Related papers: Spontaneous pattern formation in driven nonlinear …
From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
A continuum model derived from an atomistic Hamiltonian is used to examine the ordering kinetics in CuAu. A detailed description of the formation of the low and high temperature ordered and modulated superlattice states is given. The…
We analyze the properties of a Luttinger liquid under the influence of a periodic driving of the interaction strength. Irrespective of the details the driven system develops an instability due to a parametric resonance. For slow and fast…
We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatio-temporal forcing in the form of a travelling wave modulation of a control parameter. We show that from strictly spatial resonance, it is…
Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous…
Resonant mode interactions in weakly nonlinear multi-dimensional lattices and related effects are described. We concentrate on formal description of the phenomenon and consider as examples mode interactions and evolution equations for…
We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…
We investigate one-dimensional transverse modulational instability in a non local medium excited with a spatially incoherent source. Employing undoped nematic liquid crystals in a planar pre-tilted configuration, we investigate the role of…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
Violation of (semi)-detailed balance conditions in lattice gas automata gives rise to unstable spatial fluctuations that lead to phase separation and pattern formation in spinodal decomposition, unstable propagating modes, driven diffusive…
Polariton condensation can be regarded as a self-organization phenomenon, where phase ordering is established among particles in the system. In such condensed systems, further ordering can possibly occur in the particle density…
We introduce a nonequilibrium off--lattice model for anisotropic phenomena in fluids. This is a Lennard--Jones generalization of the driven lattice--gas model in which the particles' spatial coordinates vary continuously. A comparison…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
Although the pattern formation on polymer gels has been considered as a result of the mechanical instability due to the volume phase transition, we found a macroscopic surface pattern formation not caused by the mechanical instability. It…
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…
We generate experimentally different types of two-dimensional self-trapped photonic lattices in a photorefractive medium and analyze the induced refractive index change using two different methods. One method gives the first experimental…
We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently…
First we explain the concept of local deformation over a 'parameter' algebra P, in particular the notion of a P-lattice in a Lie group. Purpose of this article is to define the spaces of automorphic resp. cusp forms on the upper half plane…
We show, through analytical theory and rigorous numerical calculations, that optical binding can organize a collection of particles into stable one-dimensional lattice. This lattice, as well as other optically-bound structures, are shown to…