Related papers: Self Organization and Self Avoiding Limit Cycles
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
We study sequences of random numbers {Z[1],Z[2],Z[3],...,Z[n]} -- which can be considered random walks with reflecting barriers -- and define their "types" according to whether Z[i] > Z[i+1], (a down-movement), or Z[i] < Z[i+1]…
Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments…
We propose a general scenario to analyze social and economic changes in modern environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time,…
We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather circular trajectories. We here address self-propelled or actively driven objects that move in…
We prove that transport in the phase space of the "most strongly chaotic" dynamical systems has three different stages. Consider a finite Markov partition (coarse graining) $\xi$ of the phase space of such a system. In the first short times…
A hallmark of living systems is the ability to employ a common set of versatile building blocks that can self-organize into a multitude of different structures, in a way that can be controlled with minimal cost. This capability can only be…
Increasing evidence suggests that active matter exhibits instances of mixed symmetry that cannot be fully described by either polar or nematic formalism. Here, we introduce a minimal model that integrates self-propulsion into the active…
We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular…
Quasiperiodic behaviour is known to occur in systems with enforced quasiperiodicity or randomness, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a setting where…
With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
We introduce a phenomenological theory for a new class of soft active fluids, with the ability to synchronise. Our theoretical framework describes the macroscopic behaviour of a collection of interacting anisotropic elements with cyclic…
We examine the transport behaviour of non-interacting particles in a simple channel billiard, at equilibrium and in the presence of an external field. The channel walls are constructed from straight line-segments. We observe a sensitive…
We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…