Sublinear drag regime at mesoscopic scales in viscoelastic materials.

Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Although exponential responses are the most common, power-law time dependencies arise peculiarly in complex soft materials such as living cells. Understanding the microscale mechanisms that drive rheologic behaviors at the macroscale shall be transformative in fields such as material design and bioengineering. Using an elastic network model of macromolecules immersed in a viscous fluid, we numerically reproduce those characteristic viscoelastic relaxations and show how the microscopic interactions determine the rheologic response. The macromolecules, represented by particles in the network, interact with neighbors through a spring constant k and with fluid through a non-linear drag regime. The dissipative force is given by γvα, where v is the particle's velocity, and γ and α are mesoscopic parameters. Physically, the sublinear regime of the drag forces is related to micro-deformations of the macromolecules, while α ≥ 1 represents rigid cases. We obtain exponential or power-law relaxations or a transitional behavior between them by changing k, γ, and α. We find that exponential decays are indeed the most common behavior. However, power laws may arise when forces between the macromolecules and the fluid are sublinear. Our findings show that in materials not too soft not too elastic, the rheological responses are entirely controlled by α in the sublinear regime. More specifically, power-law responses arise for 0.3 ⪅ α ⪅ 0.45, while exponential responses for small and large values of α, namely, 0.0 ⪅ α ⪅ 0.2 and 0.55 ⪅ α ⪅ 1.0.

Trapping and sorting of active matter in a periodic background potential.

We study, numerically, a system of active particles with either a single noise value or a mixture of equal proportions of particles with two noise values under the influence of an attractive periodic background potential, and we observe their diffusion regimes and trapping states. For the single noise system, we show that the slow diffusion is correlated to a significant particle trapping, while normal diffusion is seen for partial or no trapping. Our results indicate that low noise particles are less susceptible to the background, i.e., they have a smaller chance to be trapped as compared to higher noise particles for the same background, and that denser systems achieve a no-trapping state, unless for the largest noise value we studied. For the mixtures, we study the sorting of particles based on their noise value differences and observe that particles with distinct noises are trapped at distinct radii compared to a trap minimum, and, since these radii depend on the density, the latter should be well tuned in order to have an efficient sorting.

Controlling the transport of active matter in disordered lattices of asymmetrical obstacles.

We investigate the transport of active matter in the presence of a disordered square lattice of asymmetric obstacles, which is built by removing a fraction of them from the initial full lattice. We obtain a spontaneous inversion of the net particle current, compared to the usual sense of such a current as a function of the fraction of removed obstacles and particle density. We observed that the negative current regime is the consequence of trapping of particles among the obstacles which favors that more particles move in the negative current direction. The same reasoning applies to the positive current regime as well. We show a calculation that partially reproduces our numerical results, based on the argument that the mean current is given by the product of the mean speed and the mean number of travelers in each direction; the breakdown of this assumption is responsible for the failure of our calculation to reproduce the initial negative current regime.

Steady states of non-axial dipolar rods driven by rotating fields.

We investigate a two-dimensional system of magnetic colloids with anisotropic geometry (rods) subjected to an oscillating external magnetic field. The structural and dynamical properties of the steady states are analyzed, by means of Langevin dynamics simulations, as a function of the misalignment of the intrinsic magnetic dipole moment of the rods with respect to their axial direction, and also in terms of the strength and rotation frequency of an external magnetic field. The misalignment of the dipole relative to their axial direction is inspired by recent studies, and this is extremely relevant in the microscopic aggregation states of the system. The dynamical response of the magnetic rods to the external magnetic field is strongly affected by such a misalignment. Concerning the synchronization between the magnetic rods and the direction of the external magnetic field, we define three distinct regimes of synchronization. A set of steady states diagrams are presented, showing the magnitude and rotation frequency intervals in which the distinct self-organized structures are observed.

Correction: Self-assembly and clustering of magnetic peapod-like rods with tunable directional interaction.

[This corrects the article DOI: 10.1371/journal.pone.0195552.].

Self-assembly and clustering of magnetic peapod-like rods with tunable directional interaction.

Based on extensive Langevin Dynamics simulations we investigate the structural properties of a two-dimensional ensemble of magnetic rods with a peapod-like morphology, i.e, rods consisting of aligned single dipolar beads. Self-assembled configurations are studied for different directions of the dipole with respect to the rod axis. We found that with increasing misalignment of the dipole from the rod axis, the smaller the packing fraction at which the percolation transition is found. For the same density, the system exhibits different aggregation states for different misalignment. We also study the stability of the percolated structures with respect to temperature, which is found to be affected by the microstructure of the assembly of rods.

Structure and reentrant percolation in an inverse patchy colloidal system.

Two-dimensional systems of inverse patchy colloids modeled as disks with a central charge and having their surface decorated with oppositely pointlike charged patches are investigated using molecular dynamics simulations. The self-assembly of the patchy colloids leads to diverse ground state configurations ranging from crystalline arrangements of monomers to linear clusters, ramified linear clusters and to percolated configurations. Two structural phase diagrams are constructed: (1) as a function of the net charge and area fraction, and (2) as a function of the net charge and the range of the pair interaction potential. An interesting reentrant percolation transition is obtained as a function of the net charge of the colloids. We identify distinct mechanisms that lead to the percolation transition.

Electronic properties of superlattices on quantum rings.

We present a theoretical study of the one-electron states of a semiconductor-made quantum ring (QR) containing a series of piecewise-constant wells and barriers distributed along the ring circumference. The single quantum well and the superlattice cases are considered in detail. We also investigate how such confining potentials affect the Aharonov-Bohm like oscillations of the energy spectrum and current in the presence of a magnetic field. The model is simple enough so as to allow obtaining various analytical or quasi-analytical results. We show that the well-in-a-ring structure presents enhanced localization features, as well as specific geometrical resonances in its above-barrier spectrum. We stress that the superlattice-in-a-ring structure allows giving a physical meaning to the often used but usually artificial Born-von-Karman periodic conditions, and discuss in detail the formation of energy minibands and minigaps for the circumferential motion, as well as several properties of the superlattice eigenstates in the presence of the magnetic field. We obtain that the Aharonov-Bohm oscillations of below-barrier miniband states are reinforced, owing to the important tunnel coupling between neighbour wells of the superlattice, which permits the electron to move in the ring. Additionally, we analysis a superlattice-like structure made of a regular distribution of ionized impurities placed around the QR, a system that may implement the superlattice in a ring idea. Finally, we consider several random disorder models, in order to study roughness disorder and to tackle the robustness of some results against deviations from the ideally nanostructured ring system.

Self-assembly of rigid magnetic rods consisting of single dipolar beads in two dimensions.

Molecular dynamics simulations are used to investigate the structural properties of a two-dimensional ensemble of magnetic rods, which are modeled as aligned single dipolar beads. The obtained self-assembled configurations can be characterized as (1) clusters, (2) percolated, and (3) ordered structures, and their structural properties are investigated in detail. By increasing the aspect ratio of the magnetic rods, we show that the percolation transition is suppressed due to the reduced mobility of the rods in two dimensions. Such a behavior is opposite to the one observed in three dimensions. A magnetic bulk phase is found with local ferromagnetic order and an unusual nonmonotonic behavior of the nematic order is observed.

Depletion forces on circular and elliptical obstacles induced by active matter.

Depletion forces exerted by self-propelled particles on circular and elliptical passive objects are studied using numerical simulations. We show that a bath of active particles can induce repulsive and attractive forces which are sensitive to the shape and orientation of the passive objects (either horizontal or vertical ellipses). The resultant force on the passive objects due to the active particles is studied as a function of the shape and orientation of the passive objects, magnitude of the angular noise, and distance between the passive objects. By increasing the distance between obstacles the magnitude of the repulsive depletion force increases, as long as such a distance is less than one active particle diameter. For longer distances, the magnitude of the force always decreases with increasing distance. We also found that attractive forces may arise for vertical ellipses at high enough area fraction.

Self-propelled particle transport in regular arrays of rigid asymmetric obstacles.

We report numerical results which show the achievement of net transport of self-propelled particles (SPPs) in the presence of a two-dimensional regular array of convex, either symmetric or asymmetric, rigid obstacles. The repulsive interparticle (soft disks) and particle-obstacle interactions present no alignment rule. We find that SPPs present a vortex-type motion around convex symmetric obstacles even in the absence of hydrodynamic effects. Such a motion is not observed for a single SPP, but is a consequence of the collective motion of SPPs around the obstacles. A steady particle current is spontaneously established in an array of nonsymmetric convex obstacles (which presents no cavity in which particles may be trapped), and in the absence of an external field. Our results are mainly a consequence of the tendency of the self-propelled particles to attach to solid surfaces.

Single-file and normal diffusion of magnetic colloids in modulated channels.

Diffusive properties of interacting magnetic dipoles confined in a parabolic narrow channel and in the presence of a periodic modulated (corrugated) potential along the unconfined direction are studied using Brownian dynamics simulations. We compare our simulation results with the analytical result for the effective diffusion coefficient of a single particle by Festa and d'Agliano [Physica A 90, 229 (1978)] and show the importance of interparticle interaction on the diffusion process. We present results for the diffusion of magnetic dipoles as a function of linear density, strength of the periodic modulation and commensurability factor.

Magnetic particles confined in a modulated channel: structural transitions tunable by tilting a magnetic field.

The ground state of colloidal magnetic particles in a modulated channel are investigated as a function of the tilt angle of an applied magnetic field. The particles are confined by a parabolic potential in the transversal direction while in the axial direction a periodic substrate potential is present. By using Monte Carlo simulations, we construct a phase diagram for the different crystal structures as a function of the magnetic field orientation, strength of the modulated potential, and the commensurability factor of the system. Interestingly, we found first- and second-order phase transitions between different crystal structures, which can be manipulated by the orientation of the external magnetic field. A reentrant behavior is found between two- and four-chain configurations, with continuous second-order transitions. Novel configurations are found consisting of frozen solitons of defects. By changing the orientation and/or strength of the magnetic field and/or the strength and periodicity of the substrate potential, the system transits through different phases.

Dynamical properties and melting of binary two-dimensional colloidal alloys.

A two-dimensional (2D) binary colloidal system consisting of interacting dipoles is investigated using an analytical approach. Within the harmonic approximation we obtain the phonon spectrum of the system as a function of the composition, dipole-moment ratio, and mass ratio between the small and big particles. Through a systematic analysis of the phonon spectra we are able to determine the stability region of the different lattice structures of the colloidal alloys. The gaps in the phonon frequency spectrum, the optical frequencies in the long-wavelength limit, and the sound velocity are discussed as well. Using the modified Lindemann criterion and within the harmonic approximation we estimate the melting temperature of the sublattice generated by the big particles.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel.

The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.

Bilayer crystals of charged magnetic dipoles: structure and phonon spectrum.

We study the structure and phonon spectrum of a two-dimensional bilayer system of classical charged dipoles oriented perpendicular to the plane of the layers for equal density in each layer. This system can be tuned through six different crystalline phases by changing the interlayer separation or the charge and/or dipole moment of the particle. The presence of the charge on the dipole particles is responsible for the nucleation of five staggered phases and a disordered phase which are not found in the magnetic dipole bilayer system. These extra phases are a consequence of the competition between the repulsive Coulomb and the attractive dipole interlayer interaction. We present the phase diagram and determine the order of the phase transitions. The phonon spectrum of the system was calculated within the harmonic approximation, and a nonmonotonic behavior of the phonon spectrum is found as a function of the effective strength of the interparticle interaction. The stability of the different phases is determined.

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel.

Diffusive properties of a monodisperse system of interacting particles confined to a quasi-one-dimensional channel are studied using molecular dynamics simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion to the two-dimensional diffusion regime is investigated. This transition [regarding the calculation of the scaling exponent (α) of the MSD (Δx(2)(t) ∝ t(α)] as a function of the width of the channel is shown to change depending on the channel's confinement profile. In particular, the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.

Diffusion in a quasi-one-dimensional system on a periodic substrate.

The diffusion of charged particles interacting through a repulsive Yukawa potential, exp(-r/λ)/r, confined by a parabolic potential in the y direction and subjected to a periodic substrate potential in the x direction is investigated. Langevin dynamic simulations are used to investigate the effect of the particle density, the amplitude of the periodic substrate, and the range of the interparticle interaction potential on the diffusive behavior of the particles. We found that in general the diffusion is suppressed with increasing the amplitude of the periodic potential, but for specific values of the strength of the substrate potential a remarkable increase of the diffusion is found with increasing the periodic potential amplitude. In addition, we found a strong dependence of the diffusion on the specific arrangement of the particles, e.g., single-chain versus multichain configuration. For certain particle configurations, a reentrant behavior of the diffusion is found as a function of the substrate strength due to structural transitions in the ordering of the particles.

A two-component mixture of charged particles confined in a channel: melting.

The melting of a binary system of charged particles confined in a quasi-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different kinds of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four-chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two kinds of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct kinds of charges is observed.

Ground state and normal-mode spectra of a two-dimensional system of dipole particles confined in a parabolic trap.

The ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures like chains and Y-shaped configurations when a magnetic field is applied parallel to the plane of the particles. The normal-mode spectrum of the particles and its dependence on the magnetic field and the strength of the dipole moment of the particles are studied. The vibrational and rotational modes of the spectrum, which are associated with the stability of the system, are investigated in detail. The number of particles is varied and we found different ordering of the particles for different values of the dipole moment and the magnetic field. A ring structure with a large number of particles is observed for high values of the dipole moment of the particles.