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How do topological defects affect the degree of order in active matter? To answer this question we investigate an agent-based model of self-propelled particles, which accounts for polar alignment and short-ranged repulsive interactions. For…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…
A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes depending on the strength of the oscillation and the global packing density. For intermediate packing density and oscillation…
We consider self-propelled droplets which are driven by internal flow. Tracer particles, which are advected by the flow, in general follow chaotic trajectories, even though the motion of the autonomous swimmer is completely regular. The…
Active processes drive and guide biological dynamics across scales -- from subcellular cytoskeletal remodelling, through tissue development in embryogenesis, to population-level bacterial colonies expansion. In each of these, biological…
Spontaneous motion of an oil droplet driven by chemical nonequilibricity is reported. It is shown that the droplet undergoes regular rhythmic motion under appropriately designed boundary conditions, whereas it exhibits random motion in an…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity,…
A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the…
Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
We discover a new type of nonequilibrium phase transition in a model of chromatin dynamics, which accounts for the coherent motions that have been observed in experiment. The coherent motion is due to the long-range cooperation of molecular…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study the nature of motion in a logarithmic galactic dynamical model, with an additional external perturbation. Two different cases are investigated. In the first case the external perturbation is fixed, while in the second case it is…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…