in magnetorheological suspensions in the presence of a static magnetic field, and some of their associated physical properties. In particular, we analyze the elastic modes as a function of the intensity of the applied field and for several particle concentrations. We observe that the clusters formed in these systems have multifractal characteristics, which are the result of three well defined stages of the aggregation process. In these stages three generations of clusters are produced sequentially. The structure of the suspension can be well characterized by its mass fractal dimensions and the mass radial distribution. The size distribution of the second-generation clusters written in terms of their mass fractal dimension allows us to calculate the sound speed of the longitudinal modes in the large wavelength regime. This multifractal analysis applied to several kinds of aggregates reveals that the occurrence of at least three stages of aggregation is a common feature to several physical aggregation processes.