Related papers: Localized Structures in Pattern-Forming Systems
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…
We report a new mechanism for the formation of localized states, which takes place without front propagation. Correspondingly, localized structures appear as solitary states, displaying a behavior of single independent cells. The phenomenon…
The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model is studied in order to describe the pattern formation in Langmuir-Blodgett transfer onto prestructured substrates. The occurring…
We present and analyze mechanisms for the patterned deposition of particles in a spatio-temporally driven lattice. The working principle is based on the breaking of the spatio-temporal translation symmetry, which is responsible for the…
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
Phase separation in passive systems leads to uncontrolled droplet growth, limiting structural control in soft materials and cells. We identify a generic mechanism to arrest coarsening based on chemical interconversion between molecular…
Many patterning events in multi-cellular organisms rely on cell-to-cell contact signaling, such as the Notch pathway in metazoans. A particularly interesting phenomenon in this form of communication is lateral inhibition where a cell that…
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in 1-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear…
We study the entrainment of a localized pattern by an external signal via its coupling to zero modes associated with broken symmetries. We show that when internal symmetries are broken, entrainment is governed by a multi-degree of freedom…
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…
Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
Many theories are formulated as constrained systems. We provide a mechanism that explains the origin of physical states of a constrained system by a process of selection of noiseless subsystems when the system is coupled to an external…