A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matterranging from molecular motors and cytoskeletal filaments over artificial and biological swimmers on microscopic to groups of animals on macroscopic scales-mainly originate from their out-ofequilibrium character, multiscale nature, nonlinearity, and multibody interactions. In the present review, various modeling approaches and numerical techniques are addressed, compared, and differentiated to illuminate the innovations and current challenges in understanding active matter. The complexity increases from minimal microscopic models of dry active matter toward microscopic models of active matter in fluids. Complementary, coarse-grained descriptions and continuum models are elucidated. Microscopic details are often relevant and strongly affect collective behaviors, which implies that the selection of a proper level of modeling is a delicate choice, with simple models emphasizing universal properties and detailed models capturing specific features. Finally, current approaches to further advance the existing models and techniques to cope with real-world applications, such as complex media and biological environments, are discussed.2
We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g., packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results.
We propose a stochastic model for the intersection of two urban streets. The vehicular traffic at the intersection is controlled by a set of traffic lights which can be operated subject to fix-time as well as traffic adaptive schemes. Vehicular dynamics is simulated within the framework of the probabilistic cellular automata and the delay experienced by the traffic at each individual street is evaluated for specified time intervals. Minimising the total delay of both streets gives rise to the optimum signalisation of traffic lights. We propose some traffic responsive signalisation algorithms which are based on the concept of cut-off queue length and cut-off density.
We show that the flagellar number affects the intrinsic dynamics of swimming bacteria and governs their transport efficiency.
Transmembrane receptor clustering is a ubiquitous phenomenon in pro- and eukaryotic cells to physically sense receptor/ligand interactions and subsequently translate an exogenous signal into a cellular response. Despite that receptor cluster formation has been described for a wide variety of receptors, ranging from chemotactic receptors in bacteria to growth factor and neurotransmitter receptors in mammalian cells, a mechanistic understanding of the underlying molecular processes is still puzzling. In an attempt to fill this gap we followed a combined experimental and theoretical approach by dissecting and modulating cargo binding, internalization and cellular response mediated by KDEL receptors (KDELRs) at the mammalian cell surface after interaction with a model cargo/ligand. Using a fluorescent variant of ricin toxin A chain as KDELR-ligand (eGFP-RTAH/KDEL), we demonstrate that cargo binding induces dose-dependent receptor cluster formation at and subsequent internalization from the membrane which is associated and counteracted by anterograde and microtubule-assisted receptor transport to preferred docking sites at the plasma membrane. By means of analytical arguments and extensive numerical simulations we show that cargo-synchronized receptor transport from and to the membrane is causative for KDELR/cargo cluster formation at the mammalian cell surface.
We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated and the delay experienced by the traffic at each individual street is evaluated. We discuss the impact of the geometrical properties of the roundabout on the total delay. We compare our results with traffic-light signalization schemes, and obtain the critical traffic volume over which the intersection is optimally controlled through traffic-light signalization schemes.
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.PACS numbers: 87.16. Ka, 87.16.Uv, 87.16.Nn Anomalous transport of self-propelled particles in biological environments has received much recent attention [1]. Of particular interest is the active motion of motor proteins along cytoskeletal filaments, which makes longdistance intracellular transport feasible [2]. The structural asymmetry of filaments results in a directed motion of motors with an effective processivity, denoting the tendency to move along the same filament. The processivity depends on the type of motor and filament [3] and it is strongly influenced by the presence of specific proteins or binding domains [4,5]. In the limit of small unbinding rates it has been shown [6] that a walker on simple lattice structures moves superdiffusively at short time scales followed by a normal diffusion at long times. Similar results were reported for single bead motion on radiallyorganized microtubule networks [7]. However, for general polarized cytoskeletal networks, the influence of structural complexity and motor processivity on the transport properties is not yet well understood. In this Rapid Communication, we introduce a coarse-grained perspective to the problem and show that the interplay between anisotropy and heterogeneity of the network and processivity leads to a rich transport phase diagram at short and intermediate time scales. The crossover times between different regimes and the asymptotic diffusion constant can vary by orders of magnitude when tuning the key parameters.More precisely, a general analytical framework is developed to study persistent walks with arbitrary steplength and turning-angle distributions. We obtain an exact analytical expression for the dynamical evolution of the mean square displacement (MSD), displaying anomalous diffusion on varying time scales. The results can be also interpreted within the context of random motion in continuous space, e.g. in crowded biological media where the origin of subdiffusive motion is highly debated [8][9][10][11][12][13].While subdiffusion in cytoplasm slows down the transfer of matter, it is beneficial for a variety of cellular functions [14-16], since they depend on th...
We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.
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